Free energy of sickling: A simulation analysis.

Molecular dynamics simulations were performed to calculate the difference between the dimerization free energies of normal human deoxyhemoglobin (HbA) and the mutant sickle-cell deoxyhemoglobin HbS (Glu-beta 6----Val) for one of the lateral contacts in the HbS x-ray structure. The simulations yield a value of--15 kcal/mol. Although there is no quantitative experimental value for comparison, this is in qualitative agreement with the experimental result that HbS self-assembles into multistranded fibers that are responsible for erythrocyte sickling, while HbA does not. The free-energy difference was decomposed into enthalpic and entropic terms, both of which are significant, and the contributions of individual protein residues and of the solvent were examined. Electrostatic effects play the dominant role in favoring dimerization of HbS compared with HbA; van der Waals interactions make a negligible contribution to the difference. Both differential solvation and protein-protein interactions are important. Interactions within the donor tetramer (i.e., that containing the Glu-beta 6 mutation site), as well as those with the acceptor tetramer, contribute to the preferential free energy of dimerization of HbS.     

Relative binding affinities of distamycin and its analog to d(CGCAAGTTGGC).d(GCCAACTTGCG): comparison of simulation results with experiment.

We report here an effort to use molecular dynamics/free energy perturbation methodology to calculate relative binding affinities of two related drugs to DNA. Specifically, we focus on the relative binding free energies of distamycin (Dst) and its analog, 2-imidazoledistamycin (2-ImD), to d(CGCAAGTTGGC).d(GCCAACTTGCG). The pyrrole (Dst) and the imidazole variant (2-ImD) differ only in that the C-H is substituted by an N in the central ring. The starting conformation for these calculations was the previously determined solution structure of two 2-ImD molecules in the minor groove of the above 11-residue DNA. In this complex both the ligands have the imidazole nitrogen (N3) oriented toward the amino group of G6. However only ligand 1 (site I) has N3 within the hydrogen bonding distance from N2 amino proton of G6. We have calculated the difference in free energy of binding of 2-ImD versus Dst in three different cases by mutating 2-ImD-->Dst reversibly. In the first case ligand 1 (site I) is mutated, in the second case ligand 2 (site II) is mutated, and in the third case both the ligands are mutated. These calculations show that at site I Dst has weaker binding affinity than 2-ImD by 0.7 kcal/mol, at site II Dst has stronger binding affinity than 2-ImD by 2.9 kcal/mol, and when occupying both site I and site II, Dst binds with greater affinity than 2-ImD by 1.8 kcal/mol. Recent experimental findings agree semiquantitatively (within 1 kcal/mol) with the calculations presented here. Hence the methodology presented here can be used to predict relative binding energies of two or more closely related molecules to DNA.     

Application of a polarizable force field to calculations of relative protein-ligand binding affinities

An explicitly polarizable force field based exclusively on quantum data is applied to calculations of relative binding affinities of ligands to proteins. Five ligands, differing by replacement of an atom or functional group, in complexes with three serine proteases—trypsin, thrombin, and urokinase-type plasminogen activator—with available experimental binding data are used as test systems. A special protocol of thermodynamic integration was developed and used to provide sufficiently low levels of systematic error along with high numerical efficiency and statistical stability. The calculated results are in excellent quantitative (rmsd = 1.0 kcal/mol) and qualitative (R² = 0.90) agreement with experimental data. The potential of the methodology to explain the observed differences in the ligand affinities is also demonstrated.     

