Low-dimensional projection of stochastic cell-signalling dynamics via a variational approach.

Noise and fluctuations play vital roles in signal transduction in cells. Various numerical techniques for its simulation have been proposed, most of which are not efficient in cellular networks with a wide spectrum of timescales. In this paper, based on a recently developed variational technique, low-dimensional structures embedded in complex stochastic reaction dynamics are unfolded which sheds light on new design principles of efficient simulation algorithm for treating noise in the mesoscopic world. This idea is effectively demonstrated in several popular regulation models with an empirical selection of test functions according to their reaction geometry, which not only captures complex distribution profiles of different molecular species but also considerably speeds up the computation.

[1]  D. Gillespie,et al.  Avoiding negative populations in explicit Poisson tau-leaping. , 2005, The Journal of chemical physics.

[2]  Paul Fearnhead,et al.  Inference for reaction networks using the linear noise approximation , 2012, Biometrics.

[3]  Michael E. Schuckers.  Using the Beta-Binomial Distribution to Assess Performance of a Biometric Identification Device , 2003, Int. J. Image Graph..

[4]  Linda R Petzold,et al.  Efficient step size selection for the tau-leaping simulation method. , 2006, The Journal of chemical physics.

[5]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[6]  F. Schlögl.  Chemical reaction models for non-equilibrium phase transitions , 1972 .

[7]  K. Burrage,et al.  Binomial leap methods for simulating stochastic chemical kinetics. , 2004, The Journal of chemical physics.

[8]  Darren J. Wilkinson,et al.  Modelling the actions of chaperones and their role in ageing , 2005, Mechanisms of Ageing and Development.

[9]  Ertugrul M. Ozbudak,et al.  Regulation of noise in the expression of a single gene , 2002, Nature Genetics.

[10]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[11]  João P. Hespanha,et al.  Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks , 2014, Journal of The Royal Society Interface.

[12]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[13]  P. Ray,et al.  Reactive oxygen species (ROS) homeostasis and redox regulation in cellular signaling. , 2012, Cellular signalling.

[14]  Yang Cao,et al.  Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems , 2005 .

[15]  A. van Oudenaarden,et al.  Noise Propagation in Gene Networks , 2005, Science.

[16]  A. Arkin,et al.  It's a noisy business! Genetic regulation at the nanomolar scale. , 1999, Trends in genetics : TIG.

[17]  Tatiana T Marquez-Lago,et al.  Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics. , 2007, The Journal of chemical physics.

[18]  Chetan D. Pahlajani,et al.  Stochastic reduction method for biological chemical kinetics using time-scale separation. , 2011, Journal of theoretical biology.

[19]  P. Swain,et al.  Intrinsic and extrinsic contributions to stochasticity in gene expression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[20]  D. Vlachos,et al.  Binomial distribution based tau-leap accelerated stochastic simulation. , 2005, The Journal of chemical physics.

[21]  Yuting Xu,et al.  The N-leap method for stochastic simulation of coupled chemical reactions. , 2012, The Journal of chemical physics.

[22]  G. Papoian,et al.  The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade. , 2006, The Journal of chemical physics.

[23]  Peter G Wolynes,et al.  A variational approach to the stochastic aspects of cellular signal transduction. , 2006, The Journal of chemical physics.

[24]  Layne T. Watson,et al.  Stiffness detection and reduction in discrete stochastic simulation of biochemical systems. , 2011, The Journal of chemical physics.

[25]  T. Elston,et al.  Stochasticity in gene expression: from theories to phenotypes , 2005, Nature Reviews Genetics.

[26]  C. Yeang,et al.  Integration of Metabolic Reactions and Gene Regulation , 2011, Molecular biotechnology.

[27]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Daniel T. Gillespie.  On the calculation of mean first passage times for simple random walks , 1981 .

[29]  B. Zheng,et al.  Monte Carlo simulations of short-time critical dynamics with a conserved quantity. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  J. Raser,et al.  Control of Stochasticity in Eukaryotic Gene Expression , 2004, Science.

[31]  Peter G Wolynes,et al.  Stochastic gene expression as a many-body problem , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Tianshou Zhou,et al.  Analytical Results for a Multistate Gene Model , 2012, SIAM J. Appl. Math..

[33]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[34]  J. Liao,et al.  Characteristic reaction paths of biochemical reaction systems with time scale separation , 1988, Biotechnology and bioengineering.

[35]  Linda R Petzold,et al.  Adaptive deployment of model reductions for tau-leaping simulation. , 2015, The Journal of chemical physics.

[36]  P. Phillipson,et al.  Stochastic theory of stable and bistable biochemical systems: Effects of noise on enzymatic catalysis , 1990 .

[37]  M. Lutzky,et al.  Dynamical symmetries and conserved quantities , 1979 .

[38]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[39]  G. Papoian,et al.  Evolution of complex probability distributions in enzyme cascades. , 2007, Journal of theoretical biology.