Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, December 01, 2017
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Modeling gene expression in the non-adiabatic regime using piecewise deterministic Markov processes

Abstract:   Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. One source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. In this talk, I aim to introduce a technique to coarse-grain the fully discrete and individual-based models of gene regulatory networks (GRNs). The resulting processes are termed as the piecewise deterministic Markov processes (PDMP), and we will argue that this type of the process is ideal to study the stochastic dynamics of gene expression in the non-adiabatic regime. After the method is introduced, I will introduce two research problems we recently investigated using the technique. In the first example --- a GRN regulating the pluripotency of stem cells --- the computational efficiency of the PDMP allows us to sample a vast area of the parameter space to identify feasible parameter regime. We discovered that the network topology determined the first moments of the stochastic process at stationarity, but not the dynamics of cell fate decision making. Combining higher moments of the expression distribution, we argue that the there is a unique parameter regime. Interestingly, the information entropy of our quantitative model seemed to be maximized in this unique regime, and we argue that it is how the GRN should have been evolutionarily selected. In the second example, I will present a toy model of GRN regulating biological clocks. We use PDMP to study how the oscillation is induced by promoter switching, and how the coherence of the oscillation can be improved by including a multiple-binding site mechanism. I will demonstrate that the analysis can be generalized to more sophisticated and biologically informed models and deliver important mechanistic insights about the stochastic oscillations of the GRNs.

Files:


Speaker:  Yen Ting Lin
Institution:  Los Alamos National Laboratory

Event Organizer:   Charlie Doering    doering@umich.edu

 

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