Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

Estimates of the loss of main-chain conformational entropy of different residues on protein folding.

The average contribution of conformational entropy for individual amino acid residues towards the free energy of protein folding is not well understood. We have developed empirical scales for the loss of the main-chain (torsion angles, phi and psi) conformational entropy by taking its side-chain into account. The analysis shows that the main-chain component of the total conformational entropy loss for a residue is significant and reflects intrinsic characteristics associated with individual residues. The values have direct correlation with the hydrophobicity values and this has important bearing on the folding process. Proteins 1999;36:332-339.     

Folding of polypeptide chains induced by the amino acid side-chains

Conformational calculations with the use of semi-empirical potential functions have been applied to the analysis of the folding of peptide chains. In particular, the part played by the amino acid side-chains in the adoption of folded conformations has been investigated.The results show that the preferred conformations of short peptides are mostly extended ones. However, from a given peptide chain-length, the side-chain to backbone and side-chain to side-chain interactions become strong enough so that definite sequences of amino acids can induce a transition from extended to folded conformations. We propose to call these folded structures “conformational nuclei”. The type of “nucleus” formed is dependent on both the amino acid composition and the sequence.Our results strongly support the hypothesis that folding of polypeptide chains can occur through a nucleation process that could be induced by the side-chains.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Straight-chain non-polar amino acids are good helix-formers in water

For comparison with earlier data on naturally occurring non-polar amino acids (Ala, Leu, Phe, Val, Ile), the comparative helix-forming tendencies have been measured for non-polar amino acid residues that have unbranched side-chains, with an ethyl, propyl or butyl group, and also for methionine. The substitutions are made in a 17-residue alanine-based peptide. The results show that straight-chain non-polar amino acids have high helix-forming tendencies compared to beta-branched non-polar amino acids. Restriction of side-chain conformations in the helix, with a corresponding reduction in conformational entropy, is the likely explanation. There is a small increase in helix-forming tendency as the side-chain increases in length from ethyl to butyl, which suggests that a helix-stabilizing hydrophobic interaction is being detected.     

Dynamic Monte Carlo simulations of a new lattice model of globular protein folding, structure and dynamics

A long-standing problem of molecular biology is the prediction of globular protein tertiary structure from the primary sequence. In the context of a new, 24-nearest-neighbor lattice model of proteins that includes both alpha and beta-carbon atoms, the requirements for folding to a unique four-member beta-barrel, four-helix bundles and a model alpha/beta-bundle have been explored. A number of distinct situations are examined, but the common requirements for the formation of a unique native conformation are tertiary interactions plus the presence of relatively small (but not irrelevant) intrinsic turn preferences that select out the native conformer from a manifold of compact states. When side-chains are explicitly included, there are many conformations having the same or a slightly greater number of side-chain contacts as in the native conformation, and it is the local intrinsic turn preferences that produce the conformational selectivity on collapse. The local preference for helix or beta-sheet secondary structure may be at odds with the secondary structure ultimately found in the native conformation. The requisite intrinsic turn populations are about 0.3% for beta-proteins, 2% for mixed alpha/beta-proteins and 6% for helix bundles. In addition, an idealized model of an allosteric conformational transition has been examined. Folding occurs predominantly by a sequential on-site assembly mechanism with folding initiating either at a turn or from an isolated helix or beta-strand (where appropriate). For helical and beta-protein models, similar folding pathways were obtained in diamond lattice simulations, using an entirely different set of local Monte Carlo moves. This argues strongly that the results are universal; that is, they are independent of lattice, protein model or the particular realization of Monte Carlo dynamics. Overall, these simulations demonstrate that the folding of all known protein motifs can be achieved in the context of a single class of lattice models that includes realistic backbone structures and idealized side-chains.     

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.     

Simulation of oligopeptide dynamics and folding. The use of NMR chemical shifts to analyse the MD trajectories.

