Transition path dynamics in the binding of intrinsically disordered proteins: A simulation study

Association of proteins and other biopolymers is a ubiquitous process in living systems. Recent single-molecule measurements probe the dynamics of association in unprecedented detail by measuring the properties of association transition paths, i.e., short segments of molecular trajectories between the time the proteins are close enough to interact and the formation of the final complex. Interpretation of such measurements requires adequate models for describing the dynamics of experimental observables. In an effort to develop such models, here we report a simulation study of the association dynamics of two oppositely charged, disordered polymers. We mimic experimental measurements by monitoring intermonomer distances, which we treat as "experimental reaction coordinates." While the dynamics of the distance between the centers of mass of the molecules is found to be memoryless and diffusive, the dynamics of the experimental reaction coordinates displays significant memory and can be described by a generalized Langevin equation with a memory kernel. We compute the most commonly measured property of transition paths, the distribution of the transition path time, and show that, despite the non-Markovianity of the underlying dynamics, it is well approximated as one-dimensional diffusion in the potential of mean force provided that an apparent value of the diffusion coefficient is used. This apparent value is intermediate between the slow (low frequency) and fast (high frequency) limits of the memory kernel. We have further studied how the mean transition path time depends on the ionic strength and found only weak dependence despite strong electrostatic attraction between the polymers.