Sep 14, 1982 - glycogen-rich liver contains a larger number of alpha particles, there is, to ... different areas of the lobules, but also inside the cell, rendered the.
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Biochem. J. (1983) 209, 159-165 Printed in Great Britain
The alpha particulate liver glycogen A morphometric approach to the kinetics of its synthesis and degradation
Pierre DEVOS, Pierre BAUDHUIN, Francois VAN HOOF and Henri-Gery HERS Laboratoire de Chimie Physiologique, Universiti de Louvain and International Institute ofCellular and Molecular Pathology, UCL 75.39, avenue Hippocrate 75, B-1200 Bruxelles, Belgium
(Received 29 June 1982/Accepted 14 September 1982) Electron micrographs of rat hepatocytes with a glycogen content between 0.36 and 2.55% (w/w) were submitted to morphometrical analysis. From the number and size of glycogen profiles, the distribution of radius and volume of glycogen alpha particles were computed. The 7-fold difference in glycogen content was accompanied by an only 1.8-fold increase in the mean volume of the particles while their number increased by a factor of 4. On the basis of these observations, it is proposed that the population of glycogen particles can be divided in two groups. The first one is made of growing particles, still associated with glycogen synthase; they are the only particles present at low glycogen concentration and their number is limited. Application of a simple mathematical model allows to estimate their number in hepatocytes as 49 x 1012 particles ml-'. The second group is made of glycogen particles which have reached their maximal size and the number of which is in principle unlimited. The maximal particle size is estimated to be 0.36 x 10-"5ml, corresponding to an average molecular weight of 178 x 106. The average molecular weight of glycogen, as measured from the actual size of the particles, varied from 89 x 106 to 161 x 106.
On liver micrographs, glycogen appears as electron-dense rosettes, termed alpha particles, which have three axes of symmetry; their diameter can reach 200nm. These structures appear as agglomerates of smaller particles with a diameter of 1530nm, the beta particles (Drochmans, 1960, 1962; Revel et al., 1960; Barber et al., 1966). The dimension of the beta particle is compatible with that of the tree-like structure of inner and outer chains, which is currently considered that of a glycogen molecule (Madsen & Cori, 1958). It has been reported by Devos & Hers (1979) that, in the liver, the molecules of glycogen are synthesized in a defined order and degraded in the reverse order. Indeed, pulse-labelling of glycogen with radioactive precursors performed during sustained synthesis has revealed that the glucose units incorporated first are released last during glycogenolysis and vice versa. This order in both synthesis and degradation implies the existence of some kind of link which associates glycogen molecules to each other and which, when synthesis is in progress, tracks the way to be followed during degradation. This link may join in an orderly way the beta particles which are associated inside an alpha particle; it could also associate one alpha particle to Vol. 209
another, allowing the sequential ordered synthesis and degradation of alpha particles. This second hypothesis implies that the difference between a glycogen-rich and a glycogen-poor liver is in the number of alpha particles rather than in their size. It is supported by the observation made by Parodi (1967) that the molecular weight distribution of liver glycogen, as measured by sedimentation in a sucrose gradient, was not influenced by its concentration in the tissue. The number of molecules would then be proportional to the glycogen content in the liver. Opposite results were however reported by Geddes & Stratton (1977). Although it is a current observation that a glycogen-rich liver contains a larger number of alpha particles, there is, to the best of our knowledge. no published quantitative morphological approach to this problem. The purpose of the present work was to attempt such an analysis. Materials and methods Handling of animals and preparation ofsamples Samples were removed from the livers of rats either during sustained glycogen synthesis or during intense glycogenolysis as described by Devos & 0306-3275/83/010159-07$02.00 © 1983 The Biochemical Society
