A Note on the Standard State's Binding Free Energy

Phosphate uptake in PhoX: Molecular mechanisms

PhoX is a high-affinity phosphate binding protein, present in Xanthomonas citri, a phytopathogen responsible for the citrus canker disease. Performing molecular dynamics simulations and different types of computational analyses, we study the molecular mechanisms at play in relation to phosphate binding, revealing the global functioning of the protein: PhoX naturally oscillates along its global normal modes, which allow it to explore both bound and unbound conformations, eventually attracting a nearby negative phosphate ion to the highly positive electrostatic potential on its surface, particularly close to the binding pocket. There, several hydrogen bonds are formed with the two main domains of the structure. Phosphate creates, in this way, a strong bridge that connects the domains, keeping itself between them, in a tight closed conformation, explaining its high binding affinity.

Modeling Peptide Nucleic Acid Binding Enthalpies Using MM-GBSA

The binding enthalpies of peptide nucleic acid (PNA) homoduplexes were predicted using a molecular mechanics generalized Born surface area approach. Using the nucleic acid nearest-neighbor model, these were decomposed into sequence parameters which could replicate the enthalpies from thermal melting experiments with a mean error of 8.7%. These results present the first systematic computational investigation into the relationship between sequence and binding energy for PNA homoduplexes and identified a stabilizing helix initiation enthalpy not observed for nucleic acids with phosphoribose backbones.

Combined first-principles statistical mechanics approach to sulfur structure in organic cathode hosts for polymer based lithium-sulfur (Li-S) batteries

Polymer-based batteries that utilize organic electrode materials are considered viable candidates to overcome the common drawbacks of lithium-sulfur (Li-S) batteries. A promising cathode can be developed using a conductive, flexible, and free-standing polymer, poly(4-thiophen-3-yl)benzenethiol) (PTBT), as the sulfur host material. By a vulcanization process, sulfur is embedded into this polymer. Here, we present a combination of electronic structure theory and statistical mechanics to characterize the structure of the initial state of the charged cathode on an atomic level. We perform a stability analysis of differently sulfurized TBT dimers as the basic polymer unit calculated within density-functional theory (DFT) and combine this with a statistical binding model for the binding probability distributions of the vulcanization process. From this, we deduce sulfur chain length ("rank") distributions and calculate the average sulfur rank depending on the sulfur concentration and temperature. This multi-scale approach allows us to bridge the gap between the local description of the covalent bonding process and the derivation of the macroscopic properties of the cathode. Our calculations show that the main reaction of the vulcanization process leads to high-probability states of sulfur chains cross-linking TBT units belonging to different polymer backbones, with a dominant rank around n = 5. In contrast, the connection of adjacent TBT units of the same polymer backbone by a sulfur chain is the side reaction. These results are experimentally supported by Raman spectroscopy.

How phosphorylation of peptides affects their interaction with 14-3-3η domains

Members of the 14-3-3 domain family have important functions as adapter domains. Via an amphipathic groove on their protein surface they typically bind to disordered C-terminals of other proteins. Importantly, binding partners of 14-3-3 domains usually contain a phosphorylated serine or threonine residue at their binding interface and possess one of three different sequence motifs. Binding of the respective unphosphorylated versions of the peptides is typically strongly disfavored. There is a wealth of structural and thermodynamic data available for the phosphorylated forms but not for the unphosphorylated forms as the binding affinities seem to be too weak to be measurable experimentally. Here, we characterized the mechanistic details that govern the preference for the binding of phosphorylated peptides to 14-3-3η domains by means of molecular dynamics (MD) simulations. We found that the phosphate group is ideally coordinated in the binding pocket whereas the respective unphosphorylated side-chain counterpart is not. Thus, the binding preference results from the tight coordination of the phosphorylated residue at the center of the binding interface. Furthermore, MD simulations of 14-3-3η dimers showed a preference for the simultaneous binding of two phosphorylated peptides in agreement with their experimentally observed cooperativity.

