The role of packing interactions in stabilizing folded proteins.

In order to investigate the role of nonpolar side chains in determining protein stability, we have carried out a molecular dynamics simulation study of the thermodynamics of interconverting isoleucine and valine side chains in the core of ribonuclease T1. The free energy change in the unfolded state, which we take to be fully solvated, was small and agrees qualitatively with experimental studies of alkane solvation. In the two Ile----Val mutations studied, the protein was able to relax around the smaller side chains, while in the case of the two Val----Ile mutations, the ability of the core to accommodate the extra methylene group depended on where the mutation took place. We argue that the experimentally observed decrease in stability for mutating isoleucine into valine results from a loss of favorable packing interactions of the side chain in the folded form of the protein. This supports the view that packing interactions in the folded state are an important contributor to the overall stability of the folded protein and that the core of the native protein is packed efficiently and almost completely.     

Energy functions for protein design: adjustment with protein-protein complex affinities, models for the unfolded state, and negative design of solubility and specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.     

Quinary interactions with an unfolded state ensemble

Anfinsen's thermodynamic hypothesis states that the native three‐dimensional fold of a protein represents the structure with the lowest Gibbs free energy. Changes in the free energy of denaturation can arise from changes to the folded state, the unfolded state, or both. It has been recently recognized that quinary interactions, transient contacts that take place only in cells, can modulate protein stability through interactions involving the folded state. Here we show that the cellular environment can also remodel the unfolded state ensemble.     

Effects of pH, salt, and macromolecular crowding on the stability of FK506-binding protein: an integrated experimental and theoretical study

Environmental variables can exert significant influences on the folding stability of a protein, and elucidating these influences provides insight on the determinants of protein stability. Here, experimental data on the stability of FKBP12 are reported for the effects of three environmental variables: pH, salt, and macromolecular crowding. In the pH range of 5-9, contribution to the pH dependence of the unfolding free energy from residual charge-charge interactions in the unfolded state was found to be negligible. The negligible contribution was attributed to the lack of sequentially nearest neighboring charged residues around groups that titrate in the pH range. KCl lowered the stability of FKBP12 and the E31Q/D32N double mutant at small salt concentrations but raised stability after approximately 0.5 M salt. Such a turnover behavior was accounted for by the balance of two opposing types of protein-salt interactions: the Debye-Hückel type, modeling the response of the ions to protein charges, favors the unfolded state while the Kirkwood type, accounting for the disadvantage of the ions moving toward the low-dielectric protein cavity from the bulk solvent, disfavors the unfolded state. Ficoll 70 as a crowding agent was found to have a modest effect on protein stability, in qualitative agreement with a simple model suggesting that the folded and unfolded states are nearly equally adversely affected by macromolecular crowding. For any environmental variable, it is the balance of its effects on the folded and unfolded states that determines the outcome on the folding stability.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

Polar and nonpolar atomic environments in the protein core: Implications for folding and binding

Hydrophobic interactions are believed to play an important role in protein folding and stability. Semi-empirical attempts to estimate these interactions are usually based on a model of solvation, whose contribution to the stability of proteins is assumed to be proportional to the surface area buried upon folding. Here we propose an extension of this idea by defining an environment free energy that characterizes the environment of each atom of the protein, including solvent, polar or nonpolar atoms of the same protein or of another molecule that interacts with the protein. In our model, the difference of this environment free energy between the folded state and the unfolded (extended) state of a protein is shown to be proportional to the area buried by nonpolar atoms upon folding. General properties of this environment free energy are derived from statistical studies on a database of 82 well-refined protein structures. This free energy is shown to be able to discriminate misfolded from correct structural models, to provide an estimate of the stabilization due to oligomerization, and to predict the stability of mutants in which hydrophobic residues have been substituted by site-directed mutagenesis, provided that no large structural modifications occur. © 1994 Wiley-Liss, Inc.     

Effect of backbone cyclization on protein folding stability: chain entropies of both the unfolded and the folded states are restricted

Circular versions of a large number of proteins have been designed by connecting the N and C termini via peptide linkers. A motivation for these designs is the assumed enhancement in folding stability, because backbone cyclization reduces the chain entropy of the unfolded state. Here, it is recognized that backbone cyclization also reduces the chain entropy of a flexible peptide linker in the folded state. Specifically, the end-to-end distance of the linker is restricted to fluctuations around the average displacement between the N and C termini of the folded protein. The balance of the chain-entropy reductions in the folded and unfolded states is used to predict the change in the unfolding free energy, deltadeltaG(cycl), by backbone cyclization. Predicted values of deltadeltaG(cycl) are in quantitative agreement with results of a careful study on cyclizing the 34 residue PIN1 WW domain by linkers with two to seen residues. The experimental results of an optimal linker length l=4 and a maximum stabilization of 1.7 kcal/mol are reproduced. Calculations of deltadeltaG(cycl) for a broad selection of circular proteins suggest that the stabilizing effect of backbone cyclization is modest, reflecting entropy reductions in both the unfolded and the folded states.     

