tion, and the negative slope (red) is inversely pro- ..... All species are stained with antibodies raised against D. melanogaster-Bicoid (Koss- ...... 4x. Figure 4.3: Upper left panel: Fluorescent Bcd antibody intensity profiles of 21 D. melanogaster.
Biophysics Problems in Early Embryonic Development: Precision and Dynamics in the Bicoid Morphogen Gradient
Thomas Gregor
A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy
Recommended for Acceptance by the Department of Chemistry
April 2005
c Copyright by Thomas Gregor, 2005. ° All Rights Reserved
Abstract The spatial patterns that emerge during early embryonic development of Drosophila melanogaster are governed by gradients in the concentration of specific molecules. While much is known about the identity of these molecules, relatively little work has addressed how these signals can provide the precision that is observed in developmental processes given the high variability in the underlying molecular events. Combining tools from biophysics and from biology, this thesis presents a quantitative analysis of the Bicoid gradient, which is the earliest detectable gradient in the Drosophila embryo. Bicoid regulates the expression of several other molecules, including hunchback. The input/output relation between Bicoid and Hunchback is measured, analyzing both the mean response of Hunchback to the Bicoid gradient and its noise within a single embryo. This noise corresponds to a precision of ∼ 10% in reading out the Bicoid concentration. Theory suggests that the observed precision is difficult to achieve by temporal averaging over the available developmental time scales. A mechanism is proposed in which neighboring nuclei average their concentration measurements in order to reduce noise. Bicoid gradients are measured in D. melanogaster and in embryos of other dipterans, such as D. busckii, Lucilia sericata, and Calliphora vicina, whose egg lengths differ by a factor of 5. The observed characteristic length constants of the Bicoid gradients scale with the average egg sizes of the different species, while developmental time scales are conserved across species. In vivo measurements of diffusion constants demonstrate that the physical properties of the cytoplasm cannot explain the scaling of the Bicoid gradient in eggs of varying sizes. To analyze the dynamics of the Bicoid gradient a fly construct expressing an Nterminal Bicoid-eGFP fusion was designed. The overall shape of the Bicoid gradient is shown to be stable during syncytial blastoderm stages within a given embryo, whereas Bicoid-eGFP gradients across different embryos exhibit a strong positional variability during early cell cycle 14. Cytoplasmic Bicoid-eGFP diffusion constants are estimated from photobleaching experiments. These results strongly challenge both the validity of the local concentration readout model and a purely diffusion-driven mechanism for the establishment of the Bicoid gradient.
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Preface I am a trained physicist in the Princeton Chemistry Department working in Molecular Biology and using sophisticated tools from biophysics and computational analysis. So, what am I really? In 1999, after graduating with a masters degree in physics from the University of Geneva, Switzerland, I accepted Roberto Cars offer to follow him to the United States where he had been appointed as a faculty member in Princetons Department of Chemistry. Thus, I was initially supposed to be a chemist researching quantum global optimization, but soon after my arrival, discovered that Princeton held opportunities I had never before considered. The flexibility to cross boundaries and the openness of members of different fields to engage in unique interdisciplinary collaborations struck me, and I felt compelled to explore and study biology using my unique perspective as a physicist, something I had never though possible when I was studying in Geneva. I asked John Hopfield for advice. He directed me to go and see “this guy at NEC,” a theoretical physicist with an emphasis on biology and neuroscience related issues. My first encounters with Bill Bialek were very curious. He used a vocabulary that was very unfamiliar to me, and I walked out of his office with a burning head and being glad if I was able to follow 35% of what he said. But his topics were fascinating and challenging, and after having completed his summer school class “Methods in Computational Neuroscience” at MBL in Woods Hole, I decided to switch fields. My journey, however, does not end here, as I realized quickly that I would not be content with a purely theoretical approach to biological questions. This is when I took David Tank’s Neurobiology course taught in the Molecular Biology department. Rapidly, I was exposed to many techniques borrowed from the physics community to study neuroscience, which at the time was certainly the most advanced field in the study of living organisms using quantitative methods. One of the instructors of the class was Rob de Ruyter who brought his big Calliphora flies for electrophysiological recordings of motor neurons. With Eric Wieschaus sitting across the hall it did not take long before these big flies were also used for other purposes.“Why don’t we examine their early embryonic gene expression pattern and compare them to the nice flies...?” were his words. Eric had been advertising his system, Drosophila melanogaster in the physics community for many years. At this time he had just published a paper with two physicists on a quantitative analysis of the variability of gene expression patterns in different Drosophila embryos, and he had given very lively talks about this work in Bill’s group meetings. Basically, I was at the right place at the right moment, and it did not take long till David asked me to join a meeting of Bill, Eric, Rob and himself to talk about “possibilities with the flies”. What followed were the three most exciting years of my scientific education. Being in the midst of four world-famous scientists, trying to follow their thoughts, meeting their expectations and digesting their enthusiasm has been a challenging, exciting and formative experience. Not only have they been extraordinary scientific advisors, but they have, through their personal guidance and humanity, been a great example to me. I have been very fortunate to have been in such a position and I wish to express iv
my gratitude to everybody who helped make this experience possible. I will always be thankful to Roberto for his selflessness in letting me move on in my journey after having invested two years in me, and his vision that this path I chose would be the best for my scientific development. The same goes for the Chemistry department for allowing me the flexibility to choose my own research topic and to work with faculty of different departments. I thank John Hopfield for pointing me in the right direction when I was lost and did not know how to manage moving into a new field, and for his subsequent insightful comments on my work. Bill, I am very grateful that you took me as your Ph.D student, half way through my program in Princeton, and then subsequently gave me the freedom to move beyond purely theoretical work towards a strongly experimental component. Your optimism and trust were crucial for my daily momentum. Eric, thank you very much for your seemingly insatiable enthusiasm for exploring the mysteries of life, and for your curiosity in quantitative approaches. Thank you for keeping your sanity after hours of teaching me basic developmental biology. David, thank you for your drive and loyalty, and for your trust in letting me use expensive equipment. After all, things tend to slip out of my hands from time to time, but you were always there to put my head back on between my shoulders wherever it blew off. Rob, thank you for your patience with my impatience, and for your fine art of building equipment and designing experiments. Our initial discussions helped me to believe in myself, believe that I could actually make it through this project. Finally, I would like to thank the myriad of people I have been pestered with all sorts of questions throughout the years of the this undertaking. To list them all would go beyond the scope of our time, but, they know who they are. I would just like to point out a few in particular who have strongly shaped the outcome of this work: Alistair McGregor who taught me how to pipet and how to prepare the loading dye, Girish Deshpande who taught me how to formulate my thoughts scientifically and during that process made me realize what I was actually talking about, Reba Samantha for bearing with my eagerness and for showing me her art of staining, and last but not least, Tiffy and Penny for correcting this manuscript and showing great patience with my English.
Thomas Gregor Princeton, January 2005
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To my mother
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Contents Abstract . . . . Preface . . . . . List of Tables . List of Figures .
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Introduction
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1 Physical limits to positional information during velopment 1.1 Introduction . . . . . . . . . . . . . . . . . . . . 1.2 Results . . . . . . . . . . . . . . . . . . . . . . . 1.3 Discussion . . . . . . . . . . . . . . . . . . . . . 1.4 Materials and Methods . . . . . . . . . . . . . . 2 Scaling: Developmental Characterization Sizes 2.1 Introduction . . . . . . . . . . . . . . . . . 2.1.1 Results . . . . . . . . . . . . . . . . 2.1.2 Discussion . . . . . . . . . . . . . . 2.1.3 Materials and Methods . . . . . . .
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3 Dynamics of the Bicoid Gradient Part I (Diffusion Measurements) 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Cytoplasmic properties of D. melanogaster . . . . . . . . . . . 3.4.3 Cytoplasmic diffusivity in dipteran of different egg sizes and model implications . . . . . . . . . . . . . . . . . . . . . . . .
33 33 34 40 43 43 44
4 Dynamics of the Bicoid Gradient Part II (Bcd-GFP construct) 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Biological and physical properties of the Bcd-GFP construct 4.2.2 Post-translational GFP fluorophore formation time . . . . .
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4.2.3 Stability versus dynamics of the Bcd gradient . . . . . . . 4.2.4 Effects of nuclei on the Bcd gradient . . . . . . . . . . . . 4.2.5 Nuclear dynamics: transport rates and diffusion constants 4.2.6 Summary of diffusion constant measurements . . . . . . . Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . .
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Conclusion
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List of Tables 2.1 3.1
Geometric characterization of eggs and syncytial nuclei of different dipteran species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Effective diffusion constants D of dextran molecules of different sizes in D. melanogaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective diffusion constants of 40 kD dextran molecules in dipteran species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some literature measurements of cytoplasmic diffusion constants. . . Some literature estimates of cytoplasmic viscosity. . . . . . . . . . . .
41 46 47
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Summary of diffusion constant measurements in D. melanogaster
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List of Figures 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 2.1 2.2
Triply immunostained D. melanogaster embryo at early cell cycle 14. Embryo with nuclear mask. . . . . . . . . . . . . . . . . . . . . . . . Scatter plot of nuclear Hb vs nuclear Bcd intensity. . . . . . . . . . . “Input/output” relationship between Bcd and Hb intensities. . . . . . Scatter plot and transfer function between relative Bcd and Hb concentrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective noise in Bcd concentration. . . . . . . . . . . . . . . . . . . Transfer functions for 4 individual embryos. . . . . . . . . . . . . . . Transfer function for pooled data set. . . . . . . . . . . . . . . . . . . Transfer function fitted with different Hill coefficients. . . . . . . . . . Biological noise for 4 individual embryos and average biological noise from same 4 embryos. . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of average noise level of 4 embryos and noise level of merged data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control for noise level results with de-correlated Hb data. . . . . . . . Radial correlation function of Hb noise for one individual embryo. . . Radial correlation function of Hb noise from pooled data for 4 embryos. Bcd-Hb transfer functions at different cell cycles. . . . . . . . . . . . Normalized Bcd-Hb transfer functions at different cell cycles. . . . . . Average Bcd noise level for amorphous Hb mutant strain. . . . . . . .
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Cumulative egg length distributions of dipteran eggs. . . . . . . . . . Comparison of immunofluorescence stainings of L. sericata and D. melanogaster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of immunofluorescence stainings of D. melanogaster and D. busckii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparative in situ hybridization of bcd expressions in D. melanogaster and in L. sericata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bicoid immunofluorescence staining for L. sericata, D. melanogaster and D. busckii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intensity profiles of Bicoid fluorescence. . . . . . . . . . . . . . . . . . Cumulative probability distributions of characteristic length constants for L. sericata, D. melanogaster and D. busckii. . . . . . . . . . . . . Intensity profiles of a fluorescently labelled dye. . . . . . . . . . . . .
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Two-photon image of D. melanogaster embryo before injection.
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3.2 3.3 3.4 3.5 3.6 3.7 3.8 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14
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Time evolution of fluorescence intensity after injection. . . . . . . . . Reconstructed eggshell from two-photon images of a D. melanogaster embryo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fitted fluorescence intensity profiles I. . . . . . . . . . . . . . . . . . Fitted fluorescence intensity profiles II. . . . . . . . . . . . . . . . . . Diffusion coefficients of dextran molecules of different hydrodynamic radii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Injected and fixed cross sections of D. melanogaster embryos. . . . . . Cross sections of fixed and stained D. melanogaster embryos. . . . . . Snapshot of a time laps movie taken with a two-photon microscope of an D. melanogaster embryo expressing Bcd-GFP. . . . . . . . . . . . Six snapshots of the anterior third of a D. melanogaster embryo expressing Bcd-GFP during cell cycles 9 to 14. . . . . . . . . . . . . . . Fluorescent Bcd antibody intensity profiles of fixed D. melanogaster embryos expressing Bcd-GFP. . . . . . . . . . . . . . . . . . . . . . . Cumulative probability distributions of characteristic length constants of D. melanogaster embryos expressing Bcd-GFP. . . . . . . . . . . . Average intensity profiles and fits of D. melanogaster embryos expressing Bcd-GFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average Bcd-GFP concentration extracted from a time-lapse movie of a D. melanogaster embryo expressing Bcd-GFP. . . . . . . . . . . . . Nuclear Bcd-GFP concentration during syncytial cell cycles 12 to 14. Average Bcd-GFP concentration of a time-lapse movie (different averaging regions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear diameters in nuclear cycles 9 to 14. . . . . . . . . . . . . . . Bcd-GFP intensity profiles for a single D. melanogaster embryo during cell cycles 11 to 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bcd concentration profiles for 3D computer simulation. . . . . . . . . Bcd-GFP concentration profiles for six D. melanogaster embryos. . . Bcd and Hb concentration profiles of antibody-stained, heat-fixed, wildtype D. melanogaster embryos in syncytial cell cycles 11 to 14. . . . . Average Bcd and Hb concentration profiles of antibody-stained, heatfixed, wildtype D. melanogaster embryos in syncytial cell cycles 11 to 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average Bcd-GFP concentration of a rectangular region in the center of a D. melanogaster embryo. . . . . . . . . . . . . . . . . . . . . . . Confocal images of hand-cut sections of heat-fixed wildtype D. melanogaster embryos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intensity profile of confocal images of hand-cut sections of heat fixed wildtype D. melanogaster embryos during cell cycle 14. . . . . . . . . Intensity profile of confocal images of hand-cut sections of heat fixed wildtype D. melanogaster embryos during cell cycle 14. . . . . . . . . Average Bcd-GFP concentration of a time-lapse movie of an unfertilized D. melanogaster egg expressing Bcd-GFP. . . . . . . . . . . . . . xi
37 37 38 39 41 42 42 51 52 53 54 56 57 58 59 59 60 60 61 62
63 64 65 66 67 68
4.20 Fluorescent Bcd antibody intensity profiles of unfertilized D. melanogaster eggs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Fluorescent Bcd antibody intensity profiles of wildtype D. melanogaster embryos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Summary of averages of intensity profiles from unfertilized and wildtype eggs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 Recovery curves of bleached wildtype D. melanogaster embryos expressing Bcd-GFP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.24 Bcd-GFP release of two nuclei located at approximately 20% egg length during mitosis 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.25 Recovery curve of a bleached wildtype D. melanogaster embryo that had been previously injected with fluorescently labelled 40kD-dextran dye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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68 68 69 70 71
72
Introduction All cells of an embryo contain the same genetic material which encodes for all information necessary for the organism’s development and life functions. Over the course of embryogenesis, cells have to determine their individual functions to form the diverse multitude of tissues of the organism. Genetically, this process, called differentiation, is characterized by the expression of only a subset of genes in cells of a given tissue, while all other genes are dormant in these particular cells. During early embryonic development, these different gene expression patterns are entirely determined by the position of the cell in the embryo by means of localized cytoplasmic determinants. This concept was first cited by Driesch in 1893 (Driesch, 1893) and the first experimental evidence arose in the early 1900s by Wilson (Wilson, 1904) and Conklin (Conklin, 1905), before positional determination was experimentally demonstrated by Illmensee and Mahowald in 1974 in Drosophila melanogaster eggs (Illmensee & Mahowald, 1974). The character of these cytoplasmic determinants was thought to be a substance that was called a morphogen, but it had not been found at the time and thereafter constituted a mystery in the field. However, the concept of a morphogen was not new, and goes back again to the early 1900s: Morgan postulated gradients of “formative substances” based on his experiments on regeneration of flatworms (Morgan, 1904; Morgan, 1905) and Boveri discussed “Richtungsk¨orper” and “animal” and “vegetal” gradients in sea urchin eggs (Boveri, 1901a; Boveri, 1901b). In the 1960s these morphogenetic gradient models were used to explain how cells determine their position along embryonic polarity axes. The morphogen was supposed to diffuse from a localized source to a degradation site (Lawrence, 1966; Stumpf, 1968). This idea was then further formalized by Wolpert (Wolpert, 1969) and Crick (Crick, 1970) circa 1970 with the notion of a morphogen gradient that establishes a long range pattern. In their view, cells determine their positional information by responding to different local concentrations of the diffusing morphogen. In the simplest case, cells make a sequence of binary decisions, each time comparing the local morphogen concentration to a threshold. In parallel, an alternative line of thought suggested a dynamic reading of concentration gradients for conveying positional information. In 1952 Turing showed in a seminal work that simple mathematical models based on spontaneously diffusing and reacting chemicals could give rise to stationary concentration patterns (Turing, 1952). He proposed that these reaction-diffusion models might be the underlying basis of morphogenesis. These models gained a wide popularity in the formulation of Gierer and Meinhardt in 1972 using computer simulations (Gierer & Meinhardt, 1
1972), and were applied to embryonic patterning in D. melanogaster by Meinhardt in 1989 (Meinhardt, 1989). The debate between the two coexisting models of static or dynamic gradient readout ended with the ground breaking work of Driever and N¨ usslein-Volhard in the late 1980s/early 1990s, in which they finally found a molecular substance that had the properties of a morphogen. They showed that in D. melanogaster the product of the maternal gene bicoid (bcd ) establishes a concentration gradient along the anteroposterior axis of the egg; further they demonstrated that Bicoid acts autonomously as a transcription factor at different concentration thresholds to pattern the anterior part of the embryo (Driever & N¨ usslein-Volhard, 1988a; Driever & N¨ usslein-Volhard, 1988b; Driever & N¨ usslein-Volhard, 1989). Increasing dosage of the gene shifts the patterning response posteriorly. Subsequently, many more morphogens were discovered both in D. melanogaster (Neumann & Cohen, 1997) and in other organisms including vertebrates such as chick (McMahon et al., 2003) and zebra fish (Chen & Schier, 2001) embryos. Despite all experimental evidence seemingly suggesting a simple static gradient readout model, intriguing questions remain which are difficult to answer within the scope of this model. These questions are related to the precision of positional information and the robustness of morphogenesis and of development in general. Developmental processes are extremely precise, despite the inevitable existence of large underlying molecular fluctuations. For instance, in the case of patterning in early embryos of D. melanogaster, cells obtain unique identities along the anteroposterior axis of the embryo, i.e. neighboring cells already at this stage have individual developmental fates. If this precision is achieved by local readout of concentration gradients which are established by diffusion – an inherently noisy process – other mechanisms must be in place to protect the organism’s development from the natural variation of internal and external parameters, such as concentration fluctuations and temperature. Moreover, external perturbations, such as gene dosage increase in the case of Driever’s and N¨ usslein-Volhard’s experiments with bcd, seem to be corrected by the organism over the course of its development (Namba et al., 1997). The final outcome of the developmental process is recovered, indicating that positional information is not entirely encoded in the initial conditions, but rather achieved dynamically (Furusawa & Kaneko, 2003; Jaeger et al., 2004). From a theoretical point of view, the main problem with a concentration readout process that is given by a threshold condition is that the concentration of the signalling molecules is often very low, resulting in very high concentration noise levels. In these models, the associated concentration fluctuations would propagate to downstream genes, and a reliable outcome of the morphogenic process would be questionable (Lacalli & Harrison, 1991). Finally, in 2002 Houchmandzadeh, Wieschaus and Leibler reported the first experimental evidence indicating that there are problems connected to the simple local threshold model in the case of the Bcd gradient in D. melanogaster (Houchmandzadeh et al., 2002). Houchmandzadeh et al. noticed a high embryo–to–embryo variability of the Bcd gradient, concurrent with a strong reduction of this noise in the positional information already at the next level of the gene cascade. Hunchback (hb), which is one 2
of the zygotic genes which displays a direct response to Bcd concentration along the anteroposterior axis of the egg, is induced at a sharp boundary at half-embryo length in response to the graded distribution of Bcd. Remarkably, although bcd gene expression displayed a high variability between wild-type embryos, the spatial locations of the boundary of the downstream gene products of hb were distinctly unvarying. Moreover, this boundary scaled properly with embryo size, a property that could not be attributed to the upstream Bcd gradient. These findings demonstrated that precision in embryonic development – a concept largely neglected by most developmental biologists up to this date – can not be achieved as a simple consequence of the morphogen gradient model. Instead, a subset of the genetic circuitry may be devoted to encode for the observed developmental robustness. The present work attempts to pursue this line of thought in order to better understand how developmental processes can be precise. Borrowing tools from biophysics – experimental, computational and theoretical – and combining them with well-established tools from genetics, biochemistry and molecular biology, the following chapters describe a quantitative analysis of the dynamics of the Bcd gradient and the precision of its readout in early embryos of D. melanogaster. Looking at developmental responses to changes in external parameters, Houchmandzadeh et al. measured the inter-embryonic variabilities of positional boundaries, which only captures the static aspects of robustness. A fundamentally different problem is presented in Chapter 1, in which for a given embryo the internal noise associated with the Bcd concentration readout by hb is investigated. Conceptually, this is a different question than the one raised by Houchmandzadeh et al., because by considering noise the dynamics of the underlying processes are examined. The “input/output” relation between Bcd and Hb is measured and interpreted as a transfer function. The precision at which Bcd is read out by Hb is extracted, and it is shown to be close to its physical noise limit of ∼ 10%, which translates into a positional precision of one nuclear spacing during cell cycle 14. To reconcile this experimental result with the theoretical noise level, which depends on physical constraints and on averaging over time, a mechanism is needed which is more complex than the simple local concentration readout of the Bcd gradient. Theoretical considerations show that the observed precision is difficult to achieve by temporal averaging over the available developmental time scales. A mechanism is proposed in which neighboring nuclei average their concentration measurements in order to reduce noise. Preliminary experimental results indicate that a simple model, which is based on Hb as the mediator signal, cannot explain local concentration averaging. Inspired by the observation that the Bcd gradient and the size of the egg are uncorrelated (Houchmandzadeh et al., 2002), Chapter 2 presents a comparison of gene products, and in particular of Bcd gradients, in D. melanogaster with those in embryos of other dipterans whose egg lengths differ by a factor of five. It is shown qualitatively that gene expression pattern scales with egg size, and it is demonstrated quantitatively that the average length constants of the Bcd gradients scale with the average egg sizes of the different species. On the other hand developmental time scales are shown to be conserved across species. These results are surprising, both because the Bcd gradients do not scale with egg size within a given species and because it is 3
supposedly established by an underlying diffusion driven process, which should scale only with a combination of space and time. Chapter 3 describes measurements of diffusion constants in living embryos of D. melanogaster for a series of dextran molecules spanning a size range of 10-150 kD. From these experiments, a cytoplasmic viscosity of approximately 4 cp is extracted, implying that molecules of the probed size range effectively diffuse 4 times slower in early embryonic cytoplasm than in water. Moreover, in different dipteran species the diffusion constants are of comparable value, implying that the physical properties of the cytoplasm cannot explain the scaling of the Bcd gradient in eggs of varying sizes within the dipteran family, and suggesting that more complex mechanisms may underlie the establishment of the Bcd gradient. Finally, an in vivo analysis of the Bcd gradient, its establishment and its maintenance, is given in Chapter 4. A fly construct designed to express a fusion protein of eGFP attached to the N-terminus of Bcd is presented and demonstrated to successfully reproduce the biological and physical properties of endogenous Bcd. Bcd-GFP gradients are measured and analyzed quantitatively, and an eGFP maturation time is inferred to be of the same magnitude as the lifetime of Bcd protein, estimated to lie between 5 and 20 minutes. Bcd gradients are monitored over the first 3 hours of development and it is observed that both the nuclear concentration at a given position along the anteroposterior axis of the egg and the overall shape of the gradient do not change significantly within a given embryo during syncytial blastoderm stages. In contrast, Bcd-GFP gradients across different embryos show a strong positional variability during early cell cycle 14. This constancy of Bcd concentration in the nuclei must reflect a rather precise balance between the increasing number of nuclei and the synthesis rate. Furthermore, careful analysis of nuclear import and export rates of Bcd-GFP, both during interphase and mitosis, suggests an important role of syncytial nuclei in the establishment and stability of the Bcd gradient. Moreover, comparing BcdGFP concentration in unfertilized vs. fertilized eggs, the data suggests a zygotic down-regulation of the Bcd synthesis rate. Finally, cytoplasmic Bcd-GFP diffusion constants are estimated from photobleaching experiments. It is found that their values are significantly lower than our previous estimates extracted from 40kD-dextran diffusion constant measurements in Chapter 3, indicating that cytoplasmic Bcd-GFP motion is considerably slowed down, possibly by unspecific binding within the cytoplasmic matrix. Although the exponential decay of the Bcd gradient would suggest a purely diffusion driven process being necessary for its establishment, a more careful examination reveals that transport mechanisms may be important. From phenomenological observations, it can be inferred that the dynamics of the gradient formation are not as simple as generally believed. Conceptually the current view must be altered as well, because it cannot explain the scaling of the Bcd gradient in different species of varying egg sizes. Finally, the necessity of a dynamic readout of Bcd concentration by Hb in order to suppress noise strongly challenges the validity of the local-concentrationreadout model.
