Type
Text
Type
Dissertation
Advisor
Wang, Jin | Verbaarschot, Jacobus | Averin, Dmitri | Ajitanand, Nuggehalli.
Date
2011-08-01
Keywords
diffusion equations, dynamical systems, mutations, phage lambda, stability, stochastic | Physics--Physical chemistry--Genetics
Department
Department of Physics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71158
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
The $lambda$ phage infection of an textit{E. coli} cell has become a paradigm for understanding the molecular processes involved in gene expression and signaling within a cell. This system provides an example of a genetic switch, as cells with identical DNA choose either of two cell cycles: a lysogenic cycle, in which the phage genome is incorporated into the host and copied by the host; or a lytic cycle, resulting in the death of the cell and a burst of viruses. The robustness of this switch is remarkable; although the first stages of the lysogenic and lytic cycles are identical, a lysogen virtually never spontaneously flips, and external stressors or instantaneous cell conditions are required to induce flipping. In particular, the cell fate decision can depend on the populations of two proteins, Ci and Cro, as well as their oligomerization and subsequent binding affinities to three DNA sites. These processes in turn govern the rates at which RNAp transcribes the Ci and Cro genes to produce more of their respective proteins. Although the biology in this case is well understood, the fundamental chemistry and physics underlying the bistability remains elusive. In this work, a dynamical model of the non-equilibrium statistical mechanics is revisited, generalized, and explored. The low number of proteins and other sources of noise are non-negligible and corrections to the kinetics are essential to understanding the stability. To this end, general integral forms for advection-diffusion equations appropriate for finite element methods have been developed and numerically solved for a variety of mutants and assumptions about the state of the cells. These solutions quantify the probabilistic and flux landscapes of the ensembles' evolution in concentration space and are used to predict the populations of the cell states, entropy production, passage times, and potential barriers of wild type and mutant bacteria to illuminate some structure of the configuration space from which Nature naturally selects. | 87 pages
Recommended Citation
Borggren, Nathan Andrew, "Probabilistic and Flux Landscapes of the Phage $\lambda$ Genetic Switch" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 365.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/365