Calculation of Relative Binding Free Energy in the Water-Filled Active Site of Oligopeptide-Binding Protein A

Simulated pressure changes in LacI suggest a link between hydration and functional conformational changes

The functions of many proteins are associated with interconversions among conformational substates. However, these substates can be difficult to measure experimentally, and determining contributions from hydration changes can be especially difficult. Here, we assessed the use of pressure perturbations to sample the substates accessible to the Escherichia coli lactose repressor protein (LacI) in various liganded forms. In the presence of DNA, the regulatory domain of LacI adopts an Open conformation that, in the absence of DNA, changes to a Closed conformation. Increasing the simulation pressure prevented the transition from an Open to a Closed conformation, in a similar manner to the binding of DNA and anti-inducer, ONPF. The results suggest the hydration of specific residues play a significant role in determining the population of different LacI substates and that simulating pressure perturbation could be useful for assessing the role of hydration changes that accompany functionally-relevant amino acid substitutions.

Accelerated Enveloping Distribution Sampling to Probe the Presence of Water Molecules

Determining the presence of water molecules at protein-ligand interfaces is still a challenging task in free-energy calculations. The inappropriate placement of water molecules results in the stabilization of wrong conformational orientations of the ligand. With classical alchemical perturbation methods, such as thermodynamic integration (TI), it is essential to know the amount of water molecules in the active site of the respective ligands. However, the resolution of the crystal structure and the correct assignment of the electron density do not always lead to a clear placement of water molecules. In this work, we apply the one-step perturbation method named accelerated enveloping distribution sampling (AEDS) to determine the presence of water molecules in the active site by probing them in a fast and straightforward way. Based on these results, we combined the AEDS method with standard TI to calculate accurate binding free energies in the presence of buried water molecules. The main idea is to perturb the water molecules with AEDS such that they are allowed to alternate between regular water molecules and non-interacting dummy particles while treating the ligand with TI over an alchemical pathway. We demonstrate the use of AEDS to probe the presence of water molecules for six different test systems. For one of these, previous calculations showed difficulties to reproduce the experimental binding free energies, and here, we use the combined TI-AEDS approach to tackle these issues.

Elucidation of a Thermodynamical Feature Attributed to Substrate Binding to the Prokaryotic H+/Oligopeptide Cotransporter YdgR with Calorimetric Analysis: The Substrate Binding Driven by the Change in Entropy Implies the Release of Bound Water Molecules from the Binding Pocket

Here, we have elucidated the substrate recognition mechanism by a prokaryotic H⁺/oligopeptide cotransporter, YdgR, using isothermal titration calorimetry. Under acidic conditions (pH 6.0), the binding of a dipeptide, Val-Ala, to YdgR elicited endothermic enthalpy, which compensated for the increase in entropy due to dipeptide binding. A series of dipeptides were used in the binding titration. The dipeptides represent Val-X and X-Val, where X is Ala, Ser, Val, Tyr, or Phe. Most dipeptides revealed endothermic enthalpy, which was completely compensated by the increase in entropy due to dipeptide binding. The change in enthalpy due to binding correlated well with the change in entropy, whereas the Gibbs free energy involved in the binding of the dipeptide to YdgR remained unchanged irrespective of dipeptide sequences, implying that the binding reaction was driven by entropy, that is, the release of bound water molecules in the binding pocket. It is also important to clarify that, based on the prediction of water molecules in the ligand-binding pocket of YdgR, the release of three bound water molecules in the putative substrate binding pocket occurred through binding to YdgR. In the comparison of Val-X and X-Val dipeptides, the N-terminal region of the binding pocket might contain more bound water molecules than the C-terminal region. In light of these findings, we suggest that bound water molecules might play an important role in substrate recognition and binding by YdgR.

