SSAGES: Software Suite for Advanced General Ensemble Simulations

Plugin-based interoperability and ecosystem management for the MolSSI Driver Interface Project

The MolSSI Driver Interface (MDI) Project is an effort to simplify and standardize the process of enabling tight interoperability between independently developed code bases and is supported by numerous software packages across the domain of chemical physics. It enables a wide variety of use cases, including quantum mechanics/molecular mechanics, advanced sampling, path integral molecular dynamics, machine learning, ab initio molecular dynamics, etc. We describe two major developments within the MDI Project that provide novel solutions to key interoperability challenges. The first of these is the development of the MDI Plugin System, which allows MDI-supporting libraries to be used as highly modular plugins, with MDI enforcing a standardized application programming interface across plugins. Codes can use these plugins without linking against them during their build process, and end-users can select which plugin(s) they wish to use at runtime. The MDI Plugin System features a sophisticated callback system that allows codes to interact with plugins on a highly granular level and represents a significant advancement toward increased modularity among scientific codes. The second major development is MDI Mechanic, an ecosystem management tool that utilizes Docker containerization to simplify the process of developing, validating, maintaining, and deploying MDI-supporting codes. Additionally, MDI Mechanic provides a framework for launching MDI simulations in which each interoperating code is executed within a separate computational environment. This eliminates the need to compile multiple production codes within a single computational environment, reducing opportunities for dependency conflicts and lowering the barrier to entry for users of MDI-enabled codes.

Synthetic and Computational Design Insights toward Mimicking Protein Binding of Phosphate

The unique and precise capabilities of proteins are renowned for their specificity and range of application. Effective mimicking of protein-binding offers enticing potential to direct their abilities toward useful applications, but it is nevertheless quite difficult to realize this characteristic of protein behavior in a synthetic material. Here, we design, synthesize, and evaluate experimentally and computationally a series of multicomponent phosphate-binding peptide amphiphile micelles to derive design insights into how protein binding behavior translates to synthetic materials. By inserting the Walker A P-loop binding motif into this peptide synthetic material, we successfully implemented the protein-binding design parameters of hydrogen-bonding and electrostatic interaction to bind phosphate completely and selectively in this highly tunable synthetic platform. Moreover, in this densely arrayed peptide environment, we use molecular dynamics simulations to identify an intriguing mechanistic shift of binding that is inaccessible in traditional proteins, introducing two corresponding new design elements─flexibility and minimization of the loss of entropy due to ion binding, in protein-analogous synthetic materials. We then translate these new design factors to de novo peptide sequences that bind phosphate independent of protein-extracted sequence or conformation. Overall, this work reveals that traditional complex conformational restrictions of binding by proteins can be replaced and repurposed in a multicomponent peptide amphiphile synthetic material, opening up opportunities for future enhanced protein-inspired design.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Computational Design of Peptides for Biomaterials Applications

Computer-aided molecular design and protein engineering emerge as promising and active subjects in bioengineering and biotechnological applications. On one hand, due to the advancing computing power in the past decade, modeling toolkits and force fields have been put to use for accurate multiscale modeling of biomolecules including lipid, protein, carbohydrate, and nucleic acids. On the other hand, machine learning emerges as a revolutionary data analysis tool that promises to leverage physicochemical properties and structural information obtained from modeling in order to build quantitative protein structure-function relationships. We review recent computational works that utilize state-of-the-art computational methods to engineer peptides and proteins for various emerging biomedical, antimicrobial, and antifreeze applications. We also discuss challenges and possible future directions toward developing a roadmap for efficient biomolecular design and engineering.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Engineering the formation of spin-defects from first principles

The full realization of spin qubits for quantum technologies relies on the ability to control and design the formation processes of spin defects in semiconductors and insulators. We present a computational protocol to investigate the synthesis of point-defects at the atomistic level, and we apply it to the study of a promising spin-qubit in silicon carbide, the divacancy (VV). Our strategy combines electronic structure calculations based on density functional theory and enhanced sampling techniques coupled with first principles molecular dynamics. We predict the optimal annealing temperatures for the formation of VVs at high temperature and show how to engineer the Fermi level of the material to optimize the defect's yield for several polytypes of silicon carbide. Our results are in excellent agreement with available experimental data and provide novel atomistic insights into point defect formation and annihilation processes as a function of temperature.

