Selected-node stochastic simulation algorithm

Abstract

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

Path mutual information for a class of biochemical reaction networks

“…, for which analytic expressions are not available. We have shown previously [24] that a stochastic differential equation can be found for such conditional distributions. For instance, the equation for π B (a, t) would read…”

“…The latter can be thought of as the probability laws that describe the time evolution of only A or B, respectively. We and others have previously shown how such marginal process models can be constructed for general reaction networks [28,24]. While in those studies, it was used predominantly for the purpose of model reduction and stochastic simulation, it will now serve us to find explicit expressions of the Radon-Nikodym derivative in (4).…”

“…We will provide explicit expressions for the time-evolution of λ A k (t) and λ B k (t) for some examples in Section 3. For further information on the marginal process framework and the calculation of the conditional expectations the reader may refer to [24].…”

Path integral approach to generating functions for multistep post-transcription and post-translation processes and arbitrary initial conditions

“…There exist numerous methods for modeling stochastic gene expression. Some of them are entirely numerical, such as the Gillespie algorithm [2] and its derivatives [3], [4], [5], [6], [7]; others are hybrids of the Gillespie algorithm and the Master equation [8], [9], [10], [11], [12], [13], [14]; while the rest facilitate either exact or approximate analytic solutions to the Master equation [15], [16]. Analytic solutions are of great value because they provide a more direct insight into the system's behavior, and/or allow for fast exploration of the system's parameter space.…”

Moment-based analysis of biochemical networks in a heterogeneous population of communicating cells

“…CME-based models can faithfully account for the discrete and random nature of biochemical reactions (intrinsic noise) as well as additional heterogeneity stemming from differences in each cell's microenvironment (extrinsic variability) [2,3]. The computational analysis of the CME is associated with certain difficulties but by now, there exists a repertoire of efficient numerical techniques including stochastic Monte Carlo algorithms [1], momentbased methods [4,5] and combinations thereof [6,7,8].…”