Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water.

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by com- mittee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy.

Molecular Mechanism of Labelling Functional Cysteines by Heterocyclic Thiones.

Heterocyclic thiones have recently been identified as reversible covalent warheads, consistent with their mild electrophilic nature. Little is known so far about their mechanism of action in labelling nucleophilic sidechains, especially cysteines. The vast number of tractable cysteines promotes a wide range of target proteins to examine; however, our focus was put on functional cysteines. We chose the main protease of SARS-CoV-2 harboring Cys145 at the active site that is a structurally characterized and clinically validated target of covalent inhibitors. We screened an in-house, cysteine-targeting covalent inhibitor library which resulted in several covalent fragment hits with benzoxazole, benzothiazole and benzimidazole cores. Thione derivatives and Michael acceptors were selected for further investigations with the objective of exploring the mechanism of inhibition of the thiones and using the thoroughly characterized Michael acceptors for benchmarking our studies. Classical and hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations were carried out that revealed a new mechanism of covalent cysteine labelling by thione derivatives, which was supported by QM and free energy calculations and by a wide range of experimental results. Our study shows that the molecular recognition step plays a crucial role in the overall binding of both sets of molecules.

Assessing the Performance of Non-Equilibrium Thermodynamic Integration in Flavodoxin Redox Potential Estimation.

Flavodoxins are enzymes that contain the redox-active flavin mononucleotide (FMN) cofactor and play a crucial role in numerous biological processes, including energy conversion and electron transfer. Since the redox characteristics of flavodoxins are significantly impacted by the molecular environment of the FMN cofactor, the evaluation of the interplay between the redox properties of the flavin cofactor and its molecular surroundings in flavoproteins is a critical area of investigation for both fundamental research and technological advancements, as the electrochemical tuning of flavoproteins is necessary for optimal interaction with redox acceptor or donor molecules. In order to facilitate the rational design of biomolecular devices, it is imperative to have access to computational tools that can accurately predict the redox potential of both natural and artificial flavoproteins. In this study, we have investigated the feasibility of using non-equilibrium thermodynamic integration protocols to reliably predict the redox potential of flavodoxins. Using as a test set the wild-type flavodoxin from Clostridium Beijerinckii and eight experimentally characterized single-point mutants, we have computed their redox potential. Our results show that 75% (6 out of 8) of the calculated reaction free energies are within 1 kcal/mol of the experimental values, and none exceed an error of 2 kcal/mol, confirming that non-equilibrium thermodynamic integration is a trustworthy tool for the quantitative estimation of the redox potential of this biologically and technologically significant class of enzymes.

Binding of calcium and magnesium to human cardiac troponin C.

Cardiac muscle thin filaments are composed of actin, tropomyosin, and troponin that change conformation in response to Ca2+ binding, triggering muscle contraction. Human cardiac troponin C (cTnC) is the Ca2+-sensing component of the thin filament. It contains structural sites (III/IV) that bind both Ca2+ and Mg2+ and a regulatory site (II) that has been thought to bind only Ca2+. Binding of Ca2+ at this site initiates a series of conformational changes that culminate in force production. However, the mechanisms that underpin the regulation of binding at site II remain unclear. Here, we have quantified the interaction between site II and Ca2+/Mg2+ through isothermal titration calorimetry and thermodynamic integration simulations. Direct and competitive binding titrations with WT N-terminal cTnC and full-length cTnC indicate that physiologically relevant concentrations of both Ca2+/Mg2+ interacted with the same locus. Moreover, the D67A/D73A N-terminal cTnC construct in which two coordinating residues within site II were removed was found to have significantly reduced affinity for both cations. In addition, 1 mM Mg2+ caused a 1.4-fold lower affinity for Ca2+. These experiments strongly suggest that cytosolic-free Mg2+ occupies a significant population of the available site II. Interaction of Mg2+ with site II of cTnC likely has important functional consequences for the heart both at baseline as well as in diseased states that decrease or increase the availability of Mg2+, such as secondary hyperparathyroidism or ischemia, respectively.

Modulation of human transthyretin stability by the mutations at histidine 88 studied by free energy simulation.