In this paper, a simulation of the folding process, based on a random perturbations of the phi, psi, chi1 dihedral angles, is proposed to approach the formation at the atom level of both principal elements of protein secondary structure, the alpha-helix and the beta-hairpin structures. Expecting to understand what may happen in solution during the formation of such structures, the behaviour of large sets of random conformations that are generated for small oligopeptides was analysed. Different factors that may influence the folding (as conformational propensity, hydrophobic interactions and side-chain mobility) were investigated. The difference between the corresponding theoretical folding and the real conformational diversity that is observed in solution is appraised by a comparison between the calculated and observed NMR secondary chemical shifts. From this study it appears that hydrophobic interactions and mobility represent the principal factors that initiate folding and determine the observed hydrogen-bond pattern, which subsequently allows packing between the peptide side chains.     

Side-chain conformational entropy at protein-protein interfaces

Protein-protein interactions are the key to many biological processes. How proteins selectively and correctly associate with their required protein partner(s) is still unclear. Previous studies of this "protein-docking problem" have found that shape complementarity is a major determinant of interaction, but the detailed balance of energy contributions to association remains unclear. This study estimates side-chain conformational entropy (per unit solvent accessible area) for various protein surface regions, using a self-consistent mean field calculation of rotamer probabilities. Interfacial surface regions were less flexible than the rest of the protein surface for calculations with monomers extracted from homodimer datasets in 21 of 25 cases, and in 8 of 9 for the large protomer from heterodimer datasets. In surface patch analysis, based on side-chain conformational entropy, 68% of true interfaces were ranked top for the homodimer set and 66% for the large protomer/heterodimer set. The results indicate that addition of a side-chain entropic term could significantly improve empirical calculations of protein-protein association.     

Entropy Hotspots for the Binding of Intrinsically Disordered Ligands to a Receptor Domain

Proline-rich motifs (PRMs) are widely used for mediating protein-protein interactions with weak binding affinities. Because they are intrinsically disordered when unbound, conformational entropy plays a significant role for the binding. However, residue-level differences of the entropic contribution in the binding of different ligands remain not well understood. We use all-atom molecular dynamics simulation and the maximal information spanning tree formalism to analyze conformational entropy associated with the binding of two PRMs, one from the Abl kinase and the other from the nonstructural protein 1 of the 1918 Spanish influenza A virus, to the N-terminal SH3 (nSH3) domain of the CrkII protein. Side chains of the stably folded nSH3 experience more entropy change upon ligand binding than the backbone, whereas PRMs involve comparable but heterogeneous entropy changes among the backbone and side chains. In nSH3, two conserved nonpolar residues forming contacts with the PRM experience the largest side-chain entropy loss. In contrast, the C-terminal charged residues of PRMs that form polar contacts with nSH3 experience the greatest side-chain entropy loss, although their “fuzzy” nature is attributable to the backbone that remains relatively flexible. Thus, residues that form high-occupancy contacts between nSH3 and PRM do not reciprocally contribute to entropy loss. Furthermore, certain surface residues of nSH3 distal to the interface with PRMs gain entropy, indicating a nonlocal effect of ligand binding. Comparing between the PRMs from cAbl and nonstructural protein 1, the latter involves a larger side-chain entropy loss and forms more contacts with nSH3. Consistent with experiments, this indicates stronger binding of the viral ligand at the expense of losing the flexibility of side chains, whereas the backbone experiences less entropy loss. The entropy “hotspots” as identified in this study will be important for tuning the binding affinity of various ligands to a receptor.     

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.     

Helix propensities of the amino acids measured in alanine-based peptides without helix-stabilizing side-chain interactions.

Helix propensities of the amino acids have been measured in alanine-based peptides in the absence of helix-stabilizing side-chain interactions. Fifty-eight peptides have been studied. A modified form of the Lifson-Roig theory for the helix-coil transition, which includes helix capping (Doig AJ, Chakrabartty A, Klingler TM, Baldwin RL, 1994, Biochemistry 33:3396-3403), was used to analyze the results. Substitutions were made at various positions of homologous helical peptides. Helix-capping interactions were found to contribute to helix stability, even when the substitution site was not at the end of the peptide. Analysis of our data with the original Lifson-Roig theory, which neglects capping effects, does not produce as good a fit to the experimental data as does analysis with the modified Lifson-Roig theory. At 0 degrees C, Ala is a strong helix former, Leu and Arg are helix-indifferent, and all other amino acids are helix breakers of varying severity. Because Ala has a small side chain that cannot interact significantly with other side chains, helix formation by Ala is stabilized predominantly by the backbone ("peptide H-bonds"). The implication for protein folding is that formation of peptide H-bonds can largely offset the unfavorable entropy change caused by fixing the peptide backbone. The helix propensities of most amino acids oppose folding; consequently, the majority of isolated helices derived from proteins are unstable, unless specific side-chain interactions stabilize them.     