Electrostatic contributions to the stability of a thermophilic cold shock protein

The thermophilic Bacillus caldolyticus cold shock protein (Bc-Csp) differs from the mesophilic Bacillus subtilis cold shock protein B (Bs-CspB) in 11 of the 66 residues. Stability measurements of Schmid and co-workers have implicated contributions of electrostatic interactions to the thermostability. To further elucidate the physical basis of the difference in stability, previously developed theoretical methods that treat electrostatic effects in both the folded and the unfolded states were used in this paper to study the effects of mutations, ionic strength, and temperature. For 27 mutations that narrow the difference in sequence between Bc-Csp and Bs-CspB, calculated changes in unfolding free energy (Delta G) and experimental results have a correlation coefficient of 0.98. Bc-Csp appears to use destabilization of the unfolded state by unfavorable charge-charge interactions as a mechanism for increasing stability. Accounting for the effects of ionic strength and temperature on the electrostatic free energies in both the folded and the unfolded states, explanations for two important experimental observations are presented. The disparate ionic strength dependences of Delta G for Bc-Csp and Bs-CspB were attributed to the difference in the total charges (-2e and -6e, respectively). A main contribution to the much higher unfolding entropy of Bs-CspB was found to come from the less favorable electrostatic interactions in the folded state. These results should provide insight for understanding the thermostability of other thermophilic proteins.     

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.     

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.     

Temperature-sensitive mutations of bacteriophage T4 lysozyme occur at sites with low mobility and low solvent accessibility in the folded protein

Twenty-five different temperature-sensitive point mutations at 20 sites in the lysozyme gene of bacteriophage T4 have been identified. All of the mutations alter amino acid side chains that have lower than average crystallographic thermal factors and reduced solvent accessibility in the folded protein. This suggests that the amino acids with well-defined conformations can form specific intramolecular interactions that make relatively large contributions to the thermal stability of the protein. Residues with high mobility or high solvent accessibility are much less susceptible to destabilizing substitutions, suggesting that, in general, such amino acids contribute less to protein stability. The pattern of the sites of ts substitutions observed in the folded conformation of T4 lysozyme suggests that severe destabilizing mutations that primarily affect the free energy of the unfolded state are rare. These results indicate that proteins can be stabilized by adding new interactions to regions that are rigid or buried in the folded conformation.     

Some recommendations for the practitioner to improve the precision of experimentally determined protein folding rates and phi values

The mechanism by which proteins fold from an initially random conformation into a functional, native structure remains a major unsolved question in molecular biology. Of particular interest to the protein folding community is the structure that the protein adopts in the folding transition state (the highest free energy state on the pathway from unfolded to folded), as that state forms the barrier that defines the folding pathway. Unfortunately, however, unlike those of the initial, unfolded state and the final, folded state of the protein, the structure in the transition state cannot be directly assessed via experiment. Instead, experimentalists infer the structure of the transition state, often by estimating changes in its free energy by measuring the effects of amino acid substitutions on folding and unfolding rates (Phi-value analysis). In this article we show how to obtain more efficient estimates of these important quantities via improved experimental designs, and how to avoid common pitfalls in the analysis of kinetic data during the extraction of these parameters.     

Correlation between mutational destabilization of phage T4 lysozyme and increased unfolding rates

The thermodynamics and kinetics of unfolding of 28 bacteriophage T4 lysozyme variants were compared by using urea gradient gel electrophoresis. The mutations studied cause a variety of sequence changes at different residues throughout the polypeptide chain and result in a wide range of thermodynamic stabilities. A striking relationship was observed between the thermodynamic and kinetic effects of the amino acid replacements: All the substitutions that destabilized the native protein by 2 kcal/mol or more also increased the rate of unfolding. The observed increases in unfolding rate corresponded to a decrease in the activation energy of unfolding (delta Gu) at least 35% as large as the decrease in thermodynamic stability (delta Gu). Thus, the destabilizing lesions bring the free energy of the native state closer to that of both the unfolded state and the transition state for folding and unfolding. Since a large fraction of the mutational destabilization is expressed between the transition state and the native conformation, the changes in folding energetics cannot be accounted for by effects on the unfolded state alone. The results also suggest that interactions throughout much of the folded structure are altered in the formation of the transition state during unfolding.     

