Good practices in free-energy calculations

Prediction of SAMPL3 host-guest affinities with the binding energy distribution analysis method (BEDAM)

BEDAM calculations are described to predict the free energies of binding of a series of anaesthetic drugs to a recently characterized acyclic cucurbituril host. The modeling predictions, conducted as part of the SAMPL3 host-guest affinity blind challenge, are generally in good quantitative agreement with the experimental measurements. The correlation coefficient between computed and measured binding free energies is 70% with high statistical significance. Multiple conformational stereoisomers and protonation states of the guests have been considered. Better agreement is obtained with high statistical confidence under acidic modeling conditions. It is shown that this level of quantitative agreement could have not been reached without taking into account reorganization energy and configurational entropy effects. Extensive conformational variability of the host, the guests and their complexes is observed in the simulations, affecting binding free energy estimates and structural predictions. A conformational reservoir technique is introduced as part of the parallel Hamiltonian replica exchange molecular dynamics BEDAM protocol to fully capture conformational variability. It is shown that these advanced computational strategies lead to converged free energy estimates for these systems, offering the prospect of utilizing host-guest binding free energy data for force field validation and development.

Synergistic substrate binding determines the stoichiometry of transport of a prokaryotic H(+)/Cl(-) exchanger

Active exchangers dissipate the gradient of one substrate to accumulate nutrients, export xenobiotics and maintain cellular homeostasis. Mechanistic studies suggested that all exchangers share two fundamental properties: substrate binding is antagonistic and coupling is maintained by preventing shuttling of the empty transporter. The CLC Cl⁻: H⁺ exchangers control the homeostasis of cellular compartments in most living organisms but their transport mechanism remains unclear. We show that substrate binding to CLC-ec1 is synergistic rather than antagonistic: chloride binding induces protonation of a critical glutamate. The simultaneous binding of H⁺ and Cl⁻ gives rise to a fully-loaded state incompatible with conventional mechanisms. Mutations in the Cl⁻ transport pathway identically alter the stoichiometries of Cl⁻: H⁺ exchange and binding. We propose that the thermodynamics of synergistic substrate binding determine the stoichiometry of transport rather than the kinetics of conformational changes and ion binding.

On conduction in a bacterial sodium channel

Voltage-gated Na⁺-channels are transmembrane proteins that are responsible for the fast depolarizing phase of the action potential in nerve and muscular cells. Selective permeability of Na⁺ over Ca²⁺ or K⁺ ions is essential for the biological function of Na⁺-channels. After the emergence of the first high-resolution structure of a Na⁺-channel, an anionic coordination site was proposed to confer Na⁺ selectivity through partial dehydration of Na⁺ via its direct interaction with conserved glutamate side chains. By combining molecular dynamics simulations and free-energy calculations, a low-energy permeation pathway for Na⁺ ion translocation through the selectivity filter of the recently determined crystal structure of a prokaryotic sodium channel from Arcobacter butzleri is characterised. The picture that emerges is that of a pore preferentially occupied by two ions, which can switch between different configurations by crossing low free-energy barriers. In contrast to K⁺-channels, the movements of the ions appear to be weakly coupled in Na⁺-channels. When the free-energy maps for Na⁺ and K⁺ ions are compared, a selective site is characterised in the narrowest region of the filter, where a hydrated Na⁺ ion, and not a hydrated K⁺ ion, is energetically stable.

Ion channels are integral membrane proteins that control the passive diffusion of ions down their electrochemical gradient. According to the most permeating ion species, ion channels are classified in three categories: K⁺-channels, Na⁺-channels, and Ca²⁺-channels. The atomic structure of a K⁺-channel was the first to be solved experimentally more than 10 years ago. This structure inspired numerous computational studies, which revealed the mechanisms of conduction and selectivity in K⁺-channels. Recently, the first atomic structure of a Na⁺ selective channel has been solved. Here, molecular dynamics simulations and free-energy calculations are described and a possible mechanism for Na⁺ conduction is identified. In contrast to what it is observed in K⁺-channels, ion movements through Na⁺-channels appeared highly uncorrelated.

