A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations

Unveiling Cas8 Dynamics and Regulation within a transposon-encoded Cascade-TniQ Complex

Cascade is a class 1, type 1 CRISPR-Cas system with a variety of roles in prokaryote defense, specifically against DNA-based viruses. The Vibrio Cholerae transposon, Tn6677, encodes a variant of the type 1F Cascade known as type 1F-3. This Cascade variant complexes with a homodimer of the transposition protein TniQ and leverages the sequence specificity of Cascade to direct the integration activity of the heteromeric transposase tnsA/B, resulting in site-specific transposition of Tn6677. We desire to uncover the molecular details behind R Loop formation of 'Cascade-TniQ.' Due to the lack of a complete model of Cascade-TniQ available at atom-level resolution, we first build a complete model using AlphaFold V2.1. We then simulate this model via classical molecular dynamics and umbrella sampling to study an important regulatory component within Cascade-TniQ, known as the Cas8 'bundle.' Particularly, we show that this alpha helical bundle experiences a free energy barrier to its large-scale translatory motions and relative free energies of its states primarily dependent on a loop within a Cas7 subunit in Cascade-TniQ. Further, we comment on additional structural and dynamical regulatory points of Cascade-TniQ during R Loop formation, such as Cascade-TniQ backbone rigidity, and the potential role TniQ plays in regulating bundle dynamics. In summary, our outcomes provide the first all-atom dynamic representation of one of the largest CRISPR systems, with information that can contribute to understanding the mechanism of nucleic acid binding and, eventually, to transposase recruitment itself. Such information may prove informative to advance genome engineering efforts.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

ACES: Optimized Alchemically Enhanced Sampling

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.

Who stole the proton? Suspect general base guanine found with a smoking gun in the pistol ribozyme

The pistol ribozyme (Psr) is one among the most recently discovered classes of small nucleolytic ribozymes that catalyze site-specific RNA self-cleavage through 2'-O-transphosphorylation. The Psr contains a conserved guanine (G40) that in crystal structures is in a position suggesting it plays the role of the general base to abstract a proton from the nucleophile to activate the reaction. Although some functional data is consistent with this mechanistic role, a notable exception is 2-aminopurine (2AP) substitution which has no effect on the rate, unlike similar substitutions across other so-called "G + M" and "G + A" ribozyme classes. Herein we postulate that an alternate conserved guanine, G42, is the primary general base, and provide evidence from molecular simulations that the active site of Psr can undergo local refolding into a structure that is consistent with the common "L-platform/L-scaffold" architecture identified in G + M and G + A ribozyme classes with Psr currently the notable exception. We summarize the key currently available experimental data and present new classical and combined quantum mechanical/molecular mechanical simulation results that collectively suggest a new hypothesis. We hypothesize that there are two available catalytic pathways supported by different conformational states connected by a local refolding of the active site: (1) a primary pathway with an active site architecture aligned with the L-platform/L-scaffold framework where G42 acts as a general base, and (2) a secondary pathway with the crystallographic active site architecture where G40 acts as a general base. We go on to make several experimentally testable predictions, and suggest specific experiments that would ultimately bring closure to the mystery as to "who stole the proton in the pistol ribozyme?".

Combined QM/MM, Machine Learning Path Integral Approach to Compute Free Energy Profiles and Kinetic Isotope Effects in RNA Cleavage Reactions

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. 18O and 34S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

Energetics of a protein disorder-order transition in small molecule recognition

Many proteins recognise other proteins via mechanisms that involve the folding of intrinsically disordered regions upon complex formation. Here we investigate how the selectivity of a drug-like small molecule arises from its modulation of a protein disorder-to-order transition. Binding of the compound AM-7209 has been reported to confer order upon an intrinsically disordered ‘lid’ region of the oncoprotein MDM2. Calorimetric measurements revealed that truncation of the lid region of MDM2 increases the apparent dissociation constant of AM-7209 250-fold. By contrast, lid truncation has little effect on the binding of the ligand Nutlin-3a. Insights into these differential binding energetics were obtained via a complete thermodynamic analysis that featured adaptive absolute alchemical free energy of binding calculations with enhanced-sampling molecular dynamics simulations. The simulations reveal that in apo MDM2 the ordered lid state is energetically disfavoured. AM-7209, but not Nutlin-3a, shows a significant energetic preference for ordered lid conformations, thus shifting the balance towards ordering of the lid in the AM-7209/MDM2 complex. The methodology reported herein should facilitate broader targeting of intrinsically disordered regions in medicinal chemistry.

