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

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

Conformation and hydration of aspartame

Conformational free energy calculations using an empirical potential (ECEPP/2) and the hydration shell model were carried out on the neutral, acidic, zwitterionic, and basic forms of aspartame in the hydrated state. The results indicate that as the molecule becomes more charged, the number of low energy conformations becomes smaller and the molecule becomes less flexible. The calculated free energies of hydration of charged aspartames show that hydration has a significant effect on the conformation in solution. Only two feasible conformations were found for the zwitterionic form, and these are consistent with the conformations deduced from NMR and X-ray diffraction experiments. The calculated free energy difference between these two conformations was 1.25 kcal/mol. The less favored of the two solvated conformations can be expected to be stabilized by hydrophobic interaction of the phenyl groups in the crystal.     

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.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

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.     

Quantifying the Entropy of Binding for Water Molecules in Protein Cavities by Computing Correlations

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.     

pH-dependent stability of sperm whale myoglobin in water-guanidine hydrochloride solutions

An experimental-theoretical approach for the elucidation of protein stability is proposed. The theoretical prediction of pH-dependent protein stability is based on the macroscopic electrostatic model for calculation of the pH-dependent electrostatic free energy of proteins. As a test of the method we have considered the pH-dependent stability of sperm whale metmyoglobin. Two theoretical methods for evaluation of the electrostatic free energy and p K values are applied: the finite-difference Poisson-Boltzmann method and the semiempirical approach based on the modified Tanford-Kirkwood theory. The theoretical results for electrostatic free energy of unfolding are compared with the experimental data for guanidine hydrochloride unfolding under equilibrium conditions over a wide pH range. Using the optical parameters of the Soret absorbance to monitor conformational equilibrium and Tanford's method to estimate the resulting data, it was found that the conformational free energy of unfolding of metmyoglobin is 16.3 kcal mol(-1) at neutral pH values. The total unfolding free energies were calculated on the basis of the theoretically predicted electrostatic unfolding free energies and the experimentally measured midpoints (pH(1/2)) of acidic and alkaline denaturation transitions. Experimental data for alkaline denaturation were used for the first time in theoretical analysis of the pH-dependent unfolding of myoglobin. The present results demonstrate that the simultaneous application of appropriate theoretical and experimental methods permits a more complete analysis of the pH-dependent and pH-independent properties and stability of globular proteins.     

An energetic scale for equilibrium H/D fractionation factors illuminates hydrogen bond free energies in proteins

Equilibrium H/D fractionation factors have been extensively employed to qualitatively assess hydrogen bond strengths in protein structure, enzyme active sites, and DNA. It remains unclear how fractionation factors correlate with hydrogen bond free energies, however. Here we develop an empirical relationship between fractionation factors and free energy, allowing for the simple and quantitative measurement of hydrogen bond free energies. Applying our empirical relationship to prior fractionation factor studies in proteins, we find: [1] Within the folded state, backbone hydrogen bonds are only marginally stronger on average in α‐helices compared to β‐sheets by ～0.2 kcal/mol. [2] Charge‐stabilized hydrogen bonds are stronger than neutral hydrogen bonds by ～2 kcal/mol on average, and can be as strong as –7 kcal/mol. [3] Changes in a few hydrogen bonds during an enzyme catalytic cycle can stabilize an intermediate state by –4.2 kcal/mol. [4] Backbone hydrogen bonds can make a large overall contribution to the energetics of conformational changes, possibly playing an important role in directing conformational changes. [5] Backbone hydrogen bonding becomes more uniform overall upon ligand binding, which may facilitate participation of the entire protein structure in events at the active site. Our energetic scale provides a simple method for further exploration of hydrogen bond free energies.     

