Stochastic and Agent-based Modeling of Gene Expression and Cell Fate Decisions

Abstract

As new experimental techniques expand our capacity to understand the internal states of single cells and to track the behavior of individual enzymes, classical modeling techniques for deterministic chemical kinetics break down. Thus, more flexible stochastic and agent-based modeling techniques need to be employed. Two paradigmatic are considered. First, a stochastic agent-based model of transcription with nucleosome-induced pausing that maps onto the ddTASEP was constructed to demonstrate a potential mechanism of transcriptional bursting. In lieu of using a mean-field approach, Markov chain techniques were used to calculate the moments of the first passage time from the nucleosome dynamic rate constants. A mean first passage rate was calculated and utilized to construct a new axis to the TASEP phase diagram that contained a jamming transition between initiation- and dynamic defect-limited regions. Second, an integrated Notch/Delta and Wnt/β-catenin gene circuit with crosstalk through the expression of Hes1 was constructed on a lattice model of the intestinal crypt. The distributed control of Hes1 expression, the mechanisms of Wnt secretion, and the redundant role of Paneth cells as a Wnt source were investigated. Tunable mosaic pattern formation at the crypt base was observed, and the addition of the secondary Wnt feedback loop offered a slight increase in model robustness to parameter changes and intrinsic stochasticity.