Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study

Hydrated Excess Protons Can Create Their Own Water Wires

Grotthuss shuttling of an excess proton charge defect through hydrogen bonded water networks has long been the focus of theoretical and experimental studies. In this work we show that there is a related process in which water molecules move ("shuttle") through a hydrated excess proton charge defect in order to wet the path ahead for subsequent proton charge migration. This process is illustrated through reactive molecular dynamics simulations of proton transport through a hydrophobic nanotube, which penetrates through a hydrophobic region. Surprisingly, before the proton enters the nanotube, it starts "shooting" water molecules into the otherwise dry space via Grotthuss shuttling, effectively creating its own water wire where none existed before. As the proton enters the nanotube (by 2-3 Å), it completes the solvation process, transitioning the nanotube to the fully wet state. By contrast, other monatomic cations (e.g., K(+)) have just the opposite effect, by blocking the wetting process and making the nanotube even drier. As the dry nanotube gradually becomes wet when the proton charge defect enters it, the free energy barrier of proton permeation through the tube via Grotthuss shuttling drops significantly. This finding suggests that an important wetting mechanism may influence proton translocation in biological systems, i.e., one in which protons "create" their own water structures (water "wires") in hydrophobic spaces (e.g., protein pores) before migrating through them. An existing water wire, e.g., one seen in an X-ray crystal structure or MD simulations without an explicit excess proton, is therefore not a requirement for protons to transport through hydrophobic spaces.

Computational study of Gleevec and G6G reveals molecular determinants of kinase inhibitor selectivity

Gleevec is a potent inhibitor of Abl tyrosine kinase but not of the highly homologous c-Src kinase. Because the ligand binds to an inactive form of the protein in which an Asp-Phe-Gly structural motif along the activation loop adopts a so-called DFG-out conformation, it was suggested that binding specificity was controlled by a "conformational selection" mechanism. In this context, the binding affinity displayed by the kinase inhibitor G6G poses an intriguing challenge. Although it possesses a chemical core very similar to that of Gleevec, G6G is a potent inhibitor of both Abl and c-Src kinases. Both inhibitors bind to the DFG-out conformation of the kinases, which seems to be in contradiction with the conformational selection mechanism. To address this issue and display the hidden thermodynamic contributions affecting the binding selectivity, molecular dynamics free energy simulations with explicit solvent molecules were carried out. Relative to Gleevec, G6G forms highly favorable van der Waals dispersive interactions upon binding to the kinases via its triazine functional group, which is considerably larger than the corresponding pyridine moiety in Gleevec. Upon binding of G6G to c-Src, these interactions offset the unfavorable free energy cost of the DFG-out conformation. When binding to Abl, however, G6G experiences an unfavorable free energy penalty due to steric clashes with the phosphate-binding loop, yielding an overall binding affinity that is similar to that of Gleevec. Such steric clashes are absent when G6G binds to c-Src, due to the extended conformation of the phosphate-binding loop.

Virtual high-throughput ligand screening

In Structural Genomics projects, virtual high-throughput ligand screening can be utilized to provide important functional details for newly determined protein structures. Using a variety of publicly available software tools, it is possible to computationally model, predict, and evaluate how different ligands interact with a given protein. At the Center for Structural Genomics of Infectious Diseases (CSGID) a series of protein analysis, docking and molecular dynamics software is scripted into a single hierarchical pipeline allowing for an exhaustive investigation of protein-ligand interactions. The ability to conduct accurate computational predictions of protein-ligand binding is a vital component in improving both the efficiency and economics of drug discovery. Computational simulations can minimize experimental efforts, the slowest and most cost prohibitive aspect of identifying new therapeutics.

Role of Internal Water on Protein Thermal Stability: The Case of Homologous G Domains

In this work, we address the question of whether the enhanced stability of thermophilic proteins has a direct connection with internal hydration. Our model systems are two homologous G domains of different stability: the mesophilic G domain of the elongation factor thermal unstable protein from E. coli and the hyperthermophilic G domain of the EF-1α protein from S. solfataricus. Using molecular dynamics simulation at the microsecond time scale, we show that both proteins host water molecules in internal cavities and that these molecules exchange with the external solution in the nanosecond time scale. The hydration free energy of these sites evaluated via extensive calculations is found to be favorable for both systems, with the hyperthermophilic protein offering a slightly more favorable environment to host water molecules. We estimate that, under ambient conditions, the free energy gain due to internal hydration is about 1.3 kcal/mol in favor of the hyperthermophilic variant. However, we also find that, at the high working temperature of the hyperthermophile, the cavities are rather dehydrated, meaning that under extreme conditions other molecular factors secure the stability of the protein. Interestingly, we detect a clear correlation between the hydration of internal cavities and the protein conformational landscape. The emerging picture is that internal hydration is an effective observable to probe the conformational landscape of proteins. In the specific context of our investigation, the analysis confirms that the hyperthermophilic G domain is characterized by multiple states and it has a more flexible structure than its mesophilic homologue.