Determination of membrane-insertion free energies by molecular dynamics simulations

The accurate prediction of membrane-insertion probability for arbitrary protein sequences is a critical challenge to identifying membrane proteins and determining their folded structures. Although algorithms based on sequence statistics have had moderate success, a complete understanding of the energetic factors that drive the insertion of membrane proteins is essential to thoroughly meeting this challenge. In the last few years, numerous attempts to define a free-energy scale for amino-acid insertion have been made, yet disagreement between most experimental and theoretical scales persists. However, for a recently resolved water-to-bilayer scale, it is found that molecular dynamics simulations that carefully mimic the conditions of the experiment can reproduce experimental free energies, even when using the same force field as previous computational studies that were cited as evidence of this disagreement. Therefore, it is suggested that experimental and simulation-based scales can both be accurate and that discrepancies stem from disparities in the microscopic processes being considered rather than methodological errors. Furthermore, these disparities make the development of a single universally applicable membrane-insertion free energy scale difficult.

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.

Computational investigation of glycosylation effects on a family 1 carbohydrate-binding module

Carbohydrate-binding modules (CBMs) are ubiquitous components of glycoside hydrolases, which degrade polysaccharides in nature. CBMs target specific polysaccharides, and CBM binding affinity to cellulose is known to be proportional to cellulase activity, such that increasing binding affinity is an important component of performance improvement. To ascertain the impact of protein and glycan engineering on CBM binding, we use molecular simulation to quantify cellulose binding of a natively glycosylated Family 1 CBM. To validate our approach, we first examine aromatic-carbohydrate interactions on binding, and our predictions are consistent with previous experiments, showing that a tyrosine to tryptophan mutation yields a 2-fold improvement in binding affinity. We then demonstrate that enhanced binding of 3-6-fold over a nonglycosylated CBM is achieved by the addition of a single, native mannose or a mannose dimer, respectively, which has not been considered previously. Furthermore, we show that the addition of a single, artificial glycan on the anterior of the CBM, with the native, posterior glycans also present, can have a dramatic impact on binding affinity in our model, increasing it up to 140-fold relative to the nonglycosylated CBM. These results suggest new directions in protein engineering, in that modifying glycosylation patterns via heterologous expression, manipulation of culture conditions, or introduction of artificial glycosylation sites, can alter CBM binding affinity to carbohydrates and may thus be a general strategy to enhance cellulase performance. Our results also suggest that CBM binding studies should consider the effects of glycosylation on binding and function.

GMCT : a Monte Carlo simulation package for macromolecular receptors

Generalized Monte Carlo titration (GMCT) is a versatile suite of computer programs for the efficient simulation of complex macromolecular receptor systems as for example proteins. The computational model of the system is based on a microstate description of the receptor and an average description of its surroundings in terms of chemical potentials. The receptor can be modeled in great detail including conformational flexibility and many binding sites with multiple different forms that can bind different ligand types. Membrane embedded systems can be modeled including electrochemical potential gradients. Overall properties of the receptor as well as properties of individual sites can be studied with a variety of different Monte Carlo (MC) simulation methods. Metropolis MC, Wang-Landau MC and efficient free energy calculation methods are included. GMCT is distributed as free open source software at www.bisb.uni-bayreuth.de under the terms of the GNU Affero General Public License.

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.

Best practices in free energy calculations for drug design

Free energy calculations are increasingly of interest for computing biophysical properties of novel small molecules of interest in drug design, such as protein-ligand binding affinities and small molecule partition coefficients. However, these calculations are also notoriously difficult to implement correctly. In this article, we review standard methods for computing free energy differences via simulation, discuss current best practices, and examine potential pitfalls for computational researchers without extensive experience in such calculations. We include a variety of examples and tips for how to set up and conduct these calculations, including applications to relative binding affinities and absolute binding free energies.

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations.