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Hers (1979). The concentration of glycogen was determined as follows. The tissue was dissolved at 1000C in 10vol. of 1 M-KOH. During this step, which lasts about 60min, free glucose is destroyed. After chilling, the same volume of 1.3M-acetic acid was added and the mixture was clarified by low-speed centrifugation. An aliquot (0.1ml) of the supernatant was diluted ten-fold and incubated at 370C in the presence of 0.5 mg of amyloglucosidase and 0.05 M-acetate buffer (pH 5) in order to convert all glycogen into glucose. Glucose was measured by glucose oxidase (Hugget & Nixon, 1957). For ultrastructural analysis, liver samples were fixed for 2h with OS04 (2%, w/v) and 0.05 Mpotassium ferricyanide in 0.1 M-phosphate buffer, pH 7.1, gradually dehydrated with ethanol, rinsed twice in epoxypropane and embedded in Epon (Luft, 1961). Ribbons of ultrathin sections of grey-to-silver interference colour (about 40nm thick) were stained with both lead citrate and uranyl acetate. Five series of such ultrathin sections were taken; each ribbon was separated from the preceding one by a section about 5,um thick. In each ribbon, a single section was examined with a Philips EM 301 microscope, and two to four micrographs were taken. These micrographs were developed on transparent polyester sheets (Gevaline Ortho 71 PM, Agfa-Gevaert, Mortsel, Belgium), at a magnification ranging from 39000x to 47000x. This value was accurately calculated with a grating replica (E. F. Fullam Inc., Schenectady, NY, U.S.A.). Morphometry The size and number of glycogen profiles (alpha particles) were measured on the transparent sheets with a Zeiss TGZ3 particle size analyser. The size distribution of glycogen profiles in section refers in fact to the size of the virtual envelope, of circular shape, which can be drawn around each profile. This allows the treatment of particles as spheres in the subsequent calculations. It should be clear that this is not an approximation of the shape of the particles but rather a question of definition of their size, which facilitates the mathematical procedures by introducing the triple symmetry. In order to control the accuracy of the measurements, a few micrographs were also enlarged up to 160000x and contours of glycogen particles were drawn. Size distribution of these drawings was analysed with a Quantimet 720 apparatus (Cambridge Instruments, Cambridge, U.K.) on line to a PDP 11/10 computer (Digital Equipment, Galway, Ireland). The size histograms of glycogen profiles given by the two methods were concordant. In liver specimens containing more than 2.5% of glycogen, the alpha glycogen particles were so densely packed that determination of their individual limits became unpracticable. In livers containing less
than 0.3% glycogen, the clustered distribution of the polysaccharide not only between different areas of the lobules, but also inside the cell, rendered the analysis unreliable because of the scarcity of
particles in many cell profiles. Computation
The mathematical problem in the computation of the number and of the size of spherical particles from measurements of profiles stems from the fact that particles are sectioned at different levels and, therefore, that their apparent diameter in the two-dimensional sample is not their true size. Wickseli (1925) has developed a calculation procedure which takes this fact into account. Such an analysis is presented in Fig. 1. It is obvious that the largest profiles observed in the experimental size distribution histogram represent equatorial sections through the largest glycogen particles; the abundance of these particles can thus be computed. It is then possible to calculate the contribution of these large particles to profile classes of smaller size. Subtracting this distribution from the experimental histogram yields a new distribution one class shorter, on which the same procedure can be applied. By repeating the same operation with classes of particles of progressively smaller size, one gets a size distribution which characterizes completely the distribution of radius and volume in the population. These calculations were performed on a PDP 11/10 computer using the program developed by Baudhuin (1974). An example of such a computation is given in Fig. 1. As the fractional area of profiles in sections is equal to the fractional volume of particles in the three-dimensional sample, one gets an evaluation of the number of particles per unit volume by dividing the total volume of particles by their average volume. The internal reproducibility of the results was checked by comparing the data obtained at the analysis of separate micrographs from the same liver in samples of about 200 profiles. The coefficient of variation (standard error/mean) of the mean radius and volume of the particles did not exceed 2.5 and 17% respectively. Another factor likely to affect the validity of our results is the evaluation of the thickness of the sections, which is of the order of the size of the beta particles. Assuming two extreme values, 20 and 80nm, for the thickness of the sections the calculated radius of the particles and the estimation of their mean number per unit volume changed only by 1.5 and 20% respectively. The classical value of 40nm was subsequently adopted in the computations. Morphometric analysis performed on the same sample by three different operators yielded the same mean diameter and number of glycogen particles, within the range of statistical variations.
