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ISSN 0022-0930, Journal of Evolutionary Biochemistry and Physiology, 2010, Vol. 46, No. 6, pp. 613—621. © Pleiades Publishing, Ltd., 2010. Original Russian Text © G. A. Savost’yanov, 2010, published in Zhurnal Evolyutsionnoi Biokhimii i Fiziologii, 2010, Vol. 46, No. 6, pp. 514—521.

MORPHOGICAL BASICS FOR EVOLUTION OF FUNCTIONS

Modeling of Processes of Specialization and Integration As a Basis for Development of Multicellularity G. A. Savost’yanov Sechenov Institute of Evolutionary Physiology and Biochemistry, Russian Academy of Sciences, St. Petersburg, Russia E-mail: [email protected] Received June 4, 2010

Abstract—The formalized description of the procedure of division of labor as the most important invariant of progressive development is presented. The concept of histion is introduced—the elementary unit of multicellularity that arises as a result of such division and represents the so far overlooked independent level of biological organization. Based on the division of labor there is proposed the theory of progressive development, which allows calculating the composition and structure of multitude of histions and constructing their model. It has been shown that development of these units obeys the periodic law and their classification looks like the periodic table whose parameters have biological meaning and are useful for measuring progressive development. The obtained results constitute the basis for the nomogenetic theory of the progressive development of multicellular organisms. DOI: 10.1134/S0022093010060101 Key words: division of labor, progressive development, invariant, multicellularity, histions, modeling, natural system, periodic table, nomogenesis.

INTRODUCTION One of tasks of developmental biology problem is development of such theory that would allow from uniform positions consideration of progressive development of multicellularity in phylo- and ontogenesis (evo-devo) as well as its prediction and measurement. To create such a theory, it s necessary to identify the most essential features of development and to give their formalized description by the example of an idealized model; for this it is necessary to use repeatedly the comparison of development of systems of different nature—biological, social, technical, etc. [1, 2]. This comparison allowed revealing the major invariants of develop-

ment, i.e., the common features characteristic of development as such. One of the main invariants of this kind is specialization and integration of elements as division of labor between them. This is really an interdisciplinary procedure that occurs in developing systems of quite diverse nature. There has long been noted the necessity of a formalized description of the division of labor by the example of development of an idealized system, whose performance is necessary to be carried out without taking into account the peculiar characteristics of labor and mechanisms of its division [3–5]. However, this work had not yet been performed, and understanding of the division of labor remains at qualitative and meaningful levels. 613

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Fig. 1. Scheme of elementary developmental acts. The upper line—a rise of the number m of aromorphoses and of memorizing of their sequence with aid of the priority numbers; the middle line—transformation of organism with m = 5 to the more and more specialized cell A; an increase of the number n of acts of specialization leads to a rise of cellular energidity (or productivity); the lower line—scheme of stages of specialization and integration of cells and of formation of the simplest pentacellular organism.

Beginning from 1973, with blessing of E.M. Kreps and V.V. Menshutkin, we attempted developing the formal language to describe the division of labor in an idealized Metazoa [6–8]. Here, we will present a brief exposure of recent results and will show by the example of the idealized model of elementary unit of multicellularity that the progressive development can be predicted and measured. ELEMENTS OF FORMALIZED LANGUAGE FOR DESCRIPTION OF DIVISION OF LABOR Main Concepts and Definitions Any division of labor implies the presence of its list as well as the set of its performers. It is these notions that will be accepted as the initial ones. List of labor, the set of functions providing the existence of an organism: protection, nutrition, excitability, motility, reproduction, etc. Since so far there is no commonly accepted list of organism functions, we will set this schedule formally as a set L ∋ {a, b, c, d, e…}, where a–e are the aboveenumerated functions.

Performers of functions in our case are the cells that will be indicated in figures by circles. Cells performing the complete set of functions are unicellular organisms, while those with incomplete set are specialized cells that in total provide the complete set of functions; let us call them complementary. Initial organism. Let us take as the reference point the monoergidic unicellular organism performing all functions autonomously and only for itself. The mode of autonomous performance (MAP) of functions we will also consider initial. The portions of functions performed by organism in its life cycle we will consider elementary. Such portions we will designate by lowercase letters at circles (Fig. 1, organism no. 0 in the upper part of the figure). Then, L ∋ {a, b, c, d, e…} is a set of elementary functions. Sequence of involvement of functions into division can differ; some functions can be interconnected into the synergic blocks or, on the contrary, can be incompatible. However, since the knowledge about this and about the commonly known sequence so far are absent, we will consider the functions to be involved into the procedure of division gradually in the above presented order.