Reaction pathway and free energy profiles for butyrylcholinesterase-catalyzed hydrolysis of acetylthiocholine

The catalytic mechanism for butyrylcholineserase (BChE)-catalyzed hydrolysis of acetylthiocholine (ATCh) has been studied by performing pseudobond first-principles quantum mechanical/molecular mechanical-free energy (QM/MM-FE) calculations on both acylation and deacylation of BChE. Additional quantum mechanical (QM) calculations have been carried out, along with the QM/MM-FE calculations, to understand the known substrate activation effect on the enzymatic hydrolysis of ATCh. It has been shown that the acylation of BChE with ATCh consists of two reaction steps including the nucleophilic attack on the carbonyl carbon of ATCh and the dissociation of thiocholine ester. The deacylation stage includes nucleophilic attack of a water molecule on the carboxyl carbon of substrate and dissociation between the carboxyl carbon of substrate and hydroxyl oxygen of Ser198 side chain. QM/MM-FE calculation results reveal that the acylation of BChE is rate-determining. It has also been demonstrated that an additional substrate molecule binding to the peripheral anionic site (PAS) of BChE is responsible for the substrate activation effect. In the presence of this additional substrate molecule at PAS, the calculated free energy barrier for the acylation stage (rate-determining step) is decreased by ~1.7 kcal/mol. All of our computational predictions are consistent with available experimental kinetic data. The overall free energy barriers calculated for BChE-catalyzed hydrolysis of ATCh at regular hydrolysis phase and substrate activation phase are ~13.6 and ~11.9 kcal/mol, respectively, which are in reasonable agreement with the corresponding experimentally derived activation free energies of 14.0 kcal/mol (for regular hydrolysis phase) and 13.5 kcal/mol (for substrate activation phase).     

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.     

Hydrophobicity of the peptide C=O...H-N hydrogen-bonded group

The hydrophobicity of the peptide C=O ... H-N hydrogen-bonded group is an important parameter that determines the structure of proteins in water and in biological membranes, and therefore the free energy of transferring this group from water to non-polar solvents should be determined accurately. The essential work on this problem was carried out by Klotz and co-workers, and has been summarized elsewhere. Using N-methylacetamide as a model peptide, the free energies of the following processes were determined; (1) formation of the C=O ... H-N bond in water, (2) formation of the C=O ... N-N bond in CCl4, and (3) transfer of N-methylacetamide from water to CCl4. (4) From (3), the free energy of transferring the non-hydrogen bonded (C=O, H-N) group from water to CCl4 was calculated. When the free energies of (1), (2) and (4) are combined, one finds that the free energy of transferring the C=O ... H-N group from water to CCl4 is a surprising -1.4 kcal/mol (1 cal = 4.184 J). This number does not seem reasonable, since it implies that the C=O ... H-N group is about as hydrophobic as an isopropyl group, i.e. the side-chain of valine. In the present report, it is shown that this apparent hydrophobicity results from an underestimation of the free energy contribution that the methyl groups make to the transfer of N-methylacetamide from water to CCl4. When appropriate methyl group transfer free energies are used, one finds that the free energy of transferring the C=O ... H-N group from water to CCl4 is +0.62 kcal/mol. Therefore, this group is relatively insensitive to solvent polarity. A similar calculation shows that the free energy of transferring the C=O ... H-O hydrogen-bonded group from water to benzene is +0.55 kcal/mol.     

A molecular dynamics study of thermodynamic and structural aspects of the hydration of cavities in proteins.

The structure and activity of a protein molecule are strongly influenced by the extent of hydration of its cavities. This is, in turn, related to the free energy change on transfer of a water molecule from bulk solvent into a cavity. Such free energy changes have been calculated for two cavities in a sulfate-binding protein. One of these cavities contains a crystallographically observed water molecule while the other does not. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each of the cavities from molecular dynamics simulations of two separate events: the removal of a water molecule from pure water, and the introduction of a water molecule into each protein cavity. From the simulations for the pure water system, the excess chemical potential of water was computed to be -6.4 +/- 0.4 kcal/mol, in accord with experiment and with other recent theoretical calculations. For the protein cavity containing an experimentally observed water molecule, the free energy change on hydrating it with one water molecule was calculated as -10.0 +/- 1.3 kcal/mol, indicating the high probability that this cavity is occupied by a water molecule. By contrast, for the cavity in which no water molecules were experimentally observed, the free energy change on hydrating it with one water molecule was calculated as 0.2 +/- 1.5 kcal/mol, indicating its low occupancy by water. The agreement of these results with experiment suggests that thermodynamic simulation methods may become useful for the prediction and analysis of internal hydration in proteins.     

Positional preference of proline in alpha-helices.

