Analysis of Thermodynamic Determinants in Helix Propensities of Nonpolar Amino Acids through a Novel Free Energy Calculation

FRAP analysis of peptide diffusion in extracellular matrix mimetic hydrogels as an in vitro model for subcutaneous injection

Subcutaneous (SC) injection is a common route of administration for drug compounds with poor oral bioavailability. However, bioavailability is often variable and incomplete, and there is as yet no standard accepted medium for simulation of the human SC environment. In this work we evaluate a FRAP based method for quantitative determination of local self-diffusion coefficients within extracellular matrix (ECM) mimetic hydrogels, potentially useful as in vitro models for drug transport in the ECM after SC injection. Gels were made consisting of either agarose, cross-linked collagen (COL) and hyaluronic acid (HA) or cross-linked HA. The diffusivities of uncharged FITC-dextran (FD4), the highly charged poly-lysine (PLK20) and poly-glutamic acid (PLE20) as well as the GLP-1 analogue exenatide were determined within the gels using FRAP. The diffusion coefficients in uncharged agarose gels were in the range of free diffusion in PBS. The diffusivity of cationic PLK20 in gels containing anionic HA was substantially decreased due to strong electrostatic interactions. Peptide aggregation could be observed as immobile fractions in experiments with exenatide. We conclude that the FRAP method provides useful information of peptides' interactions and transport properties in hydrogel networks, giving insight into the mechanisms affecting absorption of drug compounds after subcutaneous injection.

Searching for Aquamelt Behavior among Silklike Biomimetics during Fibrillation under Flow

In this paper, we elucidate a generic mechanism behind strain-induced phase transition in aqueous solutions of silk-inspired biomimetics by atomistic molecular dynamics simulations. We show the results of modeling of homopeptides polyglycine Gly₃₀ and polyalanine Ala₃₀ and a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)₅, i.e., the simplest and yet relevant sequences that could mimic the behavior of natural silk under stress conditions. First, we analyze hydrophobicities of the sequences by calculating the Gibbs free energy of hydration and inspecting the interchain hydrogen bonding and hydration by water. Second, the force-extension profiles are scanned and compared with the results for poly(ethylene oxide), the synthetic polymer for which the aquamelt behavior has been proved recently. Additionally, the conformational transitions of oligopeptides from coiled to extended states are characterized by a generalized order parameter and by the dependence of the solvent-accessible surface area of the chains on applied stretching. Fibrillation itself is surveyed using both the two-dimensional interchain pair correlation function and the SAXS/WAXS patterns for the aggregates formed under stress. These are compared with experimental data found in the literature on fibril structure of silk composite materials doped with oligoalanine peptides. Our results show that tensile stress introduced into aqueous oligopeptide solutions facilitates interchain interactions. The oligopeptides display both a greater resistance to extension as compared to poly(ethylene oxide) and a reduced ability for hydrogen bonding of the stretched chains between oligomers and with water. Fiber formation is proved for all simulated objects, but the most structured one is made of a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)₅: For this sequence, we obtain the highest degree of the secondary structure motifs in the fiber. We conclude that this is the most promising candidate among considered sequences to find the aquamelt behavior in further experimental studies.

Coarse-Grained Protein Model Coupled with a Coarse-Grained Water Model: Molecular Dynamics Study of Polyalanine-Based Peptides

The coupling of a coarse-grained (CG) protein model with the CG water model developed by Marrink et al. (J. Phys. Chem. B 2004, 108, 750) is presented. The model was used in the molecular dynamics studies of Ac-(Ala)6-Xaa-(Ala)7-NHMe, Xaa = Ala, Leu, Val, and Gly. A Gly mutation in the middle of polyalanine is found to destabilize the helix and stabilize the hairpin by favoring a type-II' turn and probably to speed up hairpin folding. The simulations allow us to derive thermodynamic parameters of, in particular, the helical propensities (s) of amino acids in these polyalanine-based peptides. The calculated s values are 1.18 (Ala), 0.84 (Leu), 0.30 (Val), and <0.02 (Gly) at 291 K, in excellent agreement with experimental values (R(2)=0.970). Analyses using a structural approach method show that the helical propensity difference of these amino acids mainly comes from solvation effect. Leu and Val have lower helical propensities than Ala mainly because the larger side chains shield the solvation of helical structures, while Gly has a much poorer helical propensity mainly due to the much better solvation for the coil structures than for the helical structures. Overall, the model is at least about 10(2) times faster than current all-atom MD methods with explicit solvent.

Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods

Entropy of binding constitutes a major, and in many cases a detrimental, component of the binding affinity in biomolecular interactions. While the enthalpic part of the binding free energy is easier to calculate, estimating the entropy of binding is further more complicated. A precise evaluation of entropy requires a comprehensive exploration of the complete phase space of the interacting entities. As this task is extremely hard to accomplish in the context of conventional molecular simulations, calculating entropy has involved many approximations. Most of these golden standard methods focused on developing a reliable estimation of the conformational part of the entropy. Here, we review these methods with a particular emphasis on the different techniques that extract entropy from atomic fluctuations. The theoretical formalisms behind each method is explained highlighting its strengths as well as its limitations, followed by a description of a number of case studies for each method. We hope that this brief, yet comprehensive, review provides a useful tool to understand these methods and realize the practical issues that may arise in such calculations.

Mechanism of stabilization of helix secondary structure by constrained Cα-tetrasubstituted α-amino acids

The theoretical basis behind the ability of constrained Cα-tetrasubstituted amino acids (CTAAs) to induce stable helical conformations has been studied through Replica Exchange Molecular Dynamics Potential of Mean Force Quantum Theory of Atoms In Molecules calculations on Ac-l-Ala-CTAA-l-Ala-Aib-l-Ala-NHMe peptide models. We found that the origin of helix stabilization by CTAAs can be ascribed to at least two complementary mechanisms limiting the backbone conformational freedom: steric hindrance predominantly in the (+x,+y,-z) sector of a right-handed 3D Cartesian space, where the z axis coincides with the helical axis and the Cα of the CTAA lies on the +y axis (0,+y,0), and the establishment of additional and relatively strong C-H···O interactions involving the CTAA.

Estimated secondary structure propensities within V1/V2 region of HIV gp120 are an important global antibody neutralization sensitivity determinant

Background

Neutralization sensitivity of HIV-1 virus to antibodies and anti-sera varies greatly between the isolates. Significant role of V1/V2 domain as a global neutralization sensitivity regulator has been suggested. Recent X-ray structures revealed presence of well-defined tertiary structure within this domain but also demonstrated partial disorder and conformational heterogeneity.

Methods

Correlations of neutralization sensitivity with the conformational propensities for beta-strand and alpha-helix formation over the entire folded V1/V2 domain as well as within sliding 5-residue window were investigated. Analysis was based on a set of neutralization data for 106 HIV isolates for which consistent neutralization sensitivity measurements against multiple pools of human immune sera have been previously reported.

Results

Significant correlation between beta-sheet formation propensity of the folded segments of V1/V2 domain and neutralization sensitivity was observed. Strongest correlation peaks localized to the beta-strands B and C. Correlation persisted when subsets of HIV isolates belonging to clades B, C and circulating recombinant form BC where analyzed individually or in combinations.

Conclusions

Observed correlations suggest that stability of the beta-sheet structure and/or degree of structural disorder in the V1/V2 domain is an important determinant of the global neutralization sensitivity of HIV-1 virus. While specific mechanism is to yet to be investigated, plausible hypothesis is that less ordered V1/V2s may have stronger masking effect on various neutralizing epitopes, perhaps effectively occupying larger volume and thereby occluding antibody access.

