From thermodynamics to kinetics: enhanced sampling of rare events

Graphitic nanoflakes modulate the structure and binding of human amylin

Human amylin is an inherently disordered protein whose ability to form amyloid fibrils is linked to the onset of type II diabetes. Graphitic nanomaterials have potential in managing amyloid diseases as they can disrupt protein aggregation processes in biological settings, but optimising these materials to prevent fibrillation is challenging. Here, we employ bias-exchange molecular dynamics simulations to systematically study the structure and adsorption preferences of amylin on graphitic nanoflakes that vary in their physical dimensions and surface functionalisation. Our findings reveal that nanoflake size and surface oxidation both influence the structure and adsorption preferences of amylin. The purely hydrophobic substrate of pristine graphene (PG) nanoflakes encourages non-specific protein adsorption, leading to unrestricted lateral mobility once amylin adheres to the surface. Particularly on larger PG nanoflakes, this induces structural changes in amylin that may promote fibril formation, such as the loss of native helical content and an increase in β-sheet character. In contrast, oxidised graphene nanoflakes form hydrogen bonds between surface oxygen sites and amylin, and as such restricting protein mobility. Reduced graphene oxide (rGO) flakes, featuring lower amounts of surface oxidation, are amphiphilic and exhibit substantial regions of bare carbon which promote protein binding and reduced conformational flexibility, leading to conservation of the native structure of amylin. In comparison, graphene oxide (GO) nanoflakes, which are predominantly hydrophilic and have a high degree of surface oxidation, facilitate considerable protein structural variability, resulting in substantial contact area between the protein and GO, and subsequent protein unfolding. Our results indicate that tailoring the size, oxygen concentration and surface patterning of graphitic nanoflakes can lead to specific and robust protein binding, ultimately influencing the likelihood of fibril formation. These atomistic insights provide key design considerations for the development of graphitic nanoflakes that can modulate protein aggregation by sequestering protein monomers in the biological environment and inhibit conformational changes linked to amyloid fibril formation.

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.

Exploring Chemical Space Using Ab Initio Hyperreactor Dynamics

In recent years, first-principles exploration of chemical reaction space has provided valuable insights into intricate reaction networks. Here, we introduce ab initio hyperreactor dynamics, which enables rapid screening of the accessible chemical space from a given set of initial molecular species, predicting new synthetic routes that can potentially guide subsequent experimental studies. For this purpose, different hyperdynamics derived bias potentials are applied along with pressure-inducing spherical confinement of the molecular system in ab initio molecular dynamics simulations to efficiently enhance reactivity under mild conditions. To showcase the advantages and flexibility of the hyperreactor approach, we present a systematic study of the method's parameters on a HCN toy model and apply it to a recently introduced experimental model for the prebiotic formation of glycinal and acetamide in interstellar ices, which yields results in line with experimental findings. In addition, we show how the developed framework enables the study of complicated transitions like the first step of a nonenzymatic DNA nucleoside synthesis in an aqueous environment, where the molecular fragmentation problem of earlier nanoreactor approaches is avoided.

Factorization in molecular modeling and belief propagation algorithms

Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.

QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations

Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.

Computed Protein-Protein Enthalpy Signatures as a Tool for Identifying Conformation Sampling Problems

Understanding the thermodynamic signature of protein-peptide binding events is a major challenge in computational chemistry. The complexity generated by both components possessing many degrees of freedom poses a significant issue for methods that attempt to directly compute the enthalpic contribution to binding. Indeed, the prevailing assumption has been that the errors associated with such approaches would be too large for them to be meaningful. Nevertheless, we currently have no indication of how well the present methods would perform in terms of predicting the enthalpy of binding for protein-peptide complexes. To that end, we carefully assembled and curated a set of 11 protein-peptide complexes where there is structural and isothermal titration calorimetry data available and then computed the absolute enthalpy of binding. The initial "out of the box" calculations were, as expected, very modest in terms of agreement with the experiment. However, careful inspection of the outliers allows for the identification of key sampling problems such as distinct conformations of peptide termini not being sampled or suboptimal cofactor parameters. Additional simulations guided by these aspects can lead to a respectable correlation with isothermal titration calorimetry (ITC) experiments (R2 of 0.88 and an RMSE of 1.48 kcal/mol overall). Although one cannot know prospectively whether computed ITC values will be correct or not, this work shows that if experimental ITC data are available, then this in conjunction with computed ITC, can be used as a tool to know if the ensemble being simulated is representative of the true ensemble or not. That is important for allowing the correct interpretation of the detailed dynamics of the system with respect to the measured enthalpy. The results also suggest that computational calorimetry is becoming increasingly feasible. We provide the data set as a resource for the community, which could be used as a benchmark to help further progress in this area.

