Contributions to the mathematical theory of organic form. II Asymmetric metabolism of cellular aggregates

The case is studied of a cellular aggregate forming a hollow spherical shell, the physical constants and the metabolic rate being non-uniform throughout the shell. This leads to asymmetries of concentration distributions, which are calculated here for some simple cases.     

Contributions to the theory of organismic sets: Leadership

The theory of organismic sets (Bull. Math. Biophysics,31, 159–189, 1969) is applied to the theory of leadership in human society. The ability of making decisions, required for leadership, is a product of the activities of the cells of the cerebral cortex, which are elements of the subsetS ₀₂ of the organismic set “man” (loc. cit.). Products of the activities of the elements of an organismic set do not need to be of a material nature. Such things as thoughts, feelings, attitudes, etc., are also products of the activitiesa ₁ of the elements. An individual can makeall necessary decisions for adaptation in a changing environment, when his subsetS ₀₂ contains as a proper subset a set {a ₁₂ ^′ ∼ ⊂S ₀₂ of activities. It is shown that such individuals are rare. If none exist, then the one who possesses a subset {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ of higher cardinalityc _m than any other individual, will be the leader. The possibility is discussed that fromN individualsN′ 〈N possess subsets {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ all of the same cardinalityc _m but differing in the type of their elements, thus resulting in several leaders. It is then discussed what determines which of theN −N′ individuals will choose a particular oneN′ individuals as leader. Cooperation and competition between leaders is discussed.     

Contributions to the mathematical biophysics of organic form III. Deformation of shell shaped cellular aggregates

The average concentrations of a substance diffusing into or from an open spherical shell, in which it is consumed or produced at a constant rate, are calculated by the approximation method. An application of the result to the problem of deformation of such a shell under the influence of diffusion forces is indicated.     

Contributions to the mathematical biophysics of organic form I. Formation of cavities in cellular aggregates

The action of diffusion forces in aggregates of metabolising cells is studied mathematically, and it is shown that under definite conditions these forces may lead to the formation of inner cavities inside of the cellular aggregate. Different quantitative relations are derived and the possible bearing of these results on some embryological phenomena is discussed. A possible application of these considerations to the theory of formation of vacuoles is also discussed.     

Contributions to the theory of active transport

A system consisting of two solutions separated by a membrane may be in one of four possible states: (1) transient, (2) steady, (3) equilibrium, or (4) pseudo-equilibrium. The latter state denotes that in the solutions the net flow of all components is zero but at least one of the components is not in thermodynamic equilibrium. Transient and steady-state systems may or may not have active transport. Thus only systems in either equilibrium or pseudo-equilibrium are considered in this paper, since the former indicates that there is no active transport, whereas in the latter case there always is active transport. This simplifies the problem of finding whether a system does or does not have an active transport mechanism, since it is frequently fairly easy to determine experimentally whether a system is in equilibrium or pseudo-equilibrium. The assumption that electric neutrality exists within very thin membranes is shown not to be valid. However, electric neutrality does exist in the solutions in a system in a pseudo-equilibrium state with fixed charges and impermeative ions. It is then shown how the presence and sign of an electric potential may be found by use of electroneutrality. The mechanism of active transport may be due to a general force acting on all particles of a particular component or to an individual force acting on the individual particles of a particular component. A general solvent flow or a diffusion drag force illustrates the first mechanism while the second is accomplished by either a carrier or a Maxwell Demon. The general type of active transport has been extensively treated in the literature, while the individual type has not been treated in a generalized form. Therefore, the individual type of active transport is discussed at length, and a simple illustrative model is intensively analyzed. Following this, there is a discossion of the Maxwell Demon and some models of it are presented. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600) 1454.     

Contributions of genomics to life-history theory

Life-history theory seeks to understand the factors that produce variation in life histories that are found both among and within species. At the organismal level there is a well developed mathematical framework, and an important focus of the current research is determining the biological underpinnings of this framework, with particular attention to the causal mechanisms that underlie trade-offs. Genomic approaches are proving useful in addressing this issue.     

