Abstract
The paper discusses the formal expression in biomathematical terms of a general approach to the construction and analysis of mathematical models in biological systems. It points in the direction of a possible axomatization of such constructs and their associated methodologies.โThe underlying general notion or โprimitive conceptโ of biosystem ๐ (C,S, E, F, t) is assumed to include: composition C, structure S, environment E, biological activities or functions F, and time relations t. In relation to ๐ a mathematical model is conceived as an associated mathematical construct ๐ such that there exists a correspondence ยต ๐ โ ๐ 1. between the biological objects in ๐ and the mathematical symbols in ๐ and 2. between the biological activities in ๐ and the allowable, biologically interpretable mathematical operations in the mathematical domains containing ๐.โDeterministic models are obtained by associating time-dependent, algebraic variables x with quantifiable aspects of ๐; and stochastic models by associating random variables x, usually defined with reference to a basic probability space corresponding to a discrete biological event. Stochastic and deterministic models for the kinetics of unimolecular processes are discussed in some detail as examples, and compared with each other.
The work was supported partially by Biomathematics Research Grant No. GM-10002 and Training Grant No. 5-T1-GM-984 from the National Institutes of Health, Institute of General Medical Sciences, U.S. Department of Health, Education and Welfare; and by the Howard Hughes Medical Institute.
Paper read at the Symposium by N. Arley.
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Bartholomay, A.F. (1968). Some General Ideas on Deterministic and Stochastic Models of Biological Systems. In: Locker, A. (eds) Quantitative Biology of Metabolism. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51065-6_6
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