Free-energy cost for translocon-assisted insertion of membrane proteins

Nascent membrane proteins typically insert in a sequential fashion into the membrane via a protein-conducting channel, the Sec translocon. How this process occurs is still unclear, although a thermodynamic partitioning between the channel and the membrane environment has been proposed. Experiment- and simulation-based scales for the insertion free energy of various amino acids are, however, at variance, the former appearing to lie in a narrower range than the latter. Membrane insertion of arginine, for instance, requires 14–17 kcal/mol according to molecular dynamics simulations, but only 2–3 kcal/mol according to experiment. We suggest that this disagreement is resolved by assuming a two-stage insertion process wherein the first step, the insertion into the translocon, is energized by protein synthesis and, therefore, has an effectively zero free-energy cost; the second step, the insertion into the membrane, invokes the translocon as an intermediary between the fully hydrated and the fully inserted locations. Using free-energy perturbation calculations, the effective transfer free energies from the translocon to the membrane have been determined for both arginine and leucine amino acids carried by a background polyleucine helix. Indeed, the insertion penalty for arginine as well as the insertion gain for leucine from the translocon to the membrane is found to be significantly reduced compared to direct insertion from water, resulting in the same compression as observed in the experiment-based scale.     

On the thermodynamic stability of a charged arginine side chain in a transmembrane helix

Biological membranes consist of bilayer arrangements of lipids forming a hydrophobic core that presents a physical barrier to all polar and charged molecules. This long-held notion has recently been challenged by biological translocon-based experiments that report small apparent free energies to insert charged side chains near the center of a transmembrane (TM) helix. We have carried out fully atomistic simulations to provide the free-energy profile for moving a TM helix containing a protonated Arg side chain across a lipid bilayer. Our results reveal the fundamental thermodynamics governing the stability of charged side chains in membranes and the microscopic interactions involved. Despite local membrane deformations, where large amounts of water and lipid head groups are pulled into the bilayer to interact with Arg, the free-energy barrier is 17 kcal/mol. We provide a rationale for the differences in our microscopic free energies and cell biological experiments using free-energy calculations that indicate that a protonated Arg at the central residue of a TM helix of the Leader peptidase might reside close to the interface and not at the membrane center. Our findings have implications for the gating mechanisms of voltage-gated ion channels, suggesting that movements of protonated Arg residues through the membrane will be prohibited.     

Enthalpy of hydrogen bond formation in a protein-ligand binding reaction.

Parallel measurements of the thermodynamics(free-energy, enthalpy, entropy and heat-capacity changes) of ligand binding toFK506 binding protein (FKBP-12) in H2O and D2O have been performed in an effortto probe the energetic contributions of single protein-ligand hydrogen bondsformed in the binding reactions. Changing tyrosine-82 to phenylalanine inFKBP-12 abolishes protein-ligand hydrogen bond interactions in the FKBP-12complexes with tacrolimus or rapamycin and leads to a large apparent enthalpicstabilization of binding in both H2O and D2O. High-resolution crystallographicanalysis reveals that two water molecules bound to the tyrosine-82 hydroxylgroup in unliganded FKBP-12 are displaced upon formation of the protein-ligandcomplexes. A thermodynamic analysis is presented that suggests that the removalof polar atoms from water contributes a highly unfavorable enthalpy change tothe formation of C=O...HO hydrogen bonds as they occur in the processes ofprotein folding and ligand binding. Despite the less favorable enthalpy change,the entropic advantage of displacing two water molecules upon binding leads to aslightly more favorable free-energy change of binding in the reactions withwild-type FKBP-12.     

Hydrogen bonding in water using synthetic receptors.

Four water-soluble adenine receptors were synthesized to study the influence of hydrophobic interactions and hydrogen bonding on molecular recognition in aqueous solution. Association constants were measured in aqueous solution at five temperatures from 3-27 degrees C (pH 6, 51 mM ionic strength). For the mono(imide) receptors, delta H was -5.8 kcal/mol (carbazole) and -9.2 kcal/mol (naphthalene). The entropy of association for these was -13 cal.mol-1.K-1 (carbazole) and -26 cal.mol-1.K-1 (naphthalene). The carbazole bis(imide) receptor showed a binding enthalpy of -7.4 kcal/mol and entropy of -18 cal.mol-1.K-1. From this the free energy at 298 K of a single hydrogen bond is estimated to be only 0.2 kcal/mol. The enthalpy of a single hydrogen bond in this solvent-exposed system is estimated to be, at most, 0.8 kcal/mol, indicating that enthalpy just compensates for the unfavorable entropy in this system. These values reflect stronger hydrophobic interactions with the more polarizable naphthalene, as well as enthalpy-entropy compensation effects.     