4
Chapter 1 Physical limits to positional information during early embryonic development 1.1
Introduction
The macroscopic structural patterns of multicellular organisms have their origins in spatial patterns of morphogen molecules (Lawrence, 1992; Kirschner & Gerhart, 1997). In the early stages of embryonic development these morphogens typically are transcription factors that determine the movement and organization of cells during morphogenesis by forming a concentration gradient and by regulating directly the expression of other genes. The precision of pattern formation—the reliability with which “positional information” can be read out from the morphogen gradients—thus will be limited by noise and fluctuations in the regulation of gene expression (Elowitz ˜ et al., 2002; Raser & O’Shea, 2004). Considering the fact that transcription factors act at concentrations of the order of 1 nM (Winston et al., 1999; Pedone et al., 1996; Zamore et al., 1999; Zhao et al., 2002), or ∼ 0.6 molecules/µm3 , the molecule counting noise in the concentration measurement of the cell can be excessively large, i.e. the energy of the molecular thermal fluctuations, kB T , is large enough to perturb genetic transcription. It is not yet understood whether biochemical signaling systems within cells operate close to the corresponding counting noise limits. Many years ago, in the context of bacterial chemotaxis, Berg and Purcell emphasized that concentration measurements are limited by fundamental physical noise sources that derive from the random character of diffusion and binding at the level of single molecules (Berg & Purcell, 1977). Consider a receptor of linear size a, and assume that the receptor occupancy is integrated for a time τ (e.g., by accumulation of mRNA or gene products in the case of transcriptional regulation). Berg and Purcell argued that the precision of concentration measurements is limited to 1 δc ∼√ , c Dacτ
(1.1)
where c is the concentration of the molecule to which the system is responding and 5
D is its diffusion constant in the solution surrounding the receptor1 . Recent work (Bialek & Setayeshgar, 2003) shows that this expression represents indeed a lower limit to the noise level, where additional contributions come from all the complexities of the kinetics describing the interaction of the receptor with the signaling molecule2 . These theoretical results on the generality of the Berg–Purcell limit encourage us to apply this formula to understand the sensitivity of cells not just to external chemical signals (as in chemotaxis) but also to internal signals such as transcription factors, including morphogens. Several experimental groups have recently focused attention to the stochastic nature of the regulation of gene expression (Gardner et al., 2000; Elowitz et al., 2002; Ozbudak et al., 2002; Blake et al., 2003). Their work, however, is restricted to single cell organisms, and our goal here is to attempt to extend some of these ideas to multicellular organisms such as Drosophila melanogaster. Early embryonic development of D. melanogaster is an ideal test system to investigate these questions, as most genes and their regulation have been identified, and as a vast variety of technical tools, both of molecular and of optical nature, have been developed. In D. melanogaster the earliest zygotic genes are regulated by gradients of maternal morphogens, which act as transcription factors. The best-studied example is the activation of hunchback (hb) gene by Bicoid (Bcd) protein (Driever & N¨ ussleinVolhard, 1988a; Driever & N¨ usslein-Volhard, 1988b; Driever & N¨ usslein-Volhard, 1989). The widely accepted model suggests that bcd mRNA is maternally deposited at the anterior pole of the egg, and is translated into Bcd upon fertilization. Bcd is then thought to diffuse along the anteroposterior axis of the egg to establish a gradient, due to uniform degradation in the egg, that can be very well approximated by a simple exponential decay. In this model, the steady state concentration cBcd (x) is given by cBcd (x) = c0Bcd exp(−x/λ), (1.2) √ where the length constant λ = DτBcd is a function of the diffusion constant D and 1
If the receptor counts √N ∼ a3 c molecules it makes relative errors due to Poisson counting statistics of the order of 1/ N . If the receptor averages its concentration measurement over a time τ , then it can make K = τ /t independent measurements, where t ∼ a2 /D is the time that the receptor site vicinity has √ exchanged its molecules via diffusion. This reduces the relative error by an additional factor of 1/ K, leading to δc 1 ∼√ . c N ·K Finally putting all things together, we get Eq.(1.1). 2 The intuitive picture given by Berg and Purcell has been theoretically solidified in Ref. (Bialek & Setayeshgar, 2003). Using a more rigorous approach derived from statistical mechanics considerations the authors re-derived Eq.(1.1). Their idea was to use the fluctuation-dissipation theorem and to calculate the dynamic response of the receptor occupancy to changes in binding energy, because if receptor binding is at equilibrium (transcription factor/DNA binding site interactions are thought to drive the system towards equilibrium) the occupancy fluctuations can be viewed as thermal noise. √ They obtained the exact same expression with an additional π in the denominator, which we will include subsequently in our analysis.
6
the protein lifetime τBcd 3 . It has been shown that hb activity is a direct read-out of Bcd concentration (Driever & N¨ usslein-Volhard, 1989), and that the affinity of the hb promoter for Bcd is in the nM range, i.e. ∼ 1 − 3 molecule/µm3 (Zhao et al., 2002). After 11 nuclear divisions, during interphase 11, hb starts to be expressed zygotically in the anterior half of the egg, where Bcd concentration is high. Hb itself encodes a concentration-dependent transcription factor responsible for dividing the embryo into segments (Hulskamp & Tautz, 1991). There are seven known binding sites for Bcd in a segment of the hb promoter that allow for activation of transcription of the gene over a relatively narrow change in Bcd concentration in the middle-region of the embryo (Driever et al., 1989). Increasing the dosage of the bcd gene causes a posterior-shift in the location of the Hb expression boundary, as expected of an increase in Bcd protein (Driever & N¨ usslein-Volhard, 1988a; Driever & N¨ ussleinVolhard, 1988b). Targeted disruption of binding sites as assayed in transgenic flies also disturbs the transcriptional response in several ways (Driever et al., 1989; Struhl et al., 1989): (i) it becomes less steep, reflecting loss of cooperativity; (ii) the overall level of transcription is reduced, indicating that each bound Bcd molecule contributes to transcriptional activation; and (iii) the location of the Hb expression boundary shifts anteriorly, since a higher concentration of Bcd is required to achieve similar levels of transcription. The sharp drop in expression level at 48% egg length raises a number of questions. The embryo is divided by hb into a quasi all-or-none fashion. The mRNA level drops from maximum expression to minimum expression over ∼ 10 µm and the protein levels drop over ∼ 40 µm. This observation allows for a treatment of the Bcd-hb transition as a genetic ON/OFF switch, as in the case of the lysis/lysogeny decision of lambda phage in E. coli. The underlying mechanism that generates this sharp transition is not completely understood, given that (i) the establishment of the Bcd gradient is a diffusion driven process, and (ii) that the concentration where the cell needs to make the quasi ON/OFF decision (dissociation constant of Bcd Kdbcd ) is at a level of roughly five molecules per µm3 . Both aspects are extremely prone to noise, Brownian motion (i.e. thermal fluctuations) for the first, and counting or shot noise for the second aspect. Moreover, given that at the end of cell cycle 14 neighboring nuclei have distinct levels of gene expression, it can be shown (see below), that the total accuracy or precision encoded in the developmental process is about 10%. It is unclear if this level of accuracy is already encoded in the Bcd-hb readout process. Several questions arise: How can a maternal gradient produced by diffusion provide the accuracy required during development? How can protein concentrations be measured reliably, if binding affinities are in the nM range? Is noise relevant in the regulation of gene expression? How does the probabilistic nature of transcription 3
Eq. (1.2) is the steady state solution of the modified, one-dimensional diffusion equation ∂t cBcd (x, t) = D∂x cBcd (x, t) −
1 cBcd (x, t) τBcd
where the last term on the righthand side represents protein decay. A constant synthesis rate R at the anterior pole of the egg gives a boundary condition of −D∂x cBcd (x, t) = R, which leads to c0Bcd = Rλ D .
7
influence the reliability and functionality of genetic regulation? How are errors corrected or how is noise filtered? How accurate are gene expression patterns in general? Here we are focusing on the physical limits to the readout process of Bcd by hb, and we are trying to understand how noise due to physical constraints compares to actual measurable “biological” noise. We have successfully conducted experiments that show, that the precision at which Bcd is read out by Hb in D. melanogaster, is close to its physical noise limit of ∼ 10%, which translates into a positional precision of one nuclear spacing during cell cycle 14. To reconcile this experimental finding with the theoretically derived limit we postulate a mechanism by which neighboring nuclei average their concentration measurements in order to reduce noise. We show experimentally that two simple models, which are based on Bcd or Hb as the mediator signal, cannot explain local concentration averaging.
1.2
Results
Inspired by the results of (Elowitz et al., 2002), which show that one can separate the “intrinsic” noise in gene expression (i.e. promoter cite occupancy fluctuations) from all other random events that influence the cellular response, we further separate the noise in the regulation of gene expression into two parts: the first part is due to the complicated underlying, often unknown kinetics of the system, and the second part stems from thermal fluctuations, which result in counting or shot noise. In this model, the real noise of the system is bound by the second part. To test this limit experimentally in the case of Bcd in D. melanogaster, we need to estimate the parameters of Eq. (1.1) relevant to this case: Receptor size a: Receptor sites for eukaryotic transcription factors are ∼ 10 base pair segments of DNA with linear dimensions a ∼ 3 nm. Multiple sites might make the effective size slightly larger, but wrapping of the DNA around the nucleosome could effectively convert a longer sequence of sites into a two dimensional patch of sites with the same linear dimensions, and we know from the Berg–Purcell analysis and its generalization that such a patch acts as one effective site in setting the limiting noise level. Diffusion constant D: Diffusion constants of proteins comparable in size to Bcd have been measured to be as small as ∼ 1 µm2 /s in the bacterial cytoplasm (Elowitz et al., 1999) and up to ∼ 20 µm2 /s in Dictyostelium cell cytoplasm (Potma et al., 2001), corresponding to an effective cytoplasmic viscosity just a few times smaller than that of water. In Chapter 3 we will present our own syncytial diffusion constant measurement, and we find for a dextran molecule of the size of Bcd a diffusion constant of ∼ 17 µm2 /sec. Assuming a slower diffusion constant in the nucleoplasm than in the syncytium we chose a diffusion constant of 5 µm2 /sec, based on measurements made earlier (Lang et al., 1986). Signaling molecule concentration c: Transcription factors are present in cells over a wide range of concentrations. Our interest, however, is in the reliability of the “decision” to activate or repress the expression of a target gene. The decision point 8
Figure 1.1: Triply immunostained D. melanogaster embryo at early cell cycle 14.(Hb in red (top row), Bcd in green (center row) and DNA in blue (bottom row).) The pictures in the right column show a magnification of the outlined rectangle in the respective image in the left column. Custom image analysis programs written in Matlab marked nuclei by a black dot and outlined their circumference by a black line, as indicated.
(e.g., the midpoint in the transition from high to low Hb concentration along the D. melanogaster anteroposterior axis) must occur when the transcription factors are present at concentrations comparable to their affinity or equilibrium constant for the relevant binding sites along the DNA. Measurements of these equilibrium constants, for Bcd and for other transcription factors, cluster in a range around 1 − 3 nM (Zhao et al., 2002). Putting together the different factors, using an integration time τ = 1 min, Eq.(1.1) gives a fractional accuracy of ¢−1/2 δc ¡ ∼ π5 µm2 /s · 3 nm · 2 nM · 60 s ∼ 54%. c
(1.3)
Although there are substantial uncertainties, it seems that one minute of integration is required to achieve reliable responses to three fold changes in transcription factor concentration4 . For the hb-transition point this would imply that its positional precision would vary on the order of one hundred nuclear distances. However it has been shown quantitatively, that the hb-boundary is precisely defined within three nuclear distances (Houchmandzadeh et al., 2002). On the other hand, a number of developmental decisions in D. melanogaster are sufficiently precise that in cell cycle 14 neighboring nuclei have readily distinguishable levels of expression for several genes (Wolpert, 1969; Wolpert, 1989). If this precision derives from positional information encoded in the Bcd concentration gradient, using 4
By “achieving reliable responses” we mean here that two nuclei are able to distinguish their concentration from each other: the read-out of nuclei 1 with concentration c1 and nuclei 2 with concentration c2 can be reliably distinguished if c1 − δc1 > c2 + δc2 . Rearranging leads to c1 >
1+ 1−
δc2 c2 δc1 c1
c2 .
Using the fractional accuracy from Eq.(1.3) and assuming that it does not change significantly among both nuclei, we obtain a factor of three in difference between both concentrations.
9
Figure 1.2: Embryo from top row of Figure 1.1 with ∼ 2300 recognized nuclei indicated by dots, of which ∼ 1500 were chosen for further analysis (blue dots).
an experimentally measured nuclear distance δx and λ from Chapter 2, Eq.(1.2) implies δc/c = δx/λ ∼ 6 µm/79 µm ∼ 8%. In other words, the read-out of this concentration must be accurate to ∼ 10%. This is the before mentioned total precision that is encoded in the system, and which must be achieved in the developmental process. However, ∼ 10% precision would require integration for more than one hour, which is just at the limit of plausibility, given that zygotic gene expression is determined during cell cycle 14, which lasts approximately 50 minutes. Realistically one would expect average integration times which are substantially shorter, as protein and mRNA lifetimes are on the order of minutes, and the regulation of the entire gene cascade involving hundreds of genes must happen on faster time scales than hours. To measure the precision of the Bcd concentration gradient experimentally, we fixed D. melanogaster embryos and stained for DNA, Bcd and Hb with different fluorescently labelled antibodies. The fluorescence peaks of the different labels are sufficiently distinct that we can obtain independent images of the three stains. Figure 1.1 shows a confocal image of such an embryo, fixed during early cell cycle 14. The DNA images allow us to define a template which can locate automatically the centers and outlines of the nuclei, as indicated in Figure 1.1. In a typical image of this sort we identify on average 2300 nuclei (see Figure 1.2); manual inspection of the images shows that misidentifications occur at less than the 1% level, and these are easily corrected. For our analysis we chose only nuclei that are sufficiently distant 2000 1800 1600 1400
Figure 1.3: Scatter plot of raw nuclear Hb vs nuclear Bcd intensity for 1527 nuclei of a single D. melanogaster embryo. (12 bit image depth.)
1200 1000 800 600 400 200 0 200
400
600
800
10
1000
1200
1800 1600 1400 1200 Hb
Figure 1.4: “Input/output” relationship between Bcd and Hb intensities for 5 consecutive repetitions of the data set in Figure 1.3. Different colors correspond to different repetitions. See text for details on computational procedure.
1000 800 600 400 200 300
400
500
600 700
800
900
Bcd
from the embryo edge to avoid edge effects (see Figure 1.2). Given the nuclear outlines we can measure the average intensity of Bcd and Hb staining in each nucleus. If staining is proportional to concentration of these proteins , then a single image gives us more than 1500 points on the scatter plot of Hb expression level vs Bcd concentration, as shown in Figure 1.3. Scatter plots as in Figure 1.3 contain information both about the mean “input/output” relation between Bcd and Hb and about the precision or reliability of this response. To display these relations we discretize the Bcd axis into bins, effectively grouping together nuclei which have very similar levels of staining for Bcd, insuring the same amount of nuclei in each bin; within each bin we can then compute the mean and variance of the Hb staining intensity. Figure 1.4 shows this input/output relation for the data set shown in Figure 1.3. Each color corresponds to a different repetition of the image acquisition of that same embryo, showing that the experiment is very reproducible, and that no photobleaching occurred. 1
11
0.9 0.8 0.7 c(Hb)/cmax(Hb)
Figure 1.5: Scatter plot (black dots) and transfer function (red) between relative Bcd and Hb concentrations. The data sets of the 5 repetitions shown in Figure 1.4 have been merged and an overall background intensity has been subtracted from both channels. Hb concentrations are shown in units of their maximal value, and the Bcd concentration in units of the level which generates (on average) half maximal Hb concentration. The transfer function has been generated by segregating the Bcd axis in 100 bins with equal amounts of nuclei in each bin, and by computing the mean and standard deviations within each bin.
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5 2 c(Bcd)/cKd(Bcd)
2.5
3
0.5 0.45 0.4 0.35 δc(Bcd)/c(Bcd)
Figure 1.6: Effective noise in Bcd concentration as a function of Bcd expression level. Hb standard deviations from Figure 1.5 have been converted into an effective standard deviation in Bcd concentration (see text for more details). The blue curve shows these effective Bcd standard deviations normalized by the mean Bcd concentration of the respective bin. The red curve shows the measurement noise due to instrumental inaccuracies, and the green curve represents the remaining “biological” noise, i.e. the blue curve corrected by the red curve (see text for more details).
0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.5
1 c(Bcd)/cKd(Bcd)
1.5
2
We can now merge the data sets for all repetitions and plot the mean input/output relationship for this particular embryo in Figure 1.5. The overall image intensity background has been accounted for by subtracting from each image acquisition channel a constant, which corresponds to the average minimal nuclear intensity for both Bcd and Hb, respectively. The Hb level is reported in units of its maximal value, and the Bcd level in units of the level which generates (on average) half-maximal Hb intensity. The input/output relation is now expressed in terms of relative Bcd and Hb concentrations, and can be viewed as the transfer function by which a particular Bcd concentration turns on hb and produces a particular Hb concentration as a response. Dividing the Bcd axis into 100 segments results in approximately 75 points per bin. The red curve in Figure 1.5 represents the mean Hb concentration for each center bin Bcd concentration. The error bars are the standard deviation of Hb concentration within each bin. We see that these fluctuations are ∼ 10% at high expression levels, consistent with direct measurements on artificially constructed regulatory modules (Elowitz et al., 2002). If we think of the Hb expression level as a readout of the Bcd gradient, then the standard deviation σHb (Bcd) of Hb levels at fixed Bcd concentration is equivalent to an effective noise in the Bcd concentration itself, ¯ ¯ ¯ dc(Hb) ¯−1 δc ¯ , ∼ σHb (Bcd) ¯¯ (1.4) c d ln(c(Bcd)) ¯ that is directly comparable to the limiting noise level in Eq’s. (1.1) and (1.3). This effective noise level5 is shown in Figure 1.6 (green curve), and we see even in the case of a single embryo that it is of the order of δc/c ∼ 0.1 over a wide range of Bcd expression levels corresponding to the “decision region” of the input/output relation. Mean input/output relations for four individual embryos are shown in Figure 1.7 in our 5
The noise level resulting from Eq. (1.4) (blue curve in Figure 1.6) needs to be corrected by the instrumental measurement noise σInstr , depicted in Figure 1.6 by the red curve. We estimate the instrumental noise by computing the standard deviations of the nuclear intensities of 5 consecutive imp 2 − σ2 age acquisitions of a given embryo. The final “biological noise” is obtained by σbiol = σHb Instr .
12
1 0.9 0.8
0.6 0.5
max
(Hb)
0.7
c(Hb)/c
Figure 1.7: Transfer functions for 4 individual embryos. Each curve represents the average of 5 image acquisition repetitions of the same embryo, and each color represents a different embryo. For each embryo, Hb expression levels are normalized by the respective maximal Hb expression, and Bcd expression levels are expressed in units of Bcd level where Hb expression is half maximal.