Allosteric response and substrate sensitivity in peptide binding of the signal recognition particle

We characterize the conformational dynamics and substrate selectivity of the signal recognition particle (SRP) using a thermodynamic free energy cycle approach and microsecond timescale molecular dynamics simulations. The SRP is a central component of the co-translational protein targeting machinery that binds to the N-terminal signal peptide (SP) of nascent proteins. We determined the shift in relative conformational stability of the SRP upon substrate binding to quantify allosteric coupling between SRP domains. In particular, for dipeptidyl aminopeptidase, an SP that is recognized by the SRP for co-translational targeting, it is found that substrate binding induces substantial changes in the SRP toward configurations associated with targeting of the nascent protein, and it is found that the changes are modestly enhanced by a mutation that increases the hydrophobicity of the SP. However, for alkaline phosphatase, an SP that is recognized for post-translational targeting, substrate binding induces the reverse change in the SRP conformational distribution away from targeting configurations. Microsecond timescale trajectories reveal the intrinsic flexibility of the SRP conformational landscape and provide insight into recent single molecule studies by illustrating that 10-nm lengthscale changes between FRET pairs occur via the rigid-body movement of SRP domains connected by the flexible linker region. In combination, these results provide direct evidence for the hypothesis that substrate-controlled conformational switching in the SRP provides a mechanism for discriminating between different SPs and for connecting substrate binding to downstream steps in the protein targeting pathway.

Distinguishing binders from false positives by free energy calculations: fragment screening against the flap site of HIV protease

Molecular docking is a powerful tool used in drug discovery and structural biology for predicting the structures of ligand–receptor complexes. However, the accuracy of docking calculations can be limited by factors such as the neglect of protein reorganization in the scoring function; as a result, ligand screening can produce a high rate of false positive hits. Although absolute binding free energy methods still have difficulty in accurately rank-ordering binders, we believe that they can be fruitfully employed to distinguish binders from nonbinders and reduce the false positive rate. Here we study a set of ligands that dock favorably to a newly discovered, potentially allosteric site on the flap of HIV-1 protease. Fragment binding to this site stabilizes a closed form of protease, which could be exploited for the design of allosteric inhibitors. Twenty-three top-ranked protein–ligand complexes from AutoDock were subject to the free energy screening using two methods, the recently developed binding energy analysis method (BEDAM) and the standard double decoupling method (DDM). Free energy calculations correctly identified most of the false positives (≥83%) and recovered all the confirmed binders. The results show a gap averaging ≥3.7 kcal/mol, separating the binders and the false positives. We present a formula that decomposes the binding free energy into contributions from the receptor conformational macrostates, which provides insights into the roles of different binding modes. Our binding free energy component analysis further suggests that improving the treatment for the desolvation penalty associated with the unfulfilled polar groups could reduce the rate of false positive hits in docking. The current study demonstrates that the combination of docking with free energy methods can be very useful for more accurate ligand screening against valuable drug targets.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Computational analysis of the binding specificity of Gleevec to Abl, c-Kit, Lck, and c-Src tyrosine kinases

Gleevec, a well-known cancer therapeutic agent, is an effective inhibitor of several tyrosine kinases, including Abl and c-Kit, but displays less potency to inhibit closely homologous tyrosine kinases, such as Lck and c-Src. Because many structural features of the binding site are highly conserved in these homologous kinases, the molecular determinants responsible for the binding specificity of Gleevec remain poorly understood. To address this issue, free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent was used to compute the binding affinity of Gleevec to Abl, c-Kit, Lck, and c-Src. The results of the FEP/MD calculations are in good agreement with experiments, enabling a detailed and quantitative dissection of the absolute binding free energy in terms of various thermodynamic contributions affecting the binding specificity of Gleevec to the kinases. Dominant binding free energy contributions arises from the van der Waals dispersive interaction, compensating about two-thirds of the unfavorable free energy penalty associated with the loss of translational, rotational, and conformational freedom of the ligand upon binding. In contrast, the contributions from electrostatic and repulsive interactions nearly cancel out due to solvent effects. Furthermore, the calculations show the importance of the conformation of the kinase activation loop. Among the kinases examined, Abl provides the most favorable binding environment for Gleevec via optimal protein-ligand interactions and a small free energy cost for loss of the translational, rotational, and conformational freedom upon ligand binding. The FEP/MD calculations additionally reveal that Lck and c-Src provide similar nonbinding interactions with the bound-Gleevec, but the former pays less entropic penalty for the ligand losing its translational, rotational, and conformational motions to bind, examining the empirically observed differential binding affinities of Gleevec between the two Src-family kinases.

Absolute Free Energy of Binding and Entropy of the FKBP12-FK506 Complex: Effects of the Force Field

