Robustness of protein folding kinetics to surface hydrophobic substitutions

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Escape from Adaptive Conflict follows from weak functional trade-offs and mutational robustness

A fundamental question in molecular evolution is how proteins can adapt to new functions while being conserved for an existing function at the same time. Several theoretical models have been put forward to explain this apparent paradox. The most popular models include neofunctionalization, subfunctionalization (SUBF) by degenerative mutations, and dosage models. All of these models focus on adaptation after gene duplication. A newly proposed model named "Escape from Adaptive Conflict" (EAC) includes adaptive processes before and after gene duplication that lead to multifunctional proteins, and divergence (SUBF). Support for the importance of multifunctionality for the evolution of new protein functions comes from two experimental observations. First, many enzymes have highly evolvable promiscuous side activities. Second, different structural states of the same protein can be associated with different functions. How these observations may be related to the EAC model, under which conditions EAC is possible, and how the different models relate to each other is still unclear. Here, we present a theoretical framework that uses biophysical principles to infer the roles of functional promiscuity, gene dosage, gene duplication, point mutations, and selection pressures in the evolution of proteins. We find that selection pressures can determine whether neofunctionalization or SUBF is the more likely evolutionary process. Multifunctional proteins, arising during EAC evolution, allow rapid adaptation independent of gene duplication. This becomes a crucial advantage when gene duplications are rare. Finally, we propose that an increase in mutational robustness, not necessarily functional optimization, can be the sole driving force behind SUBF.

Visualizing transient protein-folding intermediates by tryptophan-scanning mutagenesis

To understand how proteins fold, assemble and function, it is necessary to characterize the structure and dynamics of each state they adopt during their lifetime. Experimental characterization of the transient states of proteins remains a major challenge because high-resolution structural techniques, including NMR and X-ray crystallography, cannot be directly applied to study short-lived protein states. To circumvent this limitation, we show that transient states during protein folding can be characterized by measuring the fluorescence of tryptophan residues, introduced at many solvent-exposed positions to determine whether each position is native-like, denatured-like or non-native-like in the intermediate state. We use this approach to characterize a late-folding-intermediate state of the small globular mammalian protein ubiquitin, and we show the presence of productive non-native interactions that suggest a 'flycatcher' mechanism of concerted binding and folding.

Protein folding is mechanistically robust

Markov state models (MSMs) have proven to be useful tools in simulating large and slowly-relaxing biological systems like proteins. MSMs model proteins through dynamics on a discrete-state energy landscape, allowing molecules to effectively sample large regions of phase space. In this work, we use aspects of MSMs to ask: is protein folding mechanistically robust? We first provide a definition of mechanism in the context of Markovian models, and we later use perturbation theory and the concept of parametric sloppiness to show that parts of the MSM eigenspectrum are resistant to perturbation. We introduce a new, to our knowledge, Bayesian metric by which eigenspectrum robustness can be evaluated, and we discuss the implications of mechanistic robustness and possible new applications of MSMs to understanding biophysical phenomena.

Modulation of contact order effects in the two-state folding of stefins A and B

It is well established that contact order and folding rates are correlated for small proteins. The folding rates of stefins A and B differ by nearly two orders of magnitude despite sharing an identical native fold and hence contact order. We break down the determinants of this behavior and demonstrate that the modulation of contact order effects can be accounted for by the combined contributions of a framework-like mechanism, characterized by intrinsic helix stabilities, together with nonnative helical backbone conformation and nonnative hydrophobic interactions within the folding transition state. These contributions result in the formation of nonnative interactions in the transition state as evidenced by the opposing effects on folding rate and stability of these proteins.

Composition-based effective chain length for prediction of protein folding rates

Folding rate prediction is a useful way to find the key factors affecting folding kinetics of proteins. Structural information is more or less required in the present prediction methods, which limits the application of these methods to various proteins. In this work, an "effective length" is defined solely based on the composition of a protein, namely, the number of specific types of amino acids in a protein. A physical theory based on a minimalist model is employed to describe the relation between the folding rates and the effective length of proteins. Based on the resultant relationship between folding rates and effective length, the optimal sets of amino acids are found through the enumeration over all possible combinations of amino acids. This optimal set achieves a high correlation (with the coefficient of 0.84) between the folding rates and the optimal effective length. The features of these amino acids are consistent with our model and landscape theory. Further comparisons between our effective length and other factors are carried out. The effective length is physically consistent with structure-based prediction methods and has the best predictability for folding rates. These results all suggest that both entropy and energetics contribute importantly to folding kinetics. The ability to accurately and efficiently predict folding rates from composition enables the analysis of the kinetics for various kinds of proteins. The underlying physics in our method may be helpful to stimulate further understanding on the effects of various amino acids in folding dynamics.

