A Nonadaptive Origin of a Beneficial Trait: In Silico Selection for Free Energy of Folding Leads to the Neutral Emergence of Mutational Robustness in Single Domain Proteins

Proteins are regarded as being robust to the deleterious effects of mutations. Here, the neutral emergence of mutational robustness in a population of single domain proteins is explored using computer simulations. A pairwise contact model was used to calculate the ΔG of folding (ΔG _folding) using the three dimensional protein structure of leech eglin C. A random amino acid sequence with low mutational robustness, defined as the average ΔΔG resulting from a point mutation (ΔΔG _average), was threaded onto the structure. A population of 1,000 threaded sequences was evolved under selection for stability, using an upper and lower energy threshold. Under these conditions, mutational robustness increased over time in the most common sequence in the population. In contrast, when the wild type sequence was used it did not show an increase in robustness. This implies that the emergence of mutational robustness is sequence specific and that wild type sequences may be close to maximal robustness. In addition, an inverse relationship between ??G _average and protein stability is shown, resulting partly from a larger average effect of point mutations in more stable proteins. The emergence of mutational robustness was also observed in the Escherichia coli colE1 Rop and human CD59 proteins, implying that the property may be common in single domain proteins under certain simulation conditions. The results indicate that at least a portion of mutational robustness in small globular proteins might have arisen by a process of neutral emergence, and could be an example of a beneficial trait that has not been directly selected for, termed a “pseudaptation.”     

Genomic determinants of protein folding thermodynamics in prokaryotic organisms

Here we investigate how thermodynamic properties of orthologous proteins are influenced by the genomic environment in which they evolve. We performed a comparative computational study of 21 protein families in 73 prokaryotic species and obtained the following main results. (i) Protein stability with respect to the unfolded state and with respect to misfolding are anticorrelated. There appears to be a trade-off between these two properties, which cannot be optimized simultaneously. (ii) Folding thermodynamic parameters are strongly correlated with two genomic features, genome size and G+C composition. In particular, the normalized energy gap, an indicator of folding efficiency in statistical mechanical models of protein folding, is smaller in proteins of organisms with a small genome size and a compositional bias towards A+T. Such genomic features are characteristic for bacteria with an intracellular lifestyle. We interpret these correlations in light of mutation pressure and natural selection. A mutational bias toward A+T at the DNA level translates into a mutational bias toward more hydrophobic (and in general more interactive) proteins, a consequence of the structure of the genetic code. Increased hydrophobicity renders proteins more stable against unfolding but less stable against misfolding. Proteins with high hydrophobicity and low stability against misfolding occur in organisms with reduced genomes, like obligate intracellular bacteria. We argue that they are fixed because these organisms experience weaker purifying selection due to their small effective population sizes. This interpretation is supported by the observation of a high expression level of chaperones in these bacteria. Our results indicate that the mutational spectrum of a genome and the strength of selection significantly influence protein folding thermodynamics.     

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.     

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or “width” of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.     

Signatures of co-translational folding

Global and co-translational protein folding may both occur in vivo, and understanding the relationship between these folding mechanisms is pivotal to our understanding of protein-structure formation. Within this study, over 1.5 million hydrophobic-polar sequences were classified based on their ability to attain a unique, but not necessarily minimal energy conformation through co-translational folding. The sequence and structure properties of the sets were then compared to elucidate signatures of co-translational folding. The strongest signature of co-translational folding is a reduced number of possible favorable contacts in the amino terminus. There is no evidence of fewer contacts, more local contacts, or less-compact structures. Co-translational folding produces a more compact amino- than carboxy-terminal region and an amino-terminal-biased set of core residues. In real proteins these signatures are also observed and found most strongly in proteins of the alpha/beta structural class of proteins (SCOP) where 71 % have an amino-terminal set of core residues. The prominence of co-translational features in experimentally determined protein structures suggests that the importance of co-translational folding is currently underestimated.     

Multi-template approach to modeling engineered disulfide bonds

The key issue for disulfide bond engineering is to select the most appropriate location in the protein. By surveying the structure of experimentally engineered disulfide bonds, we found about half of them that have geometry incompatible with any native disulfide bond geometry. To improve the current prediction methods that tend to apply either ideal geometrical or energetical criteria to single three-dimensional structures, we have combined a novel computational protocol with the usage of multiple protein structures to take into account protein backbone flexibility. The multiple structures can be selected from either independently determined crystal structures for identical proteins, models of nuclear magnetic resonance experiments, or crystal structures of homology-related proteins. We have validated our approach by comparing the predictions with known disulfide bonds. The accuracy of prediction for native disulfide bonds reaches 99.6%. In a more stringent test on the reported engineered disulfide bonds, we have obtained a success rate of 93%. Our protocol also determines the oxido-reduction state of a predicted disulfide bond and the corresponding mutational cost. From the energy ranking, the user can easily choose top predicted sites for mutagenesis experiments. Our method provides information about local stability of the engineered disulfide bond surroundings.     

