Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist et. al., Prot Eng 1994;7:385-391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total DeltaG(bind,l;). The sum of these contributions is scaled by a factor straight theta and it is argued that obtaining a quantitative balance between these contributions should result in straight theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta and a way to understand its origin. The present approach gives straight theta values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE straight theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation,     

Absolute binding free energy calculations: On the accuracy of computational scoring of protein–ligand interactions

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer‐aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/β version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S‐LRA version) as well as the less rigorous molecular mechanics Poisson–Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/β, the LIE, the PDLD/S‐LRA/β, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S‐LRA/β performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S‐LRA/β appears to offer an appealing option for the final stages of massive screening approaches. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

On the attribution of binding energy in antigen-antibody complexes McPC 603, D1.3, and HyHEL-5

Using X-ray coordinates of antigen-antibody complexes McPC 603, D1.3, and HyHEL-5, we made semiquantitative estimates of Gibbs free energy changes (delta G) accompanying noncovalent complex formation of the McPC 603 Fv fragment with phosphocholine and the D1.3 or HyHEL-5 Fv fragments with hen egg white lysozyme. Our empirical delta G function, which implicitly incorporates solvent effects, has the following components: hydrophobic force, solvent-modified electrostatics, changes in side-chain conformational entropy, translational/overall rotational entropy changes, and the dilutional (cratic) entropy term. The calculated delta G ranges matched the experimentally determined delta G of McPC 603 and D1.3 complexes and overestimated it (i.e., gave a more negative value) in the case of HyHEL-5. Relative delta G contributions of selected antibody residues, calculated for HyHEL-5 complexes, agreed with those determined independently in site-directed mutagenesis experiments. Analysis of delta G attribution in all three complexes indicated that only a small number of amino acids probably contribute actively to binding energetics. These form a subset of the total antigen-antibody contact surface. In the antibodies, the bottom part of the antigen binding cavity dominated the energetics of binding whereas in lysozyme, the energetically most important residues defined small (2.5-3 nm2) "energetic" epitopes. Thus, a concept of protein antigenicity emerges that involves the active, attractive contributions mediated by the energetic antigenic epitopes and the passive surface complementarity contributed by the surrounding contact area. The D1.3 energetic epitope of lysozyme involved Gly 22, Gly 117, and Gln 121; the HyHEL-5 epitope consisted of Arg 45 and Arg 68. These are also the essential antigenic residues determined experimentally. The above positions belong to the most protruding parts of the lysozyme surface, and their backbones are not exceptionally flexible. Least-squares analysis of six different antibody binding regions indicated that the geometry of the VH-VL interface beta-barrel is well conserved, giving no indication of significant changes in domain-domain contacts upon complex formation.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

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

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

Interactions of calmodulin with death-associated protein kinase peptides: experimental and modeling studies

We have studied the interactions between calmodulin (CaM) and three target peptides from the death-associated protein kinase (DAPK) protein family using both experimental and modeling methods, aimed at determining the details of the underlying biological regulation mechanisms. Experimentally, calorimetric binding free energies were determined for the complexes of CaM with peptides representing the DAPK2 wild-type and S308D mutant, as well as DAPK1. The observed affinity of CaM was very similar for all three studied peptides. The DAPK2 and DAPK1 peptides differ significantly in sequence and total charge, while the DAPK2 S308D mutant is designed to model the effects of DAPK2 Ser308 phosphorylation. The crystal structure of the CaM-DAPK2 S308D mutant peptide is also reported. The structures of CaM-DAPK peptide complexes present a mode of CaM-kinase interaction, in which bulky hydrophobic residues at positions 10 and 14 are both bound to the same hydrophobic cleft. To explain the microscopic effects underlying these interactions, we performed free energy calculations based on the approximate MM-PBSA approach. For these highly charged systems, standard MM-PBSA calculations did not yield satisfactory results. We proposed a rational modification of the approach which led to reasonable predictions of binding free energies. All three complexes are strongly stabilized by two effects: electrostatic interactions and buried surface area. The strong favorable interactions are to a large part compensated by unfavorable entropic terms, in which vibrational entropy is the largest contributor. The electrostatic component of the binding free energy followed the trend of the overall peptide charge, with strongest interactions for DAPK1 and weakest for the DAPK2 mutant. The electrostatics was dominated by interactions of the positively charged residues of the peptide with the negatively charged residues of CaM. The nonpolar binding free energy was comparable for all three peptides, the largest contribution coming from the Trp305. About two-thirds of the buried surface area corresponds to nonpolar residues, showing that hydrophobic interactions play an important role in these CaM-peptide complexes. The simulation results agree with the experimental data in predicting a small effect of the S308D mutation on CaM interactions with DAPK2, suggesting that this mutation is not a good model for the S308 phosphorylation.     

