Ab initio sampling of transition paths by conditioned Langevin dynamics

MinActionPath2: path generation between different conformations of large macromolecular assemblies by action minimization

Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/minactionpath2_submission.

Sampling constrained stochastic trajectories using Brownian bridges

We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics, based on Brownian bridges. <p>The trajectories are conditioned to end at a certain point (or in a certain region) in space.</p> <p>The bridge equations can be recast exactly in the form of a non linear stochastic integro-differential equation.</p> <p>This equation can be very well approximated when the trajectories are closely bundled together in space, i.e. at low temperature, or for transition paths. The approximate equation can be solved iteratively, using a fixed point method.</p> <p>We discuss how to choose the initial trajectories and show some examples of the performance of this method on some simple problems.</p> <p>The method allows to generate conditioned trajectories with a high accuracy.

Direct Evaluation of Rare Events in Active Matter from Variational Path Sampling

Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogs, transformations between distinct metastable states in active matter proceed through rare fluctuations; however, their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.

Reinforcement learning of rare diffusive dynamics

We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.

Description of a stochastic system by a nonadapted stochastic process

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling between forward and backward variables, and it is well suited for situations in which initial and final conditions are imposed on different components of the system, and the coupling between those components is weak. The form of the stochastic equations in our approach is determined by requiring that they generate the same statistics obtained in a forward description of the dynamics. Numerical tests are carried out on a few simple two-degrees-of-freedom systems. The merit and the difficulties of the approach are discussed and compared to more traditional strategies based on transition path sampling and simple shooting algorithms.

Transition path theory from biased simulations

Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q⁺(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first we further extend the recently introduced self-consistent path sampling algorithm in order to compute the committor q⁺(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.

Generating conformational transition paths with low potential-energy barriers for proteins

The knowledge of conformational transition paths in proteins can be useful for understanding protein mechanisms. Recently, we have introduced the As-Rigid-As-Possible (ARAP) interpolation method, for generating interpolation paths between two protein conformations. The method was shown to preserve well the rigidity of the initial conformation along the path. However, because the method is totally geometry-based, the generated paths may be inconsistent because the atom interactions are ignored. Therefore, in this article, we would like to introduce a new method to generate conformational transition paths with low potential-energy barriers for proteins. The method is composed of three processing stages. First, ARAP interpolation is used for generating an initial path. Then, the path conformations are enhanced by a clash remover. Finally, Nudged Elastic Band, a path-optimization method, is used to produce a low-energy path. Large energy reductions are found in the paths obtained from the method than in those obtained from the ARAP interpolation method alone. The results also show that ARAP interpolation is a good candidate for generating an initial path because it leads to lower potential-energy paths than two other common methods for path interpolation.