Human transthyretin (TTR) is a homotetrameric plasma protein associated with a high percentage of ß-sheet, which forms amyloid fibrils and accumulates in tissues or extracellular matrix to cause amyloid diseases. Free energy simulations based on all-atom molecular dynamics simulations were carried out to analyze the effects of the His88 → Arg, Phe, and Tyr mutations on the stability of human TTR. The calculated free energy change differences (ΔΔG) caused by the His → Arg, Phe, and Tyr mutations at position 88 are 6.48 ± 0.45, -9.99 ± 0.54, and 2.66 ± 0.33 kcal/mol, respectively. These calculated free energy change differences between wild type and the mutants are in excellent agreement with prior experimental values. Our simulation results show that the wild type of the TTR is more stable than H88R and H88Y mutants, whereas it is less stable than the H88F mutant. The free energy component analysis shows that the primary contribution to the free energy change difference (ΔΔG) for the His → Arg mutation arises from electrostatic interaction; the ΔΔG for the His → Phe mutation is from van der Waals and electrostatic interactions and that for the His → Tyr mutation from covalent interaction. The simulation results show that the free energy calculation with thermodynamic integration is beneficial for understanding the detailed microscopic mechanism of protein stability. The implications of the results for understanding stabilizing and destabilizing effect of the mutation and the contribution to protein stability are discussed.

Thermodynamic integration combined with molecular dynamic simulations to explore the cross-resistance mechanism of isoniazid and ethionamide.

Tuberculosis is an ancient disease of mankind, and its causative bacterium is Mycobacterium tuberculosis. Isoniazid is one of the most effective first-line antituberculosis drugs. As prodrugs, it and its derivative ethionamide act on enoyl-acyl carrier protein reductase (InhA) after being oxidized in bacteria, and kill the bacteria by inhibiting the formation of M. tuberculosis cell walls. However, the S94A mutation of InhA causes M. tuberculosis to develop cross-resistance to isoniazid and ethionamide. This work is dedicated to studying the cross-resistance mechanism of isoniazid and ethionamide through theoretical calculations. First, thermodynamic integral simulations are used to accurately calculate the relative binding energy of two drugs in the mutant and wild-type system. Furthermore, through classic molecular dynamic simulations and molecular mechanics generalized-Born surface area calculation, some key residues are identified and the binding affinity of isoniazid and ethionamide reduced by 9-13 kcal/mol due to S94A mutation. The hydrogen bond between Ala94 and isoniazid (ethionamide) disappeared and the energy contribution of Ala94 decreased after the mutation. In addition, the dynamic network analysis indicated that the mutation of Ser94 also indirectly affected the conformation of key residues such as Met147, Thr196, and Leu97, resulting in a reduction in the energy contribution of these residues. Finally, the binding conformation of isoniazid and ethionamide has also undergone major changes. The obtained results could provide valuable information for the future molecular design to overcome the drug resistance.

Structural consequences of hereditary spastic paraplegia disease-related mutations in kinesin.

A wide range of mutations in the kinesin motor Kif5A have been linked to a neuronal disorder called hereditary spastic paraplegia (HSP). The position of these mutations can vary, and a range of different motile behaviors have been observed, indicating that the HSP mutants can alter distinct aspects of kinesin mechanochemistry. While focusing on four key HSP-associated mutants, this study examined the structural and dynamic perturbations that arise from these mutations using a series of different computational methods, ranging from bioinformatics analyses to all-atom simulations, that account for solvent effects explicitly. We show that two catalytic domain mutations (R280S and K253N) reduce the microtubule (MT) binding affinity of the kinesin head domains appreciably, while N256S has a much smaller impact. Bioinformatics analysis suggests that the stalk mutation A361V perturbs motor dimerization. Subsequent integration of these effects into a coarse-grained structure-based model of dimeric kinesin revealed that the order-disorder transition of the neck linker is substantially affected, indicating a hampered directionality and processivity of kinesin. The present analyses therefore suggest that, in addition to kinesin-MT binding and coiled-coil dimerization, HSP mutations affecting motor stepping transitions and processivity can lead to disease.

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy.

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid-base chemistry depending on temperature in small water assemblies.

Performing solvation free energy calculations in LAMMPS using the decoupling approach.

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach.

Well-tempered MCMC simulations for population pharmacokinetic models.

