Absolute Protein-ligand Binding Free Energy Research Articles

Meta-Analysis Reveals That Absolute Binding Free-Energy Calculations Approach Chemical Accuracy.

Systematic and quantitative analysis of the reliability of formally exact methods that in silico calculate absolute protein-ligand binding free energies remains lacking. Here, we provide, for the first time, evidence-based information on the reliability of these methods by statistically studying 853 cases from 34 different research groups through meta-analysis. The results show that formally exact methods approach chemical accuracy (error = 1.58 kcal/mol), even if people are challenging difficult tasks such as blind drug screening in recent years. The geometrical-pathway-based methods prove to possess a better convergence ability than the alchemical ones, while the latter have a larger application range. We also reveal the importance of always using the latest force fields to guarantee reliability and discuss the pros and cons of turning to an implicit solvent model in absolute binding free-energy calculations. Moreover, based on the meta-analysis, an evidence-based guideline for in silico binding free-energy calculations is provided.

Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

Absolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

Alchemical absolute protein-ligand binding free energies for drug design.

The recent advances in relative protein–ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains a challenging endeavour, mostly limited to small model cases. Here, we demonstrate accurate first principles based absolute binding free energy estimates for 128 pharmaceutically relevant targets. We use a novel rigorous method to generate protein–ligand ensembles for the ligand in its decoupled state. Not only do the calculations deliver accurate protein–ligand binding affinity estimates, but they also provide detailed physical insight into the structural determinants of binding. We identify subtle rotamer rearrangements between apo and holo states of a protein that are crucial for binding. When compared to relative binding free energy calculations, obtaining absolute binding free energies is considerably more challenging in large part due to the need to explicitly account for the protein in its apo state. In this work we present several approaches to obtain apo state ensembles for accurate absolute ΔG calculations, thus outlining protocols for prospective application of the methods for drug discovery.

Ligand binding free-energy calculations with funnel metadynamics.

The accurate resolution of the binding mechanism of a ligand to its molecular target is fundamental to develop a successful drug design campaign. Free-energy calculations, which provide the energy value of the ligand-protein binding complex, are essential for resolving the binding mode of the ligand. The accuracy of free-energy calculation methods is counteracted by their poor user-friendliness, which hampers their broad application. Here we present the Funnel-Metadynamics Advanced Protocol (FMAP), which is a flexible and user-friendly graphical user interface (GUI)-based protocol to perform funnel metadynamics, a binding free-energy method that employs a funnel-shape restraint potential to reveal the ligand binding mode and accurately calculate the absolute ligand-protein binding free energy. FMAP guides the user through all phases of the free-energy calculation process, from preparation of the input files, to production simulation, to analysis of the results. FMAP delivers the ligand binding mode and the absolute protein-ligand binding free energy as outputs. Alternative binding modes and the role of waters are also elucidated, providing a detailed description of the ligand binding mechanism. The entire protocol on the paradigmatic system benzamidine-trypsin, composed of ~105 k atoms, took ~2.8 d using the Cray XC50 piz Daint cluster at the Swiss National Supercomputing Centre.

PELE-MSM: A Monte Carlo Based Protocol for the Estimation of Absolute Binding Free Energies.

In this study, we present a fully automatic platform based on our Monte Carlo algorithm, the Protein Energy Landscape Exploration method (PELE), for the estimation of absolute protein-ligand binding free energies, one of the most significant challenges in computer aided drug design. Based on a ligand pathway approach, an initial short enhanced sampling simulation is performed to identify reasonable starting positions for more extended sampling. This stepwise approach allows for a significant faster convergence of the free energy estimation using the Markov State Model (MSM) technique. PELE-MSM was applied on four diverse protein and ligand systems, successfully ranking compounds for two systems. Based on the results, current limitations and challenges with physics-based methods in computational structural biology are discussed. Overall, PELE-MSM constitutes a promising step toward computing absolute binding free energies and in their application into drug discovery projects.

Absolute Binding Free Energy Calculation and Design of a Subnanomolar Inhibitor of Phosphodiesterase-10.

Accurate prediction of absolute protein-ligand binding free energy could considerably enhance the success rate of structure-based drug design but is extremely challenging and time-consuming. Free energy perturbation (FEP) has been proven reliable but is limited to prediction of relative binding free energies of similar ligands (with only minor structural differences) in binding with a same drug target in practical drug design applications. Herein, a Gaussian algorithm-enhanced FEP (GA-FEP) protocol has been developed to enhance the FEP simulation performance, enabling to efficiently carry out the FEP simulations on vanishing the whole ligand and, thus, predict the absolute binding free energies (ABFEs). Using the GA-FEP protocol, the FEP simulations for the ABFE calculation (denoted as GA-FEP/ABFE) can achieve a satisfactory accuracy for both structurally similar and diverse ligands in a dataset of more than 100 receptor-ligand systems. Further, our GA-FEP/ABFE-guided lead optimization against phosphodiesterase-10 led to the discovery of a subnanomolar inhibitor (IC50 = 0.87 nM, ∼2000-fold improvement in potency) with cocrystal confirmation.

Accelerating the Calculation of Protein-Ligand Binding Free Energy and Residence Times Using Dynamically Optimized Collective Variables.

Elucidation of the ligand/protein binding interaction is of paramount relevance in pharmacology to increase the success rate of drug design. To this end, a number of computational methods have been proposed; however all of them suffer from limitations since the ligand binding/unbinding transitions to the molecular target involve many slow degrees of freedom that hamper a full characterization of the binding process. Being able to express this transition in simple and general slow degrees of freedom would give a distinctive advantage, since it would require minimal knowledge of the system under study, while in turn it would elucidate its physics and accelerate the convergence speed of enhanced sampling methods relying on collective variables. In this study we pursuit this goal by combining for the first time variational approach to conformational dynamics with funnel metadynamics. In so doing, we predict for the benzamidine/trypsin system the ligand binding mode, and we accurately compute the absolute protein-ligand binding free energy and unbinding rate at unprecedented low computational cost. Finally, our simulation protocol reveals the energetics and structural details of the ligand binding mechanism and shows that water and binding pocket solvation/desolvation are the dominant slow degrees of freedom.