Electrostatic Reaction Inhibition in Nanoparticle Catalysis

Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products with similar charges are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on an approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reaction-controlled reactions, to account for electrostatic inhibition in the Debye-Hückel limit. We study the kinetics of reactions ranging from low to high adsorptions on the nanoparticle surface and from the surface- to diffusion-controlled limits for charge valencies 1 and 2. In the diffusion-controlled limit, electrostatic inhibition drastically slows down the reactions for strong adsorption and low ionic concentration, which is well described by our theory. In particular, the rate decreases with adsorption affinity because, in this case, the inhibiting products are generated at a high rate. In the (slow) reaction-controlled limit, the effect of electrostatic inhibition is much weaker, as semiquantitatively reproduced by our electrostatic-modified Langmuir theory. We finally propose and verify a simple interpolation formula that describes electrostatic inhibition for all reaction speeds ("diffusion-influenced" reactions) in general.

Alchemical free energy calculations via metadynamics: Application to the theophylline-RNA aptamer complex

We propose a computational workflow for robust and accurate prediction of both binding poses and their affinities at early stage in designing drug candidates. Small, rigid ligands with few intramolecular degrees of freedom, for example, fragment-like molecules, have multiple binding poses, even at a single binding site, and their affinities are often close to each other. We explore various structures of ligand binding to a target through metadynamics using a small number of collective variables, followed by reweighting to obtain the atomic coordinates. After identifying each binding pose by cluster analysis, we perform alchemical free energy calculations on each structure to obtain the overall value. We applied this protocol in computing free energy of binding for the theophylline-RNA aptamer complex. Of the six (meta)stable structures found, the most favorable binding structure is consistent with the structure obtained by NMR. The overall free energy of binding reproduces the experimental values very well.

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

Isothermal titration calorimetry (ITC) is a widely used tool to experimentally probe the heat signal of the formation of the protein corona around macromolecules or nanoparticles. If an appropriate binding model is applied to the ITC data, the heat of binding and the binding stoichiometry as well as the binding affinity per protein can be quantified and interpreted. However, the binding of the protein to the macromolecule is governed by complex microscopic interactions. In particular, due to the steric and electrostatic protein–protein interactions within the corona as well as cooperative, charge renormalization effects of the total complex, the application of standard (e.g., Langmuir) binding models is questionable and the development of more appropriate binding models is very challenging. Here, we discuss recent developments in the interpretation of the Langmuir model applied to ITC data of protein corona formation, exemplified for the well-defined case of lysozyme coating highly charged dendritic polyglycerol sulfate (dPGS), and demonstrate that meaningful data can be extracted from the fits if properly analyzed. As we show, this is particular useful for the interpretation of ITC data by molecular computer simulations where binding affinities can be calculated but it is often not clear how to consistently compare them with the ITC data. Moreover, we discuss the connection of Langmuir models to continuum binding models (where no discrete binding sites have to be assumed) and their possible extensions toward the inclusion of leading order cooperative electrostatic effects.

Improvement in predicting drug sensitivity changes associated with protein mutations using a molecular dynamics based alchemical mutation method

While molecular-targeted drugs have demonstrated strong therapeutic efficacy against diverse diseases such as cancer and infection, the appearance of drug resistance associated with genetic variations in individual patients or pathogens has severely limited their clinical efficacy. Therefore, precision medicine approaches based on the personal genomic background provide promising strategies to enhance the effectiveness of molecular-targeted therapies. However, identifying drug resistance mutations in individuals by combining DNA sequencing and in vitro analyses is generally time consuming and costly. In contrast, in silico computation of protein-drug binding free energies allows for the rapid prediction of drug sensitivity changes associated with specific genetic mutations. Although conventional alchemical free energy computation methods have been used to quantify mutation-induced drug sensitivity changes in some protein targets, these methods are often adversely affected by free energy convergence. In this paper, we demonstrate significant improvements in prediction performance and free energy convergence by employing an alchemical mutation protocol, MutationFEP, which directly estimates binding free energy differences associated with protein mutations in three types of a protein and drug system. The superior performance of MutationFEP appears to be attributable to its more-moderate perturbation scheme. Therefore, this study provides a deeper level of insight into computer-assisted precision medicine.

