The overlooked bond‐stretching contribution in free energy perturbation calculations

Adenine Methylation Enhances the Conformational Flexibility of an RNA Hairpin Tetraloop

The N6-methyladenosine modification is one of the most abundant post-transcriptional modifications in ribonucleic acid (RNA) molecules. Using molecular dynamics simulations and alchemical free-energy calculations, we studied the structural and energetic implications of incorporating this modification in an adenine mononucleotide and an RNA hairpin structure. At the mononucleotide level, we found that the syn configuration is more favorable than the anti configuration by 2.05 ± 0.15 kcal/mol. The unfavorable effect of methylation was due to the steric overlap between the methyl group and a nitrogen atom in the purine ring. We then probed the effect of methylation in an RNA hairpin structure containing an AUCG tetraloop, which is recognized by a "reader" protein (YTHDC1) to promote transcriptional silencing of long noncoding RNAs. While methylation had no significant conformational effect on the hairpin stem, the methylated tetraloop showed enhanced conformational flexibility compared to the unmethylated tetraloop. The increased flexibility was associated with the outward flipping of two bases (A6 and U7) which formed stacking interactions with each other and with the C8 and G9 bases in the tetraloop, leading to a conformation similar to that in the RNA/reader protein complex. Therefore, methylation-induced conformational flexibility likely facilitates RNA recognition by the reader protein.

Kartograf: A Geometrically Accurate Atom Mapper for Hybrid-Topology Relative Free Energy Calculations

Relative binding free energy (RBFE) calculations have emerged as a powerful tool that supports ligand optimization in drug discovery. Despite many successes, the use of RBFEs can often be limited by automation problems, in particular, the setup of such calculations. Atom mapping algorithms are an essential component in setting up automatic large-scale hybrid-topology RBFE calculation campaigns. Traditional algorithms typically employ a 2D subgraph isomorphism solver (SIS) in order to estimate the maximum common substructure. SIS-based approaches can be limited by time-intensive operations and issues with capturing geometry-linked chemical properties, potentially leading to suboptimal solutions. To overcome these limitations, we have developed Kartograf, a geometric-graph-based algorithm that uses primarily the 3D coordinates of atoms to find a mapping between two ligands. In free energy approaches, the ligand conformations are usually derived from docking or other previous modeling approaches, giving the coordinates a certain importance. By considering the spatial relationships between atoms related to the molecule coordinates, our algorithm bypasses the computationally complex subgraph matching of SIS-based approaches and reduces the problem to a much simpler bipartite graph matching problem. Moreover, Kartograf effectively circumvents typical mapping issues induced by molecule symmetry and stereoisomerism, making it a more robust approach for atom mapping from a geometric perspective. To validate our method, we calculated mappings with our novel approach using a diverse set of small molecules and used the mappings in relative hydration and binding free energy calculations. The comparison with two SIS-based algorithms showed that Kartograf offers a fast alternative approach. The code for Kartograf is freely available on GitHub (https://github.com/OpenFreeEnergy/kartograf). While developed for the OpenFE ecosystem, Kartograf can also be utilized as a standalone Python package.

Leveraging the Sampling Efficiency of RE-EDS in OpenMM Using a Shifted Reaction-Field With an Atom-Based Cutoff

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method, currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions, but not when using lattice- sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group based cutoff, which is not supported by most small-molecule force fields and other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field (GAFF) in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

RestraintMaker: a graph-based approach to select distance restraints in free-energy calculations with dual topology

The calculation of relative binding free energies (RBFE) involves the choice of the end-state/system representation, of a sampling approach, and of a free-energy estimator. System representations are usually termed "single topology" or "dual topology". As the terminology is often used ambiguously in the literature, a systematic categorization of the system representations is proposed here. In the dual-topology approach, the molecules are simulated as separate molecules. Such an approach is relatively easy to automate for high-throughput RBFE calculations compared to the single-topology approach. Distance restraints are commonly applied to prevent the molecules from drifting apart, thereby improving the sampling efficiency. In this study, we introduce the program RestraintMaker, which relies on a greedy algorithm to find (locally) optimal distance restraints between pairs of atoms based on geometric measures. The algorithm is further extended for multi-state methods such as enveloping distribution sampling (EDS) or multi-site [Formula: see text]-dynamics. The performance of RestraintMaker is demonstrated for toy models and for the calculation of relative hydration free energies. The Python program can be used in script form or through an interactive GUI within PyMol. The selected distance restraints can be written out in GROMOS or GROMACS file formats. Additionally, the program provides a human-readable JSON format that can easily be parsed and processed further. The code of RestraintMaker is freely available on GitHub https://github.com/rinikerlab/restraintmaker.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Boosting Free-Energy Perturbation Calculations with GPU-Accelerated NAMD

