Biological Applications of Physical System

It should have become evident by now that many characteristics of organismic systems, often considered vitalistic or mystical, can be derived from the system concept and the characteristics of certain, rather general system equations, in connection with thermodynamic and statistical-mechanical considerations.

If the organism is an open system, the principles generally applying to systems of this kind must apply to it (maintenance in change, dynamic order of processes, equifinality, etc.) quite ir­respective of the nature of the obviously extremely complicated relations and processes between the components.

Naturally, such a general consideration does not give an ex­planation for particular life phenomena. The principles discussed should, however, provide a general frame or scheme within which quantitative theories of specific life phenomena should be pos­sible. In other terms, theories of individual biological phenomena should turn out as special cases of our general equations. Without striving for completeness, a few examples may show that and how the conception of organism as open chemical system and steady state has proved an efficient working hypothesis in various fields.

Rashevsky (1938) investigated, as a highly simplified theoretical model of a cell, the behavior of a metabolizing droplet into which substances diffuse from outside, in which they undergo chemical reactions, and from which reaction products flow out. This con­sideration of a simple case of open system (whose equations are special cases of our equation [5-1]) allows mathematical deduction of a number of characteristics always considered as essential life phenomena. There results an order of magnitude for such sys­tems corresponding to that of actual cells, growth and periodic division, the impossibility of spontaneous generation (omnis cellula e cellula), general characteristics of cell division, etc.

Osterhout (1932-33) applied, and quantitatively elaborated, the open-system consideration to phenomena of permeability. He studied permeation in cell models consisting of a non-aqueous layer surrounded by an aqueous outer and inner fluid (the latter corresponding to cell sap). An accumulation of penetrating sub­stances takes place within this cell, explained by salt formation of the penetrating substance. The result is not an equilibrium but a steady state, in which the composition of the cell sap remains constant under increase of volume. This model is similar to that mentioned on p. 126. Mathematical expressions were derived, and the kinetics of this model is similar to that in living cells.

Open systems and steady states generally play a fundamental role in metabolism although mathematical formulation has been possible only in simple cases or models. For example, the con­tinuation of digestion is only possible because of the continuous resorption of the products of enzymatic action by the intestine; it therefore never reaches a state of equilibrium. In other cases, accumulation of reaction products may lead to stopping the reaction which explains some regulatory processes (cf. von Bert- alanffy, 1932, p. 191). This is true of the use of depot materials: Decomposition of starch stored in the endosperm of many plant seeds into soluble products is regulated by the need of the grow­ing plant for carbohydrates; if development is experimentally inhibited, the use of starch in the endosperm stops. Pfeifer and Hansteen (quoted from Hober, 1926, p. 870) made it probable that the accumulation of sugar originating from digestion of starch and not used up by the inhibited seedling is the cause for the stopping of starch breakdown in the endosperm. If the endosperm is isolated and connected with a small plaster column, the breakdown of starch continues in the endosperm if the sugar diffuses through the plaster column into a quantity of water, but is inhibited if the column is placed in a small quantity of water only so that the concentration of sugar inhibits hydrolysis.

One field where processes can already be formulated in the form of equations, is the theory of growth. It can be assumed (von Bertalanffy, 1934), that growth is based on a counteraction of anabolic and catabolic processes: The organism grows when building-up surpasses breaking-down, and becomes stationary, when both processes are balanced. It can further be assumed that, in many organisms, catabolism is proportional to volume (weight), anabolism is proportional to resorption, i.e., a surface.

This hypothesis can be supported by a number of morphological and physiological arguments and in simple cases, such as planar- ians, can be partly verified by measurement of intestinal surface (von Bertalanffy, 1940b). If k is a constant for catabolism per unit mass, total catabolism will be kw (w = weight); similar, with η as constant per unit surface, anabolism will be ηs, and weight increase defined by the difference of these magnitudes:

From this basic equation, expressions can be derived which quantitatively represent empirical growth curves and explain a considerable number of growth phenomena. In simpler cases these growth laws are realized with the exactness of physical experiments. Moreover, the rate of catabolism can be calculated from growth curves and comparing values so calculated with those directly determined in physiological experiment, an excel­lent agreement is found. This tends to show, first, that the parameters of the equations are not mathematically constructed entities but physiological realities; secondly, that basic processes of growth are rendered by the theory (cf. Chapter 7).

