Insight into the phosphodiesterase mechanism from combined QM/MM free energy simulations

Molecular dynamics simulations employing a combined quantum mechanical and molecular mechanical potential have been carried out to elucidate the reaction mechanism of the hydrolysis of a cyclic nucleotide cAMP substrate by phosphodiesterase 4B (PDE4B). PDE4B is a member of the PDE superfamily of enzymes that play crucial roles in cellular signal transduction. We have determined a two-dimensional potential of mean force (PMF) for the coupled phosphoryl bond cleavage and proton transfer through a general acid catalysis mechanism in PDE4B. The results indicate that the ring-opening process takes place through an S(N)2 reaction mechanism, followed by a proton transfer to stabilize the leaving group. The computed free energy of activation for the PDE4B-catalyzed cAMP hydrolysis is about 13 kcal·mol(-1) and an overall reaction free energy is about -17 kcal·mol(-1), both in accord with experimental results. In comparison with the uncatalyzed reaction in water, the enzyme PDE4B provides a strong stabilization of the transition state, lowering the free energy barrier by 14 kcal·mol(-1). We found that the proton transfer from the general acid residue His234 to the O3' oxyanion of the ribosyl leaving group lags behind the nucleophilic attack, resulting in a shallow minimum on the free energy surface. A key contributing factor to transition state stabilization is the elongation of the distance between the divalent metal ions Zn(2+) and Mg(2+) in the active site as the reaction proceeds from the Michaelis complex to the transition state.     

Potentiometric titration of poly-L-lysine: the coil-to-beta transition

We have performed potentiometric titrations of poly-L -lysine. From these data we have calculated the free energy and enthalpy changes for the folding of the random coil to the α-helix in 10% ethanol (?120 and ?120 cal/mole) and from the random coil to the β-structure in water (?140 and 870 cal/mole) and in 10% ethanol (?180 and 980 cal mole). Comparison of these values with each other and with values for the coil → α- helix transition in water (?78 and ?880 cal/mole) led to the following conclusions. The stabilization by ethanol of ethanol of the α-helix with respect to the coil is that predicted from the known free energy of transfer of the peptide group from water to 10% ethanol. Similar data to explain the enthalpy difference are not available. The thermodynamic functions for the transition from α-helix to β-structure, obtained by subtracting those for the coil → α-helix and coil → β-structure transitions, are explained from a consideration of the structural differences: non bonded interactions of the polypeptide backbone are less favorable in the β-structure than in the α-helix, causing an increase in the energy, while hydrophobic contacts between side chains raise the entropy of the β-structure as compared with the α-helix, so that the free energy difference between the two structures is small, but enthalpy and entropy differences are large. The observation of only small differences in the free energy and enthalpy changes for the transition from coil β-structure upon going from water to 10% ethanol is expected by considering both the free energy of transfer of the peptide group (as for the α-helix) and the free energy and enthalpy of transfer of the apolar part of the side chain involved in hydrophobic bond formation.     

The calculated free energy effects of 5-methyl cytosine on the B to Z transition in DNA

We have examined the free energy effects of 5-methylation of cytosine on the B in equilibrium Z conformational equilibrium in DNA. Free energy differences were calculated using the free energy perturbation approach, which uses an easily derived equation from classical statistical mechanics to relate the free energy difference between two states to the ensemble average of the potential energy difference between the states. Calculations were carried both in explicit solvent and (for comparison) in vacuo. The free energy values obtained for the explicit solvent systems are total free energies, with contributions from all parts of the system (solvent + solute), and so are relevant to the B in equilibrium Z transitions observed under real (physiological) conditions. We calculate that in solution, methylation makes the B in equilibrium Z transition more favorable by about -0.4 kcal/mole base pair (bp) in free energy. This value compares well with approximate experimentally derived values of about -0.3 kcal/mole-bp. We also discuss a method for determining the free energy difference between conformational states poorly maintained by a potential energy model. Finally, the effects of methylation on the melting temperature of DNA are examined.     