Molecular simulations and biophysical measurements elucidate why the ligand AM-7209 orders a disordered region of the protein MDM2 on binding. This work expands strategies available to medicinal chemists for targeting disordered proteins.

Solvation Effects on the Thermal Helix Inversion of Molecular Motors from QM/MM Calculations

Molecular motors convert light and thermal energies into mechanical work, offering good opportunities to design novel molecular devices. Among them, molecular motors alternate a photoisomerization and a thermal helix inversion to achieve unidirectional rotation. The rotational speed is limited by the helix inversion step, which in turn is governed by a barrier in the electronic ground state. In this work, we systematically study the solvation effect on the thermal process of selected molecular motors, comparing reaction barriers obtained from both density functional theory (DFT) in the isolated system and umbrella sampling within a hybrid quantum mechanics/molecular mechanics (QM/MM) model in solution. We find more prominent solvation effects on those molecular motors with larger dipole moments. The results could provide insight into how to functionalize molecular motors to speed up their rotation.

Development of Range-Corrected Deep Learning Potentials for Fast, Accurate Quantum Mechanical/Molecular Mechanical Simulations of Chemical Reactions in Solution

We develop a new deep potential─range correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of six nonenzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free-energy profiles generated from a target QM model. We perform these comparisons using the MNDO/d and DFTB2 semiempirical models because they differ in the way they treat orbital orthogonalization and electrostatics and produce free-energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free-energy profiles requires correction of the QM/MM interactions out to 6 Å. We further find that the model's initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure, so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce four different reactions and yielded good agreement with the free-energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free-energy surfaces and 1D free-energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs but was sped up almost 100-fold when using NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free-energy applications ranging from drug discovery to enzyme design.

Controlling Peptide Function by Directed Assembly Formation: Mechanistic Insights Using Multiscale Modeling on an Antimicrobial Peptide-Drug-Membrane System

Owing to their potential applicability against multidrug-resistant bacteria, antimicrobial peptides (AMPs) or host defense peptides (HDPs) gain increased attention. Besides diverse immunomodulatory roles, their classical mechanism of action mostly involves membrane disruption of microbes. Notably, their unbalanced overexpression has also been associated with host cell cytotoxicity in various diseases. Relatedly, AMPs can be subject to aggregate formation, either via self-assembly or together with other compounds, which has demonstrated a modulation effect on their biological functions, thus highly relevant both for drug targeting projects and understanding their in vivo actions. However, the molecular aspects of the related assembly formation are not understood. Here, we focused in detail on an experimentally studied AMP-drug system, i.e., CM15-suramin, and performed all-atom and coarse-grain (CG) simulations. Results obtained for all systems were in close line with experimental observations and indicate that the CM15-suramin aggregation is an energetically favorable and dynamic process. In the presence of bilayers, the peptide-drug assembly formation was highly dependent on lipid composition, and peptide aggregates themselves were also capable of binding to the membranes. Interestingly, longer CG simulations with zwitterionic membranes indicated an intermediate state in the presence of both AMP-drug assemblies and monomeric peptides located on the membrane surface. In sharp contrast, larger AMP-drug aggregates could not be detected with a negatively charged membrane, rather the AMPs penetrated its surface in a monomeric form, in line with previous in vitro observations. Considering experimental and theoretical results, it is promoted that in biological systems, cationic AMPs may often form associates with anionic compounds in a reversible manner, resulting in lower bioactivity. This is only mildly affected by zwitterionic membranes; however, membranes with a negative charge strongly alter the energetic preference of AMP assemblies, resulting in the dissolution of the complexes into the membrane. The phenomenon observed here at a molecular level can be followed in several experimental systems studied recently, where peptides interact with food colors, drug molecules, or endogenous compounds, which strongly indicates that reversible associate formation is a general phenomenon for these complexes. These results are hoped to be exploited in novel therapeutic strategies aiming to use peptides as drug targets and control AMP bioactivity by directed assembly formation.

Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis

We redevelop the variational free energy profile (vFEP) method using a cardinal B-spline basis to extend the method for analyzing free energy surfaces (FESs) involving three or more reaction coordinates. We also implemented software for evaluating high-dimensional profiles based on the multistate Bennett acceptance ratio (MBAR) method which constructs an unbiased probability density from global reweighting of the observed samples. The MBAR method takes advantage of a fast algorithm for solving the unbinned weighted histogram (UWHAM)/MBAR equations which replaces the solution of simultaneous equations with a nonlinear optimization of a convex function. We make use of cardinal B-splines and multiquadric radial basis functions to obtain smooth, differentiable MBAR profiles in arbitrary high dimensions. The cardinal B-spline vFEP and MBAR methods are compared using three example systems that examine 1D, 2D, and 3D profiles. Both methods are found to be useful and produce nearly indistinguishable results. The vFEP method is found to be 150 times faster than MBAR when applied to periodic 2D profiles, but the MBAR method is 4.5 times faster than vFEP when evaluating unbounded 3D profiles. In agreement with previous comparisons, we find the vFEP method produces superior FESs when the overlap between umbrella window simulations decreases. Finally, the associative reaction mechanism of hammerhead ribozyme is characterized using 3D, 4D, and 6D profiles, and the higher-dimensional profiles are found to have smaller reaction barriers by as much as 1.5 kcal/mol. The methods presented here have been implemented into the FE-ToolKit software package along with new methods for network-wide free energy analysis in drug discovery.

Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States

Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of the free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events, and some low-energy conformations may get oversampled in simulations of a finite length. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.

Exploring the concerted mechanistic pathway for HIV-1 PR-substrate revealed by umbrella sampling simulation

HIV-1 protease (HIV-1 PR) is an essential enzyme for the replication process of its virus, and therefore considered an important target for the development of drugs against the acquired immunodeficiency syndrome (AIDS). Our previous study shows that the catalytic mechanism of subtype B/C-SA HIV-1 PR follows a one-step concerted acyclic hydrolysis reaction process using a two-layered ONIOM B3LYP/6-31++G(d,p) method. This present work is aimed at exploring the proposed mechanism of the proteolysis catalyzed by HIV-1 PR and to ensure our proposed mechanism is not an artefact of a single theoretical technique. Hence, we present umbrella sampling method that is suitable for calculating potential mean force (PMF) for non-covalent ligand/substrate-enzyme association/dissociation interactions which provide thermodynamic details for molecular recognition. The free activation energy results were computed in terms of PMF analysis within the hybrid QM(DFTB)/MM approach. The theoretical findings suggest that the proposed mechanism corresponds in principle with experimental data. Given our observations, we suggest that the QM/MM MD method can be used as a reliable computational technique to rationalize lead compounds against specific targets such as the HIV-1 protease.

Enantiomerization of Axially Chiral Biphenyls: Polarizable MD Simulations in Water and Butylmethylether

In this study, we investigate the influence of chiral and achiral cations on the enantiomerization of biphenylic anions in n-butylmethylether and water. In addition to the impact of the cations and solvent molecules on the free energy profile of rotation, we also explore if chirality transfer between a chiral cation and the biphenylic anion is possible, i.e., if pairing with a chiral cation can energetically favour one conformer of the anion via diastereomeric complex formation. The quantum-mechanical calculations are accompanied by polarizable MD simulations using umbrella sampling to study the impact of solvents of different polarity in more detail. We also discuss how accurate polarizable force fields for biphenylic anions can be constructed from quantum-mechanical reference data.