This example well illustrates the principle of equifinality dis­cussed previously. From (5.13) follows for weight increase:

where E and k are constants related to η and k, and where wo is the initial weight. The stationary final weight is given by w* = (E/k)3; it is thus independent of the initial weight. This can also be shown experimentally since the same final weight, defined by the species-specific constants E and k, may be reached after a growth curve entirely different from the normal one (cf. von Bertalanffy, 1934).

Obviously, this growth theory follows the conceptions of kinetics of open systems; equation (5.13) is a special case of the general equation (5.1). The basic characteristic of the organism, its representing an open system, is claimed to be the principle of organismic growth.

Another field where this concept has proved itself fruitful is the phenomenon of excitation. Hering first considered the phe­nomena of irritability as reversible disturbances of the stationary flow of organismic processes. In the state of rest, assimilation and dissimilation are balanced; a stimulus causes increased dissimila­tion; but then the quantity of decomposable substances is de­creased, the counteracting assimilation process is accelerated, until a new steady state between assimilation and dissimilation is reached. This theory has proved to be extremely fruitful. The theory of Putter (1918-1920), further developed by Hecht (1931), considers the formation of excitatory substances from sensitive substances (e.g., visual purple in the rods of the vertebrate eye) and their disappearance as the basis of excitation. From the counteraction of these processes, production and removal of exci­tatory substances, the quantitative relations of sensory excitation can be derived on the basis of chemical kinetics and the law of mass action: threshold phenomena, adaptation to light and dark­ness, intensity discrimination, Weber’s law and its limitations, etc. A similar hypothesis of excitatory and inhibitory substances and of a dissimilation mechanism under the influence of stimuli forms the basis of Rashevsky’s theory (1938) of nervous excita­tion by electric stimuli, formally identical with the theory of excitation by Hill (1936). The theory of excitatory substances is not limited to sense organs and the peripheral nervous system, but applicable also to the transmission of excitation from one neuron to another at the synapses. Without entering the still unsettled question of a chemical or electrical theory of transmis­sion in the central nervous system, the first explains many of the basic features of the central nervous system compared with the peripheral nerve, such as irreciprocity of conduction, retardation of transmission in the central nervous system, summation and inhibition; here, too, is the possibility of quantitative formula­tions. Lapicque, e.g., developed a mathematical theory of sum­mation in the central nervous system; according to Umrath, it can be interpreted by the production and disappearance of excitatory substances.

We may therefore say, first, that the large areas of metabolism, growth, excitation, etc., begin to fuse into an integrated theoreti­cal field, under the guidance of the concept of open systems; secondly, that a large number of problems and possible quanti­tative formulations result from this concept.

In connection with the phenomena of excitation, it should be mentioned that this conception also is significant in pharma­cological problems. Loewe (1928) applied the concept of the organism as open system in quantitative analysis of pharma­cological effects and derived the quantitative relations for the action mechanism of certain drugs (“put-in,” “drop-in,” “block­out” systems).

Finally, problems similar to those discussed with respect to the individual organism also occur with respect to supra-individual entities which, in the continual death and birth, immigration and emigration of individuals, represent open systems of a higher nature. As a matter of fact, the equations developed by Volterra for population dynamics, biocoenoses, etc. (cf. D’Ancona, 1939) belong to the general type discussed above.

In conclusion, it may be said that consideration of organismic phenomena under the conception discussed, a few general prin­ciples of which have been developed, has already proved its importance for explanation of specific phenomena of life.

Source: Bertalanffy Ludwig Von (1969), General System Theory: Foundations, Development, Applications, George Braziller Inc.; Revised edition.

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