Interaction of Proteins with Polyelectrolytes: Comparison of Theory to Experiment

We discuss recent investigations of the interaction of polyelectrolytes with proteins. In particular, we review our recent studies on the interaction of simple proteins such as human serum albumin (HSA) and lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes. In all cases discussed here, we combined experimental work with molecular dynamics (MD) simulations and mean-field theories. In particular, isothermal titration calorimetry (ITC) has been employed to obtain the respective binding constants K_b and the Gibbs free energy of binding. MD simulations with explicit counterions but implicit water demonstrate that counterion release is the main driving force for the binding of proteins to strongly charged polyelectrolytes: patches of positive charges located on the surface of the protein become multivalent counterions of the polyelectrolyte, thereby releasing a number of counterions condensed on the polyelectrolyte. The binding Gibbs free energy due to counterion release is predicted to scale with the logarithm of the salt concentration in the system, which is verified by both simulations and experiment. In several cases, namely, for the interaction of proteins with linear polyelectrolytes and highly charged hydrophilic dendrimers, the binding constant could be calculated from simulations to very good approximation. This finding demonstrated that in these cases explicit hydration effects do not contribute to the Gibbs free energy of binding. The Gibbs free energy can also be used to predict the kinetics of protein uptake by microgels for a given system by applying dynamic density functional theory. The entire discussion demonstrates that the direct comparison of theory with experiments can lead to a full understanding of the interaction of proteins with charged polymers. Possible implications for applications, such as drug design, are discussed.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

Simple Entropy Terms for End-Point Binding Free Energy Calculations

We introduce a number of computationally inexpensive modifications to the MM/PBSA and MM/GBSA estimators for binding free energies, which are based on average receptor-ligand interaction energies in simulations of a noncovalent complex, to improve the treatment of entropy: second- and higher-order terms in a cumulant expansion and a confining potential on ligand external degrees of freedom. We also consider a filter for snapshots where ligands have drifted from the initial binding pose. The variations were tested on six sets of systems for which binding modes and free energies have previously been experimentally determined. For some data sets, none of the tested estimators led to results significantly correlated with measured free energies. In data sets with nontrivial correlation, a ligand RMSD cutoff of 3 Å and a second-order truncation of the cumulant expansion was found to be comparable or better than the average interaction energy by several statistical metrics.

Absolute Alchemical Free Energy Calculations for Ligand Binding: A Beginner's Guide

Many thermodynamic quantities can be extracted from computer simulations that generate an ensemble of microstates according to the principles of statistical mechanics. Among these quantities is the free energy of binding of a small molecule to a macromolecule, such as a protein. Here, we present an introductory overview of a protocol that allows for the estimation of ligand binding free energies via molecular dynamics simulations. While we focus on the binding of organic molecules to proteins, the approach is in principle transferable to any pair of molecules.

Dynamic Docking: A Paradigm Shift in Computational Drug Discovery

Molecular docking is the methodology of choice for studying in silico protein-ligand binding and for prioritizing compounds to discover new lead candidates. Traditional docking simulations suffer from major limitations, mostly related to the static or semi-flexible treatment of ligands and targets. They also neglect solvation and entropic effects, which strongly limits their predictive power. During the last decade, methods based on full atomistic molecular dynamics (MD) have emerged as a valid alternative for simulating macromolecular complexes. In principle, compared to traditional docking, MD allows the full exploration of drug-target recognition and binding from both the mechanistic and energetic points of view (dynamic docking). Binding and unbinding kinetic constants can also be determined. While dynamic docking is still too computationally expensive to be routinely used in fast-paced drug discovery programs, the advent of faster computing architectures and advanced simulation methodologies are changing this scenario. It is feasible that dynamic docking will replace static docking approaches in the near future, leading to a major paradigm shift in in silico drug discovery. Against this background, we review the key achievements that have paved the way for this progress.