Effects of urea and guanidine hydrochloride on peptide and nonpolar groups

The free energy transfer of several N-acetyl(glycine)n ethyl esters (n = 1-3) and side chain derivatives (Ala, Val, Nva, Leu, Nle, and Phe) from water to urea and guanidine hydrochloride solutions has been determined from the solubility and distribution coefficients of these compounds between aqueous and nonaqueous phases. These uncharged model peptides, unlike the amino acids used for a similar study, avoid complication due to charge effects for the transfer process. The compounds with an increase in the number of glycyl groups show additivity of the group free energy toward the transfer from water to urea solution but not to guanidine hydrochloride solution. The derivatives with a side chain show that the principle of group additivity does not hold true for the aliphatic side chains for the transfer to either urea or guanidine hydrochloride solutions. In fact, the free energy of transfer of the side chains, viz., aliphatic ones, is found to be energetically unfavorable in moderately high denaturant concentration. Phenylalanyl, the only aromatic side chain studied here, showed a favorable free energy of transfer to the denaturant solutions. In addition, the values of the favorable free energy obtained in this study are much smaller than the values obtained from the study of the amino acids. The transfer of the glycyl group to the denaturant solutions is exothermic whereas the transfer of the side chains is endothermic in nature.(ABSTRACT TRUNCATED AT 250 WORDS)     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Stability analysis for the cavity-filling mutations of the Myb DNA-binding domain utilizing free-energy calculations

We have analyzed the effect of cavity-filling mutations on protein stability by means of free-energy calculations based on molecular dynamics simulations to identify the factors contributing to stability changes caused by the mutations. We have studied the DNA-binding domain of Myb, which has a cavity in one of three homologous repeat units, and analyzed a series of mutations with nonnatural and natural amino acids at a single site, which change the size of the cavity. We found that the calculated free-energy changes caused by the mutations are in excellent agreement with experimental data (correlation coefficient 0.98). The free-energy changes in the native and denatured states were independently compared with the unfolding free-energy change (deltadeltaG) and cavity-volume changes (deltaV), and it was found that deltadeltaG and deltaV correlate with the native-state free-energy changes but not with the denatured-state free-energy changes. Further analyses in terms of enthalpy and entropy show that compensation between entropy and enthalpy occurs in the denatured state but not in the native state. The main contribution to the native-state free energy was found to be van der Waals interactions associated with the cavity. We estimate that the decrease in free energy per methylene group, which results from filling the cavity, is about 2 to 3 kcal/mol. These results suggest that the stabilization of a protein by cavity-filling mutations be determined primarily by the free energy associated with the cavity volume in the native state.     

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.     

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Empirical solvation models can be used to differentiate native from near-native conformations of bovine pancreatic trypsin inhibitor.

Several hydration models for peptides and proteins based on solvent accessible surface area have been proposed previously. We have evaluated some of these models as well as four new ones in the context of near-native conformations of a protein. In addition, we propose an empirical site-site distance-dependent correction that can be used in conjunction with any of these models. The set of near-native structures consisted of 39 conformations of bovine pancreatic trypsin inhibitor (BPTI) each of which was a local minimum of an empirical energy function (ECEPP) in the absence of solvent. Root-mean-square (rms) deviations from the crystallographically determined structure were in the following ranges: 1.06-1.94 A for all heavy atoms, 0.77-1.36 A for all backbone heavy atoms, 0.68-1.33 A for all alpha-carbon atoms, and 1.41-2.72 A for all side-chain heavy atoms. We have found that there is considerable variation among the solvent models when evaluated in terms of concordance between the solvation free energy and the rms deviations from the crystallographically determined conformation. The solvation model for which the best concordance (0.939) with the rms deviations of the C alpha atoms was found was derived from NMR coupling constants of peptides in water combined with an exponential site-site distance dependence of the potential of mean force. Our results indicate that solvation free energy parameters derived from nonpeptide free energies of hydration may not be transferrable to peptides. Parameters derived from peptide and protein data may be more applicable to conformational analysis of proteins. A general approach to derive parameters for free energy of hydration from ensemble-averaged properties of peptides in solution is described.     

