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 pairs of reversible reactions and irreversible reactions there is another, simple formulation of the CLE with only Wiener processes, whereas the standard approach uses . 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.
Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation
Also at the Life Sciences Interface Doctoral Training Centre, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK and at the Control Group, Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK. Electronic mail: [email protected].
Also at the Oxford Centre for Integrative Systems Biology, Department of Biochemistry, University of Oxford, South Parks Road, Oxford, OX1 3QU, UK and at the Institute for Molecular Bioscience, University of Queensland, St Lucia, QLD 4072, Australia.
Bence Mélykúti, Kevin Burrage, Konstantinos C. Zygalakis; Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation. J. Chem. Phys. 28 April 2010; 132 (16): 164109. https://doi.org/10.1063/1.3380661
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