WaterKit: Thermodynamic Profiling of Protein Hydration Sites

Water desolvation is one of the key components of the free energy of binding of small molecules to their receptors. Thus, understanding the energetic balance of solvation and desolvation resulting from individual water molecules can be crucial when estimating ligand binding, especially when evaluating different molecules and poses as done in High-Throughput Virtual Screening (HTVS). Over the most recent decades, several methods were developed to tackle this problem, ranging from fast approximate methods (usually empirical functions using either discrete atom-atom pairwise interactions or continuum solvent models) to more computationally expensive and accurate ones, mostly based on Molecular Dynamics (MD) simulations, such as Grid Inhomogeneous Solvation Theory (GIST) or Double Decoupling. On one hand, MD-based methods are prohibitive to use in HTVS to estimate the role of waters on the fly for each ligand. On the other hand, fast and approximate methods show an unsatisfactory level of accuracy, with low agreement with results obtained with the more expensive methods. Here we introduce WaterKit, a new grid-based sampling method with explicit water molecules to calculate thermodynamic properties using the GIST method. Our results show that the discrete placement of water molecules is successful in reproducing the position of crystallographic waters with very high accuracy, as well as providing thermodynamic estimates with accuracy comparable to more expensive MD simulations. Unlike these methods, WaterKit can be used to analyze specific regions on the protein surface, (such as the binding site of a receptor), without having to hydrate and simulate the whole receptor structure. The results show the feasibility of a general and fast method to compute thermodynamic properties of water molecules, making it well-suited to be integrated in high-throughput pipelines such as molecular docking.

Enhancing sampling of water rehydration upon ligand binding using variants of grand canonical Monte Carlo

Water plays an important role in mediating protein-ligand interactions. Water rearrangement upon a ligand binding or modification can be very slow and beyond typical timescales used in molecular dynamics (MD) simulations. Thus, inadequate sampling of slow water motions in MD simulations often impairs the accuracy of the accuracy of ligand binding free energy calculations. Previous studies suggest grand canonical Monte Carlo (GCMC) outperforms normal MD simulations for water sampling, thus GCMC has been applied to help improve the accuracy of ligand binding free energy calculations. However, in prior work we observed protein and/or ligand motions impaired how well GCMC performs at water rehydration, suggesting more work is needed to improve this method to handle water sampling. In this work, we applied GCMC in 21 protein-ligand systems to assess the performance of GCMC for rehydrating buried water sites. While our results show that GCMC can rapidly rehydrate all selected water sites for most systems, it fails in five systems. In most failed systems, we observe protein/ligand motions, which occur in the absence of water, combine to close water sites and block instantaneous GCMC water insertion moves. For these five failed systems, we both extended our GCMC simulations and tested a new technique named grand canonical nonequilibrium candidate Monte Carlo (GCNCMC). GCNCMC combines GCMC with the nonequilibrium candidate Monte Carlo (NCMC) sampling technique to improve the probability of a successful water insertion/deletion. Our results show that GCNCMC and extended GCMC can rehydrate all target water sites for three of the five problematic systems and GCNCMC is more efficient than GCMC in two out of the three systems. In one system, only GCNCMC can rehydrate all target water sites, while GCMC fails. Both GCNCMC and GCMC fail in one system. This work suggests this new GCNCMC method is promising for water rehydration especially when protein/ligand motions may block water insertion/removal.

Enhancing Sampling of Water Rehydration on Ligand Binding: A Comparison of Techniques

Water often plays a key role in protein structure, molecular recognition, and mediating protein-ligand interactions. Thus, free energy calculations must adequately sample water motions, which often proves challenging in typical MD simulation time scales. Thus, the accuracy of methods relying on MD simulations ends up limited by slow water sampling. Particularly, as a ligand is removed or modified, bulk water may not have time to fill or rearrange in the binding site. In this work, we focus on several molecular dynamics (MD) simulation-based methods attempting to help rehydrate buried water sites: BLUES, using nonequilibrium candidate Monte Carlo (NCMC); grand, using grand canonical Monte Carlo (GCMC); and normal MD. We assess the accuracy and efficiency of these methods in rehydrating target water sites. We selected a range of systems with varying numbers of waters in the binding site, as well as those where water occupancy is coupled to the identity or binding mode of the ligand. We analyzed the rehydration of buried water sites in binding pockets using both clustering of trajectories and direct analysis of electron density maps. Our results suggest both BLUES and grand enhance water sampling relative to normal MD and grand is more robust than BLUES, but also that water sampling remains a major challenge for all of the methods tested. The lessons we learned for these methods and systems are discussed.

