A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations

Lambda-ABF-OPES: Faster Convergence with High Accuracy in Alchemical Free Energy Calculations

Predicting the binding affinity between small molecules and target macromolecules while combining both speed and accuracy is a cornerstone of modern computational drug discovery, which is critical for accelerating therapeutic development. Despite recent progress in molecular dynamics (MD) simulations, such as advanced polarizable force fields and enhanced sampling techniques, estimating absolute binding free energies (ABFEs) remains computationally challenging. To overcome these difficulties, we introduce a highly efficient hybrid methodology that couples the Lambda-adaptive biasing force (Lambda-ABF) scheme with on-the-fly probability enhanced sampling (OPES). This approach achieves up to a 9-fold improvement in sampling efficiency and computational speed compared to the original Lambda-ABF when used in conjunction with the AMOEBA polarizable force field, yielding converged results at a fraction of the cost of standard techniques.

Improved Free-Energy Estimates for the Permeation of Bulky Antibiotic Molecules through Porin Channels Using Temperature-Accelerated Sliced Sampling

The estimation of accurate free energies for antibiotic permeation via the bacterial outer-membrane porins has proven to be challenging. Atomistic simulations of the process suffer from sampling issues that are typical of systems with complex and slow dynamics, even with the application of advanced sampling methods. Ultimately, the objective is to obtain accurate potential of mean force (PMF) for a large set of antibiotics and to predict permeation rates. Therefore, the computational expense becomes an important criterion as well. Simulation studies on the permeation process and similar complex processes have shown that both the sampling scheme employed and the procedure used for the generation of the initial states can critically affect the quality of the estimates obtained and the respective computational overhead. The temperature-accelerated sliced sampling method (TASS) has been shown to partly address the issues with efficient sampling of the important and slow degrees of freedom by enabling simultaneous biasing of a large number of collective variables. In this work, we investigate the effect of the procedure used for the generation of input conformations on the convergence of free-energy estimates obtained from TASS simulations. In particular, we compare the steered molecular dynamics (MD)-based procedure that has been used in previous TASS studies with the Monte Carlo pathway search method, which is used to obtain approximate permeation trajectories with minimum perturbation of the protein channel. We tested different input setups for enrofloxacin permeation through the porins OmpK35 and OmpE35. The best setup shows an improved agreement between independent PMFs in both cases at a much lower computational cost.

Integrative mapping reveals molecular features underlying the mechanism of nucleocytoplasmic transport

Nuclear Pore Complexes (NPCs) enable rapid, selective, and robust nucleocytoplasmic transport. To explain how transport emerges from the system components and their interactions, we used experimental data and theoretical information to construct an integrative Brownian dynamics model of transport through an NPC, coupled to a kinetic model of transport in the cell. The model recapitulates key aspects of transport for a wide range of molecular cargos, including pre-ribosomes and viral capsids. It quantifies how flexible phenylalanine-glycine (FG) repeat proteins raise an entropy barrier to passive diffusion and how this barrier is selectively lowered in facilitated diffusion by the many transient interactions of nuclear transport receptors with the FG repeats. Selective transport is enhanced by "fuzzy" multivalent interactions, redundant FG repeats, coupling to the energy-dependent RanGTP concentration gradient, and exponential dependence of transport kinetics on the transport barrier. Our model will facilitate rational modulation of the NPC and its artificial mimics.

Enhanced sampling of robust molecular datasets with uncertainty-based collective variables

Generating a dataset that is representative of the accessible configuration space of a molecular system is crucial for the robustness of machine-learned interatomic potentials. However, the complexity of molecular systems, characterized by intricate potential energy surfaces, with numerous local minima and energy barriers, presents a significant challenge. Traditional methods of data generation, such as random sampling or exhaustive exploration, are either intractable or may not capture rare, but highly informative configurations. In this study, we propose a method that leverages uncertainty as the collective variable (CV) to guide the acquisition of chemically relevant data points, focusing on regions of configuration space where ML model predictions are most uncertain. This approach employs a Gaussian Mixture Model-based uncertainty metric from a single model as the CV for biased molecular dynamics simulations. The effectiveness of our approach in overcoming energy barriers and exploring unseen energy minima, thereby enhancing the dataset in an active learning framework, is demonstrated on alanine dipeptide and bulk silica.

FESTA: A Polygon-Based Approach for Extracting Relevant Structures from Free Energy Surfaces Obtained in Molecular Simulations

An easy-to-use script named FESTA (Free Energy Surface Trajectory Analysis) is provided to streamline the extraction of equilibrium structures from free energy maps obtained with enhanced sampling simulation techniques and their associated trajectories. This approach efficiently identifies relevant structures by automatically selecting minima on the free energy surface using a connected-component labeling algorithm and extracts them utilizing a Shapely-polygon-based trajectory analysis process. The script is general and portable; it incorporates an automatic periodicity detection system; and multiprocessing is utilized to leverage all available computational resources for enhanced efficiency. The effectiveness of the proposed polygon-based approach is demonstrated through comparison with a naïve and largely inefficient loop-based script and its application across three distinct systems for benchmarking purposes.

