Self-Consistency Error Correction for Accurate Machine Learning Potentials from Variational Monte Carlo.

The integration ofmachine learning into reactive chemistry, materialsdiscovery, and drug design is transforming the development of novelmolecules and materials. Machine Learning Interatomic Potentials (MLIPs)predict potential energies and forces with quantum chemistry accuracy,surpassing traditional approaches. Incorporating force fitting inMLIP training enhances potential-energy surface predictions and improvesmodel transferability and reliability. This paper introduces and evaluatesthe integration of Hessian matrix training in MLIPs, which encodessecond-order information about the PES curvature. Our evaluation focuseson models trained only to equilibrium geometries and first-order saddlepoints (i.e., critical points on the potential surface), demonstratingtheir ability to extrapolate to nonequilibrium geometries. This integrationimproves extrapolation capabilities, allowing MLIPs to accuratelypredict energies, forces, and Hessian predictions for nonequilibriumgeometries. Hessian-trained MLIPs enhance reaction pathway modeling,transition state identification, and vibrational spectra predictions,benefiting molecular dynamics (MD) simulations and Nudged ElasticBand (NEB) calculations. By analyzing models trained with varyingcombinations of energy, force, and Hessian data on a small moleculereactive data set, we demonstrate that models including Hessian informationnot only extrapolate more accurately to unseen molecular systems,improving accuracy in reaction modeling and vibrational analysis,but also reduce the total amount of data required for effective training.However, the primary trade-off is increased computational expense,as Hessian training requires more resources than conventional energy-forcetraining. Our findings provide comprehensive insights into the advantagesand limitations of Hessian integration in MLIP training, allowingpractitioners in computational chemistry to make informed decisionsabout employing this method in accordance with their specific researchobjectives and computational constraints.

Machine learning interatomic potentials (MLIPs) enable more efficient molecular dynamics (MD) simulations with ab initio accuracy, which have been used in various domains of physical science. However, distribution shift between training and test data causes deterioration of the test performance of MLIPs, and even leads to collapse of MD simulations. In this work, we propose an online Test-time Adaptation Interatomic Potential (TAIP) framework to improve the generalization on test data. Specifically, we design a dual-level self-supervised learning approach that leverages global structure and atomic local environment information to align the model with the test data. Extensive experiments demonstrate TAIP’s capability to bridge the domain gap between training and test dataset without additional data. TAIP enhances the test performance on various benchmarks, from small molecule datasets to complex periodic molecular systems with various types of elements. TAIP also enables stable MD simulations where the corresponding baseline models collapse.

The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations. Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time. Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function. This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized. 1.1. Historical Background MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics. As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today. The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly. The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1. Open in a separate window Figure 1 Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.

Machine learning (ML) interatomic potentials (ML-IAPs) are generated for alkane and polyene hydrocarbons using on-the-fly adaptive sampling and a sparse Gaussian process regression (SGPR) algorithm. The ML model is generated based on the PBE+D3 level of density functional theory (DFT) with molecular dynamics (MD) for small alkane and polyene molecules. Intermolecular interactions are also trained with clusters and condensed phases of small molecules. It shows excellent transferability to long alkanes and closely describes the ab inito potential energy surface for polyenes. Simulation of liquid ethane also shows reasonable agreement with experimental reports. This is a promising initiative toward a universal ab initio quality force-field for hydrocarbons and organic molecules.

Dopants can tune the performance of MoS2 in various applications, but the use of molecular dynamics simulations for doped MoS2 materials discovery is limited by the lack of multidopant interatomic potentials. Universal machine learning interatomic potentials (MLIPs) could be a solution, but the accuracy of these potentials must first be evaluated. Here, we evaluate the accuracy of a recently developed MLIP, META's Universal Model for Atoms, for 25 different MoS2 dopants spanning metals, nonmetals, and transition metals in Mo-substitution, S-substitution, and intercalated positions by benchmarking the MLIP-predicted formation energy and the dopant-induced structural change against density functional theory (DFT) calculations. The computational framework for MLIP validation and simulations is described in detail, and the source code is made available online. The MLIP is then demonstrated by performing heating-cooling simulations of MoS2 supercells with all 25 dopants. These simulations capture complex phenomena including dopant clustering, MoS2 layer fracturing, interlayer diffusion, and chemical compound formation at orders-of-magnitude reduced computational cost compared to DFT. This work provides a computational workflow for the application-oriented design of doped-MoS2, enabling high-throughput screening of dopant candidates and optimization of compositions for targeted tribological, electronic, and optoelectronic performance.

