Thermodynamics of neutral protein evolution

Naturally evolving proteins gradually accumulate mutations while continuing to fold to stable structures. This process of neutral evolution is an important mode of genetic change and forms the basis for the molecular clock. We present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (delta deltaG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins and provides formulas for calculating how fluctuations in stability can overdisperse the molecular clock. It also shows that the structural influences on the rate of sequence evolution observed in earlier simulations can be calculated using just the single-mutation delta deltaG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case the proteins evolve excess mutational robustness that is manifested by extra stability and an increase in the rate of sequence evolution. All our theoretical predictions are confirmed by simulations with lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics shapes the process of evolution.     

Structural insights into the evolution of a non-biological protein: importance of surface residues in protein fold optimization

Phylogenetic profiling of amino acid substitution patterns in proteins has led many to conclude that most structural information is carried by interior core residues that are solvent inaccessible. This conclusion is based on the observation that buried residues generally tolerate only conserved sequence changes, while surface residues allow more diverse chemical substitutions. This notion is now changing as it has become apparent that both core and surface residues play important roles in protein folding and stability. Unfortunately, the ability to identify specific mutations that will lead to enhanced stability remains a challenging problem. Here we discuss two mutations that emerged from an in vitro selection experiment designed to improve the folding stability of a non-biological ATP binding protein. These mutations alter two solvent accessible residues, and dramatically enhance the expression, solubility, thermal stability, and ligand binding affinity of the protein. The significance of both mutations was investigated individually and together, and the X-ray crystal structures of the parent sequence and double mutant protein were solved to a resolution limit of 2.8 and 1.65 A, respectively. Comparative structural analysis of the evolved protein to proteins found in nature reveals that our non-biological protein evolved certain structural features shared by many thermophilic proteins. This experimental result suggests that protein fold optimization by in vitro selection offers a viable approach to generating stable variants of many naturally occurring proteins whose structures and functions are otherwise difficult to study.     

Rational engineering of enzyme stability

During the past 15 years there has been a continuous flow of reports describing proteins stabilized by the introduction of mutations. These reports span a period from pioneering rational design work on small enzymes such as T4 lysozyme and barnase to protein design, and directed evolution. Concomitantly, the purification and characterization of naturally occurring hyperstable proteins has added to our understanding of protein stability. Along the way, many strategies for rational protein stabilization have been proposed, some of which (e.g. entropic stabilization by introduction of prolines or disulfide bridges) have reasonable success rates. On the other hand, comparative studies and efforts in directed evolution have revealed that there are many mutational strategies that lead to high stability, some of which are not easy to define and rationalize. Recent developments in the field include increasing awareness of the importance of the protein surface for stability, as well as the notion that normally a very limited number of mutations can yield a large increase in stability. Another development concerns the notion that there is a fundamental difference between the "laboratory stability" of small pure proteins that unfold reversibly and completely at high temperatures and "industrial stability", which is usually governed by partial unfolding processes followed by some kind of irreversible inactivation process (e.g. aggregation). Provided that one has sufficient knowledge of the mechanism of thermal inactivation, successful and efficient rational stabilization of enzymes can be achieved.     

A microplate-based evaluation of complex denaturation pathways: structural stability of Escherichia coli transketolase

We have previously developed a rapid microplate-based approach for measuring the denaturation curves by intrinsic tryptophan fluorescence for simple monomeric and two-state unfolding proteins. Here we demonstrate that it can accurately resolve the multiple conformational transitions that occur during the denaturation of a complex multimeric and cofactor associated protein. We have also analyzed the effect of two active-site mutations, D381A and Y440A upon the denaturation pathway of transketolase using intrinsic fluorescence measurements, and we compare the results from classical and microplate-based instrumentation. This work shows that the rapid assay is able to identify changes in the denaturation pathway, due to mutations or removal of cofactors, which affect the stability of the native and intermediate states. This would be of significant benefit for the directed evolution of protein stability, optimizing enzyme stability under biocatalytic process conditions, and also for engineering specific transitions in protein unfolding pathways.     

Destabilizing mutations promote membrane protein misfolding

In this work, the relationship between stability and propensity to misfold was probed for a series of purified variants of the polytopic integral membrane protein diacylglycerol kinase. It was observed that there was a strong correlation between stability and folding efficiency. The most common mutations that promoted misfolding were those which also destabilized the protein. These results imply that by targeting unstable membrane proteins for degradation, cellular protein folding quality control can eliminate proteins that have a high intrinsic propensity to misfold into aberrant structures. Moreover, the more rare class of amino acid mutations that promote misfolding without perturbing stability may be particularly dangerous because the mutant proteins may evade the surveillance of cellular quality control systems.     

