Thermodynamics of amide hydrogen bond formation in polar and apolar solvents

The statistical-thermodynamic basis for computation of binding affinities: a critical review

Although the statistical thermodynamics of noncovalent binding has been considered in a number of theoretical papers, few methods of computing binding affinities are derived explicitly from this underlying theory. This has contributed to uncertainty and controversy in certain areas. This article therefore reviews and extends the connections of some important computational methods with the underlying statistical thermodynamics. A derivation of the standard free energy of binding forms the basis of this review. This derivation should be useful in formulating novel computational methods for predicting binding affinities. It also permits several important points to be established. For example, it is found that the double-annihilation method of computing binding energy does not yield the standard free energy of binding, but can be modified to yield this quantity. The derivation also makes it possible to define clearly the changes in translational, rotational, configurational, and solvent entropy upon binding. It is argued that molecular mass has a negligible effect upon the standard free energy of binding for biomolecular systems, and that the cratic entropy defined by Gurney is not a useful concept. In addition, the use of continuum models of the solvent in binding calculations is reviewed, and a formalism is presented for incorporating a limited number of solvent molecules explicitly.

Effects of Aqueous and Organic Solvents on the Conformational Properties of the Helix-Forming alpha-Methyl-beta-L-aspartamyl Residue

The conformational preferences of N-acetyl-N'-methyl-alpha-methyl-beta-L-aspartamide, which is the model compound for helical poly(beta-L-aspartate)s, have been determined by ab initio SCF-MO computations. Two driving patterns have been found for the existing 13 minimum energy conformations: (i) intramolecular hydrogen bonding interactions of both amide-amide and amide-ester type; and (ii) repulsive interactions between the four oxygen atoms contained in the molecule. Self-consistent reaction-field (SCRF) calculations based on the method proposed by Miertus, Scrocco, and Tomasi have been performed in order to evaluate the effect of the solvent on the conformational preferences of the compound subject of study. Water and carbon tetrachloride were the solvents chosen for this purpose, and results have been discussed and interpreted on the basis of their electronic structures. The conclusions drawn from this study are of assistance to understand some features of the conformational transitions experimentally found in poly(beta-L-aspartate)s.

Free-energy determinants of alpha-helix insertion into lipid bilayers

A detailed treatment is provided of the various free-energy terms that contribute to the transfer of a polyalanine alpha-helix from the aqueous phase into lipid bilayers. In agreement with previous work, the hydrophobic effect is found to provide the major driving force for helix insertion. However, an opposing effect of comparable magnitude is also identified and is attributed to the large free-energy penalty associated with the desolvation of peptide hydrogen bonds on transfer to the low dielectric environment of the bilayer. Lipid perturbation effects as well as the entropy loss associated with helix immobilization in the bilayer are also evaluated. Two configurations of a membrane-bound 25mer polyalanine helix were found to be lower in free energy than the isolated helix in the aqueous phase. The first corresponds to the case of vertical insertion, in which a helix terminus protrudes from each side of the bilayer. The second minimum is for the case of horizontal insertion, for which the helix is adsorbed upon the surface of the bilayer. The calculated free-energy minima are found to be in good agreement with recent measurements of related systems. Large free-energy barriers resulting from desolvation of unsatisfied hydrogen-bonding groups at the helix termini are obtained for both insertion processes. The barriers for insertion are significantly reduced if the helix termini are assumed to be "capped" through the formation of hydrogen bonds with polar sidechains. For uncapped helices, our results support recently proposed models in which helices are inserted by first adsorbing on the membrane surface and then having one terminus "swing around" so as to penetrate the bilayer.

Folding of aminosuccinyl peptides: thermodynamic data from temperature dependent circular dichroism measurements

The conformational equilibrium of aminosuccinyl peptides between extended conformations and an intramolecularly hydrogen bonded type II' beta-turn conformation has been studied on the peptide Boc-L-Asu-Gly-L-Ala-OMe (Asu = aminosuccinyl residue) by means of temperature dependence of circular dichroism spectra. Owing to the peculiar chiroptical and conformational properties of the Asu residue, this technique proved to be very useful for deriving thermodynamic data for the above folding process. The value of delta H0 (-6.6 kJ mol-1), obtained for the peptide studied in a chloroformacetonitrile mixture, shows that the lower energy of the folded conformer is primarily due to the characteristic intramolecular hydrogen bond of the beta turns.

