Memory and Inheritance in Gene Regulatory Networks

Abstract

Non-genetic heterogeneity, the emergence of phenotypic differences among genetically identical cells in the same environment, is a mechanism by which bacteria and cancer cells may evade drug treatment and proliferate further. For such heterogeneity to have lasting consequences, the gene expression state must be heritable across several cell divisions. This is referred to as ``cellular memory'' on an intermediate timescale. In this thesis, I investigate how the structure of the gene regulatory network shapes the emergence and heritability of such memory states by approaching the problem from two complementary directions. In the first part, I model a gene regulatory network as a high-dimensional deterministic dynamical system near a fixed point. Random Matrix Theory techniques can then be used to identify when a typical GRN may support a memory state, and when a memory state becomes attributable to a coordinated module of genes rather than individual genes. I derive analytical expressions for the stability boundary and the localisation of the dominant eigenmode of the Jacobian matrix. These results reveal a trade-off between inter-gene coupling strength and self-regulation, which is analogous in structure to May's criterion for ecological networks. In the second part, I model gene expression as a stochastic birth-death process in a growing and dividing cell and derive exact closed-form expressions for the covariance between related cells using the Linear Noise Approximation. These expressions reveal conditions under which a gene may exhibit heritable fluctuations, which are a property of the local regulatory context of the gene as well as its own dynamics. These predictions are validated numerically on small regulatory motifs, including a linear cascade and a feedforward loop. The results obtained in this thesis provide testable predictions about the network and motif-level determinants of cellular memory, with implications for understanding cancer drug resistance and antibiotic resistance.