Anisotropic Collective Variables with Machine Learning Potential for Ab Initio Crystallization of Complex Ceramics

Enhanced sampling molecular dynamics (MD) simulations have been extensively used in the phase transition study of simple crystalline materials, such as aluminum, silica, and ice. However, MD simulation of the crystallization process for complex crystalline materials still faces a formidable challenge due to their multicomponent induced multiphase problem. Here, we realize the ab initio accuracy MD crystallization simulations of complex ceramics by using anisotropic collective variables (CVs) and machine learning (ML) potential. The anisotropic X-ray diffraction intensity CVs provide precise identification of complex crystal structures with detailed crystallography information, while the ML potential makes it feasible to further perform enhanced sampling simulations with ab initio accuracy. We verify the universality and accuracy of this method through complex ceramics with three kinds of representative structures, i.e., Ti3SiC2 for the MAX structure, zircon for the mineral structure, and lead zirconate titanate for the perovskite structure. It demonstrates exceptional efficiency and ab initio quality in achieving crystallization and generating free energy surfaces of all these ceramics, facilitating the analysis and design of complex crystalline materials.

Assessments of Variational Autoencoder in Protein Conformation Exploration

Molecular dynamics (MD) simulations have been extensively used to study protein dynamics and subsequently functions. However, MD simulations are often insufficient to explore adequate conformational space for protein functions within reachable timescales. Accordingly, many enhanced sampling methods, including variational autoencoder (VAE) based methods, have been developed to address this issue. The purpose of this study is to evaluate the feasibility of using VAE to assist in the exploration of protein conformational landscapes. Using three modeling systems, we showed that VAE could capture high-level hidden information which distinguishes protein conformations. These models could also be used to generate new physically plausible protein conformations for direct sampling in favorable conformational spaces. We also found that VAE worked better in interpolation than extrapolation and increasing latent space dimension could lead to a trade-off between performances and complexities.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling

Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.

Molecular Modeling Insights into the Structure and Behavior of Integrins: A Review

Integrins are heterodimeric glycoproteins crucial to the physiology and pathology of many biological functions. As adhesion molecules, they mediate immune cell trafficking, migration, and immunological synapse formation during inflammation and cancer. The recognition of the vital roles of integrins in various diseases revealed their therapeutic potential. Despite the great effort in the last thirty years, up to now, only seven integrin-based drugs have entered the market. Recent progress in deciphering integrin functions, signaling, and interactions with ligands, along with advancement in rational drug design strategies, provide an opportunity to exploit their therapeutic potential and discover novel agents. This review will discuss the molecular modeling methods used in determining integrins' dynamic properties and in providing information toward understanding their properties and function at the atomic level. Then, we will survey the relevant contributions and the current understanding of integrin structure, activation, the binding of essential ligands, and the role of molecular modeling methods in the rational design of antagonists. We will emphasize the role played by molecular modeling methods in progress in these areas and the designing of integrin antagonists.

Stochastic Resetting for Enhanced Sampling

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 time scales that are unreachable in standard simulations. They are often characterized 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 the first time. We show that it accelerates long time scale processes by up to an order of magnitude in examples ranging from simple models to a molecular system. Most importantly, we recover the mean transition time without resetting, which is typically too long to be sampled directly, from accelerated simulations at a single restart rate. Stochastic resetting can be used as a standalone method or combined with other sampling algorithms to further accelerate simulations.

