Nonequilibrium dynamics of complex systems: proteins and active matter

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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.