Binding of buried structural water increases the flexibility of proteins.

Water deeply buried in proteins is considered to be an integral part of the folded structure. Such structural water molecules make strong H bonds with polar groups of the surrounding protein and therefore are believed to tighten the protein matrix. Surprisingly, our computational analysis of the binding of a buried water molecule to bovine pancreatic trypsin inhibitor shows that the protein actually becomes more flexible, as revealed by an increase in the vibrational entropy. We find that this effect must be common in proteins, because the large entropic cost of immobilizing a single water molecule [-TDeltaS = 20.6 kcal/mol (1 kcal = 4.18 kJ) for the lost translational and rotational degrees of freedom] can only be partly compensated by water-protein interactions, even when they are nearly perfect, as in the case of bovine pancreatic trypsin inhibitor (DeltaE = -19.8 kcal/mol), leaving no room for a further decrease in entropy from protein tightening. This study illustrates the importance of considering changes in protein flexibility (which in this case favor binding by 3.5 kcal/mol) for the prediction of ligand binding affinities.     

Free energies of ligand binding for structurally diverse compounds

The one-step perturbation approach is an efficient means to calculate many relative free energies from a common reference compound. Combining lessons learned in previous studies, an application of the method is presented that allows for the calculation of relative binding free energies for structurally rather diverse compounds from only a few simulations. Based on the well known statistical-mechanical perturbation formula, the results do not require any empirical parameters, or training sets, only limited knowledge of the binding characteristics of the ligands suffices to design appropriate reference compounds. Depending on the choice of reference compound, relative free energies of binding rigid ligands to the ligand-binding domain of the estrogen receptor can be obtained that show good agreement with the experimental values. The approach presented here can easily be applied to many rigid ligands, and it should be relatively easy to extend the method to account for ligand flexibility. The free-energy calculations can be straightforwardly parallelized, allowing for an efficient means to understand and predict relative binding free energies.     

Contribution of the hydrophobic effect to protein stability: analysis based on simulations of the Ile-96----Ala mutation in barnase.

Molecular dynamics simulations have been used to compute the difference in the unfolding free energy between wild-type barnase and the mutant in which Ile-96 is replaced by alanine. The simulations yield results (-3.42 and -5.21 kcal/mol) that compare favorably with experimental values (-3.3 and -4.0 kcal/mol). The major contributions to the free energy difference arise from bonding terms involving degrees of freedom of the mutated side chain and from nonbonded interactions of that side chain with its environment in the folded protein. By comparison with simulations of an extended peptide in the absence of solvent, used as a reference state, hydration effects are shown to play a minor role in the overall free energy balance for the Ile----Ala transformation. The implications of these results for our understanding of the hydrophobic effect and its contribution to protein stability are discussed.     

Energetics of peptide (pHLIP) binding to and folding across a lipid bilayer membrane

The pH low-insertion peptide (pHLIP) serves as a model system for peptide insertion and folding across a lipid bilayer. It has three general states: (I) soluble in water or (II) bound to the surface of a lipid bilayer as an unstructured monomer, and (III) inserted across the bilayer as a monomeric alpha-helix. We used fluorescence spectroscopy and isothermal titration calorimetry to study the interactions of pHLIP with a palmitoyloleoylphosphatidylcholine (POPC) lipid bilayer and to calculate the transition energies between states. We found that the Gibbs free energy of binding to a POPC surface at low pHLIP concentration (state I-state II transition) at 37 degrees C is approximately -7 kcal/mol near neutral pH and that the free energy of insertion and folding across a lipid bilayer at low pH (state II-state III transition) is nearly -2 kcal/mol. We discuss a number of related thermodynamic parameters from our measurements. Besides its fundamental interest as a model system for the study of membrane protein folding, pHLIP has utility as an agent to target diseased tissues and translocate molecules through the membrane into the cytoplasm of cells in environments with elevated levels of extracellular acidity, as in cancer and inflammation. The results give the amount of energy that might be used to move cargo molecules across a membrane.     

Probing the salt bridge in the dihydrofolate reductase-methotrexate complex by using the coordinate-coupled free-energy perturbation method.

