Kinetic View of Enzyme Catalysis from Enhanced Sampling QM/MM Simulations.

The rate constants of enzyme-catalyzed reactions (kcat) are often approximated from the barrier height of the reactive step. We introduce an enhanced sampling QM/MM approach that directly calculates the kinetics of enzymatic reactions, without introducing the transition-state theory assumptions, and takes into account the dynamical equilibrium between the reactive and non-reactive conformations of the enzyme/substrate complex. Our computed kcat values are in order-of-magnitude agreement with the experimental data for two representative enzymatic reactions.

Data-driven classification of ligand unbinding pathways.

Studying the pathways of ligand-receptor binding is essential to understand the mechanism of target recognition by small molecules. The binding free energy and kinetics of protein-ligand complexes can be computed using molecular dynamics (MD) simulations, often in quantitative agreement with experiments. However, only a qualitative picture of the ligand binding/unbinding paths can be obtained through a conventional analysis of the MD trajectories. Besides, the higher degree of manual effort involved in analyzing pathways limits its applicability in large-scale drug discovery. Here, we address this limitation by introducing an automated approach for analyzing molecular transition paths with a particular focus on protein-ligand dissociation. Our method is based on the dynamic time-warping algorithm, originally designed for speech recognition. We accurately classified molecular trajectories using a very generic descriptor set of contacts or distances. Our approach outperforms manual classification by distinguishing between parallel dissociation channels, within the pathways identified by visual inspection. Most notably, we could compute exit-path-specific ligand-dissociation kinetics. The unbinding timescale along the fastest path agrees with the experimental residence time, providing a physical interpretation to our entirely data-driven protocol. In combination with appropriate enhanced sampling algorithms, this technique can be used for the initial exploration of ligand-dissociation pathways as well as for calculating path-specific thermodynamic and kinetic properties.

Kinetics from Metadynamics: Principles, Applications, and Outlook.

Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein-ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.

Deep learning collective variables from transition path ensemble.

The study of the rare transitions that take place between long lived metastable states is a major challenge in molecular dynamics simulations. Many of the methods suggested to address this problem rely on the identification of the slow modes of the system, which are referred to as collective variables. Recently, machine learning methods have been used to learn the collective variables as functions of a large number of physical descriptors. Among many such methods, Deep Targeted Discriminant Analysis has proven to be useful. This collective variable is built from data harvested from short unbiased simulations in the metastable basins. Here, we enrich the set of data on which the Deep Targeted Discriminant Analysis collective variable is built by adding data from the transition path ensemble. These are collected from a number of reactive trajectories obtained using the On-the-fly Probability Enhanced Sampling flooding method. The collective variables thus trained lead to more accurate sampling and faster convergence. The performance of these new collective variables is tested on a number of representative examples.

A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.

Predicting residue cooperativity during protein folding: A combined, molecular dynamics and unsupervised learning approach.

Allostery in proteins involves, broadly speaking, ligand-induced conformational transitions that modulate function at active sites distal to where the ligand binds. In contrast, the concept of cooperativity (in the sense used in phase transition theory) is often invoked to understand protein folding and, therefore, function. The modern view on allostery is one based on dynamics and hinges on the time-dependent interactions between key residues in a complex network, interactions that determine the free-energy profile for the reaction at the distal site. Here, we merge allostery and cooperativity, and we discuss a joint model with features of both. In our model, the active-site reaction is replaced by the reaction pathway that leads to protein folding, and the presence or absence of the effector is replaced by mutant-vs-wild type changes in key residues. To this end, we employ our recently introduced time-lagged independent component analysis (tICA) correlation approach [Ray et al. Proc. Natl. Acad. Sci. 118(43) (2021), e2100943118] to identify the allosteric role of distant residues in the folded-state dynamics of a large protein. In this work, we apply the technique to identify key residues that have a significant role in the folding of a small, fast folding-protein, chignolin. Using extensive enhanced sampling simulations, we critically evaluate the accuracy of the predictions by mutating each residue one at a time and studying how the mutations change the underlying free energy landscape of the folding process. We observe that mutations in those residues whose associated backbone torsion angles have a high correlation score can indeed lead to loss of stability of the folded configuration. We also provide a rationale based on interaction energies between individual residues with the rest of the protein to explain this effect. From these observations, we conclude that the tICA correlation score metric is a useful tool for predicting the role of individual residues in the correlated dynamics of proteins and can find application to the problem of identifying regions of protein that are either most vulnerable to mutations or-mutatis mutandis-to binding events that affect their functionality.