Challenges and frontiers of computational modelling of biomolecular recognition

Biomolecular recognition including binding of small molecules, peptides and proteins to their target receptors plays a key role in cellular function and has been targeted for therapeutic drug design. However, the high flexibility of biomolecules and slow binding and dissociation processes have presented challenges for computational modelling. Here, we review the challenges and computational approaches developed to characterise biomolecular binding, including molecular docking, molecular dynamics simulations (especially enhanced sampling) and machine learning. Further improvements are still needed in order to accurately and efficiently characterise binding structures, mechanisms, thermodynamics and kinetics of biomolecules in the future.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Comparison of the Microsolvation of CaX2 (X = F, Cl, Br, I) in Water: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations

To understand the microsolvation of alkaline-earth dihalides in water and provide information about the dependence of solvation processes on different halides, we investigated CaBr₂(H₂O)_n^-, CaI₂(H₂O)_n^-, and CaF₂(H₂O)_n^- (n = 0-6) clusters using size-selected anion photoelectron spectroscopy and conducted theoretical calculations on these clusters and their neutrals. The results are compared with those of CaCl₂(H₂O)_n^-/0 clusters reported previously. It is found that the vertical detachment energies (VDEs) of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^- show a similar trend with increasing cluster size, while the VDEs of CaF₂(H₂O)_n^- show a different trend. The VDEs of CaF₂(H₂O)_n^- are much lower than those of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^-. A detailed probing of the structures shows that a significant increase of the Ca-X distance (separation of Ca²⁺-X^- ion pair) in CaCl₂(H₂O)_n^-/0, CaBr₂(H₂O)_n^-/0, and CaI₂(H₂O)_n^-/0 clusters occurred at about n = 5. However, for CaF₂(H₂O)_n^-/0, no abrupt change of the Ca-F distance with the increasing cluster size has been observed. In CaCl₂(H₂O)₆^-/0, CaBr₂(H₂O)₆^-/0, and CaI₂(H₂O)₆^-/0, the Ca atom coordinates directly with 5 H₂O molecules. However, in CaF₂(H₂O)_n^-/0, the Ca atom coordinates directly with only 2 or 3 H₂O molecules. The similarity or differences in the structures and coordination numbers are consistent with the fact that CaCl₂, CaBr₂, and CaI₂ have similar solubility, while CaF₂ has much lower solubility.

A perspective on the molecular simulation of DNA from structural and functional aspects

As genetic material, DNA not only carries genetic information by sequence, but also affects biological functions ranging from base modification to replication, transcription and gene regulation through its structural and dynamic properties and variations. The motion and structural properties of DNA involved in related biological processes are also multi-scale, ranging from single base flipping to local DNA deformation, TF binding, G-quadruplex and i-motif formation, TAD establishment, compartmentalization and even chromosome territory formation, just to name a few. The sequence-dependent physical properties of DNA play vital role in all these events, and thus it is interesting to examine how simple sequence information affects DNA and the formation of the chromatin structure in these different hierarchical orders. Accordingly, molecular simulations can provide atomistic details of interactions and conformational dynamics involved in different biological processes of DNA, including those inaccessible by current experimental methods. In this perspective, which is mainly based on our recent studies, we provide a brief overview of the atomistic simulations on how the hierarchical structure and dynamics of DNA can be influenced by its sequences, base modifications, environmental factors and protein binding in the context of the protein-DNA interactions, gene regulation and structural organization of chromatin. We try to connect the DNA sequence, the hierarchical structures of DNA and gene regulation.

Deterministic synthesis of Cu9S5 flakes assisted by single-layer graphene arrays

The employment of two-dimensional materials, as growth substrates or buffer layers, enables the epitaxial growth of layered materials with different crystalline symmetries with a preferential crystalline orientation and the synthesis of heterostructures with a large lattice constant mismatch. In this work, we employ single crystalline graphene to modify the sulfurization dynamics of copper foil for the deterministic synthesis of large-area Cu₉S₅ crystals. Molecular dynamics simulations using the Reax force-field are used to mimic the sulfurization process of a series of different atomistic systems specifically built to understand the role of graphene during the sulphur atom attack over the Cu(111) surface. Cu₉S₅ flakes show a flat morphology with an average lateral size of hundreds of micrometers. Cu₉S₅ presents a direct band-gap of 2.5 eV evaluated with light absorption and light emission spectroscopies. Electrical characterization shows that the Cu₉S₅ crystals present high p-type doping with a hole mobility of 2 cm² V^-1 s^-1.

