Nonlinear Dynamical Systems as Models of Development of Inorganic Cells (iCHELLs) & their Simple Assemblies

Abstract

The rapid development of synthetic biology and biomimetics in recent years leads to the creation of prototypes of inorganic artificial cells with membrane-like properties. In this regard there is an obvious need in the development of a universal formalized mathematical description of morphology, dynamics and cooperative behavior, which results in the formation of supracellular assemblies, applicable to both organic and inorganic cells. For this purpose we propose to use invariant sets of nonlinear dynamical systems, which in some variations are isomorphic to biological cells or can be considered as a good morphological metaphor of their morphogenesis and assotiation. This paper compares graphical visualization of invariant sets of nonlinear dynamical systems with the results of experiments on the chemical synthesis of biomimetic structures. A number of maps is considered: Poincare map, Henon map, Chirikov and Gumovski-Mirr maps, systems by Kepler, Volterra, Dyufing and Henon-Heiles. The possibility of approximation of the experimentally observed structures by those mathematical models is shown. The given results of computer simulations are applicable to inorganic cells (iCHELLs), obtained recently in the University of Glasgow, but the proposed method was originally developed for functionally identical inorganic cells, obtained by the author according to the Russian technique, proposed in the early 2000s. The micrographs of such inorganic cells and their assemblies are given below in comparison with the theoretical model.