A claudin5-binding peptide enhances the permeability of the blood-brain barrier in vitro

The blood-brain barrier (BBB) maintains brain homeostasis but also prevents most drugs from entering the brain. No paracellular diffusion of solutes is allowed because of tight junctions that are made impermeable by the expression of claudin5 (CLDN5) by brain endothelial cells. The possibility of regulating the BBB permeability in a transient and reversible fashion is in strong demand for the pharmacological treatment of brain diseases. Here, we designed and tested short BBB-active peptides, derived from the CLDN5 extracellular domains and the CLDN5-binding domain of Clostridium perfringens enterotoxin, using a robust workflow of structural modeling and in vitro validation techniques. Computational analysis at the atom level based on solubility and affinity to CLDN5 identified a CLDN5-derived peptide not reported previously called f1-C5C2, which was soluble in biological media, displayed efficient binding to CLDN5, and transiently increased BBB permeability. The peptidomimetic strategy described here may have potential applications in the pharmacological treatment of brain diseases.

Grand canonical Monte Carlo and deep learning assisted enhanced sampling to characterize the distribution of Mg2+ and influence of the Drude polarizable force field on the stability of folded states of the twister ribozyme

Molecular dynamics simulations are crucial for understanding the structural and dynamical behavior of biomolecular systems, including the impact of their environment. However, there is a gap between the time scale of these simulations and that of real-world experiments. To address this problem, various enhanced simulation methods have been developed. In addition, there has been a significant advancement of the force fields used for simulations associated with the explicit treatment of electronic polarizability. In this study, we apply oscillating chemical potential grand canonical Monte Carlo and machine learning methods to determine reaction coordinates combined with metadynamics simulations to explore the role of Mg2+ distribution and electronic polarizability in the context of the classical Drude oscillator polarizable force field on the stability of the twister ribozyme. The introduction of electronic polarizability along with the details of the distribution of Mg2+ significantly stabilizes the simulations with respect to sampling the crystallographic conformation. The introduction of electronic polarizability leads to increased stability over that obtained with the additive CHARMM36 FF reported in a previous study, allowing for a distribution of a wider range of ions to stabilize twister. Specific interactions contributing to stabilization are identified, including both those observed in the crystal structures and additional experimentally unobserved interactions. Interactions of Mg2+ with the bases are indicated to make important contributions to stabilization. Notably, the presence of specific interactions between the Mg2+ ions and bases or the non-bridging phosphate oxygens (NBPOs) leads to enhanced dipole moments of all three moieties. Mg2+-NBPO interactions led to enhanced dipoles of the phosphates but, interestingly, not in all the participating ions. The present results further indicate the importance of electronic polarizability in stabilizing RNA in molecular simulations and the complicated nature of the relationship of Mg2+-RNA interactions with the polarization response of the bases and phosphates.

Polymorph sampling with coupling to extended variables: enhanced sampling of polymorph energy landscapes and free energy perturbation of polymorph ensembles

A novel approach to computationally enhance the sampling of molecular crystal structures is proposed and tested. This method is based on the use of extended variables coupled to a Monte Carlo based crystal polymorph generator. Inspired by the established technique of quasi-random sampling of polymorphs using the rigid molecule constraint, this approach represents molecular clusters as extended variables within a thermal reservoir. Polymorph unit-cell variables are generated using pseudo-random sampling. Within this framework, a harmonic coupling between the extended variables and polymorph configurations is established. The extended variables remain fixed during the inner loop dedicated to polymorph sampling, enforcing a stepwise propagation of the extended variables to maintain system exploration. The final processing step results in a polymorph energy landscape, where the raw structures sampled to create the extended variable trajectory are re-optimized without the thermal coupling term. The foundational principles of this approach are described and its effectiveness using both a Metropolis Monte Carlo type algorithm and modifications that incorporate replica exchange is demonstrated. A comparison is provided with pseudo-random sampling of polymorphs for the molecule coumarin. The choice to test a design of this algorithm as relevant for enhanced sampling of crystal structures was due to the obvious relation between molecular structure variables and corresponding crystal polymorphs as representative of the inherent vapor to crystal transitions that exist in nature. Additionally, it is shown that the trajectories of extended variables can be harnessed to extract fluctuation properties that can lead to valuable insights. A novel thermodynamic variable is introduced: the free energy difference between ensembles of Z' = 1 and Z' = 2 crystal polymorphs.