The hypothetical scanning molecular dynamics (HSMD) method combined with thermodynamic integration (HSMD-TI) has been extended recently for calculating ΔA(0)-the absolute free energy of binding of a ligand to a protein. With HSMD-TI, ΔA(0) is obtained in a new way as a sum of several components, among them is ΔSligand-the change in the conformational entropy as the ligand is transferred from the bulk solvent to the active site-this entropy is obtained by a specific reconstruction procedure. This unique aspect of HSMD (which is useful in rational drug design) is in particular important for treating large ligands, where ΔSligand might be significant. Technically, one should verify that the results for ΔSligand converge-a property that might become more difficult for large ligands; therefore, studying ligands of increasing size would define the range of applicability of HSMD-TI for binding. In this paper, we check the performance of HSMD-TI by applying it to the relatively large ligand FK506 (126 atoms) complexed with the protein FKBP12, where ΔA(0) = -12.8 kcal/mol is known experimentally as well as the crystal structure of the complex. This structure was initially equilibrated by carrying out a 100 ns molecular dynamics trajectory, where the system is modeled by the AMBER force field, TIP3P water, and Particle Mesh Ewald. HSMD-TI calculations were carried out in three conformational regions defined by the intervals [0.2,2], [2,5], and [5,100] ns along the trajectory, where local equilibration of the total energy has been observed; we obtained ΔA(0) = -13.6 ± 1.1, -16.6 ± 1.4, and -16.7 ± 1.4 kcal/mol, respectively indicating the following: (1) The second and third regions belong to the same conformational subspace of the complex, which is different from the [0.2,2] ns subspace. (2) The unsatisfactory result for ΔA(0) obtained in the well equilibrated (hence theoretically preferred) latter regions reflects the nonperfect modeling used, which however (3) has led to the experimental ΔA(0) in the [0.2,2] ns region close to the crystal structure. Keeping the complex near its crystal structure has been a successful approach in the literature. To check this avenue further, we applied harmonic restraints on backbone atoms and obtained unsatisfactory results for ΔA(0), suggesting that implementation of this approach is not straightforward. Converging results for ΔSligand were obtained in all regions, where the result ΔSligand([0.2,2]) = 7.1 ± 1.2 kcal/mol is less region dependent than ΔA(0) and is relatively large probably due to the large ligand.

Ligand selectivity of estrogen receptors by a molecular dynamics study

Estrogen receptors α (ERα) and β (ERβ) have different physiological functions and expression levels in different tissues. ERα and ERβ are highly homologous and have only two residue substitutions in the binding pocket. This high similarity at the active site stimulates the interests for discovering subtype selective ligands. In this study, molecular dynamics (MD) simulations combined with molecular mechanics generalized Born surface area (MM-GBSA) method have been carried out to analyze the basis of selectivity of three ligands (659, 818 and 041). The calculated binding free energies show that all the ligands bind more tightly to ERβ than to ERα. The dominant free energy components of selectivity for 659 are similar to that for 041, but different from that for 818. The decompositions of free energy contributions and structural analysis imply that there are eight residues primarily contributing to the selectivity for 659, five residues for 041, as well as two residues for 818. The structural analysis implies that two residue substitutions in binding packet cause the position of 659 in ERβ-659 complex to shift relative to that in ERα-659 complex and also cause the conformational changes of other residues in the binding pocket. The higher selectivity for 041 is mainly caused by three residues, Ile373 (Met421), His475 (His524) and Leu476 (Leu525).

Grid inhomogeneous solvation theory: hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

The displacement of perturbed water upon binding is believed to play a critical role in the thermodynamics of biomolecular recognition, but it is nontrivial to unambiguously define and answer questions about this process. We address this issue by introducing grid inhomogeneous solvation theory (GIST), which discretizes the equations of inhomogeneous solvation theory (IST) onto a three-dimensional grid situated in the region of interest around a solute molecule or complex. Snapshots from explicit solvent simulations are used to estimate localized solvation entropies, energies, and free energies associated with the grid boxes, or voxels, and properly summing these thermodynamic quantities over voxels yields information about hydration thermodynamics. GIST thus provides a smoothly varying representation of water properties as a function of position, rather than focusing on hydration sites where solvent is present at high density. It therefore accounts for full or partial displacement of water from sites that are highly occupied by water, as well as for partly occupied and water-depleted regions around the solute. GIST can also provide a well-defined estimate of the solvation free energy and therefore enables a rigorous end-states analysis of binding. For example, one may not only use a first GIST calculation to project the thermodynamic consequences of displacing water from the surface of a receptor by a ligand, but also account, in a second GIST calculation, for the thermodynamics of subsequent solvent reorganization around the bound complex. In the present study, a first GIST analysis of the molecular host cucurbit[7]uril is found to yield a rich picture of hydration structure and thermodynamics in and around this miniature receptor. One of the most striking results is the observation of a toroidal region of high water density at the center of the host's nonpolar cavity. Despite its high density, the water in this toroidal region is disfavored energetically and entropically, and hence may contribute to the known ability of this small receptor to bind guest molecules with unusually high affinities. Interestingly, the toroidal region of high water density persists even when all partial charges of the receptor are set to zero. Thus, localized regions of high solvent density can be generated in a binding site without strong, attractive solute-solvent interactions.

Standard binding free energies from computer simulations: What is the best strategy?

Accurate prediction of standard binding free energies describing protein:ligand association remains a daunting computational endeavor. This challenge is rooted to a large extent in the considerable changes in conformational, translational and rotational entropies underlying the binding process that atomistic simulations cannot easily capture. In spite of significant methodological advances, reflected in a continuously improving agreement with experiment, a characterization of alternate strategies aimed at measuring binding affinities, notably their respective advantages and drawbacks, is somewhat lacking. Here, two distinct avenues to determine the standard binding free energy are compared in the case of a short, proline-rich peptide associating to the Src homology domain 3 of tyrosine kinase Abl. These avenues - one relying upon alchemical transformations and the other on potentials of mean force (PMFs) - invoke a series of geometrical restraints acting on collective variables designed to alleviate sampling limitations inherent to classical molecular dynamics simulations. The experimental binding free energy of ΔG_bind = -7.99 kcal/mol is well reproduced by the two strategies developed herein, with ΔG_bind = -7.7 for the alchemical route and ΔG_bind = -7.8 kcal/mol for the alternate PMF-based route. In detailing the underpinnings of these numerical strategies devised for the accurate determination of standard binding free energies, many practical elements of the proposed rigorous, conceptual framework are clarified, thereby paving way to tackle virtually any recognition and association phenomenon.

