Non-equilibrium dynamics and microphase separation in biology

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A framework for non-equilibrium statistical mechanics remains one of the major open questions in science. The project will attempt to build on recent progress in this area which has identified a general framework to find non-equilibrium steady states for a wide variety of physical systems. This new framework promises to be particularly useful for coarse-graining the dynamics and thermodynamics of systems of complex interacting particles by linking large scale dynamics to microscopic interactions.Phase separation in biology is currently an area of growing interest amongst physicists, biologists, applied mathematicians and engineers. Recently, it has been shown that liquid-liquid phase separation can be used by cells as a mechanism for self-assembly of membraneless organelles in the nucleus [Berry et al, 2018, Rep. Prog. Phys., 81, 046601]. The question we are interested in is the physical mechanism used by certain types of cancer cells, known as ALT cancers, to cluster their telomeres. There is evidence that clustering of telomeric DNA is an important step for lengthening of telomeres, leading to unrestricted growth of cancer cells. Recent experimental observations show how interactions between proteins and telomeres leads to clustering of telomeric DNA in droplets that show characteristics of liquid phase separated droplets [Zhang et al, 2019, bioRxiv, 633040]. However, telomeres are constrained by their chromosomes, which prevents global phase separation so instead we model telomeres on chromosomes as block copolymers and investigate whether microphase separation into micelle-like structures can lead to telomere clustering.Initially, we will use a mean field approach based on Flory-Huggins theory to calculate a phase diagram to understand conditions for telomere clustering, but in the next part of the project, we will use statistical mechanics to consider corrections to the mean field theory and move away from equilibrium. This more thorough analysis will enable us investigate the growth dynamics of telomere clusters.