Efficient In Silico Saturation Mutagenesis of a Member of the Caspase Protease Family

Rational-design methods have proven to be a valuable toolkit in the field of protein design. Numerical approaches such as free-energy calculations or QM/MM methods are fit to widen the understanding of a protein-sequence space but require large amounts of computational time and power. Here, we apply an efficient method for free-energy calculations that combines the one-step perturbation (OSP) with the third-power-fitting (TPF) approach. It is fit to calculate full free energies of binding from three different end states only. The nonpolar contribution to the free energies are calculated for a set of chosen amino acids from a single simulation of a judiciously chosen reference state. The electrostatic contributions, on the other hand, are predicted from simulations of the neutral and charged end states of the individual amino acids. We used this method to perform in silico saturation mutagenesis of two sites in human Caspase-2. We calculated relative binding free energies toward two different substrates that differ in their P1' site and in their affinity toward the unmutated protease. Although being approximate, our approach showed very good agreement upon validation against experimental data. 76% of the predicted relative free energies of amino acid mutations was found to be true positives or true negatives. We observed that this method is fit to discriminate amino acid mutations because the rate of false negatives is very low (<1.5%). The approach works better for a substrate with medium/low affinity with a Matthews correlation coefficient (MCC) of 0.63, whereas for a substrate with very low affinity, the MCC was 0.38. In all cases, the combined TPF + OSP approach outperformed the linear interaction energy method.

Enhancing water sampling of buried binding sites using nonequilibrium candidate Monte Carlo

Water molecules can be found interacting with the surface and within cavities in proteins. However, water exchange between bulk and buried hydration sites can be slow compared to simulation timescales, thus leading to the inefficient sampling of the locations of water. This can pose problems for free energy calculations for computer-aided drug design. Here, we apply a hybrid method that combines nonequilibrium candidate Monte Carlo (NCMC) simulations and molecular dynamics (MD) to enhance sampling of water in specific areas of a system, such as the binding site of a protein. Our approach uses NCMC to gradually remove interactions between a selected water molecule and its environment, then translates the water to a new region, before turning the interactions back on. This approach of gradual removal of interactions, followed by a move and then reintroduction of interactions, allows the environment to relax in response to the proposed water translation, improving acceptance of moves and thereby accelerating water exchange and sampling. We validate this approach on several test systems including the ligand-bound MUP-1 and HSP90 proteins with buried crystallographic waters removed. We show that our BLUES (NCMC/MD) method enhances water sampling relative to normal MD when applied to these systems. Thus, this approach provides a strategy to improve water sampling in molecular simulations which may be useful in practical applications in drug discovery and biomolecular design.

Accounting for the Central Role of Interfacial Water in Protein-Ligand Binding Free Energy Calculations

Rigorous binding free energy methods in drug discovery are growing in popularity because of a combination of methodological advances, improvements in computer hardware, and workflow automation. These calculations typically use molecular dynamics (MD) to sample from the Boltzmann distribution of conformational states. However, when part or all of the binding sites is inaccessible to the bulk solvent, the time needed for water molecules to equilibrate between bulk solvent and the binding site can be well beyond what is practical with standard MD. This sampling limitation is problematic in relative binding free energy calculations, which compute the reversible work of converting ligand 1 to ligand 2 within the binding site. Thus, if ligand 1 is smaller and/or more polar than ligand 2, the perturbation may allow additional water molecules to occupy a region of the binding site. However, this change in hydration may not be captured by standard MD simulations and may therefore lead to errors in the computed free energy. We recently developed a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between bulk solvent and buried cavities, while sampling from the intended distribution of states. Here, we report on the use of this approach in the context of alchemical binding free energy calculations. We find that using MC/MD markedly improves the accuracy of the calculations and also reduces hysteresis between the forward and reverse perturbations, relative to matched calculations using only MD with or without the crystallographic water molecules. The present method is available for use in AMBER simulation software.

Accounting for the Central Role of Interfacial Water in Protein-Ligand Binding Free Energy Calculations

Rigorous binding free energy methods in drug discovery are growing in popularity because of a combination of methodological advances, improvements in computer hardware, and workflow automation. These calculations typically use molecular dynamics (MD) to sample from the Boltzmann distribution of conformational states. However, when part or all of the binding sites is inaccessible to the bulk solvent, the time needed for water molecules to equilibrate between bulk solvent and the binding site can be well beyond what is practical with standard MD. This sampling limitation is problematic in relative binding free energy calculations, which compute the reversible work of converting ligand 1 to ligand 2 within the binding site. Thus, if ligand 1 is smaller and/or more polar than ligand 2, the perturbation may allow additional water molecules to occupy a region of the binding site. However, this change in hydration may not be captured by standard MD simulations and may therefore lead to errors in the computed free energy. We recently developed a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between bulk solvent and buried cavities, while sampling from the intended distribution of states. Here, we report on the use of this approach in the context of alchemical binding free energy calculations. We find that using MC/MD markedly improves the accuracy of the calculations and also reduces hysteresis between the forward and reverse perturbations, relative to matched calculations using only MD with or without the crystallographic water molecules. The present method is available for use in AMBER simulation software.