0.4 0.3 0.2 0.1 0 0
0.5
1
1.5 2 c(Bcd)/cKd(Bcd)
2.5
3
normalized coordinates. The apparent similarities between the curves is skewed due to scaling of the Bcd axis and normalization of the Hb axis. Close inspection reveals variability in the lower part and large differences in the upper part of the curves. This observation is consistent with inter-embryonic variabilities in Bcd gradients reported earlier (Houchmandzadeh et al., 2002). Figure 1.8 depicts the input/output relation calculated from pooling the data from four embryos. We see that the response of Hb to changes in Bcd concentration is extremely steep. Synthesis of Hb corresponds to the occupancy of Bcd binding sites on the hb promoter. The steepness of the transfer functions reflects the cooperative interaction of n sites, which can be quantified by an apparent Hill coefficient µ ¶ d ln[cHb ] nHill = max . (1.5) d ln[cBcd ] For Figure 1.8 we obtain nHill = 4.0, which is consistent with cooperative interactions among the 7 known Bcd binding sites (3 strong and 4 weak ones) on the hb promoter (Yuan et al., 1996; Ma et al., 1996; Burz et al., 1998; Burz & Hanes, 2001). Similarly, we can fit the Hill equation Chb =
C nBcd nHill CBcd + KdnHill
(1.6)
directly to the transfer function of a single embryo (see Figure 1.9). In this case, the best fit corresponds to a Hill coefficient of 4-5, which is comparable to our previous result and again in line with 3 strong and 4 weak Bcd binding sites. The fact that we observe such a high degree of cooperativity means that our measurement errors must be less than 4% rms6 . If our staining method for measuring Bcd concentrations had large random errors then these would smooth the input/output relation. 6
If we imagine a Heaviside function as a “perfect” input/output relation, smoothed by noise to give our observed curve, then the rams noise needed to generate our slope is given by σ = 2πn1 eff . Any less “perfect” transfer function can only further reduce this noise level.
13
1 0.9 0.8
Figure 1.8: Transfer function for pooled data set of the 4 embryos of Figure 1.7 with a measured Hill coefficient of 4.0. Each black dot represents one individual nucleus of the 4 embryos. The red curve is obtained by generating 100 bins along the Bcd-axis of the merged data set from 4 embryos.
c(Hb)/cmax(Hb)
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0.5
1
1.5 2 c(Bcd)/cKd(Bcd)
2.5
3
1 0.9 0.8
Figure 1.9: Transfer function for a single embryo n (red). Data is fitted by CCn +1 where n represents the Hill coefficient and C = cBcd /cKd is the normalized Bcd concentration. Black curves show fits for different n (see legend).
/max(cHb)
0.7
data n=1 n=2 n=3 n=4 n=5 n=6
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1 /cKd
1.5
2
0.5
1 c(Bcd)/cKd(Bcd)
1.5
2
0.5 0.45 0.4 0.35 δc(Bcd)/c(Bcd)
Figure 1.10: Biological noise for 4 individual embryos (colored curves) and average biological noise from same 4 embryos (black curve). Each colored curve is the effective Bcd noise for an individual embryo, corrected by its respective instrumental noise level. The average is obtained by the mean of the individual noise levels.
0.3 0.25 0.2 0.15 0.1 0.05 0 0
14
0.4 0.35
Figure 1.11: Comparison of average noise level of 4 embryos (black curve) with noise level of merged data set (blue curve). The black curve corresponds to the black curve of Figure 1.10.
δc(Bcd)/c(Bcd)
0.3 0.25 0.2 0.15 0.1 0.05 0 0.4
0.6
0.8 1 1.2 c(Bcd)/cKd(Bcd)
1.4
1.6
Moreover, the noise levels of different embryos also agree within errors in the decision region of the transfer function. Figure 1.10 shows the effective noise level σbiol for four different embryos. The average noise level of those 4 embryos (black curve in Figure 1.10) lies well at or below the 10% level. If we pool the data and compute the noise level from the merged data sets of the four embryos, the noise level in the decision region is about 50% higher than the average of the noise levels of the individually analyzed data sets (see Figure 1.11), consistent with earlier findings of high embryo–to–embryo variabilities in the Bcd gradient (Houchmandzadeh et al., 2002). To insure that the discovered noise precision is not due solely to positional correlations along the egg we repeated our noise analysis, but with randomized Hb vs. Bcd concentrations: we projected the nuclear coordinates onto the embryo’s AP-axis, and we generated 100 bins with equal amounts of nuclei in each. This generated bins 0.5 0.45 0.4 0.35 δc(Bcd)/c(Bcd)
Figure 1.12: Comparison of the noise level for merged data set (blue curves) with the same data set, but with its Hb data de-correlated from Bcd (red curves)—(see text for more explanation). In black we show the instrumental noise level resulting from the merged data set. The lower blue and red curves are the instrumental noise corrected “biological” noise levels.
0.3 0.25 0.2 0.15 0.1 0.05 0 0
15
0.5
1 c(Bcd)/cKd(Bcd)
1.5
2
1 0.9 0.8 0.7 noise correlation
Figure 1.13: Radial correlation function of Hb noise (black) for one individual embryo. Internuclear noise correlation in Hb intensity is plotted vs radial distance. The distance is normalized by the mean nuclear distance, i.e. 5.6 µm. In blue and red we show the fraction of the correlations due to instrumental or measurement noise for Bcd and Hb, respectively.
0.6 0.5 0.4 0.3 0.2 0.1 0 0
5 10 15 20 (inter−nuclear distance)/(mean nuclear spacing)
25
of a maximal size of 40µm, which is well below the size of the length constant of the exponentially decaying Bcd gradient. For the nuclei contained in each bin, we randomly re-attributed the Hb concentrations. Each nucleus still has a Hb concentration similar to before the shuffling process, but the Bcd and Hb concentrations are now de-correlated. Figure 1.12 compares the effective noise in Bcd concentration of our pooled data set from 4 embryos with the effective noise in Bcd concentration of the randomized data set. We see that the latter data set has a consistently higher noise level than the non-randomized set, and that the noise in the decision region shifts up by about 35%. This shift indicates that the observed 10% precision in Bcd concentration is due to biological factors rather than a systematic artefact of our analysis. In an attempt to reconcile the observed precision in Figure 1.11 with the limits set by Eq. (1.3), we asked whether the embryo achieves the noise level reduction by averaging over space, rather than over time: if the Hb level in one nucleus reflects the average Bcd level in N neighboring nuclei, the limiting noise level in Eq (1.3) √ should decrease by a factor of N . If we imagine that communication among nuclei is mediated by diffusion of a protein with a diffusion constant comparable to that of Bcd in the cytoplasm, then signals from a single nucleus can reach N ∼ Dcytoplasm τ√/`2 others, where ` (∼ 5.6 µm) is the spacing between nuclei. Allowing for this N improvement we find the analog of Eq (1.3), δc ` 5.6 µm p ∼ p ∼ ∼ 10%. c τ πDacDcytoplasm 60 s π5 µm2 /s · 3 nm · 2 nM · 17 µm2 /s
(1.7)
Rather than requiring > 1 hr to achieve the observed level of precision, communication and cooperation among nuclei makes this level of precision available within τ ∼ 1 − 2 min. In √ such a scheme Hb expression is controlled by Bcd levels throughout a radius of ∼ Dτ /` ∼ 5 − 6 nuclei. If each nucleus makes independent decisions in response to the local Bcd concentration, then noise in the Hb levels of individual nuclei should be independent. On the 16
1
0.8 0.7 noise correlation
Figure 1.14: Radial correlation function of Hb noise from pooled data for 4 embryos. Internuclear noise correlation in Hb intensity is plotted vs radial distance. The distance is normalized by the mean nuclear distance, i.e. 5.6 µm. The inset shows the natural logarithm of the noise correlation, and the negative slope (red) is inversely proportional to the characteristic correlation length ξ = 6.4, where ξ is a measure of the radius expressed in nuclear distances over which the noise is typically correlated.
ln(noise correlation)
0.9
0.6 0.5 0.4
0 −1 −2 −3 −4 0
10 20 nuclear distance
0.3 0.2 0.1 0 0
5 10 15 20 (inter−nuclear distance)/(mean nuclear spacing)
25
other hand, if Hb expression reflects an average over neighborhood, then noise levels necessarily become correlated within this neighborhood. Going back to our original images of Bcd and Hb levels, we can ask how the Hb level in each nucleus differs from the average (along the input/output relation of Figure 1.5) given its Bcd level, and we can compute the correlation function for this array of Hb noise fluctuations. Figure 1.13 shows the Hb noise correlation for an individual embryo. From this figure it can also be seen that the correlation due to experimental noise is negligible. The results for our pooled data for 4 embryos, shown in Figure 1.14, reveal a correlation length of 6 − 7 nuclei, as predicted if averaging occurs on the scale required to suppress noise. To further test the plausibility of our proposed averaging mechanism of neighboring nuclei, we measured transfer functions at different cell cycles. If such a mechanism would exist, then the noise level should go down with progressing cell cycles as nuclear density increases, and with it, the local concentration of averaging nuclei. Input/Output relations of raw Bcd and Hb nuclear intensities for cell cycles 11 to 140
120
100
80 I(Hb)
Figure 1.15: Transfer functions generated from raw intensities of embryos fixed at different cell cycles (cc). Average of 10 embryos at cc 14 in blue, average of 7 embryos at cc 13 in green, average of 4 embryos at cc 12 in red, and average of 6 embryos at cc 11 in cyan. (8 bit image depth.)
60
40
20
0 0
17
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100 I(Bcd)
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1 0.9 0.8
Figure 1.16: Transfer functions from Figure 1.15 background corrected and normalized as above. (For color code see caption of Figure 1.15.)
c(Hb)/cmax(Hb)
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1 c(Bcd)/cKd(Bcd)
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2
14 are shown in Figure 1.15. This data has been extracted from different embryos which have all been treated the same way throughout the entire processing procedure, from embryo collection to confocal image collection. Using the same settings and parameters all throughout permits us to compare the depicted absolute staining intensities in Figure 1.15. From this raw data set it seems to be clear that there is an almost three fold intensity increase in Hb expression from cell cycle 11 to cell cycle 14 whereas Bcd expression levels only seem to be increasing gradually by less than 20% (see similar results in Chapter 4). However, if we normalize Hb intensities for each cell cycle by their maximum expression, and if we scale Bcd intensities by the Bcd intensity corresponding to half-maximal Hb expression (see Figure 1.16), we notice that most of the differences in the input/output relation are due to an up-scaling of Hb intensity with cell cycles progressing, reflecting a strong zygotic component in hb transcription. Moreover, we notice a sharpening of the transfer functions at cell cycle 14 with an increase in Hill coefficient of a factor of 2–3. This sharpening should lead to a lower noise level, but the quality of our data did not allow for further treatment to compute the Bcd noise levels. Note however, that if the simple input/output relation would be independent of dynamics or nuclear communication, we would not see any sharpening of the transfer function. There are several plausible mechanisms by which such a local averaging scheme among neighboring nuclei could happen. We investigated a very simple mechanism, which is based on the hypothesis that Hb feeds back upon itself and mediates the local averaging signal. To test this hypothesis, we looked at a mutant fly strain with a non-functional Hb protein which is altered from wildtype Hb by a single point mutation. The protein is still nuclear which allows us to apply our analysis in the same way as we have done for wildtype embryos. Figure 1.17 compares the Bcd noise level for homozygous and heterozygous embryos of this strain, and we see that there is no clear distinction at the level of half-maximal Hb expression. If Hb were the mediator for the local averaging signal, we would expect the data from the mutant homozygote to have a significantly higher Bcd noise level. Notice that both data 18
0.5 0.45 0.4
Figure 1.17: Average Bcd noise level for 12 heterozygous embryos (blue) and 9 homozygous embryos (red) of a fly strain with a hb point mutation and a resulting non-functional Hb protein.
δcBcd/
0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.2
0.4 0.6 c(Hb)/cmax(Hb)
0.8
1
sets have higher noise levels than our wildtype data, due to the fact that we did not subtract any experimental measurement noise from these data.
1.3
Discussion
Processes during early embryonic development need to be very precise. Errors at this stage would propagate and be amplified as development proceeds, which subsequently could lead to catastrophic fates of the system. In order to prevent this outcome, the system must have built-in mechanisms that can either correct errors, or, more likely, reduce the probability of making errors early on. We showed that in the case of the early embryonic gene cascade in D. melanogaster, the transition from the maternal gene bcd to its target gene hb, the system seems to work at the limit that is imposed to it by physical constraints, such as Brownian motion. This is the first time to our knowledge that this molecular noise limit has been shown to be reached in a eukaryotic multicellular organism. Experimentally this is difficult to show due to the complication of reliable in vivo measurements of single molecular events. However, our system is special in the sense that the Bcd gradient is a naturally decaying concentration gradient which seems to be stable over a long period of time, and we can use macroscopic spatial averaging instead of temporal averaging at the microscopic level to make reliable noise measurements. Although at a very preliminary level, our results indicate for the first time that the classical arguments of Berg and Purcell about the sensitivity of chemical sensing in bacteria also apply to transcriptional regulation of gene expression in multicellular organisms. We can use the same formalism they employed for chemical sensors to discuss the limits to internal signalling of morphogen gradients. Our findings suggest that although the precise mechanisms of transcriptional regulation may be complicated, the system may be tuned to operate at or near the limits set by more fundamental physical considerations. Many functional parameters may be estimated 19
from physical principles without knowledge of all the microscopic parameters. In our model, the lower limit to the noise level arises from the physics of diffusion alone, and the precision is set by the diffusive concentration fluctuations. It only depends on the diffusion constant of the transcription factor, the linear dimension of the receptor binding site and the averaging time, and it is independent of the precise details of binding and unbinding mechanisms. The generality of the minimum noise level in different systems, both experimentally and theoretically (Bialek & Setayeshgar, 2003), suggests the existence of a more universal principle. This noise limit, derived from statistical mechanics considerations, resembles the Heisenberg principle in quantum mechanics, and it could in theory be the fundamental regime to which many molecular biological processes are driven by evolution, i.e. selection favors lower noise rather than higher. Systems that do not operate in this regime may have found an evolutionary niche, a meta-stable state, but further evolution could only lead them closer towards this fundamental noise limit. For future work it would be interesting to find a general theorem about the minimum noise level, based on theoretical considerations that incorporate the fact that the minimum noise level is independent of the complex chemical kinetics and is governed by the universal microscopic diffusive dynamics of the ligands that lead the system towards equilibrium. In this work it will be challenging to combine the diffusive processes that happen in the vicinity of the binding sites with those diffusive processes that happen at larger distances, due to the more complex cytoplasmic environment, where diffusion may be porous in the actin filament and microtubule matrix and hindered due to sticking and specific/unspecific binding. Especially in multicellular organisms, the long-range diffusive properties will become important for cell-cell-communication and for establishing morphogen gradients. Our proposed mechanism of local averaging among neighboring nuclei is not the only way to explain the observed Bcd noise level. Different gene products that regulate Hb expression may act in concert to reduce the noise. However, √ if NG different genes are involved, than the noise would be reduced by a factor of NG , just as in the case for the neighboring N nuclei. This would predict an involvement of ∼ 25 − 30 genes, which is not very plausible. Hb is most likely not the only gene that needs to be regulated to achieve the reported accuracy, but presumably other genes also need mechanisms to reduce the noise levels of their transcriptional regulators. This would then lead to an “every gene regulates every other gene” system, which is highly unlikely. A different but perhaps more likely alternative might be an analogous mechanism to kinetic proofreading in biosynthetic processes (Hopfield, 1974). Kinetic proofreading makes use of energy-dissipating enzymatic reactions to suppress thermal noise and has recently been suggested to play a role in MAP kinase signal transduction (Swain & Siggia, 2002). It is biologically conceivable that enzymatic reactions are connected to transcription factor binding and unbinding. These reactions could be organized in a way that reduces thermal noise, and hence the noise limit. Particularly in the case of Bcd where multiple binding sites are clustered on the hb promoter, an enzymatic pathway is easy to conceptualize. It is possible that there may be some errors in the estimation of the parameters 20
we are using here. They may be significantly in error. Both for D and a, plausible ranges cannot explain the difference between the observed precision in Figure 1.11 with the limits set by Eq. (1.3). But one might worry that the absolute concentration c is inferred from in vitro measurements of protein–DNA interaction. All the current techniques to measure dissociation constants are in vitro, such as gel shift assay and surface plasmon resonance. Not only are the results of these methods very variable, but it is also not clear whether those in vitro measurements are applicable to in vivo conditions. However, in our case, where we measure average protein concentrations in nuclei of D. melanogaster, we should, in principle, be able to estimate absolute concentrations and the Kd directly. If concentrations are in the nM range, we should see substantial pixel–to–pixel fluctuations in the intensity of the Bcd staining. We should be able to draw the scatter plot of the variance among intensities in a single nucleus vs. the mean for that nucleus. This relationship should be fit by a straight line through the origin, if we are able to observe the Poisson counting fluctuations of molecules. From the slope of this relation we could then infer an estimation of the number of molecules in the ∼ 0.4 µm3 volume sampled by one pixel7 . Even if this measurement would not be accurate enough to obtain absolute concentrations, observing a Poisson noise alone would suggest that the true concentrations are not orders of magnitude larger than our estimate, as would have been required to achieve the observed precision in the available time. The fact that we used Hb protein concentrations rather than mRNA concentrations to quantify the transcription read-out of our system may raise some question as to the validity of our data. However, quantifying mRNA concentrations optically in an intact multicellular organism is, to our knowledge, not feasible. It may be possible in the future to generate fluorescent single stranded mRNA tags that bind specifically to hb mRNA. Ultimately, it does not influence our results, but only their interpretation. Moreover, the mRNA amplification mechanism represents an additional possible noise amplification rather than noise reduction. On the other hand it is, of course, more difficult to interpret our result as a minimal noise level in DNA transcription because our read-out are not the transcripts but the proteins. Finally, this flaw may contribute in itself to the mechanism for local averaging: hb mRNA molecules are released by the nuclei, Hb protein is generated in the syncytial cytoplasm, diffuses back into the nuclei during which partial equilibration of local concentration gradients occurs. Furthermore, one might worry correctly about the fact that we use image intensity values from fluorescently labelled antibodies and assume their linear proportionality to the actual protein concentrations in the embryos. This assumption is central to our methodology, and a thorough justification of our findings would require a quantitative test. This could be done using a combination of immunofluorescence protocols and 7
Assuming a linear relationship between the mean fluorescence intensity in a given nucleus hIii and the average number of fluorescent particles in that nucleus hnii , we have hIii = F ·hnii , implying for the respective variances σi2 (I) = F 2 · σi2 (n). But in Poisson statistics σi2 (n) = hnii , and hence σi2 (n) = F · hIii , i.e. the slope of the scatter plot is nothing but the linear proportionality factor between the average nuclear staining intensity and the average number of molecules per nucleus.
21
quantitative Western blot analysis. However, in other systems, such as cell cultures, the linearity between protein concentrations and fluorescence intensities has been previously demonstrated (J.C. Gingrich & Nguyen., 2000; Schutz-Geschender et al., 2004). These findings suggest, that the linearity also hold in our case because the chemistry involved in antibody affinity and binding does not change significantly from single to multicellular organisms, but only the physical constraints for the proteins to penetrate the fixed perforated tissue structure change. Our interpretation of transfer functions and binding constants in our system is very novel. These transfer functions are commonly reported in biochemical titration assays, but never from nuclear staining intensities in an intact D. melanogaster embryo. Our system has the special property of a macroscopically spatially varying transcription factor concentration. The common picture is that expression levels are a function of transcription factor concentrations. The typical approach to measure transfer functions is to use an in vitro assay where the examined promoter controls reporter molecules. The problem with this approach is that the reproducibility of in vivo conditions is questionable and that the transcription factor concentration range used in the assay does not necessarily reflect the naturally occurring concentration range. Here we have stained for transcription factor and output in their natural environment, i.e. in situ of the intact multicellular organism. This ensures that the input/output relation is measured over the natural range of transcription factor concentration. In addition, we get the corresponding noise level, again within its natural dynamic range of transcription factor concentration. There is a clear generalization to in vivo dynamics using multi-color GFP constructs.
1.4
Materials and Methods
Fly Stocks. For hb functionality testing we used hb amorph hb 6N 47 /TM3,hb-lacZ (Houchmandzadeh et al., 2002). For all other experiments we used wildtype Oregon R flies. Immunostaining of embryos. All embryos were collected at 25◦ C, heat fixed, and subsequently labelled with fluorescent probes following previously published protocols (Wieschaus & N¨ usslein-Volhard, 1986). We used rat anti-Bcd and rabbit antiHB antibodies, gifts of J. Reinitz and D. Kosman (Kossman et al., 1998). Secondary antibodies were conjugated with Alexa-488, Alexa-546 and Toto3 (Molecular Probes). Embryos were mounted in AquaPolymount (Polysciences, Inc.). Microscopy. High-resolution digital images (1024 × 1024, 12 bits per pixel) of fixed eggs were obtained on a Zeiss LSM 510 confocal microscope with a Zeiss 20x/0.45NA A-plan objective. Embryos were placed under a cover slip and the image focal-plane was chosen at top surface of the flattened embryo.
22
Chapter 2 Scaling: Developmental Characterization of Flies of Varying Egg Sizes 2.1
Introduction
The fertilized egg of Drosophila melanogaster gives rise to a segmented differentiated larva over the course of a 24 hour embryonic period. The genetic, molecular, and embryological analysis of embryonic segmentation along the antero-posterior (headtail) axis in D. melanogaster embryos has furnished a detailed description of how maternally deposited spatial determinants coordinate zygotic gene expression during embryogenesis. The result is the most complete description of genetic control of a developmental process in a multicellular organism to date (N¨ usslein-Volhard & Wieschaus, 1980; N¨ usslein-Volhard et al., 1987; St. Johnston & N¨ usslein-Volhard, 1992; Rivera-Pomar & J¨ackle, 1996). Genetic studies in D. melanogaster have revealed that this process of segmentation begins with gradients of maternal information established during the formation of the egg. This is then refined into blocks of gene expression by so-called gap genes, whose transcription patterns are set up in response to these maternal gradients. The first periodic patterns of gene expression are revealed by pair-rule genes, whose transcription is controlled by the gap genes and maternal gradients. A further step in the process is controlled by segment polarity genes, which are regulated by the pair-rule genes, and act to refine and maintain the pattern of segments. However, the underlying mechanism by which segmentation is established is only partially understood. Of particular interest is the transition from the maternal to the zygotic genes, as patterning information via gene products has to be established along the entire axis of the egg, which spans about half a millimeter in D. melanogaster. One of the most studied maternal genes in D. melanogaster is bicoid (bcd ) (N¨ ussleinVolhard & Wieschaus, 1980). It is known, that bcd mRNA is deposited during oogenesis at the anterior pole of the egg. After fertilization Bcd is translated and establishes a protein gradient along the antero-posterior axis of the egg. Subsequently, Bcd acts 23
as a transcription factor and regulates genes such as hunchback, kr¨ uppel and evenskipped in a concentration dependent manner (Driever & N¨ usslein-Volhard, 1988a; Driever & N¨ usslein-Volhard, 1988b; Struhl et al., 1989). However, the establishment of the Bcd gradient is not very well understood. The most widely accepted model (Wolpert, 1969) that describes how cells in early embryos acquire their positional information, is based on the fact that at this early stage of embryonic development the embryo remains as a single continuous cytoplasmic domain, also called a syncytium. Molecules can move freely without passing through cell membranes and patterns can be established more simply. The model assumes that the protein is produced by a constant source, subsequently diffuses passively along the antero-posterior axis, and that it is uniformly degraded in the egg. To test this model further, we examined across the species to determine if this model can also explain the establishment of the Bicoid gradient in the context of larger embryos. There is reasonable evidence to suggest that the segmentation process and the early developmental gene hierarchy is evolutionarily conserved within the order of higher dipteran flies, although these species are evolutionary separated by more than 100 million years. The general developmental program is genetically and functionally conserved between species (Sommer & Tautz, 1991; Sommer et al., 1992; Sommer & Tautz, 1993; Sommer & Tautz, 1994; Tautz & Sommer, 1995; Wolff et al., 1995). Remarkably, the eggs of the different species of the dipteran order vary greatly in size, ranging from 340 µm for Drosophila busckii to 1550 µm for Calliphora vicina. How can the Bicoid gradient be established homologously, if the field over which it spans varies by a factor of ∼ 5 from the smallest to the largest eggs? This question is part of the more general problem of how spatial patterns of gene expression are established during development, and how those patterns can be maintained as physical parameters such as egg size change during evolution.
