Protein-ligand binding free energies from exhaustive docking

Solvated interaction energy: from small-molecule to antibody drug design

Scoring functions are ubiquitous in structure-based drug design as an aid to predicting binding modes and estimating binding affinities. Ideally, a scoring function should be broadly applicable, obviating the need to recalibrate and refit its parameters for every new target and class of ligands. Traditionally, drugs have been small molecules, but in recent years biologics, particularly antibodies, have become an increasingly important if not dominant class of therapeutics. This makes the goal of having a transferable scoring function, i.e., one that spans the range of small-molecule to protein ligands, even more challenging. One such broadly applicable scoring function is the Solvated Interaction Energy (SIE), which has been developed and applied in our lab for the last 15 years, leading to several important applications. This physics-based method arose from efforts to understand the physics governing binding events, with particular care given to the role played by solvation. SIE has been used by us and many independent labs worldwide for virtual screening and discovery of novel small-molecule binders or optimization of known drugs. Moreover, without any retraining, it is found to be transferrable to predictions of antibody-antigen relative binding affinities and as accurate as functions trained on protein-protein binding affinities. SIE has been incorporated in conjunction with other scoring functions into ADAPT (Assisted Design of Antibody and Protein Therapeutics), our platform for affinity modulation of antibodies. Application of ADAPT resulted in the optimization of several antibodies with 10-to-100-fold improvements in binding affinity. Further applications included broadening the specificity of a single-domain antibody to be cross-reactive with virus variants of both SARS-CoV-1 and SARS-CoV-2, and the design of safer antibodies by engineering of a pH switch to make them more selective towards acidic tumors while sparing normal tissues at physiological pH.

Ligand binding free energy evaluation by Monte Carlo Recursion

The correct evaluation of ligand binding free energies by computational methods is still a very challenging active area of research. The most employed methods for these calculations can be roughly classified into four groups: (i) the fastest and less accurate methods, such as molecular docking, designed to sample a large number of molecules and rapidly rank them according to the potential binding energy; (ii) the second class of methods use a thermodynamic ensemble, typically generated by molecular dynamics, to analyze the endpoints of the thermodynamic cycle for binding and extract differences, in the so-called 'end-point' methods; (iii) the third class of methods is based on the Zwanzig relationship and computes the free energy difference after a chemical change of the system (alchemical methods); and (iv) methods based on biased simulations, such as metadynamics, for example. These methods require increased computational power and as expected, result in increased accuracy for the determination of the strength of binding. Here, we describe an intermediate approach, based on the Monte Carlo Recursion (MCR) method first developed by Harold Scheraga. In this method, the system is sampled at increasing effective temperatures, and the free energy of the system is assessed from a series of terms W(b,T), computed from Monte Carlo (MC) averages at each iteration. We show the application of the MCR for ligand binding with datasets of guest-hosts systems (N = 75) and we observed that a good correlation is obtained between experimental data and the binding energies computed with MCR. We also compared the experimental data with an end-point calculation from equilibrium Monte Carlo calculations that allowed us to conclude that the lower-energy (lower-temperature) terms in the calculation are the most relevant to the estimation of the binding energies, resulting in similar correlations between MCR and MC data and the experimental values. On the other hand, the MCR method provides a reasonable view of the binding energy funnel, with possible connections with the ligand binding kinetics, as well. The codes developed for this analysis are publicly available on GitHub as a part of the LiBELa/MCLiBELa project (https://github.com/alessandronascimento/LiBELa).

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.

Molecular Docking at a Glance

The current chapter introduces different aspects of molecular docking technique in order to give an overview to the readers about the topics which will be dealt with throughout this volume. Like many other fields of science, molecular docking studies has experienced a lagging period of slow and steady increase in terms of acquiring attention of scientific community as well as its frequency of application, followed by a pronounced era of exponential expansion in theory, methodology, areas of application and performance due to developments in related technologies such as computational resources and theoretical as well as experimental biophysical methods. In the following sections the evolution of molecular docking will be reviewed and its different components including methods, search algorithms, scoring functions, validation of the methods, and area of applications plus few case studies will be touched briefly.

Multiple fragment docking and linking in primary and secondary pockets of dopamine receptors

A sequential docking methodology was applied to computationally predict starting points for fragment linking using the human dopamine D3 receptor crystal structure and a human dopamine D2 receptor homology model. Two focused fragment libraries were docked in the primary and secondary binding sites, and best fragment combinations were enumerated. Similar top scoring fragments were found for the primary site, while secondary site fragments were predicted to convey selectivity. Three linked compounds were synthesized that had 9-, 39-, and 55-fold selectivity in favor of D3 and the subtype selectivity of the compounds was assessed on a structural basis.

Challenges, applications, and recent advances of protein-ligand docking in structure-based drug design

The docking methods used in structure-based virtual database screening offer the ability to quickly and cheaply estimate the affinity and binding mode of a ligand for the protein receptor of interest, such as a drug target. These methods can be used to enrich a database of compounds, so that more compounds that are subsequently experimentally tested are found to be pharmaceutically interesting. In addition, like all virtual screening methods used for drug design, structure-based virtual screening can focus on curated libraries of synthesizable compounds, helping to reduce the expense of subsequent experimental verification. In this review, we introduce the protein-ligand docking methods used for structure-based drug design and other biological applications. We discuss the fundamental challenges facing these methods and some of the current methodological topics of interest. We also discuss the main approaches for applying protein-ligand docking methods. We end with a discussion of the challenging aspects of evaluating or benchmarking the accuracy of docking methods for their improvement, and discuss future directions.

