Generating High-Precision Force Fields for Molecular Dynamics Simulations to Study Chemical Reaction Mechanisms Using Molecular Configuration Transformer.

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that used enhanced sampling in molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limited the use of high-precision potential energy functions for simulations. To address this issue, we presented a scheme for training high-precision force fields for molecular modeling using a previously developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allowed for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We applied this approach to study a Claisen rearrangement reaction and a carbonyl insertion reaction catalyzed by manganese.

Deep reinforcement learning of transition states.

Combining reinforcement learning (RL) and molecular dynamics (MD) simulations, we propose a machine-learning approach, called RL‡, to automatically unravel chemical reaction mechanisms. In RL‡, locating the transition state of a chemical reaction is formulated as a game, and two functions are optimized, one for value estimation and the other for policy making, to iteratively improve our chance of winning this game. Both functions can be approximated by deep neural networks. By virtue of RL‡, one can directly interpret the reaction mechanism according to the value function. Meanwhile, the policy function allows efficient sampling of the transition path ensemble, which can be further used to analyze reaction dynamics and kinetics. Through multiple experiments, we show that RL‡ can be trained tabula rasa hence allowing us to reveal chemical reaction mechanisms with minimal subjective biases.

A Perspective on Deep Learning for Molecular Modeling and Simulations.

Deep learning is transforming many areas in science, and it has great potential in modeling molecular systems. However, unlike the mature deployment of deep learning in computer vision and natural language processing, its development in molecular modeling and simulations is still at an early stage, largely because the inductive biases of molecules are completely different from those of images or texts. Footed on these differences, we first reviewed the limitations of traditional deep learning models from the perspective of molecular physics and wrapped up some relevant technical advancement at the interface between molecular modeling and deep learning. We do not focus merely on the ever more complex neural network models; instead, we introduce various useful concepts and ideas brought by modern deep learning. We hope that transacting these ideas into molecular modeling will create new opportunities. For this purpose, we summarized several representative applications, ranging from supervised to unsupervised and reinforcement learning, and discussed their connections with the emerging trends in deep learning. Finally, we give an outlook for promising directions which may help address the existing issues in the current framework of deep molecular modeling.

Deep learning for variational multiscale molecular modeling.

Molecular simulations are widely applied in the study of chemical and bio-physical problems. However, the accessible timescales of atomistic simulations are limited, and extracting equilibrium properties of systems containing rare events remains challenging. Two distinct strategies are usually adopted in this regard: either sticking to the atomistic level and performing enhanced sampling or trading details for speed by leveraging coarse-grained models. Although both strategies are promising, either of them, if adopted individually, exhibits severe limitations. In this paper, we propose a machine-learning approach to ally both strategies so that simulations on different scales can benefit mutually from their crosstalks: Accurate coarse-grained (CG) models can be inferred from the fine-grained (FG) simulations through deep generative learning; in turn, FG simulations can be boosted by the guidance of CG models via deep reinforcement learning. Our method defines a variational and adaptive training objective, which allows end-to-end training of parametric molecular models using deep neural networks. Through multiple experiments, we show that our method is efficient and flexible and performs well on challenging chemical and bio-molecular systems.

Temperature Dependence of Homogeneous Nucleation in Ice.

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Enhanced sampling in molecular dynamics.

Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.

Dual reorientation relaxation routes of water molecules in oxyanion's hydration shell: A molecular geometry perspective.

In this study, we examine how complex ions such as oxyanions influence the dynamic properties of water and whether differences exist between simple halide anions and oxyanions. Nitrate anion is taken as an example to investigate the hydration properties of oxyanions. Reorientation relaxation of its hydration water can occur through two different routes: water can either break its hydrogen bond with the nitrate to form one with another water or switch between two oxygen atoms of the same nitrate. The latter molecular mechanism increases the residence time of oxyanion's hydration water and thus nitrate anion slows down the translational motion of neighbouring water. But it is also a "structure breaker" in that it accelerates the reorientation relaxation of hydration water. Such a result illustrates that differences do exist between the hydration of oxyanions and simple halide anions as a result of different molecular geometries. Furthermore, the rotation of the nitrate solute is coupled with the hydrogen bond rearrangement of its hydration water. The nitrate anion can either tilt along the axis perpendicularly to the plane or rotate in the plane. We find that the two reorientation relaxation routes of the hydration water lead to different relaxation dynamics in each of the two above movements of the nitrate solute. The current study suggests that molecular geometry could play an important role in solute hydration and dynamics.

Unsupervisedly Prompting AlphaFold2 for Accurate Few-Shot Protein Structure Prediction.