2.1.1
Results
In order to address these questions we chose three species from the dipteran order, the blowfly Lucilia sericata, and two members of the Drosophilae family, D. melanogaster and D. busckii. We measured the sizes of formaldehyde fixed eggs (in methanol) of each species by simple bright field imaging, focussing on the midplane of the embryo. We found the average egg lengths to be ∼ 1170 ± 125 µm, ∼ 478 ± 23 µm and ∼ 340 ± 19 µm, for L. sericata, D. melanogaster and D. busckii, respectively (see Figure 2.1). Using the immunofluorescence antibody staining technique, we demonstrated that segmental hierarchies are conserved among these three species: First, we characterized the distribution of syncytial nuclei during interphase in cell cycle 14 on the surface of the eggs of the different species. A summary of our findings is shown in Table 2.1. We measured nuclear densities by counting nuclei on the surface of fixed, DNA-stained eggs, using an automated image analysis program, developed with Matlab. This program, combined with the real image-pixel dimension, also allowed us to measure distances between nuclei and nuclear diameters. We noted that both are proportional to the size of the eggs of the three species, whereas the nuclear density is inversely correlated to species size. By approximating the eggs’ 24
1 D.busckii D.melanogaster L.sericata
0.9 0.8
Figure 2.1: Cumulative egg length distributions for 46 D. busckii eggs, 92 D. melanogaster eggs and 32 L. sericata eggs. Eggs were formaldehyde fixed and kept in methanol while measured.
Cum. Prob.
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surface by the surface area of a prolate spheroid we estimated the total number of nuclei on the eggs’ surface during interphase of cell cycle 14. We found that the number of nuclei is roughly constant across species, and that this number is between 212 (4096) and 213 (8192), which suggests that all three species undergo 13 cell divisions after fertilization. The variability we observe in nuclear count may be due to nuclear fall-out, which we observed in all species, and which is well documented in D. melanogaster (Foe et al., 1993). Overall, the number of nuclei is slightly higher than found by earlier studies (Zalokar & Erk, 1976) which reported an average count of ∼ 6100 nuclei for D. melanogaster. This considerable deviation can be accounted for by essentially three facts: 1) we did not take into account the exact shape of the egg and had to make a surface approximation; 2) nuclear densities are measured in the midsection between anterior and posterior pole of flattened eggs, where the nuclear arrangement is most regular, and hence may lead to an overestimation of the density; 3) our measurements of egg length and egg width are done using the egg shell for a reference, not the nuclear perimeter, which leads again to an overestimation. Table 2.1: Geometric characterization of eggs and syncytial nuclei of different dipteran species a
Egg Length Egg Widtha Nuclear distancea Nuclear diametera Nuclear densityb,c Total Number of Nucleid
L.sericata 1170 ± 130 297 ± 19 10.8 ± 0.7 8.4 ± 0.7 0.0092 8100 ± 700
D.melanogaster 485 ± 22 176 ± 13 4.7 ± 0.4 3.6 ± 0.4 0.0320 7100 ± 450
D.busckii 344 ± 19 138 ± 9 3.8 ± 0.3 2.9 ± 0.3 0.0600 7450 ± 500
a
in µm µm−2 data not very accurate, need to be redone more rigorously
b in c d
approximating the egg’s surface with the surface of a prolate spheroid S = π 2 r
e =
³
´ ap∗dv dv 2 + e arcsin(e) , with eccentricity
2 1 − ap2 , where ap is the long diameter of the ellipsoid, corresponding to the AP-axis of the egg and dv is the dv
short diameter of the ellipsoid, corresponding to the DV-axis of the egg
25
Figure 2.2: Immunofluorescence staining of L. sericata (top) and D. melanogaster (bottom) for Hunchback (green) and Giant (red) in the left column, and for Paired (green) and Runt (red) in the right column.
Second, we stained embryos from all three species with D. melanogaster antibodies against gap genes and pair rule genes. We observed that the primary expression domains of these genes are conserved, and that domains of gene expression pattern scale with egg size. Figure 2.2 shows two L. sericata embryos in the top row and two D. melanogaster embryos in the bottom row. The embryos have been formaldehyde fixed and stained with antibodies against proteins of the gap genes hunchback and giant, and stained with antibodies against proteins of the pair-rule genes even-skipped and paired. Figure 2.3 compares antibody stainings for D. melanogaster and D.
Figure 2.3: Anti-Hunchback (green) and antiRunt (red) immunofluorescence staining of D. melanogaster (top two embryos) and D. busckii (bottom two embryos).
26
Figure 2.4: Comparative in situ hybridization of bcd expressions in D. melanogaster (left column) and in L. sericata (right column). All embryos are oriented with the anterior to the left and with their dorsal side up. The upper, mid and lower rows shows late-, early- and pre-blastoderm expression, respectively.
busckii , against Hunchback and Runt. For each gene in both figures the scaling of it’s expression domain with egg size is readily visible. Third, we looked at the localization of bcd -RNA in L. sericata and D. melanogaster using in situ hybridizations. We used DIG-labelled RNA probes spanning the respective coding regions of L. sericata bcd and D. melanogaster bcd. The expression patterns are very similar during all pre-gastrula stages (Figure 2.4). In both cases bcd mRNA is localized at the anterior most end of the egg, but in the case of L. sericata it extends out further in space, reflecting that both, localization and amount of bcd mRNA seem to scale with egg size. To make our approach more quantitative, we developed image analysis techniques that allowed us to extract Bicoid protein profiles from images of immunofluorescently stained embryos. Figure 2.5 shows confocal images of fluorescently labelled Bicoid antibody stainings of L. sericata, D. melanogaster and D. busckii embryos. Embryos are selected from early interphase of cell cycle 14, i.e. before significant membrane invagination, and the images are focused at mid-embryo to avoid geometric distortion. All species are stained with antibodies raised against D. melanogaster -Bicoid (Kossman et al., 1998). We estimated the cross-reactivity of the antibodies with Bicoid of L. sericata and D. busckii to be sufficient for a quantitative analysis. Bicoid protein profiles were extracted by sliding a circular window of the size of a nucleus along the edges of the embryo (Houchmandzadeh et al., 2002). At each position of the center of the circle the average intensity of its pixels is computed and the coordinates of the center are projected on the anteroposterior axis of the embryo. Two curves, corresponding to dorsal and ventral sides of the embryo, were constituted. For consistency, we compared only dorsal profiles. Intensities are not normalized, instead, all images are taken under the same conditions: fixation and staining procedure for all embryos 27
Figure 2.5: Typical confocal images of Bicoid immunofluorescence staining for L. sericata (top), D. melanogaster (middle) and D. busckii (bottom). The focal plane is at mid-embryo and top-embryo in the left and right columns, respectively.
are identical: 1) all embryos are formaldehyde fixed for 20 minutes, 2) embryos are stained and washed together in the same tube, and 3) all images are taken with the same microscope settings in a single acquisition cycle. The top panel in Figure 2.6 shows Bicoid profiles of 27 L. sericata, 35 D. melanogaster and 18 D. busckii embryos. Fluorescence intensities are plotted as a function of position along the anteroposterior axes of the embryos. The same data is presented again in the lower panel of Figure 2.6, but this time, for each profile the x-axis has
Lucilia (#=27) Drosophila (#=35)
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Figure 2.6: Intensity profiles of Bicoid fluorescence of 27 L. sericata (blue), 35 D. melanogaster (red) and 18 D. busckii (green) embryos. Abscissa in top panel is absolute, in bottom panel abscissa is relative to egg length..
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Figure 2.7: Cumulative probability distributions of length constants λ for L. sericata (blue), D. melanogaster (red) and D. busckii (green). Left panel: λ in absolute units; Right panel: λ in relative units.
cumulative probability
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been normalized by its respective embryo length. Despite the large embryo to embryo variability, it is clearly apparent that if scaled to egg size, the Bicoid gradients for the different species have the same shape. To raise the level of quantification even further, we fitted to each intensity profile the steady state solution of the simple diffusion based model, a decaying exponential gradient with its own length scale λ, depending on the diffusion coefficient D and the protein lifetime τ (λ = sqrt(Dτ )). The raw data of Bicoid intensities are fitted by I = A exp(−x/λ) + B for abscissae of 15 − 85% egg length. A nonlinear NelderMead fit procedure was used to estimate the parameters A, B and λ. The slope of the exponential, λ (position at which the gradient dropped to E − 1 of its maximum value), for each embryo was then computed from all values of the raw curve, and did not depend on normalization parameters. Figure 2.7 displays probability distributions obtained from length constants of the intensity profiles of Figure 2.6. The left panel shows the cumulative probabilities for λ of the three species. The right panel shows the exact same cumulative probabilities for λ, but λ being normalized by the length of it’s corresponding embryo. In this panel the cumulative probability distributions overlap very closely, the mean values of the distributions (stars on the abscissa of Figure 2.7) are within 2%. This is a clear manifestation of the exponential length constants scaling with egg length between the different fly species. The mean values of the distributions for λ of 43 µm, 79 µm and 205 µm for L. sericata, D. melanogaster and D. busckii, respectively, may seem a bit low, compared to the value reported in (Houchmandzadeh et al., 2002) for D. melanogaster. However, we suspect that this discrepancy is a result of the different microscopic techniques used and does not constitute an actual disagreement. Houchmandzadeh et. al. used regular wide field epi-fluorescence, whereas in this work, images were taken with via confocal optics. In the former case, out of focus light is captured, which has a blurring effect on the image, i.e. it lets an intensity gradient appear less steep (Formally, the gradient we see, is a convolution of the real gradient with the point-spread-function (PSF) of the optics used in each case. The focal volume (the space integral of the PSF) obtained with confocal optics is much smaller than the one obtained with wide field optics.) 29
Figure 2.8: Intensity profiles of a fluorescently labelled dye, injected at the anterior pole of the egg, as a function of time after injection. The intensity is computed from a time series of images of the injected embryo with a focal plane at the top surface of the embryo. Pixel intensities over a circular spot at half the embryo length of the size of a nucleus are averaged for each time point. The top panel shows a D. melanogaster injection, the bottom panel shows a C. vicina injection. 3 arrow heads in each plot indicate from left to right mitosis 11, 12 and 13 (due to cytoplasmic turbulence during mitosis, the cytoplasmic intensity gradient is uniformly translated anteriorly at the onset of mitosis and posteriorly at the end of mitosis). The distance on the x-axis between adjacent arrow heads indicate the length of cell cycles 12 and 13. In the case of D. melanogaster (upper panel) the times are 655 and 765 seconds and in the case of C. vicina (lower panel) 671 and 779 seconds, for cell cylces 12 and 13, respectively.
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Furthermore, we also confirm the result from Ref. (Houchmandzadeh et al., 2002) that the length constants do not scale with egg length within a given fly species (data not shown here). These findings are hard to explain under the assumption of a purely diffusion driven transport mechanism for the Bicoid protein. The molecules in the largest eggs have to travel on average up to five times as far than in the smallest eggs. This would imply 25 times higher diffusion times. To test this hypothesis, we measured developmental time intervals, and we observed that they are conserved across species: syncytial divisions are equidistant in time (Figure 2.8, see figure caption), and all species that we investigated (C. vicina, L. sericata, Musca domestica, D. melanogaster and D. busckii ) pause with mitotic divisions after 2 hours for 1 hour, to gastrulate after 3 hours at 25◦ C. This suggests that differences in developmental time can not explain the establishment of the Bicoid gradient in differently sized species.
2.1.2
Discussion
If one wants to hold on to the simple diffusion based model, there are four possibilities in order to explain the scaling in λ: 1) The diffusion constants scale with egg size, either because the physical properties of the egg’s cytoplasm change (for example a higher viscosity for larger eggs) or because we are looking at an effective diffusion constant which results from inhomogeneities of the cytoplasm. The physical properties can be easily compared by 30
injecting dyes in the eggs and monitor their dynamics within each cytoplasmic environment, see Chapter 3 for a more detailed discussion of this point. Cytoplasmic inhomogeneities may also effectively change diffusion. If we imagine the cytoplasm as a meshwork of channels though which proteins can freely diffuse, this meshwork may be more or less dense in different species, hindering or facilitating diffusion differently. 2) Protein lifetimes may be adjusted to account for size. It is well known, that metabolic rates scale inversely with species mass or size, i.e. smaller species have a higher metabolic rate than larger ones. It is then easy to imagine, that also protein lifetimes, which are a manifestation of metabolic rates, may change with species size accordingly. Smaller species may have a higher Bicoid protein lifetime and hence producing a steeper absolute gradient. This point is more difficult to test, as protein lifetimes are not readily measurable directly. However, one could look at D. melanogaster mutations in the components of the degradation machinery is affected, and test if there is a change in the slope of the Bicoid gradient. Furthermore, one could generate and look at bcd mutants whose protein degradation sequences are affected, i.e. alterations in the so called PEST sequences that have been discovered and shown to be involved in protein degradation. Moreover, it would be interesting to look at transgenic D. melanogaster flies, where the D. melanogaster bcd gene is replaced by the bcd gene of any of the other differently sized dipteran species. 3) A differently distributed Bicoid source, i.e. more or less localized bcd mRNA in differently sized eggs. But, as Figure 2.4 shows, this does not seem to be the case, as the mRNA in L. sericata eggs would have to be localized significantly further towards the posterior pole than what we can see from our in situ hybridization. 4) It is also conceivable that none of the above points show any significant difference between different species in order to adjust the gradient for egg size, i.e. effective diffusion constants are similar, protein lifetimes are of comparable size, and, as we demonstrated already, the source distribution does not explain the scaling. Nevertheless, the possibility remains that the simple model holds: the difference may be explained by the protein gradients reaching steady state (the gradient’s equilibrium state necessary for the control of zygotic gene transcription, generally assumed to happen during early cell cycle 14) at different speeds in these species. This would imply that the longest eggs could take 25 times more time than the shortest eggs to establish an equilibrated Bicoid gradient, which would impose a considerable time constraint on the time it takes to reach this state for the smallest embryos. See discussion of chapter 3 for a more quantitative version of this point. Finally, the last possibility that would account for our findings within the purely diffusion based model, would be a fine adjustment of all the above mentioned parameters. In this case, parameter space could be explored maximally, and hence constrain dipterans to their observed size distribution. It may well be, that all parameters are adjusted in a way, that there is no more room for any smaller or larger egg sizes than the ones observed in nature, and hence that nature explored all possible egg sizes that are constrained by their physical parameters. On the other hand, besides diffusion, there may be an active transport mechanisms that is involved in the establishment of the Bicoid gradient. Proteins could be cargoed along filaments (actin cytoskeleton or microtubule network) spanning the 31
anteroposterior axis of the egg. To test this hypothesis, one could look at the Bicoid gradient in D. melanogaster mutants that have defects in the cytoplasmic or cortical actin meshwork, or mutants that are affected in their microtubule structure. Furthermore, one could treat embryos with actin or microtubule depolymerizing drugs such as Cytochalasin D or Colchicine, respectively. The advantage of the injection technique would be that it is readily possible in all mentioned dipteran species, whereas the generation of transgenic flies for other dipterans than D. melanogaster may involve more effort. To investigate all these points further, it becomes necessary to look at the establishment of the Bcd gradient dynamically. To this end, we generated a Bcd-eGFP construct which we will present in Chapter 4. Furthermore, we are in the process of generating a Calliphora-Bcd-eGFP construct, which expresses the Calliphora Bcd protein marked by eGFP in D. melanogaster flies. A comparison of both of these constructs will give us crucial insight into the different properties of Bcd from different species, and the effect of these properties on the establishment of the Bcd gradient.
2.1.3
Materials and Methods
Fly Stocks. For D. melanogaster injections wildtype Oregon R flies were used. D. busckii were a gift of Nicolas Gompel, caught in Madison, WI. L. sericata pupae were ordered from Blades Biological, Cowden, UK. C. vicina were caught in Princeton, NJ. Immunostaining of embryos. All embryos were collected at 25◦ C, heat fixed, and subsequently labelled with fluorescent probes following previously published protocols (Wieschaus & N¨ usslein-Volhard, 1986). We used rat anti-Bcd and rabbit antiHB antibodies, gifts of J. Reinitz and D. Kosman (Kossman et al., 1998). Secondary antibodies were conjugated with Alexa-488, Alexa-546 and Hoechst (Molecular Probes). Embryos were mounted in AquaPolymount (Polysciences, Inc.). Microscopy. High-resolution digital images (1024 × 1024, 12 bits per pixel) of fixed eggs were obtained on a Zeiss LSM 510 confocal microscope with a Zeiss 20x/0.45NA A-plan objective (D. melanogaster and D. busckii ) and a Zeiss 10x/0.45NA A-plan objective (L.sericata). Embryos were placed under a cover slip and the image focal-plane was chosen at top surface of the flattened embryo. Profile quantification. Relative protein concentration levels can be determined from fluorescence intensities of antibody stainings if a linear relationship between antibody binding and protein concentration is assumed. The reference intensity used was the background at low protein concentrations at the posterior end of the embryo. Embryos were stained and imaged at the same time and in the same conditions to avoid experimental procedure variabilities. Bcd profiles peak at about 5-10% egg length. Raw immunofluorescence data for Bcd are fitted by I = A exp −x/λ + B, for abscissae beyond twice the peak position to 95% egg length. This corresponds to the steady-state solution of the standard diffusion based Bcd-model, where the slope of the exponential, λ, is a characteristic length constant for the intensity profile. A nonlinear Nelder-Mead fit procedure was used to estimate the parameters. For each embryo λ was computed from the raw curve, and was independent of normalization parameters. 32
Chapter 3 Dynamics of the Bicoid Gradient Part I (Diffusion Measurements) 3.1
Introduction
One of the most basic questions in early embryonic development is how gene expression profiles can be established reliably in order to provide the accuracy required during development, i.e. how errors can be corrected and how noise can be filtered out. Boundaries of gene expression in the developing embryo are thought to be determined by the readout of concentrations of morphogens. These morphogens span the embryo in the form of protein gradients, defining the embryonic axes. However, the mechanism by which such a protein gradient is established is not very well understood. The most extensively studied protein gradient of this kind is the Bicoid gradient in Drosophila melanogaster embryos. The mother deposits bcd mRNA at the anterior pole of an egg. After egg fertilization the mRNA is translated into Bicoid protein, which is then thought to diffuse along the anteroposterior axis of the egg. Additionally, if we assume that there is uniform protein degradation, we can explain the exponentially decaying protein gradient that we measure by a simple, diffusion-based model. However, as shown in the previous chapter, this model cannot easily account for size scaling across species boundaries without significantly changing some physical parameters of the system. One possible explanation could be that the effective diffusion constant of the Bicoid protein scales with egg size. Changes in the effective diffusion constant of proteins within the cytoplasm of the egg can be achieved by changing the physical parameters of the protein itself. However, in the case of Bicoid, the bcd coding regions of several different dipteran species are highly conserved (Shaw, 2001), implying that the Bicoid proteins from different dipterans are of similar size. Moreover, it has been shown that their DNA binding properties are also conserved (Shaw, 2002). These findings indicate that the physical properties of Bicoid from these species cannot account for the significant change in length constants reported in the previous chapter. Alternatively the effective diffusion constant could vary between different species
33
due to changes in the physical parameters of the cytoplasm, such as its viscosity, sticking rates, or its effective porosity which may result in a channel meshwork through which proteins can travel. It has been shown that diffusion constants for proteins can vary over several orders of magnitude in different cytoplasmic environments, and it is not known if the cytoplasmic properties of dipteran species are conserved. To probe the physical properties of the cytoplasm of D. melanogaster we measured the diffusivity of different sized dextran molecules. Dextrans are hydrophilic polysaccharides with diverse molecular weight, good water solubility and low toxicity. Dextrans are biologically inert due to their uncommon poly-(α-D-1,6-glucose) linkages, which render them resistant to cleavage by most endogenous cellular glycosidases, and they also usually have low immunogenicity (Probes, 2004). Furthermore, globular dextran molecules can be generated, hence resembling the generally assumed shape of proteins. We mimic an inertly diffusing Bicoid molecules by injecting inert dextran molecules of similar molecular weight as Bicoid (55 kD) into the cytoplasm of fly eggs. The inert character of the molecule is one of the main assumptions of the model that we are testing. As the molecule’s radius increases, we expect the diffusivity to decrease. Using the Stokes-Einstein equation, which relates the diffusion constant with the radius of the injected molecules, we can extract the egg’s cytoplasmic viscosity. Furthermore, we also injected dextran molecules into living embryos of Lucilia sericata, Calliphora vicina and Drosophila busckii. This way we can compare directly the cytoplasmic properties among different species, using the same assay. We have successfully conducted experiments in living embryos of D. melanogaster to measure the diffusion constants for a series of dextran molecules spanning a size range of 10-150 kD. Based on these experiments we can infer a cytoplasmic viscosity of approximately 4 cp, implying that molecules of the probed size range effectively diffuse 4 times slower in early embryonic cytoplasm than in water. Moreover, we found that in different dipteran species the diffusion constants are of comparable value, implying that the physical properties of the cytoplasm cannot explain the scaling of the Bicoid gradient in eggs of varying sizes within the dipteran family. This result indicates that more complex mechanisms may underly the establishment of the Bicoid gradient.
