Abstract
BackgroundStochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models.ResultsWe propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples.ConclusionHybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.
Highlights
Stochastic simulation of gene networks by Markov processes has important applications in molecular biology
Methodology to obtain hybrid simplifications We demonstrate how hybrid simplifications can be obtained from Markov pure jump models for gene networks
In order to justify the utility of our approach we show by examples that all types of hybrid processes that we have discussed are represented in gene networks models
Summary
Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. Answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results These general results are difficult to obtain for exact models. Even the simplest stochastic model, such as the production module of a protein [11,14] contains tens of variables and biochemical reactions, and at least the same number of parameters. Direct simulation of such networks by Stochastic Simulation Algorithm (SSA) [15] is extremely time consuming. Various approximation methods were proposed, based on time discretization such as binomial, Poisson or Gaussian time leaping [16,17], or based on fast/slow partitions [18,19,20,21]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
