Computational Cellular Dynamics Based on the Chemi

Authors: Jie Liang Hong Qian

Publish Date: 2010/01/20

Volume: 25, Issue: 1, Pages: 154-168

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Abstract

Modern molecular biology has always been a great source of inspiration for computational science Half a century ago the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology Twentyfive years ago the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics In this paper we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume ie mesoscopic in terms of a stochastic discretestate continuoustime formulation called the chemical master equation CME Similar to the wavefunction in quantum mechanics the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm In contrast to the Metropolis algorithm this Monte Carlo sampling technique does not follow a process with detailed balance We shall show several examples how CMEs are used to model cellular biochemical systems We shall also illustrate the computational challenges involved multiscale phenomena the interplay between stochasticity and nonlinearity and how macroscopic determinism arises from mesoscopic dynamics We point out recent advances in computing solutions to the CME including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm We argue that the CME is an ideal system from which one can learn to understand “complex behavior” and complexity theory and from which important biological insight can be gained

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