Transfer Learning Facilitates the Prediction of Polymer-Surface Adhesion Strength

Machine learning (ML) accelerates the exploration of material properties and their links to the structure of the underlying molecules. In previous work [Shi et al. ACS Applied Materials & Interfaces 2022, 14, 37161-37169.], ML models were applied to predict the adhesive free energy of polymer-surface interactions with high accuracy from the knowledge of the sequence data, demonstrating successes in inverse-design of polymer sequence for known surface compositions. While the method was shown to be successful in designing polymers for a known surface, extensive data sets were needed for each specific surface in order to train the surrogate models. Ideally, one should be able to infer information about similar surfaces without having to regenerate a full complement of adhesion data for each new case. In the current work, we demonstrate a transfer learning (TL) technique using a deep neural network to improve the accuracy of ML models trained on small data sets by pretraining on a larger database from a related system and fine-tuning the weights of all layers with a small amount of additional data. The shared knowledge from the pretrained model facilitates the prediction accuracy significantly on small data sets. We also explore the limits of database size on accuracy and the optimal tuning of network architecture and parameters for our learning tasks. While applied to a relatively simple coarse-grained (CG) polymer model, the general lessons of this study apply to detailed modeling studies and the broader problems of inverse materials design.

Combining particle and field-theoretic polymer models with multi-representation simulations

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

A coarse-grained DNA model to study protein-DNA interactions and liquid-liquid phase separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define non-bonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), that is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond timescale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micron-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

ATESA: An Automated Aimless Shooting Workflow

Transition path sampling methods are powerful tools for studying the dynamics of rare events in molecular simulations. However, these methods are generally restricted to experts with the knowledge and resources to properly set up and analyze the often hundreds of thousands of simulations that constitute a complete study. Aimless Transition Ensemble Sampling and Analysis (ATESA) is a new open-source software program written in Python that automates a full transition path sampling workflow based on the aimless shooting algorithm, streamlining the process and reducing the barrier to use for researchers new to this approach. This introduction to ATESA includes a demonstration of a complete transition path sampling process flow for an example reaction, including finding an initial transition state, sampling with aimless shooting, building a reaction coordinate with inertial likelihood maximization, verifying that coordinate with committor analysis, and measuring the reaction energy profile with umbrella sampling. We also describe our implementation of a termination criterion for aimless shooting based on the Godambe information calculated during model building with likelihood maximization as well as a novel approach to constraining simulations to the desired rare event pathway during umbrella sampling.

Finite temperature string method with umbrella sampling using path collective variables: application to secondary structure change in a protein

The transition of an α-helix to a β-sheet in proteins is among the most complex conformational changes seen in biomolecular systems. Due to long time scales involved in the transition, it is challenging to study such protein conformational changes using direct molecular dynamics simulations. This limitation is typically overcome using an indirect approach wherein one computes the free energy landscape associated with the transition. Computation of free energy landscapes, however, requires a suitable set of collective variables that describe the transition. In this work, we demonstrate the use of path collective variables [D. Branduardi, F. L. Gervasio and M. Parrinello, J. Chem. Phys., 2007, 126, 054103] and combine it with the finite temperature string (FTS) method [E. Weinan, W. Ren and E. Vanden-Eijnden, J. Phys. Chem. B, 2005, 109, 6688-6693] to determine the molecular mechanisms involved during the structural transition of the mini G-protein from an α-helix to a β-hairpin. The transition from the α-helix proceeds via unfolding of the terminal residues, giving rise to a β-turn unfolded intermediate to eventually form the β-hairpin. Our proposed algorithm uses umbrella sampling simulations to simulate images along the string and the weighted histogram analysis to compute the free energy along the computed transition path. This work demonstrates that the string method in combination with path collective variables can be exploited to study complex protein conformational changes such as a complete change in the secondary structure.

