A recently introduced computational algorithm to extend time scales of atomically detailed simulations is illustrated. The algorithm, milestoning, is based on partitioning the dynamics to a sequence of trajectories between "milestones" and constructing a non-Markovian model for the motion along a reaction coordinate. The kinetics of a conformational transition in a blocked alanine is computed and shown to be accurate, more efficient than straightforward molecular dynamics by a factor of about 9, and nonexponential. A general scaling argument predicts a linear speedup with the number of milestones for diffusive processes and an exponential speedup for transitions over barriers. The algorithm is also trivial to parallelize. As a side result, milestoning also produces the free energy profile along the reaction coordinate and is able to describe nonequilibrium motions along one (or a few) degrees of freedom.

Myosin II is a molecular motor that converts chemical to mechanical energy and enables muscle operations. After a power stroke, a recovery transition completes the cycle and returns the molecular motor to its prestroke state. Atomically detailed simulations in the framework of the Milestoning theory are used to calculate kinetics and mechanisms of the recovery stroke. Milestoning divides the process into transitions between hyper-surfaces (Milestones) along a reaction coordinate. Decorrelation of dynamics between sequential Milestones is assumed, which speeds up the atomically detailed simulations by a factor of millions. Two hundred trajectories of myosin with explicit water solvation are used to sample transitions between sequential pairs of Milestones. Collective motions of hundreds of atoms are described at atomic resolution and at the millisecond time scale. The experimentally measured transition time of about a millisecond is in good agreement with the computed time. The simulations support a sequential mechanism. In the first step the P-loop and switch 2 close on the ATP and in the second step the mechanical relaxation is induced via the relay and the SH1 helices. We propose that the entropy of switch 2 helps to drive the power stroke. Secondary structure elements are progressing through a small number of discrete states in a network of activated transitions and are assisted by side chain flips between rotameric states. The few-state sequential mechanism is likely to enhance the efficiency of the relaxation reducing the probability of off-pathway intermediates.conformational transitions | molecular motors | rate calculations | reaction path | long time dynamics W e consider the function of the protein myosin II (for a review see ref. 1). Myosin plays a key role in the contraction of muscles and carries out a cycle of "power" and "recovery" strokes that convert chemical to mechanical energy. A concrete model for the cycle was proposed by Lymn and Taylor (2) in 1971, a model that captures the essential steps of the process. Myosin is made of a large globular head plus a long, lighter tail. Pairs of myosin molecules self-assemble by winding their tails into a coiled coil, forming double-headed structures. These pairs then aggregate to form a long thick filament that aligns itself with a thinner filament of the complementary protein actin, such that individual myosin heads bind to individual actin monomers. These filaments bundle together to form muscle fibers, and muscle contraction consists of the sliding of actin and myosin filaments past one another. The cycle requires an input of energy, which myosin obtains by hydrolyzing adenosine triphosphate (ATP).In the present manuscript we focus on one segment of the cycle, the recovery stroke. Of course, to understand the complete cycle the recovery and the power strokes are needed. While the power stroke is the step in which useful mechanical force is generated, the motions of myosin during the power stroke are similar to the transition (in reverse) of the recov...