Advances in the calculation of binding free energies

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Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Pyruvate dehydrogenase kinase activity of pig heart pyruvate dehydrogenase (E1 component of pyruvate dehydrogenase complex).

The pyruvate dehydrogenase (E1) and acetyltransferase (E2) components of pig heart and ox kidney pyruvate dehydrogenase (PDH) complex were separated and purified. The E1 component was phosphorylated (alpha-chain) and inactivated by MgATP. Phosphorylation was mainly confined to site 1. Addition of E2 accelerated phosphorylation of all three sites in E1 alpha and inactivation of E1. On the basis of histone H1 phosphorylation, E2 is presumed to contain PDH kinase, which was removed (greater than 98%) by treatment with p-hydroxymercuriphenylsulphonate. Stimulation of ATP-dependent inactivation of E1 by E2 was independent of histone H1 kinase activity of E2. The effect of E2 is attributed to conformational change(s) induced in E1 and/or E1-associated PDH kinase. PDH kinase activity associated with E1 could not be separated from it be gel filtration or DEAE-cellulose chromatography. Subunits of PDH kinase were not detected on sodium dodecyl sulphate/polyacrylamide gels of E1 or E2, presumably because of low concentration. The activity of pig heart PDH complex was increased by E2, but not by E1, indicating that E2 is rate-limiting in the holocomplex reaction. ATP-dependent inactivation of PDH complex was accelerated by E1 or by phosphorylated E1 plus associated PDH kinase, but not by E2 plus presumed PDH kinase. It is suggested that a substantial proportion of PDH kinase may accompany E1 when PDH complex is dissociated into its component enzymes. The possibility that E1 may possess intrinsic PDH kinase activity is considered unlikely, but may not have been fully excluded.     

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.     

Prediction of the binding site on E1 in the assembly of the pyruvate dehydrogenase multienzyme complex of Bacillus stearothermophilus

The beta-subunit (E1beta) of the pyruvate decarboxylase (E1, alpha(2)beta(2)) component of the Bacillus stearothermophilus pyruvate dehydrogenase complex was comparatively modelled based on the crystal structures of the homologous 2-oxoisovalerate decarboxylase of Pseudomonas putida and Homo sapiens. Based on this homology modelling, alanine-scanning mutagenesis studies revealed that the negatively charged side chain of Glu285 and the hydrophobic side chain of Phe324 are of particular importance in the interaction with the peripheral subunit-binding domain of the dihydrolipoyl acetyltransferase component of the complex. These results help to identify the site of interaction on the E1beta subunit and are consistent with thermodynamic evidence of a mixture of electrostatic and hydrophobic interactions being involved.     

Prediction of protein-protein binding free energies

We present an energy function for predicting binding free energies of protein-protein complexes, using the three-dimensional structures of the complex and unbound proteins as input. Our function is a linear combination of nine terms and achieves a correlation coefficient of 0.63 with experimental measurements when tested on a benchmark of 144 complexes using leave-one-out cross validation. Although we systematically tested both atomic and residue-based scoring functions, the selected function is dominated by residue-based terms. Our function is stable for subsets of the benchmark stratified by experimental pH and extent of conformational change upon complex formation, with correlation coefficients ranging from 0.61 to 0.66.     

Structural insight into interactions between dihydrolipoamide dehydrogenase (E3) and E3 binding protein of human pyruvate dehydrogenase complex

The 9.5 MDa human pyruvate dehydrogenase complex (PDC) utilizes the specific dihydrolipoamide dehydrogenase (E3) binding protein (E3BP) to tether the essential E3 component to the 60-meric core of the complex. Here, we report crystal structures of the binding domain (E3BD) of human E3BP alone and in complex with human E3 at 1.6 angstroms and 2.2 angstroms, respectively. The latter structure shows that residues from E3BD contact E3 across its 2-fold axis, resulting in one E3BD binding site on the E3 homodimer. Negligible conformational changes occur in E3BD upon its high-affinity binding to E3. Modifications of E3BD residues at the center of the E3BD/E3 interface impede E3 binding far more severely than those of residues on the periphery, validating the "hot spot" paradigm for protein interactions. A cluster of disease-causing E3 mutations located near the center of the E3BD/E3 interface prevents the efficient recruitment of these E3 variants by E3BP into the PDC, leading to the dysfunction of the PDC catalytic machine.     