Harnessing the power of graphics processing units (GPUs) to accelerate molecular dynamics (MD) simulations in the context of free-energy calculations has been a longstanding effort toward the development of versatile, high-performance MD engines. We report a new GPU-based implementation in NAMD of free-energy perturbation (FEP), one of the oldest, most popular importance-sampling approaches for the determination of free-energy differences that underlie alchemical transformations. Compared to the CPU implementation available since 2001 in NAMD, our benchmarks indicate that the new implementation of FEP in traditional GPU code is about four times faster, without any noticeable loss of accuracy, thereby paving the way toward more affordable free-energy calculations on large biological objects. Moreover, we have extended this new FEP implementation to a code path highly optimized for a single-GPU node, which proves to be up to nearly 30 times faster than the CPU implementation. Through optimized GPU performance, the present developments provide the community with a cost-effective solution for conducting FEP calculations. The new FEP-enabled code has been released with NAMD 3.0.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that ΔΔG_hyd, the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and ΔΔG_hyd can reach -2.0 kcal/mol and -3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.

Accurate Calculation of Free Energy Changes upon Amino Acid Mutation

Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally, we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well as large-scale mutational scans.

Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach

Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange.

Calculation of binding free energies

Molecular dynamics simulations enable access to free energy differences governing the driving force underlying all biological processes. In the current chapter we describe alchemical methods allowing the calculation of relative free energy differences. We concentrate on the binding free energies that can be obtained using non-equilibrium approaches based on the Crooks Fluctuation Theorem. Together with the theoretical background, the chapter covers practical aspects of hybrid topology generation, simulation setup, and free energy estimation. An important aspect of the validation of a simulation setup is illustrated by means of calculating free energy differences along a full thermodynamic cycle. We provide a number of examples, including protein-ligand and protein-protein binding as well as ligand solvation free energy calculations.

Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations

BACKGROUND

Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence.

METHODS

The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered.

RESULTS

We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled.

CONCLUSIONS

The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision.

GENERAL SIGNIFICANCE

The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Efficient Combination of Environment Change and Alchemical Perturbation within the Enveloping Distribution Sampling (EDS) Scheme: Twin-System EDS and Application to the Determination of Octanol-Water Partition Coefficients

The methodology of Enveloping Distribution Sampling (EDS) is extended to probe a single-simulation alternative to the thermodynamic cycle that is standardly used for measuring the effect of a modification of a chemical compound, e.g. from a given species to a chemical derivative for a ligand or solute molecule, on the free-enthalpy change associated with a change in environment, e.g. from the unbound state to the bound state for a protein-ligand system or from one solvent to another one for a solute molecule. This alternative approach relies on the coupled simulation of two systems (computational boxes) 1 and 2, and the method is therefore referred to as twin-system EDS. Systems 1 and 2 account for the two choices of environment. The end states of the alchemical perturbation for the twin-system associate the two alternative forms X and Y of the molecule to systems 1 and 2 or 2 and 1, respectively. In this way, the processes of transforming one molecule into the other are carried out simultaneously in opposite directions in the two environments, leading to a change in free enthalpy that is smaller than for the two individual processes and to an energy-difference distribution that is more symmetric. As an illustration, the method is applied to the calculation of octanol-water partition coefficients for C4 to C8 alkanes, 1-hexanol and 1,2-dimethoxyethane. It is shown in particular that the consideration of the residual hydration of octanol leads to calculated partition coefficients that are in better agreement with reported experimental numbers.

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: case study of relative binding free energies of fructose-1,6-bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase-AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional- and QM/MM-FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase-AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion.

Good practices in free-energy calculations

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in a wide range of research areas. Yet, the reliability of these calculations can often be improved significantly if a number of precepts, or good practices, are followed. Although the theory upon which these good practices rely has largely been known for many years, it is often overlooked or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. In this contribution, the current best practices for carrying out free-energy calculations using free energy perturbation and nonequilibrium work methods are discussed, demonstrating that at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. Monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway, and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision.

