BLEEP—potential of mean force describing protein–ligand interactions: I. Generating potential

We have developed BLEEP (biomolecular ligand energy evaluation protocol), an atomic level potential of mean force (PMF) describing protein–ligand interactions. The pair potentials for BLEEP have been derived from high-resolution X-ray structures of protein–ligand complexes in the Brookhaven Protein Data Bank (PDB), with a careful treatment of homology. The use of a broad variety of protein–ligand structures in the derivation phase gives BLEEP more general applicability than previous potentials, which have been based on limited classes of complexes, and thus represents a significant step forward. We calculate the distance distributions in protein–ligand interactions for all 820 possible pairs that can be chosen from our set of 40 different atom types, including polar hydrogen. We then use a reverse Boltzmann methodology to convert these into energy-like pair potential functions. Two versions of BLEEP are calculated, one including and one excluding interactions between protein and water. The pair potentials are found to have the expected forms; polar and hydrogen bonding interactions show minima at short range, around 3.0 Å, whereas a typical hydrophobic interaction is repulsive at this distance, with values above 4.0 Å being preferred. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1165–1176, 1999     

Evaluation of a knowledge‐based potential of mean force for scoring docked protein–ligand complexes

The Biomolecular Ligand Energy Evaluation Protocol (BLEEP) is a knowledge‐based potential derived from high‐resolution X‐ray structures of protein–ligand complexes. The performance of this potential in ranking the hypothetical structures resulting from a docking study has been evaluated using fifteen protein–ligand complexes from the Protein Data Bank. In the majority of complexes BLEEP was successful in identifying the native (experimental) binding mode or an alternative of low rms deviation (from the native) as the lowest in energy. Overall BLEEP is slightly better than the DOCK energy function in discriminating native‐like modes. Even when alternative binding modes rank lower than the native structure, a reasonable energy is assigned to the latter. Breaking down the BLEEP scores into the atom–atom contributions reveals that this type of potential is grossly dominated by longer range interactions (>5 Å), which makes it relatively insensitive to small local variations in the binding site. However, despite this limitation, the lack, at present, of accurate protein–ligand potentials means that BLEEP is a promising approach to improve the filtering of structures resulting from docking programs. Moreover, BLEEP should improve with the continuously increasing number of complexes available in the PDB. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 673–688, 2001     

Toward quantitative estimates of binding affinities for protein–ligand systems involving large inhibitor compounds: A steered molecular dynamics simulation route

Understanding binding mechanisms between enzymes and potential inhibitors and quantifying protein – ligand affinities in terms of binding free energy is of primary importance in drug design studies. In this respect, several approaches based on molecular dynamics simulations, often combined with docking techniques, have been exploited to investigate the physicochemical properties of complexes of pharmaceutical interest. Even if the geometric properties of a modeled protein – ligand complex can be well predicted by computational methods, it is still challenging to rank with chemical accuracy a series of ligand analogues in a consistent way. In this article, we face this issue calculating relative binding free energies of a focal adhesion kinase, an important target for the development of anticancer drugs, with pyrrolopyrimidine‐based ligands having different inhibitory power. To this aim, we employ steered molecular dynamics simulations combined with nonequilibrium work theorems for free energy calculations. This technique proves very powerful when a series of ligand analogues is considered, allowing one to tackle estimation of protein – ligand relative binding free energies in a reasonable time. In our cases, the calculated binding affinities are comparable with those recovered from experiments by exploiting the Michaelis – Menten mechanism with a competitive inhibitor.     

Theoretical calculations of homoconjugation equilibrium constants in systems modeling acid-base interactions in side chains of biomolecules using the potential of mean force

The potentials of mean force (PMFs) were determined for systems forming cationic and anionic homocomplexes composed of acetic acid, phenol, isopropylamine, n-butylamine, imidazole, and 4(5)-methylimidazole, and their conjugated bases or acids, respectively, in three solvents with different polarity and hydrogen-bonding propensity: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water (H(2)O). For each pair and each solvent a series of umbrella-sampling molecular dynamics simulations with the AMBER force field, explicit solvent, and counterions added to maintain a zero net charge of a system were carried out and the PMF was calculated by using the Weighted Histogram Analysis Method (WHAM). Subsequently, homoconjugation-equilibrium constants were calculated by numerical integration of the respective PMF profiles. In all cases but imidazole stable homocomplexes were found to form in solution, which was manifested as the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated homoconjugation constants were found to be greater for complexes with the OHO bridge (acetic acid and phenol) than with the NHN bridge and they were found to decrease with increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H(2)O), both facts being in agreement with the available experimental data. It was also found that interactions with counterions are manifested as the broadening of the contact minimum or appearance of additional minima in the PMF profiles of the acetic acid-acetate, phenol/phenolate system in acetonitrile, and the 4(5)-methylimidazole/4(5)-methylimidzole cation conjugated base system in dimethyl sulfoxide.     