Assessment of the Cruzain Cysteine Protease Reversible and Irreversible Covalent Inhibition Mechanism

Reversible and irreversible covalent ligands are advanced cysteine protease inhibitors in the drug development pipeline. K777 is an irreversible inhibitor of cruzain, a necessary enzyme for the survival of the Trypanosoma cruzi (T. cruzi) parasite, the causative agent of Chagas disease. Despite their importance, irreversible covalent inhibitors are still often avoided due to the risk of adverse effects. Herein, we replaced the K777 vinyl sulfone group with a nitrile moiety to obtain a reversible covalent inhibitor (Neq0682) of cysteine protease. Then, we used advanced experimental and computational techniques to explore details of the inhibition mechanism of cruzain by reversible and irreversible inhibitors. The isothermal titration calorimetry (ITC) analysis shows that inhibition of cruzain by an irreversible inhibitor is thermodynamically more favorable than by a reversible one. The hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) and Molecular Dynamics (MD) simulations were used to explore the mechanism of the reaction inhibition of cruzain by K777 and Neq0682. The calculated free energy profiles show that the Cys25 nucleophilic attack and His162 proton transfer occur in a single step for a reversible inhibitor and two steps for an irreversible covalent inhibitor. The hybrid QM/MM calculated free energies for the inhibition reaction correspond to -26.7 and -5.9 kcal mol^-1 for K777 and Neq0682 at the MP2/MM level, respectively. These results indicate that the ΔG of the reaction is very negative for the process involving K777, consequently, the covalent adduct cannot revert to a noncovalent protein-ligand complex, and its binding tends to be irreversible. Overall, the present study provides insights into a covalent inhibition mechanism of cysteine proteases.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanical accuracy via a semi-empirical reference potential. II. Recalibrating semi-empirical parameters with force matching

An efficient and accurate reference potential simulation protocol is proposed for producing ab initio quantum mechanical/molecular mechanical (AI-QM/MM) quality free energy profiles for chemical reactions in a solvent or macromolecular environment. This protocol involves three stages: (a) using force matching to recalibrate a semi-empirical quantum mechanical (SE-QM) Hamiltonian for the specific reaction under study; (b) employing the recalibrated SE-QM Hamiltonian (in combination with molecular mechanical force fields) as the reference potential to drive umbrella samplings along the reaction pathway; and (c) computing AI-QM/MM energy values for collected configurations from the sampling and performing weighted thermodynamic perturbation to acquire an AI-QM/MM corrected reaction free energy profile. For three model reactions (identity SN2 reaction, Menshutkin reaction, and glycine proton transfer reaction) in aqueous solution and one enzyme reaction (Claisen arrangement in chorismate mutase), our simulations using recalibrated PM3 SE-QM Hamiltonians well reproduced QM/MM free energy profiles at the B3LYP/6-31G* level of theory all within 1 kcal mol-1 with a 20 to 45 fold reduction in the computer time.

Using AMBER18 for Relative Free Energy Calculations

With renewed interest in free energy methods in contemporary structure-based drug design, there is a pressing need to validate against multiple targets and force fields to assess the overall ability of these methods to accurately predict relative binding free energies. We computed relative binding free energies using graphics processing unit accelerated thermodynamic integration (GPU-TI) on a data set originally assembled by Schrödinger, Inc. Using their GPU free energy code (FEP+) and the OPLS2.1 force field combined with the REST2 enhanced sampling approach, these authors obtained an overall MUE of 0.9 kcal/mol and an overall RMSD of 1.14 kcal/mol. In our study using GPU-TI from AMBER with the AMBER14SB/GAFF1.8 force field but without enhanced sampling, we obtained an overall MUE of 1.17 kcal/mol and an overall RMSD of 1.50 kcal/mol for the 330 perturbations contained in this data set. A more detailed analysis of our results suggested that the observed differences between the two studies arise from differences in sampling protocols along with differences in the force fields employed. Future work should address the problem of establishing benchmark quality results with robust statistical error bars obtained through multiple independent runs and enhanced sampling, which is possible with the GPU-accelerated features in AMBER.