Recognition of methylated DNA through methyl-CpG binding domain proteins

DNA methylation is a key regulatory control route in epigenetics, involving gene silencing and chromosome inactivation. It has been recognized that methyl-CpG binding domain (MBD) proteins play an important role in interpreting the genetic information encoded by methylated DNA (mDNA). Although the function of MBD proteins has attracted considerable attention and is well characterized, the mechanism underlying mDNA recognition by MBD proteins is still poorly understood. In this article, we demonstrate that the methyl-CpG dinucleotides are recognized at the MBD–mDNA interface by two MBD arginines through an interplay of hydrogen bonding and cation-π interaction. Through molecular dynamics and quantum-chemistry calculations we investigate the methyl-cytosine recognition process and demonstrate that methylation enhances MBD–mDNA binding by increasing the hydrophobic interfacial area and by strengthening the interaction between mDNA and MBD proteins. Free-energy perturbation calculations also show that methylation yields favorable contribution to the binding free energy for MBD–mDNA complex.

Calculation of the Absolute Free Energy of Binding and Related Entropies with the HSMD-TI Method: The FKBP12-L8 Complex

The hypothetical scanning molecular dynamics (HSMD) method is used here for calculating the absolute free energy of binding, ΔA(0) of the complex of the protein FKBP12 with the ligand SB2 (also denoted L8) - a system that has been studied previously for comparing the performance of different methods. Our preliminary study suggests that considering long-range electrostatics is imperative even for a hydrophobic ligand such as L8. Therefore the system is modeled by the AMBER force field using Particle Mesh Ewald (PME). HSMD consists of three stages applied to both the ligand-solvent and ligand-protein systems. (1) A small set of system configurations (frames) is extracted from an MD trajectory. (2) The entropy of the ligand in each frame is calculated by a reconstruction procedure. (3) The contribution of water and protein to ΔA(0) is calculated for each frame by gradually increasing the ligand-environment interactions from zero to their full value using thermodynamic integration (TI). Unlike the conventional methods, the structure of the ligand is kept fixed during TI, and HSMD is thus free from the end-point problem encountered with the double annihilation method (DAM); therefore, the need for applying restraints is avoided. Furthermore, unlike the conventional methods, the entropy of the ligand and water is obtained directly as a byproduct of the simulation. In this paper, in addition to the difference in the internal entropies of the ligand in the two environments, we calculate for the first time the external entropy of the ligand, which provides a measure for the size of the active site. We obtain ΔA(0) = -10.7 ±1.0 as compared to the experimental values -10.9 and -10.6 kcal/mol. However, a protein/water system treated by periodic boundary conditions grows significantly with increasing protein size and the computation of ΔA(0) would become expensive by all methods. Therefore, we also apply HSMD to FKBP12-L8 described by the GSBP/SSBP model of Roux's group (implemented in the software CHARMM) where only part of the protein and water around the active site are considered and long-range electrostatic effects are taken into account. For comparison this model was also treated by the double decoupling method (DDM). The two methods have led to comparable results for ΔA(0) which are somewhat lower than the experimental value. The ligand was found to be more confined in the active site described by GSBP/SSBP than by PME where its entropy in solvent is larger than in the active site by 1.7 and by 5.5 kcal/mol, respectively.

Linear-scaling soft-core scheme for alchemical free energy calculations

Alchemical free energy calculations involving the removal or insertion of atoms into condensed phase systems generally make use of soft-core scaling of nonbonded interactions, designed to circumvent numerical instabilities that arise from weakly interacting "hard" atoms in close proximity. Current methods model soft-core atoms by introducing a nonlinear dependence between the shape of the interaction potential and the strength of the interaction. In this article, we propose a soft-core method that avoids introducing such a nonlinear dependence, through the application of a smooth flattening of the potential energy only in a region that is energetically accessible under normal conditions. We discuss the benefits that this entails and explore a selection of applications, including enhanced methods for the estimation of free energy differences and for the automated optimization of the placement of intermediate states in multistage alchemical calculations.

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.

