Nonequilibrium dynamics of complex systems: proteins and active matter

本提案概述了理论工具的发展和应用，这些理论工具旨在描述复杂系统的长时间动力学，特别关注模型蛋白质系统的结构转变动力学和纳米运动系统的物理失平衡。这两个项目都涉及到粗粒度模拟、数值分析技术以及基础理论工作的结合。******第一个项目涉及构建和验证一个简单的模型，用于模拟溶液中的蛋白质。这些研究的目的是建立化学成分之间的联系，不同的三维结构的人口作为温度的函数，和蛋白质的动力学。该系统的模拟将与理论预测进行比较，以检查特定的相互作用如何导致与蛋白质错误折叠相关的疾病，以及不理想的分子内相互作用如何影响蛋白质的稳定性和折叠行为。******在自然界中已经进化出大量的分子机器，它们积极地利用外部环境条件来执行纳米级的基本生物功能。这类机器既可以单独操作，也可以集体协作操作。合成纳米马达是特别感兴趣的，因为它们的形态和化学性质可以被定制来执行特定的任务。在第二个项目中，我们考虑了纳米马达系统的动力学，其活性是由于马达表面发生的催化化学过程而产生的。我们的研究是基于微观模型，能够解释分子间相互作用，多体浓度梯度，流体流动和随机热波动的影响。电机悬架表现出复杂的集体现象，包括动态聚类、相分离和巨数波动。这种行为可能是由化学活性和流体动力学效应引起的综合效应引起的，其中由给定电机的运动引起的流体流动对其他电机施加不均匀的压力。我们计划详细研究这种相互作用介导集体动力学的方式，并利用我们的模拟来探索作为马达催化性能和环境条件的函数而产生的大密度波动和动态聚类的机制。我们将使用为驱动多相系统开发的统计机械工具，为在远离平衡的条件下运行的纳米电机系统的演化特征制定精确的数量表达式。**

This proposal outlines the development and application of theoretical tools designed to characterize the long time dynamics of complex systems, with a particular focus on the dynamics of structural transitions in model protein systems and the physics of nanomotor systems that operate out of equilibrium. Both projects involve a combination of coarse-grain simulations, numerical analysis techniques as well as fundamental theoretical work.******The first project concerns the construction and validation of a simple model designed to mimic a protein in solution. The goal of these studies is to establish the connection between chemical composition, the populations of different three-dimensional structures as a function of temperature, and the dynamics of proteins. Simulations of the system will be compared with theoretical predictions in order to examine how particular interactions can lead to diseases linked to the misfolding of proteins and how non-desirable intramolecular interactions influence the stability and folding behavior of proteins. ******A large number of molecular machines have evolved in the natural world that actively harness external environmental conditions to perform essential biological functions at the nanoscale. Such machines can operate both as individual units and cooperatively in large groups. Synthetic nanomotors are of particular interest since their morphology and chemical properties may be tailored to carry out specific tasks. In the second project, we consider the dynamics of a system of nanomotors operating out of equilibrium whose activity arises due to catalytic chemical processes occurring at the surface of the motors. Our studies are based on microscopic models that are able to account for intermolecular interactions, many-body concentration gradients, fluid flows and the effect of random thermal fluctuations. Suspensions of motors exhibit complex collective phenomena, including dynamical clustering, phase separation, and giant-number fluctuations. This behavior can arise from a combination of effects arising from chemical activity and hydrodynamic effects in which fluid flow induced by the motion of a given motor exerts non-uniform pressure forces on others. We plan to study in detail the way in which the collective dynamics is mediated by such interactions and use our simulations to explore the mechanisms through which large density fluctuations and dynamical clustering arise as a function of the catalytic properties of the motors and the environmental conditions. We will use statistical mechanical tools developed for driven multi-phase systems to formulate exact expressions for quantities that characterize the evolution of the nanomotor system operating under conditions that are far from equilibrium. **