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Glycogen in liver Source ofchemicals Amyloglucosidase from Aspergillus niger, OS04, potassium ferricyanide, lead citrate and uranyl acetate were purchased from Merck (Darmstadt, Germany). Glucose oxidase and peroxidase type II were from Sigma and Epon 812 was from Ladd Research Industries Inc., Burlington, VT, U.S.A. Results
Morphometrical analysis Examples of the size distribution analysis obtained by application of Wicksell's (1925) procedure are presented in Figs. 1 and 2. We have collected in Table 1 the parameters of the distributions together with the other results of the morphometrical analysis. In this Table, three livers (1, 4 and 5) were taken in the course of intense glycogen degradation (about 2 g degraded/h per lOOg of liver), whereas the other two were synthesizing the polysaccharide at maximal rate (about 1g synthesized/h per lOOg of liver). The mean particle volume tended to increase with glycogen concentration, but this increase was only 1.8-fold as opposed to a 7-fold difference in glycogen concentration. The largest variations were observed for the number of particles per unit volume, although the data of Table 1 do not suggest a simple proportionality between this parameter and the total glycogen content of hepatocytes. It is important to note that the true statistical mean volume given in this Table can be largely different from the volume of the sphere with a radius equal to the mean radius. Mathematical modelling A simple mathematical model can fit the data of Table 1 in order to account for the evolution of the number and of the average particle volume, as a function of the glycogen concentration in hepatocytes. The basic assumption of this model is the occurrence of a size limit for the alpha particle. Hence, we assume two populations of glycogen particles. The first one is made of growing particles, still associated with glycogen synthase molecules; their number is limited by the number of glycogen synthase molecules available and they are the only particles present at low glycogen concentration. The size of an alpha glycogen particle is limited to a maximal value; when this maximal volume is attained, the particle is completed, glycogen synthase molecules are released and become available to start other particles. These completed particles form the second population; their number is in principle unlimited. The average volume of a particle in this second population corresponds to the maximal volume of an a particle, V. Such a model can be represented by the following equation: (1) nv = nt35 + (n-n')V Vol. 209
E 200 z
e
40
20
0
20
40
60
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Radius (nm) Fig. 1. Example ofsize distribution analysis The upper graph illustrates the distribution of glycogen profiles in a sample of a liver containing 0.81g of glycogen/lOOg. The total area of sections through hepatocytes analysed was 675 pm2. The sum of the white and black areas represents the crude experimental data as yielded by the particle size analyser. The sum of the white and shaded areas represents the distribution of profiles in a infinitely thin section, as given by the Wicksell (1925) calculation. The black area corresponds to the correction for the thickness of sections. The lower part of the Figure shows the size distribution of glycogen particles. Results are given as statistical frequencies, i.e. number of individuals in each class divided by the width of the class.
where n is the total number of a-particles per ml, v is the average volume of an a-particle in the total population, n' is the number of growing a-particles and vg is the average volume of growing particles. In this equation, iv has to be evaluated. If the growth rate of this particle mass is a constant as a function of time, v will tend toward V/2. We have attempted to fit a function assuming that this limit value is attained exponentially as a function of the fractional
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P. Devos, P. Baudhuin, F. Van Hoof and H. G. Hers
0
20
40
80 0
60
20
60
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Radius (nm)
Fig. 2. Size distribution ofglycogen particles in livers with various concentrations of the polysaccharide The particle size histograms were obtained by application of Wicksell's (1925) procedure to the experimental profile size histograms. Values on the upper right corner of each panel give the concentration of glycogen in hepatocytes (g/lOOg). The parameters of these distributions are included in the mean values given in Table 1.
Table 1. Results of morphometrical analysis The section area analysed in each sample was approximately 500.um2; for glycogen-poor livers the area examined was extended in order to have measurements on more than 2000 profiles. In column (1) the result of the chemical determination on total liver was divided by 0.865; this value represents the fraction of liver volume corresponding to hepatocytes (Weibel et al., 1969). Columns (2), (3) and (4) are obtained by the application of Wicksell's (1925) transformation on the experimental profile size distribution (see the Material and methods section). These values are the average of two distributions evaluated independently for each glycogen concentration. 101-2 x concentration of Glycogen concentration in hepatocytes Mean radius of 10"5 x mean volume particles in hepatocytes Fractional volume of particles (ml) particles ± S.E.M. (nm) (g/lOOml) in hepatocytes (number/ml)
(1)
(2)
(3)
(4)
(5) = (3) x (4)
0.36 0.81 1.28 2.09 2.55
30.8 + 7.9 31.4 + 5.4 36.2 ± 6.4 38.4+ 10.1 37.0+ 10.5
0.164 0.145 0.236 0.289 0.267
24.5 57.7 79.0 104.5 95.0
0.0040 0.0084 0.0186 0.0302 0.0254
volume, nvt. The influence of the exponential term was however negligible for fractional volumes larger than 0.002. Hence, for the sake of simplicity, it was assumed that vi3 = V/2 for all values of nvt.
