Modeling molecular kinetics with Milestoning. (17th December 2020) - Elber, Ron; Fathizadeh, Arman; Ma, Piao; Wang, Hao
Abstract: Time scales are of paramount importance in biology. Living systems exploit variations in time scales to aim processes in desired directions. The network of biochemical reactions shapes cellular responses and metabolism. Enzymes speed up the rate of reactions and molecular machines carry on cellular tasks. Significant efforts are invested in studying dynamics of biophysical processes and understanding their mechanisms. Experiments provide important clues, but the data can be sparse. Atomically detailed Molecular Dynamics simulations hold the promise of comprehensive pictures of these events. A challenge for simulations is the wide range of time scales in biology, from femtoseconds to hours. Straightforward Molecular Dynamics simulations of kinetics are typically bound by microseconds and unable to probe slower processes. For example, membrane permeation by a small molecule can take hours, slow events in protein folding, seconds, and enzymatic reactions, hundreds of milliseconds. To address these challenges, we introduce the method of Milestoning. Milestoning is a theory and an algorithm to enhance the sampling of kinetic events using computer simulations. Milestoning exploits short trajectories between interfaces of cells in coarse space. Short trajectories are efficient to compute and provide a sequence of approximations that converge to the exact solution. The theory is discussed, and several examples illustrate the use of Milestoning. We consider an enzymatic reaction, peptide permeation through a phospholipid membrane, and the translocation of the lethal factor through the Anthrax channel. The high versatility of Milestoning suggests that it is a useful tool for investigations of complex biomolecular reactions. This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Abstract : A molecular model of the anthrax toxin. In light blue, we show the anthrax channel, which is embedded in a membrane separating the endosome and the cytosol (the membrane is not shown). In yellow and red, we show steps in the translocation process of the lethal factor of anthrax. The loose N terminal chain (red—reactant and yellow—product) slides first into the channel until it hits the ϕ clamp. Using Milestoning, we computed the free energy profile and the rate of the translocation process. The figure is adapted from reference Ma P, Carednas AE, Chaughari ML, Elber R, Rempe SB. The impact of protonation on early translocation of anthrax lethal factor: Kinetics from molecular dynamics simulations and milestoning theory. J Am Chem Soc. 2017;139:14837–14840 with permission. The model is based on the crystal structure of Feld GK, Thoren KL, Kintzer AF, et al. Structural basis for the unfolding of anthrax lethal factor by protective antigen oligomers. Nat Struct Mol Biol. 2010;17(11):1383–U245.