Importance of mutant position in Ramachandran plot for predicting protein stability of surface mutations

Understanding the mechanisms by which mutations affect protein stability is one of the most important problems in molecular biology. In this work, we analyzed the relationship between changes in protein stability caused by surface mutations and changes in 49 physicochemical, energetic, and conformational properties of amino acid residues. We found that the hydration entropy was the major contributor to the stability of surface mutations in helical segments; other properties responsible for size and volume of molecule also correlated significantly with stability. Classification of coil mutations based on their locations in the (phi-psi) map improved the correlation significantly, demonstrating the existence of a relationship between stability and strain energy, which indicates that the role of strain energy is very important for the stability of surface mutations. We observed that the inclusion of sequence and structural information raised the correlation, indicating the influence of surrounding residues on the stability of surface mutations. Further, we examined the previously reported "inverse relationship" between stability and hydrophobicity, and observed that the inverse hydrophobic effect was generally applicable only to coil mutations. The present study leads to a simple method for predicting protein stability changes caused by amino acid substitutions, which will be useful for protein engineering in designing novel proteins with increased stability and altered function.     

Origin of unusual phi-values in protein folding: evidence against specific nucleation sites

phi(f)-value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equilibrium stability. The interpretation of the results usually focuses on a few unusual phi(f)-values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experimental phi(f)-values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point phi(f)-values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point phi(f)-values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium constant. Comparison with reported phi(f)-values for 11 proteins shows that most unusual phi(f)-values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures.     

First-step mutations for adaptation at elevated temperature increase capsid stability in a virus

The relationship between mutation, protein stability and protein function plays a central role in molecular evolution. Mutations tend to be destabilizing, including those that would confer novel functions such as host-switching or antibiotic resistance. Elevated temperature may play an important role in preadapting a protein for such novel functions by selecting for stabilizing mutations. In this study, we test the stability change conferred by single mutations that arise in a G4-like bacteriophage adapting to elevated temperature. The vast majority of these mutations map to interfaces between viral coat proteins, suggesting they affect protein-protein interactions. We assess their effects by estimating thermodynamic stability using molecular dynamic simulations and measuring kinetic stability using experimental decay assays. The results indicate that most, though not all, of the observed mutations are stabilizing.     

Non‐additive stabilization by halogenated amino acids reveals protein plasticity on a sub‐angstrom scale

It has been a long‐standing goal to understand the structure‐stability relationship of proteins, as optimal stability is essential for protein function and highly desirable for protein therapeutics. Halogenation has emerged as a minimally invasive strategy to probe the physical characteristics of proteins in solution, as well as enhance the structural stabilities of proteins for therapeutic applications. Although advances in synthetic chemistry and genetic code expansion have allowed for the rapid synthesis of proteins with diverse chemical sequences, much remains to be learned regarding the impact of these mutations on their structural integrity. In this contribution, we present a systematic study of three well‐folded model protein systems, in which their structural stabilities are assessed in response to various hydrogen‐to‐halogen atom mutations. Halogenation allows for the perturbation of proteins on a sub‐angstrom scale, offering unprecedented precision of protein engineering. The thermodynamic results from these model systems reveal that in certain cases, proteins can display modest steric tolerance to halogenation, yielding non‐additive consequences to protein stability. The observed sub‐angstrom sensitivity of protein stability highlights the delicate arrangement of a folded protein core structure. The stability data of various halogenated proteins presented herein should also provide guidelines for using halogenation as a strategy to improve the stability of protein therapeutics.     

LIS1 missense mutations: variable phenotypes result from unpredictable alterations in biochemical and cellular properties

Mutations in one allele of the human LIS1 gene cause a severe brain malformation, lissencephaly. Although most LIS1 mutations involve deletions, several point mutations with a single amino acid alteration were described. Patients carrying these mutations reveal variable phenotypic manifestations. We have analyzed the functional importance of these point mutations by examining protein stability, folding, intracellular localization, and protein-protein interactions. Our data suggest that the mutated proteins were affected at different levels, and no single assay could be used to predict the lissencephaly phenotype. Most interesting are those mutant proteins that retain partial folding and interactions. In the case of LIS1 mutated in F31S, the cellular phenotype may be modified by overexpression of specific interacting proteins. Overexpression of the PAF-AH alpha1 subunit dissolved aggregates induced by this mutant protein and increased its half-life. Overexpression of NudE or NudEL localized this mutant protein to spindle poles and kinetochores but had no effect on protein stability. Our results implicate that there are probably different biochemical and cellular mechanisms obstructed in each patient yielding the varied lissencephaly phenotypes.     

