Non-equilibrium dynamics and microphase separation in biology

非平衡统计力学的框架仍然是科学中的一个主要开放问题。该项目将试图在这一领域最近取得的进展的基础上再接再厉，这些进展已经确定了一个总体框架，以找到各种物理系统的非平衡稳定状态。这一新的框架有望通过将大尺度动力学与微观相互作用联系起来，对复杂相互作用粒子系统的动力学和热力学进行粗粒化处理，生物学中的相分离是目前物理学家、生物学家、应用数学家和工程师越来越感兴趣的一个领域。最近，已经表明液-液相分离可以被细胞用作细胞核中无膜细胞器自组装的机制[Berry et al，2018，Rep. Prog.物理、81，046601]。我们感兴趣的问题是某些类型的癌细胞（称为ALT癌）聚集端粒的物理机制。有证据表明，端粒DNA的聚集是延长端粒的重要步骤，导致癌细胞不受限制地生长。最近的实验观察表明，蛋白质和端粒之间的相互作用如何导致端粒DNA在液滴中聚集，显示出液相分离液滴的特征[Zhang et al，2019，bioRxiv，633040]。然而，端粒受到染色体的限制，这阻止了全局相分离，因此我们将染色体上的端粒建模为嵌段共聚物，并研究微相分离成胶束状结构是否会导致端粒聚集。最初，我们将使用基于Flory-Huggins理论的平均场方法来计算相图，以了解端粒聚集的条件，但在项目的下一部分，我们将使用统计力学来考虑对平均场理论的修正，并远离平衡。这种更彻底的分析将使我们能够研究端粒簇的生长动力学。

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.