Application of inhomogeneous fluid solvation theory to model the distribution and thermodynamics of water molecules around biomolecules

The structures of biomolecules and the strengths of association between them depend critically on interactions with water molecules. Thus, understanding these interactions is a prerequisite for understanding the structure and function of all biomolecules. Inhomogeneous fluid solvation theory provides a framework to derive thermodynamic properties of individual water molecules from a statistical mechanical analysis. In this work, two biomolecules are analysed to probe the distribution and thermodynamics of surrounding water molecules. The great majority of hydration sites are predicted to contribute favourably to the total free energy with respect to bulk water, though hydration sites close to non-polar regions of the solute do not contribute significantly. Analysis of a biomolecule with a positively and negatively charged functional group predicts that a charged species perturbs the free energy of water molecules to a distance of approximately 6.0 Å. Interestingly, short simulations are found to provide converged predictions if samples are taken with sufficient frequency, a finding that has the potential to significantly reduce the required computational cost of such analysis. In addition, the predicted thermodynamic properties of hydration sites with the potential for direct hydrogen bonding interactions are found to disagree significantly for two different water models. This study provides important information on how inhomogeneous fluid solvation theory can be employed to understand the structures and intermolecular interactions of biomolecules.

Absolute free energy of binding of avidin/biotin, revisited

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.

Ion binding sites and their representations by reduced models

The binding of small metal ions to complex macromolecular structures is typically dominated by strong local interactions of the ion with its nearest ligands. Progress in understanding the molecular determinants of ion selectivity can often be achieved by considering simplified reduced models comprised of only the most important ion-coordinating ligands. Although the main ingredients underlying simplified reduced models are intuitively clear, a formal statistical mechanical treatment is nonetheless necessary in order to draw meaningful conclusions about complex macromolecular systems. By construction, reduced models only treat the ion and the nearest coordinating ligands explicitly. The influence of the missing atoms from the protein or the solvent is incorporated indirectly. Quasi-chemical theory offers one example of how to carry out such a separation in the case of ion solvation in bulk liquids, and in several ways, a statistical mechanical formulation of reduced binding site models for macromolecules is expected to follow a similar route. However, there are also important differences when the ion-coordinating moieties are not solvent molecules from a bulk phase but are molecular ligands covalently bonded to a macromolecular structure. Here, a statistical mechanical formulation of reduced binding site models is elaborated to address these issues. The formulation provides a useful framework to construct reduced binding site models, and define the average effect from the surroundings on the ion and the nearest coordinating ligands.

Predicting the DNA sequence dependence of nanopore ion current using atomic-resolution Brownian dynamics

It has become possible to distinguish DNA molecules of different nucleotide sequences by measuring ion current passing through a narrow pore containing DNA. To assist experimentalists in interpreting the results of such measurements and to improve the DNA sequence detection method, we have developed a computational approach that has both the atomic-scale accuracy and the computational efficiency required to predict DNA sequence-specific differences in the nanopore ion current. In our Brownian dynamics method, the interaction between the ions and DNA is described by three-dimensional potential of mean force maps determined to a 0.03 nm resolution from all-atom molecular dynamics simulations. While this atomic-resolution Brownian dynamics method produces results with orders of magnitude less computational effort than all-atom molecular dynamics requires, we show here that the ion distributions and ion currents predicted by the two methods agree. Finally, using our Brownian dynamics method, we find that a small change in the sequence of DNA within a pore can cause a large change in the ion current, and validate this result with all-atom molecular dynamics.

CALCULATING ACCURATE REDOX POTENTIALS IN ENZYMES WITH A COMBINED QM/MM FREE ENERGY PERTURBATION APPROACH

An approach for computing accurate redox potentials in enzymes is developed based on the free energy perturbation technique in a QM/MM framework. With an appropriate choice of the QM level and QM/MM coupling scheme, the intermolecular interaction between the redox center and the protein environment can be adequately described; the speed of QM/MM methods also allows a sufficient configurational sampling for the convergence of free energy derivatives. Following the implementation into the simulation package CHARMM, the method was tested with an application to the first reduction potential of FAD in cholesterol oxidase (Chox). In addition to an accurate QM level and adequate conformational samplings, the effect of long-range electrostatic interactions due to the bulk solvent was also found to be essential. Using a semi-empirical density functional theory (SCC-DFTB) as the QM level, and a multi-stage charge-scaling scheme based on Poisson–Boltzmann calculations for the solvation effect, satisfactory agreements with experimental measurements were obtained. The study of Chox also indicates that large errors in the calculated redox potential might arise if changes in the conformational properties of the protein during the redox process are not taken into account, such as in energy minimization type of studies based on only the X-ray structure of the enzyme in one redox state.

