2013/08/31 by Evelina Shamarova, Roman Chertovskih, Alexandre F. Ramos +1 · 7 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Applied mathematics #Benchmark (surveying) #Bioinformatics and Genomic Networks #Biology #Computer science #Differential equation #Diffusion #Event (particle physics) #Expression (computer science) #Gene #Gene Regulatory Network Analysis #Gene expression #Gene regulatory network #Mathematical analysis #Mathematics #Parametrization (atmospheric modeling) #Physics #Single-cell and spatial transcriptomics #Statistical physics #Statistics #Stochastic differential equation #Stochastic modelling #Stochastic process #Stochastic simulation #math.PR #physics.bio-ph #q-bio.MN
paper · pdf · doi:10.1103/physreve.95.032418
published in Physical review. E 95(3), 032418 (American Physical Society) · Accepted in Physical Review E
arxiv created 2017/02/22 · openalex publication_date 2017/03/29 · arxiv updated 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).