JOURNAL OF EVOLUTIONARY BIOCHEMISTRY AND PHYSIOLOGY Vol. 46 No. 6 2010

MODELING OF PROCESSES OF SPECIALIZATION AND INTEGRATION

Division of functions occurs with aid of elementary acts of three kinds. Act of the first kind consists in making decision about acceptability of specialization of some particular function, which is accepted separately for each function. Formally, this act consists in conversion of the chosen function from MAP to specialization-accessible mode (SAM). Let us write it as MAP → SAM. We will designate functions in this mode by capital letters at circles (Fig. 1, organisms no. 1—5 in the upper line). Since these acts create only potencies for development, they (the acts) can be related to aromorphoses (anageneses) in phylogenesis or determinations in ontogenesis. The number of functions, for which decision of separation was made (converted to SAM), is an important parameter of organism and will be designated by the letter m. In principle, this parameter is experimentally determinable. System of memorizing of development acts of the first kind. Realization of such acts for each function is counted and memorized by the organism in such a way that the organism can differentiate the order of involvement of functions in development. For example, the organism with m = 1 (Fig. 1) realized the act of development, which is designated by the unit over the capital letter. Conversion of each consecutive function to SAM is written in a similar way, with unity also being added to all functions previously converted to SAM (Fig. 1, organisms with m = 1–5). This system of recording of developmental acts allows determining their number for each function (i.e., to remember its “phylogenetic age”) and ranging functions by this parameter. Let us call the number of developmental acts of each function its priority number, or the number of potencies. An important property of the priority numbers is their additivity. Owing to it, it becomes possible to determine the total number S of the priority numbers (and, accordingly, of potencies) for all functions: it results from addition of the priority numbers of individual functions. Thus, the organism with m = 1 presented in Fig. 1 in the upper line has realized only one developmental act, the organism with m = 2 realized 2 + 1 = 3 acts, and the organism with m = 5 had 5 + 4 + 3 + 2 + 1 = 15 developmental acts. Obviously, the number S

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of these developmental acts represents the sum of members of the arithmetic progression with difference of the unit, which in our case is as follows: ,

(1)

where m is the number of functions in SAM; the same number serves the priority number of the most ancient function and it also is the last member of the progression. The sum of its members can easily be found for the list of functions of any value. Developmental acts of the second kind consist in realization of the obtained potencies by the way of cellular specialization. The organism makes a choice which function it will perform as a specialist personally and which functions can be entrusted to partners. This is achieved by conversion of functions (starting from the most ancient one) from SAM into the mode of realized specialization (MRS). Let us write it as SAM → MRS. Functions in MRS are designated by capital letters in circles. The number of functions submitted to specialization (converted to MRS) is the second important parameter of an organism and will be designated by the letter n. This number also determines the amount of specialized cells of the organism and therefore can easily be found experimentally. The meaning of specialization is shown in Fig. 1 in the middle line of the figure. Formally, such specialization consists in an increase of the number (polymerization) of identical letters inside the circles and in a decrease of their set at the circles. The measure of specialization coincides with the value n. The biological meaning of polymerization consists in that it can be compared with the increase of cellular energidity or productivity for this function. As a result of the specialization, the cell loses its status of the organism and becomes the progressively narrow and productive specialist. Specialization in other functions occurs similarly. Since the sequence of specializations of functions is regulated by their priority numbers, no special system for counting of specialization is needed. Therefore, they are not memorized and not summated. Developmental act of the third kind is integration and the appearance of histions. Since spe-


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cialized cells already cannot live independently, they are combined with complementary partners for exchange of results of labor. Formally, such combination is designated by arrows or fragments between circles, which is shown in the lower part of Fig. 1 by the example of development of organism with m = 5. We call such combination the integration. The processes of specialization and integration are realization of potencies acquired in the first act and, therefore, can be compared with idioadaptation in phylogenesis and differentiations in ontogenesis. In reality, integration can be realized by metabolic cooperation, exchange of services as well as by other cellular interactions. The cell groups resulting from such integration represent elementary units of multicellularity called histions [7]. Their number of cells is obvious to coincide with n. The meaning of zeros over some functions in this mode will be disclosed later. Since alongside with progressive development there also exists the regressive one, we will settle that the considered developmental acts are reversible, i.e., MAP ↔ SAM ↔ MRS. Algorithm of Development Let us now determine the sequence of realization of the acts described as three rules. (1) Gradualism: functions in the course of the separation process are involved one by one. (2) Repeatability: sequence of specialization of functions follows the sequence of their aromorphoses (i.e., the most ancient functions are specializes the first, whereas the youngest are the last). (3) Alternation of developmental acts: aromorphosis of each subsequent function occurs only after realization of all idioadaptations that became possible as the previous aromorphosis (i.e., after realization of all previously acquired potencies). This algorithm is characteristic of the slowest and the most consecutive variant of development of real organisms (of the anaboly type), which we consider valuable as it allows looking over all possible variants of division of labor. It is to be noted that the faster algorithms of development with incomplete searching for variants can also be formulated.