Calcium-dependent lectin I from Pseudomonas aeruginosa (PA-IL) binds specifically to oligosaccharides presenting an alpha-galactose residue at their nonreducing end, such as the disaccharides alphaGal1-2betaGalOMe, alphaGal1-3betaGalOMe, and alphaGal1-4betaGalOMe. This provides a unique model for studying the effect of the glycosidic linkage of the ligands on structure and thermodynamics of the complexes by means of experimental and theoretical tools. The structural features of PA-IL in complex with the three disaccharides were established by docking and molecular dynamics simulations and compared with those observed in available crystal structures, including PA-IL.alphaGal1-2betaGalOMe complex, which was solved at 2.4 A resolution and reported herein. The role of a structural bridge water molecule in the binding site of PA-IL was also elucidated through molecular dynamics simulations and free energy calculations. This water molecule establishes three very stable hydrogen bonds with O6 of nonreducing galactose, oxygen from Pro-51 main chain, and nitrogen from Gln-53 main chain of the lectin binding site. Binding free energies for PA-IL in complex with the three disaccharides were investigated, and the results were compared with the experimental data determined by titration microcalorimetry. When the bridge water molecule was included in the free energy calculations, the simulations predicted the correct binding affinity trends with the 1-2-linked disaccharide presenting three times stronger affinity ligand than the other two. These results highlight the role of the water molecule in the binding site of PA-IL and indicate that it should be taken into account when designing glycoderivatives active against P. aeruginosa adhesion.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning, which uses biased or unbiased molecular dynamics (MD) to generate candidate pools, aims to address this objective. Existing biased and unbiased MD-simulation methods, however, are prone to miss either rare events or extrapolative regions—areas of the configurational space where unreliable predictions are made. This work demonstrates that MD, when biased by the MLIP’s energy uncertainty, simultaneously captures extrapolative regions and rare events, which is crucial for developing uniformly accurate MLIPs. Furthermore, exploiting automatic differentiation, we enhance bias-forces-driven MD with the concept of bias stress. We employ calibrated gradient-based uncertainties to yield MLIPs with similar or, sometimes, better accuracy than ensemble-based methods at a lower computational cost. Finally, we apply uncertainty-biased MD to alanine dipeptide and MIL-53(Al), generating MLIPs that represent both configurational spaces more accurately than models trained with conventional MD.