Data-driven predictive methods that can efficiently and accurately transform protein sequences into biologically active structures are highly valuable for scientific research and medical development. Determining an accurate folding landscape using coevolutionary information is fundamental to the success of modern protein structure prediction methods. As the state of the art, AlphaFold2 has dramatically raised the accuracy without performing explicit coevolutionary analysis. Nevertheless, its performance still shows strong dependence on available sequence homologues. Based on the interrogation on the cause of such dependence, we presented EvoGen, a meta generative model, to remedy the underperformance of AlphaFold2 for poor MSA targets. By prompting the model with calibrated or virtually generated homologue sequences, EvoGen helps AlphaFold2 fold accurately in the low-data regime and even achieve encouraging performance with single-sequence predictions. Being able to make accurate predictions with few-shot MSA not only generalizes AlphaFold2 better for orphan sequences but also democratizes its use for high-throughput applications. Besides, EvoGen combined with AlphaFold2 yields a probabilistic structure generation method that could explore alternative conformations of protein sequences, and the task-aware differentiable algorithm for sequence generation will benefit other related tasks including protein design.

Artificial Intelligence Enhanced Molecular Simulations.

Molecular simulations, which simulate the motions of particles according to fundamental laws of physics, have been applied to a wide range of fields from physics and materials science to biochemistry and drug discovery. Developed for computationally intensive applications, most molecular simulation software involves significant use of hard-coded derivatives and code reuse across various programming languages. In this Review, we first align the relationship between molecular simulations and artificial intelligence (AI) and reveal the coherence between the two. We then discuss how the AI platform can create new possibilities and deliver new solutions to molecular simulations, from the perspective of algorithms, programming paradigms, and even hardware. Rather than focusing solely on increasingly complex neural network models, we introduce various concepts and techniques brought about by modern AI and explore how they can be transacted to molecular simulations. To this end, we summarized several representative applications of molecular simulations enhanced by AI, including from differentiable programming and high-throughput simulations. Finally, we look ahead to promising directions that may help address existing issues in the current framework of AI-enhanced molecular simulations.

Enhanced Sampling Simulation Reveals How Solvent Influences Chirogenesis of the Intra-Molecular Diels-Alder Reaction.

The timescale involved in chemical reactions is quite often beyond that of normal molecular dynamics simulations. Here, we combine metadynamics with selective integrated tempering sampling to simulate an intra-molecular Diels-Alder reaction in explicit solvents. Based on a one-dimensional collective variable obtained from harmonic linear discriminant analysis, four chiral isomers of products were observed in the simulation. Analyses of reactive trajectories showed that this reaction follows a concerted mechanism in all four solvents. In addition, the hydrogen bond between the reactant and water solvent plays an important role in the water-accelerated reaction mechanism. The dynamics of chirality formation varies significantly with solvents. The chirality of products forms significantly before the transition state, especially in ionic liquid.

Locating Transition Zone in Phase Space.

Understanding the reaction mechanism is required for better control of chemical reactions and is usually achieved by locating transition states (TSs) along a proper one-dimensional coordinate called reaction coordinate (RC). The identification of RC can be very difficult for high-dimensional realistic systems. A number of methods have been proposed to tackle this problem. A machine learning method is developed here to incorporate the influence of velocity on the reaction process. The method is also free of the unbalanced label problem resulting from the rather low fraction of configurations near the TS and can be easily extended to large systems. It locates the transition zone in the phase space and defines the dividing surface with a high transmission coefficient. Moreover, considering that the reaction environment can not only change the reaction path but also activate the reactive mode through energy transfer, we devise two measures to quantify the influence of these two factors on the reaction process and find that solvents can assist the reaction by directly doing work along the reactive mode. Not surprisingly, there is a positive correlation between the efficiency of energy transfer into the reactive mode and the reaction rate.

Phase Transition between Crystalline Variants of Ordinary Ice.

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

Targeted Adversarial Learning Optimized Sampling.

Boosting transitions of rare events is critical to simulations of chemical and biophysical dynamic systems in order to close the time scale gaps between theoretical modeling and experiments. We present a novel approach, called targeted adversarial learning optimized sampling (TALOS), to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free-energy barrier is lowered. Combining statistical mechanics and generative learning, TALOS formulates a competing game between a sampling engine and a virtual discriminator, enables unsupervised construction of bias potentials, and seeks for an optimal transport plan that transforms the system into a target. Through multiple experiments, we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning and thus is efficient, robust, and interpretable. TALOS is also closely connected to the actor-critic reinforcement learning and hence leads to a new way of flexibly manipulating the many-body Hamiltonian systems.

Deep Representation Learning for Complex Free-Energy Landscapes.