3.2
Experimental Procedures
We collected embryos less than one hour old embryos of L. sericata, D. melanogaster and D. busckii. Embryos were dechorionated with bleach, rinsed with deionized water and glued on a glass slide, oriented with their anterior pole to the edge of the slide. To avoid further desiccation, mounted embryos were immersed in halo-carbon oil during the entire experiment. 1 Embryos were placed under the microscope objective, where 1 We avoided further exposure of the embryos in a desiccation chamber for consistency between different species as we cannot control the exact amount of water extracted by the desiccation procedure. Desiccation is primarily used to avoid leakage upon injection, and to account for the additional volume due to the injected liquid. We estimated that the amount of leakage and the amount of injected liquid would compensate each other, and we rejected any measurement during which the
34
they could be micro-injected with a glass needle. For D. melanogaster and D. busckii we used a 25x, NA 0.8 Zeiss oil immersion lens (no coverslip, lens in direct contact with halo-carbon oil, refractive index of 1.407), and for L. sericata and C. vicina we used a 10x NA 0.45 Plane-Apochromat Zeiss lens. The glass injection needles were designed to have a long and thin taper, with a small opening. They were formed on a horizontal puller (P-2000) from borosilicate capillaries that have a thin internal filament to aid filling. We used needles with a taper that would end in a ∼ 1 µm opening and that would widen to ∼ 10 µm on the initial 150 µm from the tip. Tips were initially sealed. We hand-cut them near the tip end, and we measured electric resistance at the tip on a bevelling machine for consistency. We back-filled the glass capillary needle with a fluorescently labelled dextran solution2 and placed the needle in the holder of a micro-manipulator. The needle holder was attached to a microinjector that automatically delivered a calibrated volume by a short pressure pulse. Injection volumes varied between different species and were calibrated by injecting a bubble into the halo-carbon oil next to the embryo. The bubble forms a perfect sphere, and we adjusted the length of the injection pulse until the diameter of the injected sphere would be ∼ 4% of the length of the anteroposterior axis of the embryo (corresponding to approximately 4 − 5 pl per injection pulse). Typical injection pulse length would be 20 − 60 ms at a pressure of ∼ 20 psi. Each egg was injected only once. We used an upright, custom-built, 2-photon laser scanning microscope to image the diffusion of fluorescently labelled dextran molecules in the eggs’ cytoplasm. In our case, 2-photon excitation is superior to ordinary confocal microscopy because: a) the use of reduced power values, which is especially important for extended live imaging, b) the broad 2-photon excitation cross-section allows us to chose a laser wavelength which minimizes the strong autofluorescence of the egg’s yolk, and c) reduced power as well as a better depth penetration (due to the longer wavelength) generate less photo-bleaching, which is problematic in quantitative fluorescence measurements. Two-photon fluorescence was excited by a mode-locked Ti:Sapphire laser (Mira900, 100 fs, 76 MHz; pumped by a 10-W Verdi laser; 910 nm; Coherent, Santa Clara, CA). A dichroic mirror (789 DCSPR) was inserted close to the back aperture of the objective to reflect emitted light through external detection optics and an emission filter (515/30) onto a photomultiplier tube (Hamamatsu R6357). Image acquisition was controlled by custom software. 3 Yet another advantage of the usage of two-photon microscopy is the continuous tunability of the laser wavelength. In our case, we imaged with an excitation wavelength of 910 nm, which we determined to be the 2-photon wavelength at which the yolk autofluorescence is minimal for a green emission filter. The fluorescence was monitored at power levels that did not produce any noticeable photobleaching (∼ 15 mW at the specimen). embryo did not survive at least until gastrulation. 2 Solutions were made from powder (Molecular Probes) of fluorescein labelled dextran molecules in dH2 O to a final concentration of 10 µM . 3 CfNT, v. 1.529, written by R. Stepnoski of Bell Labs and M. M¨ uller of the Max Planck Institute for Medical Research
35
Embryo top−plane (60µm)
Figure 3.1: Two-photon image of D. melanogaster embryo before injection. Three focal planes are shown: lower panel shows the mid-plane of the embryo, middle panel shows a focal plane located 30 µm above the mid-plane, and the upper panel shows a focal plane located 30 µm above the mid-plane. Colored spots in each plane correspond to areas over which local intensity profiles are analyzed (see Experimental Procedures for more information). Blue line in the lower panel corresponds to the anteroposterior axis of the egg.
Embryo intermediate plane (30µm)
Embryo mid−plane (0µm)
The needle was placed inside the egg at a distance 25 − 50µm from the anterior pole. We recorded the evolution of the dextran diffusion every 8 − 10 seconds in a series of three lateral optical planes of the egg: a top-plane which is just below the top surface of the egg (i.e. ∼ 15µm for D. melanogaster ), a mid-plane which is at half-egg-depth (i.e. ∼ 75µm for D. melanogaster ) and an intermediate plane which lies exactly half way between top- and mid-plane. Fluorescence intensity images were acquired at 250 Hz per line at a size of 256x512 pixel with a dynamic range of 8 bits. The resulting resolution is 1024 ppmm for D. melanogaster and for D. busckii, and 492 ppmm for L. sericata and C. vicina. In each plane, we averaged each image over two frames in order to reduce noise. The diffusional spread of injected dextran molecules was monitored for at least 30 minutes. Each data set was analyzed by measuring the mean intensity within circular patches (diameter of 10 pixels) as a function of time and determining the diffusion constant D by best-fit analysis. We chose 6 patches in each optical section close to the edge of the egg, which is where nuclei reside when zygotic transcription is taking place. Figure 3.1 shows a typical stack of images before injection of a D. melanogaster embryo. Colored patches represent the areas from which we extracted intensity profiles, which are depicted in Figure 3.2. Each colored curve in Figure 3.2 corresponds to a patch in Figure 3.1 of the same color. 36
Embryo top−plane (60µm) concentration [8−bit]
200 150 100 50 2000 3000 time [sec] Embryo intermediate plane (30µm)
concentration [8−bit]
0
Figure 3.2: Changes in the fluorescence intensity of injected 70 kD fluoresceinlabelled dextran molecules with time for six points in each focal plane depicted in Figure 3.1. The intensity profiles are extracted from a time series of two-photon images.
1000
150 100 50
0
1000
2000 3000 time [sec] Embryo mid−plane (0µm)
concentration [8−bit]
150 100 50
0
Figure 3.3: Reconstructed eggshell from two-photon images from Figure 3.1. The reconstruction serves as boundary condition in our computer simulation of the injection.
37
1000
2000 3000 time [sec]
Embryo top−plane (60µm) concentration [8−bit]
200 150 100 50 0 0
2000 3000 time [sec] Embryo intermediate plane (30µm)
concentration [8−bit]
1000
150
Figure 3.4: Fluorescence intensity profiles from Figure 3.2 overlayed by individual best-fits (solid lines), using fit procedure I (see text). The resulting diffusion constant for this fit is D = 16.2 ± 1.9 µm/sec.
100 50 0 0
1000
2000 3000 time [sec] Embryo mid−plane (0µm)
concentration [8−bit]
150 100 50 0 0
1000
2000 time [sec]
3000
To determine the diffusion constant from a given data set, we fitted the fluorescence intensity profiles to theoretically predicted changes in dextran concentration, derived from our computer simulation of the injection. The computer simulation is a finite element solution of the diffusion equation using the exact geometrical conditions of the injection experiment. For the boundary conditions we reconstructed the outer egg shell. Exploiting the circular lateral egg symmetry, we can reconstruct the egg from the mid-plane image of the embryo. Figure 3.3 shows the corresponding egg reconstruction of Figure 3.1. For the fit, we varied the diffusion constant of the simulation until the corresponding concentration profiles match our data (solid lines in Figure 3.4) using a multidimensional unconstrained nonlinear minimization (Nelder-Mead). Each intensity profile is background corrected prior to fitting by subtracting the mean of the first 3 data points. For the fit we allowed a separate concentration amplitude for each intensity profile to account for systematic fluorescence 38
Embryo top−plane (60µm) concentration [8−bit]
200 150 100 50 0 0
2000 3000 time [sec] Embryo intermediate plane (30µm)
concentration [8−bit]
1000
150
Figure 3.5: Fluorescence intensity profiles from Figure 3.2 overlayed by a bestfit (solid lines) to all profiles, using fit procedure II (see text). The resulting diffusion constant for this fit is D = 16.3 µm/sec.
100 50 0 0
1000
2000 3000 time [sec] Embryo mid−plane (0µm)
concentration [8−bit]
150 100 50 0 0
1000
2000 time [sec]
3000
inhomogeneities in the images. As an internal control for the goodness of the fits, we performed two different fitting procedures on each data set. For the first procedure we used an individual diffusion constant for each intensity profile, and we computed the average diffusion constant as the mean of the individual fits (hereafter referred to as procedure I, see Figure 3.4). For the second procedure we only allowed for a single diffusion constant with which the entire data set was fitted (hereafter refereed to as procedure II, see Figure 3.5). A data set was rejected if the diffusion constant of procedure II did not lie within one standard deviation of the individual diffusion constants of procedure I.
39
3.3
Results
To study the physical properties of embryonic cytoplasm and its physical interactions with Bicoid protein, we injected inert dextran molecules in eggs of D. melanogaster. First, we examined the dynamics of injected dextran molecules. We measured effective diffusion constants of dextran molecules injected into D. melanogaster for four different nominal molecular weights: 10 kD, 40 kD, 70 kD and 150 kD.4 A typical fit with two different fitting procedures for the same data set can be seen in Figures 3.4 and 3.5, respectively. Results of 44 data sets are summarized in Table 3.1, where we report diffusion constants from procedure II averaged over the number of experiments that have been carried out for each molecular weight of dextran molecules. The reported standard deviation is comparable to the standard deviations resulting from procedure I (data not shown). As expected from inertly diffusing molecules, Table 3.1 shows that the diffusivity decreases with increasing dextran radius. The size of the injected molecules can be empirically defined by their effective hydro-dynamic radius, also called Stokes radius, which is related to the measured diffusion coefficient in a homogeneous isotropic medium by the Stokes-Einstein equation µ ¶ kB T 1 D= 6πη R where kB is Boltzmann’s constant, T is the absolute temperature, η is the viscosity and R is the radius of the diffusing molecule. The radius of dextrans used in our experiments have been determined earlier (Nicholson & Tao, 1993; Lang et al., 1986; Persky & Hendrix, 1990) and they varied from 2.3 to 9.0 nm. We assume the hydrodynamic radius of Bicoid to be of the order of 4.5 nm, based on comparative studies of proteins and dextrans of similar molecular weight (Arrio-Dupont et al., 1996; ArrioDupont et al., 2000; Stroh et al., 2003). We plotted the measured average effective diffusion constants of the injected dextran molecules as a function of their radius, and we show in Figure 3.6 that our data reproduces very closely the Stokes-Einstein relation. The solid line represents a least-squares fit of a R1 power law, with χ2 = 0.13. From the fitting parameters we extract an effective cytoplasmic viscosity of 4.2 cp. Table 3.1: Effective diffusion constants D of dextran molecules of different sizes in D. melanogaster
Dextran MW [kD] 10a 40a 70a 150c
Stokes radius [nm] 2.3b 4.5b 5.9b 9.0d
Sample sizeA 11 20 8 5
D [ µm2 /s] 29.1 ± 4.2 17.6 ± 1.8 15.3 ± 1.4 12.9 ± 3.4
A The a
sample size refers to the number of diffusion experiments analyzed. Manufacturer Molecular Probes, Eugene, OR. from Ref. (Nicholson & Tao, 1993) Manufacturer Sigma-Aldrich Co., Sigma Cemicals Co., St. Louis, MO. d Taken from ref. (Lang et al., 1986) b Taken c
4
Each dextran probe has in a broad molecular weight distribution with standard deviations up to a third of the nominal molecular weight, as reported by Molecular Probes and Sigma.
40
Viscosity = 4.21 cp ; χ2 = 0.13 32 30 28 26 D [µm2/sec]
Figure 3.6: Diffusion coefficients of dextran molecules of different hydrodynamic radii (red stars). The solid line is a theoretically predicted diffusion coefficient using the Stokes-Einstein relation with a viscosity of 4.21 cp and with χ2 = 0.13.
24 22 20 18 16 14 2
3
4 5 6 7 hydrodynamic radius [nm]
8
9
Next, to compare the cytoplasmic viscosity and the effective cytoplasmic diffusion constants in different dipteran species, we also injected 40 kD dextran molecules into eggs of D. busckii, L. sericata and C. vicina. Table 3.2 shows a summary of our results, where effective diffusion constants are averages over all data sets for a given species. As in the case of D. melanogaster, we report effective diffusion constants obtained with fitting procedure II, and the standard deviations in Table 3.2 are comparable to the standard deviations resulting from the individual fits using fitting procedure I (data not shown). The diffusion constants in the different species are of comparable size. In all our injection experiments we did not notice statistically significant differences of diffusion constants between data sets of embryos of different pre-gastrula ages, nor between data sets of fertilized versus unfertilized eggs (data not shown). The cytoplasmic viscosities and diffusion constants do not seem to be dependent on pregastrula developmental stages. These results show that the cytoplasmic viscosities in dipteran of pre-gastrula stages and for molecules of the size of our probe do not vary significantly across species. Consequently they cannot explain the scaling properties of the Bicoid gradient in eggs of varying sizes within the dipteran family. To further understand cytoplasmic properties, we examined the diffusive path of the molecules within the egg after injection and looked at the dextran distribution of equilibrated eggs. Eggs were formaldehyde fixed 1 hour after injection and hand sliced perpendicular to the anteroposterior axis. Figure 3.7 shows the frontal side of Table 3.2: Effective diffusion constants of 40 kD dextran molecules in dipteran species
Species (av. egg length) D. busckii (344 µm) D. melanogaster (485 µm) L. sericata (1170 µm) C. vicina (1420 µm)
Sample size 8 20 6 4
41
D [µm2 /sec] 14.5 ± 3.8 17.6 ± 1.8 22.8 ± 1.5 20.3 ± 1.3
B A
Figure 3.7: Cross sections of D. melanogaster embryos. A) Injected and B) non-injected eggs were formaldehyde-fixed and hand-cut. Both embryos have approximately the same age: A was injected 1h after collection and both were fixed 1h after injection.
such a slice at a focal plane of approximately 10 µm below the top surface of each slice. Comparing a slice from an injected egg to a non-injected control, we see a quasi-homogeneous distribution of dextran molecules over the entire cross-section of the egg, implying uniform diffusion of inert molecules through the entire cytoplasm, including the inner yolk part. We compared this finding with the diffusion of Bicoid molecules by repeating the experiment with fixed eggs that were stained with Bicoid antibodies, Figure 3.8. Frontal views of egg slices from the anterior half and egg slices from the posterior half are shown in Figure 3.8. The focal plane is 6 µm below the top surface of each slice. A clear distinction in staining intensity between the inner yolk part and the outer cytoplasm is visible, indicating a higher distribution of Bicoid around the edge of the egg than in its center. Hence the distribution of Bicoid molecules within the cytoplasm is different than the distribution of an inert molecule. However, we did not observe any size discrimination effects over the dextran series or in any dipteran species. This observation sets a lower bound on the permeation Hb
A
Figure 3.8: Three cross sections of D. melanogaster embryos of early (A) and late (B and C) syncytial stages. B and C are from the anterior and posterior half of the egg, respectively. Embryos were formaldehyde-fixed and stained with Hb and Bcd antibodies and with a DNA marker.
B
C
42
Bcd
DNA
size parameter of the effective cytoplasmic mesh to approximately 200 ˚ A, twice the hydrodynamic radius of the 150 kD dextran. We conclude that in principle there are no geometric constraints that could hinder Bicoid to diffuse passively through the egg’s cytoplasm. Moreover, we noticed the 40 kD dextran molecule penetrated the nuclear membrane in all dipteran species, which sets the lower bound of the nuclear pore complex for passive nuclear import to approximately 90 ˚ A. Bicoid and 40 kD dextran having hydrodynamic radii of comparable size let’s us infer that in principle Bicoid can cross the nuclear membrane passively.
3.4 3.4.1
Discussion Methodology
Our diffusion constant measurements are the first of their kind in living eucaryotic organisms. Thus far, diffusion constants in biological tissue have been measured mostly in tissue culture cells or cell extracts. Our study allows us to control the influence of traumatic effects (due to the injection, the injected dye or laser irradiation) by discarding data sets of embryos displaying subsequent abnormal developmental behavior, and hence allows for an internal control for the validity of our measurements. Furthermore, the technique of injecting living D. melanogaster embryos is a well established and widely used assay for germ-line transformation, and is hence accepted as a valid tool to act upon living embryos. Our method was designed to minimize typical systematic variability. First, by using two-photon microscopy we strongly reduce out-of-focus light which distorts the image and negatively affects the data. Thus we can monitor the fluorescence evolution in several focal planes and extract diffusion constants from three dimensional data rather than from two dimensional images alone. Second, there is no need to correct for photobleaching. With the introduction of sufficiently concentrated fluorescence into the embryo using the pressure injection technique, we can make our measurements with weak illumination. We did not notice any self-quenching at the concentrations employed. Third, the micropipette injection is well-defined and closely approximates a point source with an impulse release. Thus, the spatial and temporal information about the injection pulse is very precise. Fourth, the boundary conditions of our simulations are extracted from a three-dimensional reconstruction of the outer shell of each injected embryo. Points three and four were crucial for a good fit of data to the simulations. Nonetheless, our method does show some limitations. It is difficult to conceive a well-defined self-control for our method. In order to do so, we would need to be able to fill an egg shell with agar or water which would be very difficult to achieve. For future investigations it would be interesting to confirm our results with other methods that can provide an alternative way to measure diffusion constants in the embryo. A possible technique to use would be fluorescence recovery after photobleaching (FRAP) (Axelrod et al., 1976; Brown et al., 1999) in embryos that have been previously in43
jected with fluorescent dyes. The advantage of this approach would be the possibility of measuring local diffusion constants at different positions in the embryo. However, it will be challenging to find the right laser conditions to avoid both tissue damage and photobleaching during the recording of the recovery curve. We were unable to further reduce the high variability (for D. busckii ∼ 25%) of diffusion constants between different data sets. Possible residual sources for systematic errors could be a) poor temperature control during our measurements (the analyzed data sets have been acquired at varying temperatures from 18◦ − 24◦ C ) and b) poor accounting for the size variability of the dextran molecules employed (the actual molecular weights present in a particular dextran sample have a broad distribution). Temperature influences both the diffusibility as well as the cytoplasmic properties of the embryo’s yolk, i.e. both binding affinities for unspecific sticking of dextran to yolk particles and equilibrium constants of the yolk may be strongly temperaturedependent. The broad molecular weight distributions of the dextran samples could be narrowed by size fractionation before the injection in order to isolate molecules close to the nominal molecular weight. Finally, our simulation assumes a homogeneous egg cytoplasm and a globular symmetry of the dextran molecules; both conditions are only rough approximations to the actual biological and physical properties of cytoplasm and molecules.
3.4.2
Cytoplasmic properties of D. melanogaster
A major objective of the present study was to establish a method to measure effective global diffusion constants in living fly embryos. It has been shown previously that diffusion constants in tissue culture cells or cell extracts can be measured quite accurately, and that the numerical values vary substantially for different biophysical methods and for different cell lines (see Table 3.3). Our values for cytoplasmic diffusion constants of differently sized dextrans in D. melanogaster embryos are comparable to values of diffusion constants in other eukaryotic cells. The ultimate goal of this study was to predict the diffusion constant of Bicoid in the early embryonic cytoplasm of D. melanogaster eggs. Although the literature does not provide conclusive evidence whether proteins and dextrans of similar molecular weight diffuse equally (Popov & Poo, 1992; Stroh et al., 2003), there is a tendency for proteins to have a slightly higher mobility than dextran molecules of equal molecular weight. References (Arrio-Dupont et al., 1996; Arrio-Dupont et al., 2000) use the same method (fringe pattern photobleaching) to determine the diffusion constants of dextrans and proteins in the cytoplasm of cultured muscle cells. They find similar results for Phosphoglucomutase (60 kD) proteins as for 20 kD dextran molecules: both molecules have identical hydrodynamic radii and very similar diffusion constants. This finding suggests that the diffusion constant of Bicoid is most likely between our values found for 10 kD dextran and for 40 kD dextran, but closer to the 40 kD dextran value. To test this last point further, it would be interesting to use our assay and inject purified eGFP molecules or other fluorescently tagged proteins of approximately 55 kD (Bicoid’s molecular weight) into fly embryos. eGFP has a molecular weight of 44
31 kD and a cylindrical shape based on GFP crystal structure (2.4 nm diameter, 4.2 nm height (Ormo et al., 1996)), but it is easily available and no further pre-injection modification has to be undertaken. For the series of dextrans used in this study we could extract a value for the effective cytoplasmic viscosity that agrees reasonably well with previous determinations (see Table 3.4). Generally it is difficult to derive cytoplasmic viscosities from mobility measurements, and the reported values are the subject of considerable controversy since different methods give different values for the same cells. In addition to differences in cell type and probe molecules, three processes independently effect diffusibility and have to be dealt with thoroughly: association with immobile structural elements, steric hinderance and viscosity effects. In the case of dextrans though, the situation is largely simplified due to their hydrophilic, uncharged, inert and spherical characteristics. It has been shown previously that there is no systematic size-dependent variation of the immobile fraction, and that the immobile fraction is relatively small (Lang et al., 1986; Seksek et al., 1997). Steric hinderance could arise from impermeable inclusions such as a micromolecular lattice, intermediate filaments, microfilaments, microtubules, organelles, or chromatin. However, these inclusions are of supramolecular dimensions and would affect all macromolecules to the same degree, irrespective of their molecular size. Furthermore, we did not observe any type of size discrimination in our diffusion experiments (data not shown). Under these circumstances, our derivation of the cytoplasmic viscosity is valid. Hence diffusion in embryonic cytoplasm of fruit flies is roughly four times slower than in water. However, our viscosity measurement has to be taken with care, as we did not determine the hydrodynamic radii of the dextran series but took the values from previously published data by other investigators. Although we found the exact same dextran brands used in our study, given the sensible dependence of our viscosity calculation on the exact value of the hydrodynamic radii, it would have been advisable to repeat the measurements ourselves. We are currently setting up a system for FRAP measurements, and we hope to confirm the values that we found in the literature.