Inversion of the balance between hydrophobic and hydrogen bonding interactions in protein folding and aggregation

Identifying the forces that drive proteins to misfold and aggregate, rather than to fold into their functional states, is fundamental to our understanding of living systems and to our ability to combat protein deposition disorders such as Alzheimer's disease and the spongiform encephalopathies. We report here the finding that the balance between hydrophobic and hydrogen bonding interactions is different for proteins in the processes of folding to their native states and misfolding to the alternative amyloid structures. We find that the minima of the protein free energy landscape for folding and misfolding tend to be respectively dominated by hydrophobic and by hydrogen bonding interactions. These results characterise the nature of the interactions that determine the competition between folding and misfolding of proteins by revealing that the stability of native proteins is primarily determined by hydrophobic interactions between side-chains, while the stability of amyloid fibrils depends more on backbone intermolecular hydrogen bonding interactions.     

Principles of protein folding--a perspective from simple exact models.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.     

Sequence determinants of protein folding rates: positive correlation between contact energy and contact range indicates selection for fast folding

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.     

In silico predicted robustness of viroids RNA secondary structures. I. The effect of single mutations

Viroids are plant subviral pathogens whose genomes are constituted by a single-stranded and covalently closed small RNA molecule that does not encode for any protein. Despite this genomic simplicity, they are able of inducing devastating symptoms in susceptible plants. Most of the 29 described viroid species fold into a rodlike or quasi-rodlike structure, whereas a few of them fold as branched structures. The shape of these RNA structures is perhaps one of the most characteristic properties of viroids and sometimes is considered their only phenotype. Here we use RNA thermodynamic secondary structure prediction algorithms to compare the mutational robustness of all viroid species. After characterizing the statistical properties of the distribution of mutational effects on structure stability and the wideness of neutral neighborhood for each viroid species, we show an evolutionary trend toward increased structural robustness during viroid radiation, giving support to the adaptive value of robustness. Differences in robustness among the 2 viroid families can be explained by the larger fragility of branched structures compared with the rodlike ones. We also show that genomic redundancy can contribute to the robustness of these simple RNA genomes.     

Factors that affect the folding ability of proteins

The folding ability of a heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice is shown to be strongly correlated with the stability of the native state. We consider a number of estimates of the stability that can be determined without simulation, including the energy gap between the native state and the structurally dissimilar part of the spectrum (Z score) and, for sequences with fully compact native states, the gap in energy between the native and first excited fully compact states. These estimates are found to be more robust predictors of folding ability than a parameter sigma that requires simulation for its evaluation: sigma = 1 - Tf/Ttheta, where Tf is the temperature at which the fluctuation of an order parameter is at its maximum and Ttheta is the temperature at which the specific heat is at its maximum. We show that the interpretation of Ttheta as the collapse transition temperature is not correct in general and that the correlation between sigma and the folding ability arises from the fact that sigma is related to the energy gap (Z score).     

Recombination and the evolution of mutational robustness

Mutational robustness is the degree to which a phenotype, such as fitness, is resistant to mutational perturbations. Since most of these perturbations will tend to reduce fitness, robustness provides an immediate benefit for the mutated individual. However, robust systems decay due to the accumulation of deleterious mutations that would otherwise have been cleared by selection. This decay has received very little theoretical attention. At equilibrium, a population or asexual lineage is expected to have a mutation load that is invariant with respect to the selection coefficient of deleterious alleles, so the benefit of robustness (at the level of the population or asexual lineage) is temporary. However, previous work has shown that robustness can be favoured when robustness loci segregate independently of the mutating loci they act upon. We examine a simple two-locus model that allows for intermediate rates of recombination and inbreeding to show that increasing the effective recombination rate allows for the evolution of greater mutational robustness.     

Statistics of knots, geometry of conformations, and evolution of proteins

Like shoelaces, the backbones of proteins may get entangled and form knots. However, only a few knots in native proteins have been identified so far. To more quantitatively assess the rarity of knots in proteins, we make an explicit comparison between the knotting probabilities in native proteins and in random compact loops. We identify knots in proteins statistically, applying the mathematics of knot invariants to the loops obtained by complementing the protein backbone with an ensemble of random closures, and assigning a certain knot type to a given protein if and only if this knot dominates the closure statistics (which tells us that the knot is determined by the protein and not by a particular method of closure). We also examine the local fractal or geometrical properties of proteins via computational measurements of the end-to-end distance and the degree of interpenetration of its subchains. Although we did identify some rather complex knots, we show that native conformations of proteins have statistically fewer knots than random compact loops, and that the local geometrical properties, such as the crumpled character of the conformations at a certain range of scales, are consistent with the rarity of knots. From these, we may conclude that the known “protein universe” (set of native conformations) avoids knots. However, the precise reason for this is unknown—for instance, if knots were removed by evolution due to their unfavorable effect on protein folding or function or due to some other unidentified property of protein evolution.     

