On Inactivation of the Coronavirus Main Protease.

A deeper understanding of the inactive conformations of the coronavirus main protease (MPro) could inform the design of allosteric drugs. Based on extensive molecular dynamics simulations, we built a Markov State Model to investigate structural changes that can inactivate the SARS-CoV-2 MPro. In a subset of structures, one subunit of the homodimer assumes an inactive conformation that resembles an inactive crystal structure. However, contradicting the widely held half-of-sites activity hypothesis, the most populated enzyme structures have two active subunits. We then used transition path theory (TPT) and the Jensen-Shannon Divergence (JSD) to pinpoint residues involved in the inactivation process. A π stack between Phe140 and His163 is a key feature that can distinguish active and inactive conformations of MPro. Each subunit has unique inactive conformations stabilized by π stacking interactions involving residues Phe140, Tyr118, His163, and His172, a hydrogen bonding network centered around His163 and His172, and a modified network of interactions in the dimer interface. The importance of these residues in maintaining an active structure explains the sensitivity of enzymatic activity to site-directed mutagenesis.

Identification of the riboflavin cofactor-binding site in the Vibrio cholerae ion-pumping NQR complex: A novel structural motif in redox enzymes.

The ion-pumping NQR complex is an essential respiratory enzyme in the physiology of many pathogenic bacteria. This enzyme transfers electrons from NADH to ubiquinone through several cofactors, including riboflavin (vitamin B2). NQR is the only enzyme reported that is able to use riboflavin as a cofactor. Moreover, the riboflavin molecule is found as a stable neutral semiquinone radical. The otherwise highly reactive unpaired electron is stabilized via an unknown mechanism. Crystallographic data suggested that riboflavin might be found in a superficially located site in the interface of NQR subunits B and E. However, this location is highly problematic, as the site does not have the expected physiochemical properties. In this work, we have located the riboflavin-binding site in an amphipathic pocket in subunit B, previously proposed to be the entry site of sodium. Here, we show that this site contains absolutely conserved residues, including N200, N203, and D346. Mutations of these residues decrease enzymatic activity and specifically block the ability of NQR to bind riboflavin. Docking analysis and molecular dynamics simulations indicate that these residues participate directly in riboflavin binding, establishing hydrogen bonds that stabilize the cofactor in the site. We conclude that riboflavin is likely bound in the proposed pocket, which is consistent with enzymatic characterizations, thermodynamic studies, and distance between cofactors.

Learned mappings for targeted free energy perturbation between peptide conformations.

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. [J. Chem. Phys. 153, 144112 (2020)] demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to the free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases and different spring centers. When the neural network is trained until "early stopping"-when the loss value of the test set increases-we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å. For more distant thermodynamic states, the mapping does not produce structures representative of the target state, and the method does not reproduce reference calculations.

Bayesian Regression Quantifies Uncertainty of Binding Parameters from Isothermal Titration Calorimetry More Accurately Than Error Propagation.

We compare several different methods to quantify the uncertainty of binding parameters estimated from isothermal titration calorimetry data: the asymptotic standard error from maximum likelihood estimation, error propagation based on a first-order Taylor series expansion, and the Bayesian credible interval. When the methods are applied to simulated experiments and to measurements of Mg(II) binding to EDTA, the asymptotic standard error underestimates the uncertainty in the free energy and enthalpy of binding. Error propagation overestimates the uncertainty for both quantities, except in the simulations, where it underestimates the uncertainty of enthalpy for confidence intervals less than 70%. In both datasets, Bayesian credible intervals are much closer to observed confidence intervals.

Electrostatics and water occlusion regulate covalently-bound flavin mononucleotide cofactors of Vibrio cholerae respiratory complex NQR.

Proteins like NADH:ubiquinone oxidoreductase (NQR), an essential enzyme and ion pump in the physiology of several pathogenic bacteria, tightly regulate the redox properties of their cofactors. Although flavin mononucleotide (FMN) is fully reduced in aqueous solution, FMN in subunits B and C of NQR exclusively undergo one-electron transitions during its catalytic cycle. Here, we perform ab initio calculations and molecular dynamics simulations to elucidate the mechanisms that regulate the redox state of FMN in NQR. QM/MM calculations show that binding site electrostatics disfavor anionic forms of FMNH2 , but permit a neutral form of the fully reduced flavin. The potential energy surface is unaffected by covalent bonding between FMN and threonine. Molecular dynamics simulations show that the FMN binding sites are inaccessible by water, suggesting that further reductions of the cofactors are limited or prohibited by the availability of water and other proton donors. These findings provide a deeper understanding of the mechanisms used by NQR to regulate electron transfer through the cofactors and perform its physiologic role. They also provide the first, to our knowledge, evidence of the simple concept that proteins regulate flavin redox states via water occlusion.