Thermodynamic analysis of mRNA cap binding by the human initiation factor eIF4E via free energy perturbations

Eukaryotic mRNAs are appended at the 5' end, with the 7-methylguanosine cap linked by a 5'-5'-triphosphate bridge to the first transcribed nucleoside (m7GpppX). Initiation of cap-dependent translation of mRNA requires direct interaction between the cap structure and the eukaryotic translation initiation factor eIF4E. Biophysical studies of the association between eIF4E and various cap analogs have demonstrated that m(7)GTP binds to the protein ca. -5.0 kcal/mol more favorably than unmethylated GTP. In this work, a thermodynamic analysis of the binding process between eIF4E and several cap analogs has been conducted using Monte Carlo (MC) simulations in conjunction with free energy perturbation (FEP) calculations. To address the role of the 7-methyl group in the eIF4E/m7GpppX cap interaction, binding free energies have been computed for m(7)GTP, GTP, protonated GTP at N(7), the 7-methyldeazaguanosine 5'-triphosphate (m(7)DTP), and 7-deazaguanosine 5'-triphosphate (DTP) cap analogs. The MC/FEP simulations for the GTP-->m(7)DTP transformation demonstrate that half of the binding free energy gain of m(7)GTP with respect to GTP can be attributed to favorable van der Waals interactions with Trp166 and reduced desolvation penalty due to the N(7) methyl group. The methyl group both eliminates the desolvation penalty of the N(7) atom upon binding and creates a larger cavity within the solvent that further facilitates the desolvation step. Analysis of the pair m(7)GTP-m(7)DTP suggests that the remaining gain in affinity is related to the positive charge created on the guanine moiety due to the N(7) methylation. The charge provides favorable cation-pi interactions with Trp56 and Trp102 and decreases the negative molecular charge, which helps the transfer from the solvent, a more polar environment, to the protein.

Coupling Accelerated Molecular Dynamics Methods with Thermodynamic Integration Simulations

In this work we propose a straightforward and efficient approach to improve accuracy and convergence of free energy simulations in condensed-phase systems. We also introduce a new accelerated Molecular Dynamics (MD) approach in which molecular conformational transitions are accelerated by lowering the energy barriers while the potential surfaces near the minima are left unchanged. All free energy calculations were performed on the propane-to-propane model system. The accuracy of free energy simulations was significantly improved when sampling of internal degrees of freedom of solute was enhanced. However, accurate and converged results were only achieved when the solvent interactions were taken into account in the accelerated MD approaches. The analysis of the distribution of boost potential along the free energy simulations showed that the new accelerated MD approach samples efficiently both low- and high-energy regions of the potential surface. Since this approach also maintains substantial populations in regions near the minima, the statistics are not compromised in the thermodynamic integration calculations, and, as a result, the ensemble average can be recovered.

Free energy calculations applied to membrane proteins

Selected applications of free energy calculations to the realm of membrane proteins are reviewed. The theoretical underpinnings of these calculations are described, focusing on free energy perturbation and the use of thermodynamic integration to determine free energy changes along well-delineated order parameters. Current strategies for improving the reliability of free energy calculations, while making them somewhat more affordable are outlined. Application of the free energy methodology to understand the structure and function of membrane proteins is illustrated in three concrete examples: The binding of an agonist ligand to a G protein-coupled receptor, the assisted transport of a small permeant through a membrane channel, and the recognition and association of transmembrane alpha-helical domains.

Alchemical free energy calculations and multiple conformational substates

Thermodynamic integration (TI) was combined with (adaptive) umbrella sampling to improve the convergence of alchemical free energy simulations in which multiple conformational substates are present. The approach, which we refer to as non-Boltzmann TI (NBTI), was tested by computing the free energy differences between three five-atomic model systems, as well as the free energy difference of solvation between leucine and asparagine. In both cases regular TI failed to give converged results, whereas the NBTI results were free from hysteresis and had standard deviations well below +/-0.7 kcal/mole. We also present theoretical considerations that make it possible to compute free energy differences between simple molecules, such as the five-atomic model systems, by numerical integration of the partition functions at the respective end points.

Elucidation of fatty acid amide hydrolase inhibition by potent alpha-ketoheterocycle derivatives from Monte Carlo simulations

Fatty acid amide hydrolase (FAAH) is a serine hydrolase responsible for the degradation of anandamide, an endogenous cannabinoid agonist, and oleamide, a sleep-inducing lipid. Recently, Boger and co-workers reported a potent, selective, and efficacious class of reversible alpha-ketoheterocycle inhibitors of FAAH that produce analgesia in animal models (J. Med. Chem. 2005, 48, 1849-1856; Bioorg. Med. Chem. Lett. 2005, 15, 1423-1428). Key aspects of the structure-activity data are addressed here through computational analysis of FAAH inhibition using Monte Carlo (MC) simulations in conjunction with free energy perturbation (FEP) calculations. The MC/FEP simulations demonstrate that incorporation of pyridine at the C5 position of the 2-keto-oxazole and 2-keto-1,3,4-oxadiazole derivatives significantly enhances binding affinity by formation of a hydrogen-bonded array between the pyridyl nitrogen and Lys142 and Thr236. The results also attribute the activity boost upon substitution of oxazole by oxadiazole to reduced steric interactions in the active site and a lower torsional energy penalty upon binding.