Ion and water permeation through claudin-10b and claudin-15 paracellular channels

The structural scaffold of epithelial and endothelial tight junctions (TJs) comprises multimeric strands of claudin (Cldn) proteins that anchor adjacent cells and control the paracellular flux of water and solutes. Based on the permeability properties they confer to the TJs, Cldns are classified as channel- or barrier-forming. For instance, Cldn10b, expressed in kidneys, lungs, and other tissues, displays high permeability for cations and low permeability for water. Along with its high sequence similarity to the cation- and water-permeable TJ protein Cldn15, this makes Cldn10b a valuable test case for investigating the molecular determinants of paracellular transport. In lack of high-resolution experimental information on TJ architectures, here we use molecular dynamics simulations to determine whether atomistic models recapitulate the differences in ion and water transport between of Cldn10b and Cldn15. Our data, based on extensive standard simulations and free energy calculations, reveal that Cldn10b models form cation-permeable pores narrower than Cldn15, which, together with the stable coordination of Na+ ions to acidic pore-lining residues (E153, D36, D56), limit the passage of water molecules. By providing a mechanism driving a peculiar case of paracellular transport, these results provide a structural basis for the specific permeability properties of Cldn subtypes that define their physiological role.

Structure and Energetics of PET-Hydrolyzing Enzyme Complexes: A Systematic Comparison from Molecular Dynamics Simulations

Discovered in 2016, the enzyme PETase, secreted by bacterial Ideonella Sakaiensis 201-F6, has an excellent hydrolytic activity toward poly(ethylene terephthalate) (PET) at room temperature, while it decreases at higher temperatures due to the low thermostability. Many variants have been engineered to overcome this limitation, which hinders industrial application. In this work, we systematically compare PETase wild-type (WT) and four mutants (DuraPETase, ThermoPETase, FastPETase, and HotPETase) using standard molecular dynamics (MD) simulations and unbinding free energy calculations. In particular, we analyze the enzymes' structural characteristics and binding to a tetrameric PET chain (PET4) under two temperature conditions: T1─300 K and T2─350 K. Our results indicate that (i) PET4 forms stable complexes with the five enzymes at room temperature (∼300 K) and (ii) most of the interactions are localized close to the active site of the protein, where the W185 and Y87 residues interact with the aromatic rings of the substrate. Specifically, (iii) the W185 side-chain explores different conformations in each variant (a phenomenon known in the literature as "W185 wobbling"). This suggests that the binding pocket retains structural plasticity and flexibility among the variants, facilitating substrate recognition and localization events at moderate temperatures. Moreover, (iv) PET4 establishes aromatic interactions with the catalytic H237 residue, stabilizing the catalytic triad composed of residues S160-H237-D206, and helping the system achieve an effective configuration for the hydrolysis reaction. Conversely, (v) the binding affinity decreases at a higher temperature (∼350 K), retaining moderate interactions only for HotPETase. Finally, (vi) MD simulations of complexes formed with poly(ethylene-2,5-furan dicarboxylate) (PEF) show no persistent interactions, suggesting that these enzymes are not yet optimized for binding this alternative semiaromatic plastic polymer. Our study offers valuable insights into the structural stability of these enzymes and the molecular determinants driving PET binding onto their surfaces, sheds light on the mechanistic steps that precede the onset of hydrolysis, and provides a foundation for future enzyme optimization.

Overcoming Sampling Issues and Improving Computational Efficiency in Collective-Variable-Based Enhanced-Sampling Simulations: A Tutorial

This tutorial is designed to help users overcome sampling challenges and improve computational efficiency in collective-variable (CV)-based enhanced-sampling, or importance-sampling, simulations. Toward this end, we introduce well-tempered metadynamics-extended adaptive biasing force (WTM-eABF) and its integration with Gaussian accelerated molecular dynamics (GaMD). Additionally, use will be made of a method for identifying the least-free-energy pathway (LFEP) and multiple concurrent pathways on high-dimensional free-energy surfaces. We illustrate these sampling techniques with the conformational equilibria of trialanine and chignolin in aqueous solution as test cases. This tutorial assumes that the user has prior experience with molecular dynamics (MD) simulations, in general, with the popular program NAMD, and to some extent with Colvars, the module for CV-based calculations. This tutorial can, however, in large measure be used in conjunction with alternate MD engines that support the Colvars module such as GROMACS, LAMMPS, and Tinker-HP.

Buckets Instead of Umbrellas for Enhanced Sampling and Free Energy Calculations

Umbrella sampling has been a workhorse for free energy calculations in molecular simulations for several decades. In conventional umbrella sampling, restraining bias potentials are strategically applied along one or several collective variables. Major drawbacks associated with this method are the requirement of a large number of bias windows and the poor sampling of the transverse coordinates. In this work, we propose an alternate formalism that departs from the traditional umbrella sampling to mitigate these issues, where we replace umbrella-type restraining bias potentials with bucket-type wall potentials. This modification permits one to formulate an efficient computational strategy leveraging wall potentials and metadynamics sampling. This new method, called "bucket sampling", can significantly reduce the computational cost of obtaining converged high-dimensional free energy surfaces. Extensions of the proposed method with temperature acceleration and replica exchange solute tempering are also demonstrated.