Postulates Regulating Development of Histions and Their Structure Let us start with the simplest case when all cells of our organism exist under identical environmental conditions and under the same requirements established to them. We will formulate for these conditions the most complete and rigid set of restrictions whose modification and attenuation can provide variants of histions able to develop under different conditions. (1) Initial for development are elementary unicellular monoergidic organisms. (2) In the process of development, the qualitative composition and integrity of the set of functions L remains unchanged. This postulate reflects constancy of the main attributes of life. (3) In the process of development, the cellular nature of performers of functions is preserved and only the number of cells and their specialization are changing. (4) Provision of all organism cells with the complete set of functions L is preserved, while only the ways of such provision change by the autonomous performance of functions or integration of cells with complementary partners. (5) The total number of functions performed by each cell remains constant (Fig. 1, the middle line). (6) All specialized cells provide the equal number of partners and thereby make the equal contribution to the histion survival. (7) Each cell can be specialized for performance of only one certain function. (8) All modes of functions in specialized cells are technologically compatible and can be freely combined. (9) Integration occurs only with mutual benefit. (10) The cells are integrated without intermediaries, i.e., by direct contact according to the principle of “you to me, I to you.” (11) All organism cells are of the same origin, i.e., are descendants of the common ancestor (in the multicellular organism—zygotes). These rules give some idea as to of which nature can be the laws regulating development of real organisms. Now let us consider what provides the performed formalization.



RESULTS OF PROGRESSIVE DEVELOPMENT OF HISTIONS

or N = S + n,

Rise of total energidity E of histion is the main result of division of labor. This energidity is the sum of energidities of all its cells. By the example of histion presented in Fig. 1, the lower line on the right, it can easily be seen that its five five-energidic cells will provide the total energidity E equal to 5 × 5 = 25 elementary functions. In general terms, the value E depends on the number of specialized cells as follows: E = n2,

(2)

from which it is seen that with rise of the number of cells of histion, its energidity increases at the markedly progressive rising rate. The meaning of this energidity is that it shows how much the total number of elementary functions in MRS in histion increased as compared with the monoenergidic original organism. It is the rise of energidity of an organism, which is the gain, for which the division of labor is realized and which provides the ground of the biotechnical progress. Measure of Progressive Development of Histion with Parameters m and n As such measure, we are proposing the total number of acts of its development, which is composed of the number of all priority numbers of functions in SAM and the number n of functions converted into MRS. The first number in correspondence with (1) for any m can be found as the sum of members of the arithmetic progression from 1 to m with the difference of unit. Experimental determination of the value m so far represents some difficulties, whereas the value n coincides with the number of specialized cells, which can easily be determined experimentally. Then the histions presented in Fig. 1, the lower line, from left to right, were created for 15, 16, 17, 18, 19, and 20 developmental acts, from which 15 correspond to the priority numbers, while others—to specializations. Similarly determined is the integral number N of developmental acts of other histions. In general, this number can be written as follows:

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(3)

where N—the total number of developmental acts of histion, m—the number of functions in SAM or the priority number of the most ancient function, n—the number of specialized cells of histion (the experimentally determined parameter). With aid of this equation, it can easily determine the total number N of developmental acts for the set of functions of any value. This number is an important characteristic of histion: it serves the integral measure of its progressive development. The absence of such measure as an important gap was indicated by Timofeev-Resovskii [9]. Periodic Table of Histions The found parameters of histions have allowed revealing an important peculiarity of their development: if histions are arranged in the ascending order of the total number N of developmental acts, it turns out that the structure of histions fits the periodic law, according to which with monotonous increase of the total number of developmental acts the structure of histions is repeated periodically. Period of their unicellular state also is repeated regularly. By grouping histions in lines with equal number of functions in SAM and in columns with equal number of functions in MRS (or, which is the same, with equal number of specialized cells), we obtain a possibility to present the multitude of histions in the form of two-dimensional periodic table (Fig. 2). However, if in the accepted algorithm to modify the second rule and to accept the inverted or any other order of specializations (as a result of redistribution between cells of the priority numbers), this will lead to a variation of composition of histions. For example, the histion in the cell no. 3 of the periodic table will be able to accept the composition AB, AC, and BC. Such histions with a precision up to isomorphism preserve the initial structure and therefore remain located in the same cell of the table, which becomes threedimensional. In the general view, the number H of possible isotopes for each cell of the table can be written as follows:

H = Cnm,

(4)

i.e., this number is equal to the number of combi-


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Fig. 2. Periodic table of histions with various variants of division of functions between cells. Explanations in the text.

nations from m by n, where m—the number of the line and n—the number of the column. The biological meaning of main parameters of periodic table, i.e., the number of lines and columns, is obvious and available for quantitative characteristics of development. Thus, number of lines m shows the number of functions submitted to aromorphoses as well as the priority number of the most “ancient” function. The number of columns n shows the number of specialized functions and accordingly, the number of specialized cells of histion. The total number N of developmental acts of histions is designated by the number of the cell of the table, which is given in its upper left corner,

while the number of isotopes is presented in the right lower corner of the cells. The population of these numbers shows that the formal basis of the three-dimensional variant of the table is the Pascal’s triangle, or the table of coefficients of Newton’s binomial expansion. It is worth noting that physiological coupling of functions can decrease essentially the number of their realized combinations Hreal. By comparing it with the maximal number H of theoretically possible histions, it is possible to evaluate the physiological coupling of the functions qualitatively. As a result, the obtained parameter will be the integral measure (O) of such coupling:



.

(5)

By analyzing the specifics of functions combined in MRS, the integral evaluation of their physiological connection can be added by its differential evaluation. The Appearance of Stem Cells As an Inevitable Result of Division of Labor An important novel result following from the table is explanation of the cause of separation of histion cells to stem and specialized cells. Let us make sure in this. Each line of the table begins with an unspecialized unicellular histion with the complete set of priority numbers and location in the zero column. With movement along the line to the right, number of specialized histion cells increases. However, since the sum of priority numbers remains constant, their amount is not sufficient for all, and a part of functions in the newly appearing cells remains without priority number, i.e., without generative potencies. For obviousness, such functions are designated by zeros. As a result, the complete set of potencies is preserved only in initial unicellular organisms in columns nos. 0 and 1 of the periodic table. These histions correlate to unspecialized ancestors in phylogenesis and to zygotes in ontogenesis. Beginning from the stage of bicellularity, proportion of cells with priority numbers progressively decreased, while proportion of cells with zeros increases. Cells with non-zero functions are more special—the stem cells, while cells with zero functions—the working cells without generative potencies. Thus, it can be said that all cells of the new type arising at each consecutive step of development of histion appear as a result of asymmetric mitoses only in the stem cells, and the value m in this case can also determine the permitted number of asymmetric cell divisions. Thus, the general “stemity” becomes impossible. Thereby we have theoretically explained for first time the cause of the appearance of separation of stem and nonstem cells. Like the measure of development, it has become possible only owing to the formal approach to description of the procedure of division of labor. From this, it can be concluded that such quality is to be intrinsic

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to any system developing on the basis of division of labor. General Evaluation of Periodic Table of Histions and Its Comparison with Biological Reality Since character of functions and sequence of their involvement in development were indicated conventionally, we cannot expect that the table would reflect development of any particular group of organisms. However, it reflects well its general tendencies. Thus, both for the table and for the real development of organisms, characteristic is the presence of unspecialized ancestors or stem cells corresponding to histions of the zero column and providing the polyphyletic beginning to all major stems of life. As histions move along the lines to the right, proportion of specialized cells rises, whereas that of stem cells falls, with a narrowing of the set of their potencies. The lines are completed by the histions realizing all potencies for development, whose limit is determined by the number of the line. After reaching the limit, all specialized cells of the histion are lost (die) and specializations are forgotten. In its historic development, histion acquires again the unicellular state full of potencies, inherits all priority numbers of its predecessors, and supplements them by one more number at the expense of the next aromorphosis. As a result, it shifts to the beginning of the next, the longer line and becomes an unspecialized ancestor. At these moments it becomes sensitive to environmental effects that can affect the choice of functions involved in development. Changes of their set can be compared with archallaxes. Then, there begins realization of acquired potencies and the developmental cycle is repeated. Environment cannot change anymore the set of functions in SAM, but only can affect the order of priority of their specializations (whence, non-adaptive specializations, preadaptations, and neotenies). Besides, due to its three-dimensionality, the table reflects the ability of such trajectories of development, in which the organism passes a part of the way along the line, then deviates from it due to realization of isotopic variants and, then moves along the line again with return (or without it) to the initial line. Such trajectories can be compared with deviations and coenogeneses. The table also