Molecular Simulations of Disulfide-Rich Venom Peptides with Ion Channels and Membranes

Disulfide-rich peptides isolated from the venom of arthropods and marine animals are a rich source of potent and selective modulators of ion channels. This makes these peptides valuable lead molecules for the development of new drugs to treat neurological disorders. Consequently, much effort goes into understanding their mechanism of action. This paper presents an overview of how molecular simulations have been used to study the interactions of disulfide-rich venom peptides with ion channels and membranes. The review is focused on the use of docking, molecular dynamics simulations, and free energy calculations to (i) predict the structure of peptide-channel complexes; (ii) calculate binding free energies including the effect of peptide modifications; and (iii) study the membrane-binding properties of disulfide-rich venom peptides. The review concludes with a summary and outlook.

Computing the binding affinity of a ligand buried deep inside a protein with the hybrid steered molecular dynamics

Computing the ligand-protein binding affinity (or the Gibbs free energy) with chemical accuracy has long been a challenge for which many methods/approaches have been developed and refined with various successful applications. False positives and, even more harmful, false negatives have been and still are a common occurrence in practical applications. Inevitable in all approaches are the errors in the force field parameters we obtain from quantum mechanical computation and/or empirical fittings for the intra- and inter-molecular interactions. These errors propagate to the final results of the computed binding affinities even if we were able to perfectly implement the statistical mechanics of all the processes relevant to a given problem. And they are actually amplified to various degrees even in the mature, sophisticated computational approaches. In particular, the free energy perturbation (alchemical) approaches amplify the errors in the force field parameters because they rely on extracting the small differences between similarly large numbers. In this paper, we develop a hybrid steered molecular dynamics (hSMD) approach to the difficult binding problems of a ligand buried deep inside a protein. Sampling the transition along a physical (not alchemical) dissociation path of opening up the binding cavity---pulling out the ligand---closing back the cavity, we can avoid the problem of error amplifications by not relying on small differences between similar numbers. We tested this new form of hSMD on retinol inside cellular retinol-binding protein 1 and three cases of a ligand (a benzylacetate, a 2-nitrothiophene, and a benzene) inside a T4 lysozyme L99A/M102Q(H) double mutant. In all cases, we obtained binding free energies in close agreement with the experimentally measured values. This indicates that the force field parameters we employed are accurate and that hSMD (a brute force, unsophisticated approach) is free from the problem of error amplification suffered by many sophisticated approaches in the literature.

Hybrid Steered Molecular Dynamics Approach to Computing Absolute Binding Free Energy of Ligand-Protein Complexes: A Brute Force Approach That Is Fast and Accurate

Computing the free energy of binding a ligand to a protein is a difficult task of essential importance for which purpose various theoretical/computational approaches have been pursued. In this paper, we develop a hybrid steered molecular dynamics (hSMD) method capable of resolving one ligand–protein complex within a few wall-clock days with high enough accuracy to compare with the experimental data. This hSMD approach is based on the relationship between the binding affinity and the potential of mean force (PMF) in the established literature. It involves simultaneously steering n (n = 1, 2, 3, ...) centers of mass of n selected segments of the ligand using n springs of infinite stiffness. Steering the ligand from a single initial state chosen from the bound state ensemble to the corresponding dissociated state, disallowing any fluctuations of the pulling centers along the way, one can determine a 3n-dimensional PMF curve connecting the two states by sampling a small number of forward and reverse pulling paths. This PMF constitutes a large but not the sole contribution to the binding free energy. Two other contributors are (1) the partial partition function containing the equilibrium fluctuations of the ligand at the binding site and the deviation of the initial state from the PMF minimum and (2) the partial partition function containing rotation and fluctuations of the ligand around one of the pulling centers that is fixed at a position far from the protein. We implement this hSMD approach for two ligand–protein complexes whose structures were determined and whose binding affinities were measured experimentally: caprylic acid binding to bovine β-lactoglobulin and glutathione binding to Schistosoma japonicum glutathione S-transferase tyrosine 7 to phenylalanine mutant. Our computed binding affinities agree with the experimental data within a factor of 1.5. The total time of computation for these two all-atom model systems (consisting of 96K and 114K atoms, respectively) was less than one wall-clock week using 512 cores (32 Xeon E5-2680 processors).