Molecular Mechanism of Ciprofloxacin Translocation Through the Major Diffusion Channels of the ESKAPE Pathogens Klebsiella pneumoniae and Enterobacter cloacae

Experimental studies on the translocation and accumulation of antibiotics in Gram-negative bacteria have revealed details of the properties that allow efficient permeation through bacterial outer membrane porins. Among the major outer membrane diffusion channels, OmpF has been extensively studied to understand the antibiotic translocation process. In a few cases, this knowledge has also helped to improve the efficacy of existing antibacterial molecules. However, the extension of these strategies to enhance the efficacy of other existing and novel drugs require comprehensive molecular insight into the permeation process and an understanding of how antibiotic and channel properties influence the effective permeation rates. Previous studies have investigated how differences in antibiotic charge distribution can influence the observed permeation pathways through the OmpF channel, and have shown that the dynamics of the L3 loop can play a dominant role in the permeation process. Here, we perform all-atom simulations of the OmpF orthologs, OmpE35 from Enterobacter cloacae and OmpK35 from Klebsiella pneumoniae. Unbiased simulations of the porins and biased simulations of the ciprofloxacin permeation processes through these channels provide insight into the differences in the permeation pathway and energetics. In addition, we show that similar to the OmpF channel, antibiotic-induced dynamics of the L3 loop are also operative in the orthologs. However, the sequence and structural differences, influence the extent of the L3 loop fluctuations with OmpK35 showing greater stability in unbiased runs and subdued fluctuations in simulations with ciprofloxacin.

Coarse-Grained Molecular Dynamics with Normalizing Flows

We propose a sampling algorithm relying on a collective variable (CV) of midsize dimension modeled by a normalizing flow and using nonequilibrium dynamics to propose full configurational moves from the proposition of a refreshed value of the CV made by the flow. The algorithm takes the form of a Markov chain with nonlocal updates, allowing jumps through energy barriers across metastable states. The flow is trained throughout the algorithm to reproduce the free energy landscape of the CV. The output of the algorithm is a sample of thermalized configurations and the trained network that can be used to efficiently produce more configurations. We show the functioning of the algorithm first in a test case with a mixture of Gaussians. Then, we successfully tested it on a higher-dimensional system consisting of a polymer in solution with a compact state and an extended stable state separated by a high free energy barrier.

Data-Driven Learning of the Generalized Langevin Equation with State-Dependent Memory

We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation with a homogeneous kernel. The constructed model naturally encodes the heterogeneous energy dissipation by jointly learning a set of state features and the non-Markovian coupling among the features. Numerical results demonstrate the limitation of the standard generalized Langevin equation and the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition.

Parameter Optimization Method in Multidimensional Umbrella Sampling

Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.

A Comprehensive Study of Factors Affecting the Prediction of the pKa Shift of Asp26 in Thioredoxin Protein

The stable protonation state of ionizable amino acids in a protein can be predicted by computing the pKa shift of that residue within the protein environment. Thermodynamic Integration (TI) is an ideal molecular dynamics-based approach for predicting the pKa shift of ionizable protein residues. Here, we probe TI-based simulation protocols for their ability to accurately predict the pKa shift of Asp26 in thioredoxin. While implicit solvent models can predict the pKa shift accurately, explicit solvent models result in substantial errors. To understand the underlying reason for this surprising discrepancy, we investigate the role of various factors such as solvent models, conformational sampling, background charges, and polarization.

Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.

Information thermodynamics of transition paths between multiple mesostates

A central concern across the natural sciences is a quantitative understanding of the mechanism governing rare transitions between two metastable states. Recent research has uncovered a fundamental equality between the time-reversal asymmetry of the ensemble of such transition paths and the informativeness of system dynamics about the reactivity of a given trajectory, immediately leading to quantitative criteria for judging the importance of distinct system coordinates for the transition. Here we generalize this framework to multiple mesostates. We find that the main system-wide and coordinate-specific results generalize intuitively, while the combinatorial diversity of pairwise transitions raises new questions and points to new concepts. This work increases the previous framework's generality and applicability and forges connections to enhanced-sampling and coarse-grained dynamical approaches such as milestoning and Markov-state models.

GradNav: Accelerated Exploration of Potential Energy Surfaces with Gradient-Based Navigation

Exploring the potential energy surface (PES) of molecular systems is important for comprehending their complex behaviors, particularly through the identification of various metastable states. However, the transition between these states is often hindered by substantial energy barriers, demanding prolonged molecular simulations that consume considerable computational resources. Our study introduces the gradient-based navigation (GradNav) algorithm, which accelerates the exploration of the energy surface and enables proper reconstruction of the PES. This algorithm employs a strategy of initiating short simulation runs from updated starting points derived from prior observations to effectively navigate across potential barriers and explore new regions. To evaluate GradNav's performance, we introduce two metrics: the deepest well escape frame (DWEF) and the search success initialization ratio (SSIR). Through applications on Langevin dynamics within Müller-type PESs and molecular dynamics simulations of the Fs-peptide protein, these metrics demonstrate GradNav's enhanced ability to escape deep energy wells and its reduced reliance on initial conditions, as denoted by the reduced DWEF values and increased SSIR values, respectively. Consequently, this improved exploration capability enables more precise energy estimations from simulation trajectories.

Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

Long-range proton and hydroxide ion transfer dynamics at the water/CeO2 interface in the nanosecond regime: reactive molecular dynamics simulations and kinetic analysis

The structural properties, dynamical behaviors, and ion transport phenomena at the interface between water and cerium oxide are investigated by reactive molecular dynamics (MD) simulations employing neural network potentials (NNPs). The NNPs are trained to reproduce density functional theory (DFT) results, and DFT-based MD (DFT-MD) simulations with enhanced sampling techniques and refinement schemes are employed to efficiently and systematically acquire training data that include diverse hydrogen-bonding configurations caused by proton hopping events. The water interfaces with two low-index surfaces of (111) and (110) are explored with these NNPs, and the structure and long-range proton and hydroxide ion transfer dynamics are examined with unprecedented system sizes and long simulation times. Various types of proton hopping events at the interface are categorized and analyzed in detail. Furthermore, in order to decipher the proton and hydroxide ion transport phenomena along the surface, a counting analysis based on the semi-Markov process is formulated and applied to the MD trajectories to obtain reaction rates by considering the transport as stochastic jump processes. Through this model, the coupling between hopping events, vibrational motions, and hydrogen bond networks at the interface are quantitatively examined, and the high activity and ion transport phenomena at the water/CeO2 interface are unequivocally revealed in the nanosecond regime.

Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model

Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning

Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.

Automatic Potential Energy Surface Exploration by Accelerated Reactive Molecular Dynamics Simulations: From Pyrolysis to Oxidation Chemistry

Automatic potential energy surface (PES) exploration is important to a better understanding of reaction mechanisms. Existing automatic PES mapping tools usually rely on predefined knowledge or computationally expensive on-the-fly quantum-chemical calculations. In this work, we have developed the PESmapping algorithm for discovering novel reaction pathways and automatically mapping out the PES using merely one starting species is present. The algorithm explores the unknown PES by iteratively spawning new reactive molecular dynamics (RMD) simulations for species that it has detected within previous RMD simulations. We have therefore extended the RMD simulation tool ChemTraYzer2.1 (Chemical Trajectory Analyzer, CTY) for this PESmapping algorithm. It can generate new seed species, automatically start replica simulations for new pathways, and stop the simulation when a reaction is found, reducing the computational cost of the algorithm. To explore PESs with low-temperature reactions, we applied the acceleration method collective variable (CV)-driven hyperdynamics. This involved the development of tailored CV templates, which are discussed in this study. We validate our approach for known pathways in various pyrolysis and oxidation systems: hydrocarbon isomerization and dissociation (C4H7 and C8H7 PES), mostly dominant at high temperatures and low-temperature oxidation of n-butane (C4H9O2 PES) and cyclohexane (C6H11O2 PES). As a result, in addition to new pathways showing up in the simulations, common isomerization and dissociation pathways were found very fast: for example, 44 reactions of butenyl radicals including major isomerizations and decompositions within about 30 min wall time and low-temperature chemistry such as the internal H-shift of RO2 → QO2H within 1 day wall time. Last, we applied PESmapping to the oxidation of the recently proposed biohybrid fuel 1,3-dioxane and validated that the tool could be used to discover new reaction pathways of larger molecules that are of practical use.

Antibiotic Charge Profile Determines the Extent of L3 Dynamics in OmpF: An Expedited Passage for Molecules with a Positive Charge

Efficient permeation into Gram-negative bacterial cells is a much-desired property in the design of antibacterial agents. The goal is to arrive at one or more chemical modifications of molecules that improve their uptake into the cell while maintaining a good binding affinity to the intracellular target. Previously, we proposed a mechanistic rationale for the fast permeation of bulky antibiotics that involves induced conformational dynamics in the constriction loop L3 of the OmpF channel. This flexibility is caused by the perturbation of a hydrogen bond network stabilizing the L3 loop due to the strong interactions of the positively charged moiety on the antibiotic with the residues of the L3 loop. In the present work, we examine how differences in the charge profile of antibiotic molecules can affect the permeation process, in particular, the L3 dynamics. To this end, we have performed all-atom molecular dynamics simulations to study the permeation process of molecules with differences in the net charge through the Escherichia coli OmpF channel. The results from these simulations suggest that a positively charged moiety on the antibiotic is responsible for strong interactions with the negatively charged residues of the L3 loop, promoting conformational dynamics in the L3 loop. In contrast, antibiotics without a positively charged moiety are unable to initiate such a dynamic response in the L3 loop. This distinct behavior of the L3 loop in the presence of molecules with different charge characteristics provides a plausible mechanism whereby large molecules with an appropriate charge distribution can leverage an L3 dynamic-dependent pathway to permeate efficiently. The results are relevant to the structure-based design of molecules with improved uptake properties achieved through systematic chemical modifications that effectively engage the L3 loop.