Dissecting the Energetics of Intrinsically Disordered Proteins via a Hybrid Experimental and Computational Approach

Intrinsically disordered proteins (IDPs) play important roles in biology, but little is known about the energetics of their inter-residue interactions. Methods that have been successfully applied to analyze the energetics of globular proteins are not applicable to the fluctuating partially ordered ensembles populated by IDPs. A combined computational experimental strategy is introduced for analyzing the energetic role of individual residues in the free state of IDPs. The approach combines experimental measurements of the binding of wild-type and mutant IDPs to their partners with alchemical free energy calculations of the structured complexes. These data allow quantitative information to be deduced about the free state via a thermodynamic cycle. The approach is validated by the analysis of the effects of mutations upon the binding free energy of the ovomucoid inhibitor third binding domain to its partners and is applied to the C-terminal domain of the measles virus nucleoprotein, a 125-residue IDP involved in the RNA transcription and replication of measles virus. The analysis reveals significant inter-residue interactions in the unbound IDP and suggests a biological role for them. The work demonstrates that advances in force fields and computational hardware have now led to the point where it is possible to develop methods, which integrate experimental and computational techniques to reveal insights that cannot be studied using either technique alone.

Water in protein hydration and ligand recognition

This review describes selected basics of water in biomolecular recognition. We focus on a qualitative understanding of the most important physical aspects, how these change in magnitude between bulk water and protein environment, and how the roles that water plays for proteins arise from them. These roles include mechanical support, thermal coupling, dielectric screening, mass and charge transport, and the competition with a ligand for the occupation of a binding site. The presence or absence of water has ramifications that range from the thermodynamic binding signature of a single ligand up to cellular survival. The large inhomogeneity in water density, polarity and mobility around a solute is hard to assess in experiment. This is a source of many difficulties in the solvation of protein models and computational studies that attempt to elucidate or predict ligand recognition. The influence of water in a protein binding site on the experimental enthalpic and entropic signature of ligand binding is still a point of much debate. The strong water‐water interaction in enthalpic terms is counteracted by a water molecule's high mobility in entropic terms. The complete arrest of a water molecule's mobility sets a limit on the entropic contribution of a water displacement process, while the solvent environment sets limits on ligand reactivity.

Insights into the Molecular Mechanisms of Protein-Ligand Interactions by Molecular Docking and Molecular Dynamics Simulation: A Case of Oligopeptide Binding Protein

Protein-ligand interactions are a necessary prerequisite for signal transduction, immunoreaction, and gene regulation. Protein-ligand interaction studies are important for understanding the mechanisms of biological regulation, and they provide a theoretical basis for the design and discovery of new drug targets. In this study, we analyzed the molecular interactions of protein-ligand which was docked by AutoDock 4.2 software. In AutoDock 4.2 software, we used a new search algorithm, hybrid algorithm of random drift particle swarm optimization and local search (LRDPSO), and the classical Lamarckian genetic algorithm (LGA) as energy optimization algorithms. The best conformations of each docking algorithm were subjected to molecular dynamic (MD) simulations to further analyze the molecular mechanisms of protein-ligand interactions. Here, we analyze the binding energy between protein receptors and ligands, the interactions of salt bridges and hydrogen bonds in the docking region, and the structural changes during complex unfolding. Our comparison of these complexes highlights differences in the protein-ligand interactions between the two docking methods. It also shows that salt bridge and hydrogen bond interactions play a crucial role in protein-ligand stability. The present work focuses on extracting the deterministic characteristics of docking interactions from their dynamic properties, which is important for understanding biological functions and determining which amino acid residues are crucial to docking interactions.