Voltage gated potassium ion (Kv) channels regulate action potentials of the nervous system by responding to changes in transmembrane voltage, enabling K+ transport across the membrane to restore cells to their resting potential. Comprised of four identical subunits, Kv channels contain four voltage sensing domains arranged on the periphery of a central pore domain. Each voltage sensor is comprised of four transmembrane helices, numbered S1 through S4. The S4 helix, containing four to six highly-conserved, positively-charged arginine or lysine residues, is responsible for voltage sensitivity in Kv channels. The pore domain consists of two transmembrane helices, S5 and S6. The S5 helix constitutes the periphery of the pore domain and is believed to be relatively immobile. The S6 helices, lining the interior of the channel, gate the protein and regulate K+ permeation. Because each subunit of Kv channels contains six transmembrane helices, they are often referred to as 6TM Kv channels. The depolarization of an action potential is initiated as sodium ions enter the cell. At the cellular resting potential of -70 mV, potassium ion channels are closed, and the S4 helix is in its “down” state. As the electrochemical gradient changes, the S4 helices of Kv channels begin to reorient within the membrane. At the peak of the action potential (roughly +20 mV), the S4 helices exist in their “up” state. This conformational transition of the S4 helix is coupled to the pore domain via the S4-S5 linker, a short, amphipathic helix along the intracellular membrane-water interface. By bridging the C-terminus of the voltage sensor to the N-terminus of the pore domain, the S4-S5 linker couples the voltage sensitivity of the voltage sensor to K+ conduction in the pore domain. Because they begin opening at voltages less than 0 mV, all crystal structures of Kv channels contain an open pore domain. With no structure in the closed conformation, the mechanism of gating in Kv channels remains unclear. Nevertheless, significant biophysical studies have revealed insights into both the closed conformation and the gating transition itself. In this dissertation, I will explore questions relevant to the gating mechanism in voltage gated potassium ion channels through fully-atomistic molecular dynamics (MD) simulations. First, in Chapter 2, I will address the potential role of the 310 helical conformation found in the C-terminal end of S4 in the crystal structures of Kv channels. Spanning eight or more residues, these 310 helices are both uncharacteristically long and conserved in K+ channel crystal structures. By simulating the Kv1.2/2.1 chimera channel’s voltage sensor embedded in a lipid bilayer, I find that an alpha to 310 helical interconversion of the S4 helix reproduces many experimental measurements of the open and closed states of Kv channels. In Chapter 3, I perform molecular dynamics simulations of the entire Kv1.2/2.1 chimera channel. First, I examine the impact of an alpha to 310 helical interconversion of the S4 helix on the pore domain of the channel. Though the results are consistent with the results in Chapter 2 (and the corresponding experimental measurements), I find that this secondary structural modification is insufficient to influence the pore domain of the channel on the timescale of my simulations. In the second half of Chapter 3, I use molecular dynamics simulations to generate a closed state model of the Kv1.2/2.1 chimera from luminescence resonance energy transfer (LRET) measurements of the closed conformation of KvAP. The resulting structure is indeed closed, and also recapitulates a number of experimentally determined measurements of the closed channel. In Chapter 4, I focus on the pore domain. First, using targeted molecular dynamics simulations, I generate a transition between a closed model of the KvAP linker and pore domain to the open conformation. Then, using an umbrella sampling method, I quantify the energetics of the gating transition in KvAP and assess the physiological implications. In agreement with experimental studies of Kv channel energetics, I find that the open pore is roughly 2.7 kcal/mol lower in free energy than the closed conformation. The targeted molecular dynamics and umbrella sampling simulations reveal additional insights into the gating mechanism of KvAP. Lastly, in Chapter 5, I use MD simulations to gain insights into the binding mechanism of VSTx1, a Kv channel inhibitor. By using the experimentally determined neutron scattering density profile of the VSTx1 toxin bound to a lipid bilayer as a restraint for molecular dynamics simulations, I recreate the experimental scattering density profile, and also offer insight into the binding of VSTx1 to a lipid membrane.

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na2SO4,aq-graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaClaq-air and NaClaq-graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid-liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. We show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Machine learning interatomic potentials (MLIPs) enables molecular dynamics (MD) simulations with ab initio accuracy and has been applied to various fields of physical science. However, the performance and transferability of MLIPs are limited by insufficient labeled training data, which require expensive ab initio calculations to obtain the labels, especially for complex molecular systems. To address this challenge, we design a novel geometric structure learning paradigm that consists of two stages. We first generate a large quantity of 3D configurations of target molecular system with classical molecular dynamics simulations. Then, we propose geometry-enhanced self-supervised learning consisting of masking, denoising, and contrastive learning to better capture the topology and 3D 1 geometric information from the unlabeled 3D configurations. We evaluate our method on various benchmarks ranging from small molecule datasets to complex periodic molecular systems with more types of elements. The experimental results show that the proposed pre-training method can greatly enhance the accuracy of MLIPs with few extra computational costs and works well with different invariant or equivariant graph neural network architectures. Our method improves the generalization capability of MLIPs and helps to realize accurate MD simulations for complex molecular systems.

The suppression of heat transport in disordered crystals arises from a competition between mass fluctuations and bond disorder, but their relative contributions remain difficult to disentangle. We address this challenge using a machine-learned interatomic potential trained on ab initio data across the PbTe1-xSex alloy series. Molecular dynamics simulations with the trained machine-learned interatomic potential reproduce experimental lattice thermal conductivities and density-functional theory phonon dispersions while enabling frequency-resolved analysis of heat transport from 300 to 800 K. We find a narrow window near 1.7-2.0 THz dominates heat transport across all compositions, where heat is primarily carried by mixed longitudinal acoustic and optical modes. Alloying dramatically reduces spectral diffusivity near 2 THz leading to the deterioration of thermal conductivity. For the parent compounds both the spectral diffusivity and overall thermal conductivity decrease at elevated temperatures. However, the thermal degradation is weaker for the mid-range composition (x = 0.5) due to the greater thermal occupation of vibrational modes and increased heat capacity. Alchemical simulations show that force-constant disorder, not mass contrast, plays the dominant role in this suppression. These results highlight the microscopic mechanisms underlying thermal transport breakdown in alloys and demonstrate how machine-learned interatomic potentials now offer a tractable path toward predictive, physics-rich thermal transport modeling in complex disordered solids.