Coalescence-Induced Jumping for Removing the Deposited Heterogeneous Droplets: A Molecular Dynamics Simulation Study

The removal of the deposited droplets on a solid surface is crucial to considerable practical applications that require self-cleaning properties. In this work, a strategy of cleaning a deposited droplet ("D-droplet") by coalescing with a heterogeneous and easily jumping droplet ("J-droplet") is proposed. Molecular dynamics simulation studies have shown that the coalescence of these two kinds of droplets would not guarantee the removal of D-droplet, unless the lifting ability of J-droplet is enhanced through the reduction of the solid-liquid interaction. However, this is a bad scenario with low efficiency. Further investigation suggests that by introducing two J-droplets to produce triple-coalescence dynamics, the D-droplet could be successfully jumping from the substrates due to the coalescence-induced effect, which is also verified by the free energy calculation. Moreover, the effects of the size of the droplets and the arrangement mode of these three droplets on the jumping dynamics are both considered. The studies not only help advance our understanding of coalescence-induced jumping of heterogeneous droplets, but also open up new ways to remove the deposited impure droplets, which is expected to guide the fields of self-cleaning.

Predicting Adhesive Free Energies of Polymer-Surface Interactions with Machine Learning

Polymer-surface interactions are crucial to many biological processes and industrial applications. Here we propose a machine learning method to connect a model polymer's sequence with its adhesion to decorated surfaces. We simulate the adhesive free energies of 20000 unique coarse-grained one-dimensional polymer sequences interacting with functionalized surfaces and build support vector regression models that demonstrate inexpensive and reliable prediction of the adhesive free energy as a function of sequence. Our work highlights the promising integration of coarse-grained simulation with data-driven machine learning methods for the design of functional polymers and represents an important step toward linking polymer compositions with polymer-surface interactions.

Visualizing Conformational Space of Functional Biomolecular Complexes by Deep Manifold Learning

The cellular functions are executed by biological macromolecular complexes in nonequilibrium dynamic processes, which exhibit a vast diversity of conformational states. Solving the conformational continuum of important biomolecular complexes at the atomic level is essential to understanding their functional mechanisms and guiding structure-based drug discovery. Here, we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions that approximately visualize the conformational space of biomolecular complexes of interest. AlphaCryo4D integrates 3D deep residual learning with manifold embedding of pseudo-energy landscapes, which simultaneously improves 3D classification accuracy and reconstruction resolution via an energy-based particle-voting algorithm. In blind assessments using simulated heterogeneous datasets, AlphaCryo4D achieved 3D classification accuracy three times those of alternative methods and reconstructed continuous conformational changes of a 130-kDa protein at sub-3 Å resolution. By applying this approach to analyze several experimental datasets of the proteasome, ribosome and spliceosome, we demonstrate its potential generality in exploring hidden conformational space or transient states of macromolecular complexes that remain hitherto invisible. Integration of this approach with time-resolved cryo-EM further allows visualization of conformational continuum in a nonequilibrium regime at the atomic level, thus potentially enabling therapeutic discovery against highly dynamic biomolecular targets.

Free-Energy Landscape and Isomerization Rates of Au4 Clusters at Finite Temperatures

In metallic nanoparticles, the geometry of atomic positions controls the particle's electronic band structure, polarizability, and catalytic properties. Analyzing the structural properties is a complex problem; the structure of an assembled cluster changes from moment to moment due to thermal fluctuations. Conventional structural analyses based on spectroscopy or diffraction cannot determine the instantaneous structure exactly and can merely provide an averaged structure. Molecular simulations offer an opportunity to examine the assembly and evolution of metallic clusters, as the preferred assemblies and conformations can easily be visualized and explored. Here, we utilize the adaptive biasing force algorithm applied to first-principles molecular dynamics to demonstrate the exploration of a relatively simple system, which permits a comprehensive study of the small metal cluster Au₄ in both neutral and charged configurations. Our simulation work offers a quantitative understanding of these clusters' dynamic structure, which is significant for single-site catalytic reactions on metal clusters and provides a starting point for a detailed quantitative understanding of more complex pure metal and alloy clusters' dynamic properties.

Lattice model on the rate of DNA hybridization

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (k_{N}) is directly proportional to the collision rate and the average number of correct contacts (〈n_{cc}〉) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_{cc}〉∝L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (R_{g}) with their length as R_{g}∝sqrt[L]. Since the reaction space will be approximately a sphere with radius equals to 2R_{g} and V∝L^{3/2}, one obtains k_{N}∝1/sqrt[L]. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as k_{R}∝k_{N}L, and one finally obtains k_{R}∝sqrt[L] in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling k_{R}∝sqrt[L]/c, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.