Nanobio interfaces: charge control of enzyme/inorganic interfaces for advanced biocatalysis

Specific approaches to the rational design of nanobio interfaces for enzyme and protein binding to nanomaterials are vital for engineering advanced, functional nanobiomaterials for biocatalysis, sensing, and biomedical applications. This feature article presents an overview of our recent discoveries on structural, functional, and mechanistic details of how enzymes interact with inorganic nanomaterials and how they can be controlled in a systematic manner using α-Zr(IV)phosphate (α-ZrP) as a model system. The interactions of a number of enzymes having a wide array of surface charges, sizes, and functional groups are investigated. Interactions are carefully controlled to screen unfavorable repulsions and enhance favorable interactions for high affinity, structure retention, and activity preservation. In specific cases, catalytic activities and substrate selectivities are improved over those of the pristine enzymes, and two examples of high activity near the boiling point of water have been demonstrated. Isothermal titration calorimetric studies indicated that enzyme binding is coupled to ion sequestration or release to or from the nanobio interface, and binding is controlled in a rational manner. We learned that (1) bound enzyme stabilities are improved by lowering the entropy of the denatured state; (2) maximal loadings are obtained by matching charge footprints of the enzyme and the nanomaterial surface; (3) binding affinities are improved by ion sequestration at the nanobio interface; and (4) maximal enzyme structure retention is obtained by biophilizing the nanobio interface with protein glues. The chemical and physical manipulations of the nanobio interface are significant not only for understanding the complex behaviors of enzymes at biological interfaces but also for desiging better functional nanobiomaterials for a wide variety of practical applications.

Protein-ligand binding free energies from exhaustive docking

We explore the use of exhaustive docking as an alternative to Monte Carlo and molecular dynamics sampling for the direct integration of the partition function for protein-ligand binding. We enumerate feasible poses for the ligand and calculate the Boltzmann factor contribution of each pose to the partition function. From the partition function, the free energy, enthalpy, and entropy can be derived. All our calculations are done with a continuum solvation model that includes solving the Poisson equation. In contrast to Monte Carlo and molecular dynamics simulations, exhaustive docking avoids (within the limitations of a discrete sampling) the question of "Have we run long enough?" due to its deterministic complete enumeration of states. We tested the method on the T4 lysozyme L99A mutant, which has a nonpolar cavity that can accommodate a number of small molecules. We tested two electrostatic models. Model 1 used a solute dielectric of 2.25 for the complex apoprotein and free ligand and 78.5 for the solvent. Model 2 used a solute dielectric of 2.25 for the complex and apoprotein but 1.0 for the free ligand. For our test set of eight molecules, we obtain a reasonable correlation with a Pearson r(2) = 0.66 using model 1. The trend in binding affinity ranking is generally preserved with a Kendall τ = 0.64 and Spearman ρ = 0.83. With model 2, the correlation is improved with a Pearson r(2) = 0.83, Kendall τ = 0.93, and Spearman ρ = 0.98. This suggests that the energy function and sampling method adequately captured most of the thermodynamics of binding of the nonpolar ligands to T4 lysozyme L99A.

A combined crystallographic and molecular dynamics study of cathepsin L retrobinding inhibitors

We report the crystal structures of three noncovalent retrobinding inhibitors in complex with mature cathepsin L up to resolutions of 2.5, 1.8, and 2.5 A, respectively. These inhibitors were Bpa-(Nepsilon-Bpa)Lys-DArg-Tyr-Npe, Bpa-(Nepsilon-Bpa)Lys-DArg-Phe-Npe, and Bpa-MCys-DArg-Phe-Npe, where Bpa = biphenylacetyl and Pea = N-phenylethyl. These were selected to clarify the binding mode of the biphenyl groups in the S' subsites because the addition of a second biphenyl does not improve potency. Examination of the symmetry-related monomers in the crystal structures revealed inhibitor-inhibitor crystal packing interactions. Molecular dynamics simulations were then used to explore the structure and dynamical behavior of the isolated protein-ligand complexes in solution. In the simulations, the backbone biphenyl groups for all three inhibitors ended up in the same location despite having started out in different orientations in the initial crystal structure conformations. The lack of improved potency of the larger inhibitors over the smaller one is attributed to a correspondingly greater entropic cost of binding.

