RESUMEN
We investigate barrier-crossing processes corresponding to collective hydrogen-bond rearrangements in liquid water using Markov state modeling techniques. The analysis is based on trajectories from classical molecular dynamics simulations and accounts for the full dynamics of relative angular and separation coordinates of water clusters and requires no predefined hydrogen bond criterium. We account for the complete 12-dimensional conformational subspace of three water molecules and distinguish five well-separated slow dynamic processes with relaxation times in the picosecond range, followed by a quasi-continuum spectrum of faster modes. By analysis of the Markov eigenstates, these processes are shown to correspond to different collective interchanges of hydrogen-bond donors and acceptors. Using a projection onto hydrogen-bond states, we also analyze the switching of one hydrogen bond between two acceptor water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along alternative routes that involve different intermediate states with short-lived alternative hydrogen bonds or weakly bound states.
RESUMEN
The concept of a protein diffusing in its free-energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free-energy profiles for different RCs exhibit significant variations, some having an activation barrier, while others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free-energy and diffusivity effects into a single function, the rescaled free-energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.