Force-Correction Analysis Method for Derivation of Multidimensional Free-Energy Landscapes from Adaptively Biased Replica Simulations

A methodology is proposed for the calculation of multidimensional free-energy landscapes of molecular systems, based on analysis of multiple molecular dynamics trajectories wherein adaptive biases have been applied to enhance the sampling of different collective variables. In this approach, which we refer to as the Force-Correction Analysis Method (FCAM), local averages of the total and biasing forces are evaluated post hoc, and the latter are subtracted from the former to obtain unbiased estimates of the mean force across collective-variable space. Multidimensional free-energy surfaces and minimum free-energy pathways are then derived by integrating the mean-force landscape with a kinetic Monte Carlo algorithm. To evaluate the proposed method, a series of numerical tests and comparisons with existing approaches were carried out for small molecules, peptides, and proteins, based on all-atom trajectories generated with standard, concurrent, and replica-exchange metadynamics in collective-variable spaces ranging from one to six dimensional. The tests confirm the correctness of the FCAM formulation and demonstrate that calculated mean forces and free energies converge rapidly and accurately, outperforming other methods used to unbias this kind of simulation data.

A molecular view of plasticization of polyvinyl alcohol

Although macromolecules such as polymers are in widespread industrial use, pure formulations rarely have precisely the properties new applications demand. Pure polymer is often too brittle and inflexible, necessitating plasticizers to soften or toughen films and bulk polymer materials. In practice, new formulations are developed by extensive trial-and-error methods, as no general molecular explanations exist for the mechanism of plasticization to aid in determining the optimal structure and concentration of plasticizers. Here, through atomistic molecular simulations augmented with advanced sampling techniques, we develop an atomic-level picture of the processes in plasticization by directly calculating free energies that govern the interaction between polymers and small-molecule plasticizers. This work focuses on the influence of two common plasticizer molecules-glycerol and sorbitol-interacting with polyvinyl alcohol (PVA), a frequently used component of polymer films. In particular, we focus on conformational and hydrogen bond structure changes induced in globules of PVA by the plasticizer molecules, with the hypothesis that hydrogen bonding plays a role in the incorporation of these plasticizers into PVA and, thus, in the observed mechanical properties. While we focus on nanoscopic systems, we observe distinct preferences in the conformational free energy that can be connected to the performance of polymer materials at laboratory and industrial scales. This work presents a new molecular perspective from which effective plasticizers can be developed and presents a firm basis from which important analyses of plasticization in complex chemical environments relevant to industry may be developed.

Stability and molecular pathways to the formation of spin defects in silicon carbide

Spin defects in wide-bandgap semiconductors provide a promising platform to create qubits for quantum technologies. Their synthesis, however, presents considerable challenges, and the mechanisms responsible for their generation or annihilation are poorly understood. Here, we elucidate spin defect formation processes in a binary crystal for a key qubit candidate-the divacancy complex (VV) in silicon carbide (SiC). Using atomistic models, enhanced sampling simulations, and density functional theory calculations, we find that VV formation is a thermally activated process that competes with the conversion of silicon (VSi) to carbon monovacancies (VC), and that VV reorientation can occur without dissociation. We also find that increasing the concentration of VSi relative to VC favors the formation of divacancies. Moreover, we identify pathways to create spin defects consisting of antisite-double vacancy complexes and determine their electronic properties. The detailed view of the mechanisms that underpin the formation and dynamics of spin defects presented here may facilitate the realization of qubits in an industrially relevant material.