Site specific point mutation changes specificity: A molecular modeling study by free energy simulations and enzyme kinetics of the thermodynamics in ribonuclease T1 substrate interactions

We have theoretically and experimentally studied the binding of two different ligands to wild-type ribonuclease T₁ (RNT1) and to a mutant of RNT1 with Glu-46 replaced by Gln. The binding of the natural substrate 3′-GMP has been compared with the binding of a fluorescent probe, 2-aminopurine 3′-monophosphate (2AP), and relative free energies of binding of these ligands to the mutant and the wild-type (wt) enzyme have been calculated by free energy perturbation methods. The free energy perturbations predict that the mutant RNT1-Gln-46 binds 2AP better than 3′GMP, in agreement with experiments on dinucleotides. Four free energy perturbations, forming a closed loop, have been performed to allow the detection of systematic errors in the simulation procedure. Because of the larger number of atoms involved, it was necessary to use a much longer simulation time for the change in the protein, i.e., the perturbation from Glu to Gln, than in the perturbation from 3′-GMP to 2AP. Finally the structure of the binding site is analyzed for understanding differences in catalytic speed and binding strength. © 1993 Wiley-Liss, Inc.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).     

Contribution of the trifluoroacetyl group in the thermodynamics of antigen–antibody binding

We analyzed the binding of the 7C8 antibody to the chloramphenicol phosphonate antigens—one containing a trifluoroacetyl group (CP‐F) and the other containing an acetyl group (CP‐H)—by using isothermal titration calorimetry (ITC). The thermodynamic difference due to the substitution of F by H was evaluated using free energy calculations based on molecular dynamics (MD) simulations. We have previously shown that another antibody, namely, 6D9, binds more weakly to CP‐H than to CP‐F, mainly due to the different hydration free energies of the dissociated state and not due to the unfavorable hydrophobic interactions with the antibody in the bound state. Unlike in the binding of the trifluoroacetyl group with 6D9, in its binding with 7C8, it is exposed to the solvent, as seen in the crystal structure of the complex of 7C8 with CP‐F. The thermodynamic analysis performed in this study showed that the binding affinity of 7C8 for CP‐H is similar to that for CP‐F, but this binding to CP‐H is accompanied with less favorable enthalpy and more favorable entropy changes. The free energy calculations indicated that, upon the substitution of F by H, enthalpy and entropy changes in the associated and dissociated states were decreased, but the magnitude of enthalpy and entropy changes in the dissociated state was larger than that in the associated state. The differences in binding free energy, enthalpy, and entropy changes determined by the free energy calculations for the substitution of F by H are in good agreement with the experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

Construction and Analysis of the Model of Energy Metabolism in E. coli

Genome-scale models of metabolism have only been analyzed with the constraint-based modelling philosophy and there have been several genome-scale gene-protein-reaction models. But research on the modelling for energy metabolism of organisms just began in recent years and research on metabolic weighted complex network are rare in literature. We have made three research based on the complete model of E. coli’s energy metabolism. We first constructed a metabolic weighted network using the rates of free energy consumption within metabolic reactions as the weights. We then analyzed some structural characters of the metabolic weighted network that we constructed. We found that the distribution of the weight values was uneven, that most of the weight values were zero while reactions with abstract large weight values were rare and that the relationship between w (weight values) and v (flux values) was not of linear correlation. At last, we have done some research on the equilibrium of free energy for the energy metabolism system of E. coli. We found that (free energy rate input from the environment) can meet the demand of (free energy rate dissipated by chemical process) and that chemical process plays a great role in the dissipation of free energy in cells. By these research and to a certain extend, we can understand more about the energy metabolism of E. coli.     

