Efficient equivariant model for machine learning interatomic potentials

Comparison of different interatomic potentials for MD simulations of AlN

High-accuracy ab initio folding has remained an elusive objective despite decades of effort. To explore the folding landscape of villin headpiece subdomain HP35, we conducted two sets of replica exchange molecular dynamics for 200 ns each and three sets of conventional microsecond-long molecular dynamics simulations, using AMBER FF03 force field and a generalized-Born solvation model. The protein folded consistently to the native state; the lowest C(alpha)-rmsd from the x-ray structure was 0.46 A, and the C(alpha)- rmsd of the center of the most populated cluster was 1.78 A at 300 K. ab initio simulations have previously not reached this level. The folding landscape of HP35 can be partitioned into the native, denatured, and two intermediate-state regions. The native state is separated from the major folding intermediate state by a small barrier, whereas a large barrier exists between the major folding intermediate and the denatured states. The melting temperature T(m) = 339 K extracted from the heat-capacity profile was in close agreement with the experimentally derived T(m) = 342 K. A comprehensive picture of the kinetics and thermodynamics of HP35 folding emerges when the results from replica exchange and conventional molecular dynamics simulations are combined.

While molecular dynamics (MD) is a very useful computational method for atomistic simulations, modeling the interatomic interactions for reliable MD simulations of real materials has been a long-standing challenge. In 2007, Behler and Parrinello first proposed and demonstrated an artificial neural network machine learning (ANN-ML) scheme, opening a new paradigm for developing accurate and efficient interatomic potentials for reliable MD simulation studies of the thermodynamics and kinetics of materials. In this paper, we show that an accurate and transferable ANN-ML interatomic potential can be developed for MD simulations of the La-Si-P system. The crucial role of training data in the ML potential development is discussed. The developed ANN-ML potential accurately describes not only the energy vs volume curves for all the known elemental, binary, and ternary crystalline structures in the La-Si-P system but also the structures of La-Si-P liquids with various compositions. Using the developed ANN-ML potential, the melting temperatures of several crystalline phases in the La-Si-P system are predicted by the coexistence of solid-liquid phases from MD simulations. While the ANN-ML model systematically underestimates the melting temperatures of these phases, the overall trend agrees with experiment. The developed ANN-ML potential is also applied to study the nucleation and growth of LaP as a function of different relative concentrations of Si and P in the La-Si-P liquid, and the obtained results are consistent with experimental observations.

ABSTRACTAs opposed to traditional laboratory testing, Molecular Dynamics (MD) offers an atomistic scale method to estimate the mechanical properties of metals. However, there is limited literature that shows the effect of interatomic potentials when determining mechanical properties. Hence, the present research was conducted to investigate the accuracy of various interatomic potentials in estimating mechanical properties of aluminium. Several types of potentials, including Embedded Atom Method (EAM), Modified EAM (MEAM) and Reactive Force Field (ReaxFF) were compared with available experimental data for pure aluminium to determine the most accurate interatomic potential. A uniaxial tensile test was performed at room temperature using MD simulations for nanoscale aluminium. Results demonstrated that those potentials parameterised with elastic constants at physically realisable temperatures were consistently more accurate. Overall, the Mishin et al. EAM potential was the most accurate when compared to single-crystal experimental values. Regardless of the potential type, the error was significantly higher for those potentials that did not consider elastic constants during development. In brief, the application of the interatomic potentials to estimate mechanical properties of a nanoscale aluminium was investigated.

Grain boundary induced deformation mechanisms in nanocrystalline Al by molecular dynamics simulation: From interatomic potential perspective

Self-assembled cyclic peptide nanotubes (CPNs) show a potential use in drug delivery. In this study, the CPN composed of (Trp-d-Leu)4-Gln-d-Leu was synthesized and tested for the transport of the antitumor drug 5-fluorouracil (5-FU). CPN-mediated release of 5-FU from liposomes experimentally tested the transportation function of the synthetic CPNs. To explore the transportation mechanism of CPNs, computational studies have been performed on the CPN models stacked by 8 subuints, including conventional molecular dynamics (CMD) simulations, and steered molecular dynamics (SMD) simulations in the environment of hydrated dimyristoylphosphatidylcholine (DMPC) lipid bilayer. Our CMD simulations demonstrated that the ortho-CPN is the most stable nanotube, in which the Gln residue is in the ortho-position relative to other residues. The calculated diffusion coefficient value for inner water molecules was 1.068 × 10−5 cm2·s−1, almost half that of the bulky water and 24 times faster than that of the typical gramicidin A channel. The CPN conserved its hollow structure along the 10 ns CMD simulations, with a tile angle of 50° relative to the normal of DMPC membrane. Results from SMD simulations showed that the 5-FU molecule was transported by hopping through different potential energy minima distributed along subunits, and finally exited the nanotube by escaping from the kink region at the last two subunits. The hopping of 5-FU was driven by switching from hydrophobic interactions between 5-FU and the interior wall of the nanotube to hydrogen bonding interactions of 5-FU with the backbone carbonyl group and amide group of ortho-CPN. The calculated binding free energy profile of 5-FU interacting with the CPN indicated that there was an energy well near the outer end of the nanotube.

