DMS/NIGMS 2: The mathematics of epigenetic regulation in human cells

A major challenge at the interface of mathematics and molecular and cellular biology remains the development of accurate and predictive models of epigenetic mechanisms. While eukaryotic transcription is substantially influenced via epigenetic mechanisms, the majority of mathematical models pay little

attention to this crucial regulation modality. Herein we propose a theoretical, computational, and experimental framework to model epigenetic regulatory networks in single cells. Herein we introduce a theoretical, computational, and experimental framework to model epigenetic regulatory networks in single

cells. Specifically, we propose to assemble and stably integrate epigenetic regulators and increasingly complex circuits in human cells. These stably integrated circuits will serve as biomolecular "ground truth" for inference and characterization techniques comprising theory and computational analysis in an iterative

manner. Using theoretical analysis coupled with experimentation, we will comprehensively characterize the circuits to identify general principles of epigenetic mechanisms with emphasis on probing their dynamic behavior and stability. The transforming quality of our proposal is based on the following notions.

We will establish a methodology to rapidly assemble and stably integrate libraries of CRISPR-based epigenetic regulators in human cells. These libraries will cover a wide parameter space providing wealth of data for extracting parameters to inform the mathematic models. Our methodology for rapid library

assembly is a significant advance for the mammalian synthetic biology field, where progress is hampered by slow experimental timescales. We will study the properties of epigenetic circuits stably integrated in a panel of human cell lines. We will test the boundaries of genome editing of safe harbor loci and develop

new methods for integrating large DNA cassettes. We will develop a theoretical and computational framework to model single-cell stochastic gene expression kinetics in hybrid gene regulatory networks. We will validate and calibrate the models using experimental data generated using custom epigenetic regulators. We will correlate the effects of network topology and mode of regulation on the stationary and

dynamic behavior of stochastic gene expression. Validated models of epigenetic regulation will be used to predict the conditions capable to produce multistability, critical phase transitions, and oscillations.