Conserved residue His-257 of Vibrio cholerae flavin transferase ApbE plays a critical role in substrate binding and catalysis.

The flavin transferase ApbE plays essential roles in bacterial physiology, covalently incorporating FMN cofactors into numerous respiratory enzymes that use the integrated cofactors as electron carriers. In this work we performed a detailed kinetic and structural characterization of Vibrio cholerae WT ApbE and mutants of the conserved residue His-257, to understand its role in substrate binding and in the catalytic mechanism of this family. Bi-substrate kinetic experiments revealed that ApbE follows a random Bi Bi sequential kinetic mechanism, in which a ternary complex is formed, indicating that both substrates must be bound to the enzyme for the reaction to proceed. Steady-state kinetic analyses show that the turnover rates of His-257 mutants are significantly smaller than those of WT ApbE, and have increased Km values for both substrates, indicating that the His-257 residue plays important roles in catalysis and in enzyme-substrate complex formation. Analyses of the pH dependence of ApbE activity indicate that the pKa of the catalytic residue (pKES1) increases by 2 pH units in the His-257 mutants, suggesting that this residue plays a role in substrate deprotonation. The crystal structures of WT ApbE and an H257G mutant were determined at 1.61 and 1.92 Å resolutions, revealing that His-257 is located in the catalytic site and that the substitution does not produce major conformational changes. We propose a reaction mechanism in which His-257 acts as a general base that deprotonates the acceptor residue, which subsequently performs a nucleophilic attack on FAD for flavin transfer.

Alchemical Grid Dock (AlGDock): Binding Free Energy Calculations between Flexible Ligands and Rigid Receptors.

Alchemical Grid Dock (AlGDock) is open-source software designed to compute the binding potential of mean force-the binding free energy between a flexible ligand and a rigid receptor-for a small organic ligand and a biological macromolecule. Multiple BPMFs can be used to rigorously compute binding affinities between flexible partners. AlGDock uses replica exchange between thermodynamic states at different temperatures and receptor-ligand interaction strengths. Receptor-ligand interaction energies are represented by interpolating precomputed grids. Thermodynamic states are adaptively initialized and adjusted on-the-fly to maintain adequate replica exchange rates. In demonstrative calculations, when the bound ligand is treated as fully solvated, AlGDock estimates BPMFs with a precision within 4 kT in 65% and within 8 kT for 91% of systems. It correctly identifies the native binding pose in 83% of simulations. Performance is sometimes limited by subtle differences in the important configuration space of sampled and targeted thermodynamic states. © 2019 Wiley Periodicals, Inc.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations.

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol-1 Å-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

On the polarization of ligands by proteins.

Although ligand-binding sites in many proteins contain a high number density of charged side chains that can polarize small organic molecules and influence binding, the magnitude of this effect has not been studied in many systems. Here, we use a quantum mechanics/molecular mechanics (QM/MM) approach, in which the ligand is the QM region, to compute the ligand polarization energy of 286 protein-ligand complexes from the PDBBind Core Set (release 2016). Calculations were performed both with and without implicit solvent based on the domain decomposition Conductor-like Screening Model. We observe that the ligand polarization energy is linearly correlated with the magnitude of the electric field acting on the ligand, the magnitude of the induced dipole moment, and the classical polarization energy. The influence of protein and cation charges on the ligand polarization diminishes with the distance and is below 2 kcal mol-1 at 9 Å and 1 kcal mol-1 at 12 Å. Compared to these embedding field charges, implicit solvent has a relatively minor effect on ligand polarization. Considering both polarization and solvation appears essential to computing negative binding energies in some crystallographic complexes. Solvation, but not polarization, is essential for achieving moderate correlation with experimental binding free energies.

A Structural Model for Bax∆2-Mediated Activation of Caspase 8-Dependent Apoptosis.

Bax∆2 is a pro-apoptotic anti-tumor protein in the Bax family. While most of the Bax family causes cell death by targeting mitochondria, Bax∆2 forms cytosolic aggregates and activates caspase 8-dependent cell death. We previously showed that the Bax∆2 helix α9 is critical for caspase 8 recruitment. However, the interaction between these two proteins at the structural level is unknown. In this in silico study, we performed molecular dynamics (MD) simulations and protein-protein docking on Bax∆2 variants. The results suggest that the Bax∆2 variants have different stable states. Mutating the Baxα mitochondria-targeting signal [L26P/L27P] appears to introduce a kink into helix α1. Protein-protein docking suggests that helices α9 of both wild-type Bax∆2 and Bax∆2 caspase 8 binding-deficient mutant [L164P] can fit in the same caspase 8 binding site, but the mutant is unable to fit as well as wild-type Bax∆2. Together, these data point to a structural basis for explaining Bax∆2 function in caspase 8-dependent cell death.