Hydration processes of barium chloride: Size-selected anion photoelectron spectroscopy and theoretical calculations of BaCl2-water clusters

In order to understand the hydration processes of BaCl₂, we investigated BaCl₂(H₂O)_n ^- (n = 0-5) clusters using size-selected anion photoelectron spectroscopy and theoretical calculations. The structures of neutral BaCl₂(H₂O)_n clusters up to n = 8 were also investigated by theoretical calculations. It is found that in BaCl₂(H₂O)_n ^-/0, the Ba-Cl distances increase very slowly with the cluster size. The hydration process is not able to induce the breaking of a Ba-Cl bond in the cluster size range (n = 0-8) studied in this work. In small BaCl₂(H₂O)_n clusters with n ≤ 5, the Ba atom has a coordination number of n + 2; however, in BaCl₂(H₂O)_6-8 clusters, the Ba atom coordinates with two Cl atoms and (n - 1) water molecules, and it has a coordination number of n + 1. Unlike the previously studied MgCl₂(H₂O)_n ^- and CaCl₂(H₂O)_n ^-, negative charge-transfer-to-solvent behavior has not been observed for BaCl₂(H₂O)_n ^-, and the excess electron of BaCl₂(H₂O)_n ^- is mainly localized on the Ba atom rather on the water molecules. No observation of Ba²⁺-Cl^- separation in current work is consistent with the lower solubility of BaCl₂ compared to MgCl₂ and CaCl₂. Considering the BaCl₂/H₂O mole ratio in the saturated solution, one would expect that about 20-30 H₂O molecules are needed to break the first Ba-Cl bond in BaCl₂.

Advances in Molecular Dynamics Simulations and Enhanced Sampling Methods for the Study of Protein Systems

Molecular dynamics (MD) simulation is a rigorous theoretical tool that when used efficiently could provide reliable answers to questions pertaining to the structure-function relationship of proteins. Data collated from protein dynamics can be translated into useful statistics that can be exploited to sieve thermodynamics and kinetics crucial for the elucidation of mechanisms responsible for the modulation of biological processes such as protein-ligand binding and protein-protein association. Continuous modernization of simulation tools enables accurate prediction and characterization of the aforementioned mechanisms and these qualities are highly beneficial for the expedition of drug development when effectively applied to structure-based drug design (SBDD). In this review, current all-atom MD simulation methods, with focus on enhanced sampling techniques, utilized to examine protein structure, dynamics, and functions are discussed. This review will pivot around computer calculations of protein-ligand and protein-protein systems with applications to SBDD. In addition, we will also be highlighting limitations faced by current simulation tools as well as the improvements that have been made to ameliorate their efficiency.

Exploring Conformational Change of Adenylate Kinase by Replica Exchange Molecular Dynamic Simulation

Replica exchange molecular dynamics (REMD) simulation is a popular enhanced sampling method that is widely used for exploring the atomic mechanism of protein conformational change. However, the requirement of huge computational resources for REMD, especially with the explicit solvent model, largely limits its application. In this study, the availability and efficiency of a variant of velocity-scaling REMD (vsREMD) was assessed with adenylate kinase as an example. Although vsREMD achieved results consistent with those from conventional REMD and experimental studies, the number of replicas required for vsREMD (30) was much less than that for conventional REMD (80) to achieve a similar acceptance rate (∼0.2), demonstrating high efficiency of vsREMD to characterize the protein conformational change and associated free-energy profile. Thus, vsREMD is a highly efficient approach for studying the large-scale conformational change of protein systems.

