A rigorous framework for multiscale simulation of stochastic cellular networks

Abstract

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are modeled as continuous time discrete state Markov processes whose probability density functions evolve according to a chemical master equation ͑CME͒. The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm ͑SSA͒. Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. We apply our methods to biologically relevant test systems to demonstrate their accuracy and efficiency.

Analytic Methods for Modeling Stochastic Regulatory Networks

“…Naturally, we are not able to cover all the developments in the field, but we hope to give the reader a useful starting point. For concreteness we also limit our discussion to the case of small gene networks and do not discuss approximations used to describe larger networks, which is currently an active area of research in many communities [10,11,15,16,28,29].…”

Response-time behaviors of intercellular communication network motifs

“…Response-time modeling has the advantage that we do not need to take all details of intracellular dynamics into account, but rather focus on the key measurable events (see also [25,26]). Therefore, compared to models on the level of molecular species or even individual molecules, we can describe the behaviors of cell populations with a rather small number of parameters (few measurable response-time distributions instead of 100's of poorly accessible rate parameters) ( Figure 1D).…”

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

“…To circumvent this, future work will exploit the CTD-moment equations derived to develop faster approximate Monte Carlo methods that speed up the CTD-SSA incorporating ideas from techniques like tauleaping/Langevin 23,24 and other hybrid approaches. 25 In summary, a wide-ranging battery of methods, similar to that developed for the Markov CME/SSA framework, is necessary for the application of the CTD-CME/CTD-SSA formalism to efficiently model and analyze stochastic biochemical systems with CTD propensities.…”