Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA.
Department of Material Science and Engineering, Stanford University, Stanford, California 94305, USA.
Soft Matter. 2024 Feb 21;20(8):1694-1701. doi: 10.1039/d3sm01491f.
Active fluctuations play a significant role in the structure and dynamics of biopolymers ( 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.
活性涨落对生物聚合物（染色质和细胞骨架蛋白）的结构和动力学起着重要作用，这些聚合物在活细胞的功能中起着关键作用。对于大量可实验访问的长度和时间尺度，这些聚合物可以表示为柔性链，它们受到空间和时间变化的涨落力的影响。在这项工作中，我们引入了一个数学框架，将涨落的时空模式与描述聚合物动力学和构象的不同可观测量相关联。我们通过分析聚合物上的点涨落的情况来证明这种方法的有效性，该点涨落具有随时间呈指数衰减的相关性，且具有有限的时间常数。具体来说，我们确定了聚合物行为显著偏离 Rouse 链行为的长度和时间尺度，以及沿着链的涨落的影响范围。此外，我们表明聚合物的构象保留了来自更早时间的活性涨落的记忆。总之，这项工作为理解和解释生物聚合物在活细胞中的动力学、构象和功能中涨落的时空模式的作用奠定了基础。
