Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these states by a large set of descriptors and employ neural networks to compress this information in a lower-dimensional space, using Fisher's linear discriminant as an objective function to maximize the discriminative power of the network. We test this method on alanine dipeptide, using the non-linearly separable dataset composed by atomic distances. We then study an intermolecular aldol reaction characterized by a concerted mechanism. The resulting variables are able to promote sampling by drawing non-linear paths in the physical space connecting the fluctuations between metastable basins. Lastly, we interpret the behavior of the neural network by studying its relation to the physical variables. Through the identification of its most relevant features, we are able to gain chemical insight into the process.
A popular way to accelerate the sampling of rare events in molecular dynamics simulations is to introduce a potential that increases the fluctuations of selected collective variables. For this strategy to be successful, it is critical to choose appropriate variables. Here we review some recent developments in the data-driven design of collective variables, with a focus on the combination of Fisher's discriminant analysis and neural networks. This approach allows to compress the fluctuations of metastable states into a low-dimensional representation. We illustrate through several examples the e…
Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few generalized degrees of freedom, referred to as collective variables (CVs), to represent and drive the sampling of the free energy landscape. In theory, these CVs should separate different metastable states and correspond to the slow degrees of freedom of the studied physical process. To this aim, we propose a new method that we call multiscale reweighted stochasti…
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate set of collective variables. These are meant to describe the system's modes that most slowly approach equilibrium. Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the eigenfunctions and eigenvalues of the transfe…
Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space, and separate downstream parts map the latent space to predictions of basin class labels and potential energies. The resulting latent space is shown to be an effective lo…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that is based on constructing a model probability density from which a bias potential is derived. The model relies on the fact that in a physical system most of the configurations visited can be grouped into isolated metastable islands. To each island we associate a distribution that is fitted to a Gaussian mixture. The different distributions are linearly combin…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations. This is often caused by broad transition time distributions in which extremely slow events have a non-negligible probability. Stochastic resetting, i.e., restarting simulations at random times, was recently shown to significantly expedite processes that follow such distributions. Here, we employ resetting for enhanced sampling of molecular simulations for t…
Normal molecular dynamics simulations are usually unable to simulate chemical reactions due to the low probability of forming the transition state. Therefore, enhanced sampling methods are implemented to accelerate the occurrence of chemical reactions. In this investigation, we present an application of metadynamics in simulating an organic multi-step cascade reaction. The analysis of the reaction trajectory reveals the barrier heights of both forward and reverse reactions. We also present a discussion of the advantages and disadvantages of generating the reactive pathway using molecular dynam…
The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods are able to obtain sufficient sampling in order to draw the free energy, the transition states are often sparsely sampled. We propose an approach based on the Variationally Enhanced Sampling Method to enhance sampling in the transition region. To this effect, we introduce a dynamic target distribution which uses the derivative of the instantaneous free ener…
Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究所）；Biophysics Program, University of Maryland（马里兰大学生物物理学项目）；Department of Chemistry and Biochemistry, University of Maryland（马里兰大学化学与生物化学系）
Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation time. This review aims to present the unifying principles and differences of many of the computational methods currenly used for enhanced sampling in molecular simulations of biomolecules, soft matter and molecular crystals. Indeed, despite the apparent abundance and divergence of such methods, the principles at their core can be boiled down to a relatively li…
A key step in the development of a new drug is the design of drug-excipient complexes that lead to an optimal drug release kinetics. Computational chemistry, specifically enhanced sampling molecular dynamics methods, can play a key role in this context by minimizing the need for expensive experiments and reducing cost and time. Here, we show that recent advances in enhanced sampling methodologies can be brought to fruition in this area. We demonstrate the potential of these methodologies by simulating the release kinetics of the complex praziquantel-montmorillonite in water. Praziquantel finds…
Massachusetts Institute of Technology（麻省理工学院）；Charles University（查理大学）
Simulating rare events, such as the transformation of a reactant into a product in a chemical reaction typically requires enhanced sampling techniques that rely on heuristically chosen collective variables (CVs). We propose using differentiable simulations (DiffSim) for the discovery and enhanced sampling of chemical transformations without a need to resort to preselected CVs, using only a distance metric. Reaction path discovery and estimation of the biasing potential that enhances the sampling are merged into a single end-to-end problem that is solved by path-integral optimization. This is a…
We introduce a novel enhanced sampling approach named OPES flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the On-the-fly-Probability-Enhanced-Sampling (OPES) approach [Invernizzi and Parrinello, JPC Lett. 2020], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double well…
Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials
Professorship of Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich（多尺度流体材料建模教授职位，工程物理与计算系，技术大学慕尼黑工程与设计学院）
University of Notre Dame（圣母大学）；Technical University of Munich（慕尼黑工业大学）
Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the configurational space by enhanced sampling methods depends on the choice of collective variables (CVs). In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory. The ability to generate samples of the fine-scale atomistic configurations using limited training data a…
We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. We analyze the effect of the system size on the ice Ih-liquid free energy differ…
We calculate bubble nucleation rates in a Lennard-Jones fluid through explicit molecular dynamics simulations. Our approach -- based on a recent free energy method (dubbed reweighted Jarzynski sampling), transition state theory, and a simple recrossing correction -- allows us to probe a fairly wide range of rates in several superheated and cavitation regimes in a consistent manner. Rate predictions from this approach bridge disparate independent literature studies on the same model system. As such, we find that rate predictions based on classical nucleation theory, direct brute force molecular…