Sulfur-substitution-induced base flipping in the DNA duplex

Base flipping is widely observed in a number of important biological processes. The genetic codes deposited inside the DNA duplex become accessible to external agents upon base flipping. The sulfur substitution of guanine leads to thioguanine, which alters the thermodynamic stability of the GC base pairs and the GT mismatches. Experimental studies conclude that the sulfur substitution decreases the lifetime of the GC base pair. In this work, under three AMBER force fields for nucleotide systems, we firstly performed equilibrium and nonequilibrium free energy simulations to investigate the variation of the thermodynamic profiles in base flipping upon sulfur substitution. It is found that the bsc0 modification, the bsc1 modification and the OL15 modification of AMBER force fields are able to qualitatively describe the sulfur-substitution dependent behavior of the thermodynamics. However, only the two last-generation AMBER force fields are able to provide quantitatively correct predictions. The second computational study on the sulfur substitutions focused on the relative stability of the S6G-C base pair and the S6G-T mismatch. Two conflicting experimental observations were reported by the same authors. One suggested that the S6G-C base pair was more stable, while the other concludes that the S6G-T mismatch was more stable. We answered this question by constructing the free energy profiles along the base flipping pathway computationally.

Cleaning Up Mechanistic Debris Generated by Twister Ribozymes Using Computational RNA Enzymology

The catalytic properties of RNA have been a subject of fascination and intense research since their discovery over 30 years ago. Very recently, several classes of nucleolytic ribozymes have emerged and been characterized structurally. Among these, the twister ribozyme has been center-stage, and a topic of debate about its architecture and mechanism owing to conflicting interpretations of different crystal structures, and in some cases conflicting interpretations of the same functional data. In the present work, we attempt to clean up the mechanistic "debris" generated by twister ribozymes using a comprehensive computational RNA enzymology approach aimed to provide a unified interpretation of existing structural and functional data. Simulations in the crystalline environment and in solution provide insight into the origins of observed differences in crystal structures, and coalesce on a common active site architecture, and dynamical ensemble in solution. We use GPU-accelerated free energy methods with enhanced sampling to ascertain microscopic nucleobase pK a values of the implicated general acid and base, from which predicted activity-pH profiles can be compared directly with experiments. Next, ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with full dynamic solvation under periodic boundary conditions are used to determine mechanistic pathways through multi-dimensional free energy landscapes for the reaction. We then characterize the rate-controlling transition state, and make predictions about kinetic isotope effects and linear free energy relations. Computational mutagenesis is performed to explain the origin of rate effects caused by chemical modifications and make experimentally testable predictions. Finally, we provide evidence that helps to resolve conflicting issues related to the role of metal ions in catalysis. Throughout each stage, we highlight how a conserved L-platform structural motif, to- gether with a key L-anchor residue, forms the characteristic active site scaffold enabling each of the catalytic strategies to come together not only for the twister ribozyme, but the majority of the known small nucleolytic ribozyme classes.

Thermodynamics of Helix formation in small peptides of varying lengthin vacuo, implicit solvent and explicit solvent: Comparison between AMBER force fields