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.     

Probing the Effects of Local Frustration in the Folding of a Multidomain Protein

Our current knowledge of protein folding is primarily based on experimental data obtained from isolated domains. In fact, because of their complexity, multidomain proteins have been elusive to the experimental characterization. Thus, the folding of a domain in isolation is generally assumed to resemble what should be observed for more complex structural architectures. Here we compared the folding mechanism of a protein domain in isolation and in the context of its supramodular multidomain structure. By carrying out an extensive mutational analysis we illustrate that while the early events of folding are malleable and influenced by the absence/presence of the neighboring structures, the late events appear to be more robust. These effects may be explained by analyzing the local frustration patterns of the domain, providing critical support for the funneled energy landscape theory of protein folding, and highlighting the role of protein frustration in sculpting the early events of the reaction.     

On prediction of folding nuclei in globular proteins

The approach described in this paper on the prediction of folding nuclei in globular proteins with known three dimensional structures is based on a search of the lowest saddle points through the barrier separating the unfolded state from the native structure on the free-energy landscape of protein chain. This search is performed by a dynamic programming method. Comparison of theoretical results with experimental data on the folding nuclei of two dozen of proteins shows that our model provides good phi value predictions for proteins whose structures have been determined by X-ray analysis, with a less limited success for proteins whose structures have been determined by NMR techniques only. Consideration of a full ensemble of transition states results in more successful prediction than consideration of only the transition states with the minimal free energy. In conclusion we have predicted the localization of folding nuclei for three dimensional protein structures for which kinetics of folding is studied now but the localization of folding nuclei is still unknown.     

Calculation of mutational free energy changes in transition states for protein folding

Recent advances in experimental and computational methods have made it possible to determine with considerable accuracy the structures whose formation is rate limiting for the folding of some small proteins-the transition state ensemble, or TSE. We present a method to analyze and validate all-atom models of such structures. The method is based on the comparison of experimental data with the computation of the change in free energy of the TSE resulting from specific mutations. Each mutation is modeled individually in all members of an ensemble of transition state structures using a method originally developed to predict mutational changes in the stability of native proteins. We first apply this method to six proteins for which we have determined the TSEs with a technique that uses experimental mutational data (Phi-values) as restraints in the structure determination and find a highly significant correlation between the calculated free energy changes and those derived from experimental kinetic data. We then use the procedure to analyze transition state structures determined by molecular dynamics simulations of unfolding, again finding a high correlation. Finally, we use the method to estimate changes in folding rates of several hydrophobic core mutants of Fyn SH3. Taken together, these results show that the procedure developed here is a tool of general validity for analyzing, assessing, and improving the quality of the structures of transition states for protein folding.     

Contact order and ab initio protein structure prediction

Although much of the motivation for experimental studies of protein folding is to obtain insights for improving protein structure prediction, there has been relatively little connection between experimental protein folding studies and computational structural prediction work in recent years. In the present study, we show that the relationship between protein folding rates and the contact order (CO) of the native structure has implications for ab initio protein structure prediction. Rosetta ab initio folding simulations produce a dearth of high CO structures and an excess of low CO structures, as expected if the computer simulations mimic to some extent the actual folding process. Consistent with this, the majority of failures in ab initio prediction in the CASP4 (critical assessment of structure prediction) experiment involved high CO structures likely to fold much more slowly than the lower CO structures for which reasonable predictions were made. This bias against high CO structures can be partially alleviated by performing large numbers of additional simulations, selecting out the higher CO structures, and eliminating the very low CO structures; this leads to a modest improvement in prediction quality. More significant improvements in predictions for proteins with complex topologies may be possible following significant increases in high-performance computing power, which will be required for thoroughly sampling high CO conformations (high CO proteins can take six orders of magnitude longer to fold than low CO proteins). Importantly for such a strategy, simulations performed for high CO structures converge much less strongly than those for low CO structures, and hence, lack of simulation convergence can indicate the need for improved sampling of high CO conformations. The parallels between Rosetta simulations and folding in vivo may extend to misfolding: The very low CO structures that accumulate in Rosetta simulations consist primarily of local up-down beta-sheets that may resemble precursors to amyloid formation.     

Selection Shapes the Robustness of Ligand-Binding Amino Acids

The phenotypes of biological systems are to some extent robust to genotypic changes. Such robustness exists on multiple levels of biological organization. We analyzed this robustness for two categories of amino acids in proteins. Specifically, we studied the codons of amino acids that bind or do not bind small molecular ligands. We asked to what extent codon changes caused by mutation or mistranslation may affect physicochemical amino acid properties or protein folding. We found that the codons of ligand-binding amino acids are on average more robust than those of non-binding amino acids. Because mistranslation is usually more frequent than mutation, we speculate that selection for error mitigation at the translational level stands behind this phenomenon. Our observations suggest that natural selection can affect the robustness of very small units of biological organization.