Protein stability, flexibility and function

Proteins rely on flexibility to respond to environmental changes, ligand binding and chemical modifications. Potentially, a perturbation that changes the flexibility of a protein may interfere with its function. Millions of mutations have been performed on thousands of proteins in quests for a delineation of the molecular details of their function. Several of these mutations interfered with the binding of a specific ligand with a concomitant effect on the stability of the protein scaffold. It has been ambiguous and not straightforward to recognize if any relationships exist between the stability of a protein and the affinity for its ligand. In this review, we present examples of proteins where changes in stability results in changes in affinity and of proteins where stability and affinity are uncorrelated. We discuss the possibility for a relationship between stability and binding. From the data presented is it clear that there are specific sites (flexibility hotspots) in proteins that are important for both binding and stability. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Exploring folding free energy landscapes using computational protein design

Recent advances in computational protein design have allowed exciting new insights into the sequence dependence of protein folding free energy landscapes. Whereas most previous studies have examined the sequence dependence of protein stability and folding kinetics by characterizing naturally occurring proteins and variants of these proteins that contain a small number of mutations, it is now possible to generate and characterize computationally designed proteins that differ significantly from naturally occurring proteins in sequence and/or structure. These computer-generated proteins provide insights into the determinants of protein structure, stability and folding, and make it possible to disentangle the properties of proteins that are the consequence of natural selection from those that reflect the fundamental physical chemistry of polypeptide chains.     

Filling small, empty protein cavities: structural and energetic consequences

Most proteins contain small cavities that can be filled by replacing cavity-lining residues by larger ones. Since shortening mutations in hydrophobic cores tend to destabilize proteins, it is expected that cavity-filling mutations may conversely increase protein stability. We have filled three small cavities in apoflavodoxin and determined by NMR and equilibrium unfolding analysis their impact in protein structure and stability. The smallest cavity (14 A3) has been filled, at two different positions, with a variety of residues and, in all cases, the mutant proteins are locally unfolded, their structure and energetics resembling those of an equilibrium intermediate of the thermal unfolding of the wild-type protein. In contrast, two slightly larger cavities of 20 A3 and 21 A3 have been filled with Val to Ile or Val to Leu mutations and the mutants preserve both the native fold and the equilibrium unfolding mechanism. From the known relationship, observed in shortening mutations, between stability changes and the differential hydrophobicity of the exchanged residues and the volume of the cavities, the filling of these apoflavodoxin cavities is expected to stabilize the protein by approximately 1.5 kcal mol(-1). However, both urea and thermal denaturation analysis reveal much more modest stabilizations, ranging from 0.0 kcal mol(-1) to 0.6 kcal mol(-1), which reflects that the accommodation of single extra methyl groups in small cavities requires some rearrangement, necessarily destabilizing, that lowers the expected theoretical stabilization. As the size of these cavities is representative of that of the typical small, empty cavities found in most proteins, it seems unlikely that filling this type of cavities will give rise to large stabilizations.     

Why are proteins so robust to site mutations?

There have been repeated observations that proteins are surprisingly robust to site mutations, enduring significant numbers of substitutions with little change in structure, stability, or function. These results are almost paradoxical in light of what is known about random heteropolymers and the sensitivity of their properties to seemingly trivial mutations. To address this discrepancy, the preservation of biological protein properties in the presence of mutation has been interpreted as indicating the independence of selective pressure on such properties. Such results also lead to the prediction that de novo protein design should be relatively easy, in contrast to what is observed. Here, we use a computational model with lattice proteins to demonstrate how this robustness can result from population dynamics during the evolutionary process. As a result, sequence plasticity may be a characteristic of evolutionarily derived proteins and not necessarily a property of designed proteins. This suggests that this robustness must be re-interpreted in evolutionary terms, and has consequences for our understanding of both in vivo and in vitro protein evolution.     

