Stochastic Simulation Of Biochemical Networks Research Articles

Selected-node stochastic simulation algorithm.

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.

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.

Eliminating fast reactions in stochastic simulations of biochemical networks: A bistable genetic switch

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.

Stochastic simulation GUI for biochemical networks

This article describes the development of a useful graphical user interface for stochastic simulation of biochemical networks which allows model builders to run stochastic simulations of their models and perform statistical analysis on the results. These include the construction of correlations, power-spectral densities and transfer functions between selected inputs and outputs. The software is licensed under the BSD open source license and is available at http://sourceforge.net/projects/jdesigner. In addition, a more detailed account of the algorithms employed in the tool can be found at the Wiki at http://www.sys-bio.org/sbwWiki. Supplementary data are available at Bioinformatics online.

Automatic generation of cellular reaction networks with Moleculizer 1.0

Accurate simulation of intracellular biochemical networks is essential to furthering our understanding of biological system behavior. The number of protein complexes and of chemical interactions among them has traditionally posed significant problems for simulation algorithms. Here we describe an approach to the exact stochastic simulation of biochemical networks that emphasizes the contribution of protein complexes to these systems. This simulation approach starts from a description of monomeric proteins and specifications for binding, unbinding and other reactions. This manageable specification is reasonably intuitive for biologists. Rather than requiring the inclusion of all possible complexes and reactions from the outset, our approach incorporates new complexes and reactions only when needed as the simulation proceeds. As a result, the simulation generates much smaller reaction networks, which can be exported to other simulators for further analysis. We apply this approach to the automatic generation of reaction systems for the study of signal transduction networks.