On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions

This paper describes a methodology to calculate the binding free energy (ΔG) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the binding free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as purely nonpolar entities, and the final complex is then recharged. The total electrostatic free energies of the protein, the ligand, and the complex in water are calculated with the finite difference Poisson-Boltzmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a single alkane/water surface tension coefficient (γ_aw). The loss in backbone and side-chain configurational entropy upon binding is estimated and added to the electrostatic and the nonpolar components of ΔG. The methodology is applied to the binding of the murine MHC class I protein H-2K^b with three distinct peptides, and to the human MHC class I protein HLA-A2 in complex with five different peptides. Despite significant differences in the amino acid sequences of the different peptides, the experimental binding free energy differences (ΔΔG_exp) are quite small (<0.3 and <2.7 kcal/mol for the H-2K^b and HLA-A2 complexes, respectively). For each protein, the calculations are successful in reproducing a fairly small range of values for ΔΔG_calc (<4.4 and <5.2 kcal/mol, respectively) although the relative peptide binding affinities of H-2K^b and HLA-A2 are not reproduced. For all protein-peptide complexes that were treated, it was found that electrostatic interactions oppose binding whereas nonpolar interactions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are generally opposed by increased electrostatic contributions favoring dissociation. The factors that drive the binding of peptides to MHC proteins are discussed in light of our results.     

A Computational Analysis of ATP Binding of SV40 Large Tumor Antigen Helicase Motor

Simian Virus 40 Large Tumor Antigen (LTag) is an efficient helicase motor that unwinds and translocates DNA. The DNA unwinding and translocation of LTag is powered by ATP binding and hydrolysis at the nucleotide pocket between two adjacent subunits of an LTag hexamer. Based on the set of high-resolution hexameric structures of LTag helicase in different nucleotide binding states, we simulated a conformational transition pathway of the ATP binding process using the targeted molecular dynamics method and calculated the corresponding energy profile using the linear response approximation (LRA) version of the semi-macroscopic Protein Dipoles Langevin Dipoles method (PDLD/S). The simulation results suggest a three-step process for the ATP binding from the initial interaction to the final tight binding at the nucleotide pocket, in which ATP is eventually “locked” by three pairs of charge-charge interactions across the pocket. Such a “cross-locking” ATP binding process is similar to the binding zipper model reported for the F1-ATPase hexameric motor. The simulation also shows a transition mechanism of Mg²⁺ coordination to form the Mg-ATP complex during ATP binding, which is accompanied by the large conformational changes of LTag. This simulation study of the ATP binding process to an LTag and the accompanying conformational changes in the context of a hexamer leads to a refined cooperative iris model that has been proposed previously.     

Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.     