Eqn. (1) thus becomes: V nv = n'-+ (n-n')V 2
(2) 1983
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Glycogen in liver
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Fractional volume
Fig. 3. Abundance of alpha particles as a function of the volumefraction occupied by glycogen Each point is the, average of two experiments, in which the number of particles and the fractional volume were determined by morphometry. The line corresponds to the model described by eqn. (3) with n' = 49 x 1012particles/ml and V=0.36 x 10-15 ml.
Fig. 4. Average volume ofalpha particles as afunction of the volumefraction occupied by glycogen Each point is the average of two experiments, in which average particle volume and fractional volume were determined by morphometry. The curve corresponds to the model described by eqn. (3), with n' = 49 x 1012particles/ml and V= 0.36 x 10-15 ml.
The relation between the number of particles and the fractional volume (nv) is easily deduced from this equation: (nvi) n' n= V+-2 (3)
content per ml, measured chemically, should in principle yield a direct estimate of the 'specific volume, provided a correction is introduced for non-hepatic cells as shown in Table 1. An average value of 1.22ml/g is then obtained. It corresponds to the apparent V'olume for glycogen particles as stained in sections and considered as spheres; this is of course different from the true specific volume of hydrated glycogen particles, which should be up to three times greater (Fenn, 1939). More annoying is, however, the fact that the apparent specific volume is rather different from one experiment to the other: it varies between 1.04 and 1.5. This may reflect either a lack of reproducibility of the staining procedure, or a heterogeneity of the liver cells, which would affect mostly the morphological analysis. Whatever the reason, it was found preferable to use for each experiment the apparent specific volume determined experimentally to deduce the mass of a single particle, which can be expressed in daltons by multiplying by Avogadro's number. Estimate's of the average molecular weight can be found in Table 2. In order to evaluate the dispersion of the distribution, we have performed the same computation for the smallest and largest particles of the distribution. An average maximal molecular weight can'also be estimated from the maximal particle volume estimated in the mathematical model presented in the previous section. Assuming the apparent specific
V
2
Fig. 3 illustrates this linear relation for the experimental values of n and nv given in Table 1. The line which fits best the data is obtained with n' = 49x 102nml-' and V=0.36x 10-l5ml. An equation giving the relation between the average volume of particles and the fractional volume of glycogen, which are both experimental data obtained by morphometry, can easily be derived from eqn. (3). Substituting (nv)/V for n in eqn. (3) and rearranging yields: V
1 n'V 1 +2 (nv)
(4)
This relation is graphically expressed in Fig. 4 using the same parameters as for Fig. 3. Distribution ofmolecular weight A distribution of particle volume can easily be deduced from the size distribution analysis. Hence, provided the apparent specific volume of glycogen is known, the molecular weight can be estimated. In fact, dividing the fractional volume by the glycogen Vol. 209
164 Table 2. Molecular weight ofalpha particles In column (1) the specific volume is obtained by dividing the fractional volume by the glycogen content per ml (see Table 1). The values in columns (2) are calculated by multiplying the alpha particle mass by the Avogadro number. The mass of an alpha particle is obtained by dividing its volume by its specific volume. 10-6 x molecular mass (Da) Specific volume of glycogen (2) A (ml/g) (1) Average Range 1.111 88.9 4.8-1582 84.2 1.037 17.8-580 1.453 98.0 8.7-504 1.445 120.8 8.9-565 161.4 8.5-880 0.996
volume of 1.22ml/g, a maximal volume of 0.36 x 10-15ml corresponds to a molecular mass of 178 x 106Da. Discussion The sequential synthesis and degradation of glycogen in the liver The main conclusion arising from this work is that, within the range of concentrations that have been explored, our results are compatible with a model implying a size-limited population of alpha particles, and are in opposition with a numberlimited population kinetics. This latter model would indeed result in very different theoretical relationships in Figs. 3 and 4. Indeed, the number of particles would be constant in Fig. 3, and the data would be grouped along one horizontal. In Fig. 4, the average particle volume would be directly proportional to the fractional volume, with a proportionality factor equal to 1/n. The dispersion of experimental points is important and is probably to be accounted for mostly by the uneven distribution of glycogen within hepatic lobules (Welsh, 1972) as well as within hepatocytes (Cardell, 1973 and the present work). Notwithstanding these variations, our data allow a clear choice between the two models described above. It therefore appears that, in the course of glycogen synthesis, most of the pre-existing a particles are not further enlarged by the addition of new beta particles but that alpha particles are formed de novo. Conversely, glycogenolysis occurs by destruction of one alpha particle after the other. These conclusions are in good agreement with our previous observations (Devos & Hers, 1979), which have shown that newly added glycosyl units are evenly distributed in inner and outer chains of the glycogen particles. On basis of the biochemical results,
P. Devos, P. Baudhuin, F. Van Hoof and H. G. Hers
increase in glycogen content of the liver was proposed to occur by addition of new particles. Our present approach yields a new argument in favor of this hypothesis.
