Mesoscale, long-time mixing of chromosomes and its connection to polymer dynamics

Life sets off a cascade of machines

Life is invasive, occupying all physically accessible scales, stretching between almost nothing (protons, electrons, and photons) and almost everything (the whole biosphere). Motivated by seventeenth-century insights into this infinity, this paper proposes a language to discuss life as an infinite double cascade of machines making machines. Using this simplified language, we first discuss the micro-cascade proposed by Leibniz, which describes how the self-reproducing machine of the cell is built of smaller submachines down to the atomic scale. In the other direction, we propose that a macro-cascade builds from cells larger, organizational machines, up to the scale of the biosphere. The two cascades meet at the critical point of 103 s in time and 1 micron in length, the scales of a microbial cell. We speculate on how this double cascade evolved once a self-replicating machine emerged in the salty water of prebiotic earth.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.