Bulletin of Mathematical Biology

Rashevsky, N.

doi: 10.1007/BF02481853pmid: N/A

Abstract It has been shown previously (Bull. Math. Biophysics,17, 207–218, 1955) that within the framework of the general principle of biotopological mapping a number of different specific hypotheses can be made about the topological structure of the primordial organism and the transformation which lead to the description of higher organisms. Each set of such hypotheses leads to different conclusions and different predictions of specific biological relations. In the present paper it is shown that while the specific predictions depend on the specific assumptions within the framework of the general principle of biotopological mapping, the type of the predicted relation is characteristic of the general topological approach. Relations of this kind would hardly ever be considered in the usual metric approach to mathematical biology. As specific examples it is shown how topological considerations lead to the problem of the total number of possible organisms, the problem of relations between number of organs and number of cell types in an organism, the problem of the number of cell types in different organs, a possible approach to the problem of the number of different endocrine secretions in different organisms, and other similar problems. All this shows the predictive value of topological biology.

Rashevsky, N.

doi: 10.1007/BF02481854pmid: N/A

Abstract A general mechanism is studied which adapts the value of some biological parameter so as to maximize or to minimize the value of another parameter. In the process of visual accommodation, the thickness of the lens is determined by the maximum sharpness of the image on the retina. A neural mechanism which provides for such an optimum adjustment is described. A similar mechanism may play a role in such phenomena as hedonistic behavior where activity is adjusted to a maximum of satisfaction. The mechanism discussed here does not provide for an absolutely sharp retinal image, but leads to a conclusion that the sharpness of that image fluctuates within narrow limits which are determined by the parameters of the systems.

O'Sullivan, D. G.

doi: 10.1007/BF02481855pmid: N/A

Abstract Further consideration is given to assessing the degree of precision achieved in the localization of enzymes in cells by chemical staining techniques. Procedures discussed are those in which the enzyme acts on a substrate by a zero-order reaction, producing an intermediate which is then converted by an irreversible first-order reaction (velocity constantk) into a non-diffusible colored product. A relationship is obtained which permits the degree of localization for this type of process to be easily calculated. This localization factor is independent of the activity per unit volume of the site; it increases with the size of the site and, for experimental time ranges, is virtually independent of the time of staining. It is shown that, under usual circumstances, satisfactory localization is achieved in sites of radius 1 μ ifk/D is of the order 109 cm−2 and that when this ratio has the value 1011 cm−2 localization is very good.

Macey, Robert

doi: 10.1007/BF02481856pmid: N/A

Abstract The problem of exchange of substances between circulating blood and tissue is discussed in terms of a model with continuously distributed tissue characteristics. Consideration is given to the distribution of perfusion rates, the distribution of metabolism coefficients for a substance consumed at a rate proportional to its concentration, and the distribution of permeability coefficients for a slowly penetrating inert substance. Equations are derived for obtaining crude estimates of the moments of these distributions from exchange data.

Foster, Caxton;Rapoport, Anatol

doi: 10.1007/BF02481857pmid: N/A

Abstract A non-constant-sum continuous game analyzed in a previous paper by one of the authors (A. Rapoport,Bull. Math. Biophysics,18, 15–30, 1956) is extended from two toN players with special emphasis onN=3. It is shown that the concept of stability becomes in this case one of “pairwise stability,” and depends on the so-called distribution matrix of rewards. The distribution matrix and the collusion structure jointly determine the end states of the game. Conditions which lead to the emergence of one, two, or no “parasites” are derived. An apparatus is described which provides a physical analogue of the game, making possible the isolation of behavioral variables under the prescribed conditions of the game.

Rashevsky, N.

doi: 10.1007/BF02481858pmid: N/A

Trucco, Ernesto

doi: 10.1007/bf02481859pmid: N/A

The idea of assigning an information content to a graph is extended to include the following two situations: (a) Combinations of sets of topologically equivalent points are used as symbols; (b) Points of the graph may exist in different states.

Harris, Joseph D.

doi: 10.1007/bf02481860pmid: N/A

A simple model of a membrane is used to obtain relations among five measurable quantities: the inward and outward ionic fluxes, the internal and external ionic concentrations, and the difference of electrical potential across the membrane. The Goldman equation is generalized to arbitrary geometrical shapes.

O'Sullivan, D. G.

doi: 10.1007/BF02481861pmid: N/A

O'Sullivan, D. G.

doi: 10.1007/BF02481862pmid: N/A