The molecular weight of alpha particles and related parameters Estimates of the molecular weight distribution of alpha particles have been obtained previously by sedimentation analysis (Parodi, 1967; Geddes et al., 1977). As pointed out by Geddes et al. (1977) such techniques yield weight average parameters rather than the true, arithmetic, statistical mean given here. Although these authors do not state a value for the average molecular weight of the glycogen content of the liver, our average molecular weight seems to be in reasonable agreement. This is also true for the dispersion observed (see range in Table 2). This is important, for the problem of aggregated particles, which is difficult to control in sedimentation experiments, can be easily avoided by the morphological approach. The size or molecular weight limit presented here applies to the average particles. Our model does not take into consideration the heterogeneity of the particles, which stems probably from a continuous modification of the affinity of enzymes for the particles, as a function of the latter rather than from an all-or-none phenomenon, such as assumed here. Our data bring also information on the relation between alpha and beta particles. Assuming a molecular weight of 4 x 106 for a beta particle (Revel, 1963), it can easily be seen that an average alpha particle contains between 20 and 40 beta particles. Since the concentration of glycogen synthase in rat liver has been estimated to be 0.22pM (Devos & Hers, 1979) or 132 x 1012molecules/ml, this value is of the same order as our estimate of the number of growing particles in the liver. In view of the approximation involved, the agreement may be considered as fairly satisfactory. This work was supported by N.I.H. grant AM 9235 and the Fonds de la Recherche Scientifique Medicale.
References Barber, A. A., Harris, W. W. & Anderson, N. G. (1966) Natl. Cancer Inst. Monograph. 21, 285-302 Baudhuin, P. (1974) Methods Enzymol. 32B, 3-20 Cardell, R. R., Larner, J., Jr. & Babcock, M. B. (1973) A nat. Record 177, 23-38 Devos, P. & Hers, H. G. (1979) Eur. J. Biochem. 99, 161-167 Drochmans, P. (1960) J. Biophys. Biochem. Cytol. 8, 553-558
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Glycogen in liver Drochmans, P. (1962) J. Ultrastruct. Res. 6, 141-163 Fenn, W. 0. (1939) Biochem. J. 128, 297-307 Geddes, R. & Stratton, G. C. (1977) Carbohydr. Res. 57, 291-299 Geddes, R., Harvey, J. D. & Wills, P. (1977) Biochem. J. 163, 201-209 Hugget, A. St. G. & Nixon, D. A. (1957) Biochem. J. 66, 12P Luft, J. H. (1961) J. Biophys. Biochem. Cytol. 9, 409-414 Madsen, N. B. & Cori, C. F. (1958) J. Biol. Chem. 233, 1251-1256
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165 Parodi, A. J. (1967) Arch. Biochem. Biophys. 120, 547-552 Revel, J. P. (1963) Histochem. Soc. Symp. Application of Cytochemistry to Electron Microscopy, pp. 104-114 Revel, J. P., Napolitano, L. & Fawcett, D. W. (1960) J. Biophys. Biochem. Cytol. 8, 575-589 Weibel, E. R., Staubli, W., Gnagi, H. R. & Hess, F. A. (1969) J. Cell Biol. 42, 68-91 Welsh, F. A. (1972) J. Histochem. Cytochem. 20, 112-115 Wicksell, S. D. (1925) Biometrika 17, 84-99