The theoretical physics of the cell as a basis for a general physico-chemical theory of organic form

Summary It is shown by thermodynamical considerations, that in general regardless to the particular nature of a cell, there must be two kinds of forces between cells: a force of repulsion, due to metabolism, and a force of attraction, due to irritability. It is shown, that the various geometrical forms, which cellular aggregates may assume under the influence of those forces, correspond in general features to various forms, found in nature. In conclusion I wish to express my profound indebtedness to ProfessorDavenport Hooker, for frequent discussions of the subject and a great amount of valuable information. With 1 Text-figure     

Contributions to the theory of organismic sets: Why are there only two sexes

Ever since 1927 when the author began his work in mathematical biology, one of the most intriguing problems in biology appeared to him to be: Why are there only two sexes? The question may seem to be utterly absurd, possibly because we are empirically so used to the existence of two opposite sexes that we take this fact for granted. Genetics shows us the usefulness of sexual reproduction compared with asexual reproduction. The former provides for the possibility of producing a number of new combinations of genes and thus a number of different varieties of individuals of a species. But why only two sexes? It is logically conceivable that biological structures may exist such that their multiplication may require the fusion not of two but of three, four or any other numberk of cells. Such situations are quite easily imagined for unicellulars, such as bacteria or paramecia. But with some greater effort of our imagination we may well imagine such a situation to occur also in higher organisms and men. Why does this not occur? This paper discusses some possible answers to this question.     

Contributions to the theory of active transport: III. The effect of drugs on active transport systems

The addition of a drug to a system which contains an active transport mechanism may produce a large number of effects on both the active transport mechanism and the permeability of the system. A general model of such a system is presented, and various possible results of the drug's addition are discussed. Methods of experimentally separating these effects on the active transport mechanism and the permeabilities of the system are then listed and analyzed.     

Contributions of plant scientists to the development of the germ theory of disease

Investigations demonstrating the causal role of microbes in diseases of plants were completed decades before Pasteur and Koch presented conclusive evidence in support of the germ theory of disease in man and animals. The limited recognition of these and other contributions in understanding the nature of plant diseases has delayed recognition of the commonality that exists among pathogens in general and mechanisms of pathogenesis.     

Functionality of probiotics and intestinal lactobacilli: light in the intestinal tract tunnel.

The commercial interest in functional foods that contain live microorganisms, also termed probiotics, is paralleled by increasing scientific attention to their functionality in the digestive tract. Most studies are focused on intestinal Lactobacillus species, which are part of the natural gastro-intestinal microbiota, and include analysis of colonisation factors and other interactions with the host, the design of novel or improved strains with specific health benefits, and the application of sophisticated molecular tools to determine their fate and activity in situ.     

Contributions to the theory of imitative behavior: The number of political parties as determined by biological and social factors

The theory of imitative behavior as applied tow mutually exclusive behavior patterns (N. Rashevsky,Mathematical Biology of Social Behavior, Rev. Ed., 1959; The University of Chicago Press) leads to the possibility of any numberw of different behavior patterns existing in a social group. Mutually inhibitory effects suppress the effectiveness of behavior of groups that are very small numerically. The manner in which the different biological and social parameters that enter into the theory of imitative behavior determine the number of different effective behaviors is discussed. The results are applied to the problem of what determines the number of political parties in different countries. This number is expected to increase with increasing spread of the distribution curves for the tendencies towards different behaviors, with decreasing imitation factors, and with increasing instability of psychophysical judgments of the average individuals.     

Contributions to the theory of invariance of color under the condition of varying illumination

Any visual-processing algorithm aimed at attaining color constancy will in fact attain it only for restricted spectral classes of illuminants and reflectances. These classes constitute implicit heuristics for the physical world, in an artificial-intelligence sense. In the present work, physically reasonable spectral classes are presented which insure that von Kries's law of chromatic adaptation will — in its simplest form — restore object colors in human tristimulus space to illuminant-invariant positions in the space. Algebraic functions of the adapted tristimulus values are presented which are illuminant-invariant for some departures from the spectral heuristics. These functions, a hierarchy of invariants, may be useful in developing lighting and pigment standards for partially controlled viewing environments.