Improved Binding Free Energy Predictions from Single-Reference Thermodynamic Integration Augmented with Hamiltonian Replica Exchange

Reliable predictions of relative binding free energies are essential in drug discovery, where chemists modify promising compounds with the aim of increasing binding affinity. Conventional Thermodynamic Integration (TI) approaches can estimate corresponding changes in binding free energies, but suffer from inadequate sampling due to ruggedness of the molecular energy surfaces. Here, we present an improved TI strategy for computing relative binding free energies of congeneric ligands. This strategy employs a specific, unphysical single-reference (SR) state and Hamiltonian replica exchange (HREX) to locally enhance sampling. We then apply this strategy to compute relative binding free energies of twelve ligands in the L99A mutant of T4 Lysozyme. Besides the ligands, our approach enhances hindered rotations of the important V111, as well as V87 and L118 sidechains. Concurrently, we devise practical strategies to monitor and improve HREX-SRTI efficiency. Overall, the HREX-SRTI results agree well (R(2) = 0.76, RMSE = 0.3 kcal/mol) with available experimental data. When optimized for efficiency, the HREX-SRTI precision matches that of experimental measurements.

The inefficiency of re-weighted sampling and the curse of system size in high-order path integration

Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques—which is based on re-weighted sampling—is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average.

A molecular mechanics approach to modeling protein-ligand interactions: relative binding affinities in congeneric series

We introduce the "Prime-ligand" method for ranking ligands in congeneric series. The method employs a single scoring function, the OPLS-AA/GBSA molecular mechanics/implicit solvent model, for all stages of sampling and scoring. We evaluate the method using 12 test sets of congeneric series for which experimental binding data is available in the literature, as well as the structure of one member of the series bound to the protein. Ligands are "docked" by superimposing a common stem fragment among the compounds in the series using a crystal complex from the Protein Data Bank and sampling the conformational space of the variable region. Our results show good correlation between our predicted rankings and the experimental data for cases in which binding affinities differ by at least 1 order of magnitude. For 11 out of 12 cases, >90% of such ligand pairs could be correctly ranked, while for the remaining case, Factor Xa, 76% of such pairs were correctly ranked. A small number of compounds could not be docked using the current protocol because of the large size of functional groups that could not be accommodated by a rigid receptor. CPU requirements for the method, involving CPU minutes per ligand, are modest compared with more rigorous methods that use similar force fields, such as free energy perturbation. We also benchmark the scoring function using series of ligands bound to the same protein within the CSAR data set. We demonstrate that energy minimization of ligands in the crystal structures is critical to obtain any correlation with experimentally determined binding affinities.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

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.

Avoiding the van der Waals endpoint problem using serial atomic insertion

In the past analyses of the so-called van der Waals end point problem focused on thermodynamic integration. Here we investigate which of the recommendations, such as the need for soft-core potentials, are still valid when Bennett's acceptance ratio method is used. We show that in combination with Bennett's acceptance ratio method intermediate states characterized by the coupling parameter λ can be replaced by intermediate states in which Lennard-Jones interactions are turned on or off on an "atom by atom" basis. By doing so, there is no necessity to use soft-core potentials. In fact, one can compute free energy differences without dedicated code, making it possible to use any molecular dynamics program to compute alchemical free energy differences. Such an approach, which we illustrate by several examples, makes it possible to exploit the tremendous computational power of the graphics processing unit.

Biophysical probes reveal a "compromise" nature of the methyl-lysine binding pocket in L3MBTL1

Histone lysine methylation (Kme) encodes essential information modulating many biological processes including gene expression and transcriptional regulation. However, the atomic-level recognition mechanisms of methylated histones by their respective adaptor proteins are still elusive. For instance, it is unclear how L3MBTL1, a methyl-lysine histone code reader, recognizes equally well both mono- and dimethyl marks but ignores unmodified and trimethylated lysine residues. We made use of molecular dynamics (MD) and free energy perturbation (FEP) techniques in order to investigate the energetics and dynamics of the methyl-lysine recognition. Isothermal titration calorimetry (ITC) was employed to experimentally validate the computational findings. Both computational and experimental methods were applied to a set of designed "biophysical" probes that mimic the shape of a single lysine residue and reproduce the binding affinities of cognate histone peptides. Our results suggest that, besides forming favorable interactions, the L3MBTL1 binding pocket energetically penalizes both methylation states and has most probably evolved as a "compromise" that nonoptimally fits to both mono- and dimethyl-lysine marks.