Bringing Clarity to the Prediction of Protein-Ligand Binding Free Energies via "Blurring"

We present a method to evaluate the free energies of ligand binding utilizing a Monte Carlo estimation of the configuration integrals concomitant with uncertainty quantification. Ensembles for integration are built through systematically perturbing an initial ligand conformation in a rigid binding pocket, which is optimized separately prior to incorporation of the ligand. We call the procedure producing the ensembles "blurring", and it is carried out using an in-house developed code. The Boltzmann factor contribution of each pose to the configuration integral is computed and from there the free energy is obtained. Potential function uncertainties are estimated using a fragment-based error propagation method. This method has been applied to a set of small aromatic ligands complexed with T4 Lysozyme L99A mutant. Microstate energies have been determined with the force fields ff99SB and ff94, and the semiempirical method PM6DH2 in conjunction with continuum solvation models including Generalized Born (GB), the Conductor-like Screening Model (COSMO), and SMD. Of the methods studied, PM6DH2-based scoring gave binding free energy estimates, which yielded a good correlation to the experimental binding affinities (R2 = 0.7). All methods overestimated the calculated binding affinities. We trace this to insufficient sampling, the single static protein structure, and inaccuracies in the solvent models we have used in this study.

Exhaustive docking and solvated interaction energy scoring: lessons learned from the SAMPL4 challenge

We continued prospective assessments of the Wilma-solvated interaction energy (SIE) platform for pose prediction, binding affinity prediction, and virtual screening on the challenging SAMPL4 data sets including the HIV-integrase inhibitor and two host-guest systems. New features of the docking algorithm and scoring function are tested here prospectively for the first time. Wilma-SIE provides good correlations with actual binding affinities over a wide range of binding affinities that includes strong binders as in the case of SAMPL4 host-guest systems. Absolute binding affinities are also reproduced with appropriate training of the scoring function on available data sets or from comparative estimation of the change in target's vibrational entropy. Even when binding modes are known, SIE predictions lack correlation with experimental affinities within dynamic ranges below 2 kcal/mol as in the case of HIV-integrase ligands, but they correctly signaled the narrowness of the dynamic range. Using a common protein structure for all ligands can reduce the noise, while incorporating a more sophisticated solvation treatment improves absolute predictions. The HIV-integrase virtual screening data set consists of promiscuous weak binders with relatively high flexibility and thus it falls outside of the applicability domain of the Wilma-SIE docking platform. Despite these difficulties, unbiased docking around three known binding sites of the enzyme resulted in over a third of ligands being docked within 2 Å from their actual poses and over half of the ligands docked in the correct site, leading to better-than-random virtual screening results.

Identifying ligand binding sites and poses using GPU-accelerated Hamiltonian replica exchange molecular dynamics

We present a method to identify small molecule ligand binding sites and poses within a given protein crystal structure using GPU-accelerated Hamiltonian replica exchange molecular dynamics simulations. The Hamiltonians used vary from the physical end state of protein interacting with the ligand to an unphysical end state where the ligand does not interact with the protein. As replicas explore the space of Hamiltonians interpolating between these states, the ligand can rapidly escape local minima and explore potential binding sites. Geometric restraints keep the ligands from leaving the vicinity of the protein and an alchemical pathway designed to increase phase space overlap between intermediates ensures good mixing. Because of the rigorous statistical mechanical nature of the Hamiltonian exchange framework, we can also extract binding free energy estimates for all putative binding sites. We present results of this methodology applied to the T4 lysozyme L99A model system for three known ligands and one non-binder as a control, using an implicit solvent. We find that our methodology identifies known crystallographic binding sites consistently and accurately for the small number of ligands considered here and gives free energies consistent with experiment. We are also able to analyze the contribution of individual binding sites to the overall binding affinity. Our methodology points to near term potential applications in early-stage structure-guided drug discovery.

Identification of small-molecule binding pockets in the soluble monomeric form of the Aβ42 peptide

The aggregation of intrinsically disordered peptides and proteins is associated with a wide range of highly debilitating neurological and systemic disorders. In this work we explored the potential of a structure-based drug discovery procedure to target one such system, the soluble monomeric form of the Aβ42 peptide. We utilised for this purpose a set of structures of the Aβ42 peptide selected from clusters of conformations within an ensemble generated by molecular dynamics simulations. Using these structures we carried out fragment mapping calculations to identify binding "hot spots" on the monomeric form of the Aβ42 peptide. This procedure provided a set of hot spots with ligand efficiencies comparable to those observed for structured proteins, and clustered into binding pockets. Such binding pockets exhibited a propensity to bind small molecules known to interact with the Aβ42 peptide. Taken together these results provide an initial indication that fragment-based drug discovery may represent a potential therapeutic strategy for diseases associated with the aggregation of intrinsically disordered proteins.