3.4.3
Cytoplasmic diffusivity in dipteran of different egg sizes and model implications
The final goal of this study was to compare the cytoplasmic mobility of Bicoid among different dipteran species. Even if we are not able to predict the diffusion constant of Bicoid accurately due to the discrepancy of dextran versus protein diffusivity, we can nevertheless use our assay to compare the physical cytoplasmic properties of the investigated dipteran embryos. To a first approximation, the diffusion constants are conserved among early embryonic cytoplasm of dipteran species (see Table 3.2). We do notice a slight trend for increased diffusivity and decreased variability with increasing egg length. The finding of a nearly conserved cytoplasmic mobility has significant implications on the protein lifetime within the assumed purely diffusion-based model for the establishment of the Bicoid gradient during early embryonic development. Recalling 45
46 Phosphoglucomutase (60kD) eGFP (31kD) eGFP (31kD) eGFP (31kD) NGF (13kD) Dextran (70kD)
Cultured muscle cell (rabbit)
Chinese hamster ovary cell
E. coli
Dictyostelium cell
Rat brain (striatum)
Rat brain (striatum)
Dextran (∼ 10 kD)
Cultured muscle cell (rabbit)
Dextran (∼ 70 kD)
Dextran (40 kD)
Rat brain (cortex)
Cultured muscle cell (rabbit)
Dextran (70 kD)
Xenopus neurite
Dextran (∼ 40 kD)
Dextran (60 kD)
Swiss 3T3 (human fibroblast)
Cultured muscle cell (rabbit)
Dextran (20 kD)
Swiss 3T3 (human fibroblast)
Dextran (∼ 20 kD)
Dextran (40 kD)
Hepatoma cell
Cultured muscle cell (rabbit)
Tracer molecule
Cell type
8.5
27.5
24
7.7
27.2
16.5
4
10
16
29
9.1
16.6
18
29
4.5
D [µm2 /sec]
MPFPR/pressure injection (Stroh et al., 2003)
MPFPR/pressure injection (Stroh et al., 2003)
FRAP (Potma et al., 2001)
FRAP (Elowitz et al., 1999)
FRAP (Swaminathan et al., 1997)
Fringe pattern photobleaching (Arrio-Dupont et al., 2000)
Fringe pattern photobleaching (Arrio-Dupont et al., 1996)
Fringe pattern photobleaching (Arrio-Dupont et al., 1996)
Fringe pattern photobleaching (Arrio-Dupont et al., 1996)
Fringe pattern photobleaching (Arrio-Dupont et al., 1996)
Pressure injection/fluorescence microscopy (Nicholson & Tao, 1993)
Quantitative fluorescence microscopy (Popov & Poo, 1992)
FRAP (Luby-Phelps et al., 1986)
FRAP (Luby-Phelps et al., 1986)
Fluorescence microphotolysis (Lang et al., 1986)
Measurement technique
Table 3.3: Some literature measurements of cytoplasmic diffusion constants.
Table 3.4: Some literature estimates of cytoplasmic viscosity. Cell type Squid giant axon Human fibroblast Frog oocyte Unilamellar phospholipid vesicle Erythrocyte interior Chinese hamster lung fibroblast Baby hamster kidney Lobster nerve Frog muscle Human fibroblast Amoeba cell Sea urchin egg Hepatoma cell Swiss 3T3 cell Sea urchin egg Xenopus neurite Rat brain (cortex) Cultured muscle cell (rabbit) Chinese hamster ovary cell Xenopus egg extracts Dictyostelium cell Rat brain (striatum) cell Xenopus egg extracts
Viscosity [cP] 4 6 − 13 4.0 − 5.5 3−4 2−3 3.8 ∼2 5.5 15 − 30 2 − 50 2−4 8 6.6 4 2 − 2.5 5 2.5 − 5 2.3 3.2 3 3.6 4.4 ∼ 20
Measurement technique Fluorescence decay (Hodgkin & Keynes, 1956) Fluorescence decay (Burns, 1969) Autoradiography (Paine et al., 1975; Horowitz & Moore, 1974) Fluorescence polarization (Clement & Gould, 1980) Electron spin resonance (Morse et al., 1979) Electron spin resonance (Lepock et al., 1983) Electron spin resonance (Mastro & Keith, 1984) Oil drop movement (Rieser, 1949a) Oil drop movement (Rieser, 1949b) FRAP (Wojcieszyn et al., 1981) FRAP (Wang et al., 1982) FRAP (Salmon et al., 1984) Fluorescence microphotolysis (Lang et al., 1986) FRAP (Luby-Phelps et al., 1986) Polarization microfluorimetry (Periasamy et al., 1991) Quantitative fluorescence microscopy (Popov & Poo, 1992) Pressure injection/microscopy (Nicholson & Tao, 1993) Fringe pattern photobleaching (Arrio-Dupont et al., 1996) FRAP (Swaminathan et al., 1997) Tracer beads (Salman et al., 2001) FRAP (Potma et al., 2001) MPFPR/pressure injection (Stroh et al., 2003) Microrheology (Valentin & Weitz, 2004)
that the length constant λ is given by λ=
√ Dτ
where τ is the protein lifetime, we can express τ as a function of λ and D. From the length constant measurements from the previous chapter we know that the length constants scale for D.busckii, D. melanogaster and L. sericata as 43 : 79 : 205 µm. Using the scaling of the diffusion constants of 14.5 : 17.6 : 22.8 µm2 /sec that we measured, we infer protein lifetimes to scale as 2.5 : 6 : 31 min This result is surprising as we know that the bcd DNA sequences are highly conserved among the three species, which suggests that their physical properties are conserved as well. Hence the question arises whether evolution accounts for size regulation by adjusting the decay rates of homologous proteins with otherwise similar physical properties. There are two possible ways to achieve varying decay rates: either the entire decay machinery is altered for the different species, or the slight sequence variations alter the intrinsic physical properties of the Bicoid protein itself. In order to test these hypotheses further we made a D. melanogaster Bcd-eGFP construct. This construct will allow us to study the physical properties of Bicoid directly. We will be able to follow the dynamic evolution of the Bicoid gradient, or measure diffusion constants locally at different points in the embryo. Moreover, we can purify Bcd-eGFP protein by immunoprecipitation and inject it into living embryos in order to measure its fluorescence decay. We will be able to extract the Bcd-eGFP lifetime by comparing its diffusion and its decay to our dextran injections, and we will be able to compare the decay rates in different dipteran species by the same method or by quantitative Western blot analysis. 47
Furthermore, we are in the process of generating a fly construct that expresses Calliphora-Bcd marked with eGFP. With this construct we will be able to compare the Bcd-GFP gradient to a gradient of Calliphora-Bcd-GFP, expressed in D. melanogaster embryos. The outcome of this comparison may shed more light on the apparent discrepancy between the finding of comparable diffusion constants across embryos from differently sized fly species on one hand, but length scaled gradient shapes across species on the other hand.
48
Chapter 4 Dynamics of the Bicoid Gradient Part II (Bcd-GFP construct) 4.1
Introduction
Positional information in early embryonic development has been shown to be determined by protein gradients that span across different axes of the developing embryo (Wolpert, 1969; Driever & N¨ usslein-Volhard, 1988a; Driever & N¨ usslein-Volhard, 1988b; Struhl et al., 1989). Cells at different positions along these axes respond differently according to different concentrations of the protein, i.e. the morphogen. However, it remains unclear how such protein gradients are established as well as by which means the gradients can be kept stable over a sufficiently long period of time for the read-out process to happen reliably. In an attempt to answer these questions, it becomes necessary to be able to examine the temporal dynamics of the gradients. For instance, it is not clear what happens to the gradients and the protein concentration over time; during different nuclear cycles and at the transition between pre-syncytial to syncytial blastoderm stage. Moreover, it is not clear how the gradient in nuclei compares to the cytoplasmic gradient. Nor is the effect of rapid cleavage divisions on the protein gradients known. If maternal gradients are in fact established via passive mechanisms, such as protein diffusion, then the gradients should be readily visible also in unfertilized eggs. How can protein gradients be reliably and stably established and maintained, if the underlying processes that govern the establishment are prone to noise and fluctuations? How robust are the gradients in general, over time within a single embryo as well as between different embryos? One of the most suitable systems to study these questions is the gradient of the gene product of the maternal bicoid gene (bcd ) in Drosophila melanogaster, which acts as an anterior determinant in early embryogenesis. bcd mRNA is deposited maternally at the anterior pole of the egg. Its translation is initiated with egg fertilization, and the resulting protein is then thought to diffuse along the anteroposterior axis of the embryo to establish a concentration gradient. To analyze in vivo the dynamics of this gradient, its establishment and maintenance, we made a construct designed to express a fusion protein of eGFP (Tsien,
49
1998) attached to the N-terminus of Bcd, based on P[gfp-bcd ] made by Hazelrigg et al. (1998) just using GFP (Hazelrigg et al., 1998). P[egfp-bcd ] transcription is driven by known bcd enhancers upstream of the 5’ UTR and in the first intron. This transcript contains bcd ’s natural 5’ and 3’ UTRs which are known to mediate the localization and translation of normal bcd mRNA. Thus by using the endogenous regulates of bcd transcription and translation, our construct was designed to be maternally expressed and localized to the anterior pole. The resulting eGFP-Bcd protein (hereafter referred to as Bcd-GFP) is not translated until early embryogenesis begins. Here we show that our Bcd-GFP construct successfully reproduces the biological and physical properties of endogenous Bcd. We measure and analyze quantitatively Bcd-GFP gradients from which we can infer that the fluorophore formation time is between 3 and 20 minutes. We monitored Bcd gradients over the first 3 hours of development and we observed that both the nuclear concentration at a given position along the anteroposterior axis of the egg and the overall shape of the gradient do not change significantly during syncytial blastoderm stages. In contrast, Bcd-GFP gradients across different embryos show a strong positional variability during early cell cycle 14. Furthermore, careful analysis of nuclear input and export rates of Bcd-GFP, both during interphase and mitosis led us to attribute an important role of syncytial nuclei to the establishment and stability of the Bcd gradient. Moreover, comparing Bcd-GFP concentration in unfertilized vs. fertilized eggs our data suggests a zygotic down-regulation of Bcd synthesis rate. Finally, we estimated cytoplasmic Bcd-GFP diffusion constants, and found that their value was significantly lower than our previous estimate extracted from 40kD-dextran diffusion constant measurements in Chapter 3.
4.2 4.2.1
Results and Discussion Biological and physical properties of the Bcd-GFP construct
We examined embryos expressing Bcd-GFP for eGFP fluorescence during the first 3 hours of development with a custom-built, two-photon laser scanning microscope. D. melanogaster embryos contain large amounts of yolk, which auto-fluorescence is detected with filter sets typically used for eGFP. However, the broad two-photon excitation cross-section allows us to choose a laser wavelength which minimizes the strong autofluorescence of the egg’s yolk. Wildtype Oregon R (OreR) embryos served as a control to determine background autofluorescence. In our experiments, 0- to 15-minold embryos were dechorionated and mounted in halocarbon oil. A typical snapshot of three focal planes of a two-photon time-lapse movie is shown in Figure 4.1. Bcd being a transcription factor, Bcd-GFP is targeted to nuclei. The integrated concentration over each focal plane as a function of time reveals a strong dynamic behavior during mitosis, suggesting that Bcd-GFP is indeed targeted to and transported into the nuclei, just like wildtype Bcd. The development of pre-gastrula D.melanogaster embryos has been reviewed pre50
Figure 4.1: Snapshot of a time laps movie taken with a two-photon microscope of three focal planes of a D. melanogaster embryo expressing Bcd-GFP. Focal planes are at 30 µm (top panel), 60 µm (mid panel) and 90 µm (bottom panel) below the top surface of the embryo. Highlighted rectangles correspond to intensity averaging regions of Figure 4.15.
viously (Wieschaus & N¨ usslein-Volhard, 1986; Foe et al., 1993). After egg fertilization 8 rapid nuclear divisions occur deep within the interior of the embryo. At nuclear cycle 9, some nuclei have migrated to the cortex at the posterior end of the embryo, and pole buds form. Most nuclei migrate to the periphery of the embryo during nuclear cycle 10, pole cells form, and cycles 10–13 constitute the syncytial blastoderm stage in which the embryo remains until nuclear cycle 14. The embryo arrests nuclear division and cell membranes form, after the completion of which the cells undergo morphological changes, i.e. gastrulation. At a temperature of 25◦ C nuclear cell cycle 14 begins after about 2h after fertilization and about 1h later the embryo gastrulates. We first detected a fluorescent signal from Bcd-GFP in anterior nuclei of approximately 1 hour old embryos, i.e. during nuclear cycle 9 (Figure 4.2). The P[egfp-bcd ] transgene completely rescues the bcd mutant anterior defect. We did not see any developmental defect throughout the flies’ entire life cycle. Moreover, we measured the position of the cephalic furrow, a strong indicator of the shape of the Bcd gradient and of the total amount of Bcd protein. In embryos of the BcdGFP construct in both a wildtype and in a null-mutant bcd background (data not shown) the average cephalic furrow location coincide respectively with their position in embryos of flies possessing two extra copies of the bcd gene (Driever & N¨ ussleinVolhard, 1988b) for the wildtype background case, and in wildtype embryos for the 51
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Figure 4.2: Six snapshots of a time-lapse movie taken with a two-photon microscope of the anterior third of a D. melanogaster embryo expressing Bcd-GFP. Each snapshot corresponds to a time point during interphases 9 to 14. Red arrows indicate the locations of the respective nuclei in Figure 4.9.
null-mutant bcd case. By these criteria, fluorescent egfp-bcd behaves indistinguishably from wild-type bcd in its physical and biological properties in the early embryo, indicating that its localization and translational regulation are conserved, and that the protein is folded properly despite the attached eGFP epitope. To carefully quantitate the Bcd protein level, we used formaldehyde fixed embryos to measure protein gradients of fluorescently-labelled antibody stainings and of eGFP autofluorescence. Figure 4.3 shows intensity profiles of Bcd immunofluorescence stainings and of eGFP expression for embryos during cell cycle 14 that express Bcd-GFP in wildtype background (15 embryos) and in mutant bcd background (21 embryos). All of the gradients have a similar shape. Notice the higher level of the Bcd immunofluorescence staining in a wildtype background (upper right panel) as opposed to all other configurations who have similar expression levels. This is presumably due to the fact that the Bcd antibody picks up both the endogenous Bcd distribution as well as the Bcd-GFP distribution to effectively result in a distribution that has 4 copies of the bcd gene. To quantify the shape of the gradients we fitted the steady state solution to the standard Bcd model, presented in Chapter 1, Eq. (1.2). From the fit we can extract the characteristic length constant λ that describes the shape (or the “curvature”) of the protein gradient. In Figure 4.4 we show the cumulative probability distributions for λ of three kinds of protein gradients for 21 formaldehyde fixed embryos during cell cycle 14, expressing Bcd-GFP in a Bcd-null background: (1) immunofluorescence stainings using Bcd and (2) GFP antibodies and (3) eGFP autofluorescence. The shapes of both immunofluorescence stainings are identical, indicating, that the anti52
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Figure 4.3: Upper left panel: Fluorescent Bcd antibody intensity profiles of 21 D. melanogaster embryos that are mutant for endogenous Bcd, expressing Bcd-GFP. Upper right panel: Fluorescent Bcd antibody intensity profiles of 15 D. melanogaster embryos expressing Bcd-GFP. Lower left panel: Bcd-GFP intensity profiles of 21 embryos that are mutant for endogenous Bcd, expressing Bcd-GFP. Lower right panel: Bcd-GFP intensity profiles of 15 embryos expressing Bcd-GFP. — All embryos were formaldehyde fixed and imaged with a confocal microscope. The AP-axes have been normalized for each individual embryo by its egg length. Colors represent individual embryos, black lines are a fit of the data.
bodies recognize different epitopes of the exact same Bcd-GFP protein. This suggests that the level of free Bcd or GFP is zero or very low, further implying that the degradation of eGFP and of Bcd-GFP are very similar, if not identical. However, from this result it is not clear if the physical properties of the diffusing Bcd-GFP protein and the Bcd-protein are identical; the average values for both λ are considerably lower than in the case of λ for wildtype Bcd. In Chapter 2 we found for wildtype OreR λ = 14 − 15% egg length, whereas here we find λ ≈ 11% egg length, which is 25% less. If this difference is real and not due to experimental inaccuracies1 , then it is possible that either the diffusion constant or the life-time of Bcd-GFP is altered from the ones of endogenous Bcd protein. A reduction of λ for Bcd-GFP of 25% would imply a reduction in the diffusion constant or in the protein lifetime of over 40% of 1
Both types of experiments have not been done under the same conditions which could easily distort the quantitative result. Moreover, the well-known notorious difficulty of fitting exponentials to real data may also be at the origin of the difference in λ. A new set of control experiments is needed in order to exclude a systematic experimental effect. These experiments will require simultaneous and identical fixation and staining of wildtype embryos and embryos expressing Bcd-GFP in a null bcd background.
53
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Figure 4.4: Cumulative probability distributions of length constants λ for 21 D. melanogaster embryos that are mutant for endogenous Bcd, expressing Bcd-GFP (left panels in Figure 4.3). λs are extracted from a fit to fluorescence intensity profiles of Bcd antibody stainings (blue curve), GFP antibody stainings (red curve) and GFP autofluorescence (green curve). λ is reported in units of % egg length. (See Figure 4.3 for more details.)
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the respective values for endogenous Bcd protein. This sounds exorbitantly large and merits further investigation. Furthermore, we notice a significant difference in shape between the gradients extracted from Bcd and GFP antibodies and the gradients that correspond to the GFP autofluorescence. The gradients in the lower left panel of Figure 4.3 are shallower and extend further out than the gradients in the upper left panel of Figure 4.3. This effect is made quantitatively apparent in Figure 4.4 by the shift of the GFP distribution by 25% with respect to the antibody distributions. The effect is significant, and the points raised in the last paragraph (see footnote 1) are not relevant in this case because the experiments have been done simultaneously, on the same embryos, using the same protocols. A possible explanation for this shift in λ may be that the maturation time of GFP is longer than its folding time, which would imply that the GFP antibody recognizes the protein prior to the time when the protein is “mature” enough to undergo the photochemical processes necessary for its fluorescence detection.
4.2.2
Post-translational GFP fluorophore formation time
Post-translational modifications, such as internal cyclization and oxidation steps, are required for the formation of the GFP chromophore (Heim et al., 1994). Reports published previously concluded that GFP fluorophore formation in D. melanogaster is a slow process. Four different accounts, published between 1995 and 1997, report fluorescence acquisition times of 2-5 hours (Davis et al., 1995; Brand, 1995; Edwards et al., 1997; Timmons et al., 1997). Finally, Hazelrigg et al. (1998) could first detect Bcd-GFP fluorescence in nuclei of larval salivary glands after a 40-min recovery period following induction of gene expression with a 10-min heat shock (Hazelrigg et al., 1998). Our data allows for a different approach to gain insight into the eGFP maturation time. Let us assume that there is a time difference between the folding time of BcdGFP and its maturation time τmat and that the Bcd-GFP lifetime τ is larger than 54
τmat . We can write down a system of two coupled differential equations, describing a mature, “fluorescent” Bcd-GFP protein distribution with concentration CF and a non-mature, folded, “dark” Bcd-GFP distribution with concentration CD by: 1 1 C˙ F (x, t) = D∇2 CF (x, t) − CF (x, t) + CD (x, t) τ τmat 1 1 C˙ D (x, t) = D∇2 CD (x, t) − CD (x, t) − CD (x, t) τ τmat
(4.1)
where D is the diffusion constant of Bcd-GFP, and where we further assumed that τ is identical for mature and non-mature Bcd-GFP. The steady-state solution for this system follows immediately with p CF (x) = C0 ( 1 + τ /τmat exp(−x/λF ) − exp(−x/λD )) (4.2) CD (x) = C0 exp(−x/λD ) (4.3) p √ with λD = Dτ τmat /(τ + τmat ) and λF = Dτ . Furthermore, the ratio between the length constants is given by r τ λF = 1+ . (4.4) λD τmat Identifying the gradient generated by eGFP autofluorescence with CF (x) and the gradient generated by the fluorescently labelled antibodies against Bcd or GFP with CD (x) + CF (x) (the total amount of Bcd-GFP protein), we can extract λF and λD from our data, and find a relationship between τ and τmat using Eq. (4.4). Based on this calculation we cannot calculate the eGFP maturation time from our data, but we can relate its value to Bcd-GFP’s lifetime. Figure 4.5 shows the average concentration profiles of each distribution of Figure 4.4. It is readily visible that the gradient extracted from eGFP autofluorescence is shallower than the gradients extracted from the antibody stainings. The fits of Eqs (4.3) and (4.3) to the data (black and blue curves, respectively) are very good, and Eq. (4.4) predicts a 2.3–fold longer protein lifetime than the eGFP maturation time. Additionally, λF is almost twice as large as λD , suggesting that the data really fits two distinct exponentials. Combining this result with our estimation of the Bcd-lifetime from Chapter 3, we obtain a eGFP maturation time of 2.6 minutes, assuming the lifetimes of Bcd and of Bcd-GFP are comparable. This assumption is justified by the fact that the antibody stainings to Bcd and to GFP are identical. The estimated maturation time is significantly smaller than what has been assumed thus far. The smallest value for D. melanogaster reported in the literature to our knowledge is 40 minutes (Hazelrigg et al., 1998). According to our finding, this would result in a BcdGFP lifetime of over 90 minutes. But a protein lifetime of 90 minutes is extremely long compared to typical developmental time scales for D. melanogaster. There are two probable explanations for the difference of more than an order of magnitude in the time-lag required for chromophore formation between our estimation and the values found in the literature: (1) Our estimation can only be seen as a preliminary estimation, mainly because we extract our result from fitting single and double exponentials (see also footnote 1). Notice that we also obtain a very good 55
1
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Figure 4.5: Average intensity profiles of 21 D. melanogaster embryos that are mutant for endogenous Bcd, expressing Bcd-GFP (left panels in Figure 4.3). Averages are taken over 200 bins along the AP-axis. Concentration is normalized by the average maximum intensity. Shown intensity profiles are of staining with Bcd antibodies (blue dots), of staining with GFP antibodies (red dots) and of endogenous GFP fluorescence (green dots). Blue and red curves are a fit of the data to I = A exp −x/λ + B, where λ is a characteristic length constant for the intensity profile. The black curve represents a fit of a double-exponential to the green data points. The fit solves a system of differential equations with two underlying Bcd-GFP distributions, one consisting of matured fluorescent GFP, the other consisting of non-fluorescent not-matured GFP (see text for more details). From this fit we obtain a relationship between the Bcd-GFP lifetime τ and the GFP maturation time τmat of τ = 2.3τmat .