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details

The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model-let alone to actually understand-be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavor almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects, such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

Multiscale Reweighted Stochastic Embedding: Deep Learning of Collective Variables for Enhanced Sampling

Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few generalized degrees of freedom, referred to as collective variables (CVs), to represent and drive the sampling of the free energy landscape. In theory, these CVs should separate different metastable states and correspond to the slow degrees of freedom of the studied physical process. To this aim, we propose a new method that we call multiscale reweighted stochastic embedding (MRSE). Our work builds upon a parametric version of stochastic neighbor embedding. The technique automatically learns CVs that map a high-dimensional feature space to a low-dimensional latent space via a deep neural network. We introduce several new advancements to stochastic neighbor embedding methods that make MRSE especially suitable for enhanced sampling simulations: (1) weight-tempered random sampling as a landmark selection scheme to obtain training data sets that strike a balance between equilibrium representation and capturing important metastable states lying higher in free energy; (2) a multiscale representation of the high-dimensional feature space via a Gaussian mixture probability model; and (3) a reweighting procedure to account for training data from a biased probability distribution. We show that MRSE constructs low-dimensional CVs that can correctly characterize the different metastable states in three model systems: the Müller-Brown potential, alanine dipeptide, and alanine tetrapeptide.

Advanced Materials for Energy-Water Systems: The Central Role of Water/Solid Interfaces in Adsorption, Reactivity, and Transport

The structure, chemistry, and charge of interfaces between materials and aqueous fluids play a central role in determining properties and performance of numerous water systems. Sensors, membranes, sorbents, and heterogeneous catalysts almost uniformly rely on specific interactions between their surfaces and components dissolved or suspended in the water-and often the water molecules themselves-to detect and mitigate contaminants. Deleterious processes in these systems such as fouling, scaling (inorganic deposits), and corrosion are also governed by interfacial phenomena. Despite the importance of these interfaces, much remains to be learned about their multiscale interactions. Developing a deeper understanding of the molecular- and mesoscale phenomena at water/solid interfaces will be essential to driving innovation to address grand challenges in supplying sufficient fit-for-purpose water in the future. In this Review, we examine the current state of knowledge surrounding adsorption, reactivity, and transport in several key classes of water/solid interfaces, drawing on a synergistic combination of theory, simulation, and experiments, and provide an outlook for prioritizing strategic research directions.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

Defining the Energetic Basis for a Conformational Switch Mediating Ligand-Independent Activation of Mutant Estrogen Receptors in Breast Cancer

Although most primary estrogen receptor (ER)-positive breast cancers respond well to endocrine therapies, many relapse later as metastatic disease due to endocrine therapy resistance. Over one third of these are associated with mutations in the ligand-binding domain (LBD) that activate the receptor independent of ligand. We have used an array of advanced computational techniques rooted in molecular dynamics simulations, in concert with and validated by experiments, to characterize the molecular mechanisms by which specific acquired somatic point mutations give rise to ER constitutive activation. By comparing structural and energetic features of constitutively active mutants and ligand-bound forms of ER-LBD with unliganded wild-type (WT) ER, we characterize a spring force originating from strain in the Helix 11-12 loop of WT-ER, opposing folding of Helix 12 into the active conformation and keeping WT-ER off and disordered, with the ligand-binding pocket open for rapid ligand binding. We quantify ways in which this spring force is abrogated by activating mutations that latch (Y537S) or relax (D538G) the folded form of the loop, enabling formation of the active conformation without ligand binding. We also identify a new ligand-mediated hydrogen-bonding network that stabilizes the active, ligand-bound conformation of WT-ER LBD, and similarly stabilizes the active conformation of the ER mutants in the hormone-free state. IMPLICATIONS: Our investigations provide deep insight into the energetic basis for the structural mechanisms of receptor activation through mutation, exemplified here with ER in endocrine-resistant metastatic breast cancers, with potential application to other dysregulated receptor signaling due to driver mutations.

Bias free multiobjective active learning for materials design and discovery

The design rules for materials are clear for applications with a single objective. For most applications, however, there are often multiple, sometimes competing objectives where there is no single best material and the design rules change to finding the set of Pareto optimal materials. In this work, we leverage an active learning algorithm that directly uses the Pareto dominance relation to compute the set of Pareto optimal materials with desirable accuracy. We apply our algorithm to de novo polymer design with a prohibitively large search space. Using molecular simulations, we compute key descriptors for dispersant applications and drastically reduce the number of materials that need to be evaluated to reconstruct the Pareto front with a desired confidence. This work showcases how simulation and machine learning techniques can be coupled to discover materials within a design space that would be intractable using conventional screening approaches.

