Modeling implicit reorganization in continuum descriptions of protein-protein interactions

The determination of free energies that govern protein-protein recognition is essential for a detailed molecular understanding of biological specificity. Continuum models of macromolecular interactions, in which the solvent is treated by an implicit representation and the proteins are treated semi-microscopically, are computationally tractable for estimating free energies, yet many questions remain concerning their accuracy. This article reports a continuum analysis of the free-energy changes underlying the binding of 31 interfacial alanine substitutions of two complexes of the antihen egg white lysozyme (HEL) antibody D1.3 bound with HEL or the antibody E5.2. Two implicit schemes for modeling the effects of protein and solvent relaxation were examined, in which the protein environment was treated as either homogeneous with a "protein dielectric constant" of epsilon(p) = 4 or inhomogeneous, with epsilon(p) = 4 for neutral residues and epsilon(p) = 25 for ionized residues. The results showed that the nonuniform dielectric model reproduced the experimental differences better, with an average absolute error of +/-1.1 kcal/mol, compared with +/-1.4 kcal/mol for the uniform model. More importantly, the error for charged residues in the nonuniform model is +/-0.8 kcal/mol and is nearly half of that corresponding to the uniform model. Several substitutions were clearly problematic in determining qualitative trends and probably required explicit structural reorganization at the protein-protein interface.     

Reciprocal cooperative effects of multiple ligand binding to pyruvate kinase

The formation of multiple ligand complexes with muscle pyruvate kinase was measured in terms of dissociation constants and the standard free energies of formation were calculated. The binding of Mn2+ to the enzyme (KA = 55 +/- 5 X 10(-6) M; deltaF degrees = -5.75 +/- 0.05 kcal/mol) and to the enzyme saturated with phosphoenolpyruvate (conditional free energy) KA' = 0.8 +/- 0.4 X 10(-6) M; deltaF degrees = -8.22 +/- 0.34 kcal/mol) has been measured under identical conditions giving a free energy of coupling, delta(deltaF degrees) = -2.47 +/- 0.34 kcal/mol. Such a large negative free energy of coupling is diagnostic of a strong positively cooperative effect in ligand binding. The binding of the substrate phosphoenolpyruvate to free enzyme and the enzyme-Mn2+ complex was, by necessity, measured by different methods. The free energy of phosphoenolpyruvate binding to free enzyme (KS = 1.58 +/- 0.10 X 10(-4)M; deltaF degrees = -5.13 +/- 0.04 kcal/mol) and to the enzyme-Mn2+ complex (K3 = 0.75 +/- 0.10 X 10(-6)M; deltaF degrees = -8.26 +/- 0.07 kcal/mol) also gives a large negative free energy of coupling, delta(deltaF degrees) = -3.16 +/- 0.08 kcal/mol. Such a large negative value confirms reciprocal binding effects between the divalent cation and the substrate phosphoenolpyruvate. The binding of Mn2+ to the enzyme-ADP complex was also investigated and a free energy of coupling, delta(deltaF degrees) = -0.08 +/- 0.08 kcal/mol, was measured, indicative of little or no cooperativity in binding. The free energy of coupling with Mn2+ and pyruvate was measured as -1.52 +/- 0.14 kcal/mol, showing a significant amount of cooperativity in ligand binding but a substantially smaller effect than that observed for phosphoenolpyruvate binding. The magnitude of the coupling free energy may be related to the role of the divalent cation in the formation of the enzyme-substrate complexes. In the absence of the activating monovalent cation, the coupling free energies for phosphoenolpyruvate and pyruvate binding decrease by 40-60% and 25%, respectively, substantiating a role for the monovalent cation in the formation of enzyme-substrate complexes with phosphoenolpyruvate and with pyruvate.     

Free energy perturbation calculations on binding and catalysis after mutating threonine 220 in subtilisin

We present the results of free energy perturbation calculations on binding and catalysis of a tetrapeptide substrate, acetyl-Phe-Ala-Ala-Phe-NMe, by native subtilisin BPN' and a subtilisin BPN' mutant (Thr220----Ala220). The calculated difference in the free energy of binding was 0.70 +/- 0.72 kcal/mol. The calculated difference in the free energy of catalysis was 1.48 +/- 0.89 kcal/mol. These calculated values compare well with the experimental values in which another substrate, succinyl-Ala-Ala-Pro-Phe-p-nitroanilide, was used. These findings suggest that Thr220 is more important for catalysis than substrate binding.     