The importance of the ionic interaction due to the formation of the salt bridge between the Asp-27 and the pteridine ring in Escherichia coli dihydrofolate reductase-methotrexate complex has been studied by using the free-energy perturbation method. The calculation suggests that the ion-pair contribution to the binding energy is insignificant, as the enzyme surroundings do not stabilize the salt bridge to the extent of the desolvation of the charged groups. The activation barrier for the proton exchange between the pteridine ring and the Asp-27 is calculated to be 20.1 kcal/mol (1 cal = 4.184 J) by using the coordinate-coupled perturbation method, implying that this may be a channel to the proton exchange from the pteridine ring to the solvent. The Gibbs-energy difference of binding between the Asn-27 and Ser-27 is calculated to be 3.2 kcal/mol and is mainly due to the electrostatic interactions.     

Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: a thermodynamic cycle-perturbation approach.

Peptidomimetic inhibitors of the human immunodeficiency virus 1 protease show considerable promise for treatment of AIDS. We have, therefore, been seeking computer-assisted drug design methods to aid in the systematic design of such inhibitors from a lead compound. Here we report thermodynamic cycle-perturbation calculations (using molecular dynamics simulations) to compute the relative difference in free energy of binding that results when one entire residue (valine) is deleted from one such inhibitor. In particular, we studied the "alchemic" mutation of the inhibitor Ac-Ser-Leu-Asn-(Phe-Hea-Pro)-Ile-Val-OMe (S1) to Ac-Ser-Leu-Asn-(Phe-Hea-Pro)-Ile-OMe (S2), where Hea is hydroxyethylamine, in two different (R and S) diastereomeric configurations of the hydroxyethylene group. The calculated (averaged for R and S) difference in binding free energy [3.3 +/- 1.1 kcal/mol (mean +/- SD); 1 cal = 4.184 J] is in good agreement with the experimental value of 3.8 +/- 1.3 kcal/mol, obtained from the measured Ki values for an equilibrium mixture of R and S configurations. Precise testing of our predictions will be possible when binding data become available for the two disastereomers separately. The observed binding preference for S1 is explained by the stronger ligand-protein interaction, which dominates an opposing contribution arising from the large desolvation penalty of S1 relative to S2. This calculation suggests that the thermodynamic cycle-perturbation approach can be useful even when a relatively large change in the ligand is simulated and supports the use of the thermodynamic cycle-perturbation algorithm for screening proposed derivatives of a lead inhibitor/drug prior to their synthesis.     

Ligand binding to protein-binding pockets with wet and dry regions

Biological processes often depend on protein-ligand binding events, yet accurate calculation of the associated energetics remains as a significant challenge of central importance to structure-based drug design. Recently, we have proposed that the displacement of unfavorable waters by the ligand, replacing them with groups complementary to the protein surface, is the principal driving force for protein-ligand binding, and we have introduced the WaterMap method to account this effect. However, in spite of the adage "nature abhors vacuum," one can occasionally observe situations in which a portion of the receptor active site is so unfavorable for water molecules that a void is formed there. In this paper, we demonstrate that the presence of dry regions in the receptor has a nontrivial effect on ligand binding affinity, and suggest that such regions may represent a general motif for molecular recognition between the dry region in the receptor and the hydrophobic groups in the ligands. With the introduction of a term attributable to the occupation of the dry regions by ligand atoms, combined with the WaterMap calculation, we obtain excellent agreement with experiment for the prediction of relative binding affinities for a number of congeneric ligand series binding to the major urinary protein receptor. In addition, WaterMap when combined with the cavity contribution is more predictive than at least one specific implementation [Abel R, Young T, Farid R, Berne BJ, Friesner RA (2008) J Am Chem Soc 130:2817-2831] of the popular MM-GBSA approach to binding affinity calculation.     

A free-energy perturbation study of the binding of methotrexate to mutants of dihydrofolate reductase.

