Insights from free-energy calculations: protein conformational equilibrium, driving forces, and ligand-binding modes

Accurate free-energy calculations provide mechanistic insights into molecular recognition and conformational equilibrium. In this work, we performed free-energy calculations to study the thermodynamic properties of different states of molecular systems in their equilibrium basin, and obtained accurate absolute binding free-energy calculations for protein-ligand binding using a newly developed M2 algorithm. We used a range of Asp-Phe-Gly (DFG)-in/out p38α mitogen-activated protein kinase inhibitors as our test cases. We also focused on the flexible DFG motif, which is closely connected to kinase activation and inhibitor binding. Our calculations explain the coexistence of DFG-in and DFG-out states of the loop and reveal different components (e.g., configurational entropy and enthalpy) that stabilize the apo p38α conformations. To study novel ligand-binding modes and the key driving forces behind them, we computed the absolute binding free energies of 30 p38α inhibitors, including analogs with unavailable experimental structures. The calculations revealed multiple stable, complex conformations and changes in p38α and inhibitor conformations, as well as balance in several energetic terms and configurational entropy loss. The results provide relevant physics that can aid in designing inhibitors and understanding protein conformational equilibrium. Our approach is fast for use with proteins that contain flexible regions for structure-based drug design.     

B3LYP/6-311++G** study of alpha- and beta-D-glucopyranose and 1,5-anhydro-D-glucitol: 4C1 and 1C4 chairs, (3,O)B and B(3,O) boats, and skew-boat conformations

Geometry optimization, at the B3LYP/6-311++G** level of theory, was carried out on 4C1 and 1C4 chairs, (3,O)B and B(3,O) boats, and skew-boat conformations of alpha- and beta-D-glucopyranose. Similar calculations on 1,5-anhydro-D-glucitol allowed examination of the effect of removal of the 1-hydroxy group on the energy preference of the hydroxymethyl rotamers. Stable minimum energy boat conformers of glucose were found, as were stable skew boats, all having energies ranging from approximately 4-15 kcal/mol above the global energy 4C1 chair conformation. The 1C4 chair electronic energies were approximately 5-10 kcal/mol higher than the 4C1 chair, with the 1C4 alpha-anomers being lower in energy than the beta-anomers. Zero-point energy, enthalpy, entropy, and relative Gibbs free energies are reported at the harmonic level of theory. The alpha-anomer 4C1 chair conformations were found to be approximately 1 kcal/mol lower in electronic energy than the beta-anomers. The hydroxymethyl gt conformation was of lowest electronic energy for both the alpha- and beta-anomers. The glucose alpha/beta anomer ratio calculated from the relative free energies is 63/37%. From a numerical Hessian calculation, the tg conformations were found to be approximately 0.4-0.7 kcal/mol higher in relative free energy than the gg or gt conformers. Transition-state barriers to rotation about the C-5-C-6 bond were calculated for each glucose anomer with resulting barriers to rotation of approximately 3.7-5.8 kcal/mol. No energy barrier was found for the path between the alpha-gt and alpha-gg B(3,O) boat forms and the equivalent 4C1 chair conformations. The alpha-tg conformation has an energy minimum in the 1S3 twist form. Other boat and skew-boat forms are described. The beta-anomer boats retained their starting conformations, with the exception of the beta-tg-(3,O)B boat that moved to a skew form upon optimization.     

Thermodynamics of protein-peptide interactions in the ribonuclease-S system studied by molecular dynamics and free energy calculations.