Hydrophobically gated memristive nanopores for neuromorphic applications

Signal transmission in the brain relies on voltage-gated ion channels, which exhibit the electrical behaviour of memristors, resistors with memory. State-of-the-art technologies currently employ semiconductor-based neuromorphic approaches, which have already demonstrated their efficacy in machine learning systems. However, these approaches still cannot match performance achieved by biological neurons in terms of energy efficiency and size. In this study, we utilise molecular dynamics simulations, continuum models, and electrophysiological experiments to propose and realise a bioinspired hydrophobically gated memristive nanopore. Our findings indicate that hydrophobic gating enables memory through an electrowetting mechanism, and we establish simple design rules accordingly. Through the engineering of a biological nanopore, we successfully replicate the characteristic hysteresis cycles of a memristor and construct a synaptic device capable of learning and forgetting. This advancement offers a promising pathway for the realization of nanoscale, cost- and energy-effective, and adaptable bioinspired memristors.

Investigation of Rare Protein Conformational Transitions via Dissipation-Corrected Targeted Molecular Dynamics

To sample rare events, dissipation-corrected targeted molecular dynamics (dcTMD) applies a constant velocity constraint along a one-dimensional reaction coordinate s, which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski's identity, the free energy ΔG(s) is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ(s) from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation. While so far dcTMD has been mostly applied to study the unbinding of protein-ligand complexes, here its applicability to rare conformational transitions within a protein and the prediction of their kinetics are investigated. As this typically requires the introduction of multiple collective variables {xj} = x, a theoretical framework is outlined to calculate the associated free energy ΔG(x) and friction Γ(x) from dcTMD simulations along coordinate s. Adopting the α-β transition of alanine dipeptide as well as the open-closed transition of T4 lysozyme as representative examples, the virtues and shortcomings of dcTMD to predict protein conformational transitions and the related kinetics are studied.

Charting Nanocluster Structures via Convolutional Neural Networks

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory

We introduce a machine-learning-based coarse-grained molecular dynamics model that faithfully retains the many-body nature of the intermolecular dissipative interactions. Unlike the common empirical coarse-grained models, the present model is constructed based on the Mori-Zwanzig formalism and naturally inherits the heterogeneous state-dependent memory term rather than matching the mean-field metrics such as the velocity autocorrelation function. Numerical results show that preserving the many-body nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations.

Temperature Accelerated Sliced Sampling to Probe Ligand Dissociation from Protein

Modeling ligand unbinding in proteins to estimate the free energy of binding and probing the mechanism presents several challenges. They primarily pertain to the entropic bottlenecks resulting from protein and solvent conformations. While exploring the unbinding processes using enhanced sampling techniques, very long simulations are required to sample all of the conformational states as the system gets trapped in local free energy minima along transverse coordinates. Here, we demonstrate that temperature accelerated sliced sampling (TASS) is an ideal approach to overcome some of the difficulties faced by conventional sampling methods in studying ligand unbinding. Using TASS, we study the unbinding of avibactam inhibitor molecules from the Class C β-lactamase (CBL) active site. Extracting CBL-avibactam unbinding free energetics, unbinding pathways, and identifying critical interactions from the TASS simulations are demonstrated.

Fast prediction of antibiotic permeability through membrane channels using Brownian dynamics

The efficient permeation across the Gram-negative bacterial membrane is an important step in the overall process of antibacterial action of a molecule and the one that has posed a significant hurdle on the way toward approved antibiotics. Predicting the permeability for a large library of molecules and assessing the effect of different molecular transformations on permeation rates of a given molecule is critical to the development of effective antibiotics. We present a computational approach for obtaining estimates of molecular permeability through a porin channel in a matter of hours using a Brownian dynamics approach. The fast sampling using a temperature acceleration scheme enables the approximate estimation of permeability using the inhomogeneous solubility diffusion model. Although the method is a significant approximation to similar all-atom approaches tested previously, we show that the present approach predicts permeabilities that correlate fairly well with the respective experimental permeation rates from liposome swelling experiments and accumulation rates from antibiotic accumulation assays, and is significantly, i.e., about 14 times, faster compared with a previously reported approach. The possible applications of the scheme in high-throughput screening for fast permeators are discussed.

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the "feature importance" approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.

Milk Protein Adsorption on Metallic Iron Surfaces

Food processing and consumption involves multiple contacts between biological fluids and solid materials of processing devices, of which steel is one of the most common. Due to the complexity of these interactions, it is difficult to identify the main control factors in the formation of undesirable deposits on the device surfaces that may affect safety and efficiency of the processes. Mechanistic understanding of biomolecule-metal interactions involving food proteins could improve management of these pertinent industrial processes and consumer safety in the food industry and beyond. In this work, we perform a multiscale study of the formation of protein corona on iron surfaces and nanoparticles in contact with cow milk proteins. By calculating the binding energies of proteins with the substrate, we quantify the adsorption strength and rank proteins by the adsorption affinity. We use a multiscale method involving all-atom and coarse-grained simulations based on generated ab initio three-dimensional structures of milk proteins for this purpose. Finally, using the adsorption energy results, we predict the composition of protein corona on iron curved and flat surfaces via a competitive adsorption model.