Taming Rugged Free Energy Landscapes Using an Average Force

The observation of complex structural transitions in biological and abiological molecular objects within time scales amenable to molecular dynamics (MD) simulations is often hampered by significant free energy barriers associated with entangled movements. Importance-sampling algorithms, a powerful class of numerical schemes for the investigation of rare events, have been widely used to extend simulations beyond the time scale common to MD. However, probing processes spanning milliseconds through microsecond molecular simulations still constitutes in practice a daunting challenge because of the difficulty of taming the ruggedness of multidimensional free energy surfaces by means of naive transition coordinates. To address this limitation, in recent years we have elaborated importance-sampling methods relying on an adaptive biasing force (ABF). In this Account, we review recent developments of algorithms aimed at mapping rugged free energy landscapes that correspond to complex processes of physical, chemical, and biological relevance. Through these developments, we have broadened the spectrum of applications of the popular ABF algorithm while improving its computational efficiency, notably for multidimensional free energy calculations. One major algorithmic advance, coined meta-eABF, merges the key features of metadynamics and an extended Lagrangian variant of ABF (eABF) by simultaneously shaving the barriers and flooding the valleys of the free energy landscape, and it possesses a convergence rate up to 5-fold greater than those of other importance-sampling algorithms. Through faster convergence and enhanced ergodic properties, meta-eABF represents a significant step forward in the simulation of millisecond-time-scale events. Here we introduce extensions of the algorithm, notably its well-tempered and replica-exchange variants, which further boost the sampling efficiency while gaining in numerical stability, thus allowing quantum-mechanical/molecular-mechanical free energy calculations to be performed at a lower cost. As a paradigm to bridge microsecond simulations to millisecond events by means of free energy calculations, we have applied the ABF family of algorithms to decompose complex movements in molecular objects of biological and abiological nature. We show here how water lubricates the shuttling of an amide-based rotaxane by altering the mechanism that underlies the concerted translation and isomerization of the macrocycle. Introducing novel collective variables in a computational workflow for the rigorous determination of standard binding free energies, we predict with utmost accuracy the thermodynamics of protein-ligand reversible association. Because of their simplicity, versatility, and robust mathematical foundations, the algorithms of the ABF family represent an appealing option for the theoretical investigation of a broad range of problems relevant to physics, chemistry, and biology.

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.

Exploring the Ligand Binding/Unbinding Pathway by Selectively Enhanced Sampling of Ligand in a Protein-Ligand Complex

Understanding the protein-ligand binding is of fundamental biological interest and is essential for structure-based drug design. The difficulty in capturing the dynamic process, however, poses a great challenge for current experimental and theoretical simulation techniques. A selective integrated-tempering-sampling molecular dynamics (SITSMD) method offering an option for selectively enhanced sampling of the ligand in a protein-ligand complex was utilized to quantitatively illuminate the binding of benzamidine to the wild-type trypsin protease and its two mutants (S214E and S214K). The SITSMD simulations could produce consistent results as the extensive conventional MD simulation and gave additional insights into the binding pathway for the test protein-ligand complex system using significantly saved computational resource and time, indicating the potential of such a method in investigating protein-ligand binding. Additionally, the simulations identified the different roles of trypsin-benzamidine van der Waals (vdW) and electrostatic interactions in the binding: the former interaction works as the driving force for dragging the benzamidine close to the native binding pocket, and the latter interaction mainly contributes to stabilizing the benzamidine inside the pocket. The S214E mutation introduces more favorable electrostatic interactions, and as a result, both vdW and electrostatic interactions drive the benzamidine binding, lowering the binding and unbinding free energy barrier. In contrast, the S214K mutation prohibits the binding of the benzamidine to the native ligand binding pocket by introducing disliked charge-charge interactions. In summary, these findings suggest that the change in specific residues could modify the protein druggability, including the binding kinetics and thermodynamics.

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.

Revealing Transition States during the Hydration of Clay Minerals

A molecular-scale understanding of the transition between hydration states in clay minerals remains a challenging problem because of the very fast stepwise swelling process observed from X-ray diffraction (XRD) experiments. XRD profile modeling assumes the coexistence of multiple hydration states in a clay sample to fit the experimental XRD pattern obtained under humid conditions. While XRD profile modeling provides a macroscopic understanding of the heterogeneous hydration structure of clay minerals, a microscopic model of the transition between hydration states is still missing. Here, for the first time, we use molecular dynamics simulation to investigate the transition states between a dry interlayer, one-layer hydrate, and two-layer hydrate. We find that the hydrogen bonds that form across the interlayer at the clay particle edge make an important contribution to the energy barrier to interlayer hydration, especially for initial hydration.

