2021/03/19 by John J. Vastola, Gennady Gorin, Vastola, John J. +5
Biochemistry, Genetics and Molecular Biology · #Bacterial Genetics and Biotechnology #DNA and Nucleic Acid Chemistry #Evolution and Genetic Dynamics #FOS: Biological sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Quantitative Methods (q-bio.QM) #Subcellular Processes (q-bio.SC)
paper · pdf · doi:10.48550/arxiv.2103.10992
openalex publication_date 2021/03/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The chemical master equation (CME), which describes the discrete and\nstochastic molecule number dynamics associated with biological processes like\ntranscription, is difficult to solve analytically. It is particularly hard to\nsolve for models involving bursting/gene switching, a biological feature that\ntends to produce heavy-tailed single cell RNA counts distributions. In this\npaper, we present a novel method for computing exact and analytic solutions to\nthe CME in such cases, and use these results to explore approximate solutions\nvalid in different parameter regimes, and to compute observables of interest.\nOur method leverages tools inspired by quantum mechanics, including ladder\noperators and Feynman-like diagrams, and establishes close formal parallels\nbetween the dynamics of bursty transcription, and the dynamics of bosons\ninteracting with a single fermion. We focus on two problems: (i) the chemical\nbirth-death process coupled to a switching gene/the telegraph model, and (ii) a\nmodel of transcription and multistep splicing involving a switching gene and an\narbitrary number of downstream splicing steps. We work out many special cases,\nand exhaustively explore the special functionology associated with these\nproblems. This is Part I in a two-part series of papers; in Part II, we explore\nan alternative solution approach that is more useful for numerically solving\nthese problems, and apply it to parameter inference on simulated RNA counts\ndata.\n