A full Bayesian statistical treatment of complex pharmacokinetic or pharmacodynamic models, in particular in a population context, gives access to powerful inference, including on model structure. Markov Chain Monte Carlo (MCMC) samplers are typically used to estimate the joint posterior parameter distribution of interest. Among MCMC samplers, the simulated tempering algorithm (TMCMC) has a number of advantages: it can sample from sharp multi-modal posteriors; it provides insight into identifiability issues useful for model simplification; it can be used to compute accurate Bayes factors for model choice; the simulated Markov chains mix quickly and have assured convergence in certain conditions. The main challenge when implementing this approach is to find an adequate scale of auxiliary inverse temperatures (perks) and associated scaling constants. We solved that problem by adaptive stochastic optimization and describe our implementation of TMCMC sampling in the GNU MCSim software. Once a grid of perks is obtained, it is easy to perform posterior-tempered MCMC sampling or likelihood-tempered MCMC (thermodynamic integration, which bridges the joint prior and the posterior parameter distributions, with assured convergence of a single sampling chain). We compare TMCMC to other samplers and demonstrate its efficient sampling of multi-modal posteriors and calculation of Bayes factors in two stylized case-studies and two realistic population pharmacokinetic inference problems, one of them involving a large PBPK model.

Rapid and accurate structure-based therapeutic peptide design using GPU accelerated thermodynamic integration.

Peptide-based therapeutics are an alternative to small molecule drugs as they offer superior specificity, lower toxicity, and easy synthesis. Here we present an approach that leverages the dramatic performance increase afforded by the recent arrival of GPU accelerated thermodynamic integration (TI). GPU TI facilitates very fast, highly accurate binding affinity optimization of peptides against therapeutic targets. We benchmarked TI predictions using published peptide binding optimization studies. Prediction of mutations involving charged side-chains was found to be less accurate than for non-charged, and use of a more complex 3-step TI protocol was found to boost accuracy in these cases. Using the 3-step protocol for non-charged side-chains either had no effect or was detrimental. We use the benchmarked pipeline to optimize a peptide binding to our recently discovered cancer target: EME1. TI calculations predict beneficial mutations using both canonical and non-canonical amino acids. We validate these predictions using fluorescence polarization and confirm that binding affinity is increased. We further demonstrate that this increase translates to a significant reduction in pancreatic cancer cell viability.

Molecular dynamics study of solubilization of cyclohexane, benzene, and phenol into mixed micelles composed of sodium dodecyl sulfate and octaethylene glycol monododecyl ether.

Molecular dynamics calculations of a mixed micelle composed of sodium dodecyl sulfate (SDS) and octaethylene glycol monododecyl ether (C12 E8 ) were performed for six compositions (SDS/C12 E8 = 100/0, 80/20, 60/40, 40/60, 20/80, and 0/100) to investigate the composition dependence of the mixed micelle structure and solubilization of cyclohexane, benzene, and phenol molecules by the micelle. The radial density distribution of the hydrophilic polyoxyethylene (POE) group of C12 E8 as a function of distance from the micelle center is very sharp for micelles with high SDS content because the POE group captures a Na+ ion in solution and wraps around it to form a compact crown-ether-like complex. The hydrophobic dodecyl groups of SDS and C12 E8 were separately distributed in the mixed micelle core. ΔG(r) evaluated for each solute showed that despite the structural changes of the micelle the binding strength of the solute molecules to the micelle did not change significantly. © 2019 Wiley Periodicals, Inc.

Blinded prediction of protein-ligand binding affinity using Amber thermodynamic integration for the 2018 D3R grand challenge 4.

In the framework of the 2018 Drug Design Data Resource grand challenge 4, blinded predictions on relative binding free energy were performed for a set of 39 ligands of the Cathepsin S protein. We leveraged the GPU-accelerated thermodynamic integration of Amber 18 to advance our computational prediction. When our entry was compared to experimental results, a good correlation was observed (Kendall's τ: 0.62, Spearman's ρ: 0.80 and Pearson's R: 0.82). We designed a parallelized transformation map that placed ligands into several groups based on common alchemical substructures; TI transformations were carried out for each ligand to the relevant substructure, and between substructures. Our calculations were all conducted using the linear potential scaling scheme in Amber TI because we believe the softcore potential/dual-topology approach as implemented in current Amber TI is highly fault-prone for some transformations. The issue is illustrated by using two examples in which typical preparation for the dual-topology approach of Amber TI fails. Overall, the high accuracy of our prediction is a result of recent advances in force fields (ff14SB and GAFF), as well as rapid calculation of ensemble averages enabled by the GPU implementation of Amber. The success shown here in a blinded prediction strongly suggests that alchemical free energy calculation in Amber is a promising tool for future commercial drug design.

Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System.

Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations. The formalism is applied to analyze the 4-body cluster probabilities for the quaternary system Cr-Fe-Mn-Ni as a function of temperature and alloy concentration. It is shown that, for two specific compositions (Cr 25Fe 25Mn 25Ni 25 and Cr 18Fe 27Mn 27Ni 28), the high value of probabilities for Cr-Fe-Fe-Fe and Mn-Mn-Ni-Ni are strongly correlated with the presence of the ordered phases L1 2 -CrFe 3 and L1 0-MnNi, respectively. These results are in an excellent agreement with predictions of these ground state structures by ab initio calculations. The general formalism is used to investigate the configuration entropy as a function of temperature and for 285 different alloy compositions. It is found that our matrix formulation of cluster probabilities provides an efficient tool to compute configuration entropy in multi-component alloys in a comparison with the result obtained by the thermodynamic integration method. At high temperatures, it is shown that many-body cluster correlations still play an important role in understanding the configuration entropy before reaching the solid solution limit of high-entroy alloys (HEAs).

Thermodynamic integration network approach to ion transport through protein channels: Perspectives and limits.

We present a molecular dynamics simulation study of alkali metal cation transport through the double-helical and the head-to-head conformers of the gramicidin ion channel. Our approach is based on a thermodynamic integration network, which consists of a sequence of transport reactions, absolute free energies of solvation and cycles of alchemical transmutations of the ions. In this manner, we can reliably estimate free energies and their statistical errors via a least-squares method without imposing external forces on the system. Within the double helical channel, we find a free energy surface typical for hopping transport between isoenergetic sites of ion localization, separated by comparatively large activation barriers. For fast transport through the head-to-head conformation, the thermodynamic network scheme starts to break down. © 2018 Wiley Periodicals, Inc.

Revised mechanism of carboxylation of ribulose-1,5-biphosphate by rubisco from large scale quantum chemical calculations.

Here, we describe a computational approach for studying enzymes that catalyze complex multi-step reactions and apply it to Ribulose 1,5-bisphosphate carboxylase-oxygenase (Rubisco), the enzyme that fixes atmospheric carbon dioxide within photosynthesis. In the 5-step carboxylase reaction, the substrate Ribulose-1,5-bisphosphate (RuBP) first binds Rubisco and undergoes enolization before binding the second substrate, CO2 . Hydration of the RuBP.CO2 complex is followed by CC bond scission and stereospecific protonation. However, details of the roles and protonation states of active-site residues, and sources of protons and water, remain highly speculative. Large-scale computations on active-site models provide a means to better understand this complex chemical mechanism. The computational protocol comprises a combination of hybrid semi-empirical quantum mechanics and molecular mechanics within constrained molecular dynamics simulations, together with constrained gradient minimization calculations using density functional theory. Alternative pathways for hydration of the RuBP.CO2 complex and associated active-site protonation networks and proton and water sources were investigated. The main findings from analysis of the resulting energetics advocate major revision to existing mechanisms such that: hydration takes place anti to the CO2 ; both hydration and CC bond scission require early protonation of CO2 in the RuBP.CO2 complex; CC bond scission and stereospecific protonation reactions are concerted and, effectively, there is only one stable intermediate, the C3-gemdiolate complex. Our main conclusions for interpreting enzyme kinetic results are that the gemdiolate may represent the elusive Michaelis-Menten-like complex corresponding to the empirical Km (=Kc ) with turnover to product via bond scission concerted with stereospecific protonation consistent with the observed catalytic rate. © 2018 Wiley Periodicals, Inc.

Free energy calculations on the stability of the 14-3-3ζ protein.

