Energetics of the interaction between water and the helical peptide group and its role in determining helix propensities.

The alanine helix provides a model system for studying the energetics of interaction between water and the helical peptide group, a possible major factor in the energetics of protein folding. Helix formation is enthalpy-driven (-1.0 kcal/mol per residue). Experimental transfer data (vapor phase to aqueous) for amides give the enthalpy of interaction with water of the amide group as approximately -11.5 kcal/mol. The enthalpy of the helical peptide hydrogen bond, computed for the gas phase by quantum mechanics, is -4.9 kcal/mol. These numbers give an enthalpy deficit for helix formation of -7.6 kcal/mol. To study this problem, we calculate the electrostatic solvation free energy (ESF) of the peptide groups in the helical and beta-strand conformations, by using the delphi program and parse parameter set. Experimental data show that the ESF values of amides are almost entirely enthalpic. Two key results are: in the beta-strand conformation, the ESF value of an interior alanine peptide group is -7.9 kcal/mol, substantially less than that of N-methylacetamide (-12.2 kcal/mol), and the helical peptide group is solvated with an ESF of -2.5 kcal/mol. These results reduce the enthalpy deficit to -1.5 kcal/mol, and desolvation of peptide groups through partial burial in the random coil may account for the remainder. Mutant peptides in the helical conformation show ESF differences among nonpolar amino acids that are comparable to observed helix propensity differences, but the ESF differences in the random coil conformation still must be subtracted.

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins.

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.

Role of main-chain electrostatics, hydrophobic effect and side-chain conformational entropy in determining the secondary structure of proteins.

The physiochemical bases of amino acid preferences for alpha-helical, beta-strand, and other main-chain conformational states in proteins is controversial. Hydrophobic effect, side-chain conformational entropy, steric factors, and main-chain electrostatic interactions have all been advanced as the dominant physical factors which determine these preferences. Many attempts to resolve the controversy have focused on small model systems. The disadvantage of such systems is that the amino acids in small molecules are largely exposed to the solvent. In proteins, however, the amino acids are in contact with the solvent to a different degree, causing a large variability of strengths of all interactions. The estimates of mean strengths of interactions in the actual protein environment are therefore essential to resolve the controversy. In this work the experimental protein structures are used to estimate the mean strengths of various interactions in proteins. The free energy contributions of the interactions are implemented into the Lifson-Roig theory to calculate the helix and strand free energy profiles. From the profiles the secondary structures of proteins and peptides are predicted using simple rules. The role of hydrophobic effect, side-chain conformational entropy, and main-chain electrostatic interactions in determining the secondary structure of proteins is assessed from the abilities of different models, describing stability of secondary structures, to correctly predict alpha-helices, beta-strands and coil in 130 proteins. The three-state accuracy of the model, which contains only the free energy terms due to the main-chain electrostatics with 40 coefficients, is 68.7%. This accuracy is approaching to the accuracy of currently the best secondary structure prediction algorithm based on neural networks (72%); however, many thousands of parameters have to be optimized during the training of the neural networks to reach this level of accuracy. The correlation coefficient between the calculated and the experimental helix contents of 37 alanine based peptides is 0.91. If the hydrophobic and the side-chain conformational entropy terms are included into the helix-coil transition parameters, the accuracy of the algorithm does not improve significantly. However, if the main-chain electrostatic interactions are excluded from the helix-coil and strand-coil transition parameters, the accuracy of the algorithm reaches only 59.5%. These results support the dominant role of the short-range main-chain electrostatics in determining the secondary structure of proteins and peptides. The role of the hydrophobic effect and the side-chain conformational entropy is small.

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation.

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28-110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the alpha-helices. The method fails to predict the native 3-D structure of proteins with a predominantly beta secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from beta-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment.

Determination of the conformation of folding initiation sites in proteins by computer simulation.

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11-14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested.

Structure, dynamics and energetics of initiation sites in protein folding: I. Analysis of a 1 ns molecular dynamics trajectory of an early folding unit in water: the helix I/loop I-fragment of barnase.

The dynamic and energetic behavior of an initiation site of protein folding (helix I/loop I fragment of barnase) isolated from the tertiary environment of the rest protein is investigated in a 1 ns molecular dynamics simulation. All atom representation, explicit solvent description, and periodic boundary conditions are applied. In the course of the simulation several steps of structural disintegration are observed, followed by events partially rebuilding the initial structure. The phase of disintegration results in a fragment conformation completely lacking hydrogen bonds, with one residue in the center of the helix changed from alpha to beta conformation. The transition state of helix disintegration is characterized by a complete i-->i + 4/i + 5 hydrogen bonding network which undergoes gradual hydrolysis starting at the solvent exposed flank and proceeding towards the interior of the fragment perpendicular to the axis of the helix. Energetic analysis of the helix transitions shows that the i-->i + 4/i-->i + 5 network of hydrogen bonds accommodates one helical residue in beta conformation with only slightly worse hydrogen bonding energy and Van der Waals packing compared to the regular alpha-helix. The stability of the fragment is primarily due to hydrophobic interactions of residues shown to be essential in mutagenesis experiments.

