Revival of variational method in noisy cell signaling with Fourier observer

Abstract Signal transduction in a cell is mostly mediated with biochemical reactions which are noisy and often modeled with chemical master equations or Langevin type of dynamics. Thus stochastic simulation constitutes a major part of computation in cell signaling. Nevertheless, the presence of a wide span of time scales or molecular numbers in various pathways may lead to trouble in computation efficiency or accuracy. To avoid this problem, the commonly employed variational method evolves the whole probability distribution and reduces the stochastic equations to deterministic ones of only a few parameters. However, the design of the left variational basis is essential for its successful application, especially to large networks. In this paper, we extend the conventional polynomial basis to the Fourier and further the Gaussian basis, much facilitating description of multi-peaked or localized non-Gaussian distributions and at the same time avoiding numerical instability and computational complexity frequently encountered with conventional basis. The extension here is demonstrated in several typical biochemical signaling networks and achieves similar accuracy as the benchmark Gillespie algorithm, but with much less running time, which seems to open new opportunities in the variational approach to efficient analysis of noisy dynamics.