Comparison of free-energy methods using a tripeptide-water model system

We investigate the ability of several free-energy calculation methods to combine two alchemical changes. We use Bennett acceptance ratio (BAR), thermodynamic integration (TI), extended TI (X-TI), and enveloping distribution sampling (EDS) to perturb a water molecule, which is restrained to an amino acid that is also being perturbed. In addition to these pairwise methods, we present two two-dimensional approaches, EDS-TI and two-dimensional TI (2D-TI). We compare feasibility, efficiency and usability of these methods in regard to our simple model system, which mimics the displacement of a water molecule in the active site of a protein on residue mutation. The correct treatment of structural water has been shown to greatly aid binding affinity calculations in some cases that remained elusive otherwise. This is of broad interest in, for example, drug design, and we conclude that thus far, the pairwise method BAR and also the newer X-TI remain the most suitable methods to treat this problem as long as few end states are involved. © 2018 Wiley Periodicals, Inc.

Prediction of Ordered Water Molecules in Protein Binding Sites from Molecular Dynamics Simulations: The Impact of Ligand Binding on Hydration Networks

Water plays a major role in ligand binding and is attracting increasing attention in structure-based drug design. Water molecules can make large contributions to binding affinity by bridging protein–ligand interactions or by being displaced upon complex formation, but these phenomena are challenging to model at the molecular level. Herein, networks of ordered water molecules in protein binding sites were analyzed by clustering of molecular dynamics (MD) simulation trajectories. Locations of ordered waters (hydration sites) were first identified from simulations of high resolution crystal structures of 13 protein–ligand complexes. The MD-derived hydration sites reproduced 73% of the binding site water molecules observed in the crystal structures. If the simulations were repeated without the cocrystallized ligands, a majority (58%) of the crystal waters in the binding sites were still predicted. In addition, comparison of the hydration sites obtained from simulations carried out in the absence of ligands to those identified for the complexes revealed that the networks of ordered water molecules were preserved to a large extent, suggesting that the locations of waters in a protein–ligand interface are mainly dictated by the protein. Analysis of >1000 crystal structures showed that hydration sites bridged protein–ligand interactions in complexes with different ligands, and those with high MD-derived occupancies were more likely to correspond to experimentally observed ordered water molecules. The results demonstrate that ordered water molecules relevant for modeling of protein–ligand complexes can be identified from MD simulations. Our findings could contribute to development of improved methods for structure-based virtual screening and lead optimization.

Saturation Mutagenesis by Efficient Free-Energy Calculation

Single-point mutations in proteins can greatly influence protein stability, binding affinity, protein function or its expression per se. Here, we present accurate and efficient predictions of the free energy of mutation of amino acids. We divided the complete mutational free energy into an uncharging step, which we approximate by a third-power fitting (TPF) approach, and an annihilation step, which we approximate using the one-step perturbation (OSP) method. As a diverse set of test systems, we computed the solvation free energy of all amino acid side chain analogues and obtained an excellent agreement with thermodynamic integration (TI) data. Moreover, we calculated mutational free energies in model tripeptides and established an efficient protocol involving a single reference state. Again, the approximate methods agreed excellently with the TI references, with a root-mean-square error of only 3.6 kJ/mol over 17 mutations. Our combined TPF+OSP approach does show not only a very good agreement but also a 2-fold higher efficiency than full blown TI calculations.

Effective lead optimization targeting the displacement of bridging receptor–ligand water molecules

Enhancing the binding affinities of ligands by means of lead modifications that displace bridging water molecules at protein–ligand interfaces is an important and widely studied lead optimization strategy.

Free-energy calculations of residue mutations in a tripeptide using various methods to overcome inefficient sampling

Previous free-energy calculations have shown that the seemingly simple transformation of the tripeptide KXK to KGK in water holds some unobvious challenges concerning the convergence of the forward and backward thermodynamic integration processes (i.e., hysteresis). In the current study, the central residue X was either alanine, serine, glutamic acid, lysine, phenylalanine, or tyrosine. Interestingly, the transformation from alanine to glycine yielded the highest hysteresis in relation to the extent of the chemical change of the side chain. The reason for that could be attributed to poor sampling of φ2 /ψ2 dihedral angles along the transformation. Altering the nature of alanine's Cβ atom drastically improved the sampling and at the same time led to the identification of high energy barriers as cause for it. Consequently, simple strategies to overcome these barriers are to increase simulation time (computationally expensive) or to use enhanced sampling techniques such as Hamiltonian replica exchange molecular dynamics and one-step perturbation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.