Mathematical models of cell self-organization

Self organization and evolution in mathematical models

Through several examples we illustrate to non mathematicians how biological situations can be translated in mathematical terms. Even simple mathematical models can be very efficient to clarify a complex biological situation and the same basic mathematical procedures can be found in different biological frameworks. In particular stability analysis under small fluctuations of non linear models po...

Self-organization of Supervised Models

Self-organization using Potts models

-In this work, we use Potts neurons for the competitive mechanism in a self-organization model. We obtain new algorithms on the basis of a Potts neural network for coherent mapping, and we remodel the Durbin algorithm and the Kohonen algorithm with mean field annealing. The resulting dimension-reducing mappings possess a highly reliable topology preservation such that the nearby elements in the...

A mathematical model of the metabolism of a cell. Self-organization and chaos

Using the classical tools of nonlinear dynamics, we study the process of selforganization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The os...

Self-Organization with Constraints - A Mathematical Model for Functional Differentiation

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional differentiation in cortical modules are typical ex...