Effect of localized active fluctuations in conformation and dynamics of chromosomal DNA*

Active fluctuations play a significant role in the structure and dynamics of biopolymers that are instrumental in the functioning of living cells, including the proteins and nucleic acids that comprise chromosomal DNA. For a large range of experimentally accessible length and time scales, chromosomal DNA subject to varying transcriptional and topoisomerase activity can be represented as a flexible chain that is subject to active fluctuations that depends on genomic position. In this work, we introduce a mathematical framework that integrates the spatial and temporal patterns of the fluctuations on a flexible polymer to different observables that describe the dynamics and conformations of the polymer. We identify the length and time scale where the behavior of the polymer takes a significant departure from the behavior of an equilibrium chain. Furthermore, we show that the localized nature of fluctuation introduces a distinction of behavior between the segments near and far from the source of the fluctuation both in position and time. We then consolidate these predictions into a framework to interpret the active-force distribution from experimental measurements of chromosomal dynamics. Altogether, this work sets the basis for understanding and interpreting the role of spatiotemporal pattern of fluctuations in the dynamics, conformation, and eventually the functionality of the biopolymers such as chromosomes in living cells and in vitro DNA subject to varying biological processes.