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

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

Molecular Dynamics Simulations of Ion Permeation in Human Voltage-Gated Sodium Channels

The recent determination of cryo-EM structures of voltage-gated sodium (Na_v) channels has revealed many details of these proteins. However, knowledge of ionic permeation through the Na_v pore remains limited. In this work, we performed atomistic molecular dynamics (MD) simulations to study the structural features of various neuronal Na_v channels based on homology modeling of the cryo-EM structure of the human Na_v1.4 channel and, in addition, on the recently resolved configuration for Na_v1.2. In particular, single Na⁺ permeation events during standard MD runs suggest that the ion resides in the inner part of the Na_v selectivity filter (SF). On-the-fly free energy parametrization (OTFP) temperature-accelerated molecular dynamics (TAMD) was also used to calculate two-dimensional free energy surfaces (FESs) related to single/double Na⁺ translocation through the SF of the homology-based Na_v1.2 model and the cryo-EM Na_v1.2 structure, with different realizations of the DEKA filter domain. These additional simulations revealed distinct mechanisms for single and double Na⁺ permeation through the wild-type SF, which has a charged lysine in the DEKA ring. Moreover, the configurations of the ions in the SF corresponding to the metastable states of the FESs are specific for each SF motif. Overall, the description of these mechanisms gives us new insights into ion conduction in human Na_v cryo-EM-based and cryo-EM configurations that could advance understanding of these systems and how they differ from potassium and bacterial Na_v channels.

Conformational Dynamics of Loop L3 in OmpF: Implications toward Antibiotic Translocation and Voltage Gating

In the present work, we delineate the molecular mechanism of a bulky antibiotic permeating through a bacterial channel and uncover the role of conformational dynamics of the constriction loop in this process. Using the temperature accelerated sliced sampling approach, we shed light onto the dynamics of the L3 loop, in particular the F118 to S125 segment, at the constriction regions of the OmpF porin. We complement the findings with single channel electrophysiology experiments and applied-field simulations, and we demonstrate the role of hydrogen-bond stabilization in the conformational dynamics of the L3 loop. A molecular mechanism of permeation is put forward wherein charged antibiotics perturb the network of stabilizing hydrogen-bond interactions and induce conformational changes in the L3 segment, thereby aiding the accommodation and permeation of bulky antibiotic molecules across the constriction region. We complement the findings with single channel electrophysiology experiments and demonstrate the importance of the hydrogen-bond stabilization in the conformational dynamics of the L3 loop. The generality of the present observations and experimental results regarding the L3 dynamics enables us to identify this L3 segment as the source of gating. We propose a mechanism of OmpF gating that is in agreement with previous experimental data that showed the noninfluence of cysteine double mutants that tethered the L3 tip to the barrel wall on the OmpF gating behavior. The presence of similar loop stabilization networks in porins of other clinically relevant pathogens suggests that the conformational dynamics of the constriction loop is possibly of general importance in the context of antibiotic permeation through porins.

Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.

Collective Variables for Crystallization Simulations-from Early Developments to Recent Advances

Crystallization is an important physicochemical process which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental symmetry-breaking transition. While experiments provide equilibrium structures and shapes of crystals, they are limited to unraveling how molecules aggregate to form crystal nuclei that subsequently transform into bulk crystals. Computer simulations, mainly molecular dynamics (MD), can provide such microscopic details during the early stage of a crystallization event. Crystallization is a rare event that takes place in time scales much longer than a typical equilibrium MD simulation can sample. This inadequate sampling of the MD method can be easily circumvented by the use of enhanced sampling (ES) simulations. In most of the ES methods, the fluctuations of a system's slow degrees of freedom, called collective variables (CVs), are enhanced by applying a bias potential. This transforms the system from one state to the other within a short time scale. The most crucial part of such CV-based ES methods is to find suitable CVs, which often needs intuition and several trial-and-error optimization steps. Over the years, a plethora of CVs has been developed and applied in the study of crystallization. In this review, we provide a brief overview of CVs that have been developed and used in ES simulations to study crystallization from melt or solution. These CVs can be categorized mainly into four types: (i) spherical particle-based, (ii) molecular template-based, (iii) physical property-based, and (iv) CVs obtained from dimensionality reduction techniques. We present the context-based evolution of CVs, discuss the current challenges, and propose future directions to further develop effective CVs for the study of crystallization of complex systems.

DeepCV: A Deep Learning Framework for Blind Search of Collective Variables in Expanded Configurational Space

We present Deep learning for Collective Variables (DeepCV), a computer code that provides an efficient and customizable implementation of the deep autoencoder neural network (DAENN) algorithm that has been developed in our group for computing collective variables (CVs) and can be used with enhanced sampling methods to reconstruct free energy surfaces of chemical reactions. DeepCV can be used to conveniently calculate molecular features, train models, generate CVs, validate rare events from sampling, and analyze a trajectory for chemical reactions of interest. We use DeepCV in an example study of the conformational transition of cyclohexene, where metadynamics simulations are performed using DAENN-generated CVs. The results show that the adopted CVs give free energies in line with those obtained by previously developed CVs and experimental results. DeepCV is open-source software written in Python/C++ object-oriented languages, based on the TensorFlow framework and distributed free of charge for noncommercial purposes, which can be incorporated into general molecular dynamics software. DeepCV also comes with several additional tools, i.e., an application program interface (API), documentation, and tutorials.