Rare Event Kinetics from Adaptive Bias Enhanced Sampling.

We introduce a novel enhanced sampling approach named on-the-fly probability enhanced sampling (OPES) flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the OPES approach [Invernizzi and Parrinello, J. Phys. Chem. Lett. 2020, 11, 7, 2731-2736], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double-well potential, conformational transition in the alanine dipeptide in the gas phase, and the folding and unfolding of the chignolin polypeptide in an aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.

Force-Field-Dependent DNA Breathing Dynamics: A Case Study of Hoogsteen Base Pairing in A6-DNA.

The Hoogsteen (HG) base pairing conformation, commonly observed in damaged and mutated DNA helices, facilitates DNA repair and DNA recognition. The free energy difference between HG and Watson-Crick (WC) base pairs has been computed in previous studies. However, the mechanism of the conformational transition is not well understood. A detailed understanding of the process of WC to HG base pair transition can provide a deeper understanding of DNA repair and recognition. In an earlier study, we explored the free energy landscape for this process using extensive computer simulation with the CHARMM36 force field. In this work, we study the impact of force field models in describing the WC to HG base pairing transition using meta-eABF enhanced sampling, quasi-harmonic entropy calculation, and nonbonded energy analysis. The secondary structures of both base pairing forms and the topology of the free energy landscapes were consistent over different force field models, although the relative free energy, entropy, and the interaction energies tend to vary. The relative stability of the WC and HG conformations is dictated by a delicate balance between the enthalpic stabilization and the reduced entropy of the structurally rigid HG structure. These findings highlight the impact that subtleties in force field models can have on accurately modeling DNA base pair dynamics and should stimulate further computational investigations into other dynamically important motions in DNA.

Point mutations in SARS-CoV-2 variants induce long-range dynamical perturbations in neutralizing antibodies.

Monoclonal antibodies are emerging as a viable treatment for the coronavirus disease 19 (COVID-19). However, newly evolved variants of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) can reduce the efficacy of currently available antibodies and can diminish vaccine-induced immunity. Here, we demonstrate that the microscopic dynamics of neutralizing monoclonal antibodies can be profoundly modified by the mutations present in the spike proteins of the SARS-COV-2 variants currently circulating in the world population. The dynamical perturbations within the antibody structure, which alter the thermodynamics of antigen recognition, are diverse and can depend both on the nature of the antibody and on the spatial location of the spike mutation. The correlation between the motion of the antibody and that of the spike receptor binding domain (RBD) can also be changed, modulating binding affinity. Using protein-graph-connectivity networks, we delineated the mutant-induced modifications in the information-flow along allosteric pathway throughout the antibody. Changes in the collective dynamics were spatially distributed both locally and across long-range distances within the antibody. On the receptor side, we identified an anchor-like structural element that prevents the detachment of the antibodies; individual mutations there can significantly affect the antibody binding propensity. Our study provides insight into how virus neutralization by monoclonal antibodies can be impacted by local mutations in the epitope via a change in dynamics. This realization adds a new layer of sophistication to the efforts for rational design of monoclonal antibodies against new variants of SARS-CoV2, taking the allostery in the antibody into consideration.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories.

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Distant residues modulate conformational opening in SARS-CoV-2 spike protein.