Optimal region of average side-chain entropy for fast protein folding

Search and study the general principles that govern kinetics and thermodynamics of protein folding generates new insight into the factors that control this process. Here, we demonstrate based on the known experimental data and using theoretical modeling of protein folding that side-chain entropy is one of the general determinants of protein folding. We show for proteins belonging to the same structural family that there exists an optimal relationship between the average side-chain entropy and the average number of contacts per residue for fast folding kinetics. Analysis of side-chain entropy for proteins that fold without additional agents demonstrates that there exists an optimal region of average side-chain entropy for fast folding. Deviation of the average side-chain entropy from the optimal region results in an anomalous protein folding process (prions, alpha-lytic protease, subtilisin, some DNA-binding proteins). Proteins with high or low side-chain entropy would have extended unfolded regions and would require some additional agents for complete folding. Such proteins are common in nature, and their structure properties have biological importance.     

Hydrophilicity of polar amino acid side-chains is markedly reduced by flanking peptide bonds

Several amino acid side-chain hydropathy scales have been devised on the basis of solubility and water/organic solvent partitioning data obtained with free amino acids or side-chain analogs. In nearly all cases, these scales are based upon the structure-additivity assumption; it has been assumed that the transfer free energies of the amino acid side-chains are the same in these model compounds as they are in a polypeptide. This assumption is probably wrong. In the present study, deviations from additivity for amino acid side-chains are demonstrated by comparing a theoretically derived scale, which N-acetylamino acid amides. The results show that the flanking peptide bonds dramatically reduce the hydrophilicity of the polar side-chains, with deviations up to several kilocalories (1 kcal = 4.184 kJ) for the charged side-chains at pH 7.0. Further calculation shows that these deviations are due to reductions of 40 to 85% in the unfavorable transfer free energy of the polar functional groups. In addition, proximity of the neighboring amide bonds in the parent molecule (N-acetylglycine amide) decreases the hydrophilicity of the -CONH-backbone unit by 36%. This decrease is expected to be twice as large for -CONH- units in the interior of a polypeptide backbone. The significance of these observations is: (1) valid hydropathy scales can be obtained only with model peptides; (2) deviations from additivity are expected in all solvent systems, including non-polar solvents that are thought to mimic the interior of a membrane; (3) the spontaneous insertion of polypeptides into membranes is likely to occur much more readily than has been previously thought. In order to estimate the free energy of transferring the side-chains and the polypeptide backbone from water to the interior of a lipid bilayer, the results of this study are used to construct a hydropathy scale based upon the partitioning of solutes between water and non-polar solvents. The validity of hydropathy scales that are based on criteria other than solubility and water/organic solvent partitioning data is also discussed.     

Side-chain dynamics of the SAP SH2 domain correlate with a binding hot spot and a region with conformational plasticity

X-linked lymphoproliferative disease is caused by mutations in the protein SAP, which consists almost entirely of a single SH2 domain. SAP interacts with the Tyr281 site of the T<-->B cell signaling protein SLAM via its SH2 domain. Interestingly, binding is not dependent on phosphorylation but does involve interactions with residues N-terminal to the Tyr. We have used 15N and 2H NMR relaxation experiments to investigate the motional properties of the SAP SH2 domain backbone amides and side-chain methyl groups in the free protein and complexes with phosphorylated and non-phosphorylated peptides derived from the Tyr281 site of SLAM. The most mobile methyl groups are in side-chains with large RMSD values between the three crystal structures of SAP, suggesting that fast time-scale dynamics in side-chains is associated with conformational plasticity. The backbone amides of two residues which interact with the C-terminal part of the peptides experience fast time-scale motions in the free SH2 domain that are quenched upon binding of either the phosphorylated or non-phosphorylated peptide. Of most importance, the mobility of methyl groups in and around the binding site for residues in the N-terminus of the peptide is significantly restricted in the complexes, underscoring the dominance of this interaction with SAP and demonstrating a correlation between changes in rapid side-chain motion upon binding with local binding energy.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Side-chain conformational entropy in protein folding.