Characterization of the Pseudomonas aeruginosa NQR complex, a bacterial proton pump with roles in autopoisoning resistance.

Pseudomonas aeruginosa is a Gram-negative bacterium responsible for a large number of nosocomial infections. The P. aeruginosa respiratory chain contains the ion-pumping NADH:ubiquinone oxidoreductase (NQR). This enzyme couples the transfer of electrons from NADH to ubiquinone to the pumping of sodium ions across the cell membrane, generating a gradient that drives essential cellular processes in many bacteria. In this study, we characterized P. aeruginosa NQR (Pa-NQR) to elucidate its physiologic function. Our analyses reveal that Pa-NQR, in contrast with NQR homologues from other bacterial species, is not a sodium pump, but rather a completely new form of proton pump. Homology modeling and molecular dynamics simulations suggest that cation selectivity could be determined by the exit ion channels. We also show that Pa-NQR is resistant to the inhibitor 2-n-heptyl-4-hydroxyquinoline N-oxide (HQNO). HQNO is a quinolone secreted by P. aeruginosa during infection that acts as a quorum sensing agent and also has bactericidal properties against other bacteria. Using comparative analysis and computational modeling of the ubiquinone-binding site, we identified the specific residues that confer resistance toward this inhibitor. In summary, our findings indicate that Pa-NQR is a proton pump rather than a sodium pump and is highly resistant against the P. aeruginosa-produced compound HQNO, suggesting an important role in the adaptation against autotoxicity. These results provide a deep understanding of the metabolic role of NQR in P. aeruginosa and provide insight into the structural factors that determine the functional specialization in this family of respiratory complexes.

Alchemical Grid Dock (AlGDock) calculations in the D3R Grand Challenge 3 : Binding free energies between flexible ligands and rigid receptors.

We participated in Subchallenges 1 and 2 of the Drug Design Data Resource (D3R) Grand Challenge 3. To prepare our submissions, we performed molecular docking with UCSF DOCK 6 and binding potential of mean force (BPMF) calculations-free energy calculations between flexible ligands and rigid receptors-using our open-source software package Alchemical Grid Dock (AlGDock). For each system, submissions were based on the minimum BPMF calculated for a selected set of crystal structures. In Subchallenge 1, our workflow performed poorly. Possible reasons for the poor performance include the neglect of cooperative ligands and limited sampling of ligand binding poses. In Subchallenge 2, our workflow led to some of most highly correlated submissions (Pearson R = 0.5) for vascular endothelial growth factor receptor 2. However, our results were poorly correlated for Janus Kinase 2 and Mitogen-activated protein kinase 14. Affinity prediction could potentially be improved by systematic selection of more diverse receptor configurations.

Nonequilibrium path-ensemble averages for symmetric protocols.

According to the nonequilibrium work relations, path-ensembles generated by irreversible processes in which a system is driven out of equilibrium according to a predetermined protocol may be used to compute equilibrium free energy differences and expectation values. Estimation has previously been improved by considering data collected from the reverse process, which starts in equilibrium in the final thermodynamic state of the forward process and is driven according to the time-reversed protocol. Here, we develop a theoretically rigorous statistical estimator for nonequilibrium path-ensemble averages specialized for symmetric protocols, in which forward and reverse processes are identical. The estimator is tested with a number of model systems: a symmetric 1D potential, an asymmetric 1D potential, the unfolding of deca-alanine, separating a host-guest system, and translocating a potassium ion through a gramicidin A ion channel. When reconstructing free energies using data from symmetric protocols, the new estimator outperforms existing rigorous unidirectional and bidirectional estimators, converging more quickly and resulting in a smaller error. However, in most cases, using the bidirectional estimator with data from a forward and reverse pair of asymmetric protocols outperforms the corresponding symmetric protocol and estimator with the same amount of simulation time. Hence, the new estimator is only recommended when the bidirectional estimator is not feasible or is expected to perform poorly. The symmetric estimator shows similar performance to a unidirectional protocol of half the length and twice the number of trajectories.

Identification of the Catalytic Ubiquinone-binding Site of Vibrio cholerae Sodium-dependent NADH Dehydrogenase: A NOVEL UBIQUINONE-BINDING MOTIF.

