University of North Carolina at Chapel Hill Graduate School
Doi
Abstract
The spatio-temporal organization of the genome is critical to the ability of the cell to store huge amounts of information in highly compacted DNA while also performing vital cellular functions. Experimental methods provide a window into the geometry of the chromatin but cannot provide a full picture in space and time.Polymer models have been shown to reproduce properties of chromatin and can be used to make simulated observations, informing biological experimentation. We apply a previously-studied model of the full yeast genome with dynamic protein crosslinking in the nucleolus which showed the emergence of clustering when the crosslinking timescale was sufficiently fast. We investigate the the crosslinking timescale at finer resolution and newly identify the presence of a \textit{flexible clustering} regime for intermediate timescales, which maximizes mixing of nucleolar beads, of significant interest due to the role mixing plays in nuclear processes. In order to robustly identify spatio-temporal clustering structure, we map our problem to a multi-layer network and then apply the multi-layer modularity community detection algorithm, showing the presence of spatio-temporal community structure in the fast and intermediate clustering regimes. We perform analysis of the relationship between cluster size and the ensuing stability of clusters,revealing a heterogeneous collection of clusters in which cluster size correlates with stability. We view the stochastic switching as producing an effective thermal equilibrium byextending the WKB approach for deriving quasipotentials in switching systems to the case of an overdamped Langevin equation with switching force term, and derive the associated Hamilton-Jacobi equation. We apply the string method for finding most-probable transition paths, revealing previously unreported numerical challenges; we present modifications to the algorithms to overcome them. We show that our methods can correctly compute asymptotic escape times by comparison to Monte Carlo simulations, and verified an important principle: the effective force is often significantly weaker than a naive average of the switching suggests. Through this multifaceted approach, we have shown how stochastic crosslinking leads to complex emergent structure, with different timescales optimizing different properties, and shown how the structure can be analyzed using both network data based tools and through stochastic averaging principles.Doctor of Philosoph