Crystal structure of the transcriptional regulator CmeR from Campylobacter jejuni

The CmeABC multidrug efflux pump, which belongs to the resistance-nodulation-division (RND) family, recognizes and extrudes a broad range of antimicrobial agents and is essential for Campylobacter jejuni colonization of the animal intestinal tract by mediating the efflux of bile acids. The expression of CmeABC is controlled by the transcriptional regulator CmeR, whose open reading frame is located immediately upstream of the cmeABC operon. To understand the structural basis of CmeR regulation, we have determined the crystal structure of CmeR to 2.2 A resolution, revealing a dimeric two-domain molecule with an entirely helical architecture similar to members of the TetR family of transcriptional regulators. Unlike the rest of the TetR regulators, CmeR has a large center-to-center distance (54 A) between two N termini of the dimer, and a large flexible ligand-binding pocket in the C-terminal domain. Each monomer forms a 20 A long tunnel-like cavity in the ligand-binding domain of CmeR and is occupied by a fortuitous ligand that is identified as glycerol. The binding of glycerol to CmeR induces a conformational state that is incompatible with target DNA. As glycerol has a chemical structure similar to that of potential ligands of CmeR, the structure obtained mimics the induced form of CmeR. These findings reveal novel structural features of a TetR family regulator, and provide new insight into the mechanisms of ligand binding and CmeR regulation.

The backbone conformational entropy of protein folding: experimental measures from atomic force microscopy

The energy dissipated during the atomic force microscopy-based mechanical unfolding and extension of proteins is typically an order of magnitude greater than their folding free energy. The vast majority of the "excess" energy dissipated is thought to arise due to backbone conformational entropy losses as the solvated, random-coil unfolded state is stretched into an extended, low-entropy conformation. We have investigated this hypothesis in light of recent measurements of the energy dissipated during the mechanical unfolding of "polyproteins" comprised of multiple, homogeneous domains. Given the assumption that backbone conformational entropy losses account for the vast majority of the energy dissipated (an assumption supported by numerous lines of experimental evidence), we estimate that approximately 19(+/-2)J/(mol K residue) of entropy is lost during the extension of three mechanically stable beta-sheet polyproteins. If, as suggested by measured peak-to-peak extension distances, pulling proceeds to near completion, this estimate corresponds to the absolute backbone conformational entropy of the unfolded state. As such, it is exceedingly close to previous theoretical and semi-empirical estimates that place this value at approximately 20J/(mol K residue). The estimated backbone conformational entropy lost during the extension of two helical polyproteins, which, in contrast to the mechanically stable beta-sheet polyproteins, rupture at very low applied forces, is three- to sixfold less. Either previous estimates of the backbone conformational entropy are significantly in error, or the reduced mechanical strength of the helical proteins leads to the rupture of a subsequent domain before full extension (and thus complete entropy loss) is achieved.

Ab initio prediction of helical segments in polypeptides

An ab initio method has been developed to predict helix formation for polypeptides. The approach relies on the systematic analysis of overlapping oligopeptides to determine the helical propensity for individual residues. Detailed atomistic level modeling, including entropic contributions, and solvation/ionization energies calculated through the solution of the Poisson-Boltzmann equation, is utilized. The calculation of probabilities for helix formation is based on the generation of ensembles of low energy conformers. The approach, which is easily amenable to parallelization, is shown to perform very well for several benchmark polypeptide systems, including the bovine pancreatic trypsin inhibitor, the immunoglobulin binding domain of protein G, the chymotrypsin inhibitor 2, the R69 N-terminal domain of phage 434 repressor, and the wheat germ agglutinin.

Structure and conformational behavior of biopolymers by density functional calculations employing periodic boundary conditions. I. The case of polyglycine, polyalanine, and poly-alpha-aminoisobutyric acid in vacuo

Fully quantum mechanical calculations exploiting periodic boundary conditions (PBC) have been applied to the study of four different regular structures (alpha- and 3(10)-helix, fully extended and repeated gamma-turns) of the infinite polypeptides of glycine, alanine, and alpha-aminoisobutyric acid (Aib) in vacuo. alpha-Helix is predicted to be the most stable conformer for polyalanine and polyglycine, being stabilized over the 3(10)-helix mainly by more favorable dipole-dipole interactions. Contrary to previous suggestions, steric effects and hydrogen-bond strengths are comparable for both helix structures. 3(10)-Helix is preferred for poly-Aib, since in this case alpha-helix is strongly distorted due to unfavorable intrachain repulsions. Extended structures and repeated gamma-turns are much less stable than helix structures for all of the polypeptides examined, mainly due to the absence of favorable long-range interactions. The optimized geometries are in good agreement with the available experimental data and reveal a remarkable dependence on the nature of the residue forming the polypeptides; at the same time the electronic and structural parameters of each residue strongly depend on the secondary structure of the polypeptides.