Helix formation is of great significance in protein folding. The helix-forming tendencies of amino acids are accumulated along the sequence to determine the helix-forming tendency of peptides. Computer simulation can be used to model this process in atomic details and give structural insights. In the current work, we employ equilibrate-state free energy simulation to systematically study the folding/unfolding thermodynamics of a series of mutated peptides. Two AMBER force fields including AMBER99SB and AMBER14SB are compared. The new 14SB force field uses refitted torsion parameters compared with 99SB and they share the same atomic charge scheme. We find that in vacuo the helix formation is mutation dependent, which reflects the different helix propensities of different amino acids. In general, there are helix formers, helix indifferent groups and helix breakers. The helical structure becomes more favored when the length of the sequence becomes longer, which arises from the formation of additional backbone hydrogen bonds in the lengthened sequence. Therefore, the helix indifferent groups and helix breakers will become helix formers in long sequences. Also, protonation-dependent helix formation is observed for ionizable groups. In 14SB, the helical structures are more stable than in 99SB and differences can be observed in their grouping schemes, especially in the helix indifferent group. In solvents, all mutations are helix indifferent due to protein–solvent interactions. The decrease in the number of backbone hydrogen bonds is the same with the increase in the number of protein–water hydrogen bonds. The 14SB in explicit solvent is able to capture the free energy minima in the helical state while 14SB in implicit solvent, 99SB in explicit solvent and 99SB in implicit solvent cannot. The helix propensities calculated under 14SB agree with the corresponding experimental values, while the 99SB results obviously deviate from the references. Hence, implicit solvent models are unable to correctly describe the thermodynamics even for the simple helix formation in isolated peptides. Well-developed force fields and explicit solvents are needed to correctly describe the protein dynamics. Aside from the free energy, differences in conformational ensemble under different force fields in different solvent models are observed. The numbers of hydrogen bonds formed under different force fields agree and they are mostly determined by the solvent model.

Determination of Base-Flipping Free-Energy Landscapes from Nonequilibrium Stratification

Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free-energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free-energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for the efficient calculation of the free-energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free-energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of the equilibrium umbrella sampling and the nonequilibrium stratification is given. The results show that nonequilibrium free-energy simulation achieves similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size.

Fluorinated synthetic anion carriers: experimental and computational insights into transmembrane chloride transport

A series of fluorinated tripodal tris-thioureas function as highly active anion transporters across lipid bilayers and cell membranes. Here, we investigate their mechanism of action using anion transport assays in cells and synthetic vesicles and molecular modelling of transporter-lipid interactions. When compared with non-fluorinated analogues, fluorinated compounds demonstrate a different mechanism of membrane transport because the free transporter cannot effectively diffuse through the membrane. As a result, in H+/Cl- cotransport assays, fluorinated transporters require the presence of oleic acid to form anionic oleate complexes for recycling of the transporter, whereas non-fluorinated analogues readily diffuse through the membrane as free transporters and show synergistic transport with the proton transporter gramicidin. Molecular dynamics simulations revealed markedly stronger transporter-lipid interactions for fluorinated compounds compared with non-fluorinated analogues and hence, higher energy barriers for fluorinated compounds to cross the membrane as free transporters. With use of appropriate proton transporters to ensure measurement of the correct rate-limiting steps, the transport rates determined in synthetic vesicle assays show excellent agreement with the anion transport rates determined in cell-based assays. We conclude that integration of computational and experimental methods provides a strategy to optimise transmembrane anion transporter design for biomedical applications.

The Good, the Bad, and the Ugly: "HiPen", a New Dataset for Validating (S)QM/MM Free Energy Simulations

Indirect (S)QM/MM free energy simulations (FES) are vital to efficiently incorporating sufficient sampling and accurate (QM) energetic evaluations when estimating free energies of practical/experimental interest. Connecting between levels of theory, i.e., calculating Δ A l o w → h i g h , remains to be the most challenging step within an indirect FES protocol. To improve calculations of Δ A l o w → h i g h , we must: (1) compare the performance of all FES methods currently available; and (2) compile and maintain datasets of Δ A l o w → h i g h calculated for a wide-variety of molecules so that future practitioners may replicate or improve upon the current state-of-the-art. Towards these two aims, we introduce a new dataset, "HiPen", which tabulates Δ A g a s M M → 3 o b (the free energy associated with switching from an M M to an S C C - D F T B molecular description using the 3ob parameter set in gas phase), calculated for 22 drug-like small molecules. We compare the calculation of this value using free energy perturbation, Bennett's acceptance ratio, Jarzynski's equation, and Crooks' equation. We also predict the reliability of each calculated Δ A g a s M M → 3 o b by evaluating several convergence criteria including sample size hysteresis, overlap statistics, and bias metric ( Π ). Within the total dataset, three distinct categories of molecules emerge: the "good" molecules, for which we can obtain converged Δ A g a s M M → 3 o b using Jarzynski's equation; "bad" molecules which require Crooks' equation to obtain a converged Δ A g a s M M → 3 o b ; and "ugly" molecules for which we cannot obtain reliably converged Δ A g a s M M → 3 o b with either Jarzynski's or Crooks' equations. We discuss, in depth, results from several example molecules in each of these categories and describe how dihedral discrepancies between levels of theory cause convergence failures even for these gas phase free energy simulations.