Hydrophobic interactions between the S-peptide and S-protein in the ribonuclease-S complex are probed using molecular dynamics simulations and free energy calculations. Three successive mutations at the buried position Met13 are simulated: Met----Leu, Leu----Ile, and Ile----Val, for which X-ray structures and experimental thermodynamic data are available. The calculations give theoretical estimates of the changes in binding free energies associated with these mutations. The calculated free energy differences are small (0-1.6 kcal/mol), in agreement with experiment. However the simulated structures deviate significantly from the experimental ones (mean deviation approximately 1.5-2 A), and a large uncertainty in the calculated free energies (1-2 kcal/mol) arises from the multiple minimum problem. Indeed, multiple conformations are available to the side chains around the mutation site, and the sampling of dihedral rotamer transitions is limited, despite long simulations. Fluctuations within each local minimum give rise to a small statistical error. However the uncertainty due to multiple conformations is much greater than the uncertainty due to random statistical errors. In our work, an artificial cancellation of errors arose because we studied conformations of the RNase complex and of the S-peptide that were very similar. In general, the criterion for a precise simulation is not merely to reduce the random statistical error, as has been suggested, but rather to sample all the important local minima along the mutation pathway, and to reduce the statistical error for each one. Our calculations suggest that the packing changes associated with the mutations are energetically small and localized, and largely cancel when the complex and the S-peptide are compared. Solvation of the methionine side chain partial charges in the S-peptide and the complex appear to be energetically equivalent, so that removing them (as in Met13----Leu, Ile, Val) does not affect binding. Enthalpy and entropy changes could not be estimated reliably.     

The role of backbone motions in ligand binding to the c-Src SH3 domain.

The Src homology 3 (SH3) domain of pp60(c-src) (Src) plays dual roles in signal transduction, through stabilizing the repressed form of the Src kinase and through mediating the formation of activated signaling complexes. Transition of the Src SH3 domain between a variety of binding partners during progression through the cell cycle requires adjustment of a delicate free energy balance. Although numerous structural and functional studies of SH3 have provided an in-depth understanding of structural determinants for binding, the origins of binding energy in SH3-ligand interactions are not fully understood. Considering only the protein-ligand interface, the observed favorable change in standard enthalpy (DeltaH=-9.1 kcal/mol) and unfavorable change in standard entropy (TDeltaS=-2.7 kcal/mol) upon binding the proline-rich ligand RLP2 (RALPPLPRY) are inconsistent with the predominantly hydrophobic interaction surface. To investigate possible origins of ligand binding energy, backbone dynamics of free and RLP2-bound SH3 were performed via (15)N NMR relaxation and hydrogen-deuterium (H/(2)H) exchange measurements. On the ps-ns time scale, assuming uncorrelated motions, ligand binding results in a significant reduction in backbone entropy (-1.5(+/-0.6) kcal/mol). Binding also suppresses motions on the micros-ms time scale, which may additionally contribute to an unfavorable change in entropy. A large increase in protection from H/(2)H exchange is observed upon ligand binding, providing evidence for entropy loss due to motions on longer time scales, and supporting the notion that stabilization of pre-existing conformations within a native state ensemble is a fundamental paradigm for ligand binding. Observed changes in motion on all three time scales occur at locations both near and remote from the protein-ligand interface. The propagation of ligand binding interactions across the SH3 domain has potential consequences in target selection through altering both free energy and geometry in intact Src, and suggests that looking beyond the protein-ligand interface is essential in understanding ligand binding energetics.     

RNA bulge entropies in the unbound state correlate with peptide binding strengths for HIV-1 and BIV TAR RNA because of improved conformational access.

For the binding of peptides to wild-type HIV-1 and BIV TAR RNA and to mutants with bulges of various sizes, changes in the DeltaDelta G values of binding were determined from experimental K d values. The corresponding entropies of these bulges are estimated by enumerating all possible RNA bulge conformations on a lattice and then applying the Boltzmann relationship. Independent calculations of entropies from fluctuations are also carried out using the Gaussian network model (GNM) recently introduced for analyzing folded structures. Strong correlations are seen between the changes in free energy determined for binding and the two different unbound entropy calculations. The fact that the calculated entropy increase with larger bulge size is correlated with the enhanced experimental binding free energy is unusual. This system exhibits a dependence on the entropy of the unbound form that is opposite to usual binding models. Instead of a large initial entropy being unfavorable since it would be reduced upon binding, here the larger entropies actually favor binding. Several interpretations are possible: (i) the higher conformational freedom implies a higher competence for binding with a minimal strain, by suitable selection amongst the set of already accessible conformations; (ii) larger bulge entropies enhance the probability of the specific favorable conformation of the bound state; (iii) the increased freedom of the larger bulges contri-butes more to the bound state than to the unbound state; (iv) indirectly the large entropy of the bound state might have an unfavorable effect on the solvent structure. Nonetheless, this unusual effect is interesting.     

