148 research outputs found
Construction and accuracy of partial differential equation approximations to the chemical master equation
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
Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells
Frequency domain analysis of fluctuations of mRNA and protein copy numbers within a cell lineage:Theory and experimental validation
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
Holimap: an accurate and efficient method for solving stochastic gene network dynamics
Gene-gene interactions are crucial to the control of sub-cellular processes but our understanding of their stochastic dynamics is hindered by the lack of simulation methods that can accurately and efficiently predict how the distributions of gene product numbers vary across parameter space. To overcome these difficulties, here we present Holimap (high-order linear-mapping approximation), an approach that approximates the protein or mRNA number distributions of a complex gene regulatory network by the distributions of a much simpler reaction system. We demonstrate Holimap’s computational advantages over conventional methods by applying it to predict the stochastic time-dependent dynamics of various gene networks, including transcriptional networks ranging from simple autoregulatory loops to complex randomly connected networks, post-transcriptional networks, and post-translational networks. Holimap is ideally suited to study how the intricate network of gene-gene interactions results in precise coordination and control of gene expression
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
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
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