Divided Saddle Theory: A New Idea for Rate Constant Calculation

Toward Convergence in Free Energy Calculations for Protein Conformational Changes: A Case Study on the Thin Gate of Mhp1 Transporter

It has been challenging to obtain reliable free energies for protein conformational changes from all-atom molecular dynamics simulations, despite the availability of many enhanced sampling techniques. To alleviate the difficulties associated with the enormous complexity of the conformational space, here we propose a few practical strategies for such calculations, including (1) a stringent method to examine convergence by comparing independent simulations starting from different initial coordinates, (2) adoption of multistep schemes in which the complete conformational change consists of multiple transition steps, each sampled using a distinct reaction coordinate, and (3) application of boundary restraints to simplify the conformational space. We demonstrate these strategies on the conformational changes between the outward-facing and outward-occluded states of the Mhp1 membrane transporter, obtaining the equilibrium thermodynamics of the relevant metastable states, the kinetic rates between these states, and the reactive trajectories that reveal the atomic details of spontaneous transitions. Our approaches thus promise convergent and reliable calculations to examine intuition-based hypotheses and to eventually elucidate the underlying molecular mechanisms of reversible conformational changes in complex protein systems.

Study on the Formation of Glycine by Hydantoin and Its Kinetics

The preparation of glycine by the hydantoin method is currently a relatively advanced process. The raw materials of this process are nontoxic, the operation process is simple and safe, the side reactions are few, and the yield of glycine is high. The core reaction of the hydantoin method is the hydrolysis of hydantoin. The hydrolysis is divided into two steps: first, hydantoin is hydrolyzed into hydantoin acid, and hydantoin acid is further hydrolyzed into glycine. At a temperature of 423.15 K, a molar ratio of sodium hydroxide to hydantoin of 1:3, and a total reaction time of 6 h, the conversion rate of hydantoin reached 100% and the yield of glycine reached 91%. At the same time, by calculating the hydrolysis kinetic parameters, the reaction was determined to be a first-order series reaction, and a kinetic model was established, which laid the foundation for the development of a green glycine process and a new reactor.

Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.

Molecular mechanism for cavitation in water under tension

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.

S-shooting: a Bennett–Chandler-like method for the computation of rate constants from committor trajectories

Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett–Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.