Enhancing sampling with free-energy calculations

In recent years, considerable progress has been made to enhance sampling and help address biological questions, including, but not limited to conformational transitions in biomolecules and protein-ligand reversible binding, hitherto intractable by brute-force computer simulations. Many of these advances result from the development of a palette of methods aimed at exploring rare events through reliable free-energy calculations. The advent of new, often conceptually related methods has also rendered difficult the choice of the best suited option for a given problem. Here, we focus on geometrical transformations and algorithms designed to enhance sampling along adequately chosen progress variables, tracing their theoretical foundations, and showing how they are connected and can be blended together for improved performance.

Sampling rare conformational transitions with a quantum computer

Structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, Molecular Dynamics (MD) simulations enable us to investigate these thermally activated processes with an atomic level of resolution. In practice, an exponentially large fraction of computational resources must be invested to simulate thermal fluctuations in metastable states. Path sampling methods focus the computational power on sampling the rare transitions between states. One of their outstanding limitations is to efficiently generate paths that visit significantly different regions of the conformational space. To overcome this issue, we introduce a new algorithm for MD simulations that integrates machine learning and quantum computing. First, using functional integral methods, we derive a rigorous low-resolution spatially coarse-grained representation of the system's dynamics, based on a small set of molecular configurations explored with machine learning. Then, we use a quantum annealer to sample the transition paths of this low-resolution theory. We provide a proof-of-concept application by simulating a benchmark conformational transition with all-atom resolution on the D-Wave quantum computer. By exploiting the unique features of quantum annealing, we generate uncorrelated trajectories at every iteration, thus addressing one of the challenges of path sampling. Once larger quantum machines will be available, the interplay between quantum and classical resources may emerge as a new paradigm of high-performance scientific computing. In this work, we provide a platform to implement this integrated scheme in the field of molecular simulations.

The Conformational Transition Pathways and Hidden Intermediates in DFG-Flip Process of c-Met Kinase Revealed by Metadynamics Simulations

Protein kinases intrinsically translate their conformations between active and inactive states, which is key to their enzymatic activities. The conformational flipping of the three-residue conservative motif, Asp-Phe-Gly (DFG), is crucial for many kinases' biological functions. Obtaining a detailed demonstration of the DFG flipping process and its corresponding dynamical and thermodynamical features could broaden our understanding of kinases' conformation-activity relationship. In this study, we employed metadynamics simulation, a widely used enhanced sampling technique, to analyze the conformational transition pathways of the DFG flipping for the c-Met kinase. The corresponding free energy landscape suggested two distinct transition pathways between the "DFG-in" and "DFG-out" states of the DFG-flip from c-Met. On the basis of the orientation direction of the F1223 residue, we correspondingly named the two pathways the "DFG-up" path, featuring forming a commonly discovered "DFG-up" transition state, and the "DFG-down" path, a unique transition pathway with F1223 rotating along the opposite direction away from the hydrophobic cavity. The free energies along the two pathways were then calculated using the Path Collective Variable (PCV) metadynamics simulation. The simulation results showed that, though having similar free energy barriers, the free energy cuve for the DFG-down path suggested a two-step conformational transition mechanism, while that for the DFG-up path showed the one-step transition feature. The c-Met DFG flipping mechanism and the new intermediate state discovered in this work could provide a deeper understanding of the conformation-activity relationship for c-Met and, possibly, reveal a new conformational state as the drug target for c-Met and other similar kinases.

Turning Molecular Springs into Nano-Shock Absorbers: The Effect of Macroscopic Morphology and Crystal Size on the Dynamic Hysteresis of Water Intrusion-Extrusion into-from Hydrophobic Nanopores

Controlling the pressure at which liquids intrude (wet) and extrude (dry) a nanopore is of paramount importance for a broad range of applications, such as energy conversion, catalysis, chromatography, separation, ionic channels, and many more. To tune these characteristics, one typically acts on the chemical nature of the system or pore size. In this work, we propose an alternative route for controlling both intrusion and extrusion pressures via proper arrangement of the grains of the nanoporous material. To prove the concept, dynamic intrusion-extrusion cycles for powdered and monolithic ZIF-8 metal-organic framework were conducted by means of water porosimetry and in operando neutron scattering. We report a drastic increase in intrusion-extrusion dynamic hysteresis when going from a fine powder to a dense monolith configuration, transforming an intermediate performance of the ZIF-8 + water system (poor molecular spring) into a desirable shock-absorber with more than 1 order of magnitude enhancement of dissipated energy per cycle. The obtained results are supported by MD simulations and pave the way for an alternative methodology of tuning intrusion-extrusion pressure using a macroscopic arrangement of nanoporous material.

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.