Thermodynamics of water mediating protein-ligand interactions in cytochrome P450cam: a molecular dynamics study.

Ordered water molecules are observed by crystallography and nuclear magnetic resonance to mediate protein-ligand interactions. Here, we examine the energetics of hydrating cavities formed at protein-ligand interfaces using molecular dynamics simulations. The free energies of hydrating two cavities in the active site of two liganded complexes of cytochrome P450cam were calculated by multiconfigurational thermodynamic integration. The complex of cytochrome P450cam with 2-phenyl-imidazole contains a crystallographically well defined water molecule mediating hydrogen bonds between the protein and the inhibitor. We calculate that this water molecule is stabilized by a binding free energy of -11.6 +/- kJ/mol. The complex of cytochrome P450cam with its natural substrate, camphor, contains a cavity that is empty in the crystal structure although a water molecule in it could make a hydrogen bond to camphor. Here, solvation of this cavity is calculated to be unfavorable by +15.8 +/- 5.0 kJ/mol. The molecular dynamics simulations can thus distinguish a hydrated interfacial cavity from an empty one. They also provide support for the notion that protein-ligand complexes can accommodate empty interfacial cavities and that such cavities are likely to be unhydrated unless more than one hydrogen bond can be made to a water molecule in the cavity.     

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.     

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

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

Free energy calculations for the relative binding affinity between DNA and lambda-repressor

The change in the binding free energy between DNA and lambda-repressor resulting from a base substitution, thymine (T)-->deoxyuracil (abbreviated as U), was evaluated by the free energy perturbation method on the basis of molecular dynamics simulations for the DNA-lambda-repressor complex in water with all degrees of freedom and including long-range Coulomb interactions. The binding free energy change that we calculated (1.47 +/- 0.40 kcal/mol) was in good agreement with an experimental value (1.8 kcal/mol). We clarified why the small difference between T and U (CH(3) in T is replaced with H in U) caused such a significant change in the binding free energy: The substitution of CH(3) in T with H in U lowered the dissociated-state free energy level due to the gain of the hydration free energy. Furthermore, the T-->U substitution raised the free energy level in the associated state due to the loss of the favored van der Waals (vdW) interactions with the lambda-repressor amino acid residues. In other words, the amino acid residues of lambda-repressor can recognize the CH(3) in T through the vdW interactions with the CH(3). This recognition is enhanced in a water environment, because the hydrophobic CH(3) prefers the amino acid residues of lambda-repressor to water molecules.     

Evaluating the energetics of empty cavities and internal mutations in proteins.

The energetics of cavity formation in proteins is evaluated with two different approaches and results are analyzed and compared to experimental data. In the first approach, free energy of cavity formation is extracted by RMS fitting from the distribution of numbers of cavities, N, with different volumes, Vcav, in 80 high-resolution protein structures. It is assumed that the distribution of number of cavities according to their volume follows the Boltzmann law, N(Vcav) = exp [(-a.Vcav-b)/kT], or its simplified form. Specific energy cost of cavity formation, a, extracted by RMS fitting from these distributions is compared to a values extracted from experimental free energies of cavity formation in T4 lysozyme fitted to similar expressions. It is found that fitting of both sets of data leads to similar magnitudes and uncertainties in the calculated free energy values. It is shown that Boltzmann-like distribution of cavities can be derived for a simple model of an equilibrium interconversion between mutants in an extracellular system. We, however, suggest that a partitioning into cavity-dependent and cavity-independent terms may lose meaning when one attempts to describe mutation effects on protein stability in terms of specific free energy contributions. As an alternative approach, a direct molecular mechanics evaluation is attempted of T4 lysozyme destabilization by five single cavity-creating mutations. The calculations are based on the approach used in calculations of the energetics of packing defects in crystals. For all mutations calculated destabilizations agree with the corresponding experimental values within +/-0.6 kcal/mol. A computational relaxation of the mutant was most difficult to achieve for the mutation producing the smallest cavity. However, calculations do not always reproduce crystallographically observed contraction/expansion of cavities. It is suggested that this may be related to usually observed large RMS differences (> 1 A) between crystallographic and energy-minimized protein structures, and thus correct energetics might be easier to calculate than the correct geometry.     

