Date of Award
Master of Science (MS)
Department of Mathematics
Genes are responsible for producing proteins that are essential to the construction of complex biological systems. The mechanisms by which this production is regulated have long been the center of wide spread research efforts. Deterministic Boolean gene regulatory models have been a particularly effective avenue of research in this field. However these models fall short of accounting for variations in the gene functionality due to the uncertain internal or external environmental conditions. One of the recent attempts to overcome this weakness is by (Murrugarra, 2012), in which a probabilistic component is introduced as the fixed activation/degradation propensities at the cellular level. This approach still falls short of accounting for cell-to-cell variability as well as the variability at the molecular level. With this study we introduce an additional stochastic element by modeling the activation/degradation propensities using statistical distributions. This in turn allows us to quantify the variability of the different connections within the dynamical system formed by the gene activation/degradation behavior. Finally we present a converse method of determining the most likely propensity set for a given stochastic gene regulatory network.
Li, Yuezhe, "On the Dynamics of Boolean Gene Regulatory Networks with Stochasticity" (2016). Theses and Dissertations. 518.