title: Probability distributions for multimeric systems.
abstract: 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 Euclidian 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.
authors.affiliation: BioModeling, BioInformatics & Bioprocesses, Université Libre de Bruxelles, Brussels, Belgium. jaroslavalbert81@gmail.com.
authors.forename: Jaroslav
authors.initials: J
authors.lastname: Albert
authors.affiliation: BioModeling, BioInformatics & Bioprocesses, Université Libre de Bruxelles, Brussels, Belgium.
authors.forename: Marianne
authors.initials: M
authors.lastname: Rooman
mesh_terms: D000465:Algorithms; D019281:Dimerization; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009690:Nucleic Acid Conformation; D011336:Probability; D012333:RNA, Messenger / Q000737:chemistry / Q000235:genetics / Q000378:metabolism; D013269:Stochastic Processes; D049490:Systems Biology
chemical_list: D012333:RNA, Messenger
keywords: 62E20; 65C20; 65C50
references.citation: Phys Biol. 2004 Dec;1(3-4):205-10
references.pmid: 16204840
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041921
references.pmid: 19905356
references.citation: Bioinformatics. 2005 Jan 15;21(2):208-17
references.pmid: 15319259
references.citation: J Chem Phys. 2009 Apr 7;130(13):134107
references.pmid: 19355717
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031117
references.pmid: 19905072
references.citation: BMC Syst Biol. 2010 Apr 08;4:42
references.pmid: 20377904
references.citation: BMC Syst Biol. 2008 Nov 03;2:94
references.pmid: 18980697
references.citation: Methods Mol Biol. 2012;880:273-322
references.pmid: 23361990
references.citation: J Chem Phys. 2012 Apr 21;136(15):154105
references.pmid: 22519313
references.citation: Nat Rev Genet. 2005 Jun;6(6):451-64
references.pmid: 15883588
references.citation: J Theor Biol. 2003 Jan 21;220(2):261-9
references.pmid: 12468297