Theoretical study of the ligand-CYP2B4 complexes: effect of structure on binding free energies and heme spin state

The molecular origins of temperature-dependent ligand-binding affinities and ligand-induced heme spin state conversion have been investigated using free energy analysis and DFT calculations for substrates and inhibitors of cytochrome P450 2B4 (CYP2B4), employing models of CYP2B4 based on CYP2C5(3LVdH)/CYP2C9 crystal structures, and the results compared with experiment. DFT calculations indicate that large heme-ligand interactions (ca. -15 kcal/mol) are required for inducing a high to low spin heme transition, which is correlated with large molecular electrostatic potentials (approximately -45 kcal/mol) at the ligand heteroatom. While type II ligands often contain oxygen and nitrogen heteroatoms that ligate heme iron, DFT results indicate that BP and MF heme complexes, with weak substrate-heme interactions (ca. -2 kcal/mol), and modest MEPS minima (>-35 kcal/mol) are high spin. In contrast, heme complexes of the CYP2B4 inhibitor, 4PI, the product of benzphetamine metabolism, DMBP, and water are low spin, have substantial heme-ligand interaction energies (<-15 kcal/mol) and deep MEPS minima (<-45 kcal/mol) near their heteroatoms. MMPBSA analysis of MD trajectories were made to estimate binding free energies of these ligands at the heme binding site of CYP2B4. In order to initially assess the realism of this approach, the binding free energy of 4PI inhibitor was computed and found to be a reasonable agreement with experiment: -7.7 kcal/mol [-7.2 kcal/mol (experiment)]. BP was determined to be a good substrate [-6.3 kcal/mol (with heme-ligand water), -7.3 kcal/mol (without ligand water)/-5.8 kcal/mol (experiment)], whereas the binding of MF was negligible, with only marginal binding binding free energy of -1.7 kcal/mol with 2-MF bound [-3.8 kcal/mol (experiment)], both with and without retained heme-ligand water. Analysis of the free energy components reveal that hydrophobic/nonpolar contributions account for approximately 90% of the total binding free energy of these substrates and are the source of their differential and temperature-dependent CYP2B4 binding. The results indicate the underlying origins of the experimentally observed differential binding affinities of BP and MF, and indicate the plausibility of the use of models derived from moderate sequence identity templates in conjunction with approximate free energy methods in the estimation of ligand-P450 binding affinities.     

Brownian dynamics of interactions between glyceraldehyde-3-phosphate dehydrogenase (GAPDH) mutants and F-actin

Brownian dynamics simulations of computer models of GAPDH mutants interacting with F-actin emphasized the electrostatic nature of such interactions, and confirmed the importance of four previously identified lysine residues on the GAPDH structure in these interactions. Mutants were GAPDH models in which one or more of the previously identified lysines had been replaced with alanine. Simulations showed reduced binding of these mutants to F-actin compared to wild-type GAPDH. Binding was significantly reduced by mutating the four lysines; the specific electrostatic interaction energy of the quadruple mutant was -7.3 +/- 1.0 compared to -11.4 +/- 0.5 kcal/mol for the wild enzyme. The BD simulations also reaffirmed the importance of quaternary structure for GAPDH binding F-actin.     

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.     

Stability mutants of staphylococcal nuclease: large compensating enthalpy-entropy changes for the reversible denaturation reaction

By use of intrinsic fluorescence to determine the apparent equilibrium constant Kapp as a function of temperature, the midpoint temperature Tm and apparent enthalpy change delta Happ on reversible thermal denaturation have been determined over a range of pH values for wild-type staphylococcal nuclease and six mutant forms. For wild-type nuclease at pH 7.0, a Tm of 53.3 +/- 0.2 degrees C and a delta Happ of 86.8 +/- 1.4 kcal/mol were obtained, in reasonable agreement with values determined calorimetrically, 52.8 degrees C and 96 +/- 2 kcal/mol. The heat capacity change on denaturation delta Cp was estimated at 1.8 kcal/(mol K) versus the calorimetric value of 2.2 kcal/(mol K). When values of delta Happ and delta Sapp for a series of mutant nucleases that exhibit markedly altered denaturation behavior with guanidine hydrochloride and urea were compared at the same temperature, compensating changes in enthalpy and entropy were observed that greatly reduce the overall effect of the mutations on the free energy of denaturation. In addition, a correlation was found between the estimated delta Cp for the mutant proteins and the d(delta Gapp)/dC for guanidine hydrochloride denaturation. It is proposed that both the enthalpy/entropy compensation and this correlation between two seemingly unrelated denaturation parameters are consequences of large changes in the solvation of the denatured state that result from the mutant amino acid substitutions.     