Evaluating the Molecular Mechanics Poisson−Boltzmann Surface Area Free Energy Method Using a Congeneric Series of Ligands to p38 MAP Kinase

The recently described molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method for calculating free energies is applied to a congeneric series of 16 ligands to p38 MAP kinase whose binding constants span approximately 2 orders of magnitude. These compounds have previously been used to test and compare other free energy calculation methods, including thermodynamic integration (TI), OWFEG, ChemScore, PLPScore, and Dock Energy Score. We find that the MM-PBSA performs relatively poorly for this set of ligands, yielding results much inferior to those from TI or OWFEG, inferior to Dock Energy Score, and not appreciably better than ChemScore or PLPScore but at an appreciably larger computational cost than any of these other methods. This suggests that one should be selective in applying the MM-PBSA method and that for systems that are amenable to other free energy approaches, these other approaches may be preferred. We also examine the single simulation approximation for MM-PBSA, whereby the required ligand and protein trajectories are extracted from a single MD simulation rather than two separate MD runs. This assumption, sometimes used to speed the MM-PBSA calculation, is found to yield significantly inferior results with only a moderate net percentage reduction in total simulation time.

Free energy simulations and MM-PBSA analyses on the affinity and specificity of steroid binding to antiestradiol antibody

Antiestradiol antibody 57-2 binds 17beta-estradiol (E2) with moderately high affinity (K(a) = 5 x 10(8) M(-1)). The structurally related natural estrogens estrone and estriol as well synthetic 17-deoxy-estradiol and 17alpha-estradiol are bound to the antibody with 3.7-4.9 kcal mol(-1) lower binding free energies than E2. Free energy perturbation (FEP) simulations and the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were applied to investigate the factors responsible for the relatively low cross-reactivity of the antibody with these four steroids, differing from E2 by the substituents of the steroid D-ring. In addition, computational alanine scanning of the binding site residues was carried out with the MM-PBSA method. Both the FEP and MM-PBSA methods reproduced the experimental relative affinities of the five steroids in good agreement with experiment. On the basis of FEP simulations, the number of hydrogen bonds formed between the antibody and steroids, which varied from 0 to 3 in the steroids studied, determined directly the magnitude of the steroid-antibody interaction free energies. One hydrogen bond was calculated to contribute about 3 kcal mol(-1) to the interaction energy. Because the relative binding free energies of estrone (two antibody-steroid hydrogen bonds), estriol (three hydrogen bonds), 17-deoxy-estradiol (no hydrogen bonds), and 17alpha-estradiol (two hydrogen bonds) are close to each other and clearly lower than that of E2 (three hydrogen bonds), the water-steroid interactions lost upon binding to the antibody make an important contribution to the binding free energies. The MM-PBSA calculations showed that the binding of steroids to the antiestradiol antibody is driven by van der Waals interactions, whereas specificity is solely due to electrostatic interactions. In addition, binding of steroids to the antiestradiol antibody 57-2 was compared to the binding to the antiprogesterone antibody DB3 and antitestosterone antibody 3-C4F5, studied earlier with the MM-PBSA method.

Structure-activity relationship for extracellular block of K+channels by tetraalkylammonium ions

External tetraalkylammonium ion binding to potassium channels is studied using microscopic molecular modelling methods and the experimental structure of the KcsA channel. Relative binding free energies of the KcsA complexes with Me4N+, Et4N+, and n-Pr4N+ are calculated with the molecular dynamics free energy perturbation approach together with automated ligand docking. The four-fold symmetry of the entrance cavity formed by the Tyr82 residues is found to provide stronger binding for the D2d than for the S4 conformation of the ligands. In agreement with experiment the Et4N+ blocker shows several kcal/mol better binding than the other tetraalkylammonium ions.

