Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA

The linear noise approximation is commonly used to obtain intrinsic noise statistics for biochemical networks. These estimates are accurate for networks with large numbers of molecules. However it is well known that many biochemical networks are characterized by at least one species with a small number of molecules. We here describe version 0.3 of the software intrinsic Noise Analyzer (iNA) which allows for accurate computation of noise statistics over wide ranges of molecule numbers. This is achieved by calculating the next order corrections to the linear noise approximation's estimates of variance and covariance of concentration fluctuations. The efficiency of the methods is significantly improved by automated just-in-time compilation using the LLVM framework leading to a fluctuation analysis which typically outperforms that obtained by means of exact stochastic simulations. iNA is hence particularly well suited for the needs of the computational biology community.Comment: 5 pages, 2 figures, conference proceeding IEEE International Conference on Bioinformatics and Biomedicine (BIBM) 201

Modeling Reaction Kinetics in Low-dimensional Environments with Conformon P Systems: Comparison with Cellular Automata and New Rate Laws

Recently it has been shown that simulations of complex biological systems using conformon P systems and cellular automata do not necessarily give the same pre- dictions. To further elucidate these di®erences we simulate a simple model of intracellular reactions involving a single bimolecular reaction occurring on a biological membrane us- ing conformon P systems. We ¯nd that the predictions broadly agree with results from both the theory of ran- dom walks in low-dimensional environments and with previously published simulations using cellular automata. Moreover, a re-analysis of the data enables us to deduce novel rate laws for the kinetics of reactions occurring on biological membranes

MomentClosure.jl:Automated moment closure approximations in Julia

SUMMARY: MomentClosure.jl is a Julia package providing automated derivation of the time-evolution equations of the moments of molecule numbers for virtually any chemical reaction network using a wide range of moment closure approximations. It extends the capabilities of modelling stochastic biochemical systems in Julia and can be particularly useful when exact analytic solutions of the chemical master equation are unavailable and when Monte Carlo simulations are computationally expensive. AVAILABILITY AND IMPLEMENTATION: MomentClosure.jl is freely accessible under the MIT licence. Source code and documentation are available at https://github.com/augustinas1/MomentClosure.jl

Coupling gene expression dynamics to cell size dynamics and cell cycle events:Exact and approximate solutions of the extended telegraph model

Summary: The standard model describing the fluctuations of mRNA numbers in single cells is the telegraph model which includes synthesis and degradation of mRNA, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by the cell cycle phase, cellular growth and division, and other crucial aspects of cellular biology. Here, we derive the analytical time-dependent solution of an extended telegraph model that explicitly considers the doubling of gene copy numbers upon DNA replication, dependence of the mRNA synthesis rate on cellular volume, gene dosage compensation, partitioning of molecules during cell division, cell-cycle duration variability, and cell-size control strategies. Based on the time-dependent solution, we obtain the analytical distributions of transcript numbers for lineage and population measurements in steady-state growth and also find a linear relation between the Fano factor of mRNA fluctuations and cell volume fluctuations. We show that generally the lineage and population distributions in steady-state growth cannot be accurately approximated by the steady-state solution of extrinsic noise models, i.e. a telegraph model with parameters drawn from probability distributions. This is because the mRNA lifetime is often not small enough compared to the cell cycle duration to erase the memory of division and replication. Accurate approximations are possible when this memory is weak, e.g. for genes with bursty expression and for which there is sufficient gene dosage compensation when replication occurs

Charting the landscape of stochastic gene expression models using queueing theory

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queuing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and non-stationary distributions and/or moments of mRNA/protein numbers, and bounds on the Fano factor. This approach may enable the solution of complex models which have hitherto evaded analytical solution.Comment: 24 pages, 6 figure