Characterizing a partially folded intermediate of the villin headpiece domain under non-denaturing conditions: contribution of His41 to the pH-dependent stability of the N-terminal subdomain

The contribution of interactions involving the imidazole ring of His41 to the pH-dependent stability of the villin headpiece (HP67) N-terminal subdomain has been investigated by nuclear magnetic resonance (NMR) spin relaxation. NMR-derived backbone N-H order parameters (S2) for wild-type (WT) HP67 and H41Y HP67 indicate that reduced conformational flexibility of the N-terminal subdomain in WT HP67 is due to intramolecular interactions with the His41 imidazole ring. These interactions, together with desolvation effects, contribute to significantly depress the pKa of the buried imidazole ring in the native state. 15N R1rho relaxation dispersion data indicate that WT HP67 populates a partially folded intermediate state that is 10.9 kJ mol(-1) higher in free energy than the native state under non-denaturing conditions at neutral pH. The partially folded intermediate is characterized as having an unfolded N-terminal subdomain while the C-terminal subdomain retains a native-like fold. Although the majority of the residues in the N-terminal subdomain sample a random-coil distribution of conformations, deviations of backbone amide 1H and 15N chemical shifts from canonical random-coil values for residues within 5A of the His41 imidazole ring indicate that a significant degree of residual structure is maintained in the partially folded ensemble. The pH-dependence of exchange broadening is consistent with a linear three-state exchange model whereby unfolding of the N-terminal subdomain is coupled to titration of His41 in the partially folded intermediate with a pKa,I=5.69+/-0.07. Although maintenance of residual interactions with the imidazole ring in the unfolded N-terminal subdomain appears to reduce pKa,I compared to model histidine compounds, protonation of His41 disrupts these interactions and reduces the difference in free energy between the native state and partially folded intermediate under acidic conditions. In addition, chemical shift changes for residues Lys70-Phe76 in the C-terminal subdomain suggest that the HP67 actin binding site is disrupted upon unfolding of the N-terminal subdomain, providing a potential mechanism for regulating the villin-dependent bundling of actin filaments.     

Can contact potentials reliably predict stability of proteins?

The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Hammond behavior versus ground state effects in protein folding: evidence for narrow free energy barriers and residual structure in unfolded states

Apparent transition state movement upon mutation or changes in solvent conditions is frequently observed in protein folding and is often interpreted in terms of Hammond behavior. This led to the conclusion that barrier regions in protein folding are broad maxima on the free energy landscape. Here, we use the concept of self-interaction and cross-interaction parameters to test experimental data of 21 well-characterized proteins for Hammond behavior. This allows us to characterize the origin of transition state movements along different reaction coordinates. Only one of the 21 proteins shows a small but coherent transition state movement in agreement with the Hammond postulate. In most proteins the structure of the transition state is insensitive to changes in protein stability. The apparent change in the position of the transition state upon mutation, which is frequently observed in phi-value analysis, is in most cases due to ground-state effects caused by structural changes in the unfolded state. This argues for significant residual structure in unfolded polypeptide chains of many proteins. Disruption of these residual interactions by mutation often leads to decreased folding rates, which implies that these interactions are still present in the transition state. The failure to detect Hammond behavior shows that the free energy barriers encountered by a folding polypeptide chain are generally rather narrow and robust maxima for all experimentally explorable reaction coordinates.     

The contribution of cross-links to protein stability: A normal mode analysis of the configurational entropy of the native state

The vibrational entropy of native BPTI, with three disulfide bonds, was determined by use of normal mode calculations and compared with that of folded variants having either one less disulfide bond or lacking a peptide bond at the trypsin-reactive site. Favorable contributions to the free energy of 2.5–5.1 kcal/mol at 300 K were calculated for the reduction of disulfide bonds in the folded state, whereas no favorable contribution was found for the hydrolysis of the peptide bond cleaved by trypsin. This is on the order of the effect of disulfides in the unfolded state. The implications of these results for the stabilization of a folded protein by the introduction of crosslinks are discussed. © 1993 Wiley-Liss, Inc.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

A shorter peptide model from staphylococcal nuclease for the folding-unfolding equilibrium of a beta-hairpin shows that unfolded state has significant contribution from compact conformational states

It is important to understand the conformational features of the unfolded state in equilibrium with folded state under physiological conditions. In this paper, we consider a short peptide model LMYKGQPM from staphylococcal nuclease to model the conformational equilibrium between a hairpin conformation and its unfolded state using molecular dynamics simulation under NVT conditions at 300K using GROMOS96 force field. The free energy landscape has overall funnel-like shape with hairpin conformations sampling the minima. The "unfolded" state has a higher free energy of approximately 12kJ/mol with respect to native hairpin minimum and occupies a plateau region. We find that the unfolded state has significant contributions from compact conformations. Many of these conformations have hairpin-like topology. Further, these compact conformational forms are stabilized by hydrophobic interactions. Conversion between native and non-native hairpins occurs via unfolded states. Frequent conversions between folded and unfolded hairpins are observed with single exponential kinetics. We compare our results with the emerging picture of unfolded state from both experimental and theoretical studies.