Statistical clustering techniques for the analysis of long molecular dynamics trajectories: analysis of 2.2-ns trajectories of YPGDV

The microscopic interactions and mechanisms leading to nascent protein folding events are generally unknown. While such short time-scale events are difficult to study experimentally, molecular dynamics simulations of peptides can provide a useful model for studying events related to protein folding initiation. Recently, two extremely long molecular dynamics simulations (2.2 ns each) were carried out on the pentapeptide Tyr-Pro-Gly-Asp-Val [Tobias, D. J., Mertz, J. E., & Brooks, C. L., III (1991) Biochemistry 30, 6054-6058] that forms stable reverse turns in solution. Tobias et al. examined folding events in this large system (approximately 30,000 conformations) using traditional methods of trajectory analysis. The shear magnitude of this problem prompted us to develop an automated approach, based on self-organizing neural nets, to extract the key features of the molecular dynamics trajectory. The neural net is used to perform conformational clustering, which reduces the complexity of a system while minimizing the loss of information. The conformations were grouped together using distances in dihedral angle space as a measure of conformational similarity. The resulting clusters represent "conformational states", and transitions between these states were examined to identify mechanisms of conformational change. Many conformational changes involved the rotation of only a single dihedral angle, but concerted angle changes were also found. Most of the conformational information in the 30,000 samples from the full trajectories was retained in the relatively few resultant clusters, providing a powerful tool for analysis of an expanding base of large molecular simulations.

Stability of a model beta-sheet in water

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

Conformational preferences of oligopeptides rich in alpha-aminoisobutyric acid. II. A model for the 3(10)/alpha-helix transition with composition and sequence sensitivity

The analysis of the factors that control the helical folding of Aib-rich peptides is extended to include sensitivity to sequence patterns, and in particular the presence of contiguous non-Aib alpha-mono-alkylated residues. The distinct hydrogen-bonding network of the 3(10)-helix, as contrasted with that of the competing alpha-helical structure, is explicitly incorporated into a theoretical model for the 3(10)-helix/alpha-helix equilibrium constant for a given peptide. Finite length effects and the "extra" intrahelical hydrogen bond of the 3(10) form are expressed naturally as a result of this loop analysis. This semiempirical model captures all the established features of existing empirical rules for helical conformational transitions in Aib-rich sequences, as well as the recently detected helical transition induced solely by sequence permutation.

Calorimetric determination of the enthalpy change for the alpha-helix to coil transition of an alanine peptide in water

The enthalpy change (delta H) accompanying the alpha-helix to random coil transition in water has been determined calorimetrically for a 50-residue peptide of defined sequence that contains primarily alanine. The enthalpy of helix formation is one of the basic parameters needed to predict thermal unfolding curves for peptide helices and it provides a starting point for analysis of the peptide hydrogen bond. The experimental uncertainty in delta H reflects the fact that the transition curve is too broad to measure in its entirety, which precludes fitting the baselines directly. A lower limit for delta H of unfolding, 0.9 kcal/mol per residue, is given by assuming that the change in heat capacity (delta Cp) is zero, and allowing the baseline to intersect the transition curve at the lowest measured Cp value. Use of the van't Hoff equation plus least-squares fitting to determine a more probable baseline gives delta H = 1.3 kcal/mol per residue. Earlier studies of poly(L-lysine) and poly(L-glutamate) have given 1.1 kcal/mol per residue. Those investigations, along with our present result, suggest that the side chain has little effect on delta H. The possibility that the peptide hydrogen bond shows a correspondingly large delta H, and the implications for protein stability, are discussed.

Reverse turns in blocked dipeptides are intrinsically unstable in water

We have carried out molecular dynamics simulations to study the conformational equilibria of two blocked dipeptides, Ac-Ala-Ala-NHMe and trans-Ac-Pro-Ala-NHMe, in water (Ac, amino-terminal blocking group COCH3; NHMe, carboxy-terminal blocking group NHCH3). Using specialized sampling techniques we computed free-energy surfaces as functions of a conformation co-ordinate that corresponds to hydrogen-bonded reverse turns at small values and to extended conformations at large values. The free-energy difference between hydrogen-bonded reverse turn conformations and extended conformations, determined from the equilibrium constants for reverse turn unfolding, is approximately -5 kcal/mole for Ac-Ala-Ala-NHMe, and -10 kcal/mole for Ac-Pro-Ala-NHMe. These results demonstrate that reverse turns in blocked dipeptides are intrinsically unstable in water. That is, in the absence of strongly stabilizing sequence-specific inter-residue interactions involving side-chains and/or charged terminal groups, the extended conformations of small peptides are highly favored in solution. By thermodynamically decomposing the free-energy differences, we found that the peptide-water entropy is the primary reason for the exceptional stability of the extended conformations of both peptides, and that the differences between the two peptides are primarily due to differences in the peptide-water interactions. In addition, we assessed the "proline effect" on the conformational equilibria by comparing the differences in configurational entropies between the reverse turn and extended conformations of the two peptides. As expected, the extended conformation of the Pro-Ala peptide is destabilized by reduced configurational entropy, but the effect is negligible in the blocked dipeptides. Finally, we compared our results with the results of several other experimental studies to identify some of the specific interactions that may be responsible for stabilizing reverse turns in small peptides in solution.