Biochemical and genetic studies of four patients with pyruvate dehydrogenase E1α deficiency

We report studies of four patients with pyruvate dehydrogenase complex (PDH) deficiency caused by mutations in the E1α subunit. Two unrelated male patients presented with Leigh syndrome and a R263G missense mutation in exon 8. This mutation has previously been described in males with the same phenotype. The two other patients had different novel mutations: (1) an 8-bp deletion at the C-terminus (exon 11) was found in one allele of a young girl suffering from microcephaly and (2) a C88S missense mutation (exon 3) in a boy who only presented with motor neuropathy. These mutations were not found in the mothers of any of the four cases. Immunoblot analysis revealed decreased immunoreactivity for the E1α and E1β subunits in three out of the four patients. These findings confirm that: (1) PDH deficiencies are genetically heterogeneous, (2) the R263G mutation is more frequent in male cases than are other mutations and this amino acid is a hot spot for gene mutations, (3) the last eight amino acids may be important for the conformation of the tetrameric E1-PDH enzyme, and (4) the amino acids at positions 88, 263 and 382–387 are essential for the linking of the α subunit with the β subunit and for the activity of the holoenzyme. Received: 28 October 1996 / Revised: 13 January 1997     

Additional binding sites for the pyruvate dehydrogenase kinase but not for protein X in the assembled core of the mammalian pyruvate dehydrogenase complex: binding region for the kinase.

A standard resolution of the bovine kidney pyruvate dehydrogenase complex yields a subcomplex composed of approximately 60 dihydrolipoyl transacetylase (E2) subunits, approximately 6 protein X subunits, and approximately 2 pyruvate dehydrogenase kinase heterodimers (KcKb). Using a preparation of resolved kinase in which Kc much greater than Kb, E2-X-KcKb subcomplex additionally bound at least 15 catalytic subunits of the kinase (Kc) and a much lower level of Kb. The binding of Kc to E2 greatly enhanced kinase activity even at high levels of bound kinase. Free protein X, functional in binding the E3 component, did not bind to E2-X-KcKb subcomplex. This pattern of binding Kc but not protein X was unchanged either with a preparation of E2 oligomer greatly reduced in protein X or with subcomplex from which the lipoyl domain of protein X was selectively removed. The bound inner domain of protein X associated with the latter subcomplex did not exchange with free protein X. These data support the conclusion that E2 subunits bind the Kc subunit of the kinase and suggest that the binding of the inner domain of protein X to the inner domain of the transacetylase occurs during the assembly of the oligomeric core. Selective release of a fragment of E2 subunits that contain the lipoyl domains (E2L fragment) releases the kinase (M. Rahmatullah et al., 1990, J. Biol. Chem. 265, 14,512-14,517). Sucrose gradient centrifugation yielded an E2L-kinase fraction with an increased ratio of the kinase to E2L fragment. A monoclonal antibody specific for E2L was attached to a gel matrix. Binding of E2L fragment also led to specific binding of the kinase. Extensive washing did not reduce the level of bound kinase. Thus, the kinase is tightly bound by the lipoyl domain region of E2.     

Theoretical binding energies of inhibitors to enzymes

Modified quantum mechanical calculations predict the binding enthalpies of saccharide inhibitors of lysozyme to within a few kilocalories of experimental measurements.     

Characterization of interactions of dihydrolipoamide dehydrogenase with its binding protein in the human pyruvate dehydrogenase complex

Unlike pyruvate dehydrogenase complexes (PDCs) from prokaryotes, PDCs from higher eukaryotes have an additional structural component, E3-binding protein (BP), for binding of dihydrolipoamide dehydrogenase (E3) in the complex. Based on the 3D structure of the subcomplex of human (h) E3 with the di-domain (L3S1) of hBP, the amino acid residues (H348, D413, Y438, and R447) of hE3 for binding to hBP were substituted singly by alanine or other residues. These substitutions did not have large effects on hE3 activity when measured in its free form. However, when these hE3 mutants were reconstituted in the complex, the PDC activity was significantly reduced to 9% for Y438A, 20% for Y438H, and 18% for D413A. The binding of hE3 mutants with L3S1 determined by isothermal titration calorimetry revealed that the binding affinities of the Y438A, Y438H, and D413A mutants to L3S1 were severely reduced (1019-, 607-, and 402-fold, respectively). Unlike wild-type hE3 the binding of the Y438A mutant to L3S1 was accompanied by an unfavorable enthalpy change and a large positive entropy change. These results indicate that hE3-Y438 and hE3-D413 play important roles in binding of hE3 to hBP.     

An immunochemical assay model system for the sensitive detection of pyruvate dehydrogenase complex (PDHc) and its decarboxylating subunit pyruvate dehydrogenase (E1).

An immunochemical enzyme immunoassay model system was developed and compared for maximum sensitivity with a radioimmunoassay method and the classic enzyme activity method for the detection of pyruvate dehydrogenase complex (PDHc) and its decarboxylating subunit, pyruvate dehydrogenase (E1), isolated from Escherichia coli. Cross-linked large molecular weight antibody-enzyme conjugate systems are compared with heterobifunctional singular antibody conjugates substituted with high levels of horseradish peroxidase. Both polyclonal and monoclonal antibodies generated to the Escherichia coli PDHc and E1 antigens were used to develop a double-antibody sandwich microtiter plate enzyme-linked immunosorbent assay. It is demonstrated that a double sandwich immunochemical assay system can be quantitative for PDHc, can detect PDHc in crude cell lysates and has levels of sensitivity of 2.0.10(-16) mol for the detection of PDHc. This assay model system provides specific antibody selection criteria and coupling methods needed to select specific antisera that cross-react with human PDHc. This rapid and sensitive immunochemical assay method clearly demonstrates that sensitive mass assay systems can be developed for the detection of PDHc. Different from Western blot, this methodology could be used to generate mass assays which could be applied to the rapid detection of mammalian antigens (employing the corresponding antibodies) implicated in a number of pyruvate dehydrogenase deficiencies associated with human disorders.     