Structural insights into the role of mutations in amyloidogenesis

Mechanisms of amyloidogenesis are not well understood, including potential structural contributions of mutations in the process. Our previous research indicated that the dimer interface of amyloidogenic immunoglobulin light chain protein AL-09 is twisted 90 degrees relative to the protein from its germline sequence, kappaI O18/O8. Here we report a systematic restoration of AL-09 to its germline sequence by mutating the non-conservative somatic mutations located in the light chain dimer interface. Among these mutants, we find a correlation between increased thermodynamic stability and an increase in the lag time for fibril formation. The restorative mutant AL-09 H87Y completes the trifecta and restores the dimer interface observed in kappaI O18/O8, emphasizing the potential importance of the structural integrity of these proteins to protect against amyloidogenicity. We also find that adding amyloidogenic mutations into the germline protein illustrates mutational cooperativity in promoting amyloidogenesis.     

Diffusion-collision of foldons elucidates the kinetic effects of point mutations and suggests control strategies of the folding process of helical proteins

In this article we use mutation studies as a benchmark for a minimal model of the folding process of helical proteins. The model ascribes a pivotal role to the collisional dynamics of a few crucial residues (foldons) and predicts the folding rates by exploiting information drawn from the protein sequence. We show that our model rationalizes the effects of point mutations on the kinetics of folding. The folding times of two proteins and their mutants are predicted. Stability and location of foldons have a critical role as the determinants of protein folding. This allows us to elucidate two main mechanisms for the kinetic effects of mutations. First, it turns out that the mutations eliciting the most notable effects alter protein stability through stabilization or destabilization of the foldons. Secondly, the folding rate is affected via a modification of the foldon topology by those mutations that lead to the birth or death of foldons. The few mispredicted folding rates of some mutants hint at the limits of the current version of the folding model proposed in the present article. The performance of our folding model declines in case the mutated residues are subject to strong long-range forces. That foldons are the critical targets of mutation studies has notable implications for design strategies and is of particular interest to address the issue of the kinetic regulation of single proteins in the general context of the overall dynamics of the interactome.     

Do proteins always benefit from a stability increase? Relevant and residual stabilisation in a three-state protein by charge optimisation

The vast majority of our knowledge on protein stability arises from the study of simple two-state models. However, proteins displaying equilibrium intermediates under certain conditions abound and it is unclear whether the energetics of native/intermediate equilibria is well represented in current knowledge. We consider here that the overall conformational stability of three-state proteins is made of a "relevant" term and a "residual" one, corresponding to the free energy differences of the native to intermediate (N-to-I) and intermediate to denatured (I-to-D) equilibria, respectively. The N-to-I free energy difference is considered to be the relevant stability because protein-unfolding intermediates are likely devoid of biological activity. We use surface charge optimisation to first increase the overall (N-to-D) stability of a model three-state protein (apoflavodoxin) and then investigate whether the stabilisation obtained is realised into relevant or into residual stability. Most of the mutations designed from electrostatic calculations or from simple sequence conservation analysis produce large increases in the overall stability of the protein. However, in most cases, this simply leads to similarly large increases of the residual stability. Two mutations, nevertheless, show a different trend and increase the relevant stability of the protein substantially. When all the mutations are mapped onto the structure of the apoflavodoxin thermal-unfolding intermediate (obtained independently by equilibrium phi-analysis and NMR) they cluster perfectly so that the mutations increasing the relevant stability appear in the small unstructured region of the intermediate and the others in the native-like region. This illustrates the need for specific investigation of N-to-I equilibria and the structure of protein intermediates, and indicates that it is possible to rationally stabilise a protein against partial unfolding once the structure of the intermediate conformation is known, even if at low resolution.     

The evolution and evolutionary consequences of marginal thermostability in proteins

When we seek to explain the characteristics of living systems in their evolutionary context, we are often interested in understanding how and why certain properties arose through evolution, and how these properties then affected the continuing evolutionary process. This endeavor has been assisted by the use of simple computational models that have properties characteristic of natural living systems but allow simulations over evolutionary timescales with full transparency. We examine a model of the evolution of a gene under selective pressure to code for a protein that exists in a prespecified folded state at a given growth temperature. We observe the emergence of proteins with modest stabilities far below those possible with the model, with a denaturation temperature tracking the simulation temperature, despite the absence of selective pressure for such marginal stability. This demonstrates that neither observations of marginally stable proteins, nor even instances where increased stability interferes with function, provide evidence that marginal stability is an adaptation. Instead the marginal stability is the result of a balance between predominantly destabilizing mutations and selection that shifts depending on effective population size. Even if marginal stability is not an adaptation, the natural tendency of proteins toward marginal stability, and the range of stabilities that occur during evolution, may have significant effect on the evolutionary process.