Role of electrostatic screening in determining protein main chain conformational preferences.

Amino acids display significant variation in propensity for the alpha R-helical, beta-sheet, and other main chain conformational states in proteins and peptides. The physical reason for these preferences remains controversial. Conformational entropy, steric factors, and the hydrophobic effect have all been advanced as the dominant underlying cause. In this work, we explore the role of a fourth factor, electrostatics, in determining the main chain conformation in protein molecules. Potentials of mean force derived from experimental protein structures are used to evaluate the free energy of electrostatic and other interactions of a residue in a protein environment. The local and nonlocal electrostatic interactions of main chain polar atoms are found to be crucial for determining the preferences of residues for the alpha R-helical state and other main chain conformational states of a residue. Further, the strength of local and nonlocal electrostatic interactions is shown to depend on the electrostatic screening by solvent and protein groups. Residue specific modulation of this screening in a manner related to side chain bulk and squatness produces a model that fits the observed distribution of residue conformations in proteins and recent experimental mutagenesis data on protein stability better than any other single factor.

On achieving better than 1-A accuracy in a simulation of a large protein: Streptomyces griseus protease A.

Computational methods are frequently used to simulate the properties of proteins. In these studies accuracy is clearly important, and the improvement of accuracy of protein simulation methodology is one of the major challenges in the application of theoretical methods, such as molecular dynamics, to structural studies of biological molecules. Much effort is being devoted to such improvements. Here, we present an analysis of a 187-ps molecular dynamics simulation of the serine protease Streptomyces griseus protease A in its crystal environment. The reproduction of the experimental structure is considerably better than has been achieved in earlier simulations--the root mean square deviation of the simulated structure from the x-ray structure being less than 1 A, a significant step toward the goal of simulating proteins to within experimental error. The use of a longer cutoff with truncation rather than a switching function, inclusion of all crystalline water and the counterions in the crystallization medium, and use of the consistent valence force field characterize the differences in this calculation.

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.

Molecular dynamics study of the structure and dynamics of a protein molecule in a crystalline ionic environment, Streptomyces griseus protease A.

A large-scale molecular dynamics simulation of the behavior of a serine protease (Streptomyces griseus protease A) in a crystalline environment has been performed. All atoms (including hydrogens) of two protein molecules and the surrounding solvent of crystallization, consisting of both water and salt ions, were explicitly represented, and a relatively long range of interactions (up to 15 A) were included. The simulation is the longest so far reported for a protein in such an environment (60 ps). The use of the full crystalline environment allows a direct comparison of the structure and dynamic properties of the protein and surrounding solvent to be made with the experimental X-ray structure. Here we report the comparison of the protein structures and analyze the energetics of the system, including interaction with the aqueous environment. Subsequent papers will deal with other aspects of the simulation. The overall root mean square differences between the time-averaged molecular dynamics structure and that from crystallography, for all well-ordered, non-hydrogen atoms, are 1.67 and 1.25 A for the two molecules taken as the asymmetric unit. An extensive analysis of the conformation of substructural elements and individual residues and their deviation from experiment has revealed a strong influence of the ionic medium on their behavior. Implications of the results for free energy calculations and for future directions are also discussed.

Potential energy functions and the role of the conformational entropy of clonidine-like imidazolidines in determining their affinity for alpha-adrenergic receptors.

Energy as a function of the ring interplanar torsional angle was calculated for 12 2-(phenylimino)imidazolidines by the method of perturbation configuration interaction using localized orbitals. The potential energy functions indicate that the molecules may assume any conformation within rather broad limits. The functions were used in calculating the gas phase and solution conformational entropies. The latter were used as the independent variable in regression analysis to derive equations connecting the conformational entropy with pKi (pKi = -log Ki) for [3H]clonidine displacement (literature data). As a comparison, correlations between pKi and several other parameters (modified neglect of diatomic overlap-computed highest occupied and lowest unoccupied molecular orbital energies and dipole moments; pKa; log P; substituent steric parameters) were sought. Correlation coefficients C greater than 0.6 were obtained with the conformational entropy (-0.77), and the ortho steric parameters (-0.71). The correlation with the conformational entropy was not markedly improved by adding other parameters in multiple regression analysis. This result is discussed in terms of the contribution to the ligand-receptor complexation free energy arising from the conformational restriction of the ligands upon binding to the receptor.