Investigation of an anomalously accelerating substitution in the folding of a prototypical two-state protein

The folding rates of two-state single-domain proteins are generally resistant to small-scale changes in amino acid sequence. For example, having surveyed here over 700 single-residue substitutions in 24 well-characterized two-state proteins, we find that the majority (55%) of these substitutions affect folding rates by less than a factor of 2, and that only 9% affect folding rates by more than a factor of 8. Among those substitutions that significantly affect folding rates, we find that accelerating substitutions are an order of magnitude less common than those that decelerate the process. One of the most extreme outliers in this data set, an arginine-to-phenylalanine substitution at position 48 (R48F) of chymotrypsin inhibitor 2 (CI2), accelerates the protein's folding rate by a factor of 36 relative to that of the wild-type protein and is the most accelerating substitution reported to date in a two-state protein. In order to better understand the origins of this anomalous behavior, we have characterized the kinetics of multiple additional substitutions at this position. We find that substitutions at position 48 in CI2 fall into two distinct classes. The first, comprising residues that ablate the charge of the wild-type arginine but retain the hydrophobicity of its alkane chain, accelerate folding by at least 10-fold. The second class, comprising all other residues, produces folding rates within a factor of two of the wild-type rate. A significant positive correlation between hydrophobicity and folding rate across all of the residues we have characterized at this position suggests that the hydrophobic methylene units of the wild-type arginine play a significant role in stabilizing the folding transition state. Likewise, studies of the pH dependence of the histidine substitution indicate a strong correlation between folding rate and charge state. Thus, mutations that ablate the arginine's positive charge while retaining the hydrophobic contacts of its methylene units tend to dramatically accelerate folding. Previous studies have suggested that arginine 48 plays an important functional role in CI2, which may explain why it is highly conserved despite the anomalously large deceleration it produces in the folding of this protein.

Improved Gō-like Models Demonstrate the Robustness of Protein Folding Mechanisms Towards Non-native Interactions

The use of simple theoretical models has provided a considerable contribution to our present understanding of the means by which proteins adopt their native fold from the plethora of available unfolded states. A common assumption in building computationally tractable models has been the neglect of stabilizing non-native interactions in the class of models described as "Gō-like." The focus of this study is the characterization of the folding of a number of proteins via a Gō-like model, which aims to map a maximal amount of information reflecting the protein sequence onto a "minimalist" skeleton. This model is shown to contain sufficient information to reproduce the folding transition states of a number of proteins, including topologically analogous proteins that fold via different transition states. Remarkably, these models also demonstrate consistency with the general features of folding transition states thought to be stabilized by non-native interactions. This suggests that native interactions are the primary determinant of most protein folding transition states, and that non-native interactions lead only to local structural perturbations. A prediction is also included for an asymmetrical folding transition state of bacteriophage lambda protein W, which has yet to be subjected to experimental characterization.

A thermodynamic and kinetic analysis of the folding pathway of an SH3 domain entropically stabilised by a redesigned hydrophobic core

The folding thermodynamics and kinetics of the alpha-spectrin SH3 domain with a redesigned hydrophobic core have been studied. The introduction of five replacements, A11V, V23L, M25V, V44I and V58L, resulted in an increase of 16% in the overall volume of the side-chains forming the hydrophobic core but caused no remarkable changes to the positions of the backbone atoms. Judging by the scanning calorimetry data, the increased stability of the folded structure of the new SH3-variant is caused by entropic factors, since the changes in heat capacity and enthalpy upon the unfolding of the wild-type and mutant proteins were identical at 298 K. It appears that the design process resulted in an increase in burying both the hydrophobic and hydrophilic surfaces, which resulted in a compensatory effect upon the changes in heat capacity and enthalpy. Kinetic analysis shows that both the folding and unfolding rate constants are higher for the new variant, suggesting that its transition state becomes more stable compared to the folded and unfolded states. The phi(double dagger-U) values found for a number of side-chains are slightly lower than those of the wild-type protein, indicating that although the transition state ensemble (TSE) did not change overall, it has moved towards a more denatured conformation, in accordance with Hammond's postulate. Thus, the acceleration of the folding-unfolding reactions is caused mainly by an improvement in the specific and/or non-specific hydrophobic interactions within the TSE rather than by changes in the contact order. Experimental evidence showing that the TSE changes globally according to its hydrophobic content suggests that hydrophobicity may modulate the kinetic behaviour and also the folding pathway of a protein.