The sodium-dependent NADH dehydrogenase (Na+-NQR) is a key component of the respiratory chain of diverse prokaryotic species, including pathogenic bacteria. Na+-NQR uses the energy released by electron transfer between NADH and ubiquinone (UQ) to pump sodium, producing a gradient that sustains many essential homeostatic processes as well as virulence factor secretion and the elimination of drugs. The location of the UQ binding site has been controversial, with two main hypotheses that suggest that this site could be located in the cytosolic subunit A or in the membrane-bound subunit B. In this work, we performed alanine scanning mutagenesis of aromatic residues located in transmembrane helices II, IV, and V of subunit B, near glycine residues 140 and 141. These two critical glycine residues form part of the structures that regulate the site's accessibility. Our results indicate that the elimination of phenylalanine residue 211 or 213 abolishes the UQ-dependent activity, produces a leak of electrons to oxygen, and completely blocks the binding of UQ and the inhibitor HQNO. Molecular docking calculations predict that UQ interacts with phenylalanine 211 and pinpoints the location of the binding site in the interface of subunits B and D. The mutagenesis and structural analysis allow us to propose a novel UQ-binding motif, which is completely different compared with the sites of other respiratory photosynthetic complexes. These results are essential to understanding the electron transfer pathways and mechanism of Na+-NQR catalysis.

Power transformations improve interpolation of grids for molecular mechanics interaction energies.

A common strategy for speeding up molecular docking calculations is to precompute nonbonded interaction energies between a receptor molecule and a set of three-dimensional grids. The grids are then interpolated to compute energies for ligand atoms in many different binding poses. Here, I evaluate a smoothing strategy of taking a power transformation of grid point energies and inverse transformation of the result from trilinear interpolation. For molecular docking poses from 85 protein-ligand complexes, this smoothing procedure leads to significant accuracy improvements, including an approximately twofold reduction in the root mean square error at a grid spacing of 0.4 Å and retaining the ability to rank docking poses even at a grid spacing of 0.7 Å. © 2018 Wiley Periodicals, Inc.

Using the fast fourier transform in binding free energy calculations.

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc.

Efficiency of Stratification for Ensemble Docking Using Reduced Ensembles.

Molecular docking can account for receptor flexibility by combining the docking score over multiple rigid receptor conformations, such as snapshots from a molecular dynamics simulation. Here, we evaluate a number of common snapshot selection strategies using a quality metric from stratified sampling, the efficiency of stratification, which compares the variance of a selection strategy to simple random sampling. We also extend the metric to estimators of exponential averages (which involve an exponential transformation, averaging, and inverse transformation) and minima. For docking sets of over 500 ligands to four different proteins of varying flexibility, we observe that, for estimating ensemble averages and exponential averages, many clustering algorithms have similar performance trends: for a few snapshots (less than 25), medoids are the most efficient, while, for a larger number, optimal (the allocation that minimizes the variance) and proportional (to the size of each cluster) allocation become more efficient. Proportional allocation appears to be the most consistently efficient for estimating minima.

Implicit ligand theory for relative binding free energies.

Implicit ligand theory enables noncovalent binding free energies to be calculated based on an exponential average of the binding potential of mean force (BPMF)-the binding free energy between a flexible ligand and rigid receptor-over a precomputed ensemble of receptor configurations. In the original formalism, receptor configurations were drawn from or reweighted to the apo ensemble. Here we show that BPMFs averaged over a holo ensemble yield binding free energies relative to the reference ligand that specifies the ensemble. When using receptor snapshots from an alchemical simulation with a single ligand, the new statistical estimator outperforms the original.

Effects of Catalytic Action and Ligand Binding on Conformational Ensembles of Adenylate Kinase.

Crystal structures of adenylate kinase (AdK) from Escherichia coli capture two states: an "open" conformation (apo) obtained in the absence of ligands and a "closed" conformation in which ligands are bound. Other AdK crystal structures suggest intermediate conformations that may lie on the transition pathway between these two states. To characterize the transition from open to closed states in solution, X-ray solution scattering data were collected from AdK in the apo form and with progressively increasing concentrations of five different ligands. Scattering data from apo AdK are consistent with scattering predicted from the crystal structure of AdK in the open conformation. In contrast, data from AdK samples saturated with Ap5A do not agree with that calculated from AdK in the closed conformation. Using cluster analysis of available structures, we selected representative structures in five conformational states: open, partially open, intermediate, partially closed, and closed. We used these structures to estimate the relative abundances of these states for each experimental condition. X-ray solution scattering data obtained from AdK with AMP are dominated by scattering from AdK in the open conformation. For AdK in the presence of high concentrations of ATP and ADP, the conformational ensemble shifts to a mixture of partially open and closed states. Even when AdK is saturated with Ap5A, a significant proportion of AdK remains in a partially open conformation. These results are consistent with an induced-fit model in which the transition of AdK from an open state to a closed state is initiated by ATP binding.