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fit to the gradient of eGFP autofluorescence with the conventional single-exponential steady-state solution (green curve in Figure 4.5), as used in Figure 4.3. The leastsquares sum of this fit is comparable to the least-squares sum of the more complicated model from above. This fact makes it difficult to view our estimation as more than a first order approximation; (2) Most values reported in the literature are too high. We conclude this from the fact that we can see Bcd-GFP during cell-cycle 9, i.e. less than 70 minutes after fertilization, which puts an upper bound on the maturation time. The reported maturation time of 40 minutes was recorded after heat shock induction, for which it is difficult to determine a precise translation termination time. No quantitative data is provided, nor any control experiment with a different reporter construct that would allow the estimation of the efficiency and time scales of the system used. Moreover, in this reference, the acquisition of fluorescence by GFP was observed in nuclei of larval salivary glands, which provide a different cellular environment than the early embryonic syncytium. The efficiency of posttranslational fluorophore formation is dependent on many factors which all depend on the cellular environment, such as solubility vs. formation of inclusion bodies, the availability of chaperones, the availability of O2 , the pH, and the intrinsic rate of cyclization/oxidation. Recognizing these differences, we nonetheless believe that we can use this construct to examine the dynamic establishment of the Bcd gradient. Having characterized the physical properties of Bcd-GFP, and realizing that its biological effects are not very different than those of the endogenous Bcd protein, we continue our investigation of the Bcd gradient with Bcd-GFP expressing embryos that are mutant for endogenous Bcd. 56
4.2.3
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Figure 4.6: Average Bcd-GFP concentration of a time-lapse movie taken with a two-photon microscope of three focal planes of a D. melanogaster embryo expressing Bcd-GFP. For a snapshot image of time-lapse movie see Figure 4.1. Averages are taken separately for each focal plane over the entire inner region of the embryo. Focal planes are at 30µm (red curve), 60µm (green curve) and 90µm (blue curve) below the top surface of the embryo. Concentration is normalized by the average concentration over 10 time points of the first minimum located at approximately 10 min. Each dot corresponds to a single time point of the timelapse movie. Time points are 25 seconds apart. The black curve is generated by the average of all three focal planes.
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Stability versus dynamics of the Bcd gradient
The results from the last section allow us to use our Bcd-GFP construct to study the dynamics of the Bcd-GFP gradient in D. melanogaster and extrapolate our observations to the actual dynamics of the Bcd gradient. We recorded time-lapse movies of Bcd-GFP embryos with a two-photon microscope. Figure 4.1 shows a snapshot of such a movie. In a movie dataset we can separate space and time to compute the total fluorescence intensity for a given time point by spatially averaging over each embryo slice. Assuming that the fluorescence intensity is proportional to the actual Bcd-GFP concentration, we show in Figure 4.6 the time evolution of Bcd-GFP concentration for the first 3 hours of embryonic development. We notice that the concentration is nonstationary and that the total amount of Bcd-GFP is changing. Moreover, this dataset shows that the apparent Bcd-GFP concentration occasionally dips, corresponding to the dilution of Bcd-GFP as it diffuses out of the focal plane during mitosis. The observed mitotic Bcd-GFP concentration dips suggest a non-trivial dynamics in the re-establishment of the Bcd gradient with each mitotic division. To further investigate this observation, we measured the nuclear Bcd-GFP concentration at a given location in the embryo during different cell cycles. Figure 4.7 shows that nuclear Bcd-GFP concentrations stay within a 20% band over the time interval from cell cycle 12 to 14, suggesting a stable Bcd-GFP gradient during this period. This result is supported by our earlier finding in Chapter 1 where we report a full dynamic range in Bcd concentration already in cell cycle 11, see Figure 1.15. Given the increase in Bcd-GFP concentration depicted in Figure 4.6 and the conservation of Bcd-GFP concentration from cell cycle to cell cycle, it is plausible that the Bcd synthesis rate is matched with the increasing number of nuclei with each mitotic division. If this is the case, then the total nuclear concentration should be conserved across cell cycles as well. To test this hypothesis, we looked at anterior nuclei in our Bcd-GFP time-lapse movies such as in Figure 4.2. We chose a focal plane near the surface of the embryo to avoid a decrease in photo-efficiency. The 57
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Figure 4.7: Nuclear Bcd-GFP concentration during syncytial cell cycles 12 to 14. Nuclei are situated at approximately 25% egg length and have been chosen individually for positional matching (upper panel). The lower panel shows the mean nuclear concentration, normalized by the overall mean concentration, as a function of time for five nuclei. Pointed lines serve as a guide, linking the mean concentration over an entire syncytial cell cycle for each nucleus.
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intensity of a band along the anterior edge of the embryo containing these nuclei is shown as a function of time in Figure 4.8 (upper panel, red curve). Nuclear cycles are clearly distinguishable due to prominent mitotic intensity dips. The first and last peaks of this curve correspond to interphases 10 and 14, respectively. The intensity increases by a factor of 5.6 whereas the nuclear count increases by a factor of 24 = 16. But measuring the nuclear diameter during different nuclear cycles (see Figure 4.9), we found that the nuclear volume decreases by a factor of 2.76, which compensates for the increase in nuclear count, yielding an effective nuclear intensity increase of 16/2.76 = 5.8. We conclude that the overall nuclear Bcd-GFP intensity is conserved, suggesting a regulation of synthesis rate that is nuclear cycle dependent. Knowing that the total nuclear concentration is conserved, the Bcd-GFP gradients, extracted by the method of a sliding window along the cortical edge of an embryo at mid-focal plane (Houchmandzadeh et al., 2002), should also be conserved, except for a scaling factor due to the fact that the number of nuclei per window area changes from cell cycle to cell cycle. We computed the average intensity of the pixels of the sliding window and projected the coordinates of its center on the two (anteroposterior and dorsoventral) axes of the embryo. Dorsal and ventral profiles were both constituted, but we report only the dorsal side for consistency. Figure 4.10 compares Bcd-GFP gradients during interphases of nuclear cycles 11 to 14, averaging over 5 minutes of recording time. Although the absolute concentration increases by a factor of 5 from nuclear cycle 11 to cell cycle 14, surprisingly, normalized concentration gradients show very little cell-cycle–to–cell-cycle variability. This suggests that the system establishes the gradient and subsequently keeps its shape fixed. With a strongly changing protein synthesis rate of Bcd-GFP (see Figures 4.6 and 4.8), this is only possible if non-passive regulatory mechanisms are considered. 58
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Figure 4.8: Average Bcd-GFP concentration of the same time-lapse movie as in Figure 4.6, but with different averaging regions. Upper panel: Bcd-GFP concentration averaged over a rim around the inner edge of the anterior half of the egg. This region monitors the nuclear Bcd-GFP concentration during interphases. Peaks correspond to interphases 10 to 14. Lower panel: BcdGFP concentration averaged over a rim around the inner edge of the anterior half of the egg between the nuclei and the inner yolk of the egg. This region contains no nuclei and monitors the cytoplasmic Bcd-GFP concentration. Peaks correspond to minima of the upper panel, i.e. times when nuclei are undergoing mitosis, releasing BcdGFP into the cytoplasm.
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To check whether a passive diffusion-driven process can provide a stable gradient in the observed time frame (i.e. before cell cycle 11, or in less than 70 min), we computed the time it takes for a passive gradient establishment mechanism to reach steady state, assuming an initially constant synthesis rate. Figure 4.11 shows concentration profiles of gradients at different equilibration times of a 3D computer simulation. From this simulation we extract a time of 30 to 60 minutes to reach steady-state2 at 4% to 1%, respectively, which is well below the time within which the embryo reaches its syncytial blastoderm stage, the time at which we first see Bcd target genes being turned on. It would be interesting to repeat this computational experiment by implementing a rapidly changing synthesis rate as development proceeds to check 2
We define steady-state here by the gradient reached after a long equilibration of 320 minutes. reported percentages are deviations from this gradient at 50% egg length.
Figure 4.9: Nuclear diameters in nuclear cycles 9 to 14. Each image is a magnified section of the respective images in Figure 4.2. The pixel dimension is 1.14µm.
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Figure 4.10: Upper panel: Bcd-GFP intensity profiles for a single D. melanogaster embryo vs. projection along AP-axis. Curves are averaged over 5 min (12 time points) during interphase 14 (blue), 13 (green), 12 (red) and 11 (cyan). Dots represent real data points, stars correspond to a sliding average over 5 data points. Lower panel: Starred curves from upper panel, x-axis normalized by egg length and y-axis normalized by average maximum intensity.
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whether this mechanism influences the time it takes to reach steady state. The observed stability of the Bcd gradient over different cell cycles is surprising, given the results of earlier work. In 2002, Houchmandzadeh et al. notice a high embryo–to–embryo variability of the Bcd gradient (Houchmandzadeh et al., 2002), but that this variability in the positional information is greatly decreased already at the next level of the gene cascade of hunchback (hb) gene expression: the read-out of Bcd concentration along the anteroposterior axis of the egg. In this work we already encountered the same variability multiple times (see Figure 1.11 in Chapter 1 and Figure 2.6 in Chapter 2), including the gradients of Bcd-GFP in Figure 4.3. How-
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Figure 4.11: Bcd concentration profiles for 3D computer simulation, solving the differential equation dc(x, t)/dx = D∇2 c(x, t) − kc(x, t), with a 2 diffusion constant p D = 15 µm /sec and a length constant λ = D/k = 100 µm. The boundary conditions were generated using a 3D stack of twophoton images of a D. melanogaster embryo to reconstruct the egg’s shell. The synthesis rate was chosen to be constant by setting the concentration at the dorsal rim of the anterior pole to 1. Colors represent different equilibration times of the simulation (see legend for code). At 50% egg length steady state is reached to 4% after 32 min (magenta) and to 1% after 1h (yellow). Percentages are deviations from a long equilibration of over 5h (black +).
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Figure 4.12: Bcd-GFP concentration profiles for six D. melanogaster embryos. Concentration is normalized to average maximum concentration for individual embryos. AP-axis has been normalized by egg length. Each curve is averaged over the first 10 minutes of cell cycle 14, i.e. 24 time points. Each color corresponds to a different embryo.
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ever, in all these instances, the embryos were fixed and the gradient was extracted by immunofluorescence labelling techniques. The fixation may alter the distribution of Bcd and its affinity to bind to antibodies. The exact affinity, selectivity and degree of amplification (linearity vs. non-linearity) of immunofluorescence techniques is unknown. Moreover, experimental conditions have to be precisely controlled to minimize systematic errors when different datasets are employed. These considerations substantiated the main criticism of the Houchmandzadeh et al. paper. By monitoring the Bcd gradient live in Bcd-GFP embryos, we can circumvent most of these concerns because we can look at the Bcd gradient in its natural conditions. Moreover, we can reduce noise due to the optical excitation and detection mechanisms by averaging over several consecutive time points. To test whether the inter-embryonic variability persisted, we averaged the gradient of all time points of the first 10 minutes of cell cycle 14 for each of six time-lapse movies of different embryos (data shown in Figure 4.12). Our data manipulation, i.e. gradient extraction and normalization, has been kept identical to the one used by Houchmandzadeh et al. Due to the strong autofluorescence of the outer edge of the embryo from the vitelline membrane, and the fact that it is difficult for the image analysis to completely avoid this membrane, we introduce an additional variability. But this variability does not affect the gradient globally along the entire anteroposterior axis, but rather locally at specific spots along the edge where the averaging rectangle touches the membrane. Taken these considerations into account, it is clear from Figure 4.12 that the variability found by Houchmandzadeh et al. is not due to systematic errors resulting from embryo handling techniques, but is intrinsic to the physical properties of the early embryonic syncytium of D. melanogaster. The coexistence of high embryo–to–embryo variabilities of the Bcd gradient and its stability over different syncytial cell cycles is intriguing, and requires further investigation to be understood. However, note that the stability from cell cycle to cell cycle is not a statement that the gradient is static because our data also shows that there exists a fine tuned balance between the Bcd synthesis rate and the number of nuclei that causes the gradient appear stable. 61
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Figure 4.13: Bcd (green) and Hb (red) concentration profiles of antibody-stained, heat-fixed, wildtype D. melanogaster embryos in syncytial cell cycles 11 to 14 (cc11, cc12, cc13 and cc14). Each dot corresponds to the average nuclear fluorescence intensity, normalized by the maximum intensity, and projected onto the AP-axis of the embryo. X-axis is normalized by egg length. Blue curves are average concentrations for 6 embryos in cc11, 4 embryos in cc12, 7 embryos in cc13 and 10 embryos in cc14. Averages are taken over 100 bins along the AP-axis.
This apparent Bcd gradient stability combined with the sharpening of the Bcd-Hb input/output relation shown in Chapter 1 led us to reconsider the same data from Chapter 1 by examining it in the spatial domain, i.e. plot protein concentrations as a function of nuclear location along the anteroposterior axis of the embryo. Figure 4.13 shows immunofluorescent Bcd and Hb profiles of syncytial blastoderm nuclear cycles 11 to 14 of several heat-fixed D. melanogaster embryos. Again, we see a high embryo-to-embryo variability in Bcd. For Hb, the variability seems to decrease with progressing nuclear cycles; and the gradient seems to steepen. The latter observation is clearly visible in Figure 4.14. Notice the steepening of the Hb gradient and the constancy of the Bcd gradient over nuclear cycles 11 to 14, similar to previously shown data for the Bcd-GFP gradient (see lower panel in Figure 4.10). The reason why the steepening of the Hb boundary is more apparent here than in Figure 1.16 of Chapter 1 is because here the data is effectively plotted logarithmically in the spatial domain, 62
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Figure 4.14: Average Bcd (circles) and Hb (stars) concentration profiles of antibody-stained, heatfixed, wildtype D. melanogaster embryos in syncytial cell cycles 11 to 14 (cc11 (cyan), cc12 (red), cc13 (green) and cc14 (blue)). These curves are the blue average curves replotted from Figure 4.13.
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due to the exponential shape of the Bcd gradient. One might have thought that the system works with a fixed local Bcd concentration readout and if there are any dynamics in the process that have to be considered, then they are the dynamics of the Bcd gradient. However, what we see here is the exact opposite: Bcd concentration is stable nucleus per nucleus, whereas the readout is highly dynamic. Further notice the fact that the Hb-steepening seems to occur in a pivoting process around a point at approximately 45% egg length, which is well within error of the commonly reported position of the Hb boundary of cell cycle 14. This finding suggests that the information for the position of the boundary for Hb is already integrated in the system at nuclear cycle 11. The findings in this section suggest a crucial role of the nuclear dynamics to the establishment of the Bcd gradient. The protein synthesis rate is clearly non-uniform, yet the nuclear concentrations and the shape of the Bcd gradient do not seem to change between syncytial nuclear cycles. Moreover, the stability of the Bcd gradient during syncytial nuclear cycles, the rigidity of the Hb boundary over the same time period, and the sharpening of the response (the Hb gradient) suggest a non-static, non-local readout of the Bcd gradient by hb.
4.2.4
Effects of nuclei on the Bcd gradient
The most prominent feature in the time-lapse movies of embryos expressing BcdGFP is the rapid emptying and refilling of nuclei during mitosis. We have shown in the last section, that nuclear transport mechanisms must have a strong effect, given the “magic” compensation of Bcd synthesis rate and the number of nuclei. The obvious question of whether this dynamic feature of Bcd molecules has an effect on the formation, the stability and the maintenance of the Bcd gradient arises. For instance, it seems important to understand how Bcd is distributed throughout the 63
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Figure 4.15: Average Bcd-GFP concentration of rectangular regions in Figure 4.1 plotted vs. time. Concentration is normalized by maximum concentration over shown time window. Each dot corresponds to a single time point of the timelapse movie. Colored curves correspond to different focal planes: 30µm (blue), 60µm (green) and 90µm (red) below the top surface of the embryo. Black curve: mean Bcd-GFP concentration of inter-nuclear space of the same time-lapse movie.
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embryo during mitosis and interphase of different cell cylces. From the data of a typical time-lapse movie depicted in Figure 4.8 we notice a strong concentration decrease at the cortex of the embryo during mitosis due to fluorophore dilution in the cytoplasm, and simultaneously a noticeable increase in cytoplasmic concentration (lower panel). To understand how far the Bcd-GFP molecules redistribute basally during mitosis, we measured fluorescence intensities in focal planes 30, 60 and 90 µm below the top surface of the embryo. The highlighted rectangles in Figure 4.1 depict the areas within the embryo over which we average the concentration for each time point. Figure 4.15 shows the average concentration of the rectangles of Figure 4.1 as a function of time. We see that the curve corresponding to the upper focal plane (blue curve), 30 µm below the top surface of the embryo, correlates with the cytoplasmic mitotic concentration increase (black curve), whereas the concentration averages of the two lowest focal planes do not correlate. This demonstrates that Bcd-GFP molecules are redistributed during mitosis in the cytoplasm at least to a depth of 30 µm. From the rising and falling edges of the peaks of the blue curve in Figure 4.15 we can also obtain an estimate of the characteristic timescales τ of the redistribution and relocalization processes, respectively. We estimate timescales to be on the order of approximately 3 minutes. From the Einstein-Smoluchowsky equation for the characteristic path length of a random walk in a 3D diffusion process √ (4.5) ρ = 6Dτ we estimate a diffusion constant of D ∼ 1 µm2 /sec. This value is over an order 64
Figure 4.16: Confocal images of hand-cut sections of heat-fixed wildtype D. melanogaster embryos. Embryos have been stained with Bcd antibodies prior to cutting. Left panel shows posterior (left) and anterior (right) cuts of embryos fixed during syncytial cell cycles 10 to 14. Right panel shows posterior (left) and anterior (right) cuts of embryos fixed during nuclear cycles 7 to 9. Lower three rows in right panel show Bcd antibody staining of fixed unfertilized eggs.
of magnitude smaller than the diffusion constant we measured in Chapter 3 for a 40kD-dextran molecule. See next section for a discussion. The result from Figure 4.15 also show that the cytoplasm is rapidly depleted of Bcd-GFP molecules. To examine if this finding holds for Bcd antibody-stainings of fixed embryos, we looked at dorsoventral intensity profiles of sections of hand-cut D. melanogaster embryos, shown in Figure 4.16. It is readily visible by eye-inspection of these sections that unfertilized eggs and embryos during early nuclear cycles both have a nearly uniform distribution of Bcd in anterior sections. On the other hand, embryos in blastoderm stages show that the protein is concentrated around the cortex at the expense of total depletion in the inner egg. For a control of our protocol, we tested and quantified two versions of this exper65
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Figure 4.17: Intensity profile of confocal images of hand-cut sections of heat fixed wildtype D. melanogaster embryos during cell cycle 14. Embryos have been stained with Hb (left column) and Bcd (right column) antibodies before cutting. Each profile is taken along the diameter of each section and averaged over ±10 µm on both sides of the diameter. In every panel colored curves correspond to six focal planes of the same embryo section (depth below top of section: 3 µm (yellow), 6 µm (magenta), 9 µm (cyan), 12 µm (red), 15 µm (green), 18 µm (blue)).
iment: in the first version we heat-fixed embryos, stained with Bcd antibodies and hand-cut the eggs after the staining procedure was completed; in the second version of the experiment we heat-fixed the embryos and hand-cut them before running the staining procedure. This way we exclude a misrepresentation of our experiment due to permeabilization and antibody penetration into the embryo. However, a comparison of Figures 4.17 and 4.18 shows that the order does not matter. In both cases, the cortex is 4 to 6-fold brighter than the core of the embryo. To further understand the effect of nuclei on the Bcd gradient, we looked at the synthesis rate and Bcd gradients of unfertilized eggs where these nuclear effects are completely eliminated. Figure 4.19 shows that in unfertilized eggs, the synthesis rate increases quasi-linearly for more than 4 hours after egg deposition. Previously we have shown data for fertilized eggs, Figures 4.6 and 4.8, where the concentration did not increase uniformly and did drop dramatically during cellularization. This suggests that the synthesis rate is zygotically down-regulated. Figure 4.20 shows Bcd gradients in unfertilized, fixed eggs of D. melanogaster that have been labelled with Bcd antibodies. The embryos are of three different age 66
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Figure 4.18: Intensity profile of confocal images of hand-cut sections of heat fixed wildtype D. melanogaster embryos during cell cycle 14. Embryos have been stained with Hb (left column) and Bcd (right column) antibodies after cutting. (see caption of Figure 4.17 for more details)
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groups: 0-1h, 1-2h and 2-3h. The length constants of the gradients increase with age, most significantly from less than 1h old eggs to more than 1h old eggs. This suggests that also in the case of unfertilized eggs there seems to be a point at which the shape of the gradient is established and maintained, regardless of an increasing absolute concentration. Notice, however, the large variability in length constants within each age group. It is difficult to measure gradients of unfertilized eggs reliably because of their erratic and unpredictable cytoplasmic movement and streaming. As a control we repeated the same experiment with wildtype D. melanogaster embryos (data shown in Figure 4.21). For this set of data we recover the length constant range that we have found previously in Chapter 2. However, here we show length constants for both dorsal and ventral sides of the embryo during early cell cycle 14, and we see a 20% difference between the two sets of length constants. Figure 4.22 shows a summary of the data presented in Figures 4.20 and 4.21. Notice the fact that the unfertilized eggs are significantly shorter than the OreR embryos. Unfertilized eggs lack the internal microtubule support and actin filament structure, which gets rapidly established in fertilized eggs over the first 2 hours. Due to this fact unfertilized eggs may be more fragile and hence more prone to deformation 67
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Figure 4.20: Upper panel: Fluorescent Bcd antibody intensity profiles of unfertilized D. melanogaster eggs. Eggs were formaldehyde fixed and imaged with a confocal microscope. Colors represent unfertilized eggs of different ages: 0-1 hours old (blue, 21 eggs), 1-2 hours old (green, 20 eggs) and 2-3 hours old (red, 20 eggs). Solid colored lines are respective fits of data from individual eggs. Black curves represent the average intensity profile over the entire data set of each age group, also shown in Figure 4.22. Lower panel: Histogram of λ-distributions for each age group, same color code as upper panel.