Alchemical free energy methods for drug discovery: progress and challenges

Improved rational drug design methods are needed to lower the cost and increase the success rate of drug discovery and development. Alchemical binding free energy calculations, one potential tool for rational design, have progressed rapidly over the past decade, but still fall short of providing robust tools for pharmaceutical engineering. Recent studies, especially on model receptor systems, have clarified many of the challenges that must be overcome for robust predictions of binding affinity to be useful in rational design. In this review, inspired by a recent joint academic/industry meeting organized by the authors, we discuss these challenges and suggest a number of promising approaches for overcoming them.

An improved coarse-grained model of solvation and the hydrophobic effect

We present a coarse-grained lattice model of solvation thermodynamics and the hydrophobic effect that implements the ideas of Lum-Chandler-Weeks theory [J. Phys. Chem. B 134, 4570 (1999)] and improves upon previous lattice models based on it. Through comparison with molecular simulation, we show that our model captures the length-scale and curvature dependence of solvation free energies with near-quantitative accuracy and 2-3 orders of magnitude less computational effort, and further, correctly describes the large but rare solvent fluctuations that are involved in dewetting, vapor tube formation, and hydrophobic assembly. Our model is intermediate in detail and complexity between implicit-solvent models and explicit-water simulations.

Free-energy cost for translocon-assisted insertion of membrane proteins

Nascent membrane proteins typically insert in a sequential fashion into the membrane via a protein-conducting channel, the Sec translocon. How this process occurs is still unclear, although a thermodynamic partitioning between the channel and the membrane environment has been proposed. Experiment- and simulation-based scales for the insertion free energy of various amino acids are, however, at variance, the former appearing to lie in a narrower range than the latter. Membrane insertion of arginine, for instance, requires 14-17 kcal/mol according to molecular dynamics simulations, but only 2-3 kcal/mol according to experiment. We suggest that this disagreement is resolved by assuming a two-stage insertion process wherein the first step, the insertion into the translocon, is energized by protein synthesis and, therefore, has an effectively zero free-energy cost; the second step, the insertion into the membrane, invokes the translocon as an intermediary between the fully hydrated and the fully inserted locations. Using free-energy perturbation calculations, the effective transfer free energies from the translocon to the membrane have been determined for both arginine and leucine amino acids carried by a background polyleucine helix. Indeed, the insertion penalty for arginine as well as the insertion gain for leucine from the translocon to the membrane is found to be significantly reduced compared to direct insertion from water, resulting in the same compression as observed in the experiment-based scale.

Recent theoretical and computational advances for modeling protein-ligand binding affinities

We review recent theoretical and algorithmic advances for the modeling of protein ligand binding free energies. We first describe a statistical mechanics theory of noncovalent association, with particular focus on deriving the fundamental formulas on which computational methods are based. The second part reviews the main computational models and algorithms in current use or development, pointing out the relations with each other and with the theory developed in the first part. Particular emphasis is given to the modeling of conformational reorganization and entropic effect. The methods reviewed are free energy perturbation, double decoupling, the Binding Energy Distribution Analysis Method, the potential of mean force method, mining minima and MM/PBSA. These models have different features and limitations, and their ranges of applicability vary correspondingly. Yet their origins can all be traced back to a single fundamental theory.

New method for calculating the absolute free energy of binding: the effect of a mobile loop on the avidin/biotin complex

Hypothetical scanning molecular dynamics (HSMD) is a relatively new method for calculating the absolute free energy and entropy. HSMD is extended here for the first time for calculating the absolute free energy of binding, ΔA(0), as applied to the avidin-biotin complex. With HSMD the ligand is built (more accurately reconstructed) from nothing in solvent and in the protein, in contrast to the commonly used methods where the ligand is annihilated (by thermodynamic integration) in these environments. Therefore, the end-point problem encountered with the latter methods does not exist with HSMD and the need for restraints is avoided. Also, the entropy of the ligand and water in both environments is obtained directly as a byproduct of the simulation. The binding mechanism of biotin to avidin involves a mobile loop that is expected to be in an open conformation in unbound avidin, which is changed to a closed one upon binding, that is, the loop moves to cover biotin in the active site. The contribution of the loop's conformational change to the total free energy of binding is calculated here for the first time. Our result, ΔA(0) = -24.9 ± 7 covers the experimental value -20.7 kcal/mol within the error bars.