Mutations of cysteine are often introduced to e.g. avoid formation of non-physiological inter-molecular disulfide bridges in in-vitro experiments, or to maintain specificity in labeling experiments. Alanine or serine is typically preferred, which usually do not alter the overall protein stability, when the original cysteine was surface exposed. However, selecting the optimal mutation for cysteines in the hydrophobic core of the protein is more challenging. In this work, the stability of selected Cys mutants of 14-3-3ζ was predicted by free-energy calculations and the obtained data were compared with experimentally determined stabilities. Both the computational predictions as well as the experimental validation point at a significant destabilization of mutants C94A and C94S. This destabilization could be attributed to the formation of hydrophobic cavities and a polar solvation of a hydrophilic side chain. A L12E, M78K double mutant was further studied in terms of its reduced dimerization propensity. In contrast to naïve expectations, this double mutant did not lead to the formation of strong salt bridges, which was rationalized in terms of a preferred solvation of the ionic species. Again, experiments agreed with the calculations by confirming the monomerization of the double mutants. Overall, the simulation data is in good agreement with experiments and offers additional insight into the stability and dimerization of this important family of regulatory proteins.

Effect of Atomic Charges on Octanol-Water Partition Coefficient Using Alchemical Free Energy Calculation.

The octanol-water partition coefficient (logPow) is an important index for measuring solubility, membrane permeability, and bioavailability in the drug discovery field. In this paper, the logPow values of 58 compounds were predicted by alchemical free energy calculation using molecular dynamics simulation. In free energy calculations, the atomic charges of the compounds are always fixed. However, they must be recalculated for each solvent. Therefore, three different sets of atomic charges were tested using quantum chemical calculations, taking into account vacuum, octanol, and water environments. The calculated atomic charges in the different environments do not necessarily influence the correlation between calculated and experimentally measured ∆Gwater values. The largest correlation coefficient values of the solvation free energy in water and octanol were 0.93 and 0.90, respectively. On the other hand, the correlation coefficient of logPow values calculated from free energies, the largest of which was 0.92, was sensitive to the combination of the solvation free energies calculated from the calculated atomic charges. These results reveal that the solvent assumed in the atomic charge calculation is an important factor determining the accuracy of predicted logPow values.

Computational modeling and in-vitro/in-silico correlation of phospholipid-based prodrugs for targeted drug delivery in inflammatory bowel disease.

Targeting drugs to the inflamed intestinal tissue(s) represents a major advancement in the treatment of inflammatory bowel disease (IBD). In this work we present a powerful in-silico modeling approach to guide the molecular design of novel prodrugs targeting the enzyme PLA2, which is overexpressed in the inflamed tissues of IBD patients. The prodrug consists of the drug moiety bound to the sn-2 position of phospholipid (PL) through a carbonic linker, aiming to allow PLA2 to release the free drug. The linker length dictates the affinity of the PL-drug conjugate to PLA2, and the optimal linker will enable maximal PLA2-mediated activation. Thermodynamic integration and Weighted Histogram Analysis Method (WHAM)/Umbrella Sampling method were used to compute the changes in PLA2 transition state binding free energy of the prodrug molecule (∆∆Gtr) associated with decreasing/increasing linker length. The simulations revealed that 6-carbons linker is the optimal one, whereas shorter or longer linkers resulted in decreased PLA2-mediated activation. These in-silico results were shown to be in excellent correlation with experimental in-vitro data. Overall, this modern computational approach enables optimization of the molecular design of novel prodrugs, which may allow targeting the free drug specifically to the diseased intestinal tissue of IBD patients.

Absolute binding free energies for octa-acids and guests in SAMPL5 : Evaluating binding free energies for octa-acid and guest complexes in the SAMPL5 blind challenge.

As part of the SAMPL5 blind prediction challenge, we calculate the absolute binding free energies of six guest molecules to an octa-acid (OAH) and to a methylated octa-acid (OAMe). We use the double decoupling method via thermodynamic integration (TI) or Hamiltonian replica exchange in connection with the Bennett acceptance ratio (HREM-BAR). We produce the binding poses either through manual docking or by using GalaxyDock-HG, a docking software developed specifically for this study. The root mean square deviations for our most accurate predictions are 1.4 kcal mol-1 for OAH with TI and 1.9 kcal mol-1 for OAMe with HREM-BAR. Our best results for OAMe were obtained for systems with ionic concentrations corresponding to the ionic strength of the experimental solution. The most problematic system contains a halogenated guest. Our attempt to model the σ-hole of the bromine using a constrained off-site point charge, does not improve results. We use results from molecular dynamics simulations to argue that the distinct binding affinities of this guest to OAH and OAMe are due to a difference in the flexibility of the host. We believe that the results of this extensive analysis of host-guest complexes will help improve the protocol used in predicting binding affinities for larger systems, such as protein-substrate compounds.