Solvation and the hidden thermodynamics of a zinc finger probed by nonstandard repair of a protein crevice

The classical Zn finger contains a phenylalanine at the crux of its three architectural elements: a beta-hairpin, an alpha-helix, and a Zn(2+)-binding site. Surprisingly, phenylalanine is not required for high-affinity Zn2+ binding, but instead contributes to the specification of a precise DNA-binding surface. Substitution of phenylalanine by leucine leads to a floppy but native-like structure whose Zn affinity is maintained by marked entropy-enthalpy compensation (DeltaDeltaH -8.3 kcal/mol and -TDeltaDeltaS 7.7 kcal/mol). Phenylalanine and leucine differ in shape, size, and aromaticity. To distinguish which features correlate with dynamic stability, we have investigated a nonstandard finger containing cyclohexanylalanine at this site. The structure of the nonstandard finger is similar to that of the native domain. The cyclohexanyl ring assumes a chair conformation, and conformational fluctuations characteristic of the leucine variant are damped. Although the nonstandard finger exhibits a lower affinity for Zn2+ than does the native domain (DeltaDeltaG -1.2 kcal/mol), leucine-associated perturbations in enthalpy and entropy are almost completely attenuated (DeltaDeltaH -0.7 kcal/mol and -TDeltaDeltaS -0.5 kcal/mol). Strikingly, global changes in entropy (as inferred from calorimetry) are in each case opposite in sign from changes in configurational entropy (as inferred from NMR). This seeming paradox suggests that enthalpy-entropy compensation is dominated by solvent reorganization rather than nominal molecular properties. Together, these results demonstrate that dynamic and thermodynamic perturbations correlate with formation or repair of a solvated packing defect rather than type of physical interaction (aromatic or aliphatic) within the core.     

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.     

Stability of a model beta-sheet in water.

We have used molecular dynamics simulations to determine the stability in water of a model beta-sheet formed by two alanine dipeptide molecules with two intermolecular hydrogen bonds in the closely spaced antiparallel arrangement. In this paper we describe our computations of the binding free energy of the model sheet and a portion of the free energy surface as a function of a reaction co-ordinate for sheet formation. We used the free energy surface to identify stable conformations along the reaction co-ordinate. To determine whether or not the model sheet with two hydrogen bonds is more stable than a single amide hydrogen bond in water, we compared the results of the present calculations to results from our earlier study of linear hydrogen bond formation between two formamide molecules (the formamide "dimer"). The free energy surfaces for the sheet and formamide dimer each have two minima corresponding to locally stable hydrogen-bonded and solvent-separated configurations. The binding free energies of the model sheet and the formamide dimer are -5.5 and -0.34 kcal/mol, respectively. Thus, the model sheet with two hydrogen bonds is quite stable while the simple amide hydrogen bond is only marginally stable. To understand the relative stabilities of the model sheet and formamide dimer in terms of solute-solute and solute-water interactions, we decomposed the free energy differences between hydrogen-bonded and solvent-separated conformations into energetic and entropic contributions. The changes in the peptide-peptide energy and the entropy are roughly twice as large for the sheet as they are for the formamide dimer. The magnitude of the peptide-water energy difference for the sheet is less than twice (by about 3.5 kcal/mol) that for the formamide dimer, and this accounts for the stability of the sheet. The presence of the side-chains and/or blocking groups apparently prevents the amide groups in the sheet from being solvated as favorably in the separated arrangement as in the formamide dimer, where the amide groups are completely exposed to the solvent.     