The importance of hydrophobic residues to the binding of methotrexate in the active site of dihydrofolate reductase (EC 1.5.1.3) was examined by a free-energy perturbation method. The replacement of a strictly conserved residue, Phe-31, by tyrosine or valine costs 1.8 and 5.1 kcal/mol, respectively, to the binding of the drug (1 cal = 4.184 J). In the case of the Phe31----Tyr mutation, the loss of the binding energy is due to the desolvation of the phenolic group; in the case of Phe31----Val mutation, it is mainly due to the loss of the interaction with the drug. The replacement of Leu-54 by glycine decreases the binding energy by 4.0 kcal/mol. A calculation on the mutation of Phe-31 to serine shows that the alteration could reduce the binding energy of methotrexate by 9.7 kcal/mol. The calculations clearly show that the hydrophobic interactions are as important as the hydrophilic ones in the binding of methotrexate.     

A continuous hyperchromicity assay to characterize the kinetics and thermodynamics of DNA lesion recognition and base excision

We report a continuous hyperchromicity assay (CHA) for monitoring and characterizing enzyme activities associated with DNA processing. We use this assay to determine kinetic and thermodynamic parameters for a repair enzyme that targets nucleic acid substrates containing a specific base lesion. This optically based kinetics assay exploits the free-energy differences between a lesion-containing DNA duplex substrate and the enzyme-catalyzed, lesion-excised product, which contains at least one hydrolyzed phosphodiester bond. We apply the assay to the bifunctional formamidopyrimidine glycosylase (Fpg) repair enzyme (E) that recognizes an 8-oxodG lesion within a 13-mer duplex substrate (S). Base excision/elimination yields a gapped duplex product (P) that dissociates to produce the diagnostic hyperchromicity signal. Analysis of the kinetic data at 25 degrees C yields a K(m) of 46.6 nM for the E.S interaction, and a k(cat) of 1.65 min(-1) for conversion of the ES complex into P. The temperature dependence reveals a free energy (DeltaG(b)) of -10.0 kcal.mol(-1) for the binding step (E + S <--> ES) that is enthalpy-driven (DeltaH(b) = -16.4 kcal.mol(-1)). The activation barrier (DeltaG) of 19.6 kcal.mol(-1) for the chemical step (ES <--> P) also is enthalpic in nature (DeltaH = 19.2 kcal.mol(-1)). Formation of the transition state complex from the reactants (E + S <--> ES), a pathway that reflects Fpg catalytic specificity (k(cat)/K(m)) toward excision of the 8-oxodG lesion, exhibits an overall activation free energy (DeltaG(T)) of 9.6 kcal.mol(-1). These parameters characterize the driving forces that dictate Fpg enzyme efficiency and specificity and elucidate the energy landscape for lesion recognition and repair.     

Linkage between ligand binding and the dimer-tetramer equilibrium in the Monod-Wyman-Changeux model of hemoglobin.

G. Weber [(1984) Proc. Natl. Acad. Sci. USA 81, 7098-7102] has inferred that the Monod-Wyman-Changeux (MWC) model for ligand binding by hemoglobin would require (contrary to experimental evidence) that increased ligand binding must promote stabilization of alpha 2 beta 2 tetramers with respect to dissociation into alpha beta dimers. Reexamination of the MWC model, however, in the light of general linkage principles and the specific analysis by G. K. Ackers and M. L. Johnson [(1981) J. Mol. Biol. 147, 559-582] shows that the opposite relation must hold, in agreement with experiment. The T form of the tetramer, with low ligand affinity, must be destabilized and progressively dissociates into the high-affinity dimers, designated D, as ligand binding increases. Each ligand molecule bound shifts the standard Gibbs free energy delta G2T for the D-T equilibrium by approximately 3 kcal/mol in favor of the dimer. Thus, T must exist in (at least) five delta G levels of cooperative free energy as it becomes progressively destabilized by successive binding of ligand molecules. Dissociation of the R tetramer to dimers, in contrast, is independent of the amount of ligand bound, so long as dimers and R-state tetramers possess the same (high) affinity for ligand. While the intrinsic ligand-binding constants of the T and R states (KT and KR) remain unchanged throughout by the postulates of the model, the model should not be regarded as a strictly two-state system in view of the multiple free-energy levels indicated above. The present analysis gives approximate, though not precise, agreement with experimental findings on the dimer-tetramer equilibrium considered by Weber and provides a rationale for interpreting other recent experiments concerning this equilibrium.     