Virtual screening of integrase inhibitors by large scale binding free energy calculations: the SAMPL4 challenge

As part of the SAMPL4 blind challenge, filtered AutoDock Vina ligand docking predictions and large scale binding energy distribution analysis method binding free energy calculations have been applied to the virtual screening of a focused library of candidate binders to the LEDGF site of the HIV integrase protein. The computational protocol leveraged docking and high level atomistic models to improve enrichment. The enrichment factor of our blind predictions ranked best among all of the computational submissions, and second best overall. This work represents to our knowledge the first example of the application of an all-atom physics-based binding free energy model to large scale virtual screening. A total of 285 parallel Hamiltonian replica exchange molecular dynamics absolute protein-ligand binding free energy simulations were conducted starting from docked poses. The setup of the simulations was fully automated, calculations were distributed on multiple computing resources and were completed in a 6-weeks period. The accuracy of the docked poses and the inclusion of intramolecular strain and entropic losses in the binding free energy estimates were the major factors behind the success of the method. Lack of sufficient time and computing resources to investigate additional protonation states of the ligands was a major cause of mispredictions. The experiment demonstrated the applicability of binding free energy modeling to improve hit rates in challenging virtual screening of focused ligand libraries during lead optimization.

Funnel metadynamics as accurate binding free-energy method

A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein-ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein-ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science.

Theory of binless multi-state free energy estimation with applications to protein-ligand binding

The weighted histogram analysis method (WHAM) is routinely used for computing free energies and expectations from multiple ensembles. Existing derivations of WHAM require observations to be discretized into a finite number of bins. Yet, WHAM formulas seem to hold even if the bin sizes are made arbitrarily small. The purpose of this article is to demonstrate both the validity and value of the multi-state Bennet acceptance ratio (MBAR) method seen as a binless extension of WHAM. We discuss two statistical arguments to derive the MBAR equations, in parallel to the self-consistency and maximum likelihood derivations already known for WHAM. We show that the binless method, like WHAM, can be used not only to estimate free energies and equilibrium expectations, but also to estimate equilibrium distributions. We also provide a number of useful results from the statistical literature, including the determination of MBAR estimators by minimization of a convex function. This leads to an approach to the computation of MBAR free energies by optimization algorithms, which can be more effective than existing algorithms. The advantages of MBAR are illustrated numerically for the calculation of absolute protein-ligand binding free energies by alchemical transformations with and without soft-core potentials. We show that binless statistical analysis can accurately treat sparsely distributed interaction energy samples as obtained from unmodified interaction potentials that cannot be properly analyzed using standard binning methods. This suggests that binless multi-state analysis of binding free energy simulations with unmodified potentials offers a straightforward alternative to the use of soft-core potentials for these alchemical transformations.

A water-swap reaction coordinate for the calculation of absolute protein–ligand binding free energies

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.

Calculation of absolute protein-ligand binding free energy using distributed replica sampling

Distributed replica sampling [T. Rodinger et al., J. Chem. Theory Comput. 2, 725 (2006)] is a simple and general scheme for Boltzmann sampling of conformational space by computer simulation in which multiple replicas of the system undergo a random walk in reaction coordinate or temperature space. Individual replicas are linked through a generalized Hamiltonian containing an extra potential energy term or bias which depends on the distribution of all replicas, thus enforcing the desired sampling distribution along the coordinate or parameter of interest regardless of free energy barriers. In contrast to replica exchange methods, efficient implementation of the algorithm does not require synchronicity of the individual simulations. The algorithm is inherently suited for large-scale simulations using shared or heterogeneous computing platforms such as a distributed network. In this work, we build on our original algorithm by introducing Boltzmann-weighted jumping, which allows moves of a larger magnitude and thus enhances sampling efficiency along the reaction coordinate. The approach is demonstrated using a realistic and biologically relevant application; we calculate the standard binding free energy of benzene to the L99A mutant of T4 lysozyme. Distributed replica sampling is used in conjunction with thermodynamic integration to compute the potential of mean force for extracting the ligand from protein and solvent along a nonphysical spatial coordinate. Dynamic treatment of the reaction coordinate leads to faster statistical convergence of the potential of mean force than a conventional static coordinate, which suffers from slow transitions on a rugged potential energy surface.

Calculation of absolute protein–ligand binding free energy from computer simulations

A general methodology for calculating the equilibrium binding constant of a flexible ligand to a protein receptor is formulated on the basis of potentials of mean force. The overall process is decomposed into several stages that can be computed separately: the free ligand in the bulk is first restrained into the conformation it adopts in the bound state, position, and orientation by applying biasing potentials, then it is translated into the binding site, where it is released completely. The conformational restraining potential is based on the root-mean-square deviation of the peptide coordinates relative to its average conformation in the bound complex. Free energy contributions from each stage are calculated by means of free energy perturbation potential of mean force techniques by using appropriate order parameters. The present approach avoids the need to decouple the ligand from its surrounding (bulk solvent and receptor protein) as is traditionally performed in the double-decoupling scheme. It is believed that the present formulation will be particularly useful when the solvation free energy of the ligand is very large. As an application, the equilibrium binding constant of the phosphotyrosine peptide pYEEI to the Src homology 2 domain of human Lck has been calculated. The results are in good agreement with experimental values.