Splitting probabilities as optimal controllers of rare reactive events.

The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analog of the committor that solves a generalized bridge problem to the splitting probability that solves a boundary value problem under a bistable assumption. By invoking stochastic optimal control and spectral theory, we derive a general form for the optimal controller of a bridge process that connects two metastable states expressed in terms of the splitting probability. This formalism offers an alternative perspective into the role of the committor and its gradients in that they encode force fields that guarantee reactivity, generating trajectories that are statistically identical to the way that a system would react autonomously.

Variational deep learning of equilibrium transition path ensembles.

We present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

Solid-liquid coexistence of neon, argon, krypton, and xenon studied by simulations.

The noble elements constitute the simplest group of atoms. At low temperatures or high pressures, they freeze into the face-centered cubic (fcc) crystal structure (except helium). This paper investigates neon, argon, krypton, and xenon by molecular dynamics using the simplified atomic potentials recently proposed by Deiters and Sadus [J. Chem. Phys. 150, 134504 (2019)], which are parameterized using data from accurate ab initio quantum-mechanical calculations by the coupled-cluster approach at the single-double-triple level. We compute the fcc freezing lines and find good agreement with the empirical values. At low pressures, predictions are improved by including many-body corrections. Hidden scale invariance of the potential-energy function is established by showing that mean-squared displacement and the static structure factor are invariant along the lines of constant excess entropy (isomorphs). The isomorph theory of melting [Pedersen et al., Nat. Commun. 7, 12386 (2016)] is used to predict from simulations at a single state point the freezing line's shape, the entropy of melting, and the Lindemann parameter of the crystal at melting. Finally, our results suggest that the body-centered cubic crystal is the thermodynamically stable phase at high pressures.

Peptide Isomerization is Suppressed at the Air-Water Interface.

We use molecular dynamics simulations to study the thermodynamics and kinetics of alanine dipeptide isomerization at the air-water interface. Thermodynamically, we find an affinity of the dipeptide to the interface. This affinity arises from stabilizing intramolecular interactions that become unshielded as the dipeptide is desolvated. Kinetically, we consider the rate of transitions between the αL and ß conformations of alanine dipeptide and evaluate it as a continuous function of the distance from the interface using a recent extension of transition path sampling, TPS+U. The rate of isomerization at the Gibbs dividing surface is suppressed relative to the bulk by a factor of 3. Examination of the ensemble of transition states elucidates the role of solvent degrees of freedom in mediating favorable intramolecular interactions along the reaction pathway of isomerization. Near the air-water interface, water is less effective at mediating these intramolecular interactions.

Liquid-Liquid Phase Separation As the Second Step of Complex Coacervation.

Liquid-liquid phase separation (LLPS) between tyrosine- and arginine-rich peptides are of biological importance. To understand the interactions between proteins in the condensed phase in close analogy to complex coacervation, we run multiple umbrella calculations between oligomers containing tyrosine (pY) and arginine (pR). We find pR-pY complexation to be energetically driven. Metadynamics simulations on monomers suggest that this energy of complexation is correlated with the number of π-cation bonds. Free energy calculations for the binding between pairs of poly glutamate-pR dimers show striking similarities between this process and LLPS. These calculations suggest that proteins containing arginine and tyrosine residues do not undergo complexation followed by coacervation. The mechanism, rather, is akin to phase separation of neutral polyion pairs.

Driving Force for the Complexation of Charged Polypeptides.

The phase separation of oppositely charged polyelectrolytes in solution is of current interest. In this work, we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different force fields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all force fields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water does not play a significant role. For fully charged peptides, we find that the driving force for association is entropic in all cases when small ions either neutralize the poly ions, or are in excess. The removal of all counterions switches the driving force, making complexation energetic. This suggests that the entropy of complexation is dominated by the counterions. When only 6 residues of a 11-mer are charged, however, the driving force is energetic in the abscence of excess salt. The simulations shed insight into the mechanism of complex coacervation and the importance of realistic models for the polyions.