title: Protein Synthesis Driven by Dynamical Stochastic Transcription.
abstract: In this manuscript, we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations, while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time-dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.
authors.affiliation: Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP, 05508-090, Brazil. ginnocentini@gmail.com.|DIMNP, UMR 5235, Université de Montpellier 2, Pl. E. Bataillon, Bat. 24, 34095, Montpellier Cedex 5, France. ginnocentini@gmail.com.
authors.forename: Guilherme C P
authors.initials: GC
authors.lastname: Innocentini
authors.affiliation: Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP, 05508-090, Brazil. forger@ime.usp.br.
authors.forename: Michael
authors.initials: M
authors.lastname: Forger
authors.affiliation: DIMNP, UMR 5235, Université de Montpellier 2, Pl. E. Bataillon, Bat. 24, 34095, Montpellier Cedex 5, France. ovidiu.radulescu@univ-montp2.fr.
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
authors.affiliation: Laboratório de Genômica Evolutiva e Biocomplexidade & DIS, Escola Paulista de Medicina, Universidade Federal de São Paulo, Rua Pedro de Toledo, 669, 4th floor, São Paulo, SP, 04039-032, Brazil. fernando.antoneli@unifesp.br.
authors.forename: Fernando
authors.initials: F
authors.lastname: Antoneli
mesh_terms: D003198:Computer Simulation; D015870:Gene Expression; D055641:Mathematical Concepts; D008957:Models, Genetic; D011336:Probability; D014176:Protein Biosynthesis / Q000235:genetics*; D012333:RNA, Messenger / Q000096:biosynthesis / Q000235:genetics; D013269:Stochastic Processes; D014158:Transcription, Genetic
chemical_list: D012333:RNA, Messenger
keywords: Dynamics; Exact solutions; Gene expression; Stochasticity