Infection by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) involves the attachment of the receptor-binding domain (RBD) of its spike proteins to the ACE2 receptors on the peripheral membrane of host cells. Binding is initiated by a down-to-up conformational change in the spike protein, the change that presents the RBD to the receptor. To date, computational and experimental studies that search for therapeutics have concentrated, for good reason, on the RBD. However, the RBD region is highly prone to mutations, and is therefore a hotspot for drug resistance. In contrast, we here focus on the correlations between the RBD and residues distant to it in the spike protein. This allows for a deeper understanding of the underlying molecular recognition events and prediction of the highest-effect key mutations in distant, allosteric sites, with implications for therapeutics. Also, these sites can appear in emerging mutants with possibly higher transmissibility and virulence, and preidentifying them can give clues for designing pan-coronavirus vaccines against future outbreaks. Our model, based on time-lagged independent component analysis (tICA) and protein graph connectivity network, is able to identify multiple residues that exhibit long-distance coupling with the RBD opening. Residues involved in the most ubiquitous D614G mutation and the A570D mutation of the highly contagious UK SARS-CoV-2 variant are predicted ab initio from our model. Conversely, broad-spectrum therapeutics like drugs and monoclonal antibodies can target these key distant-but-conserved regions of the spike protein.

Kinetics and free energy of ligand dissociation using weighted ensemble milestoning.

We consider the recently developed weighted ensemble milestoning (WEM) scheme [D. Ray and I. Andricioaei, J. Chem. Phys. 152, 234114 (2020)] and test its capability of simulating ligand-receptor dissociation dynamics. We performed WEM simulations on the following host-guest systems: Na+/Cl- ion pair and 4-hydroxy-2-butanone ligand with FK506 binding protein. As a proof of principle, we show that the WEM formalism reproduces the Na+/Cl- ion pair dissociation timescale and the free energy profile obtained from long conventional MD simulation. To increase the accuracy of WEM calculations applied to kinetics and thermodynamics in protein-ligand binding, we introduced a modified WEM scheme called weighted ensemble milestoning with restraint release (WEM-RR), which can increase the number of starting points per milestone without adding additional computational cost. WEM-RR calculations obtained a ligand residence time and binding free energy in agreement with experimental and previous computational results. Moreover, using the milestoning framework, the binding time and rate constants, dissociation constants, and committor probabilities could also be calculated at a low computational cost. We also present an analytical approach for estimating the association rate constant (kon) when binding is primarily diffusion driven. We show that the WEM method can efficiently calculate multiple experimental observables describing ligand-receptor binding/unbinding and is a promising candidate for computer-aided inhibitor design.

Free Energy Landscape and Conformational Kinetics of Hoogsteen Base Pairing in DNA vs. RNA.

Genetic information is encoded in the DNA double helix, which, in its physiological milieu, is characterized by the iconical Watson-Crick nucleo-base pairing. Recent NMR relaxation experiments revealed the transient presence of an alternative, Hoogsteen (HG) base pairing pattern in naked DNA duplexes, and estimated its relative stability and lifetime. In contrast with DNA, such structures were not observed in RNA duplexes. Understanding HG base pairing is important because the underlying "breathing" motion between the two conformations can significantly modulate protein binding. However, a detailed mechanistic insight into the transition pathways and kinetics is still missing. We performed enhanced sampling simulation (with combined metadynamics and adaptive force-bias method) and Markov state modeling to obtain accurate free energy, kinetics, and the intermediates in the transition pathway between Watson-Crick and HG base pairs for both naked B-DNA and A-RNA duplexes. The Markov state model constructed from our unbiased MD simulation data revealed previously unknown complex extrahelical intermediates in the seemingly simple process of base flipping in B-DNA. Extending our calculation to A-RNA, for which HG base pairing is not observed experimentally, resulted in relatively unstable, single-hydrogen-bonded, distorted Hoogsteen-like bases. Unlike B-DNA, the transition pathway primarily involved base paired and intrahelical intermediates with transition timescales much longer than that of B-DNA. The seemingly obvious flip-over reaction coordinate (i.e., the glycosidic torsion angle) is unable to resolve the intermediates. Instead, a multidimensional picture involving backbone dihedral angles and distance between hydrogen bond donor and acceptor atoms is required to gain insight into the molecular mechanism.

Interfacial water and ion distribution determine ζ potential and binding affinity of nanoparticles to biomolecules.