New angle‐dependent potential energy function for backbone–backbone hydrogen bond in protein–protein interactions

Backbone–backbone hydrogen bonds (BBHBs) are one of the most abundant interactions at the interface of protein–protein complex. Here, we propose an angle‐dependent potential energy function for BBHB based on density functional theory (DFT) calculations and the operation of a genetic algorithm to find the optimal parameters in the potential energy function. The angular part of the energy funtion is assumed to be the product of the power series of sine and cosine functions with respect to the two angles associated with BBHB. Two radial functions are taken into account in this study: Morse and Leonard‐Jones 12‐10 potential functions. Of these two functions under consideration, the former is found to be more accurate than the latter in terms of predicting the binding energies obtained from DFT calculations. The new HB potential function also compares well with the knowledge‐based potential derived by applying Boltzmann statistics for a variety of protein–protein complexes in protein data bank. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effect of interprotein polarization on protein–protein binding energy

Molecular dynamics simulation in explicit water for the binding of the benchmark barnase‐barstar complex was carried out to investigate the effect polarization of interprotein hydrogen bonds on its binding free energy. Our study is based on the AMBER force field but with polarized atomic charges derived from fragment quantum mechanical calculation for the protein complex. The quantum‐derived atomic charges include the effect of polarization of interprotein hydrogen bonds, which was absent in the standard force fields that were used in previous theoretical calculations of barnase‐barstar binding energy. This study shows that this polarization effect impacts both the static (electronic) and dynamic interprotein electrostatic interactions and significantly lowers the free energy of the barnase‐barstar complex. © 2012 Wiley Periodicals, Inc.     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Update of the ATTRACT force field for the prediction of protein–protein binding affinity

Determining the protein–protein interactions is still a major challenge for molecular biology. Docking protocols has come of age in predicting the structure of macromolecular complexes. However, they still lack accuracy to estimate the binding affinities, the thermodynamic quantity that drives the formation of a complex. Here, an updated version of the protein–protein ATTRACT force field aiming at predicting experimental binding affinities is reported. It has been designed on a dataset of 218 protein–protein complexes. The correlation between the experimental and predicted affinities reaches 0.6, outperforming most of the available protocols. Focusing on a subset of rigid and flexible complexes, the performance raises to 0.76 and 0.69, respectively. © 2017 Wiley Periodicals, Inc.     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.     

Delineating Protein–Protein Curvilinear Dissociation Pathways and Energetics with Naïve Multiple-Walker Umbrella Sampling Simulations

The protein–protein interaction energetics can be obtained by calculating the potential of mean force (PMF) from umbrella sampling (US) simulations, in which samplings are often enhanced along a predefined vector as the reaction coordinate. However, any slight change in the vector may significantly vary the calculated PMF, and therefore the energetics using a random choice of vector may mislead. A non-predefined curve path-based sampling enhancement approach is a natural alternative, but was relatively less explored for protein–protein systems. In this work, dissociation of the barnase–barstar complex is simulated by implementing non-predefined curvilinear pathways in US simulations. A simple variational principle is applied to determine the lower bound PMF, which could be used to derive the standard free energy of binding. Two major dissociation pathways, which include interactions with the RNA-binding loop and the Val 36 to Gly 40 loop, are observed. Further, the proposed approach was used to discriminate the decoys from protein–protein docking studies. © 2019 Wiley Periodicals, Inc.     

Including ligand‐induced protein flexibility into protein tunnel prediction

In proteins with buried active sites, understanding how ligands migrate through the tunnels that connect the exterior of the protein to the active site can shed light on substrate specificity and enzyme function. A growing body of evidence highlights the importance of protein flexibility in the binding site on ligand binding; however, the influence of protein flexibility throughout the body of the protein during ligand entry and egress is much less characterized. We have developed a novel tunnel prediction and evaluation method named IterTunnel, which includes the influence of ligand‐induced protein flexibility, guarantees ligand egress, and provides detailed free energy information as the ligand proceeds along the egress route. IterTunnel combines geometric tunnel prediction with steered molecular dynamics in an iterative process to identify tunnels that open as a result of ligand migration and calculates the potential of mean force of ligand egress through a given tunnel. Applying this new method to cytochrome P450 2B6, we demonstrate the influence of protein flexibility on the shape and accessibility of tunnels. More importantly, we demonstrate that the ligand itself, while traversing through a tunnel, can reshape tunnels due to its interaction with the protein. This process results in the exposure of new tunnels and the closure of preexisting tunnels as the ligand migrates from the active site. © 2014 Wiley Periodicals, Inc.     

A comparison of methods to compute the potential of mean force.

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.     

Methodology for the calculation of the potential of mean force for a cation-pi complex in water.

We report potential of mean force (PMF) calculations on the interaction between the p-sulfonatocalix[4]arene and a monovalent cation (Cs(+)). It has been recently shown from microcalorimetry and (133)Cs NMR experiments that the association with Cs(+) is governed by favourable cation-pi interactions and is characterized by the insertion of the cation into the cavity of the macrocycle. We show that the PMF calculation based upon a classical model is not able to reproduce both the thermodynamic properties of association and the insertion of the cation. In order to take into account the different contributions of the cation-pi interactions, we develop a new methodology consisting of changing the standard PMF by an additional contribution resulting from quantum calculations. The calculated thermodynamic properties of association are thus in line with the microcalorimetry and (133)Cs NMR experiments and the structure of the complex at the Gibbs free-energy minimum shows the insertion of the cation into the cavity of the calixarene.     