Ischemic heart diseases are responsible for more than one-third of all deaths worldwide. Radix notoginseng is widely used to treat ischemic heart disease in China and other Asian countries, and notoginsenoside R1 (NGR1) is its characteristic and large-amount ingredient. However, the potential molecular mechanisms of NGR1 in improving ischemic heart diseases are unclear. In this study, we combined pharmacological evaluation with network pharmacology, myocardial proteomics, and conventional molecular dynamics (MD) simulation to explore the cardio-protection mechanisms of NGR1. Our results revealed that NGR1 improved the echocardiographic, tissue pathological, and serum biochemical perturbations in myocardial ischemic rats. The network pharmacology studies indicated that NGR1 mainly regulated smooth muscle cell proliferation, vasculature development, and lipid metabolism signaling, especially in the PI3K/AKT pathway. Myocardial proteomics revealed that the function of NGR1 was focused on regulating metabolic and energy supply processes. The research combined reverse-docked targets with differential proteins and demonstrated that NGR1 modulated lipid metabolism in ischemic myocardia by interacting with mTOR and AKT. Conventional MD simulation was applied to investigate the influence of NGR1 on the structural stabilization of the mTOR and AKT complex. The results suggested that NGR1 can strengthen the affinity stabilization of mTOR and AKT. Our study first revealed that NGR1 enhanced the affinity stabilization of mTOR and AKT, thus promoting the activation of the AKT/mTOR pathway and improving lipid metabolic abnormity in myocardial ischemic rats.

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.

Molecular dynamics and atomistic based continuum studies of the interfacial behavior of nanoreinforced epoxy

Pt-water interfaces have been of immense interest in the field of energy storage and conversion. Studying this interface using both experimental and theoretical tools is challenging. On the theoretical front, typically one uses classical molecular dynamics (MD) simulations to handle large system sizes or time scales while for a more accurate quantum mechanical description Born Oppenheimer MD (BOMD) is typically used. The latter is limited to smaller system sizes and time-scales. In this study using quantum-mechanics-molecular-mechanics (QMMM), we have performed atomistic MD simulations to have a microscopic understanding of the structure of the Pt-water interface using a system size that is much larger than that accessible when using BOMD simulations. In contrast to recent reports using BOMD simulations, our study reveals that the water molecules typically form two distinct layers above the Pt-surface before they form bulk like structures. Further, we also find that a significant fraction of the water molecules at the interface are pointed towards the surface thereby disrupting the H-bond network. Consistent with this observation, the layer resolved oxygen-oxygen radial distribution function for the water molecules belonging to the solvating water layer shows a high density liquid like behaviour even though the overall water behaves like a low density liquid. A charge transfer analysis reveals that this solvating water layer donates electrons to the Pt atoms in contact with it thereby resulting in the formation of an interface dipole that is pointing towards the surface. Our results suggest that, using QMMM-MD, on one hand it is possible to study more realistic models of solid-liquid interfaces that are inaccessible with BOMD, while on the other hand one also has access to information about such systems that are not obtained from conventional classical MD simulations.

Both machine learning (ML) and molecular dynamics (MD) techniques have benefited substantially from the growing accessibility to computational resources, enabling more sophisticated ML models and more extensive MD simulations. Over recent years, the use of ML and MD methods has become increasingly prevalent in computer-aided drug discovery. To exploit the synergies between these methodologies, researchers have started to explore approaches that combine ML techniques and MD simulations. We start this chapter with a brief introduction of the basics of MD simulations as well as ML applications in drug discovery. Next, three broad ways of marrying MD with ML are discussed: (1) use of ML to parameterise systems for MD simulations with increased accuracy, (2) use of ML to improve sampling efficiency during MD simulations, and (3) use of ML to post-process MD trajectories in order to gain quantitative insights into molecular processes. We conclude the chapter with our perspective on areas for further development of this emerging interdisciplinary field.

