Multi-modality in gene regulatory networks with slow promoter kinetics
Name
journal.pcbi.1006784.pdf
Description
Published version
Size
3.14 MB
Format
Adobe PDF
Checksum (MD5)
c6549ddb149377d5c1fee166096d4c72
Author(s)
Del Vecchio, Domitilla
Date Issued
February 19, 2019
Journal
PLoS one
Publisher
Public Library of Science (PLoS)
Citation
Al-Radhawi, M. Ali, Domitilla Del Vecchio and Eduardo D. Sontag. "Multi-modality in gene regulatory networks with slow promoter kinetics." PLoS one 15 (2019): e100678 © 2019 The Author(s)
Version
Final published version
Abstract
Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network.
Subjects
Ecology
Modelling and Simulation
Computational Theory and Mathematics
Genetics
Ecology, Evolution, Behavior and Systematics
Molecular Biology
Cellular and Molecular Neuroscience
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1371/journal.pcbi.1006784