Novel urushiol derivatives as HDAC8 inhibitors: rational design,virtual screening,molecular docking and molecular dynamics studies

Three series of novel urushiol derivatives were designed by introducing a hydroxamic acid moiety into the tail of an alkyl side chain and substituents with differing electronic properties or steric bulk onto the benzene ring and alkyl side chain. The compounds’ binding affinity toward HDAC8 was screened by Glide docking. The highest-scoring compounds were processed further with molecular docking, MD simulations, and binding free energy studies to analyze the binding modes and mechanisms. Ten compounds had Glide scores of ?8.2 to ?10.2, which revealed that introducing hydroxy, carbonyl, amino, or methyl ether groups into the alkyl side chain or addition of –F, –Cl, sulfonamide, benzamido, amino, or hydroxy substituents on the benzene ring could significantly increase binding affinity. Molecular docking studies revealed that zinc ion coordination, hydrogen bonding, and hydrophobic interactions contributed to the high calculated binding affinities of these compounds toward HDAC8. MD simulations and binding free energy studies showed that all complexes possessed good stability, as characterized by low RMSDs, low RMSFs of residues, moderate hydrogen bonding and zinc ion coordination and low values of binding free energies. Hie147, Tyr121, Phe175, Hip110, Phe119, Tyr273, Lys21, Gly118, Gln230, Leu122, Gly269, and Gly107 contributed favorably to the binding; and Van der Waals and electrostatic interactions provided major contributions to the stability of these complexes. These results show the potential of urushiol derivatives as HDAC8 binding lead compounds, which have great therapeutic potential in the treatment of various malignancies, neurological disorders, and human parasitic diseases.     

Probing the electronic structures and properties of neutral and anionic ScSi n (0,−1) (n = 1–6) clusters using ccCA-TM and G4 theory

We apply molecular docking, molecular dynamics (MD) simulation, and binding free energy calculation to investigate and reveal the binding mechanism between five xanthine inhibitors and DPP-4. The electrostatic and van der Waals interactions of the five inhibitors with DPP-4 are analyzed and discussed. The computed binding free energies using MM-PBSA method are in qualitatively agreement with experimental inhibitory potency of five inhibitors. The hydrogen bonds of inhibitors with Ser630 and Asp663 can stabilize the inhibitors in binding sites. The van der Waals interactions, especially the key contacts with His740, Asn710, Trp629, and Tyr666 have larger contributions to the binding free energy and play important roles in distinguishing the variant bioactivity of five inhibitors.     

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.     

Exploration micromechanism of VP35 IID interaction and recognition dsRNA: A molecular dynamics simulation

Multifunctional viral protein (VP35) encoded by the highly pathogenic Ebola viruses (EBOVs) can antagonize host double‐stranded RNA (dsRNA) sensors and immune response because of the simultaneous recognition of dsRNA backbone and blunt ends. Mutation of select hydrophobic conserved basic residues within the VP35 inhibitory domain (IID) abrogates its dsRNA‐binding activity, and impairs VP35‐mediated interferon (IFN) antagonism. Herein the detailed binding mechanism between dsRNA and WT, single mutant, and double mutant were investigated by all‐atom molecular dynamics (MD) simulation and binding energy calculation. R312A/R322A double mutations results in a completely different binding site and orientation upon the structure analyses. The calculated binding free energy results reveal that R312A, R322A, and K339A single mutations decrease the binding free energies by 17.82, 13.18, and 13.68 kcal mol^?1, respectively. The binding energy decomposition indicates that the strong binding affinity of the key residues is mainly due to the contributions of electrostatic interactions in the gas phase, where come from the positively charged side chain and the negatively charged dsRNA backbone. R312A, R322A, and K339A single mutations have no significant effect on VP35 IID conformation, but the mutations influence the contributions of electrostatic interactions in the gas phase. The calculated results reveal that end‐cap residues which mainly contribute VDW interactions can recognize and capture dsRNA blunt ends, and the central basic residues (R312, R322, and K339) which mainly contribute favorable electrostatic interactions with dsRNA backbone can fix dsRNA binding site and orientation. Proteins 2017; 85:1008–1023. © 2017 Wiley Periodicals, Inc.     

Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor

The importance of including different energy contributions in calculations of electrostatic energies in proteins is examined by calculating the intrinsic pKa values of the acidic groups of bovine pancreatic trypsin inhibitor. It appears that such calculations provide a powerful and revealing test; the relevant solvation energies of the ionized acids are of the order of -70 kcal/mol (1 cal = 4.184 J), and microscopic calculations that do not attempt to simulate the complete protein dielectric effect (including the surrounding solvent) can underestimate the solvation energy by as much as 50 kcal/mol. Reproducing correctly, by the same set of parameters, the solvation energies of ionized acids in different sites of a protein cannot be accomplished by including only part of the key energy contributions. The problems associated with macroscopic calculations are also considered and illustrated by the specific case of bovine pancreatic trypsin inhibitor. A promising approach is shown to be provided by a refinement of the previously developed Protein Dipoles Langevin Dipoles model. This model seems to represent consistently the microscopic dielectric of the protein and the surrounding water molecules. The model overcomes the problems associated with the macroscopic models (by treating explicitly the solvent molecules) and avoids the convergence problems associated with all-atom solvent models (by treating the average solvent polarization rather than averaging the actual polarization energy). This paper describes in detail the actual implementation of the model and examines its performance in evaluating intrinsic pKa values. Preliminary microscopic considerations of charge-charge interactions are presented.     

Energetic analysis of binding of progesterone and 5 beta-androstane-3,17-dione to anti-progesterone antibody DB3 using molecular dynamics and free energy calculations.

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the energetics of the binding of progesterone (PRG) and 5 beta-androstane-3,17-dione (5AD) to anti-PRG antibody DB3. Although the two steroids bind to DB3 in different orientations, their binding affinities are of the same magnitude, 1 nM for PRG and 8 nM for 5AD. The calculated relative binding free energy of the steroids, 8.8 kJ/mol, is in fair agreement with the experimental energy, 5.4 kJ/mol. In addition, computational alanine scanning was applied to study the role of selected amino acid residues of the ligand-binding site on the steroid cross-reactivity. The electrostatic and van der Waals components of the total binding free energies were found to favour more the binding of PRG, whereas solvation energies were more favourable for the binding of 5AD. The differences in the free energy components are due to the binding of the A rings of the steroids to different binding pockets: PRG is bound to a pocket in which electrostatic antibody-steroid interactions are dominating, whereas 5AD is bound to a pocket in which van der Waals and hydrophobic interactions dominate.     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

Binding free energy calculations of galectin-3-ligand interactions

Galectins show remarkable binding specificity towards beta-galactosides. A recently developed method for calculating binding free energies between a protein and its substrates has been used to evaluate the binding specificity of galectin-3. Five disaccharides and a tetrasaccharide were used as the substrates. The calculated binding free energies agree quite well with the experimental data and the ranking of binding affinities is well reproduced. For all the six protein-ligand complexes it was observed that electrostatic interactions oppose binding whereas the non-polar contributions drive complex formation. The observed binding specificity of galectin-3 for galactosides rather than glucosides is discussed in light of our results.     

A comprehensive examination of the contributions to the binding entropy of protein–ligand complexes

One of the most important requirements in computer‐aided drug design is the ability to reliably evaluate the binding free energies. However, the process of ligand binding is very complex because of the intricacy of the interrelated processes that are difficult to predict and quantify. In fact, the deeper understanding of the origin of the observed binding free energies requires the ability to decompose these free energies to their contributions from different interactions. Furthermore, it is important to evaluate the relative entropic and enthalpic contributions to the overall free energy. Such an evaluation is useful for assessing temperature effects and exploring specialized options in enzyme design. Unfortunately, calculations of binding entropies have been much more challenging than calculations of binding free energies. This work is probably the first to present microscopic evaluation of all of the relevant components to the binding entropy, namely configurational, polar solvation, and hydrophobic entropies. All of these contributions are evaluated by the restraint release approach. The calculated results shed an interesting light on major compensation effects in both the solvation and hydrophobic effect and, despite some overestimate, can provide very useful insight. This study also helps in analyzing some problems with the widely used molecular mechanics/Poisson‐Boltzmann surface area approach. Proteins 2010. © 2010 Wiley‐Liss, Inc.