Theoretical prediction of the binding free energy for mutants of replication protein A

The replication protein A (RPA) is a heterotrimeric (70, 32, and 14 kDa subunits), single stranded DNA (ssDNA) binding protein required for pivotal functions in the cell metabolism, such as chromosomal replication, prevention of hairpin formation, DNA repair and recombination, and signaling after DNA damage. Studies based on deletions and mutations have identified the high affinity ssDNA binding domains in the 70 kDa subunit of RPA, regions A and B. Individually, the domain A and B have a low affinity for ssDNA, while tandems composed of AA, AB, BB, and BA sequences bind the ssDNA with moderate to high affinity. Single and double point mutations on polar residues in the binding domains leads to a reduction in affinity of RPA for ssDNA, in particular when two hydrophilic residues are involved. In view of these results, we performed a study based on molecular dynamics simulation aimed to reproduce the experimental change in binding free energy, ΔΔG, of RPA70 mutants to further elucidate the nature of the protein-ssDNA interaction. The MM-PB(GB)SA methods implemented in Amber10 and the code FoldX were used to estimate the binding free energy. The theoretical and experimental ΔΔG values correlate better when the results are obtained by MM-PBSA calculated on individual trajectories for each mutant. In these conditions, the correlation coefficient between experimental and theoretical ΔΔG reaches a value of 0.95 despite the overestimation of the energy change by one order of magnitude. The decomposition of the MM-GBSA energy per residue allows us to correlate the change of the affinity with the residue polarity and energy contribution to the binding. The method revealed reliable predictions of the change in the affinity in function of mutations, and can be used to identify new mutants with distinct binding properties.

Accurate prediction of the binding free energy and analysis of the mechanism of the interaction of replication protein A (RPA) with ssDNA

The eukaryotic replication protein A (RPA) has several pivotal functions in the cell metabolism, such as chromosomal replication, prevention of hairpin formation, DNA repair and recombination, and signaling after DNA damage. Moreover, RPA seems to have a crucial role in organizing the sequential assembly of DNA processing proteins along single stranded DNA (ssDNA). The strong RPA affinity for ssDNA, K(A) between 10(-9)-10(-10) M, is characterized by a low cooperativity with minor variation for changes on the nucleotide sequence. Recently, new data on RPA interactions was reported, including the binding free energy of the complex RPA70AB with dC(8) and dC(5), which has been estimated to be -10 ± 0.4 kcal mol(-1) and -7 ± 1 kcal mol(-1), respectively. In view of these results we performed a study based on molecular dynamics aimed to reproduce the absolute binding free energy of RPA70AB with the dC(5) and dC(8) oligonucleotides. We used several tools to analyze the binding free energy, rigidity, and time evolution of the complex. The results obtained by MM-PBSA method, with the use of ligand free geometry as a reference for the receptor in the separate trajectory approach, are in excellent agreement with the experimental data, with ±4 kcal mol(-1) error. This result shows that the MM-PB(GB)SA methods can provide accurate quantitative estimates of the binding free energy for interacting complexes when appropriate geometries are used for the receptor, ligand and complex. The decomposition of the MM-GBSA energy for each residue in the receptor allowed us to correlate the change of the affinity of the mutated protein with the ΔG(gas+sol) contribution of the residue considered in the mutation. The agreement with experiment is optimal and a strong change in the binding free energy can be considered as the dominant factor in the loss for the binding affinity resulting from mutation.

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.

Elucidating the energetics of entropically driven protein-ligand association: calculations of absolute binding free energy and entropy

The binding of proteins and ligands is generally associated with the loss of translational, rotational, and conformational entropy. In many cases, however, the net entropy change due to binding is positive. To develop a deeper understanding of the energetics of entropically driven protein-ligand binding, we calculated the absolute binding free energies and binding entropies for two HIV-1 protease inhibitors Nelfinavir and Amprenavir using the double-decoupling method with molecular dynamics simulations in explicit solvent. For both ligands, the calculated absolute binding free energies are in general agreement with experiments. The statistical error in the computed ΔG(bind) due to convergence problem is estimated to be ≥2 kcal/mol. The decomposition of free energies indicates that, although the binding of Nelfinavir is driven by nonpolar interaction, Amprenavir binding benefits from both nonpolar and electrostatic interactions. The calculated absolute binding entropies show that (1) Nelfinavir binding is driven by large entropy change and (2) the entropy of Amprenavir binding is much less favorable compared with that of Nelfinavir. Both results are consistent with experiments. To obtain qualitative insights into the entropic effects, we decomposed the absolute binding entropy into different contributions based on the temperature dependence of free energies along different legs of the thermodynamic pathway. The results suggest that the favorable entropic contribution to binding is dominated by the ligand desolvation entropy. The entropy gain due to solvent release from binding site appears to be more than offset by the reduction of rotational and vibrational entropies upon binding.

