Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm to compute efficiently a sequence of isocommittor surfaces. These surfaces are considered an optimal reaction coordinate. The algorithm analyzes Milestoning results to determine the committor function. It requires only the transition probabilities between the milestones, and not transition times. We discuss the following numerical examples: (i) a transition in the Mueller potential; (ii) a conformational change of a solvated peptide; and (iii) cholesterol aggregation in membranes.

We report atomically detailed molecular dynamics simulations of the permeation of the lethal factor (LF) N-terminal segment through the anthrax channel. The N-terminal chain is unstructured and leads the permeation process for the LF protein. The simulations are conducted in explicit solvent with Milestoning theory, making it possible to extract kinetic information from nanoseconds to milliseconds time scales. We illustrate that the initial event is strongly influenced by the protonation states of the permeating amino acids. While the N-terminal segment passes easily at high protonation state through the anthrax channel (and the ϕ clamp), the initial permeation represents a critical step, which can be irreversible and establishes a hook in the channel mouth.

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

Reaction coordinates chart pathways from reactants to products of chemical reactions. Determination of reaction coordinates from ensembles of molecular trajectories has thus been the focus of many studies. A widely used and insightful choice of a reaction coordinate is the committor function, defined as the probability that a trajectory will reach the product before the reactant. Here, we consider alternatives to the committor function that add useful mechanistic information, the mean first passage time, and the exit time to the product. We further derive a simple relationship between the functions of the committor, the mean first passage time, and the exit time. We illustrate the diversity of mechanisms predicted by alternative reaction coordinates with several toy problems and with a simple model of protein searching for a specific DNA motif.

ranging from 0.4 to 23 mM. The other class of molecules are halogenated cisimidazoline analogs such as Nutlin-3a that inhibit MDM2 with IC50 values ranging from 0.086 to 26 mM. To study the thermodynamics and kinetics of binding for these inhibitors, we build multi-ensemble Markov models (MEMMs) from explicit-solvent molecular dynamics trajectories of the binding/unbinding reactions biased by umbrella sampling (US) and scaled nonbonded interactions. This methodology allows us to observe significantly more binding and unbinding events than would be observed with unbiased sampling. We discuss the accuracy of estimated affinities and binding kinetics.