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| Keywords | |
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biochemical networks |
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cellular signaling |
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epigenetics |
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master equation |
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nonlinear reactions |
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stochastic |
| Authors | |
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Jie Liang |
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Hong Qian |
Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity
Jie Liang1,2 (梁杰) and Hong Qian3,4(钱纮)
1Department of Bioengineering, University of Illinois at Chicago, Chicago, IL 60607, U.S.A.
2Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
3Department of Applied Mathematics, University of Washington, Seattle, WA 98195, U.S.A.
4Kavli Institute for Theoretical Physics China, Chinese Academy of Sciences, Beijing 100190, China
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. Twenty-five 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 (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time 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.
This work is supported by US NIH under Grant Nos. GM079804, GM081682, GM086145, GM068610, NSF of USA under Grant Nos. DBI-0646035 and DMS-0800257, and `985' Phase II Grant of Shanghai Jiao Tong University under Grant No. T226208001.
Jie Liang is a professor in the Department of Bioengineering at the University of Illinois at Chicago, and holds a visiting position at Shanghai Jiao Tong University. He received his B.S. degree from Fudan University (1986), MCS and Ph.D. degree from the University of Illinois at Urbana-Champaign (1994). He was an NSF CISE postdoctoral research associate (1994$sim$1996) at the Beckman Institute and National Center for Supercomputing and its Applications (NCSA) in Urbana, Illinois. He was a visiting fellow at the Institute of Mathematics and Applications at Minneapolis, Minnesota in 1996, and an Investigator at SmithKline Beecham Pharmaceuticals in Philadelphia from 1997 to 1999. He was a recipient of the NSF CAREER award in 2003. He is a fellow of American Institute of Medical and Biological Engineering, and served as regular member of the NIH Biological Data Management and Analysis study section. His research interests are in biogeometry, biophysics, computational proteomics, stochastic molecular networks, and cellular pattern formation. His recent work can be accessed at (http://www.uic.edu/$~jliang).
Hong Qian received his B.S. degree in astrophysics from Peking University. He worked on fluorescence correlation spectroscopy (FCS) and single-particle tracking (SPT) and obtained his Ph.D. degree in biochemistry from Washington University (St. Louis). His research interests turned to theoretical biophysical chemistry and mathematical biology when he was a postdoctoral fellow at the University of Oregon and at the California Institute of Technology. In that period of time, he worked on protein thermodynamics, fluctuations and folding. Between 1994 and 1997, he was with the Department of Biomathematics at the UCLA School of Medicine, where he worked on the theory of motor proteins and single-molecule biophysics. This work led to his current interest in mesoscopic open chemical systems. He joined the University of Washington (Seattle) in 1997 and is now professor of applied mathematics, and an adjunct professor of bioengineering. His current research is in stochastic analysis and statistical physics of cellular systems. His recent book "Chemical Biophysics: Quantitative Analysis of Cellular Systems", co-authored with Daniel A. Beard, has been published by the Cambridge University Press.