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Figure 4.19: Average Bcd-GFP concentration of a time-lapse movie taken with a two-photon microscope of three focal planes of an unfertilized D. melanogaster egg expressing Bcd-GFP. Averages are taken separately for each focal plane over the entire inner region of the embryo. Focal planes are at 30 µm (red curve), 60µm (green curve) and 90µm (blue curve) below the top surface of the egg. Concentration is normalized by the average concentration over 10 time points of the first minimum located at approximately 10 min. Each dot corresponds to a single time point of the time-lapse movie. Time points are 1 minute apart. For comparison, the black curve is taken from Figure 4.6 (black curve).
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Figure 4.21: Control for Figure 4.20. Upper panel: Fluorescent Bcd antibody intensity profiles of 22 wildtype D. melanogaster embryos. Embryos were formaldehyde fixed during early cell cycle 14 and imaged with a confocal microscope. Colors represent dorsal (blue) and ventral (red) side of each embryo. Solid colored lines are respective fits of data from individual embryos. Black curves represent the average intensity profile over the entire data set, also shown in Figure 4.22. Lower panel: Histogram of λ-distributions of fits to data in upper panel.
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Figure 4.22: Summary of averages from Figures 4.20 and 4.21. Unfertilized egg data 0-1 hours old (blue), unfertilized egg data 1-2 hours old (green) and unfertilized egg data 2-3 hours old (red); dorsal wildtype embryo profiles (black circles) and ventral wildtype embryo profiles (black squares).
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during the fixation and permeabilization process. Our results on unfertilized eggs, summarized in Figure 4.22 confirm our finding from above, that the Bcd gradient gets established within the first 1-1.5 hours of development and is maintained stably thereafter. Moreover, our data suggest a zygotic down-regulation of the Bcd synthesis rate.
4.2.5
Nuclear dynamics: transport rates and diffusion constants
From the upper panel of Figure 4.8 it is apparent that the time constants of nuclear import and export of Bcd-GFP are not symmetric. However, time constants of cytoplasmic depletion and refilling of Bcd-GFP between interphase and mitotic time segments seem to be symmetric (lower panel Figure 4.8). To investigate this point further, we measured nuclear import and export rates of Bcd-GFP. To measure the nuclear import rate, we photobleached an entire nucleus of an embryo expressing Bcd-GFP and monitored the fluorescence of the refilling process. The upper panel of Figure 4.23 shows a typical recovery curve of a photobleached cell cycle 14 nucleus. To infer the input and output rates for this process from our data, we solve the differential equation for the nuclear concentration c˙in (t) =
1 1 cout (t) − cin (t). τin τout
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∞ Using the steady state condition of τin c∞ in = τout cout we get the solution for Eq. (4.6) as τout (1 − exp(−t/τout )). (4.7) cin (t) = c∞ out τin
From a fit of Eq. (4.7) to the data in Figure 4.23 we get τout = 120 sec and using our c∞ previous result for the ratio c∞in = 6 we obtain for the input rate τin = 20 sec. out To investigate the reverse process of Bcd-GFP release from the nucleus, we closely monitored two nuclei during the transition between interphase 12 and mitosis 13. Representative data for any two neighboring nuclei is shown in Figure 4.24. During 69
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Figure 4.23: Recovery curves of bleached wildtype D. melanogaster embryos expressing BcdGFP. Bleaching was done with a scanning twophoton microscope and a 25x Zeiss oil immersion objective with a large focal volume (lateral 1 µm, axial 15 µm). The bleaching pulse was generated by reducing the scan-field 8-fold while keeping the laser power constant, effectively increasing the power per pixel 64-fold. Bleach duration was 3 seconds. Data points are spaced 0.5 sec and shown as red dots. Black curves represent first order fits to extract recovery time constant τ (see text for more details on fitting procedure). Upper panel: Recovery curve for a single bleached nucleus during early interphase 14, located at approximately 20% egg length; lower panel: Recovery curve for cubic bleach volume of the size of a nucleus during mitosis 13, located at approximately 20% egg length with an time constant of τ = 28 sec.
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interphase we noticed a 6-fold intensity difference between nuclear and cytoplasmic Bcd-GFP concentration, cin and cout , respectively (blue curve lower left panel). This finding broadly agrees with measurements of Bcd concentrations in cytoplasmic and nuclear extracts using Western blot analysis (Zhao et al., 2002). In the lower right panel we can identify two distinct time intervals. Over a time of 150 seconds we observed a decrease in nuclear concentration of 25% without noticing a cytoplasmic concentration increase or an increase in nuclear diameter. The time constant associated with this concentration decrease would be c ∗ ∆t/∆c = 150 sec/25% = 10 min, which is within a plausible range for the protein lifetime. It could be possible that nuclear import of Bcd-GFP is down regulated at a particular moment during interphase, from which point on the nuclear protein concentration would decay. A closer look at Figure 4.7 would support a decrease in nuclear concentration also during interphases 13 and 14. However, the time constants seem to increase significantly, which contradicts the hypothesis of nuclear protein decay. The second time interval corresponds to the nuclear membrane breakdown and 70
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Figure 4.24: Bcd-GFP release of two nuclei located at approximately 20% egg length during mitosis 13. Upper panel shows two snapshots of a time laps movie taken with a two-photon microscope of a developing D. melanogaster embryo expressing Bcd-GFP. The Upper left image was taken before membrane opening during interphase 12, and the upper right image was taken during mitosis 13 at the same location as the image on the left. Lower left panel shows the mean intensity on a line between the two nuclei during interphase 12 (blue curve) and during mitosis 13 (red curve). Lower right panel shows the mean intensity within a nucleus (blue curve) and between the two nuclei (red curve) as a function of time. The green curve is a fit of a single exponential to the part of the data that corresponds to the diffusive flux of Bcd-GFP protein. The time constant of the fit is τ = 41 sec. From a fit of this data to the solution of a simple 2D computer simulation we extract a diffusion constant of 0.1 µm2 /sec.
subsequent Bcd-GFP release into the cytoplasm. The cytoplasmic intensity increases by 50% while the nuclear intensity decreases by a factor of 3. We fit the nuclear intensity decay with an exponential curve (green points in lower right panel of Figure 4.24) and extract a time constant of 41 sec. From a fit of this data set to the solution of a 2D computer simulation of the nuclear release of fluorophores, we get a diffusion constant of 0.1 µm2 /sec. This diffusion constant seems low compared to the diffusion constants we measured in Chapter 3. To verify our results, we photobleached a cubic volume in the anterior cytoplasm of Bcd-GFP-expressing embryos during mitosis 13, when BcdGFP is uniformly distributed throughout the embryonic cortex. The lower panel in Figure 4.23 shows a typical recovery curve after a 3 second bleach pulse. For a cubic bleach volume we can solve the diffusion equation in three dimensions exactly3 . From the fit of this solution to the data in the lower panel in Figure 4.23 we extract a diffusion constant D = 0.1 µm2 /sec, identical to the diffusion constant associated previously with the protein release at the onset of mitosis. 3
The temporal solution of the diffusion equation C(t, r) = D∇2 C(t, r), with initial conditions of
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Figure 4.25: Recovery curve of a bleached wildtype D. melanogaster embryo that had been previously injected with fluorescently labelled 40kDdextran dye (Molecular Probes, Eugene, OR). Bleaching was done with a scanning two-photon microscope and a 25x Zeiss oil immersion objective with a large focal volume (lateral 1 µm, axial 15 µm). The bleach volume had cubic dimensions of 40x40x35 µm and was located at approximately 50% egg length below the top surface of the embryo. The bleach pulse was 3 sec long and of 10fold higher laser intensity than the recording intensity for the recovery curve. Data points are spaced 0.5 sec and shown as blue dots. The black curve represents a first order fit with a time constant of τ = 7.9 sec. The red curve represents the fit to the exact solution of the diffusion equation over the cubic bleach volume with an extracted diffusion constant of D = 5.2 µm2 /sec (see text for more details on fitting procedure).
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A value of 0.1 µm2 /sec for the diffusion constant is two orders of magnitude lower than the diffusion constants found previously. To compare our results from Chapter 3 with the diffusion constants extracted from pattern photobleaching experiments, we injected a D. melanogaster egg with fluorescently labelled 40kD-dextran dye (for details on injection procedure see Chapter 3) and we repeated our pattern photobleaching experiments. We bleached a cubic volume within the cortex of the egg at approximately 50% egg length. The data is shown in Figure 4.25. Using the same fitting procedure as above, we obtained a diffusion constant of 5.2 µm2 /sec.
4.2.6
Summary of diffusion constant measurements
In the present Chapter we have presented four different measurements of diffusion constants which are all meant to estimate the diffusion constant of Bcd in addition to the one measured in Chapter 3. Table 4.1 summarizes the different methods and values of the diffusion constants. Notice there are two orders of magnitude in difference between these measurements. However, we are comparing invasive and non-invasive methods of diffusion constant measurements of both dextran molecules and Bcd-GFP protein with different physical properties. C = −1 within a cube of linear dimensions a × b × c and C = 0 elsewhere, is given by Z C(t) = V
µ ¶6 X n2 ∞ n2 n2 exp[π 2 Dt( a2x + b2y + c2z +)] 4 . drC(t, r) = 8abc π [(2nx − 1)(2ny − 1)(2nz − 1)]2 n =1 x,y,z
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. Table 4.1: Summary of diffusion constant measurements in D. melanogaster
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Presented in Chapter 3; b Presented in Chapter 4.2.5; c Presented in Chapter 4.2.4.
More specifically: With methods 1 and 2, we measure diffusion constants of 40kDdextran molecules, and in both cases the egg has been ruptured and injected. In principle, both methods should give very similar results. However, in method 1 we are measuring long range diffusion, whereas method 2 is a short range diffusion measurement. Moreover, in method 1 the pressure pulse may effectively increase the diffusion constant, whereas in method 2, due to heat development during the bleach pulse, proteins and cellular matrix components may crosslink, which could potentially slow down the diffusive process. Finally, due to the crudeness of both methods for measuring in vivo diffusion constants of injected dextran molecules, a factor of 3.5 in difference is not unreasonable. To investigate its origin further, we suggest two kinds of experiments. First, to link the FRAP measurements more closely to the experiments presented in Chapter 3, dextran molecules of different molecular weights could be injected into D. melanogaster eggs and their diffusion could be measured using FRAP. Second, diffusion constant measurements of injected dextran molecules could be done in the different species presented in Chapter 3, to see whether we can reproduce the results from Chapter 3 using FRAP. Methods 2 and 3 are directly comparable. The fact that we observe a relative difference of a factor of 50 can be for two reasons: 1) different processes are governing the diffusion of Bcd-GFP versus the diffusion of dextran molecules of comparable size. In this case, reversible binding of Bcd-GFP to an immobile or slowly moving ” buffer” of binding sites could be responsible for the difference in D (dextran molecules are assumed to be “inert” and are not supposed to bind). With β = 50 being the ratio of bound/free Bcd-GFP, D would be reduced to Deffective = D/β. 2) The physical properties of the cytoplasm during mitosis are different than the cytoplasmic properties during interphase, which could imply that measurements of diffusion constants during mitosis are not comparable to free cytoplasmic diffusion. During mitosis Bcd-GFP could be kept in the vicinity of the chromosomes (as is the case for the decomposing parts of the nuclear membrane) which would effectively slow down the diffusive process. This scenario is further illustrated in the comparison between methods 4 and 5 (see below). To test whether mitosis alters the physical properties of the interaction between cytoplasm and Bcd-GFP, it would be interesting to measure the diffusion constant of Bcd-GFP using FRAP in unfertilized eggs. In this case, the mechanisms that would be responsible to slow down Bcd-GFP’s diffusion during mitosis would 73
be non-active and we could directly probe the diffusive properties of Bcd-GFP in the cytoplasm alone. Methods 4 and 5 are both non-invasive. We observe Bcd-GFP’s diffusion as it naturally occurs during mitosis when concentrated nuclear Bcd-GFP is released into the cytoplasmic matrix. Again, there are two plausible scenarios to explain the difference of a factor of 10 between methods 4 and 5: 1) Mitosis lasts for 3 − 4 min. However, if the diffusion constant would be 0.1 µm2 /sec it would take approximately 30 min for Bcd-GFP molecules to diffuse 30 µm basally. In this case it would be impossible to measure τ , the diffusion time, correctly. As a result, D could easily appear larger by a factor of 10. 2) As pointed out previously, diffusion of Bcd-GFP may be reduced during mitosis due to processes that keep nuclear components, including transcription factors, close to the nuclei during nuclear membrane breakdown. In this case, the diffusion constant would be slowed down in the nuclear vicinity during mitosis, and only at a certain distance from the nuclei would actual cytoplasmic diffusion be observed. Close inspection of Figure 4.24 may hint at such a process: Notice the difference between the relative shapes of the red and blue curves at the moment of nuclear membrane breakdown (onset of the green curve). The red curve, representing cytoplasmic refilling with Bcd-GFP, has a much shorter equilibration time than the blue curve, representing nuclear exhaust of Bcd-GFP. This difference in time constants may reflect the same observed difference between methods 4 and 5. Further investigation of this point is necessary for clarification. From the data presented in Figure 4.24, the time constant associated with the red curve can not be estimated accurately enough. Slight alterations of both experiments (methods 4 and 5) should reveal the origin of the factor of 10 difference. For method 4, recording cytoplasmic Bcd-GFP replenishment not only at a depth of 30 µm but in every slice of a 2µm spaced z-stack starting at the apical surface of the egg down to 40 µm deep should reveal if the diffusion constant is altered in a layer around the nuclei during mitosis. Method 5 could be altered by increasing the dynamic range of our fluorescence signal in order to stretch out the cytoplasmic concentration increase in our data, and by reducing the time interval of successive image acquisitions, thus increasing the accuracy of our data and reducing the measurement error in τ for the red curve.
4.3
Materials and Methods
Construction of P[egfp-bcd ]. The P[gfp-bcd ] plasmid used in Hazelrigg et al., named pNBGA1 (Hazelrigg et al., 1998), was gratefully provided to us by Tulle Hazelrigg. We cut out the wildtype gfp coding sequence using NheI and SphI restriction sites. egfp was PCR-amplified with appended NheI and SphI restriction sites and subsequently fused in-frame at the N-terminus of the bcd coding sequence in pNBGa1. Subcloning this fusion gene as a 6.5-kb BamHIEcoRI fragment into pCaSpeR4 (Thummel & Pirrotta, 1992) resulted in P[egfp-bcd ]. Fly transformation. We followed standard P-element transformation procedures (Spradling & Rubin, 1982). We injected 0.4 mg/ml concentrated DNA together with 0.1 mg/ml concentrated enhancer plasmid pTURBO, which expresses the trans74
posase. into the yw fly strain. We scored several different P[egfp-bcd ] insertions, including insertions on chromosomes I, II and X. Stocks were established for each of these. Fly Stocks and genetics. For all experiments with flies expressing egfp-bcd we used a stock with an X-chromosomal insertion of P[egfp-bcd ]. For substitution of endogenous bcd we conducted the mutant crosses of egfp-bcd with bcd E1 ,pp /TM3,Sb to generate egfp-bcd ;bcd E1 ,pp . Unfertilized eggs of Oregon R wildtype flies and of bcd E1 ;egfp-bcd flies were produced using sterile males generated from C(1,Y),yB/0. Immunostaining of embryos. All embryos were collected at 25◦ C. Embryos expressing Bcd-GFP were formaldehyde fixed (for 20 min in 3.7% formaldehyde/PBS:heptane and devitellinized in heptane:methanol), all other embryos were heat fixed, and embryos were subsequently labelled with fluorescent probes following previously published protocols (Wieschaus & N¨ usslein-Volhard, 1986). We used rat anti-Bcd and rabbit anti-HB antibodies, gifts of J. Reinitz and D. Kosman (Kossman et al., 1998), as well as guinea pig anti-GFP (Molecular Probes). Secondary antibodies were conjugated with Alexa-488, Alexa-546 and Cy5-633 (Molecular Probes). Embryos were mounted in AquaPolymount (Polysciences, Inc.). Microscopy. High-resolution digital images (1024 × 1024, 12 bits per pixel) of fixed eggs were obtained on a Zeiss LSM 510 confocal microscope with a Zeiss 20x/0.45NA A-plan objective. Image focal-plane was chosen at mid-embryo. Living embryos were collected 0-15 minutes after egg deposition, dechorionated in 90% bleach, glued onto a coverslip and immersed in halocarbon oil and imaged on a custombuilt scanning two-photon microscope with a tunable mode-locked Ti:sapphire laser (Tsunami; Spectra Physics, Mountain View, CA) that produces 80-fs pulses at a repetition rate of 80 MHz (see Chapter 3 for more details). A Zeiss Plan-Neofluar multi-immersion objective (25X, 0.8 NA) was used for all in vivo experiments. A wavelength of 900-915nm minimized embryonic yolk autofluorescence. The laser power at the specimen was between 10 and 20mW. For whole embryo recordings, embryos were oriented with their anteroposterior axis perpendicular to the image plane. Digital images (256 × 512) were taken every 25 seconds in three focal planes, 30, 60 and 90 µm below the top surface of the embryo. Photobleaching experiments. Embryos were mounted as described above. Bcd-GFP expressing embryos were photobleached using our scanning two-photon microscope by reducing the scan-field 8-fold while keeping the laser power constant, effectively increasing the power per pixel 64-fold for a duration of 3 seconds. Subsequently the recovery curve was recorded in 0.5 sec time bins with the original scanfield, where the recording power has been adjusted to avoid further photobleaching. The bleach-volume (8 × 8 × 30 µm3 ) generated with the Zeiss Plan-Neofluar multiimmersion objective (25X, 0.8 NA, focal volume 0.4 µm3 ) was measured separately, using fluorescently-labelled 40kD-dextran dH2 O solution, diluted in 90% glycerol. Micro-injected embryos with fluorescently-labelled 40kD-dextran dye were bleached by rapid modulation of the beam with a KDP* Pockels Cell (model 350-50; Conoptics, Danbury, CT) to generate the bleaching and monitoring intensities. In these experiments the bleach pulse was 3 seconds and the bleach-volume was 40 × 40 × 30 µm3 . Image analysis. Techniques to extract intensity profiles were inspired by Houch75
mandzadeh et al. (Houchmandzadeh et al., 2002) and are described throughout the text. Profile quantification. Relative protein concentration levels can be determined from fluorescence intensities of antibody stainings if a linear relationship between antibody binding and protein concentration is assumed. The reference intensity used was the background at low protein concentrations at the posterior end of the embryo. Embryos were stained and imaged at the same time and in the same conditions to avoid experimental procedure variabilities. Bcd profiles peak at about 5-10% egg length. Raw immunofluorescence data for Bcd are fitted by I = A exp −x/λ + B, for abscissae beyond twice the peak position to 95% egg length. This corresponds to the steady-state solution of the standard diffusion based Bcd-model, where the slope of the exponential, λ, is a characteristic length constant for the intensity profile. A nonlinear Nelder-Mead fit procedure was used to estimate the parameters. For each embryo λ was computed from the raw curve, and was independent of normalization parameters.
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Conclusion This work explored a number of questions of fundamental importance to developmental biology using novel approaches. For the first time, the precision and dynamics that govern the initial underlying mechanisms of developmental systems have been investigated using quantitative methods, both theoretical and experimental. The findings of this investigation are surprising in light of current knowledge and its implications are rich in its prospects for further investigation. First, the precision by which Bcd is read out by hb was quantified, demonstrating that already at the initial step of the gene cascade of early embryonic development in D. melanogaster, the inherent noise associated with this readout process - due to molecular and diffusion-driven events - is suppressed to the physical limit proscribed by theory. This finding cannot be explained under the current model of a static, local readout of the Bcd concentration by hb. An alternative mechanism is necessary which incorporates more complicated dynamic features in the readout process. These findings shine new light on well-established developmental processes, with implications not only to the development of D. melanogaster, but also for other systems reliant on morphogenic cell–to–cell signalling processes. Given the inherent underlying stochasticity of genetic activation, understanding the necessary mechanism to achieve the observed precision in developmental processes becomes of prime interest for an understanding of the fundamental molecular mechanisms of living systems. Second, a more careful examination of the establishment of the Bcd gradient revealed that a purely diffusion-driven process – as insinuated by the gradient’s exponential decay – may not be enough to explain our observations and findings. Phenomenologically, nuclear import and export as well as a precisely tuned synthesis rate may be of importance. New conceptual models have to be found; the current view cannot explain the scaling of the Bcd gradient in different species of varying egg sizes. Further investigation of how the scaling of the Bcd gradient across dipteran species of varying egg size is achieved may prove key to our understanding of how genes adapt across species boundaries in order to function in different environments. Ultimately, size variation among members of the dipteran family may already be set and limited at the level of the Bcd gradient. Finally, the stable maintenance of the relative shape and the absolute concentration of the Bcd gradient during syncytial nuclear cycles combined with a sharpening but non-shifting position of the Hb boundary suggests that the positional information encoded in the Hb gradient is already present before the syncytial blastoderm stages. Moreover, an underlying dynamic process is most likely responsible for the hb 77
boundary sharpening, again defying the local concentration readout model. This type of analysis underlines the importance of recognizing the inherently dynamic nature of developmental processes. Development is a time-driven process; understanding its mechanisms requires moving beyond static methods of investigation. In a larger context, this work highlights the strength of using the tools and methods of physics to examine some fundamental biological questions. The intellectual exchange between these two fields has until recently been limited. Physicists used biological systems as a mere tool for further understanding complex physical phenomena, rather than see the exploration of these systems as an end unto itself. On the other hand, biologists have neglected the potential of physicists’ sophisticated quantitative tools to advance their knowledge of complex phenomena. Over the past few decades, a growing interest in the physics community has led to the development of new and innovative tools to address biological systems more quantitatively. However, these tools have been mainly used on molecular or subcellular systems. This work has attempted to break with these conventions by using physics along with traditional tools from biology to investigate a complex multicellular organism in order to reveal fundamental underlying biological mechanisms of its development. It shows that quantitative approaches are particularly useful when applied to mature fields such as early embryonic development in D. melanogaster, having the potential to reveal new aspects that have not been considered before.
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