DFT study of alpha- and beta-D-allopyranose at the B3LYP/6-311++G ** level of theory

One hundred and two conformations of alpha- and beta-D-allopyranose, the C-3 substituted epimer of glucopyranose, were geometry optimized using the density functional, B3LYP, and the basis set, 6-311++G **. Full geometry optimization was performed on different ring geometries and on the hydroxymethyl rotamers (gg/gt/tg). Analytically derived Hessians were used to calculate zero point energy, enthalpy, and entropy. The lowest energy and free energy conformation found is the alpha-tg(g-)-4C1-c conformation, which is only slightly higher in electronic (approximately 0.2 kcal/mol) and free energy than the lowest energy alpha-D-glucopyranose. The in vacuo calculations showed a small (approximately 0.3 kcal/mol) energetic preference for the alpha- over the beta-anomer for allopyranose in the 4C1 conformation, whereas in the 1C4 conformation a considerable (approximately 1.6 kcal/mol) energetic preference for the beta- over the alpha-anomer for allopyranose was encountered. The results are compared to previous aldohexose calculations in vacuo. Boat and skew forms were found that remained stable upon gradient optimization although many starting boat conformations moved to other skew forms upon optimization. As found for glucose, mannose, and galactose the orientation and interaction of the hydroxyl groups make the most significant contributions to the conformation/energy relationship in vacuo. A comparison of different basis sets and density functionals is made in the Discussion section, confirming the appropriateness of the level of theory used here.     

DFT study of alpha- and beta-D-mannopyranose at the B3LYP/6-311++G** level

Thirty-five conformations of alpha- and beta-d-mannopyranose, the C-2 substituted epimer of glucopyranose, were geometry optimized using the density functional (B3LYP), and basis set (6-311++G**). Full geometry optimization was performed on the hydroxymethyl rotamers (gg/gt/tg) and an analytical hessian program was used to calculate the harmonic vibrational frequencies, zero point energy, enthalpy, and entropy. The lowest energy conformation investigated is the beta-tg in the (4)C(1) chair conformation. The in vacuo calculations showed little energetic preference for either the alpha or beta anomer for mannopyranose in the (4)C(1) chair conformation. Results are compared to similar glucopyranose calculations in vacuo where the alpha anomer is approximately 1kcal/mol lower in electronic energy than the beta anomer. In the case of the generally higher energy (1)C(4) chair conformations, one low-energy, low-entropy beta-gg-(1)C(4) chair conformation was identified that is within approximately 1.4kcal/mol of the lowest energy (4)C(1) conformation of mannopyranose. Other (1)C(4) chair conformations in our investigation are approximately 2.9-7.9kcal/mol higher in overall energy. Many of the (3,O)B, B(3,O), (1,4)B, and B(1,4) boat forms passed through transitions without barriers to (1)S(3), (5)S(1), (1)S(5) skew forms with energies between approximately 3.6 and 8.9kcal/mol higher in energy than the lowest energy conformation of mannopyranose. Boat forms were found that remained stable upon gradient optimization. As with glucopyranose, the orientation and interaction of the hydroxy groups make a significant contribution to the conformation/energy relationship in vacuo.     

The Fe-CO bond energy in myoglobin: a QM/MM study of the effect of tertiary structure

The Fe-CO bond dissociation energy (BDE) in myoglobin (Mb) has been calculated with B3LYP quantum mechanics/molecular mechanics methods for 22 different Mb conformations, generated from molecular dynamics simulations. Our average BDE of 8.1 kcal/mol agrees well with experiment and shows that Mb weakens the Fe-CO bond by 5.8 kcal/mol; the calculations provide detailed atomistic insight into the origin of this effect. BDEs for Mb conformations with the R carbonmonoxy tertiary structure are on average 2.6 kcal/mol larger than those with the T deoxy tertiary structure, suggesting two functionally distinct allosteric states. This allostery is partly explained by the reduction in distal cavity steric crowding as Mb moves from its T to R tertiary structure.     

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.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

Analysis of the binding energies of testosterone, 5alpha-dihydrotestosterone,androstenedione and dehydroepiandrosterone sulfate with an antitestosterone antibody

