2015/10/02 by Andrew Mugler, Mugler, Andrew, Sean Fancher +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bacterial Genetics and Biotechnology #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Protein Structure and Dynamics #Quantitative Methods (q-bio.QM) #physics.bio-ph #q-bio.MN #q-bio.QM
paper · pdf · doi:10.48550/arxiv.1510.00675
10 pages, 2 figures. To appear in the q-bio Methods Textbook
arxiv created 2015/10/02 · openalex publication_date 2015/10/02 · arxiv updated 2015/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal stochastic models of three fundamental cellular processes: gene expression, protein modification, and polymerization. We introduce key analytic tools for solving each model, including the generating function, eigenfunction expansion, and operator methods, and we discuss how these tools are extended to more complicated models. These analytic tools provide an elegant, efficient, and often insightful alternative to stochastic simulation.