Computational Approaches to the Chemical Equilibrium Constant in Protein-ligand Binding

Alchemical Free Energy Calculations on Membrane-Associated Proteins

Membrane proteins have diverse functions within cells and are well-established drug targets. The advances in membrane protein structural biology have revealed drug and lipid binding sites on membrane proteins, while computational methods such as molecular simulations can resolve the thermodynamic basis of these interactions. Particularly, alchemical free energy calculations have shown promise in the calculation of reliable and reproducible binding free energies of protein-ligand and protein-lipid complexes in membrane-associated systems. In this review, we present an overview of representative alchemical free energy studies on G-protein-coupled receptors, ion channels, transporters as well as protein-lipid interactions, with emphasis on best practices and critical aspects of running these simulations. Additionally, we analyze challenges and successes when running alchemical free energy calculations on membrane-associated proteins. Finally, we highlight the value of alchemical free energy calculations calculations in drug discovery and their applicability in the pharmaceutical industry.

ChemFlow─From 2D Chemical Libraries to Protein-Ligand Binding Free Energies

The accurate prediction of protein-ligand binding affinities is a fundamental problem for the rational design of new drug entities. Current computational approaches are either too expensive or inaccurate to be effectively used in virtual high-throughput screening campaigns. In addition, the most sophisticated methods, e.g., those based on configurational sampling by molecular dynamics, require significant pre- and postprocessing to provide a final ranking, which hinders straightforward applications by nonexpert users. We present a novel computational platform named ChemFlow to bridge the gap between 2D chemical libraries and estimated protein-ligand binding affinities. The software is designed to prepare a library of compounds provided in SMILES or SDF format, dock them into the protein binding site, and rescore the poses by simplified free energy calculations. Using a data set of 626 protein-ligand complexes and GPU computing, we demonstrate that ChemFlow provides relative binding free energies with an RMSE < 2 kcal/mol at a rate of 1000 ligands per day on a midsize computer cluster. The software is publicly available at https://github.com/IFMlab/ChemFlow.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Binding reactions at finite systems

A perpetual yearn exists among computational scientists to scale down the size of physical systems, a desire shared as well with experimentalists able to track single molecules. A question then arises whether averages observed at small systems are the same as those observed at large or macroscopic systems. Utilizing statistical-mechanics formulations in ensembles in which the total numbers of particles are fixed, we demonstrate that properties of binding reactions are not homogeneous functions. This means that averages of intensive parameters, such as the concentration of the bound-state, at finite systems are different than those at large systems. The discrepancy increases with decreasing temperature, volume, and to some extent, numbers of particles. As perplexing as it may sound, despite variations in average quantities, extracting the equilibrium constant from systems of different sizes does yield the same value. The reason is that correlations in reactants' concentrations ought to be accounted for in the expression of the equilibrium constant, being negligible at large-scale but significant at small-scale. Similar arguments pertain to the calculations of the reaction rate constants, more specifically, the bimolecular rate of the forward reaction is related to the average of the product (and not to the product of the averages) of the reactants' concentrations. Furthermore, we derive relations aiming to predict the composition only from the equilibrium constant and the system's size. All predictions are validated by Monte-Carlo and molecular dynamics simulations. An important consequence of these findings is that the expression of the equilibrium constant at finite systems is not dictated solely by the chemical equation of the reaction but requires knowledge of the elementary processes involved.

Nicotinic receptors: From protein allostery to computational neuropharmacology

We propose an extension and further development of the Monod-Wyman-Changeux model for allosteric transitions of regulatory proteins to brain communications and specifically to neurotransmitters receptors, with the nicotinic acetylcholine receptor (nAChR) as a model of ligand-gated ion channels. The present development offers an expression of the change of the gating isomerization constant caused by pharmacological ligand binding in terms of its value in the absence of ligands and several "modulation factors", which vary with orthosteric ligand binding (agonists/antagonists), allosteric ligand binding (positive allosteric modulators/negative allosteric modulators) and receptor desensitization. The new - explicit - formulation of such "modulation factors", provides expressions for the pharmacological attributes of potency, efficacy, and selectivity for the modulatory ligands (including endogenous neurotransmitters) in terms of their binding affinity for the active, resting, and desensitized states of the receptor. The current formulation provides ways to design neuroactive compounds with a controlled pharmacological profile, opening the field of computational neuro-pharmacology.

Multibasin Quasi-Harmonic Approach for the Calculation of the Configurational Entropy of Small Molecules in Solution

Entropy is a key thermodynamic property governing most biomolecular processes, including binding. Nonetheless, quantification of the configurational entropy of a single molecule in solution remains a grand challenge. Here, we present an original approach for the calculation of absolute molecular entropies based on the analysis of converged molecular dynamics (MD) simulations. Our method, named quasi-harmonic multibasin (QHMB), relies on a multibasin decomposition of the simulated trajectory by root-mean-square deviation clustering and subsequent quasi-harmonic analysis (QHA) of extracted sub-trajectories. Last, the entropy of the landscape is evaluated using the Gibbs formula. Because of the nature of QHA, this method is directly applicable to explicit-solvent simulations to access configurational entropies in solution. When compared with calorimetric data from NIST, QHMB is shown to predict absolute entropies in the gas phase for 23 small molecules with a root-mean-squared error of 0.36 kcal/mol from the experiments. In addition, the introduction of a QHMB correction in MM/GBSA calculations to account for the ligand configurational entropy loss on binding is shown to improve the correlation between calculated and experimental binding affinities with R² increasing from 0.67 to 0.78. Because this entropy correction penalizes large and flexible ligands more strongly, it might be useful to reduce the false-positive rate in virtual screening. The availability of an automatic procedure to compute QHMB entropies makes it a new available tool in the field of drug discovery.