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provides transition from diachrony to synchrony, from incomplete-term histions to full-term ones, which is also characteristic for reality. Lastly, development of histions in the framework of each line is characterized by mosaicism, because their function is performed in various modes and, therefore, is characterized by a combination of progressive and archaic features. The cell specializations with respect to ancient functions occurs gradually, whereas to the new ones—by jumps. For example, specialization of the cell by the function A reaches its highest level during five steps, while the cell E turned out to be at this level from the moment of its appearance. In ontogenesis, repetition of development occurs in the framework of the same line and no new potencies are acquired. However, the randomness caused by fusion of gametes in the sexual process makes possible the redistribution of priority numbers among the cells (i.e., a change of set of their potencies) with preservation of constancy of their sum. This can be manifested in some variability of development, which is restricted to transdeterminations or also to changes in the order of specializations. Thus, in the frameworks of each line, histions are born, reach flourishing, and die. This makes their development cyclic, and within the cycles provides directivity, parallelism, and finality with the extinction of specialized members. The same properties are characteristic of historic development and real individuals as well as of species and the larger taxons. Examples of Measurement of Progressive Development of Histions The developed here approach makes it possible to determine the ordinal numbers in histions of real organisms and, thereby, to provide a tentative evaluation of degree of their development. In correspondence with (3), measurement of development necessitates information about the number m of functions submitted to aromorphoses and about the number n of specialized cells of histion, i.e., the numbers of its line and column. However, since in practice it is easy to find only the parameter n (by calculation of the number of types of the organism specialized cells), whereas to establish

directly the number m of functions submitted to aromorphoses is more complicated, this number can be roughly determined on the basis of statement that m = n within the limit. Let us now consider how the serial number of histion can be determined in a human as an example. Histologists are known to distinguish in the human body more than two hundred types of different cells [10]. Let us round this number to two hundred and take in the first approximation that m = n. By increasing the number of lines and columns in the table, we place the human histion in the cell whose number of line and column will have nos. 200. From this it follows that its energidity in correspondence with (2) is equal to 40 000 and the isotopic diversity possible for it in the end of the line is 1. In correspondence with expression (3), we find that in total of all functions, histion realized 20 100 acts of aromorphoses. Adding 200 specializations to this, we find that the total number of acts of its development (and accordingly, the ordinal number in the table) is 20 300. Similarly, it is also possible to measure development of histions with another number of specialized cells. The meaning of the number of aromorphoses consists in that it shows how many developmental acts from the path previously passed by the taxons is stored in the genetic memory of the organism and is inherited, while the number of specializations shows the number of developmental acts that are not a subject for such a transfer. Also solvable is the reverse problem, such as from the given number to restore composition and structure of histion and to determine the number of its aromorphoses and specializations [7]. CONCLUSIONS Thus, the obtained periodic table emerges from the very essence of the procedure of division of labor, and its construction has become possible owing to the performed formalization. The table is the natural parametric system of histions—elementary units of multicellularity. It explains theoretically for the first time the inevitability of the appearance of stem and nonstem cells. The main parameters of the table (numbers of lines and columns) can be determined experimentally, while other param-



eters (the priority and ordinal numbers) can easily be calculated and they are suitable for quantitative measurement of the progressive development. These parameters allow meaningful interpretation in terms of physiology and genetics and raise the problem of deciphering molecular mechanisms of the priority numbers. This distinguishes favorably the table of histions from other versions of the periodic table [11]. Position of histions in the table provides unanimously all their properties, the table being able to predict development and to measure it. It is important to emphasize that disposition of histions in the table in the general case does not reflect genealogy, while their neighborhood does not indicate at all their relationship. It indicates merely the space of logic probabilities. Trajectories of development and sequence of the appearance of histions can be different. The presence of the parameters that do not depend on such these trajectories also distinguishes the table from the currently popular genealogic systems. The table parameters can be recommended for construction of natural systems and real organisms as well as for evaluation of degree of their development. In conclusion, we are to note that if to soften rigidity of the accepted postulates, the diversity of histion structures increases essentially and there appear their extractable versions [7]. It is clear obvious that diversity of probable trajectories of development also increases significantly. It is to be emphasized that histions are not only the elementary units of multicellularity. As recently demonstrated, they are also the elementary morphofunctional units of tissues, which are to be considered as polymerized histions [7]. Thus, histions represent a new, missed so far level of biological organization located between the cell and tissue levels. Further analysis of the appearance and development of histions as well as of their polymerization with formation of cellular networks opens a perspective of development of the nomogenetic theory of progressive development of real organisms and their tissues as well as of finding parameters for its measurement.

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