Insights into scFv:drug binding using the molecular dynamics simulation and free energy calculation

Molecular dynamics simulations and free energy calculation have been performed to study how the single-chain variable fragment (scFv) binds methamphetamine (METH) and amphetamine (AMP). The structures of the scFv:METH and the scFv:AMP complexes are analyzed by examining the time-dependence of their RMSDs, by analyzing the distance between some key atoms of the selected residues, and by comparing the averaged structures with their corresponding crystallographic structures. It is observed that binding an AMP to the scFv does not cause significant changes to the binding pocket of the scFv:ligand complex. The binding free energy of scFv:AMP without introducing an extra water into the binding pocket is much stronger than scFv:METH. This is against the first of the two scenarios postulated in the experimental work of Celikel et al. (Protein Science 18, 2336 (2009)). However, adding a water to the AMP (at the position of the methyl group of METH), the binding free energy of the scFv:AMP-H2O complex, is found to be significantly weaker than scFv:METH. This is consistent with the second of the two scenarios given by Celikel et al. Decomposition of the binding energy into ligand-residue pair interactions shows that two residues (Tyr175 and Tyr177) have nearly-zero interactions with AMP in the scFv:AMP-H2O complex, whereas their interactions with METH in the scFv:METH complex are as large as -0.8 and -0.74 kcal mol(-1). The insights gained from this study may be helpful in designing more potent antibodies in treating METH abuse.

Calculation of configurational entropy with a Boltzmann-quasiharmonic model: the origin of high-affinity protein-ligand binding

Accurate assessment of configurational entropy remains a large challenge in biology. While many methods exist to calculate configurational entropy, there is a balance between accuracy and computational demands. Here we calculate ligand and protein conformational entropies using the Boltzmann-quasiharmonic (BQH) method, which treats the first-order entropy term by the Boltzmann expression for entropy while determining correlations using the quasiharmonic model. This method is tested by comparison with the exact Clausius expression for entropy on a range of test molecules ranging from small ligands to a protein. Using the BQH method, we then analyze the rotational and translational (R/T) entropy change upon ligand binding for five protein complexes to explore the origins of extremely tight affinity. The results suggest that in these systems such affinity is achieved by a combination of simultaneously maintaining good protein-ligand contacts while allowing significant residual R/T motion of the ligand through suitable protein motions.

Probing carbohydrate product expulsion from a processive cellulase with multiple absolute binding free energy methods

Understanding the enzymatic mechanism that cellulases employ to degrade cellulose is critical to efforts to efficiently utilize plant biomass as a sustainable energy resource. A key component of cellulase action on cellulose is product inhibition from monosaccharide and disaccharides in the product site of cellulase tunnel. The absolute binding free energy of cellobiose and glucose to the product site of the catalytic tunnel of the Family 7 cellobiohydrolase (Cel7A) of Trichoderma reesei (Hypocrea jecorina) was calculated using two different approaches: steered molecular dynamics (SMD) simulations and alchemical free energy perturbation molecular dynamics (FEP/MD) simulations. For the SMD approach, three methods based on Jarzynski's equality were used to construct the potential of mean force from multiple pulling trajectories. The calculated binding free energies, -14.4 kcal/mol using SMD and -11.2 kcal/mol using FEP/MD, are in good qualitative agreement. Analysis of the SMD pulling trajectories suggests that several protein residues (Arg-251, Asp-259, Asp-262, Trp-376, and Tyr-381) play key roles in cellobiose and glucose binding to the catalytic tunnel. Five mutations (R251A, D259A, D262A, W376A, and Y381A) were made computationally to measure the changes in free energy during the product expulsion process. The absolute binding free energies of cellobiose to the catalytic tunnel of these five mutants are -13.1, -6.0, -11.5, -7.5, and -8.8 kcal/mol, respectively. The results demonstrated that all of the mutants tested can lower the binding free energy of cellobiose, which provides potential applications in engineering the enzyme to accelerate the product expulsion process and improve the efficiency of biomass conversion.

Energetics of double-ion occupancy in the gramicidin A channel

To understand the energetics of double-ion occupancy in gramicidin A (gA) channels, the 2D potential of mean force (PMF) is calculated for two ions at different positions along the channel axis. The cross sections of this 2D PMF are compared with available one-ion PMFs to highlight the effect of one ion on the permeation dynamics of the other. It is found that, if the first ion stays on one side in the channel, the second ion has to pass over an additional barrier to move into the outer binding site. At the same time, both outer and inner binding sites for the second ion become shallower than those in the one-ion PMF. The calculated ion-ion repulsion for a doubly occupied channel is about 2 kcal/mol, in good agreement with previous experimental estimates. The number of water molecules inside the channel and their dipole moment are calculated to interpret the energetics of double-ion occupancy. As the first ion moves into the outer binding site and then further into the channel, the oxygen atoms of the single-file water column in the channel are oriented to point toward the ion. The observed dipole moment distribution of a singly occupied channel has only one sharp peak, and the water alignment is essentially perfect once the ion is in the inner binding site. For this reason, there is an energy penalty to accommodate a second ion at the opposite end of the channel.

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.