Protein-protein recognition: an experimental and computational study of the R89K mutation in Raf and its effect on Ras binding

Binding of the protein Raf to the active form of Ras promotes activation of the MAP kinase signaling pathway, triggering cell growth and differentiation. Raf/Arg89 in the center of the binding interface plays an important role determining Ras-Raf binding affinity. We have investigated experimentally and computationally the Raf-R89K mutation, which abolishes signaling in vivo. The binding to [gamma-35S]GTP-Ras of a fusion protein between the Raf-binding domain (RBD) of Raf and GST was reduced at least 175-fold by the mutation, corresponding to a standard binding free energy decrease of at least 3.0 kcal/mol. To compute this free energy and obtain insights into the microscopic interactions favoring binding, we performed alchemical simulations of the RBD, both complexed to Ras and free in solution, in which residue 89 is gradually mutated from Arg into Lys. The simulations give a standard binding free energy decrease of 2.9+/-1.9 kcal/mol, in agreement with experiment. The use of numerous runs with three different force fields allows insights into the sources of uncertainty in the free energy and its components. The binding decreases partly because of a 7 kcal/mol higher cost to desolvate Lys upon binding, compared to Arg, due to better solvent interactions with the more concentrated Lys charge in the unbound state. This effect is expected to be general, contributing to the lower propensity of Lys to participate in protein-protein interfaces. Large contributions to the free energy change also arise from electrostatic interactions with groups up to 8 A away, namely residues 37-41 in the conserved effector domain of Ras (including 4 kcal/mol from Ser39 which loses a bifurcated hydrogen bond to Arg89), the conserved Lys84 and Lys87 of Raf, and 2-3 specific water molecules. This analysis will provide insights into the large experimental database of Ras-Raf mutations.     

Hydration energy landscape of the active site cavity in cytochrome P450cam

Hydration of protein cavities influences protein stability, dynamics, and function. Protein active sites usually contain water molecules that, upon ligand binding, are either displaced into bulk solvent or retained to mediate protein–ligand interactions. The contribution of water molecules to ligand binding must be accounted for to compute accurate values of binding affinities. This requires estimation of the extent of hydration of the binding site. However, it is often difficult to identify the water molecules involved in the binding process when ligands bind on the surface of a protein. Cytochrome P450cam is, therefore, an ideal model system because its substrate binds in a buried active site, displacing partially disordered solvent, and the protein is well characterized experimentally. We calculated the free energy differences for having five to eight water molecules in the active site cavity of the unliganded enzyme from molecular dynamics simulations by thermodynamic integration employing a three-stage perturbation scheme. The computed free energy differences between the hydration states are small (within 12 kJ mol⁻¹) but distinct. Consistent with the crystallographic determination and studies employing hydrostatic pressure, we calculated that, although ten water molecules could in principle occupy the volume of the active site, occupation by five to six water molecules is thermodynamically most favorable. Proteins 32:381–396, 1998. © 1998 Wiley-Liss, Inc.     

A procedure for detection and quantitation of cavity volumes proteins. Application to measure the strength of the hydrophobic driving force in protein folding

Accurate identification of cavities is important in the study of protein structure, stability, design, and ligand binding. Identification and quantitation of cavities is a nontrivial problem because most cavities are connected to the protein exterior. We describe a computational procedure for quantitating cavity volumes and apply this to derive an estimate of the hydrophobic driving force in protein folding. A grid-based Monte Carlo procedure is used to position water molecules on the surface of a protein. A Voronoi procedure is used to identify and quantitate empty space within the solvated protein. Additional cavities not detected by other existing procedures can be identified. Most of these are close to surface concavities. Residue volumes for both the interior and the surface residues as well as cavity volumes are in good agreement with volumes calculated from fully hydrated protein structures obtained from molecular dynamic simulations. We show that the loss of stability because of cavity-creating mutations correlates better with cavity volumes determined by this procedure than with cavity volumes determined by other methods. Available structural and thermodynamic data for a number of cavity-containing mutants were analyzed to obtain estimates of 26.1 cal x mol(-1) x A(-3) and 18.5 cal x mol(-1) x A(-2) for the relative contributions of cavity formation and the hydrophobic effect to the observed stability changes. The present estimate for the hydrophobic driving force is at the lower end of estimates derived from model compound studies and considerably lower than previous estimates of approximately 50 cal x mol(-1) x A(-2) derived from protein mutational data. In the absence of structural rearrangement, on average, deletion of a single methylene group is expected to result in losses in stability of 0.41 and 0.70 kcal x mol(-1) resulting from decrease in hydrophobicity and packing, respectively.     