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

Harnessing Peptide Binding to Capture and Reclaim Phosphate

With rising consumer demands, society is tapping into wastewater as an innovative source to recycle depleting resources. Novel reclamation technologies have been recently explored for this purpose, including several that optimize natural biological processes for targeted reclamation. However, this emerging field has a noticeable dearth of synthetic material technologies that are programmed to capture, release, and recycle specified targets; and of the novel materials that do exist, synthetic platforms incorporating biologically inspired mechanisms are rare. We present here a prototype of a materials platform utilizing peptide amphiphiles that has been molecularly engineered to sequester, release, and reclaim phosphate through a stimuli-responsive pH trigger, exploiting a protein-inspired binding mechanism that is incorporated directly into the self-assembled material network. This material is able to harvest and controllably release phosphate for multiple cycles of reuse, and it is selective over nitrate and nitrite. We have determined by simulations that the binding conformation of the peptide becomes constrained in the dense micelle corona at high pH such that phosphate is expelled when it otherwise would be preferentially bound. However, at neutral pH, this dense structure conversely employs multichain binding to further stabilize phosphate when it would otherwise be unbound, opening opportunities for higher-order conformational binding design to be engineered into this controllably packed corona. With this work, we are pioneering a new platform to be readily altered to capture other valuable targets, presenting a new class of capture and release materials for recycling resources on the nanoscale.

Molecular Dynamics-Based Thermodynamic and Kinetic Characterization of Membrane Protein Conformational Transitions

Molecular dynamics (MD) simulations are routinely used to study structural dynamics of membrane proteins. However, conventional MD is often unable to sample functionally important conformational transitions of membrane proteins such as those involved in active membrane transport or channel activation process. Here we describe a combination of multiple MD based techniques that allows for a rigorous characterization of energetics and kinetics of large-scale conformational changes in membrane proteins. The methodology is based on biased, nonequilibrium, collective-variable based simulations including nonequilibrium pulling, string method with swarms of trajectories, bias-exchange umbrella sampling, and rate estimation techniques.

In search of a novel chassis material for synthetic cells: emergence of synthetic peptide compartment

Giant lipid vesicles have been used extensively as a synthetic cell model to recapitulate various life-like processes, including in vitro protein synthesis, DNA replication, and cytoskeleton organization. Cell-sized lipid vesicles are mechanically fragile in nature and prone to rupture due to osmotic stress, which limits their usability. Recently, peptide vesicles have been introduced as a synthetic cell model that would potentially overcome the aforementioned limitations. Peptide vesicles are robust, reasonably more stable than lipid vesicles and can withstand harsh conditions including pH, thermal, and osmotic variations. This mini-review summarizes the current state-of-the-art in the design, engineering, and realization of peptide-based chassis materials, including both experimental and computational work. We present an outlook for simulation-aided and data-driven design and experimental realization of engineered and multifunctional synthetic cells.

Extensible and Scalable Adaptive Sampling on Supercomputers

The accurate sampling of protein dynamics is an ongoing challenge despite the utilization of high-performance computer (HPC) systems. Utilizing only "brute force" molecular dynamics (MD) simulations requires an unacceptably long time to solution. Adaptive sampling methods allow a more effective sampling of protein dynamics than standard MD simulations. Depending on the restarting strategy, the speed up can be more than 1 order of magnitude. One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity of efficiently running adaptive sampling on HPC systems. We discuss how the ExTASY framework can set up new adaptive sampling strategies and reliably execute resulting workflows at scale on HPC platforms. Here, the folding dynamics of four proteins are predicted with no a priori information.

Machine learning for condensed matter physics

Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.