The molecular features that dictate interactions between functionalized nanoparticles and biomolecules are not well understood. This is in part because for highly charged nanoparticles in solution, establishing a clear connection between the molecular features of surface ligands and common experimental observables such as ζ potential requires going beyond the classical models based on continuum and mean field models. Motivated by these considerations, molecular dynamics simulations are used to probe the electrostatic properties of functionalized gold nanoparticles and their interaction with a charged peptide in salt solutions. Counterions are observed to screen the bare ligand charge to a significant degree even at the moderate salt concentration of 50 mM. As a result, the apparent charge density and ζ potential are largely insensitive to the bare ligand charge densities, which fall in the range of ligand densities typically measured experimentally for gold nanoparticles. While this screening effect was predicted by classical models such as the Manning condensation theory, the magnitudes of the apparent surface charge from microscopic simulations and mean-field models are significantly different. Moreover, our simulations found that the chemical features of the surface ligand (e.g., primary vs. quaternary amines, heterogeneous ligand lengths) modulate the interfacial ion and water distributions and therefore the interfacial potential. The importance of interfacial water is further highlighted by the observation that introducing a fraction of hydrophobic ligands enhances the strength of electrostatic binding of the charged peptide. Finally, the simulations highlight that the electric double layer is perturbed upon binding interactions. As a result, it is the bare charge density rather than the apparent charge density or ζ potential that better correlates with binding affinity of the nanoparticle to a charged peptide. Overall, our study highlights the importance of molecular features of the nanoparticle/water interface and underscores a set of design rules for the modulation of electrostatic driven interactions at nano/bio interfaces.

Weighted ensemble milestoning (WEM): A combined approach for rare event simulations.

To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. However, developing methods for obtaining the kinetics of long timescale processes from simulation at atomic detail is comparatively less developed an area. Milestoning and the weighted ensemble (WE) method are two different stratification strategies; both have shown promise for computing long timescales of complex biomolecular processes. Nevertheless, both require a significant investment of computational resources. We have combined WE and milestoning to calculate observables in orders-of-magnitude less central processing unit and wall-clock time. Our weighted ensemble milestoning method (WEM) uses WE simulation to converge the transition probability and first passage times between milestones, followed by the utilization of the theoretical framework of milestoning to extract thermodynamic and kinetic properties of the entire process. We tested our method for a simple one-dimensional double-well potential, for an eleven-dimensional potential energy surface with energy barrier, and on the biomolecular model system alanine dipeptide. We were able to recover the free energy profiles, time correlation functions, and mean first passage times for barrier crossing events at a significantly small computational cost. WEM promises to extend the applicability of molecular dynamics simulation to slow dynamics of large systems that are well beyond the scope of present day brute-force computations.

Controlling Electron Dynamics with Carrier-Envelope Phases of a Laser Pulse.

A theoretical study on the ionization dynamics of carbon atom irradiated with a few-cycle, intense laser field is performed within a quasiclassical model to get mechanistic insights into an earlier reported carrier-envelope phase dependency of ionization probabilities of an atom [ Phys. Rev. Lett. 2013, 110, 083602]. The carrier-envelope phase of the laser pulse is found to govern the overall dynamics, reflecting its importance in controlling electronic motion. To understand the origin of this effect, individual trajectories were analyzed at a particular laser intensity. We found that a variation in the carrier-envelope phase affects the angle of ejection of the electrons and subsequently the attainment of the desired final state.

Effects of alloying on mode-selectivity in H2O dissociation on Cu/Ni bimetallic surfaces.

The influence of alloying on mode-selectivity in H2O dissociation on Cu/Ni bimetallic surfaces has been studied using a fully quantum approach based on reaction path Hamiltonian. Both the metal alloy catalyst surface and the normal modes of H2O impact the chemical reactivity of H2O dissociation. A combination of these two different factors will enhance their influence reasonably. Among all the bimetallic surfaces, one monolayer (Ni4_Cu(111)) and 12 monolayer of Ni on Cu surface (Ni2_Cu(111)) show lowest barrier to the dissociation. Excitation of bending mode and symmetric stretching mode enhances the reactivity remarkably due to a significant decrease in their frequencies near the transition state in the vibrational adiabatic approximation. In the presence of non-adiabatic coupling between the modes, asymmetric stretching also shows similar enhancement in reactivity to that of symmetric stretching for all the systems. Inclusion of lattice motion using a sudden model enhances the dissociation probability at surface temperature 300 K and at lower incident energy, compared to that of the static surface approximation. The mode selective behaviour of H2O molecules is almost similar on all the Cu- and Ni-based surfaces. The excitation of symmetric stretching vibration by one quantum is shown to have largest efficacy for promoting reactions for all the systems. Overall, the dissociation probabilities for all the systems are enhanced by vibrational excitation of normal modes and become more significant with the non-adiabatic coupling effect.