In this Letter, we analyzed the inductive bias underlying complex free-energy landscapes (FELs) and exploited it to train deep neural networks that yield reduced and clustered representation for the FEL. Our parametric method, called information distilling of metastability (IDM), is end-to-end differentiable and thus scalable to ultralarge data sets. IDM is able to perform clustering in the meantime of reducing the dimensionality. Besides, as an unsupervised learning method, IDM differs from many existing dimensionality reduction and clustering methods in that it requires neither a cherry-picked distance metric nor the ground-true number of clusters defined a priori, and it can be used to unroll and zoom in on the hierarchical FEL with respect to different time scales. Through multiple experiments, we show that IDM can achieve physically meaningful representations that partition the FEL into well-defined metastable states that hence are amenable for downstream tasks such as mechanism analysis and kinetic modeling.

Refining Collective Coordinates and Improving Free Energy Representation in Variational Enhanced Sampling.

Collective variables are used often in many enhanced sampling methods, and their choice is a crucial factor in determining sampling efficiency. However, at times, searching for good collective variables can be challenging. In a recent paper, we combined time-lagged independent component analysis with well-tempered metadynamics in order to obtain improved collective variables from metadynamics runs that use lower quality collective variables [ McCarty, J.; Parrinello, M. J. Chem. Phys. 2017 , 147 , 204109 ]. In this work, we extend these ideas to variationally enhanced sampling. This leads to an efficient scheme that is able to make use of the many advantages of the variational scheme. We apply the method to alanine-3 in water. From an alanine-3 variationally enhanced sampling trajectory in which all the six dihedral angles are biased, we extract much better collective variables able to describe in exquisite detail the protein complex free energy surface in a low dimensional representation. The success of this investigation is helped by a more accurate way of calculating the correlation functions needed in the time-lagged independent component analysis and from the introduction of a new basis set to describe the dihedral angles arrangement.

Combining Metadynamics and Integrated Tempering Sampling.

The simulation of rare events is one of the key problems in atomistic simulations. Toward its solution, a plethora of methods have been proposed. Here we combine two such methods: metadynamics and integrated tempering sampling. In metadynamics, the fluctuations of a carefully chosen collective variable are amplified, while in integrated tempering sampling the system is pushed to visit an approximately uniform interval of energies and allows exploring a range of temperatures in a single run. We describe our approach and apply it to the two prototypical systems a SN2 chemical reaction and to the freezing of silica. The combination of metadynamics and integrated tempering sampling leads to a powerful method. In particular in the case of silica we have measured more than 1 order of magnitude acceleration.

Rich Dynamics Underlying Solution Reactions Revealed by Sampling and Data Mining of Reactive Trajectories.

Efficient sampling in both configuration and trajectory spaces, combined with mechanism analyses via data mining, allows a systematic investigation of the thermodynamics, kinetics, and molecular-detailed dynamics of chemical reactions in solution. Through a Bayesian learning algorithm, the reaction coordinate(s) of a (retro-)Claisen rearrangement in bulk water was variationally optimized. The bond formation/breakage was found to couple with intramolecular charge separation and dipole change, and significant dynamic solvent effects manifest, leading to the "in-water" acceleration of Claisen rearrangement. In addition, the vibrational modes of the reactant and the solvation states are significantly coupled to the reaction dynamics, leading to heterogeneous and oscillatory reaction paths. The calculated reaction rate is well interpreted by the Kramers' theory with a diffusion term accounting for solvent-solute interactions. These findings demonstrated that the reaction mechanisms can be complicated in homogeneous solutions since the solvent-solute interactions can profoundly influence the reaction dynamics and the energy transfer process.

Conformational Preadjustment in Aqueous Claisen Rearrangement Revealed by SITS-QM/MM MD Simulations.

An efficient sampling method was implemented in QM/MM hybrid molecular simulations to study aliphatic Claisen rearrangement in aqueous solutions. On the basis of the computational results, the necessary conformational adjustment to trap the reactant into a favorable compact conformation specifically in water was observed. The conformational equilibrium was shown to be important to the elucidation of the "water-acceleration" effect of Claisen rearrangement. Thus, a two-step process of aqueous Claisen rearrangement was proposed. It was similar to the pseudodiaxial-pseudodiequatorial conformational equilibrium observed in the enzymatic reaction of chorismate acid but with explicit inclusion of the solvent coordinates to explain the solvation effects. Polarization was found to occur during the reactant conformational transition. A solvent with high cohesive energy density (CED) like water was suggested to accommodate compact conformers better, thus facilitating the following reaction by concentrating the real "active" reactant. The substituent effects also manifested, leading to varied conformational distributions of different substituted allyl vinyl ethers (AVEs). The application of the enhanced sampling method allowed a systematic analysis of thermodynamic information without loss of solvent coordinates. These data showed the conformational transition of AVEs was an entropy-driving process which was sensitive to the substituent, and enthalpy played an important role in the solvation effect on the conformational equilibrium.