Phospholipid binding of synthetic talin peptides provides evidence for an intrinsic membrane anchor of talin

Talin, an actin-binding protein, is assumed to anchor at the membrane via an intrinsic amino acid sequence. Three N-terminal talin fragments, 21-39 (S19), 287-304 (H18), and 385-406 (H17) have been proposed as potential membrane anchors. The interaction of the corresponding synthetic peptides with lipid model systems was investigated with CD spectroscopy, isothermal titration calorimetry, and monolayer expansion measurements. The membrane model systems were neutral or negatively charged small unilamellar vesicles or monolayers with a lateral packing density of bilayers (32 mN/m). S19 partitions into charged monolayers/bilayers with a penetration area A(p) = 140 +/- 30 A(2) and a free energy of binding of DeltaG(0) = -5.7 kcal/mol, thereby forming a partially alpha-helical structure. H18 does not interact with lipid monolayers or bilayers. H17 penetrates into neutral and charged monolayers/bilayers with A(p) = 148 +/- 23 A(2) and A(p) = 160 +/- 15 A(2), respectively, forming an alpha-helix in the membrane-bound state. Membrane partitioning is mainly entropy-driven. Under physiological conditions the free energy of binding to negatively charged membranes is DeltaG(0) = -9. 4 kcal/mol with a hydrophobic contribution of DeltaG(h) = -7.8 kcal/mol, comparable to that of post-translationally attached membrane anchors, and an electrostatic contribution of DeltaG(h) = -1.6 kcal/mol. The latter becomes more negative with decreasing pH. We show that H17 provides the binding energy required for a membrane anchor.     

Glycogen phosphorylase inhibitors: a free energy perturbation analysis of glucopyranose spirohydantoin analogues

GP catalyzes the phosphorylation of glycogen to Glc-1-P. Because of its fundamental role in the metabolism of glycogen, GP has been the target for a systematic structure-assisted design of inhibitory compounds, which could be of value in the therapeutic treatment of type 2 diabetes mellitus. The most potent catalytic-site inhibitor of GP identified to date is spirohydantoin of glucopyranose (hydan). In this work, we employ MD free energy simulations to calculate the relative binding affinities for GP of hydan and two spirohydantoin analogues, methyl-hydan and n-hydan, in which a hydrogen atom is replaced by a methyl- or amino group, respectively. The results are compared with the experimental relative affinities of these ligands, estimated by kinetic measurements of the ligand inhibition constants. The calculated binding affinity for methyl-hydan (relative to hydan) is 3.75 +/- 1.4 kcal/mol, in excellent agreement with the experimental value (3.6 +/- 0.2 kcal/mol). For n-hydan, the calculated value is 1.0 +/- 1.1 kcal/mol, somewhat smaller than the experimental result (2.3 +/- 0.1 kcal/mol). A free energy decomposition analysis shows that hydan makes optimum interactions with protein residues and specific water molecules in the catalytic site. In the other two ligands, structural perturbations of the active site by the additional methyl- or amino group reduce the corresponding binding affinities. The computed binding free energies are sensitive to the preference of a specific water molecule for two well-defined positions in the catalytic site. The behavior of this water is analyzed in detail, and the free energy profile for the translocation of the water between the two positions is evaluated. The results provide insights into the role of water molecules in modulating ligand binding affinities. A comparison of the interactions between a set of ligands and their surrounding groups in X-ray structures is often used in the interpretation of binding free energy differences and in guiding the design of new ligands. For the systems in this work, such an approach fails to estimate the order of relative binding strengths, in contrast to the rigorous free energy treatment.     

Flanking DNA-sequences contribute to the specific binding of cI-repressor and OR1.