Kinetic stabilization of Bacillus licheniformis alpha-amylase through introduction of hydrophobic residues at the surface

It is generally assumed that in proteins hydrophobic residues are not favorable at solvent-exposed sites, and that amino acid substitutions on the surface have little effect on protein thermostability. Contrary to these assumptions, we have identified hyperthermostable variants of Bacillus licheniformis alpha-amylase (BLA) that result from the incorporation of hydrophobic residues at the surface. Under highly destabilizing conditions, a variant combining five stabilizing mutations unfolds 32 times more slowly and at a temperature 13 degrees C higher than the wild-type. Crystal structure analysis at 1.7 A resolution suggests that stabilization is achieved through (a) extension of the concept of increased hydrophobic packing, usually applied to cavities, to surface indentations, (b) introduction of favorable aromatic-aromatic interactions on the surface, (c) specific stabilization of intrinsic metal binding sites, and (d) stabilization of a beta-sheet by introducing a residue with high beta-sheet forming propensity. All mutated residues are involved in forming complex, cooperative interaction networks that extend from the interior of the protein to its surface and which may therefore constitute "weak points" where BLA unfolding is initiated. This might explain the unexpectedly large effect induced by some of the substitutions on the kinetic stability of BLA. Our study shows that substantial protein stabilization can be achieved by stabilizing surface positions that participate in underlying cooperatively formed substructures. At such positions, even the apparently thermodynamically unfavorable introduction of hydrophobic residues should be explored.

Combinatorial protein design

Combinatorial protein libraries permit the examination of a wide range of sequences. Such methods are being used for denovo design and to investigate the determinants of protein folding. The exponentially large number of possible sequences, however, necessitates restrictions on the diversity of sequences in a combinatorial library. Recently, progress has been made in developing theoretical tools to bias and characterize the ensemble of sequences that fold into a given structure - tools that can be applied to the design and interpretation of combinatorial experiments.

Protein engineering study of protein L by simulation

We examine the ability of our recently introduced minimalist protein model to reproduce experimentally measured thermodynamic and kinetic changes upon sequence mutation in the well-studied immunoglobulin-binding protein L. We have examined five different sequence mutations of protein L that are meant to mimic the same mutation type studied experimentally: two different mutations which disrupt the natural preference in the beta-hairpin #1 and beta-hairpin #2 turn regions, two different helix mutants where a surface polar residue in the alpha-helix has been mutated to a hydrophobic residue, and a final mutant to further probe the role of nonnative hydrophobic interactions in the folding process. These simulated mutations are analyzed in terms of various kinetic and thermodynamic changes with respect to wild type, but in addition we evaluate the structure-activity relationship of our model protein based on the phi-value calculated from both the kinetic and thermodynamic perspectives. We find that the simulated thermodynamic phi-values reproduce the experimental trends in the mutations studied and allow us to circumvent the difficult interpretation of the complicated kinetics of our model. Furthermore, the level of resolution of the model allows us to directly predict what experiments seek in regard to protein engineering studies of protein folding--namely the residues or portions of the polypeptide chain that contribute to the crucial step in the folding of the wild-type protein.

