engleski

Stohastic Model of Cell Reaction Systems

Mathematical modelling of microbial cells can be developed by application of chemical en-gineering principles of mass and energy balances for chemical reactors. Cell as a reactor is a viewed as a multiphase catalytic reactor with an expanding volume due to growth, with about 50· ; 106 molecules, 105 reactions, and with hierarchical organised and spatially distrib-uted internal control systems. The robust approach to modelling is based on standard chemical engineering picture of a well mixed cup with deterministic kinetics. However, due to small number of individual molecules present in a cell, stochastic effects in molecular in-teractions become important. Application of Gillespie [1] algorithm for exact simulation of stochastic chemical reaction systems can be applied for computer cell simulation. Stochas-tic models are formulated by translation of deterministic mechanisms and kinetic parame-ters into evaluation of probabilities of individual molecular interactions. It is, like in chemi-cal engineering, a "scale down procedure", where kinetic parameters are experimentally de-termined in large systems (deterministic, "in vitro" enzyme reactors), and than are extrapo-lated down to the molecular level (cells). Such stochastic modelling provides deterministic solutions as an asymptotic case of a stochastic model. However, this is an "ad hoc" proce-dure which may be hopefully resolved by computer simulation and experimental molecular biology. In this work are by computer simulation analysed stochastic interactions on Mi-chaelis-Menten mechanism, oscillatory Lotka-Volterra reactions, and cell infection by hepatitis-C virus [2-3]. W.R. Mathematica software language and numerical procedure are applied. The analysis is focused on determination of bifurcation conditions between sto-chastic and deterministic behaviour, stochastic effects on critical stability, and development of chaos.

stochastic modelling; cell metabolisma

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