Concept of a formal system aimed at modelling biological processes in cell

In this paper a concept of a formal system aimed at modelling biological processes in cell is introduced. The aim of this formulation is to provide a theoretical basis for numerical simulations of the biological processes taking into account accessibility to various levels of details and possible full complexity of phenomena associated with them. The main segment of this formal system is a method of multiscale modelling called here the collection of dynamical systems with dimensional reduction. This approach allows one to integrate various mathematical methods applied in cell biology. It is especially related to continuum mechanics and molecular dynamics. Such a formal mathematical approach is supplemented by a set of notions which characterizes specific properties of biological systems. They are: the molecular recognition, integrity property for a chain of chemical reactions and molecular reactive structures. Nanoscale models of molecules are suggested to be a central segment of the multiscale modelling and are designed to direct cooperation withmolecular dynamics. They are aimed at describingmultimolecular processes in cell. It is shown that the nanoscale level of description is convenient for modelling molecular motors. Status of the present stage of formulation of the formal system is discussed taking into account further development directions.