Computing Protein-Protein Association Affinity with Hybrid Steered Molecular Dynamics

Computing protein-protein association affinities is one of the fundamental challenges in computational biophysics/biochemistry. The overwhelming amount of statistics in the phase space of very high dimensions cannot be sufficiently sampled even with today's high-performance computing power. In this article, we extend a potential of mean force (PMF)-based approach, the hybrid steered molecular dynamics (hSMD) approach we developed for ligand-protein binding, to protein-protein association problems. For a protein complex consisting of two protomers, P1 and P2, we choose m (≥3) segments of P1 whose m centers of mass are to be steered in a chosen direction and n (≥3) segments of P2 whose n centers of mass are to be steered in the opposite direction. The coordinates of these m + n centers constitute a phase space of 3(m + n) dimensions (3(m + n)D). All other degrees of freedom of the proteins, ligands, solvents, and solutes are freely subject to the stochastic dynamics of the all-atom model system. Conducting SMD along a line in this phase space, we obtain the 3(m + n)D PMF difference between two chosen states: one single state in the associated state ensemble and one single state in the dissociated state ensemble. This PMF difference is the first of four contributors to the protein-protein association energy. The second contributor is the 3(m + n - 1)D partial partition in the associated state accounting for the rotations and fluctuations of the (m + n - 1) centers while fixing one of the m + n centers of the P1-P2 complex. The two other contributors are the 3(m - 1)D partial partition of P1 and the 3(n - 1)D partial partition of P2 accounting for the rotations and fluctuations of their m - 1 or n - 1 centers while fixing one of the m/n centers of P1/P2 in the dissociated state. Each of these three partial partitions can be factored exactly into a 6D partial partition in multiplication with a remaining factor accounting for the small fluctuations while fixing three of the centers of P1, P2, or the P1-P2 complex, respectively. These small fluctuations can be well-approximated as Gaussian, and every 6D partition can be reduced in an exact manner to three problems of 1D sampling, counting the rotations and fluctuations around one of the centers as being fixed. We implement this hSMD approach to the Ras-RalGDS complex, choosing three centers on RalGDS and three on Ras (m = n = 3). At a computing cost of about 71.6 wall-clock hours using 400 computing cores in parallel, we obtained the association energy, -9.2 ± 1.9 kcal/mol on the basis of CHARMM 36 parameters, which well agrees with the experimental data, -8.4 ± 0.2 kcal/mol.

II. Dissociation free energies in drug–receptor systems via nonequilibrium alchemical simulations: application to the FK506-related immunophilin ligands

The fast switch double annihilation method (FS-DAM) provides an effective mean to the compute the binding free energies in drug-receptor systems. Here we present an application to the FK506-related ligands of the FKBP12 protein.

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

In this contribution I critically discuss the alchemical approach for evaluating binding free energies in drug–receptor systems, placing this methodology into the broader context of non-equilibrium thermodynamics.

Energetics of Hydrophilic Protein-Protein Association and the Role of Water

Hydrophilic protein-protein interfaces constitute a major part of all protein-protein interfaces and are thus of great importance. However, the quantitative characterization of their association is still an ongoing challenge and the driving force behind their association remains poorly characterized. Here, we have addressed the association of hydrophilic proteins and the role of water by means of extensive molecular dynamics simulations in explicit water using three well studied protein complexes; Barnase-Barstar, cytochrome c-cytochrome c peroxidase, and the N-terminal domain of enzyme I-histidine-containing phosphocarrier. The one-dimensional free energy profiles obtained from umbrella sampling simulations are downhill or, in other words, barrierless. Using these one-dimensional free energy profiles, the computed standard free energies of binding are -12.7 ± 1.1 kcal/mol, -9.4 ± 0.7 kcal/mol, and -8.4 ± 1.9 kcal/mol that are in reasonable to very good agreement with the experimental values of -19.6 kcal/mol, -8.8 kcal/mol, and -7.8 kcal/mol. As expected, analysis of the confined water between the hydrophilic complex partners shows that the density and the orientational order parameter deviate noticeably from the bulk values, especially at close separations of the confining proteins.