The proficiency of a thermophilic chorismate mutase enzyme is solely through an entropic advantage in the enzyme reaction

A study of the Thermus thermophilus chorismate mutase (TtCM) is described by using quantum mechanics (self-consistent-charge density-functional tight binding)/molecular mechanics, umbrella sampling, and the weighted histogram analysis method. The computed free energies of activation for the reactions in water and TtCM are comparable to the experimental values. The free energies for formation of near attack conformer have been determined to be 8.06 and 0.05 kcal/mol in water and TtCM, respectively. The near attack conformer stabilization contributes approximately 90% to the proficiency of the enzymatic reaction compared with the reaction in water. The transition state (TS) structures and partial atom charges are much the same in the enzymatic and water reactions. The difference in the electrostatic interactions of Arg-89 with O13 in the enzyme-substrate complex and enzyme-TS complex provides the latter with but 0.55 kcal/mol of 1.92 kcal/mol total TS stabilization. Differences in electrostatic interactions between components at the active site in the enzyme-substrate complex and enzyme-TS complex are barely significant, such that TS stabilization is of minor importance and the enzymatic catalysis is through an entropic advantage.     

Ligand-promoted transfer of proteins between phases: spontaneous and electrically helped.

A model system for the partitioning of peripheral membrane proteins into membranes by ligand binding has been examined experimentally. Both bovine serum albumin and lysozyme partition between water and 1-butanol by the addition of sodium p-toluene sulfonate at pH 2.4. The partitioning is characterized by high orders of reaction: 25 and 10, respectively. Theory indicates that these high orders of reaction need not result from cooperative ligand binding in either phase, but depend primarily upon the number N of protein sites at which the transfer-promoting ligant binds, and on the difference in free energy of formation delta F0s of the protein--ligand complexes in the two phases. From the reaction orders and the experimental values of N, 80 for albumin and 11 for lysozyme, delta F0s was calculated to be --0.5 kcal/mol (--2.1 kJ/mol) and --0.8 kcal/mol (--2.5 kJ/mol) per ligand bound, respectively. Experiments measuring the dependence on ligand concentration of the rate of protein electrophoresis across the water/butanol interface are described. These rates increase by more than two orders of magnitude as the ligand concentration approaches the critical value for partition and are inversely dependent on the number of ligant sites for the two proteins studied.     

Transition state stabilization by general acid catalysis, water expulsion, and enzyme reorganization in Medicago savita chalcone isomerase

In aqueous solution, Medicago savita chalcone isomerase (CHI) enhances the reaction rate for the unimolecular rearrangement of chalcone (CHN) into flavanone by seven orders of magnitude. Conformations of CHN and their relative free energies in water and CHI were investigated by the thermodynamic perturbation method. In water, CHN adopts two conformations (I and II) with conformation I being higher in energy than conformation II by 3 kcal/mol. Only I can give rise to a near attack conformer (NAC) where the nucleophile O2' and the electrophile C9 are placed in proximity. In CHI, I binds less tightly than II by approximately 2 kcal/mol, resulting in the free energy for NAC formation being approximately 2 kcal/mol higher in the enzyme than in water. This unfavorable feature in the ground state of the CHI reaction requires the predominant catalytic advantage to be taken in the step of NAC --> transition state (TS). From the molecular dynamics simulations of apo-CHI, CHI complexed with CHN (CHI.CHN) and CHI.TS, we found: (i) Lys-97-general-acid catalysis of the O2'(-) nucleophilic addition; (ii) expulsion of three water molecules in the process of TS formation; (iii) release of enzyme structural distortion on TS formation. In the conclusion, CHI's remarkable efficiency of stabilizing the TS and its relatively poor ability in organizing the ground state is compared with chorismate mutase whose catalytic prowess, when compared with water, originates predominantly from the enhanced NAC population at the active site.