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.

The relative order of helical propensity of amino acids changes with solvent environment

A model peptide of sequence Ac-Y-VAXAK-VAXAK-VAXAK-NH(2), where X is substituted with one of nineteen amino acids (P excluded), was synthesized and titrated with methanol to study helical propensity as a function of solvent environment. The CD spectra of these peptides are largely random coil in 2 mM sodium phosphate buffer (pH 5.5) and show a conformational change to alpha-helix with increasing methanol content. Singular value decomposition was used to correct the CD spectra for the absorbing side chains of W, Y, F, C, and M, and this correction can be substantial. With correction both W and F become good helix formers. The free energy for helix propagation was calculated using the Lifson-Roig statistical model for each of the nineteen amino acids at each point in their titration. The results show that the rank order of helical propensity for the nineteen amino acids changes with solvent environment. This result will be particularly important if proteins undergo hydrophobic collapse before secondary structures are formed, because amino acids can then see different solvent environments as the secondary structures are formed. Related amino acids are found to have interesting correlations in the shape of their titration curves. This finding provides one explanation for the limiting 70% accuracy in predicting secondary structure from sequence, since the helical propensities used are calculated for an average solvent environment. Proteins 2000;39:132-141.

Structure-based conformational preferences of amino acids

Proteins can be very tolerant to amino acid substitution, even within their core. Understanding the factors responsible for this behavior is of critical importance for protein engineering and design. Mutations in proteins have been quantified in terms of the changes in stability they induce. For example, guest residues in specific secondary structures have been used as probes of conformational preferences of amino acids, yielding propensity scales. Predicting these amino acid propensities would be a good test of any new potential energy functions used to mimic protein stability. We have recently developed a protein design procedure that optimizes whole sequences for a given target conformation based on the knowledge of the template backbone and on a semiempirical potential energy function. This energy function is purely physical, including steric interactions based on a Lennard-Jones potential, electrostatics based on a Coulomb potential, and hydrophobicity in the form of an environment free energy based on accessible surface area and interatomic contact areas. Sequences designed by this procedure for 10 different proteins were analyzed to extract conformational preferences for amino acids. The resulting structure-based propensity scales show significant agreements with experimental propensity scale values, both for alpha-helices and beta-sheets. These results indicate that amino acid conformational preferences are a natural consequence of the potential energy we use. This confirms the accuracy of our potential and indicates that such preferences should not be added as a design criterion.

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed.

A helix propensity scale based on experimental studies of peptides and proteins

The average globular protein contains 30% alpha-helix, the most common type of secondary structure. Some amino acids occur more frequently in alpha-helices than others; this tendency is known as helix propensity. Here we derive a helix propensity scale for solvent-exposed residues in the middle positions of alpha-helices. The scale is based on measurements of helix propensity in 11 systems, including both proteins and peptides. Alanine has the highest helix propensity, and, excluding proline, glycine has the lowest, approximately 1 kcal/mol less favorable than alanine. Based on our analysis, the helix propensities of the amino acids are as follows (kcal/mol): Ala = 0, Leu = 0.21, Arg = 0.21, Met = 0.24, Lys = 0.26, Gln = 0.39, Glu = 0.40, Ile = 0.41, Trp = 0.49, Ser = 0.50, Tyr = 0. 53, Phe = 0.54, Val = 0.61, His = 0.61, Asn = 0.65, Thr = 0.66, Cys = 0.68, Asp = 0.69, and Gly = 1.

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.

Trifluoroethanol effects on helix propensity and electrostatic interactions in the helical peptide from ribonuclease T1

Trifluoroethanol (TFE) is often used to increase the helicity of peptides to make them usable as models of helices in proteins. We have measured helix propensities for all 20 amino acids in water and two concentrations of trifluoroethanol, 15 and 40% (v/v) using, as a model system, a peptide derived from the sequence of the alpha-helix of ribonuclease T1. There are three main conclusions from our studies. (1) TFE alters electrostatic interactions in the ribonuclease T1 helical peptide such that the dependence of the helical content on pH is lost in 40% TFE. (2) Helix propensities measured in 15% TFE correlate well with propensities measured in water, however, the correlation with propensities measured in 40% TFE is significantly worse. (3) Propensities measured in alanine-based peptides and the ribonuclease T1 peptide in TFE show very poor agreement, revealing that TFE greatly increases the effect of sequence context.

