×

Probability distributions for multimeric systems. (English) Zbl 1351.92013

Summary: We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidean distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

MSC:

92C40 Biochemistry, molecular biology
65C50 Other computational problems in probability (MSC2010)
65C20 Probabilistic models, generic numerical methods in probability and statistics
62E20 Asymptotic distribution theory in statistics

Software:

Mathematica
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew normal distribution. J R Statist Soc B 61:579-602 · Zbl 0924.62050 · doi:10.1111/1467-9868.00194
[2] Barzel B, Biham O (2009) Stochastic analysis of dimerization systems. Phys Rev E 80:031117 · doi:10.1103/PhysRevE.80.031117
[3] Bundchuh R, Hayot F, Jayaprakash C (2003) The role of dimerization in noise reduction of simple genetic networks. J Theor Biol 220:261-269 · Zbl 1464.92166 · doi:10.1006/jtbi.2003.3164
[4] Ghim CM, Almaas E (2008) Genetic noise control via protein oligomerization. BMC Syet Biol 2:94 · doi:10.1186/1752-0509-2-94
[5] Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem 104:1876-1889 · doi:10.1021/jp993732q
[6] Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2 · doi:10.1021/j100540a008
[7] Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 115:1716-1733 · doi:10.1063/1.1378322
[8] Gillespie DT, Petzold LR (2003) Improved leap-size selection for accelerated stochastic simulation. J Chem Phys 119:8229-8234 · doi:10.1063/1.1613254
[9] Grima R (2012) A study of the accuracy of moment-closure approximations for stochastic chemical kinetics. J Phys Chem 136:154105 · doi:10.1063/1.3702848
[10] Hayot F, Jayaprakash C (2004) The linear noise approximation for molecular fluctuations within cells. Phys Biol 1:205-210 · doi:10.1088/1478-3967/1/4/002
[11] Koern M, Elston TC, Blake JW, Collins JJ (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genetics 6:451-464 · doi:10.1038/nrg1615
[12] Lee CH, Kim K-H, Kim P (2009) A moment closure method for stochastic reaction networks. J Phys Chem 130:134107 · doi:10.1063/1.3103264
[13] Mugler A, Walczak AM, Wiggins CH (2011) Spectral solutions to stochastic models of gene expression with bursts and regulation. Phys Rev E 80:041921 · doi:10.1103/PhysRevE.80.041921
[14] Orrell D, Ramsey S, Atauri PD, Bolouri H (2004) A method for estimating stochastic noise in large genetic regulatory networks. Bioinformatics 21(2):208-217 · doi:10.1093/bioinformatics/bth479
[15] Van Kampen NG (2007) Stochastic processes in physics and chemistry. Elsevier, New York
[16] Walczak AM, Mugler A, Wiggins CH (2012) Analytic methods for modeling stochastic regulatory networks. Methods Mol Biol 880:273-322 · doi:10.1007/978-1-61779-833-7_13
[17] Wolf V, Goel R, Mateescu M, Henzinger TA (2010) Solving the chemical master equation using sliding windows. BMC Syst Biol 4:42 · doi:10.1186/1752-0509-4-42
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.