Analysis of the binding energies of testosterone, 5alpha-dihydrotestosterone, androstenedione and dehydroepiandrosterone sulfate with an antitestosterone antibody

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the binding of testosterone (TES), 5alpha-dihydrotestosterone (5ADHT), androstenedione (AND), and dehydroepiandrosterone sulfate (DHEAS) to the monoclonal antitestosterone antibody 3-C(4)F(5). The relative binding free energy of TES and AND was also calculated with free energy perturbation (FEP) simulations. The antibody 3-C(4)F(5) has a relatively high affinity (3 x 10(8) M(-1)) and on overall good binding profile for testosterone but its cross-reactivity with DHEAS has been the main reason for the failure to use this antibody in clinical immunoassays. The relative binding free energies obtained with the MM-PBSA method were 1.5 kcal/mol for 5ADHT, 3.8 kcal/mol for AND, and 4.3 kcal/mol for DHEAS, as compared to TES. When a water molecule of the ligand binding site, observed in the antibody-TES crystal structure, was explicitly included in MM-PBSA calculations, the relative binding energies were 3.4, 4.9, and 5.4 kcal/mol for 5ADHT, AND, and DHEAS, respectively. The calculated numbers are in correct order but larger than the corresponding experimental energies of 1.3, 1.5, and 2.6 kcal/mol, respectively. The fact that the MM-PBSA method reproduced the relative binding free energies of DHEAS, a steroid having a negatively charged sulfate group, and the neutrally charged TES, 5ADHT, and AND in satisfactory agreement with experiment shows the robustness of the method in predicting relative binding affinities. The 800-ps FEP simulations predicted that the antibody 3-C(4)F(5) binds TES 1.3 kcal/mol tighter than AND. Computational mutagenesis of selected amino acid residues of the ligand binding site revealed that the lower affinities of AND and DHEAS as compared to TES are due to a combined effect of several residues, each contributing a small fraction to the tighter binding of TES. An exception to this is Tyr99H, whose mutation to Ala lowered the binding of DHEAS 0.7 kcal/mol more than the binding of TES. This is probably due to the hydrogen bonding interaction formed between the OH group of Tyr99H and the sulfate group of DHEAS. Computational mutagensis data also showed that the affinity of the steroids to the antitestosterone antibody 3-C(4)F(5) would be enhanced if Trp47H were repositioned so that it would make more extensive contacts with the bound ligands. In addition, the binding of steroids to antitestosterone, antiprogesterone, and antiestradiol antibodies is discussed.

A computer simulation of functional group contributions to free energy in water and a DPPC lipid bilayer

A series of all-atom molecular dynamics simulations has been performed to evaluate the contributions of various functional groups to the free energy of solvation in water and a dipalmitoylphospatidylcholine lipid bilayer membrane and to the free energies of solute transfer (Delta(DeltaG(o))X) from water into the ordered-chain interior of the bilayer. Free energies for mutations of the alpha-H atom in p-toluic acid to six different substituents (-CH3, -Cl, -OCH3, -CN, -OH, -COOH) were calculated by a combined thermodynamic integration and perturbation method and compared to literature results from vapor pressure measurements, partition coefficients, and membrane transport experiments. Convergence of the calculated free energies was indicated by substantial declines in standard deviations for the calculated free energies with increased simulation length, by the independence of the ensemble-averaged Boltzmann factors to simulation length, and the weak dependence of hysteresis effects on simulation length over two different simulation lengths and starting from different initial configurations. Calculated values of Delta(DeltaG(o))X correlate linearly with corresponding values obtained from lipid bilayer transport experiments with a slope of 1.1 and from measurements of partition coefficients between water and hexadecane or decadiene, with slopes of 1.1 and 0.9, respectively. Van der Waals interactions between the functional group of interest and the acyl chains in the ordered chain region account for more than 95% of the overall potential energy of interaction. These results support the view that the ordered chain region within the bilayer interior is the barrier domain for transport and that solvation interactions within this region resemble those occurring in a nonpolar hydrocarbon.

Computed free energy differences between point mutations in a collagen-like peptide

We studied the results of mutating alanine --> glycine at three positions of a collagen-like peptide in an effort to develop a computational method for predicting the energetic and structural effects of a single point genetic mutation in collagen, which is associated with the clinical diagnosis of Osteogenesis Imperfecta (OI). The differences in free energy of denaturation were calculated between the collagen-like peptides [(POG)(4)(POA)(POG)(4)](3) and [(POG)(10)](3) (POG: proline-hydroxyproline-glycine).* Our computational results, which suggest significant destabilization of the collagen-like triple-helix upon the glycine --> alanine mutations, correlate very well with the experimental free energies of denaturation. The robustness of our collagen-like peptide model is shown by its reproduction of experimental results with both different simulation paths and different lengths of the model peptide. The individual free energy for each alanine --> glycine mutation (and the reverse free energy, glycine --> alanine mutation) in the collagen-like peptide has been calculated. We find that the first alanine introduced into the triple helix causes a very large destabilization of the helix, but the last alanine introduced into the same position of an adjacent chain causes a very small change in the peptide stability. Thus, our results demonstrate that each mutation does not contribute equally to the free energy. We find that the sum of the calculated individual residues' free energy can accurately model the experimental free energy for the whole peptide.