Abstract: In this talk, I will briefly discuss some projects done in my lab and some potential projects we can perform at CSRC. Recent breakthroughs of cell phenotype reprogramming impose theoretical challenge on unraveling the complexity of large circuits maintaining cell phenotypes coupled at many different epigenetic and gene regulation levels, and quantitatively describing the phenotypic transition dynamics. A popular picture proposed by Waddington views cell differentiation as a ball sliding down a landscape with valleys corresponding to different cell types separated by ridges. Based on theories of dynamical systems we establish a novel “epigenetic state network” framework that captures the global architecture of cell phenotypes, which allows us to translate the metaphorical low- dimensional Waddington’s epigenetic landscape concept into a simple-yet-predictive rigorous mathematical framework of cell phenotypic transitions. Specifically, we simplify a high dimensional epigenetic landscape into a collection of discrete states corresponding to stable cell phenotypes connected by optimal transition pathways among them. We then apply the approach to the reprogramming process of fibroblasts to induced pluripotent stem cells (iPSC) and cardiomyocyte. Our approach provides a theoretical framework for studying cell phenotypic transitions.
Cells sharing the same set of genomes may exist in different and inheritable cell fates. Epigenetic histone covalent modification is one of the main mechanisms regulating this non-genetic inheritance. However, the exact molecular mechanism for epigenetic memory is not clear. Using experimentally observed molecular properties and estimated parameters, we construct a discrete-state Potts model describing the dynamics of a linear chain of nucleosomes, formed by histones wrapped with DNA, with both their binding states of histone modification enzymes, and their covalent modification states. Changing of the binding states, which is often in subsecond time scales, is treated as an equilibrium process and can be represented by transfer matrices. Our stochastic simulations and analysis reveal that cooperative enzyme binding leads to effective nonlocal influence of a nucleosome on the covalent state of others; this nonlocal cooperative effect, together with a positive feedback caused by nucleosome covalent state dependent enzyme binding affinity, allow a nucleosome to "read” the covalent state of others, and recruit corresponding enzyme to “write” on itself a covalent state biased to the majority of others. The resultant epigenetic histone modification patterns are robustly inheritable against strong perturbations due to stochastic enzymatic reactions, histone turnovers, and cell cycle dependent histone replacements.
The Zwanzig-Mori projection formalism is widely used in studying systems with many degrees of freedom. Recently Xing and Kim used the projection formalism and derived the generalized Langevin equations (GLEs) for a general stochastic system not necessarily obeying detailed balance. In this study we develop a numerical procedure to reconstruct the GLEs from data. Numerical tests on two biological networks show remarkable agreement between the results calculated from the reconstructed GLEs and those of full model simulations. We suggest that the procedure can be applied in model reduction and a novel way of nonlinear time series analysis.