Controlling Heterogeneous Catalysis of Water Dissociation Using Cu-Ni Bimetallic Alloy Surfaces: A Quantum Dynamics Study.

Copper-Nickel bimetallic alloys are emerging heterogeneous catalysts for water dissociation which is the rate-determining step of the industrially important water gas shift (WGS) reaction. Yet, the detailed quantum dynamics studies of water-surface scattering in the literature are limited to pure metal surfaces. We present here a three-dimensional wave packet dynamics study of water dissociation on Cu-Ni alloy surfaces, using a pseudodiatomic model of water on a London-Eyring-Polanyi-Sato (LEPS) potential energy surface in order to study the effect of initial vibration, rotation, and orientation of the water molecule on the reactivity. For all the chosen surfaces, reactivity increases significantly with vibrational excitation. In general, for lower vibrational states the reactivity increases with increasing rotational excitation but it decreases in higher vibrational states. Molecular orientation strongly affects reactivity by helping the molecule to align along the reaction path at higher vibrational states. For different alloys, the reaction probability follows the trend of barrier heights and the surfaces having all Ni atoms in the uppermost layer are much more reactive than the ones with Cu atoms. Hence the nature of the alloy surface and initial quantum state of the incoming molecule significantly influence the reactivity in surface catalyzed water dissociation.

Sodium carboxymethylcellulose-induced aggregation of 1-decyl-3-methylimidazolium chloride in aqueous solutions.

Aggregation behavior of a surface active ionic liquid 1-decyl-3-methylimidazolium chloride (C10MeImCl) was studied in aqueous solutions in absence and in presence of sodium carboxymethylcellulose (NaCMC) by electrical conductivity, surface tension, vapor pressure, and fluorescence measurements. Ion-association behavior of C10MeImCl (aq) in the premicellar regime has also been investigated. Two characteristic concentrations, namely the critical aggregation concentration and polymer saturation concentration, before free C10MeImCl micelles appear in C10MeImCl-NaCMC solutions were identified. Effects of temperature, NaCMC concentration, and the bulk solution structural property on the self-aggregation of C10MeImCl have been discussed to elucidate C10MeImCl-NaCMC interactions. Thermodynamics of the micellization processes provided important insight regarding the (a) release of water molecules from the hydration layer around the hydrophilic domain, and from the water cage around the hydrophobic moiety of the SAIL, and (b) transfer of the hydrocarbon chains into the micelle and restoration of the H-bonding structure of the water around the micelle.

Influence of sodium carboxymethylcellulose on the aggregation behavior of aqueous 1-hexadecyl-3-methylimidazolium chloride solutions.

The influence of sodium carboxymethylcellulose (NaCMC) on the aggregation phenomena of a surface active ionic liquid 1-hexadecyl-3-methylimidazolium chloride (C16MeImCl) was studied in aqueous solutions using electrical conductivity and surface tension measurements. The counterion condensation behavior of NaCMC (aq) and the premicellar ion-association behavior of C16MeImCl (aq) were also investigated. Two characteristic concentrations, namely the critical aggregation concentration and polymer saturation concentration, before free C16MeImCl micelles appear in C16MeImCl-NaCMC solutions have been identified. Effects of temperature, NaCMC concentration, and the charge density parameter of NaCMC on the self-aggregation of the C16MeImCl have been discussed to elucidate C16MeImCl-NaCMC interactions. The thermodynamic parameters for micellization of C16MeImCl were estimated both in absence and in the presence of NaCMC. The observed enthalpy-entropy compensation effect in C16MeImCl and C16MeImCl-NaCMC systems provided important insight as to how micellization processes are governed by the bulk structural property of the solution with respect to that of the water.