Molecular features of hydration layers probed by atomic force microscopy

Structurally-ordered layers of water are universally formed on a solid surface in aqueous solution or under ambient conditions. Although such hydration layers are commonly probed via atomic force microscopy (AFM), the current understanding on how the hydration layers manifest themselves in an AFM experiment is far from complete. By using molecular dynamics simulation, we investigate the hydration layers on a hydrophilic or hydrophobic surface probed by a nanoscale tip. We study the density and molecular orientation of water, the free energy, and the force on the tip by varying the tip-surface distance. The force-distance curve oscillates due to the transition between the mono-, bi-, and tri-layers of water confined between the tip and the surface. If both the tip and the surface are hydrophobic, water confined between the tip and the surface evaporates due to the dewetting transition, giving a hydrophobic force without oscillation. The periodicity of oscillation in the force differs from the structural periodicity of water. With a close proximity of the tip, the molecular dipoles align parallel to the surface, regardless of whether the tip and the surface are hydrophilic or hydrophobic.

Computational Probing of Watson-Crick/Hoogsteen Breathing in a DNA Duplex Containing N1-Methylated Adenine

DNA breathing is a local conformational fluctuation spontaneously occurring in double-stranded DNAs. In particular, the possibility of individual base pairs (bps) in duplex DNA to flip between alternate bp modes, i.e., Watson-Crick (WC)-like and Hoogsteen (HG)-like, at relevant time scales has impacted DNA research fields for many years. In this study, to computationally probe effects of chemical modification on the DNA breathing, we present a free energy landscape of spontaneous thermal transitions between WC and HG bps in a free DNA duplex containing N1-methylated adenine (m1A). For the current free energy computation, a variant of well-tempered metadynamics simulation was extensively performed for a total of 40 μs to produce free energy surfaces. The free energy profile indicated that, upon the chemical modification of adenine, the HG bp (m1A·T) was located in the most favorable conformation (96.7%); however, the canonical WC bp (m1A·T) was distorted into two WC-like bps of WC* (2.8%) and WC** (0.5%). The conformational exchange between these two minor WC-like bps occurs with the first hundred nanoseconds. The transition between WC-like and HG bp features multiple transition pathways displaying various extents of base flipping in combination with glycosidic rotation. Analysis of the simulated ensemble showed that the m1A-induced changes of the backbone and sugar pucker were in a reasonable agreement with previous results inferred from NMR experiments. Also, this study revealed that the formation of the stable HG bp upon the mutation alters the characteristics of dynamic fluctuations of the neighboring WC residues of m1A. We expect this simulation approach to be a robust computational scheme to complement and guide future high-resolution experiments on many outstanding issues of duplex DNA breathing.

Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching

The calculation of free energy differences between levels of theory has numerous potential pitfalls. Chief among them is the lack of overlap, i.e., ensembles generated at one level of theory (e.g., "low") not being good approximations of ensembles at the other (e.g., "high"). Numerous strategies have been devised to mitigate this issue. However, the most straightforward approach is to ensure that the "low" level ensemble more closely resembles that of the "high". Ideally, this is done without increasing computational cost. Herein, we demonstrate that by reparametrizing classical intramolecular potentials to reproduce high level forces (i.e., force matching) configurational overlap between a "low" (i.e., classical) and "high" (i.e., quantum) level can be significantly improved. This procedure is validated on two test cases and results in vastly improved convergence of free energy simulations.