The binding of cI-repressor to a series of mutant operators containing OR1 of the right operator of bacteriophage lambda was investigated. Sites OR2 and/or OR3 were inactivated by either point or deletion mutations. The free energy of binding repressor to OR1 in the wildtype operator, delta G1, is -13.7 +/- 0.3 kcal/mol. delta G1 determined for an OR2- operator created by a single point mutation in OR2 is -13.6 +/- 0.2 kcal/mol. In contrast, delta G1 for the binding of repressor to a cloned synthetic OR1 operator containing only 24 bp of lambda sequence is -12.2 +/- 0.1 kcal/mol. When sequence 5' to OR1 is present, the binding affinity increases to -13.0 +/- 0.1 kcal/mol. In addition, the proximity of OR1 to a fragment-end decreases delta G1 from -13.7 to -12.3 +/- 0.1 kcal/mol. These results suggest that the DNA sequence outside the 17 bp OR1 binding-site contributes to the specific binding of cI-repressor.     

High free energy of lipid/protein interaction in biological membranes

The free energy of lipid/protein interaction in biological membranes is still unknown although extensive partitioning and modelling studies have revealed many partial energetic increments. Multiple site binding kinetics are now applied to four well-studied functional membrane proteins, and mean free energy values (+/-S.D.) of -4.23+/-0.49 kcal/mol for single lipid binding sites and of -89.7+/-35.4 kcal/mol for complete lipid substitution are obtained. These high free energy values point to an important bioenergetic role of lipid/protein interaction in membrane functions.     

The thermodynamics of hapten and antigen binding by rabbit anti-dinitrophenyl antibody.

Rabbit anti-dinitrophenyl antibody from a serum pool was obtained as five fractions of purified specific antibody by a limiting antigen precipitation method. Each fraction had a different binding affinity for epsilon-N-2,4-dinitrophenyl-L-lysine. The free energy changes for hapten binding to the five antibody fractions varied from -8.35 to -10.0 kcal/mol. An average deltaH of -13.9 kcal/mol was measured for the fractions with a batch calorimeter. The results indicate no significant correlation between enthalpy changes and free energy changes. However, a statistically significant correlation between the free energy changes and the entropy changes was found. The enthalpy of the anti-dinitrophenyl antibody interaction with multivalent dinitrophenyl human serum albumin was determined. These are the first enthalpy measurements of an antibody antigen reaction in which the intrinsic binding enthalpy between the antibody and the determinant group is known. The deltaH for the antigen binding reaction was -10.1 kcal/mol which is 3.8 kcal/mol less exothermic than the deltaH for the hapten binding reaction. The interactions that could lead to such a difference in enthalpy are discussed.     

Membrane binding of the colicin E1 channel: activity requires an electrostatic interaction of intermediate magnitude.

In vitro channel activity of the C-terminal colicin E1 channel polypeptide under conditions of variable electrostatic interaction with synthetic lipid membranes showed distinct maxima with respect to pH and membrane surface potential. The membrane binding energy was determined from fluorescence quenching of the intrinsic tryptophans of the channel polypeptide by liposomes containing N-trinitrophenyl-phosphatidylethanolamine. Maximum in vitro colicin channel activity correlated with an intermediate magnitude of the electrostatic interaction. For conditions associated with maximum activity (40% anionic lipid, I = 0.12 M, pH 4.0), the free energy of binding was delta G approximately -9 kcal/mol, with nonelectrostatic and electrostatic components, delta Gnel approximately -5 kcal/mol and delta Gel approximately -4 kcal/mol, and an effective binding charge of +7 at pH 4.0. Binding of the channel polypeptide to negative membranes at pH 8 is minimal, whereas initial binding at pH 4 followed by a shift to pH 8 causes only 3-10% reversal of binding, implying that it is kinetically trapped, probably by a hydrophobic interaction. It was inferred that membrane binding and insertion involves an initial electrostatic interaction responsible for concentration and binding to the membrane surface. This is followed by insertion into the bilayer driven by hydrophobic forces, which are countered in the case of excessive electrostatic binding.     

In vivo non-specific binding of lambda CI and Cro repressors is significant

We propose a thermodynamic model that includes the non-specific binding of the lambda phage regulatory proteins CI and Cro. By fitting the model to experimental in vivo data on activities of the two promoters P(RM) and P(R) versus concentration, we estimate the free energy upon non-specific binding to be -4.1+/-0.9 kcal/mol for CI and -4.2+/-0.8 kcal/mol for Cro. For concentrations >100 nM of CI or Cro, we find that >50% of these proteins are non-specifically bound. In particular, in a lysogen (approximately 250 CI monomeric equivalents per cell) nearly 90% of CI is non-specifically bound.     