Computed free energy differences between point mutations in a collagen-like peptide

We studied the results of mutating alanine --> glycine at three positions of a collagen-like peptide in an effort to develop a computational method for predicting the energetic and structural effects of a single point genetic mutation in collagen, which is associated with the clinical diagnosis of Osteogenesis Imperfecta (OI). The differences in free energy of denaturation were calculated between the collagen-like peptides [(POG)(4)(POA)(POG)(4)](3) and [(POG)(10)](3) (POG: proline-hydroxyproline-glycine).* Our computational results, which suggest significant destabilization of the collagen-like triple-helix upon the glycine --> alanine mutations, correlate very well with the experimental free energies of denaturation. The robustness of our collagen-like peptide model is shown by its reproduction of experimental results with both different simulation paths and different lengths of the model peptide. The individual free energy for each alanine --> glycine mutation (and the reverse free energy, glycine --> alanine mutation) in the collagen-like peptide has been calculated. We find that the first alanine introduced into the triple helix causes a very large destabilization of the helix, but the last alanine introduced into the same position of an adjacent chain causes a very small change in the peptide stability. Thus, our results demonstrate that each mutation does not contribute equally to the free energy. We find that the sum of the calculated individual residues' free energy can accurately model the experimental free energy for the whole peptide.     

Molecular dynamics simulation of six β-blocker drugs passing across POPC bilayer

Six selected β-blocker drugs (alprenolol, atenolol, metoprolol, nadolol, pindolol and propranolol) passing across 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer were studied using all-atom molecular dynamics simulation. The free energy profiles can be divided into two groups, according to their shapes: the free energy curve of group one (atenolol, nadolol and pindolol) has an obvious minimum while that of the other group (propranolol, metoprolol and alprenolol) is flat inside membrane. Energy analysis shows that electrostatic interaction plays an important role for the first group drugs. The hydrogen bond analysis results also certify that the first group drugs form more hydrogen bonds than the other β-blockers. The calculated permeability sequence agrees with the experimental ones. Our calculation suggests that the permeability model using potential of mean force (PMF) method can be also applied to chemically similar compounds besides chemically diverse compounds.     

Accurate determination of the binding free energy for KcsA-charybdotoxin complex from the potential of mean force calculations with restraints

Free energy calculations for protein-ligand dissociation have been tested and validated for small ligands (50 atoms or less), but there has been a paucity of studies for larger, peptide-size ligands due to computational limitations. Previously we have studied the energetics of dissociation in a potassium channel-charybdotoxin complex by using umbrella sampling molecular-dynamics simulations, and established the need for carefully chosen coordinates and restraints to maintain the physiological ligand conformation. Here we address the ligand integrity problem further by constructing additional potential of mean forces for dissociation of charybdotoxin using restraints. We show that the large discrepancies in binding free energy arising from simulation artifacts can be avoided by using appropriate restraints on the ligand, which enables determination of the binding free energy within the chemical accuracy. We make several suggestions for optimal choices of harmonic potential parameters and restraints to be used in binding studies of large ligands.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

Structure-based thermodynamic analysis of the dissociation of protein phosphatase-1 catalytic subunit and microcystin-LR docked complexes

The relationship between the structure of a free ligand in solution and the structure of its bound form in a complex is of great importance to the understanding of the energetics and mechanism of molecular recognition and complex formation. In this study, we use a structure-based thermodynamic approach to study the dissociation of the complex between the toxin microcystin-LR (MLR) and the catalytic domain of protein phosphatase-1 (PP-1c) for which the crystal structure of the complex is known. We have calculated the thermodynamic parameters (enthalpy, entropy, heat capacity, and free energy) for the dissociation of the complex from its X-ray structure and found the calculated dissociation constant (4.0 x 10(-11)) to be in excellent agreement with the reported inhibitory constant (3.9 x 10(-11)). We have also calculated the thermodynamic parameters for the dissociation of 47 PP-1c:MLR complexes generated by docking an ensemble of NMR solution structures of MLR onto the crystal structure of PP-1c. In general, we observe that the lower the root-mean-square deviation (RMSD) of the docked complex (compared to the X-ray complex) the closer its free energy of dissociation (deltaGd(o)) is to that calculated from the X-ray complex. On the other hand, we note a significant scatter between the deltaGd(o) and the RMSD of the docked complexes. We have identified a group of seven docked complexes with deltaGd(o) values very close to the one calculated from the X-ray complex but with significantly dissimilar structures. The analysis of the corresponding enthalpy and entropy of dissociation shows a compensation effect suggesting that MLR molecules with significant structural variability can bind PP-1c and that substantial conformational flexibility in the PP-1c:MLR complex may exist in solution.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.