Computational studies of the interaction of myoglobin and xenon

Computational studies are used to investigate the energies of xenon binding to myoglobin and to describe pathways through the protein interior for a metmyoglobin-xenon complex. Empirical energy calculations indicate a favorable enthalpic contribution of 0.6 to 4.2 kcal/mol to xenon binding for four experimentally determined xenon sites. These calculated enthalpies help to explain the different xenon occupancies observed experimentally. A fifth site, modeled in place of the iron co-ordinated water molecule in the distal cavity, is also predicted to bind xenon. The largest contribution to the binding energy is from van der Waals' interactions with smaller contributions from polarization and protein strain terms. Ligand trajectory calculations as well as a new geometric algorithm define a connecting network of channel-like pathways through the static protein structure. One or two pathways appear to lead most easily from each major internal cavity to the protein surface. The importance of these channels in protein dynamics and their implications as routes for ligand motion are discussed.     

Molecular Dynamics Free Energy Calculations to Assess the Possibility of Water Existence in Protein Nonpolar Cavities

Are protein nonpolar cavities filled with water molecules? Although many experimental and theoretical investigations have been done, particularly for the nonpolar cavity of IL-1β, the results are still conflicting. To study this problem from the thermodynamic point of view, we calculated hydration free energies of four protein nonpolar cavities by means of the molecular dynamics thermodynamic integration method. In addition to the IL-1β cavity (69 ų), we selected the three largest nonpolar cavities of AvrPphB (81 ų), Trp repressor (87 ų), and hemoglobin (108 ų) from the structural database, in view of the simulation result from another study that showed larger nonpolar cavities are more likely to be hydrated. The calculations were performed with flexible and rigid protein models. The calculated free energy changes were all positive; hydration of the nonpolar cavities was energetically unfavorable for all four cases. Because hydration of smaller cavities should happen more rarely, we conclude that existing protein nonpolar cavities are not likely to be hydrated. Although a possibility remains for much larger nonpolar cavities, such cases are not found experimentally. We present a hypothesis to explain this: hydrated nonpolar cavities are quite unstable and the conformation could not be maintained.     

A small molecule inhibits and misdirects assembly of hepatitis B virus capsids

Hepatitis B virus (HBV) capsids play an important role in viral nucleic acid metabolism and other elements of the virus life cycle. Misdirection of capsid assembly (leading to formation of aberrant particles) may be a powerful approach to interfere with virus production. HBV capsids can be assembled in vitro from the dimeric capsid protein. We show that a small molecule, bis-ANS, binds to capsid protein, inhibiting assembly of normal capsids and promoting assembly of noncapsid polymers. Using equilibrium dialysis to investigate binding of bis-ANS to free capsid protein, we found that only one bis-ANS molecule binds per capsid protein dimer, with an association energy of -28.0 +/- 2.0 kJ/mol (-6.7 +/- 0.5 kcal/mol). Bis-ANS inhibited in vitro capsid assembly induced by ionic strength as observed by light scattering and size exclusion chromatography. The binding energy of bis-ANS for capsid protein calculated from assembly inhibition data was -24.5 +/- 0.9 kJ/mol (-5.9 +/- 0.2 kcal/mol), essentially the same binding energy observed in studies of unassembled protein. These data indicate that capsid protein bound to bis-ANS did not participate in assembly; this mechanism of assembly inhibition is analogous to competitive or noncompetitive inhibition of enzymes. While assembly of normal capsids is inhibited, our data suggest that bis-ANS leads to formation of noncapsid polymers. Evidence of aberrant polymers was identified by light scattering and electron microscopy. We propose that bis-ANS acts as a molecular "wedge" that interferes with normal capsid protein geometry and capsid formation; such wedges may represent a new class of antiviral agent.     

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.     

