Intrinsic Noise Analyzer: A Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion

Abstract

The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen’s system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNA’s performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with circadian rhythms. The software iNA is freely available as executable binaries for Linux, MacOSX and Microsoft Windows, as well as the full source code under an open source license.

Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators

“…However, the ssLNA enjoys the further advantage that it is available in closed form for any monostable reaction network and hence can be readily constructed from knowledge of the stoichiometric matrix and deterministic rate equations. The disadvantage of the ssLNA is that for pathways composed of some second-order reactions, the ssLNA (and the LNA on which it is based) is valid only for large enough molecule numbers [30,31]. This limitation can be lifted by consideration of higher order terms in the system size expansion; such calculations present more formidable analytical challenges than encountered in the derivation of the ssLNA and are under current investigation.…”

Modeling heterogeneous responsiveness of intrinsic apoptosis pathway

“…A more standard and frequently used measure of cellular noise is the dimensionless coefficient of variation, which is defined as standard deviation divided by mean. It measures the inverse signal-to-noise ratio and has been widely employed to characterize intrinsic and extrinsic noises of gene and protein expression and their determining factors with respect to cellular network organization [36,43,47-52]. For the latter measure, the coefficient of variation squared may be alternatively used [53].…”

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

“…After parameterizing the models with the values given in the legend of Fig. 3, the models were simulated using the exact stochastic simulation implementation in the freely available software iNA (intrinsic noise analyser)35.…”