Conformational free energy calculations have been carried out for proline-containing alanine-based pentadecapeptides with the sequence Ac-(Ala)n-Pro-(Ala)m-NHMe, where n + m = 14, to figure out the positional preference of proline in alpha-helices. The relative free energy of each peptide was calculated by subtracting the free energy of the extended conformation from that of the alpha-helical one, which is used here as a measure of preference. The highest propensity is found for the peptide with proline at the N-terminus (i.e., Ncap + 1 position), and the next propensities are found at Ncap, N' (Ncap - 1), and C' (Ccap + 1) positions. These computed results are reasonably consistent with the positional propensities estimated from X-ray structures of proteins. The breaking in hydrogen bonds around proline is found to play a role in destabilizing alpha-helical conformations, which, however, provides the favored hydration of the corresponding N-H and C=O groups. The highest preference of proline at the beginning of alpha-helix appears to be due to the favored electrostatic and nonbonded energies between two residues preceding proline and the intrinsic stability of alpha-helical conformation of the proline residue itself as well as no disturbance in hydrogen bonds of alpha-helix by proline. The average free energy change for the substitution of Ala by Pro in a alpha-helix is computed to be 4.6 kcal/mol, which is in good agreement with the experimental value of approximately 4 kcal/mol estimated for an oligopeptide dimer and proteins of barnase and T4 lysozyme.     

Packaging of DNA in bacteriophage heads: some considerations on energetics

We have made quantitative estimates of some of the energetic factors to be considered in packaging of double-stranded DNA in virus particles. Numerical calculations were made using parameters appropriate for T4 bacteriophage. The unfavorable factors, and the Gibbs free energies per mole virus at 20°C associated with them, are bending, 1.5 × 10³ kcal/mol; conformational restriction upon condensation, 5.1 × 10² kcal/mol; polyelectrolyte repulsion, 2.1 × 10⁵kcal/mol; and melting or kinking, 6.9 × 10³ kcal/mol. These must be counterbalanced in the assembled phage by noncovalent bonding interactions between protein subunits in the phage-head shell; by interactions between the DNA and polyvalent cations, especially putrescine and spermidine; nad perhaps by repulsive excluded volume and electrostatic interaction between the DNA and acidic polypeptides. Indeed, a rough estimate of the standard free energey of interaction between T4 DNA and the putrescine and spermidine contained in the head is --2.1 × 10⁵ kcal/mol. In the absence of the other two sources of stabilization, each head protein subunit must contribute about 210 kcal/mol of binding energy.     

Aromatic-aromatic interactions and protein stability. Investigation by double-mutant cycles

The side-chains of phenylalanine and tyrosine residues in proteins are frequently found to be involved in pairwise interactions. These occur both within repeating elements of secondary structure and in tertiary and quaternary interactions. It has been suggested that they are important in protein folding and stability, and non-bonded potential energy calculations indicate that a typical aromatic-aromatic interaction has an energy of between -1 and -2 kcal/mol and contributes between -0.6 and -1.3 kcal/mol to protein stability. There is such an aromatic pair on the solvent-exposed face of the first alpha-helix of barnase, the small ribonuclease from Bacillus amyloliquefaciens. The edge of the aromatic ring of Tyr17 interacts with the face of that of Tyr13. The two residues have been mutated both singly and pairwise to alanine, and their free energies of unfolding determined by denaturation with urea. Application of the double-mutant cycle analysis gives an interaction energy of -1.3 kcal/mol for the aromatic pair in the folded protein relative to solvation by water in the unfolded protein. This value is similar to that calculated from the change in surface-accessible area between the rings on the formation of the pair. Analysis of a further double-mutant cycle in which the Tyr residues are mutated to Phe indicates that the aromatic-aromatic interactions of Tyr/Tyr and Phe/Phe make identical contributions to protein stability. However, Tyr is preferred to Phe by 0.3(+/- 0.04) kcal/mol at the solvent-exposed face of the alpha-helix.     

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).     

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.     

Ab initio studies of aromatic-aromatic and aromatic-polar interactions in the binding of substrate and inhibitor to dihydrofolate reductase.

Aromatic-aromatic and aromatic-polar interactions are investigated by performing ab initio Hartree-Fock calculations. Binding energies and optimum distances between subsystems are obtained. It is found that the binding energy between two benzene rings is of 3.1 kcal/mol when correlation effects are included, while the serine aromatic complexes energies of binding range from 1.9 to 3.1 kcal/mol.