Evaluation of protein-protein association energies by free energy perturbation calculations

The association energy upon binding of different amino acids in the specificity pocket of trypsin was evaluated by free energy perturbation calculations on complexes between bovine trypsin (BT) and bovine pancreatic trypsin inhibitor (BPTI). Three simulations of mutations of the primary binding residue (P(1)) were performed (P(1)-Ala to Gly, P(1)-Met to Gly and P(1)-Met to Ala) and the resulting differences in association energy (DeltaDeltaG(a)) are 2. 28, 5.08 and 2.93 kcal/mol for P(1)-Ala to Gly, P(1)-Met to Gly and to Ala with experimental values of 1.71, 4.62 and 2.91 kcal/mol, respectively. The calculated binding free energy differences are hence in excellent agreement with the experimental binding free energies. The binding free energies, however, were shown to be highly dependent on water molecules at the protein-protein interface and could only be quantitatively estimated if the correct number of such water molecules was included. Furthermore, the cavities that were formed when a large amino acid side-chain is perturbed to a smaller one seem to create instabilities in the systems and had to be refilled with water molecules in order to obtain reliable results. In addition, if the protein atoms that were perturbed away were not replaced by water molecules, the simulations dramatically overestimated the initial state of the free energy perturbations.     

Molecular Dynamics/Free Energy Perturbation Studies of the Thermostable V74I Mutant of Ribonuclease HI

Abstract

Recent site-directed mutagenesis and thermodynamic studies have shown that the V74I mutant of Escherichia coli ribonuclease HI (RNase HI) is more stable than the wild type protein [Ishikawa et al., Biochemistry 32, 6171 (1993)]. In order to clarify the stabilization mechanism of this mutant, we calculated the free energy change due to the mutation Val 74→Ile in both the native and denatured states by free energy perturbations based on molecular dynamics (MD) simulations. We carried out inclusive MD simulations for the protein in water; i.e., fully solvated, no artificial constraints applied, and all long-range Coulomb interactions included. We found that the free energy of the mutant increased slightly relative to the wild type, in the native state by 1.60 kcal/mol, and in the denatured state by 2.25 kcal/mol. The unfolding free energy increment of the mutant (0.66 ± 0.19 kcal/mol) was in good agreement with the experimental value (0.6 kcal/mol). The hysteresis error in the free energy calculations, i.e., forward and reverse perturbations, was only ±0.19 kcal/mol. These results show that the V74I mutant is stabilized relative to the wild type by the increased free energy of the denatured state and not by a decrease in the free energy of the native state as had been proposed earlier based on the mutant X-ray structure. It was found that the stabilization was caused by a loss of solvation energy in the mutant denatured state and not by improved packing interactions inside the native protein.     

Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study.

The proton transfer activity of the light-driven proton pump, bacteriorhodopsin (bR) in the photochemical cycle might imply internal water molecules. The free energy of inserting water molecules in specific sites along the bR transmembrane channel has been calculated using molecular dynamics simulations based on a microscopic model. The existence of internal hydration is related to the free energy change on transfer of a water molecule from bulk solvent into a specific binding site. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each hydrated model from molecular dynamics simulations of the creation of water molecules into specific protein-binding sites. A rigorous statistical mechanical formulation allowing the calculation of the free energy of transfer of water molecules from the bulk to a protein cavity is used to estimate the probabilities of occupancy in the putative bR proton channel. The channel contains a region lined primarily by nonpolar side-chains. Nevertheless, the results indicate that the transfer of four water molecules from bulk water to this apparently hydrophobic region is thermodynamically permitted. The column forms a continuous hydrogen-bonded chain over 12 A between a proton donor, Asp 96, and the retinal Schiff base acceptor. The presence of two water molecules in direct hydrogen-bonding association with the Schiff base is found to be strongly favorable thermodynamically. The implications of these results for the mechanism of proton transfer in bR are discussed.     

Free energy perturbation study on a Trp-binding mutant (Ser88-->Cys) of the trp-repressor.

The Ser88-->Cys mutant of the trp-repressor showed a lower affinity for the corepressor than the wild-type repressor [delta delta G = 1.7 +/- 0.3 kcal/mol, Chou and Matthews (1989) J. Biol. Chem., 264, 18314-18319]. A molecular dynamics/free energy cycle perturbation study was performed to understand the origin of the decreased affinity. A value (delta delta G = 1.58 +/- 0.28 kcal/mol) comparable with the experimental value was obtained by the simulation. Free energy component analysis revealed that destabilization of the van der Waals interaction between Ser88 and Trp109 (corepressor) mainly contributed to the decreased affinity of the mutant. The rotational transition of the hydroxyl (sulfhydryl) group of Ser88 (Cys88) during the simulations affected the contributions of Arg84 and water to the free energy change in the aporepressor and those of Arg84 and Trp109 to that in the holorepressor. However, the contributions from different residues compensated each other, and the total free energy changes were almost invariable in the various simulations.     