15N backbone dynamics of the S-peptide from ribonuclease A in its free and S-protein bound forms: toward a site-specific analysis of entropy changes upon folding

Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the "model-free" approach (Lipari & Szabo, 1982). Order parameters obtained from "model-free" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding.

Consistency in structural energetics of protein folding and peptide recognition

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.

The energy landscape of a fast-folding protein mapped by Ala-->Gly substitutions

A moderately stable protein with typical folding kinetics unfolds and refolds many times during its cellular lifetime. In monomeric lambda repressor this process is extremely rapid, with an average folded state lifetime of only 30 milliseconds. A thermostable variant of this protein (G46A/G48A) unfolds with the wild-type rate, but it folds in approximately 20 microseconds making it the fastest-folding protein yet observed. The effects of alanine to glycine substitutions on the folding and unfolding rate constants of the G46A/G48A variant, measured by dynamic NMR spectroscopy, indicate that the transition state is an ensemble comprised of a disperse range of conformations. This structural diversity in the transition state is consistent with the idea that folding chains are directed towards the native state by a smooth funnel-like conformational energy landscape. The kinetic data for the folding of monomeric lambda repressor can be understood by merging the new energy landscape view of folding with traditional models. This hybrid model incorporates the conformational diversity of denatured and transition state ensembles, a transition state activation energy, and the importance of intrinsic helical stabilities.

Entropy in protein folding and in protein-protein interactions

The reduction of conformational entropy is a major barrier that has to be overcome in protein folding and binding. Changes in solvent entropy are also a major factor. Recent advances include clarification of the fundamental issues concerning the separation of entropy into components, the treatment of association entropy in binding, and the role of size and shape effects in solvation entropy. Advances in the application of entropy calculations include an emerging consensus for estimates of backbone and sidechain entropy loss in protein folding via use of numerically intensive methods for sampling, and use of the expanding protein-structure database.

A new class of models for computing receptor-ligand binding affinities

Models for predicting the binding affinities of molecules in solution are either very detailed, making them computationally intensive and hard to test, or very simple, and thus less informative than one might wish. A new class of models that focus on the predominant states of the binding molecules promise to capture the essential physics of binding at modest computational cost.

Helix propagation and N-cap propensities of the amino acids measured in alanine-based peptides in 40 volume percent trifluoroethanol

The helix propagation and N-cap propensities of the amino acids have been measured in alanine-based peptides in 40 volume percent trifluoroethanol (40% TFE) to determine if this helix-stabilizing solvent uniformly affects all amino acids. The propensities in 40% TFE are compared with revised values of the helix parameters of alanine-based peptides in water. Revision of the propensities in water is the result of redefining the capping statistical weights and evaluating the helix nucleation constant with N-capping explicitly included in the helix-coil model. The propagation propensities of all amino acids increase in 40% TFE relative to water, but the increases are highly variable. In water, all beta-branched and beta-substituted amino acids are helix breakers. In 40% TFE, the propagation propensities of the nonpolar amino acids increase greatly, leaving charged and neutral polar, beta-substituted amino acids as helix breakers. Glycine and proline are strong helix breakers in both solvents. Free energy differences for helix propagation (delta delta G) between alanine and other nonpolar amino acids are twice as large in water as predicted from side-chain conformational entropies, but delta delta G values in 40% TFE are close to those predicted from side-chain entropies. This dependence of delta delta G on the solvent points to a specific role of water in determining the relative helix propensities of the nonpolar amino acids. The N-cap propensities converge toward a common value in 40% TFE, suggesting that differential solvation by water contributes to the diversity of N-cap values shown by the amino acids.

On the entropy of protein folding

The failure to appreciate that the hydration of polar groups is a major contribution to the entropy of protein unfolding has led to considerable underestimates for the loss of configurational freedom when a protein chain folds.