TY - JOUR

T1 - Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

AU - Mélykúti, Bence

AU - Burrage, Kevin

AU - Zygalakis, Konstantinos C.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The authors wish to thank Thomas G. Kurtz for observing a mistake in an earlier version of this material which has been corrected subsequently. B.M.’s work was funded by the Engineering and Physical Sciences Research Council through a Doctoral Training Centre grant for the Life Sciences Interface Doctoral Training Centre, University of Oxford (Grant No. EP/E501605/1). K. C. Z. was supported by Award No. KUK-C1-013-04 made by the King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/4/26

Y1 - 2010/4/26

N2 - The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.

AB - The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.

UR - http://hdl.handle.net/10754/598320

UR - http://aip.scitation.org/doi/10.1063/1.3380661

UR - http://www.scopus.com/inward/record.url?scp=77952331714&partnerID=8YFLogxK

U2 - 10.1063/1.3380661

DO - 10.1063/1.3380661

M3 - Article

C2 - 20441260

SN - 0021-9606

VL - 132

SP - 164109

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

IS - 16

ER -