Partition, orientation and mobility of ubiquinones in a lipid bilayer

Ubiquinone is the universal mobile charge carrier involved in biological electron transfer processes. Its redox properties and biological function depend on the molecular partition and lateral diffusion over biological membranes. However, ubiquinone localization and dynamics within lipid bilayers are long debated and still uncertain. Here we present molecular dynamics simulations of several ubiquinone homologs with variable isoprenoid tail lengths complexed to phosphatidylcholine bilayers. Initially, a new force-field parametrization for ubiquinone is derived from and compared to high level quantum chemical data. Free energy profiles for ubiquinone insertion in the lipid bilayer are obtained with the new force-field. The profiles allow for the determination of the equilibrium location of ubiquinone in the membrane as well as for the validation of the simulation model by direct comparison with experimental partition coefficients. A detailed analysis of structural properties and interactions shows that the ubiquinone polar head group is localized at the water-bilayer interface at the same depth of the lipid glycerol groups and oriented normal to the membrane plane. Both the localization and orientation of ubiquinone head groups do not change significantly when increasing the number of isoprenoid units. The isoprenoid tail is extended and packed with the lipid acyl chains. For ubiquinones with long tails, the terminal isoprenoid units have high flexibility. Calculated ubiquinone diffusion coefficients are similar to that found for the phosphatidylcholine lipid. These results may have further implications for the mechanisms of ubiquinone transport and binding to respiratory and photosynthetic protein complexes.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Monte Carlo Free Ligand Diffusion with Markov State Model Analysis and Absolute Binding Free Energy Calculations

Obtaining absolute binding free energies from unbiased ligand diffusion has attracted a significant amount of attention due to its implications in drug design. Several studies have used special purpose computers and software to achieve microsecond molecular dynamics which, combined with a Markov state model analysis, are capable of providing absolute binding free energies. We have recently developed a Monte Carlo based technique, PELE, capable of performing a dynamical exploration of the protein-ligand energy landscape including free ligand diffusion into the active site, at a fraction of the computational cost of molecular dynamics techniques. We demonstrate here the capabilities of our Monte Carlo technique in obtaining absolute binding free energies for a series of benzamidine like inhibitors into trypsin. Our results are in good agreement with experimental data and other molecular dynamics simulations, indicating that PELE can be a useful tool for quick estimates of binding free energies and mechanisms.

Prediction of the binding affinity of compounds with diverse scaffolds by MP-CAFEE

Accurate methods to predict the binding affinities of compounds for target molecules are powerful tools in structure-based drug design (SBDD). A recently developed method called massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) successfully predicted the binding affinities of compounds with relatively similar scaffolds. We investigate the applicability of MP-CAFEE for predicting the affinity of compounds having more diverse scaffolds for the target p38α, a mitogen-activated protein kinase. The calculated and experimental binding affinities correlate well, showing that MP-CAFEE can accurately rank the compounds with diverse scaffolds. We propose a method to determine the optimal number of sampling runs with respect to a predefined level of accuracy, which is established according to the stage in the SBDD process being considered. The optimal number of sampling runs for two key stages-lead identification and lead optimization-is estimated to be five and eight or more, respectively, in our model system using Cochrans sample size formula.

Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design

Recent calorimetric studies of interactions between small molecules and biomolecular targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in experimental measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and experimental methodologies to directly assess changes in binding free energy.

