David D. L. Minh

Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

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 sites 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.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.

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.

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.

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.

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Isothermal titration calorimetry (ITC) is the only technique able to determine both the enthalpy and entropy of noncovalent association in a single experiment. The standard data analysis method based on nonlinear regression, however, provides unrealistically small uncertainty estimates due to its neglect of dominant sources of error. Here, we present a Bayesian framework for sampling from the posterior distribution of all thermodynamic parameters and other quantities of interest from one or more ITC experiments, allowing uncertainties and correlations to be quantitatively assessed. For a series of ITC measurements on metal:chelator and protein:ligand systems, the Bayesian approach yields uncertainties which represent the variability from experiment to experiment more accurately than the standard data analysis. In some datasets, the median enthalpy of binding is shifted by as much as 1.5 kcal/mol. A Python implementation suitable for analysis of data generated by MicroCal instruments (and adaptable to other calorimeters) is freely available online.

Alchemical Grid Dock (AlGDock) calculations in the D3R Grand Challenge 3

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.

Simple Entropy Terms for End-Point Binding Free Energy Calculations

We introduce a number of computationally inexpensive modifications to the MM/PBSA and MM/GBSA estimators for binding free energies, which are based on average receptor-ligand interaction energies in simulations of a noncovalent complex, to improve the treatment of entropy: second- and higher-order terms in a cumulant expansion and a confining potential on ligand external degrees of freedom. We also consider a filter for snapshots where ligands have drifted from the initial binding pose. The variations were tested on six sets of systems for which binding modes and free energies have previously been experimentally determined. For some data sets, none of the tested estimators led to results significantly correlated with measured free energies. In data sets with nontrivial correlation, a ligand RMSD cutoff of 3 Å and a second-order truncation of the cumulant expansion was found to be comparable or better than the average interaction energy by several statistical metrics.

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.