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the binding of testosterone (TES), 5alpha-dihydrotestosterone (5ADHT), androstenedione (AND), and dehydroepiandrosterone sulfate (DHEAS) to the monoclonal antitestosterone antibody 3-C(4)F(5). The relative binding free energy of TES and AND was also calculated with free energy perturbation (FEP) simulations. The antibody 3-C(4)F(5) has a relatively high affinity (3 x 10(8) M(-1)) and on overall good binding profile for testosterone but its cross-reactivity with DHEAS has been the main reason for the failure to use this antibody in clinical immunoassays. The relative binding free energies obtained with the MM-PBSA method were 1.5 kcal/mol for 5ADHT, 3.8 kcal/mol for AND, and 4.3 kcal/mol for DHEAS, as compared to TES. When a water molecule of the ligand binding site, observed in the antibody-TES crystal structure, was explicitly included in MM-PBSA calculations, the relative binding energies were 3.4, 4.9, and 5.4 kcal/mol for 5ADHT, AND, and DHEAS, respectively. The calculated numbers are in correct order but larger than the corresponding experimental energies of 1.3, 1.5, and 2.6 kcal/mol, respectively. The fact that the MM-PBSA method reproduced the relative binding free energies of DHEAS, a steroid having a negatively charged sulfate group, and the neutrally charged TES, 5ADHT, and AND in satisfactory agreement with experiment shows the robustness of the method in predicting relative binding affinities. The 800-ps FEP simulations predicted that the antibody 3-C(4)F(5) binds TES 1.3 kcal/mol tighter than AND. Computational mutagenesis of selected amino acid residues of the ligand binding site revealed that the lower affinities of AND and DHEAS as compared to TES are due to a combined effect of several residues, each contributing a small fraction to the tighter binding of TES. An exception to this is Tyr99H, whose mutation to Ala lowered the binding of DHEAS 0.7 kcal/mol more than the binding of TES. This is probably due to the hydrogen bonding interaction formed between the OH group of Tyr99H and the sulfate group of DHEAS. Computational mutagensis data also showed that the affinity of the steroids to the antitestosterone antibody 3-C(4)F(5) would be enhanced if Trp47H were repositioned so that it would make more extensive contacts with the bound ligands. In addition, the binding of steroids to antitestosterone, antiprogesterone, and antiestradiol antibodies is discussed.     

Association entropy in adsorption processes

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, DeltaS(o), have been derived from the root-mean-square fluctuations in protein crystals, suggesting DeltaS(o) approximately -50 e.u., i.e., TDeltaS degrees approximately -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TDeltaS(o) approximately -1.7 kT approximately -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much "softer."     

Mapping heat exchange in an allosteric protein

Nicotinic acetylcholine receptors (AChRs) are synaptic ion channels that spontaneously isomerize (i.e., gate) between resting and active conformations. We used single-molecule electrophysiology to measure the temperature dependencies of mouse neuromuscular AChR gating rate and equilibrium constants. From these we estimated free energy, enthalpy, and entropy changes caused by mutations of amino acids located between the transmitter binding sites and the middle of the membrane domain. The range of equilibrium enthalpy change (13.4 kcal/mol) was larger than for free energy change (5.5 kcal/mol at 25°C). For two residues, the slope of the rate-equilibrium free energy relationship (Φ) was approximately constant with temperature. Mutant cycle analysis showed that both free energies and enthalpies are additive for energetically independent mutations. We hypothesize that changes in energy associated with changes in structure mainly occur close to the site of the mutation, and, hence, that it is possible to make a residue-by-residue map of heat exchange in the AChR gating isomerization. The structural correlates of enthalpy changes are discussed for 12 different mutations in the protein.     

Interaction of synthetic HA2 influenza fusion peptide analog with model membranes.