Ligand binding effects on the activation of the EGFR extracellular domain

The epidermal growth factor receptor (EGFR) is one of the most common target proteins in anti-cancer therapy. The binding of the EGF ligand to the EGFR extracellular domain (EGFR-ECD) promotes its inactive-to-active conformational transition (activation) but the relevant detailed mechanism remains elusive still. Here, the structural characterization and energetics of the EGFR-ECD conformational transition with and without the binding of the EGF are quantitatively explored using an innovative enhanced sampling MD simulation method. Intriguingly, the EGF offers hydrophobic interactions (e.g., EGF residues of Tyr44 and Leu47) and electrostatic interactions (e.g., the EGF residues of Glu5, Asp11, Asp17, and Arg41) to play a dominant role in dragging domain III to close the ligand binding domain gap. Subsequently, the correlation between domains III and II is enhanced through salt-bridges among Glu376, Arg403, and Arg405 from domain III and Glu293, Glu295, and Arg300 from domain II. Finally, the structural bending of domain II is regulated to facilitate the disengagement of domain II from domain IV. In this regard, the functional conformational transition of EGFR-ECD is a consequence of the cooperative motion of protein domains driven by the EGF ligand binding. The present study shows a detailed scenario of the EGF induced activation of EGFR-ECD and provides valuable information for drug discovery targeting the EGFR.

Enhanced QM/MM sampling for free energy calculation of chemical reactions: A case study of double proton transfer

Free energy calculations for chemical reactions with a steep energy barrier require well defined reaction coordinates (RCs). However, when multiple parallel channels exist along selected RC, the application of conventional enhanced samplings is difficult to generate correct sampling within limited simulation time and thus cannot give correct prediction about the favorable pathways, the relative stability of multiple products or intermediates. Here, we implement the selective integrated tempering sampling (SITS) method with quantum mechanical and molecular mechanical (QM/MM) potential to investigate the chemical reactions in solution. The combined SITS-QM/MM scheme is used to identify possible reaction paths, intermediate and product states, and the free energy profiles for the different reaction paths. Two double proton transfer reactions were studied to validate the implemented method and simulation protocol, from which the independent and correlated proton transfer processes are identified in two representative systems, respectively. This protocol can be generalized to various kinds of chemical reactions for both academic studies and industry applications, such as in exploration and optimization of potential reactions in DNA encoded compound library and halogen or deuterium substitution of the hit discovery and lead optimization stages of drug design via providing a better understanding of the reaction mechanism along the designed chemical reaction pathways.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

Selective enhanced sampling in dihedral energy facilitates overcoming the dihedral energy increase in protein folding and accelerates the searching for protein native structure

A dihedral-energy-based selective enhanced sampling method (D-SITSMD) is presented with improved capabilities for searching a protein's natively folded structure and for providing the underlying folding pathway.

Assessing AMBER force fields for protein folding in an implicit solvent

Molecular dynamics (MD) simulation implemented with a state-of-the-art protein force field and implicit solvent model is an attractive approach to investigate protein folding, one of the most perplexing problems in molecular biology. But how well can force fields developed independently of implicit solvent models work together in reproducing diverse protein native structures and measuring the corresponding folding thermodynamics is not always clear. In this work, we performed enhanced sampling MD simulations to assess the ability of six AMBER force fields (FF99SBildn, FF99SBnmr, FF12SB, FF14ipq, FF14SB, and FF14SBonlysc) as coupled with a recently improved pair-wise GB-Neck2 model in modeling the folding of two helical and two β-sheet peptides. Whilst most of the tested force fields can yield roughly similar features for equilibrium conformational ensembles and detailed folding free-energy profiles for short α-helical TC10b in an implicit solvent, the measured counterparts are significantly discrepant in the cases of larger or β-structured peptides (HP35, 1E0Q, and GTT). Additionally, the calculated folding/unfolding thermodynamic quantities can only partially match the experimental data. Although a combination of the force fields and GB-Neck2 implicit model able to describe all aspects of the folding transitions towards the native structures of all the considered peptides was not identified, we found that FF14SBonlysc coupled with the GB-Neck2 model seems to be a reasonably balanced combination to predict peptide folding preferences.

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 S_N2 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.

The effects of implicit modeling of nonpolar solvation on protein folding simulations

Implicit solvent models, in which the polar and nonpolar solvation free-energies of solute molecules are treated separately, have been widely adopted for molecular dynamics simulation of protein folding. While the development of the implicit models is mainly focused on the methodological improvement and key parameter optimization for polar solvation, nonpolar solvation has been either ignored or described by a simplistic surface area (SA) model. In this work, we performed the folding simulations of multiple β-hairpin and α-helical proteins with varied surface tension coefficients embedded in the SA model to clearly demonstrate the effects of nonpolar solvation treated by a popular SA model on protein folding. The results indicate that the change in the surface tension coefficient does not alter the ability of implicit solvent simulations to reproduce a protein native structure but indeed controls the components of the equilibrium conformational ensemble and modifies the energetic characterization of the folding transition pathway. The suitably set surface tension coefficient can yield explicit solvent simulations and/or experimentally suggested folding mechanism of protein. In addition, the implicit treatment of both polar and nonpolar components of solvation free-energy contributes to the overestimation of the secondary structure in implicit solvent simulations.