Absolute binding free energy calculations of sparsomycin analogs to the bacterial ribosome

The interactions of the 50S subunit of bacterial ribosome with antibiotic sparsomycin (SPS) and five analogs (AN) are investigated through the calculation of the standard (absolute) binding free energy and the characterization of conformational dynamics. The standard binding free energies of the complexes are computed using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. Restraining potentials are applied and then released during the simulation to efficiently sample the changes in translational, orientational, and conformational freedom of the ligand and receptor upon binding. The biasing effects of the restraining potentials are rigorously removed. The loss of conformational freedom of the ligand upon binding is determined by introducing a potential of mean force (PMF) as a function of the root-mean-square deviation (rmsd) of the ligand relative to its conformation in the bound state. To reduce the size of the simulated system, the binding pocket of the ribosome is simulated in the framework of the generalized solvent boundary potential (GSBP). The number of solvent molecules in the buried binding site is treated via grand canonical Monte Carlo (GCMC) during the FEP/MD simulations. The correlation coefficient between the calculated and measured binding free energies is 0.96, and the experimentally observed ranking order for the binding affinities of the six ligands is reproduced. However, while the calculated affinities of the strong binders agree well with the experimental values, those for the weak binders are underestimated.

Water in the polar and nonpolar cavities of the protein interleukin-1β

Water in the protein interior serves important structural and functional roles and is also increasingly recognized as a relevant factor in drug binding. The nonpolar cavity in the protein interleukin-1β has been reported to be filled by water on the basis of some experiments and simulations and to be empty on the basis of others. Here we study the thermodynamics of filling the central nonpolar cavity and the four polar cavities of interleukin-1β by molecular dynamics simulation. We use different water models (TIP3P and SPC/E) and protein force fields (amber94 and amber03) to calculate the semigrand partition functions term by term that quantify the hydration equilibria. We consistently find that water in the central nonpolar cavity is thermodynamically unstable, independent of force field and water model. The apparent reason is the relatively small size of the cavity, with a volume less than ∼80 Å(3). Our results are consistent with the most recent X-ray crystallographic and simulation studies but disagree with an earlier interpretation of nuclear magnetic resonance (NMR) experiments probing protein-water interactions. We show that, at least semiquantitatively, the measured nuclear Overhauser effects indicating the proximity of water to the methyl groups lining the nonpolar cavity can, in all likelihood, be attributed to interactions with buried and surface water molecules near the cavity. The same methods applied to determine the occupancy of the polar cavities show that they are filled by the same number of water molecules observed in crystallography, thereby validating the theoretical and simulation methods used to study the water occupancy in the nonpolar protein cavity.

Molecular dynamics free energy calculations to assess the possibility of water existence in protein nonpolar cavities

Are protein nonpolar cavities filled with water molecules? Although many experimental and theoretical investigations have been done, particularly for the nonpolar cavity of IL-1 beta, the results are still conflicting. To study this problem from the thermodynamic point of view, we calculated hydration free energies of four protein nonpolar cavities by means of the molecular dynamics thermodynamic integration method. In addition to the IL-1 beta cavity (69 A(3)), we selected the three largest nonpolar cavities of AvrPphB (81 A(3)), Trp repressor (87 A(3)), and hemoglobin (108 A(3)) from the structural database, in view of the simulation result from another study that showed larger nonpolar cavities are more likely to be hydrated. The calculations were performed with flexible and rigid protein models. The calculated free energy changes were all positive; hydration of the nonpolar cavities was energetically unfavorable for all four cases. Because hydration of smaller cavities should happen more rarely, we conclude that existing protein nonpolar cavities are not likely to be hydrated. Although a possibility remains for much larger nonpolar cavities, such cases are not found experimentally. We present a hypothesis to explain this: hydrated nonpolar cavities are quite unstable and the conformation could not be maintained.

A computational analysis of the binding model of MDM2 with inhibitors

It is a new and promising strategy for anticancer drug design to block the MDM2-p53 interaction using a non-peptide small-molecule inhibitor. We carry out molecular dynamics simulations to study the binding of a set of six non-peptide small-molecule inhibitors with the MDM2. The relative binding free energies calculated using molecular mechanics Poisson-Boltzmann surface area method produce a good correlation with experimentally determined results. The study shows that the van der Waals energies are the largest component of the binding free energy for each complex, which indicates that the affinities of these inhibitors for MDM2 are dominated by shape complementarity. The A-ligands and the B-ligands are the same except for the conformation of 2,2-dimethylbutane group. The quantum mechanics and the binding free energies calculation also show the B-ligands are the more possible conformation of ligands. Detailed binding free energies between inhibitors and individual protein residues are calculated to provide insights into the inhibitor-protein binding model through interpretation of the structural and energetic results from the simulations. The study shows that G1, G2 and G3 group mimic the Phe19, Trp23 and Leu26 residues in p53 and their interactions with MDM2, but the binding model of G4 group differs from the original design strategy to mimic Leu22 residue in p53.

A Note on the Standard State's Binding Free Energy

The relation between the equilibrium constant of a given chemical reaction and the associated free energy is an issue well studied in chemistry books, but when the reaction involves changes in the number of components in the system, as is the case in binding, things become a little more obscure since one needs to define the so-called standard state. This is reflected in the literature, especially in computational studies of binding, where contradicting approaches are followed when treating this problem. In this work, we present a detailed and unifying explanation of the concepts involved and derive the necessary relations to convert a binding free energy from an arbitrary state to some given standard state. This is done in three independent ways, from the point of view of (1) the dimensions of the quantities involved, (2) the energy and entropy of the molecules, and (3) their chemical potentials.