Unspecific hydrophobic stabilization of folding transition states

Here we present a method for determining the inference of non-native conformations in the folding of a small domain, alpha-spectrin Src homology 3 domain. This method relies on the preservation of all native interactions after Tyr/Phe exchanges in solvent-exposed, contact-free positions. Minor changes in solvent exposure and free energy of the denatured ensemble are in agreement with the reverse hydrophobic effect, as the Tyr/Phe mutations slightly change the polypeptide hydrophilic/hydrophobic balance. Interestingly, more important Gibbs energy variations are observed in the transition state ensemble (TSE). Considering the small changes induced by the H/OH replacements, the observed energy variations in the TSE are rather notable, but of a magnitude that would remain undetected under regular mutations that alter the folded structure free energy. Hydrophobic residues outside of the folding nucleus contribute to the stability of the TSE in an unspecific nonlinear manner, producing a significant acceleration of both unfolding and refolding rates, with little effect on stability. These results suggest that sectors of the protein transiently reside in non-native areas of the landscape during folding, with implications in the reading of phi values from protein engineering experiments. Contrary to previous proposals, the principle that emerges is that non-native contacts, or conformations, could be beneficial in evolution and design of some fast folding proteins.

Genomic biodiversity, phylogenetics and coevolution in proteins

Comprehensive sampling of genomic biodiversity is fast becoming a reality for some genomic regions and complete organelle genomes. Genomic biodiversity is defined as large genomic sequences from many species, and here some recent work is reviewed that demonstrates the potential benefits of genomic biodiversity for molecular evolutionary analysis and phylogenetic reconstruction. This work shows that using likelihood-based approaches, taxon addition can dramatically improve phylogenetic reconstruction. Features or dynamics of the evolutionary process are much more easily inferred with large numbers of taxa, and large numbers are essential for discriminating differences in evolutionary patterns between sites. Accurate prediction of site-specific patterns can improve phylogenetic reconstruction by an amount equivalent to quadrupling sequence length. Genomic biodiversity is particularly central to research relating patterns of evolution, adaptation and coevolution to structural and functional features of proteins. Research on detecting coevolution between amino acid residues in proteins demonstrates a clear need for much greater numbers of closely related taxa to better discriminate site-specific patterns of interaction, and to allow more detailed analysis of coevolutionary interactions between subunits in protein complexes. It is argued that parsing out coevolutionary and other context-dependent substitution probabilities is essential for discriminating between coevolution and adaptation, and for more realistically modelling the evolution of proteins. Also reviewed is research that argues for increasing the efficiency of acquiring genomic biodiversity, and suggests that this might be done by simultaneously shotgun cloning and sequencing genomic mixtures from many species. Increased efficiency is a prerequisite if genomic biodiversity levels are to rapidly increase by orders of magnitude, and thus lead to dramatically improved understanding of interactions between protein structure, function and sequence evolution.

Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure

Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.

Progressive stabilization of intermediate and transition states in protein folding reactions by introducing surface hydrophobic residues

It can be argued from the principle of solvent exclusion that the introduction of hydrophobic residues onto the surface of a protein will not destabilize the folded state because the nonpolar side chain will be at least as exposed in the unfolded state as it is when the protein chain is folded. A comparison of the folding pathway of wild type and 11 site-directed mutants of CD2.d1 shows this to be true. In fact, owing to partial burial of nonpolar groups as folding proceeds, we find that the rapidly formed intermediate state and, to a greater extent, the transition state are generally stabilized by hydrophobic surface mutations. This effect is slightly moderated in the folded state presumably by the perturbation of van der Waals' contacts and/or local electrostatic interactions that have a greater influence in this fully compact structure. The fact that in all but one case we find that stabilization of the rapidly collapsed intermediate is accompanied by a faster acquisition of the folded state refutes the argument that I states are generally "off pathway" conformations or ensembles that lead to the inhibition of otherwise more rapid folding trajectories.

A breakdown of symmetry in the folding transition state of protein L

The 62 residue IgG binding domain of protein L consists of a central alpha-helix packed on a four-stranded beta-sheet formed by N and C-terminal beta-hairpins. The overall topology of the protein is quite symmetric: the beta-hairpins have similar lengths and make very similar interactions with the central helix. Characterization of the effects of 70 point mutations distributed throughout the protein on the kinetics of folding and unfolding reveals that this symmetry is completely broken during folding; the first beta-hairpin is largely structured while the second beta-hairpin and helix are largely disrupted in the folding transition state ensemble. The results are not consistent with a "hydrophobic core first" picture of protein folding; the first beta-hairpin appears to be at least as ordered at the rate limiting step in folding as the hydrophobic core.