Structural determinants of enzyme binding affinity: the E1 component of pyruvate dehydrogenase from Escherichia coli in complex with the inhibitor thiamin thiazolone diphosphate

Thiamin thiazolone diphosphate (ThTDP), a potent inhibitor of the E1 component from the Escherichia coli pyruvate dehydrogenase multienzyme complex (PDHc), binds to the enzyme with greater affinity than does the cofactor thiamin diphosphate (ThDP). To identify what determines this difference, the crystal structure of the apo PDHc E1 component complex with ThTDP and Mg(2+) has been determined at 2.1 A and compared to the known structure of the native holoenzyme, PDHc E1-ThDP-Mg(2+) complex. When ThTDP replaces ThDP, reorganization occurs in the protein structure in the vicinity of the active site involving positional and conformational changes in some amino acid residues, a change in the V coenzyme conformation, addition of new hydration sites, and elimination of others. These changes culminate in an increase in the number of hydrogen bonds to the protein, explaining the greater affinity of the apoenzyme for ThTDP. The observed hydrogen bonding pattern is not an invariant feature of ThDP-dependent enzymes but rather specific to this enzyme since the extra hydrogen bonds are made with nonconserved residues. Accordingly, these sequence-related hydrogen bonding differences likewise explain the wide variation in the affinities of different thiamin-dependent enzymes for ThTDP and ThDP. The sequence of each enzyme determines its ability to form hydrogen bonds to the inhibitor or cofactor. Mechanistic roles are suggested for the aforementioned reorganization and its reversal in PDHc E1 catalysis: to promote substrate binding and product release. This study also provides additional insight into the role of water in enzyme inhibition and catalysis.     

X-chromosome localization of the functional gene for the E1 alpha subunit of the human pyruvate dehydrogenase complex

The functional gene locus for the E1 alpha subunit of the human pyruvate dehydrogenase complex has been localized to the p22.1-22.2 region of the X chromosome by in situ hybridization and analysis of somatic cell hybrids with various human X-chromosome rearrangements. Another locus showing significant cross-hybridization with an E1 alpha cDNA probe was detected on chromosome 4, in the region q22. The X-chromosome localization of the pyruvate dehydrogenase E1 alpha subunit gene provides a number of possible explanations for the clinical and biochemical variability which is a major feature of human pyruvate dehydrogenase deficiency.     

Elongation factor Tu and E1 beta subunit of pyruvate dehydrogenase complex act as fibronectin binding proteins in Mycoplasma pneumoniae

The interactions between pathogenic bacteria and extracellular matrix (ECM) components markedly influence the initiation and establishment of infection. We have identified two surface proteins of virulent Mycoplasma pneumoniae with molecular masses of 45 and 30 kDa that bind to the ECM constituent, fibronectin (Fn). These Fn-binding proteins (FnBPs) were purified to near homogeneity using Fn-coupled Sepharose 4B-affinity column chromatography, and amino acid sequence analysis of the 45 and the 30 kDa proteins identified them as elongation factor Tu (EF-Tu) and pyruvate dehydrogenase E1 beta subunit (PDH-B) respectively. The genes for EF-Tu and PDH-B were cloned, and the entire EF-Tu gene and NH2-terminus of PDH-B (NPDH (pyruvate dehydrogenase E1 beta subunit from amino acid 1-244)-B) gene were overexpressed in Escherichia coli. The recombinant proteins, rEF-Tu and rNPDH-B, were purified to homogeneity by His-tag affinity column chromatography and used to immunize rabbits. Purified rEF-Tu and rNPDH-B bound to Fn using a ligand immunoblot assay and ELISA. Immunogold electron microscopy with polyclonal antibodies reactive against rEF-Tu (antirEF-Tu) and rNPDH-B (antirNPDH-B) and whole cell radioimmunoprecipitation (WCRIP) revealed the surface location of these proteins. Adherence of viable M. pneumoniae to immobilized Fn was inhibited by antirEF-Tu and antirNPDH-B antisera in a dose-dependent and cumulative manner. These results demonstrate that M. pneumoniae EF-Tu and PDH-B, in addition to their major cytoplasmic biosynthetic and metabolic roles, can be surface translocated, which confers additional important biological functions.     

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.