Machine-learning interatomic potentials (MLIPs) enable large-scale atomistic simulations at moderate computational cost while retaining ab initio accuracy. In recent years, MLIPs trained on coupled-cluster data─particularly CCSD(T), which includes single, double, and perturbative triple excitations─have emerged as a promising route to achieve chemical accuracy (1 kcal/mol) beyond the limits of density functional theory (DFT) and to incorporate nonempirical van der Waals (vdW) interactions. Most existing approaches are, however, still not straightforwardly applicable for systems with extended covalent networks such as covalent organic frameworks (COFs) due to the limited availability of CCSD(T) under periodic boundary conditions. Here we present a methodology to train MLIPs with CCSD(T) accuracy for systems with extended covalent networks. The approach is based on the Δ-learning method with a dispersion-corrected tight-binding baseline and an MLIP trained on the differences of the target CCSD(T) energies from the baseline. This Δ-learning strategy enables training on compact molecular fragments while preserving transferability toward the periodic systems. Dispersion interactions are accounted for by including vdW-bound multimers in the training set, and the combination with a vdW-aware tight-binding baseline allows the formally local MLIP to attain CCSD(T)-level accuracy even for systems dominated by long-range vdW forces. The resulting potential yields root-mean-square energy errors below 0.4 meV/atom on both training and test sets and reproduces electronic total atomization energies, bond lengths, harmonic vibrational frequencies, and intermolecular interaction energies for benchmark molecular systems. We apply the method to a prototypical quasi-two-dimensional covalent organic framework (COF) composed of carbon and hydrogen. The COF structure, interlayer binding energies, and hydrogen absorption are analyzed at CCSD(T) accuracy. Overall, the developed methodology opens a practical route to large-scale atomistic simulations for systems with extended covalent networks and vdW interactions with chemical accuracy.

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macromolecules could in principle lead to important scientific advances and provide a powerful new tool for drug discovery. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond - several orders of magnitude beyond the duration of the longest current MD simulations. Our research group is currently building a specialized, massively parallel machine, called Anton, which should soon be capable of executing millisecond-scale MD simulations of proteins at an atomic level of detail. Antonpsilas highly accelerated execution of such simulations is attributable in large part to specialized logic for the high-speed calculation of pairwise interactions between particles and/or gridpoints separated by no more than some specified cutoff radius.In particular, each of Anton's 512 ASICs, which are implemented using 90-nm technology,includes a "high-throughput interaction subsystem" incorporating 32 highly specialized pipelines running at 800 MHz. During every cycle, each of these pipelines produces a pairwise-interaction result that would require approximately 50 arithmetic operations to calculate on a general-purpose processor. Novel algorithms and architectural features are used to greatly reduce the requirements for inter- and intra-chip communication, allowing Anton to feed these pipelines and collect their results at a speed sufficient to take advantage of the machine's computational power. The ASIC also includes a "flexible subsystem" based on eight programmable "geometry cores", each containing eight arithmetic pipelines. This talk will provide an overview of our work on parallel algorithms and machine architectures for high-speed MD simulation, with special attention to the respective roles of specialized vs. general-purpose hardware, and to the techniques used to minimize communication at various levels within the system.

Multiscale Modeling of Microtubules and Actin Filaments

Hydroxyapatite (HAp) nucleation requires incorporation of hydroxyl (OH), yet how hydroxylation emerges, and OH groups become stabilized during Ca-P assembly, particularly under nanoconfinement and with organic molecules, remains unclear. Here, we employ machine learning interatomic potentials (MLIPs) in molecular dynamics (MD) simulations to track hydroxylation pathways and cluster evolution in bulk solution and between graphene sheets containing l-aspartate (Asp). Hydroxylation occurs mainly through proton transfer (PT) events that directly generate Ca-OH, ∼103 times more frequently than capture of existing free OH- from solution, consistent with Grotthuss-type PT. Graphene confinement suppresses the emergence of HAp-relevant, three-Ca-coordinated hydroxyl motifs. Under confinement, l-Asp reorganizes local ion distributions and stabilizes Ca-rich microenvironments, producing the most persistent planar three-Ca-coordinated OH motifs and more highly coordinated Ca, thereby forming more HAp-like early nuclei. Our results support a nucleation sequence in which a CaP framework forms first, hydroxylation proceeds continuously, and under confinement, acidic amino acids later select and stabilize HAp-like hydroxyl coordination, clarifying HAp formation in synthetic and biological nanoenvironments.