Accounting for ligand conformational restriction in calculations of protein-ligand binding affinities

The conformation adopted by a ligand on binding to a receptor may differ from its lowest-energy conformation in solution. In addition, the bound ligand is more conformationally restricted, which is associated with a configurational entropy loss. The free energy change due to these effects is often neglected or treated crudely in current models for predicting binding affinity. We present a method for estimating this contribution, based on perturbation theory using the quasi-harmonic model of Karplus and Kushick as a reference system. The consistency of the method is checked for small model systems. Subsequently we use the method, along with an estimate for the enthalpic contribution due to ligand-receptor interactions, to calculate relative binding affinities. The AMBER force field and generalized Born implicit solvent model is used. Binding affinities were estimated for a test set of 233 protein-ligand complexes for which crystal structures and measured binding affinities are available. In most cases, the ligand conformation in the bound state was significantly different from the most favorable conformation in solution. In general, the correlation between measured and calculated ligand binding affinities including the free energy change due to ligand conformational change is comparable to or slightly better than that obtained by using an empirically-trained docking score. Both entropic and enthalpic contributions to this free energy change are significant.

Calculation of the standard binding free energy of sparsomycin to the ribosomal peptidyl-transferase P-site using molecular dynamics simulations with restraining potentials

The standard (absolute) binding free energy of the antibiotic sparsomycin with the 50S bacteria ribosomal subunit is calculated using molecular dynamics (MD) free energy perturbation (FEP) simulations with restraining potentials developed by Wang et al. [Biophys. J. 91:2798-2814 (2006)]. In the simulation protocol, restraining potentials are activated for the orientational and translational movements of the ligand relative to the binding site when it is decoupled from the binding pocket, and then released once the ligand fully interacts with the rest of the system. A reduced system is simulated to decrease the computational cost of the FEP/MD calculations and the effects of the surrounding atoms are incorporated using the generalized solvent boundary potential (GSBP) method. The loss of conformational freedom of the ligand upon binding is characterized using the potential of mean force (PMF) as a function of the root-mean-square deviation (RMSD) relative to the bound conformation. The number of water molecules in the binding pocket is allowed to fluctuate dynamically in response to the ligand during the calculations by combining FEP/MD with grand canonical Monte Carlo (GCMC) simulations. The calculated binding free energy is about -6 kcal/mol, which is in reasonable agreement with the experimental value. The information gleaned from this study provides new insight on the recognition of ribosome by sparsomycin and highlights the challenges in calculations of absolute binding free energies in these systems.

Alchemical free energy simulations for biological complexes: powerful but temperamental

Free energy simulations compare multiple ligand:receptor complexes by "alchemically" transforming one into another, yielding binding free energy differences. Since their introduction in the 1980s, many technical and theoretical obstacles were surmounted, and the method ("MDFE," since molecular dynamics are often used) has matured into a powerful tool. We describe its current status, its effectiveness, and the challenges it faces. MDFE has provided chemical accuracy for many systems but remains expensive, with significant human overhead costs. The bottlenecks have shifted, partly due to increased computer power. To study diverse sets of ligands, force field availability and accuracy can be a major difficulty. Another difficulty is the frequent need to consider multiple states, related to sidechain protonation or buried waters, for example. Sophisticated, automated methods to sample these states are maturing, such as constant pH simulations. Meanwhile, combinations of MDFE and simpler approaches, like continuum dielectric models, can be very effective. As illustrations, we show how, with careful force field parameterization, MDFE accurately predicts binding specificities between complex tetracycline ligands and their targets. We describe substrate binding to the aspartyl-tRNA synthetase enzyme, where many distinct electrostatic states play a role, and a histidine and a Mg(2+) ion act as coupled switches that help enforce a strict preference for the aspartate substrate, relative to several analogs. Overall, MDFE has achieved a predictive status, where novel ligands can be studied and molecular recognition elucidated in depth. It should play an increasing role in the analysis of complex cellular processes and biomolecular engineering.

Binding selectivity of RecA to a single stranded DNA, a computational approach

Homologous recombination (HR) is the major DNA double strand break repair pathway which maintains the genomic integrity. It is fundamental for the survivability and functionality of all organisms. One of the initial steps in HR is the formation of the nucleoprotein filament composed by a single stranded DNA chain surrounded by the recombinases protein. The filament orchestrates the search for an undamaged homologue, as a template for the repair process. Our theoretical study was aimed at elucidating the selectivity of the interaction between a monomer of the recombinases enzyme in the Escherichia coli, EcRecA, the bacterial homologue of human Rad51, with a series of oligonucleotides of nine bases length. The complex, equilibrated for 20 ns with Langevian dynamics, was inserted in a periodic box with a 8 Å buffer of water molecules explicitly described by the TIP3P model. The absolute binding free energies are calculated in an implicit solvent using the Poisson-Boltzmann (PB) and the generalized Born (GB) solvent accessible surface area, using the MM-PB(GB)SA model. The solute entropic contribution is also calculated by normal mode analysis. The results underline how a significant contribution of the binding free energy is due to the interaction with the Arg196, a critical amino acid for the activity of the enzyme. The study revealed how the binding affinity of EcRecA is significantly higher toward dT₉ rather than dA₉, as expected from the experimental results.