Molecular dynamics (MD) simulation is a fundamental approach to allow researchers to study the molecular interactions of protein-ligand binding via the dynamics of protein-ligand complexes at atomic level. It can be observed precisely the motion of atoms and interactions involved in receptor and ligand binding using MD simulations. In this thesis, conventional MD simulations is applied to investigate the basis of mutation induced resistance HIV-1 integrase inhibitors, and positive agreement with experimental result has been observed and reasonable explanations are presented. Nevertheless, the deficiency of conventional molecular dynamics simulation is not negligible either. It lacks polarization effects in classical force fields utilized in traditional MD simulations, consequently the capability of describing the specific electrostatic properties of different biological systems is absent. Previously developed polarized protein-specific charge (PPC) allows electrostatic polarization effect to be introduced into molecular dynamics simulation as static charges. In this thesis, this method is employed in MD simulations to explore the mechanism of governing resistance to its inhibitor while HIV-1 protease Ile mutates to Val at position 50 in both chains; and the importance of electrostatic polarization effect and advantages compare to classical force field is demonstrated. The result shows polarization effect included simulations are more reliable comparing with experimental data. However, static PPC charges are calculated based on single conformation, and it causes bias of atomic charges, e.g. overestimate particular hydrogen bond strength resulting extra stability during simulation. As conformations of the systems varying dynamically would lead to electrostatic environment change, atomic charges in system should also be re-calculated during MD simulations. Environmentally corresponding local polarized protein-specific charge (ECLPPC) scheme and environmentally corresponding hydrogen bond dependent polarized protein-specific charge (ECHBPPC) scheme have been newly developed and applied in protein-ligand MD simulations. They update the atomic charges of ligand and selected residues in certain criteria surrounding the ligand periodically to incorporate polarization into MD simulations. MD simulations are conducted by employing ECLPPC and ECHBPPC respectively to investigate the basis of avidin-biotin interaction and give reasonable results with agreement to experiment.

Sintering of alumina nanoparticles is of interest both from the view of fundamental research as well as for industrial applications. Atomistic simulations are tailor-made for understanding and predicting the time- and temperature-dependent sintering behaviour. However, the quality and predictability of such analysis is strongly dependent on the performance of the underlying interatomic potentials. In this work, we investigate and benchmark four empirical interatomic potentials and discuss the resulting properties and drawbacks based on experimental and density functional theory data from the literature. The potentials, which have different origins and formulations, are then used in molecular dynamics (MD) simulations to perform a systematic study of the sintering process. To analyse the results, we develop a number of tailored data analysis approaches that are able to characterise and quantify the sintering process. Subsequently, the disparities in the sintering behaviour predicted by the potentials are critically discussed. Finally, we conclude by providing explanations for the differences in performance of the potentials, together with recommendations for MD sintering simulations of alumina.