On the Role of Dewetting Transitions in Host-Guest Binding Free Energy Calculations

We use thermodynamic integration (TI) and explicit solvent molecular dynamics (MD) simulation to estimate the absolute free energy of host–guest binding. In the unbound state, water molecules visit all of the internally accessible volume of the host, which is fully hydrated on all sides. Upon binding of an apolar guest, the toroidal host cavity is fully dehydrated; thus, during the intermediate λ stages along the integration, the hydration of the host fluctuates between hydrated and dehydrated states. Estimating free energies by TI can be especially challenging when there is a considerable difference in hydration between the two states of interest. We investigate these aspects using the popular TIP3P and TIP4P water models. TI free energy estimates through MD largely depend on water-related interactions, and water dynamics significantly affect the convergence of binding free energy calculations. Our results indicate that wetting/dewetting transitions play a major role in slowing the convergence of free energy estimation. We employ two alternative approaches—one analytical and the other empirically based on actual MD sampling—to correct for the standard state free energy. This correction is sizable (up to 4 kcal/mol), and the two approaches provide corrections that differ by about 1 kcal/mol. For the system considered here, the TIP4P water model combined with an analytical correction for the standard state free energy provides higher overall accuracy. This observation might be transferable to other systems in which water-related contributions dominate the binding process.

Thermodynamic integration to predict host-guest binding affinities

An alchemical free energy method with explicit solvent molecular dynamics simulations was applied as part of the blind prediction contest SAMPL3 to calculate binding free energies for seven guests to an acyclic cucurbit-[n]uril host. The predictions included determination of protonation states for both host and guests, docking pose generation, and binding free energy calculations using thermodynamic integration. We found a root mean square error (RMSE) of 3.6 kcal mol(-1) from the reference experimental results, with an R(2) correlation of 0.51. The agreement with experiment for the largest contributor to this error, guest 6, is improved by 1.7 kcal mol(-1) when a periodicity-induced free energy correction is applied. The corrections for the other ligands were significantly smaller, and altogether the RMSE was reduced by 0.4 kcal mol(-1). We link properties of the host-guest systems during simulation to errors in the computed free energies. Overall, we show that charged host-guest systems studied here, initialized in unconfirmed docking poses, present a challenge to accurate alchemical simulation methods.

Independent-Trajectory Thermodynamic Integration: a practical guide to protein-drug binding free energy calculations using distributed computing

The Independent-Trajectory Thermodynamic Integration (IT-TI) approach for free energy calculation with distributed computing is described. IT-TI utilizes diverse conformational sampling obtained from multiple, independent simulations to obtain more reliable free energy estimates compared to single TI predictions. The latter may significantly under- or over-estimate the binding free energy due to finite sampling. We exemplify the advantages of the IT-TI approach using two distinct cases of protein-ligand binding. In both cases, IT-TI yields distributions of absolute binding free energy estimates that are remarkably centered on the target experimental values. Alternative protocols for the practical and general application of IT-TI calculations are investigated. We highlight a protocol that maximizes predictive power and computational efficiency.

Effects of Biomolecular Flexibility on Alchemical Calculations of Absolute Binding Free Energies

The independent trajectory thermodynamic integration (IT-TI) approach (Lawrenz et. al J. Chem. Theory. Comput. 2009, 5:1106-1116(1)) for free energy calculations with distributed computing is employed to study two distinct cases of protein-ligand binding: first, the influenza surface protein N1 neuraminidase bound to the inhibitor oseltamivir, and second, the M. tuberculosis enzyme RmlC complexed with the molecule CID 77074. For both systems, finite molecular dynamics (MD) sampling and varied molecular flexibility give rise to IT-TI free energy distributions that are remarkably centered on the target experimental values, with a spread directly related to protein, ligand, and solvent dynamics. Using over 2 μs of total MD simulation, alternative protocols for the practical, general implementation of IT-TI are investigated, including the optimal use of distributed computing, the total number of alchemical intermediates, and the procedure to perturb electrostatics and van der Waals interactions. A protocol that maximizes predictive power and computational efficiency is proposed. IT-TI outperforms traditional TI predictions and allows a straightforward evaluation of the reliability of free energy estimates. Our study has broad implications for the use of distributed computing in free energy calculations of macromolecular systems.