Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling.

A method is derived to coarse-grain the dynamics of complex molecular systems to a Markov jump process (MJP) describing how the system jumps between cells that fully partition its state space. The main inputs are relaxation times for each pair of cells, which are shown to be robust with respect to positioning of the cell boundaries. These relaxation times can be calculated via molecular dynamics simulations performed in each cell separately and are used in an efficient estimator for the rate matrix of the MJP. The method is illustrated through applications to Sinai billiards and a cluster of Lennard-Jones discs.

Force-clamp experiments reveal the free-energy profile and diffusion coefficient of the collapse of protein molecules.

We present force-clamp data on the collapse of ubiquitin polyproteins from a highly extended state to the folded length, in response to a quench in the force from 110 pN to 5 or 10 pN. Using a recent method for free-energy reconstruction from the observed nonequilibrium trajectories, we find that their statistics is captured by simple diffusion along the end-to-end length. The estimated diffusion coefficient of ∼ 100 nm(2) s(-1) is significantly slower than expected from viscous effects alone, possibly because of the internal degrees of freedom of the protein. The free-energy profiles give validity to a physical model in which the multiple protein domains collapse all at once and the role of the force is approximately captured by the Bell model.

A conformational transition in the myosin VI converter contributes to the variable step size.

Myosin VI (MVI) is a dimeric molecular motor that translocates backwards on actin filaments with a surprisingly large and variable step size, given its short lever arm. A recent x-ray structure of MVI indicates that the large step size can be explained in part by a novel conformation of the converter subdomain in the prepowerstroke state, in which a 53-residue insert, unique to MVI, reorients the lever arm nearly parallel to the actin filament. To determine whether the existence of the novel converter conformation could contribute to the step-size variability, we used a path-based free-energy simulation tool, the string method, to show that there is a small free-energy difference between the novel converter conformation and the conventional conformation found in other myosins. This result suggests that MVI can bind to actin with the converter in either conformation. Models of MVI/MV chimeric dimers show that the variability in the tilting angle of the lever arm that results from the two converter conformations can lead to step-size variations of ∼12 nm. These variations, in combination with other proposed mechanisms, could explain the experimentally determined step-size variability of ∼25 nm for wild-type MVI. Mutations to test the findings by experiment are suggested.