An important, but often neglected, contribution to the thermodynamics of protein folding is the loss of entropy that results from restricting the number of accessible side-chain conformers in the native structure. Conformational entropy changes can be found by comparing the number of accessible rotamers in the unfolded and folded states, or by estimating fusion entropies. Comparison of several sets of results using different techniques shows that the mean conformational free energy change (T delta S) is 1 kcal.mol-1 per side chain or 0.5 kcal.mol-1 per bond. Changes in vibrational entropy appear to be negligible compared to the entropy change resulting from the loss of accessible rotamers. Side-chain entropies can help rationalize alpha-helix propensities, predict protein/inhibitor complex structures, and account for the distribution of side chains on the protein surface or interior.     

α-Helix-forming propensities in peptides and proteins

Much effort has been invested in seeking to understand the thermodynamic basis of helix stability in both peptides and proteins. Recently, several groups have measured the helix-forming propensities of individual residues (Lyu, P. C., Liff, M. I., Marky, L. A., Kallenbach, N. R. Science 250:669–673, 1990; O'Neil, K. T., DeGrado, W. F. Science 250:646–651, 1990; Padmanabhan, S., Marqusee, S., Ridgeway, T., Laue, T. M., Baldwin, R. L. Nature (London) 344:268–270, 1990). Using Monte Carlo computer simulations, we tested the hypothesis that these differences in measured helix-forming propensity are due primarily to loss of side chain conformational entropy upon helix formation (Creamer, T. P., Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 89:5937–5941, 1992). Our previous study employed a rigid helix backbone, which is here generalized to a completely flexible helix model in order to ensure that earlier results were not a methodological artifact. Using this flexible model, side chain rotamer distributions and entropy losses are calculated and shown to agree with those obtained earlier. We note that the side chain conformational entropy calculated for Trp in our previous study was in error; a corrected value is presented. Extending earlier work, calculated entropy losses are found to correlate strongly with recent helix propensity scales derived from substitutions made within protein helices (Horovitz, A., Matthews, J. M., Fersht, A. R. J. Mol. Biol. 227:560–568, 1992; Blaber, M., Zhang, X.-J., Matthews, B. M. Science 260:1637–1640, 1993). In contrast, little correlation is found between these helix propensity scales and the accessible surface area buried upon formation of a model polyalanyl α-helix. Taken in sum, our results indicate that loss of side chain entropy is a major determinant of the helix-forming tendency of residues in both peptide and protein helices. © 1994 Wiley-Liss, Inc.     

Engineering a compact non-native state of intestinal fatty acid-binding protein

The last three C-terminal residues (129-131) of intestinal fatty acid-binding protein (IFABP) participate in four main-chain hydrogen bonds and two electrostatic interactions to sequentially distant backbone and side-chain atoms. To assess if these interactions are involved in the final adjustment of the tertiary structure during folding, we engineered an IFABP variant truncated at residue 128. An additional mutation, Trp-6-->Phe, was introduced to simplify the conformational analysis by optical methods. Although the changes were limited to a small region of the protein surface, they resulted in an IFABP with altered secondary and tertiary structure. Truncated IFABP retains some cooperativity, is monomeric, highly compact, and has the molecular dimensions and shape of the native protein. Our results indicated that residues 129-131 are part of a crucial conformational determinant in which several long-range interactions, essential for the acquisition of the native state, are established. This work suggests that carefully controlled truncation can populate equilibrium non-native states under physiological conditions. These non-native states hold a great promise as experimental models for protein folding.