Energetics and structural characterization of the “DFG-flip” conformational transition of B-RAF kinase: a SITS molecular dynamics study

A combination of a homology modeling technique and an enhanced sampling molecular dynamics simulation implemented using the SITS method is employed to compute a detailed map of the free-energy landscape and explore the conformational transition pathway of B-RAF kinase.

Initial hydration processes of magnesium chloride: size-selected anion photoelectron spectroscopy and ab initio calculations

Separation of Cl⁻–Mg²⁺ ion pairs starts at n = 4 in MgCl₂(H₂O)_n⁻ anions and at n = 7 in neutral MgCl₂(H₂O)_n.

Efficient sampling over rough energy landscapes with high barriers: A combination of metadynamics with integrated tempering sampling

In order to efficiently overcome high free energy barriers embedded in a complex energy landscape and calculate overall thermodynamics properties using molecular dynamics simulations, we developed and implemented a sampling strategy by combining the metadynamics with (selective) integrated tempering sampling (ITS/SITS) method. The dominant local minima on the potential energy surface (PES) are partially exalted by accumulating history-dependent potentials as in metadynamics, and the sampling over the entire PES is further enhanced by ITS/SITS. With this hybrid method, the simulated system can be rapidly driven across the dominant barrier along selected collective coordinates. Then, ITS/SITS ensures a fast convergence of the sampling over the entire PES and an efficient calculation of the overall thermodynamic properties of the simulation system. To test the accuracy and efficiency of this method, we first benchmarked this method in the calculation of ϕ - ψ distribution of alanine dipeptide in explicit solvent. We further applied it to examine the design of template molecules for aromatic meta-C-H activation in solutions and investigate solution conformations of the nonapeptide Bradykinin involving slow cis-trans isomerizations of three proline residues.

Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations

Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.

Simulation Studies of Protein and Small Molecule Interactions and Reaction

Computational studies of protein and small molecule (protein-ligand/enzyme-substrate) interactions become more and more important in biological science and drug discovery. Computer modeling can provide molecular details of the processes such as conformational change, binding, and transportation of small molecules/proteins, which are not easily to be captured in experiments. In this chapter, we discussed simulation studies of both protein and small molecules from three aspects: conformation sampling, transportations of small molecules in enzymes, and enzymatic reactions involving small molecules. Both methodology developments and examples of simulation studies in this field were presented.

Enhancing pairwise state-transition weights: A new weighting scheme in simulated tempering that can minimize transition time between a pair of conformational states

Simulated tempering (ST) is a widely used enhancing sampling method for Molecular Dynamics simulations. As one expanded ensemble method, ST is a combination of canonical ensembles at different temperatures and the acceptance probability of cross-temperature transitions is determined by both the temperature difference and the weights of each temperature. One popular way to obtain the weights is to adopt the free energy of each canonical ensemble, which achieves uniform sampling among temperature space. However, this uniform distribution in temperature space may not be optimal since high temperatures do not always speed up the conformational transitions of interest, as anti-Arrhenius kinetics are prevalent in protein and RNA folding. Here, we propose a new method: Enhancing Pairwise State-transition Weights (EPSW), to obtain the optimal weights by minimizing the round-trip time for transitions among different metastable states at the temperature of interest in ST. The novelty of the EPSW algorithm lies in explicitly considering the kinetics of conformation transitions when optimizing the weights of different temperatures. We further demonstrate the power of EPSW in three different systems: a simple two-temperature model, a two-dimensional model for protein folding with anti-Arrhenius kinetics, and the alanine dipeptide. The results from these three systems showed that the new algorithm can substantially accelerate the transitions between conformational states of interest in the ST expanded ensemble and further facilitate the convergence of thermodynamics compared to the widely used free energy weights. We anticipate that this algorithm is particularly useful for studying functional conformational changes of biological systems where the initial and final states are often known from structural biology experiments.