Markovian milestoning with Voronoi tessellations

Maddalena Venturoli
New York University
Courant Institute of Mathematical Sciences

Milestoning is a procedure to reduce the dynamics of a molecular dynamics (MD) trajectory to a continuous-time Markov chain describing the succession of transitions between hypersurfaces (the milestones). The main issue then becomes the estimation of the rate matrix specifying this chain. In this talk I will discuss a new milestoning procedure in which the edges of Voronoi cells define the milestones, and the rate matrix is calculated by running MD simulations restricted to these cells. This procedure bypasses the need to reinitialize trajectories on the milestones, as it is done in traditional milestoning, and thereby avoids the approximation made in traditional milestoning that the distribution to be used to reinitialize the trajectories is the equilibrium one. I will describe the new milestoning procedure in detail, justify it, and use it to study the kinetics of protein insertion into a lipid bilayer by means of a coarse-grained model.

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