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On a structure of mathematical theory which reflects multiscale aspects and integrity of biological systems. II. (English) Zbl 1326.37054

Summary: In this paper, considered as the second one of the two-part paper [the author, ibid. 76, No. 2, 79–117 (2013; Zbl 1345.37097)], we discuss a structure of mathematical theory which would be convenient for description of biological systems accentuating to more degree multiscale aspects of modelling. In the first part, we have discussed two levels of modelling. The first one has been related to electronic structure and the second one has been related to atomic level of description. The third level of description considered here is called functional and is related to scale larger than atomic one. Models related to such a scale are designed to description of selective functions of biological systems. In order to join of all descriptions introduced in both parts of the two-part paper,one proposes application of collection of dynamical systems with dimensional reduction as a multiscale method of modelling. Within this method, a scale of averaging applied in modelling is formalized. By this step, we obtain convenient conditions for unification of discrete and continuum descriptions and a framework for whole structure for theory describing biological systems. Role of mechanics of reactive nanostructures is accentuated. By this step, we try to change the point of view that biology is related predominantly to chemistry.

MSC:

37N25 Dynamical systems in biology
92B05 General biology and biomathematics
92C05 Biophysics

Citations:

Zbl 1345.37097
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