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A relational theory of biological systems II

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Abstract

The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism.

A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed. In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence is obtained. Some further implications of the above assumptions are then discussed.

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Authors and Affiliations

  1. Committee on Mathematical Biology, The University of Chicago, Chicago, USA

    Robert Rosen

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  1. Robert Rosen
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Rosen, R. A relational theory of biological systems II. Bulletin of Mathematical Biophysics 21, 109–128 (1959). https://doi.org/10.1007/BF02476354

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  • DOI: https://doi.org/10.1007/BF02476354

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