Thermodynamic analysis of inducer binding to the lactose repressor protein: contributions of galactosyl hydroxyl groups and beta substituents

Kinetic and equilibrium studies of the binding of modified beta-D-galactoside sugars to the lac repressor were carried out to generate thermodynamic data for protein-inducer interactions. The energetic contributions of the galactosyl hydroxyl groups to binding were assessed by using a series of methyl deoxyfluoro-beta-D-galactosides. The C-3 and C-6 hydroxyls contributed less than or equal to -2.3 and -1.7 +/- 0.3 kcal/mol to the binding free energy change, respectively, whereas the C-4 hydroxyl provided only a nominal contribution (-0.1 +/- 0.2 kcal/mol). Favorable contributions to the total binding free energy change were observed for replacement of O-methyl by S-methyl at the beta-anomeric position and for S-methyl by S-isopropyl. Negative delta H degrees values characteristic of protein-sugar complexes [Quiocho, F. A. (1986) Annu. Rev. Biochem. 55, 287-315] were observed for a series of beta-D-galactosides differing at the beta-glycosidic position. A decrease in delta H degrees of approximately 6 kcal/mol upon replacement of the O-methyl substituent by S-methyl indicates a substantial increase in van der Waals' interactions and/or hydrogen bonding in this region of the ligand binding site. The more favorable free energy change for the binding of the S-isopropyl vs S-methyl compound is due mainly to more positive entropic contributions, consistent with an increase in apolar interactions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Theoretical study on the interaction of titanocene dichloride with deoxyguanosine monophosphate

The completely hydrolyzed titanocene dichloride, [Cp₂Ti(H₂O)₂]²⁺ binding to guanine (G) and phosphate group sites of DNA were investigated by DFT method, with using deoxyguanosine monophosphate (dGMP) as incoming ligand. In the first substitutions, the calculations reveal that the diaquated titanocene binding to O6 shows the lowest activation free energy with 17.9 kcal/mol, closely followed by N7 is 20.5 kcal/mol and the O of phosphate group is 26.3 kcal/mol, respectively. It was also found that all the titanation processes are mildly endothermic. In addition, for the Ti-B(dGMP) in all separated products, the bond dissociation free energies (BDFE) of Ti-O(P, P = phosphate) is higher than those of Ti-N7/O6. In the second substitutions, the reactions leading to the didentate adducts are considered. For bidentate-bridging N7, O6 binding mode, the path of the metal Ti binding to O6 has the lower activation free energy (11.3 kcal/mol) than that of the metal Ti binding to N7 (15.3 kcal/mol). For the bidentate-bridging N7, O(P) binding mode, the path of the metal Ti binding to O(P) has the lower activation free energies (25.3 kcal/mol) than that of the metal Ti binding to N7 (26.2 kcal/mol).     

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.     

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.     

Binding of small basic peptides to membranes containing acidic lipids: theoretical models and experimental results.

We measured directly the binding of Lys3, Lys5, and Lys7 to vesicles containing acidic phospholipids. When the vesicles contain 33% acidic lipids and the aqueous solution contains 100 mM monovalent salt, the standard Gibbs free energy for the binding of these peptides is 3, 5, and 7 kcal/mol, respectively. The binding energies decrease as the mol% of acidic lipids in the membrane decreases and/or as the salt concentration increases. Several lines of evidence suggest that these hydrophilic peptides do not penetrate the polar headgroup region of the membrane and that the binding is mainly due to electrostatic interactions. To calculate the binding energies from classical electrostatics, we applied the nonlinear Poisson-Boltzmann equation to atomic models of the phospholipid bilayers and the basic peptides in aqueous solution. The electrostatic free energy of interaction, which arises from both a long-range coulombic attraction between the positively charged peptide and the negatively charged lipid bilayer, and a short-range Born or image charge repulsion, is a minimum when approximately 2.5 A (i.e., one layer of water) exists between the van der Waals surfaces of the peptide and the lipid bilayer. The calculated molar association constants, K, agree well with the measured values: K is typically about 10-fold smaller than the experimental value (i.e., a difference of about 1.5 kcal/mol in the free energy of binding). The predicted dependence of K (or the binding free energies) on the ionic strength of the solution, the mol% of acidic lipids in the membrane, and the number of basic residues in the peptide agree very well with the experimental measurements. These calculations are relevant to the membrane binding of a number of important proteins that contain clusters of basic residues.