The [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquid is a promising prototype electrolyte for aluminum-ion batteries (AIBs). Its ionic transport behavior involves multiple mobile species (Al<sup>3+</sup>, AlCl<sub>3</sub>, [AlCl<sub>4</sub>]<sup>–</sup> and [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup>), with ion migration mechanisms and conversion reactions among these species unsolved experimentally. This complexity results in heterogeneous ion migration mechanisms and sluggish diffusion kinetics, which cannot be accurately and reliably captured by the traditional first-principles molecular dynamics (FPMD) simulations within the very limited time duration (tens of ps) and relatively small modelling structure (less than 10<sup>3</sup> atoms). The classic molecular dynamics simulations based on various force fields are also scarce for studying and predicting the atomic structure evolution and ion diffusion dynamics of the complex electrolyte system such as ion liquids. In this work, a deep neural network interatomic potential (DP-potential) is developed through machine learning techniques, combining first-principles accuracy with classical molecular dynamics efficiency, to systematically investigate various chemical and physical properties for [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion-liquid at finite temperatures. Training and validating of DP potential for [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquid are implemented with a two-stage protocol, including the primary training stage and the refining stage. Before initiating the two training stages, a series of first-principles molecular dynamics (FPMD) simulations is performed for [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquids with different molar ratios (1.0, 1.3, 1.5, 1.7 and 2.0) and equilibrium densities (1.09—1.56 g/cm<sup>3</sup>) at finite temperatures (300 K and 400 K), resulting in a highly diverse training datasets spanning a board range of chemical compositions and densities during the primary training stage for DP potential. Then, the trained DP-potential is employed to conduct long-timescale classic molecular dynamics simulations by using LAMMPS program for the [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquids to produce the atomic configurations that either show significant errors in the calculated atomic forces and total energies or exhibit the unusual atomic evolution before crashing. Those highly extrapolated atomic configurations are merged with the initial training datasets to reoptimize the DP potential in the second refining stage. Through this two-stage training approach, a deep learning neural network interatomic potential with high accuracy is successfully constructed, achieving an energy prediction error of 5×10<sup>–4</sup> eV/atom and a force prediction error of 5×10<sup>–2</sup> eV/Å. The reliability of the finally obtained machine learning potential is further validated through a systematic comparison of radial distribution functions (RDF) for some representative atomic pairs such as C—N, C—H, Al—Cl and Cl—H, obtained from both DP-MD and FPMD, demonstrating excellent consistency for the results from the two methods. The DP-MD simulations are systematically carried out to investigate vibrational spectrum and Al<sup>3+</sup> diffusion dynamics as well as possible conversion reactions among molecular or ionic species (Al<sup>3+</sup>, AlCl<sub>3</sub>, [AlCl<sub>4</sub>]<sup>–</sup> and [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup>) in [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquids within 10<sup>4</sup> atoms at finite temperatures. From the calculated vibrational density of states (VDOS), it can be seen that the VDOS of [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquid can be approximated as a simple superposition of the vibrational spectra of individual species ([EMIm]<sup>+</sup>, [AlCl<sub>4</sub>]<sup>–</sup>, and [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup>), with H related vibrational modes dominating above 90 THz and the Al—Cl modes dominating below 20 THz. At 300 K, DP-MD predicts that regardless of the chemical compositions, the diffusion coefficient of Al<sup>3+</sup> remains around 4 × 10<sup>–7</sup> cm<sup>2</sup>/s at 300 K and the estimated diffusion activation energy is about 0.20 eV, which is very close to the experimental measurement value (0.15 eV). In addition, the calculated ionic conductivity of [EMIm]<sup>+</sup>Cl<sup>–</sup> + AlCl<sub>3</sub> at room temperature is 27.37 mS/cm, with a deviation of only 18.2% from the experimental value (23.15 mS/cm). Notably, two different Al<sup>3+</sup> diffusion mechanisms are identified in [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquid: 1) direct migration processes conducted solely by molecular species including [AlCl<sub>4</sub>]<sup>–</sup> and [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup>, and 2) the migration of the neutral AlCl<sub>3</sub> molecule mediated with two neighboring [AlCl<sub>4</sub>]<sup>–</sup> anions through the conversion reaction between [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup> and AlCl<sub>3</sub>+[AlCl<sub>4</sub>]<sup>–</sup> moieties. Furthermore, first-principles calculations on the probable dissociation pathways of [Al<sub>2</sub>Cl<sub>7</sub>]<sup>–</sup> revealed from DP-MD predict a reaction energy barrier height of 0.49 eV for the AlCl<sub>3</sub> transferring between two [AlCl<sub>4</sub>]<sup>–</sup> anions with an increased reaction probability from 0.00047 events/(ps·Al<sup>3+</sup>) at 1∶1.3 molar ratio to 0.00347 events/(ps·Al<sup>3+</sup>) at 1∶1.75 molar ratio. Overall, a highly efficient and reliable workflow to train and validate the deep neural network interatomic potential for complex electrolyte system is successfully proposed, such as [EMIm]<sup>+</sup>Cl<sup>–</sup>+AlCl<sub>3</sub> ion liquids, thus providing a more comprehensive investigation of Al<sup>3+</sup> transport mechanisms in ionic liquid electrolytes for aluminum-ion batteries. In conclusion, this work can further advance the application of machine learning-based potentials in simulating electrolyte systems characterized by complex molecular architectures and sluggish diffusion dynamics.

This study integrates atomistic molecular dynamics (MD) simulations with stochastic modeling to unravel the gene regulatory mechanism mediated by nuclear receptors (NRs), ligand-activated transcription factors. We specifically study the heterodimeric RXR-RAR nuclear receptor system. We use MD simulations to investigate ligand-induced allosteric communication, receptor dynamics, and DNA recognition. The results suggest that receptor dimerization precedes DNA binding, and even single-ligand occupancy induces allosteric signaling that stabilizes the complex, indicating ligand binding as a modulator of gene expression. In contrast, we propose a ligand-induced downregulation mechanism of gene expression that involves disruption of allosteric pathways, weakening of the receptor-DNA interface, and promotion of complex dissociation, as inferred from binding free energy calculations. To bridge the time scale gap between molecular events and gene-level regulation, we integrate MD-derived data into a stochastic modeling framework to construct an NR-mediated gene regulatory network. This analysis reveals that ligand-specific allosteric activation predominantly drives gene expression. The results further demonstrate that the system maintains an ordered transcriptional response despite noisy intermediate dynamics, ensuring minimal mRNA production through a balance between synthesis and degradation. This integrated approach connects molecular-scale interactions with long-time scale regulatory dynamics, providing mechanistic insights into NR-mediated regulation. Using RXR-RAR as a representative system, we establish a computational framework to explore the principles of NR function and dysfunction that are often inaccessible through experiments or conventional MD simulations.