Conformational Free-Energy Landscapes of Alanine Dipeptide in Hydrated Ionic Liquids from Enhanced Sampling Methods

Understanding the interaction of the ionic liquid (IL) with protein is vital to find the origin of the conformational changes of proteins in these alternative solvents. Here, we performed biased molecular dynamics simulations of alanine dipeptide (ADP), a widely used model for protein backbone structure, in water and two hydrated ionic liquids (ILs): 80% (w/w) 1-ethyl-3-methylimidazolium acetate ([EMIm][Ac]) and 80% (w/w) choline dihydrogen phosphate ([Cho][DHP]). We employed three different biasing methods, metadynamics (metaD), well-tempered metadynamics (WT-metaD), and adaptive biasing force (ABF), to construct the free-energy landscapes of the ADP conformations using the backbone dihedral angles (ϕ and ψ) as the collective variables. The calculations were also performed in water; the free-energy landscapes of ADP in water obtained from three methods are similar and agree well with the previously reported results. In hydrated [EMIm][Ac], α-planar conformation emerges as a minimum, which is comparable to that of α and β conformations corresponding to α-helix and β-sheet-like conformations of proteins. Investigation of corresponding conformations suggests that the imidazolium ring of [EMIm] cation is stacked with the amide bonds of ADP. Acetate anion makes hydrogen bonds with the amide hydrogens of the ADP. The amide-π stacking interaction is the driving force for α-planar conformation to become one of the minimum energy conformations in this IL, which destabilizes the protein conformation. However, α and β conformations are more stable in hydrated [Cho][DHP] compared to α-planar and β-planar conformations; therefore, this IL stabilizes the protein conformation. These findings are in good correlation with the previous study of proteins in these ILs. Our study helps to understand the interaction of proteins with the ionic entities and their stability in ILs.

Dissociation of salts in water under pressure

The investigation of salts in water at extreme conditions is crucial to understanding the properties of aqueous fluids in the Earth. We report first principles (FP) and classical molecular dynamics simulations of NaCl in the dilute limit, at temperatures and pressures relevant to the Earth’s upper mantle. Similar to ambient conditions, we observe two metastable states of the salt: the contact (CIP) and the solvent-shared ion-pair (SIP), which are entropically and enthalpically favored, respectively. We find that the free energy barrier between the CIP and SIP minima increases at extreme conditions, and that the stability of the CIP is enhanced in FP simulations, consistent with the decrease of the dielectric constant of water. The minimum free energy path between the CIP and SIP becomes smoother at high pressure, and the relative stability of the two configurations is affected by water self-dissociation, which can only be described properly by FP simulations.

Salts in water at extreme conditions play a fundamental role in determining the properties of the Earthʼs mantle constituents. Here the authors shed light on ion-water and ion-ion interactions for NaCl dissolved in water at conditions relevant to the Earthʼs upper mantle by molecular dynamics simulations.

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn-Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

Surveying the free energy landscape of clusters of attractive colloidal spheres

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.

The role of cations in uranyl nanocluster association: a molecular dynamics study

Actinyl ions can self-assemble in aqueous solution to form closed cage clusters ranging from 1.5 to 4.0 nm in diameter. The self-assembly, stability, and behavior of the nanoclusters depend on the nature of the aqueous environment, such as the pH and cations present. In this work, a classical force field for [(UO2)20(O2)30]20- (U20) peroxide nanoclusters in aqueous solution was developed from quantum-mechanical calculations. Using molecular dynamics simulations, the preferred binding sites of six cations (Li+, Na+, K+, Rb+, Cs+, and Ca2+) to the nanocluster were determined. Replica exchange molecular dynamics was used to equilibrate the structure and determine the equilibrium distribution of cations and water with respect to the nanocluster cage. In addition, the free energy barriers associated with cations entering the cluster were computed. Finally, the association of two cages was investigated by computing the free energy as a function of intercage distance. The free energy profiles reveal that the nanoclusters prefer to be associated when neutralized with divalent cations, but do not associate when neutralized with monovalent cations. This could explain the formation of tertiary structures observed experimentally.

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.

Manipulation of Confined Polyelectrolyte Conformations through Dielectric Mismatch

We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations and a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra "confinement" effect, which is most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an increased amount of counterions adsorbed in the outer side, further compressing the confined polyelectrolyte into a four-fold symmetry morphology. The equilibrium conformation of the chain is dependent upon several key factors including the relative permittivities of the media inside and outside the cavity, multivalent counterion concentration, cavity radius relative to the chain length, and interface charge density. Our findings offer insights into the effects of dielectric mismatch in packaging and delivery of polyelectrolytes across media with different relative permittivities. Moreover, the reversible transformation of the polyelectrolyte conformations in response to environmental permittivity allows for potential applications in biosensing and medical monitoring.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.