The interaction of the synthetic 21 amino acid peptide (AcE4K) with 1-oleoyl-2-[caproyl-7-NBD]-sn-glycero-3-phosphocholine membranes is used as a model system for the pH-sensitive binding of fusion peptides to membranes. The sequence of AcE4K (Ac-GLFEAIAGFIENGWEGMIDGK) is based on the sequence of the hemagglutinin HA2 fusion peptide and has similar partitioning into phosphatidylcholine membranes as the viral peptide. pH-dependent partitioning in the membrane, circular dichroism, tryptophan fluorescence, change of membrane area, and membrane strength, are measured to characterize various key aspects of the peptide-membrane interaction. The experimental results show that the partitioning of AcE4K in the membrane is pH dependent. The bound peptide inserts in the membrane, which increases the overall membrane area in a pH-dependent manner, however the depth of insertion of the peptide in the membrane is independent of pH. This result suggests that the binding of the peptide to the membrane is driven by the protonation of its three glutamatic acids and the aspartic acid, which results in an increase of the number of bound molecules as the pH decreases from pH 7 to 4.5. The transition between the bound state and the free state is characterized by the Gibbs energy for peptide binding. This Gibbs energy for pH 5 is equal to -30.2 kJ/mol (-7.2 kcal/mol). Most of the change of the Gibbs energy during the binding of AcE4K is due to the enthalpy of binding -27.3 kJ/mol (-6.5 kcal/mol), while the entropy change is relatively small and is on the order of 6.4 J/mol.K (2.3 cal/mol.K). The energy barrier separating the bound and the free state, is characterized by the Gibbs energy of the transition state for peptide adsorption. This Gibbs energy is equal to 51.3 kJ/mol (12.3 kcal/mol). The insertion of the peptide into the membrane is coupled with work for creation of a vacancy for the peptide in the membrane. This work is calculated from the measured area occupied by a single peptide molecule (220 A(2)) and the membrane elasticity (190 mN/m), and is equal to 15.5 kJ/mol (3.7 kcal/mol). The comparison of the work for creating a vacancy and the Gibbs energy of the transition state shows that the work for creating a vacancy may have significant effect on the rate of peptide insertion and therefore plays an important role in peptide binding. Because the work for creating a vacancy depends on membrane elasticity and the elasticity of the membrane is dependent on membrane composition, this provides a tool for modulating the pH for membrane instability by changing membrane composition. The insertion of the peptide in the membrane does not affect the membrane permeability for water, which shows that the peptide does not perturb substantially the packing of the hydrocarbon region. However, the ability of the membrane to retain solutes in the presence of peptide is compromised, suggesting that the inserted peptide promotes formation of short living pores. The integrity of the membrane is substantially compromised below pH 4.8 (threshold pH), when large pores are formed and the membrane breaks down. The binding of the peptide in the pore region is reversible, and the pore size varies on the experimental conditions, which suggests that the peptide in the pore region does not form oligomers.     

Thermodynamic dissection of the binding energetics of KNI-272, a potent HIV-1 protease inhibitor

KNI-272 is a powerful HIV-1 protease inhibitor with a reported inhibition constant in the picomolar range. In this paper, a complete experimental dissection of the thermodynamic forces that define the binding affinity of this inhibitor to the wild-type and drug-resistant mutant V82F/184V is presented. Unlike other protease inhibitors, KNI-272 binds to the protease with a favorable binding enthalpy. The origin of the favorable binding enthalpy has been traced to the coupling of the binding reaction to the burial of six water molecules. These bound water molecules, previously identified by NMR studies, optimize the atomic packing at the inhibitor/protein interface enhancing van der Waals and other favorable interactions. These interactions offset the unfavorable enthalpy usually associated with the binding of hydrophobic molecules. The association constant to the drug resistant mutant is 100-500 times weaker. The decrease in binding affinity corresponds to an increase in the Gibbs energy of binding of 3-3.5 kcal/mol, which originates from less favorable enthalpy (1.7 kcal/mol more positive) and entropy changes. Calorimetric binding experiments performed as a function of pH and utilizing buffers with different ionization enthalpies have permitted the dissection of proton linkage effects. According to these experiments, the binding of the inhibitor is linked to the protonation/deprotonation of two groups. In the uncomplexed form these groups have pKs of 6.0 and 4.8, and become 6.6 and 2.9 in the complex. These groups have been identified as one of the aspartates in the catalytic aspartyl dyad in the protease and the isoquinoline nitrogen in the inhibitor molecule. The binding affinity is maximal between pH 5 and pH 6. At those pH values the affinity is close to 6 x 10(10) M(-1) (Kd = 16 pM). Global analysis of the data yield a buffer- and pH-independent binding enthalpy of -6.3 kcal/mol. Under conditions in which the exchange of protons is zero, the Gibbs energy of binding is -14.7 kcal/mol from which a binding entropy of 28 cal/K mol is obtained. Thus, the binding of KNI-272 is both enthalpically and entropically favorable. The structure-based thermodynamic analysis indicates that the allophenylnorstatine nucleus of KNI-272 provides an important scaffold for the design of inhibitors that are less susceptible to resistant mutations.