A Multidimensional B-Spline Correction for Accurate Modeling Sugar Puckering in QM/MM Simulations

The computational efficiency of approximate quantum mechanical methods allows their use for the construction of multidimensional reaction free energy profiles. It has recently been demonstrated that quantum models based on the neglect of diatomic differential overlap (NNDO) approximation have difficulty modeling deoxyribose and ribose sugar ring puckers and thus limit their predictive value in the study of RNA and DNA systems. A method has been introduced in our previous work to improve the description of the sugar puckering conformational landscape that uses a multidimensional B-spline correction map (BMAP correction) for systems involving intrinsically coupled torsion angles. This method greatly improved the adiabatic potential energy surface profiles of DNA and RNA sugar rings relative to high-level ab initio methods even for highly problematic NDDO-based models. In the present work, a BMAP correction is developed, implemented, and tested in molecular dynamics simulations using the AM1/d-PhoT semiempirical Hamiltonian for biological phosphoryl transfer reactions. Results are presented for gas-phase adiabatic potential energy surfaces of RNA transesterification model reactions and condensed-phase QM/MM free energy surfaces for nonenzymatic and RNase A-catalyzed transesterification reactions. The results show that the BMAP correction is stable, efficient, and leads to improvement in both the potential energy and free energy profiles for the reactions studied, as compared with ab initio and experimental reference data. Exploration of the effect of the size of the quantum mechanical region indicates the best agreement with experimental reaction barriers occurs when the full CpA dinucleotide substrate is treated quantum mechanically with the sugar pucker correction.

Optimization and Automation of the Construction of Smooth Free Energy Profiles

An adaptive procedure is introduced to construct smooth analytical profiles of the free energy along a reaction coordinate using sampled data from multiple biased simulations. The procedure is based upon identifying problematic regions encountered in maximum likelihood estimators of the profile where there are statistically relevant discrepancies between the empirical and parametrized cumulative distribution functions and preferentially improving the construction of the parametric profile in these regions. The method is designed to produce continuous and smooth analytical fits that satisfy statistical goodness-of-fit tests with a minimum number of parameters. The accuracy of the profile obtained from the adaptive construction is compared by numerical computation to that of smooth interpolations based on an optimally chosen weighted histogram method for a solvated ion pair system and for an activated process for which the analytical form of the potential of mean force is available. In the model where the exact profile is known, the adaptive procedure is shown to reduce the integrated error relative to the optimal histogram construction by a factor of 3 or more in the typical case where the sampling is not extensive. It is demonstrated that the adaptive procedure can be used to produce statistically accurate smooth analytical representations of the free energy profile that can be evaluated with little computational effort and require little user input.

Divalent Metal Ion Activation of a Guanine General Base in the Hammerhead Ribozyme: Insights from Molecular Simulations

The hammerhead ribozyme is a well-studied nucleolytic ribozyme that catalyzes the self-cleavage of the RNA phosphodiester backbone. Despite experimental and theoretical efforts, key questions remain about details of the mechanism with regard to the activation of the nucleophile by the putative general base guanine (G12). Straightforward interpretation of the measured activity-pH data implies the pK_a value of the N1 position in the G12 nucleobase is significantly shifted by the ribozyme environment. Recent crystallographic and biochemical work has identified pH-dependent divalent metal ion binding at the N7/O6 position of G12, leading to the hypothesis that this binding mode could induce a pK_a shift of G12 toward neutrality. We present computational results that support this hypothesis and provide a model that unifies the interpretation of available structural and biochemical data and paints a detailed mechanistic picture of the general base step of the reaction. Experimentally testable predictions are made for mutational and rescue effects on G12, which will give further insights into the catalytic mechanism. These results contribute to our growing knowledge of the potential roles of divalent metal ions in RNA catalysis.