Buried waters and internal cavities in monomeric proteins

We have analyzed the buried water molecules and internal cavities in a set of 75 high-resolution, nonhomologous, monomeric protein structures. The number of hydrogen bonds formed between each water molecule and the protein varies from 0 to 4, with 3 being most common. Nearly half of the water molecules are found in pairs or larger clusters. Approximately 90% are shown to be associated with large cavities within the protein, as determined by a novel program, PRO_ACT. The total volume of a protein's large cavities is proportional to its molecular weight and is not dependent on structural class. The largest cavities in proteins are generally elongated rather than globular. There are many more empty cavities than hydrated cavities. The likelihood of a cavity being occupied by a water molecule increases with cavity size and the number of available hydrogen bond partners, with each additional partner typically stabilizing the occupied state by 0.6 kcal/mol.     

Reciprocal cooperative effects of multiple ligand binding to pyruvate kinase

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

B3LYP/6-311++G** study of monohydrates of alpha- and beta-D-glucopyranose: hydrogen bonding, stress energies, and effect of hydration on internal coordinates

Twenty-six monohydrates of alpha- and beta-D-glucopyranose were studied using gradient methods at the B3LYP/6-311++G** level of theory. Geometry optimization was carried out with the water molecules at different configurations around the glucose molecule. A new nomenclature for hydrated carbohydrates was developed to describe the water configurations. Zero-point vibrational energy, enthalpy, entropy, and relative free energy were obtained using the harmonic approximation. Hydrogen-bond energies for the monohydrates range from approximately -5 to -12 kcal/mol, and the average relative free energy is approximately 5 kcal/mol. The 1-hydroxy position is the most energetically favored site for hydration, and the region between the two and three positions is the next-most favored site. A water molecule approaching alpha-D-glucose between the 1- and 2-hydroxy positions pulls the 2-hydroxyl hydrogen atom away from the 1-hydroxy oxygen atom, thus increasing the hydrogen-bond length and also increasing the alpha-D-glucose energy. The increase in energy that occurs with a similar interaction on the beta-anomer is much less effective since the hydrogen bond is much longer. Using the calculated free energies of all 26 configurations, the anomer population (alpha/beta) increases in the beta-anomer population relative to the in vacuo case by approximately 10% at the expense of the alpha-anomer, giving an (alpha/beta) ratio of approximately 50/50. This result arises from entropy contributions favoring the beta-anomer more than the alpha-anomer. From analysis of donor and acceptor hydrogen-bond lengths, excellent correlation is found between the DFT calculated distances and those taken from carbohydrate structures in the Cambridge Crystallographic Data Bank.     

Free-energy simulations of the oxidation of c-terminal methionines in calmodulin

In the course of aging or under conditions of oxidative stress, methionine residues of calmodulin undergo oxidation, leading to loss of biological activity of the protein. We have performed free-energy simulations of the effects of C-terminal methionine side-chain oxidation on the properties of calmodulin. The simulation results indicate that oxidation should have a destabilizing effect on all three protein functional states: calcium free, calcium loaded, and with both calcium and target peptide bound. Because the different states are destabilized by different amounts, this leads to a more complex pattern in the observable effects on protein thermal stability, calcium affinity, and binding of a target peptide. The influence of oxidation on the free energy of CaM unfolding is estimated by comparing the free-energy cost of oxidizing a Met residue in a Gly-Met-Gly peptide and in the protein. The protein thermal stability of the oxidized forms is lowered by a moderate amount 1-3 kcal/mol, in qualitative agreement with experimental results of 0.3 kcal/mol. The calculated changes in affinity for calcium and for the target peptide show opposing trends. Oxidation at position 144 is predicted to enhance peptide binding and weaken calcium binding, whereas oxidation at 145 weakens peptide binding and enhances affinity for calcium. The lower affinity of Met 145-oxidized calmodulin toward the target peptide correlates with experimentally observed lowering of calmodulin-activated Ca-ATPase activity when oxidized calmodulin from aged rat brains is used. Thus, our simulations suggest that Met 145 is the oxidation site in the C-terminal fragment of calmodulin. The microscopic mechanism behind the calculated free energy changes appears to be a greater affinity for water of the oxidized Met side-chain relative to normal Met. Structures with Met exposed to solvent had consistently lower free energies than those with buried Met sidechains.