Theoretical thermodynamic study of the adenine–thymine tautomeric equilibrium: Electronic structure calculations and steered molecular dynamic simulations

Free energy of the tautomeric equilibrium A‐T ? A*‐T* between the canonical and noncanonical DNA base equilibrium in aqueous solution was theoretically determined by applying electronic structure methods (at the M06‐2X‐PCM/6‐311++G(d,p) level) and steered molecular dynamic simulations. Concerted and stepwise mechanisms were considered for the double proton transfer in an effort to explain the anomalous behavior of this system where an unfavorable process without a transition state can be observed depending on the level of calculation used. Of the different mechanisms used in the simulations, the stepwise mechanism, in which the first step implies the transference of a proton from thymine to adenine, and a second step with the transference of a different proton from adenine to thymine, was the only one that showed two transition states and a reaction intermediate. However, a concerted and stepwise mechanism has similar kinetic and thermodynamic behavior, with similar reaction and activation energies. Simple proton transfer was more favorable for the transference of the hydrogen from the adenine to the thymine. The inclusion of an aqueous medium in this study only slightly modified these energies, but the barrier energy was higher when the solvent was described as a discrete medium. Transition states and intermediate structures were analyzed at molecular dynamic level.     

Nonspecific interaction forces at water-membrane interface by forced molecular dynamics simulations

Nonspecific interactions are the main driving forces for the behavior of molecules with great affinity for biologic membranes. To investigate not only the molecular details of these interactions but to estimate their magnitude as well, the theoretical method of Forced Molecular Dynamics Simulations, based on the Atomic Force Spectroscopy experimental technique, was applied. In this approach, an additional one-dimensional elastic force, representing the cantilever probe, was incorporated to the force field of a Molecular Dynamics computational program. This force represents a spring fixed on one end to a selected atom of the molecule; the other end of the spring is displaced at constant velocity to pull the molecule out of the membrane. The force experimented by the molecule due to the spring, is proportional to the spring elongation relative to its equilibrium position. This value is registered during the entire simulation, and its maximum value will determine the molecule-membrane interaction force. Nonexplicit medium simulations were carried out. Polar and apolar media were considered according to their polarizability degree and a specific dielectric constant value was assigned. In this approach, the membrane was considered as the apolar region limited by two flat surfaces with a polar aqueous medium. The potential energy discontinuity at the interfaces was smoothed by considering the polarization-induced effects using the image method. The results of this methodology are presented using a small system, a single Alanine amino acid model, which enables extended simulations in a microsecond time scale. The confinement of this amino acid at the interface reduces its degrees of freedom and forces it to adopt one of the six defined conformations. A correlation between these stable structures at the water-membrane interface and the interaction force value was determined.     

Binding structures of tri‐N‐acetyl‐β‐glucosamine in hen egg white lysozyme using molecular dynamics with a polarizable force field

Lysozyme is a well‐studied enzyme that hydrolyzes the β‐(1,4)‐glycosidic linkage of N‐acetyl‐β‐glucosamine (NAG)_n oligomers. The active site of hen egg‐white lysozyme (HEWL) is believed to consist of six subsites, A‐F that can accommodate six sugar residues. We present studies exploring the use of polarizable force fields in conjunction with all‐atom molecular dynamics (MD) simulations to analyze binding structures of complexes of lysozyme and NAG trisaccharide, (NAG)₃. MD trajectories are applied to analyze structures and conformation of the complex as well as protein–ligand interactions, including the hydrogen‐bonding network in the binding pocket. Two binding modes (ABC and BCD) of (NAG)₃ are investigated independently based on a fixed‐charge model and a polarizable model. We also apply molecular mechanics with generalized born and surface area (MM‐GBSA) methods based on MD using both nonpolarizable and polarizable force fields to compute binding free energies. We also study the correlation between root‐mean‐squared deviation and binding free energies of the wildtype and W62Y mutant; we find that for this prototypical system, approaches using the MD trajectories coupled with implicit solvent models are equivalent for polarizable and fixed‐charge models. © 2012 Wiley Periodicals, Inc.     

Semiempirical calculations of binding enthalpy for protein–ligand complexes

A systematic semiempirical quantum mechanical study of the interactions between proteins and ligands has been performed to determine the ability of this approach for the accurate estimation of the enthalpic contribution to the binding free energy of the protein–ligand systems. This approach has been applied for eight test protein–ligand complexes with experimentally known binding enthalpies. The calculations were performed using the semiempirical PM3 approach incorporated in the MOPAC 97, ZAVA originally elaborated in Algodign, and MOPAC 2002 with MOZYME facility packages. Special attention was paid to take into account structural water molecules, which were located in the protein–ligand binding site. It was shown that the results of binding enthalpy calculations fit experimental data within ～2 kcal/mol in the presented approach. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004