Why are proteins so robust to site mutations?

On the conservative nature of intragenic recombination

Intragenic recombination rapidly creates protein sequence diversity compared with random mutation, but little is known about the relative effects of recombination and mutation on protein function. Here, we compare recombination of the distantly related beta-lactamases PSE-4 and TEM-1 to mutation of PSE-4. We show that, among beta-lactamase variants containing the same number of amino acid substitutions, variants created by recombination retain function with a significantly higher probability than those generated by random mutagenesis. We present a simple model that accurately captures the differing effects of mutation and recombination in real and simulated proteins with only four parameters: (i) the amino acid sequence distance between parents, (ii) the number of substitutions, (iii) the average probability that random substitutions will preserve function, and (iv) the average probability that substitutions generated by recombination will preserve function. Our results expose a fundamental functional enrichment in regions of protein sequence space accessible by recombination and provide a framework for evaluating whether the relative rates of mutation and recombination observed in nature reflect the underlying imbalance in their effects on protein function.

A Survey of Flexible Protein Binding Mechanisms and their Transition States Using Native Topology Based Energy Landscapes

Many cellular functions rely on interactions between protein pairs and higher oligomers. We have recently shown that binding mechanisms are robust and owing to the minimal frustration principle, just as for protein folding, are governed primarily by the protein's native topology, which is characterized by the network of non-covalent residue-residue interactions. The detailed binding mechanisms of nine dimers, a trimer, and a tetramer, each involving different degrees of flexibility and plasticity during assembly, are surveyed here using a model that is based solely on the protein topology, having a perfectly funneled energy landscape. The importance of flexibility in binding reactions is manifested by the fly-casting effect, which is diminished in magnitude when protein flexibility is removed. Many of the grosser and finer structural aspects of the various binding mechanisms (including binding of pre-folded monomers, binding of intrinsically unfolded monomers, and binding by domain-swapping) predicted by the native topology based landscape model are consistent with the mechanisms found in the laboratory. An asymmetric binding mechanism is often observed for the formation of the symmetric homodimers where one monomer is more structured at the binding transition state and serves as a template for the folding of the other monomer. Phi values were calculated to show how the structure of the binding transition state ensemble would be manifested in protein engineering studies. For most systems, the simulated Phi values are reasonably correlated with the available experimental values. This agreement suggests that the overall binding mechanism and the nature of the binding transition state ensemble can be understood from the network of interactions that stabilize the native fold. The Phi values for the formation of an antibody-antigen complex indicate a possible role for solvation of the interface in biomolecular association of large rigid proteins.

Energy landscapes and solved protein-folding problems

Energy-landscape theory has led to much progress in protein folding kinetics, protein structure prediction and protein design. Funnel landscapes describe protein folding and binding and explain how protein topology determines kinetics. Landscape-optimized energy functions based on bioinformatic input have been used to correctly predict low-resolution protein structures and also to design novel proteins automatically.

Engineered protein function by selective amino acid diversification

Almost all protein engineering methods rely upon making changes to naturally occurring proteins that already possess some of the desired properties. This will probably remain the case as long as we lack a complete understanding of the way that an amino acid sequence gives rise to a protein with a precisely defined biological function. Common to all methods for altering an existing protein is the selection of a subset of amino acids in the protein for variation and a choice of which substitutions to make at each position. Variants are then tested empirically and further variants are created based upon their performance. Differences between protein engineering methods are the ways in which amino acids are chosen for variation, the protocols followed for creating the variants, and how information regarding variant properties is used in creating subsequent variants. In this article, we describe these differences and provide examples of how the experimental parameters of specific projects determine which method is most suitable.

Thermodynamic prediction of protein neutrality

We present a simple theory that uses thermodynamic parameters to predict the probability that a protein retains the wild-type structure after one or more random amino acid substitutions. Our theory predicts that for large numbers of substitutions the probability that a protein retains its structure will decline exponentially with the number of substitutions, with the severity of this decline determined by properties of the structure. Our theory also predicts that a protein can gain extra robustness to the first few substitutions by increasing its thermodynamic stability. We validate our theory with simulations on lattice protein models and by showing that it quantitatively predicts previously published experimental measurements on subtilisin and our own measurements on variants of TEM1 beta-lactamase. Our work unifies observations about the clustering of functional proteins in sequence space, and provides a basis for interpreting the response of proteins to substitutions in protein engineering applications.

The 'evolvability' of promiscuous protein functions

How proteins with new functions (e.g., drug or antibiotic resistance or degradation of man-made chemicals) evolve in a matter of months or years is still unclear. This ability is dependent on the induction of new phenotypic traits by a small number of mutations (plasticity). But mutations often have deleterious effects on functions that are essential for survival. How are these seemingly conflicting demands met at the single-protein level? Results from directed laboratory evolution experiments indicate that the evolution of a new function is driven by mutations that have little effect on the native function but large effects on the promiscuous functions that serve as starting point. Thus, an evolving protein can initially acquire increased fitness for a new function without losing its original function. Gene duplication and the divergence of a completely new protein may then follow.

Hidden complexity of free energy surfaces for peptide (protein) folding

An understanding of the thermodynamics and kinetics of protein folding requires a knowledge of the free energy surface governing the motion of the polypeptide chain. Because of the many degrees of freedom involved, surfaces projected on only one or two progress variables are generally used in descriptions of the folding reaction. Such projections result in relatively smooth surfaces, but they could mask the complexity of the unprojected surface. Here we introduce an approach to determine the actual (unprojected) free energy surface and apply it to the second beta-hairpin of protein G, which has been used as a model system for protein folding. The surface is represented by a disconnectivity graph calculated from a long equilibrium folding-unfolding trajectory. The denatured state is found to have multiple low free energy basins. Nevertheless, the peptide shows exponential kinetics in folding to the native basin. Projected surfaces obtained from the present analysis have a simple form in agreement with other studies of the beta-hairpin. The hidden complexity found for the beta-hairpin surface suggests that the standard funnel picture of protein folding should be revisited.

Theoretical and experimental study of the D2194G mutation in the C2 domain of coagulation factor V

Coagulation factor V (FV) is a large plasma glycoprotein with functions in both the pro- and anticoagulant pathways. In carriers of the so-called R2-FV haplotype, the FV D2194G mutation, in the C2 membrane-binding domain, is associated with low expression levels, suggesting a potential folding/stability problem. To analyze the molecular mechanisms potentially responsible for this in vitro phenotype, we used molecular dynamics (MD) and continuum electrostatic calculations. Implicit solvent simulations were performed on the x-ray structure of the wild-type C2 domain and on a model of the D2194G mutant. Because D2194 is located next to a disulfide bond (S-S bond), MD calculations were also performed on S-S bond depleted structures. D2194 is part of a salt-bridge network and investigations of the stabilizing/destabilizing role of these ionic interactions were carried out. Five mutant FV molecules were created and the expression levels measured with the aim of assessing the tolerance to amino acid changes in this region of molecule. Analysis of the MD trajectories indicated increased flexibility in some areas and energetic comparisons suggested overall destabilization of the structure due to the D2194G mutation. This substitution causes electrostatic destabilization of the domain by approximately 3 kcal/mol. Together these effects likely explain the lowered expression levels in R2-FV carriers.

Molecular clock in neutral protein evolution

BACKGROUND

A frequent observation in molecular evolution is that amino-acid substitution rates show an index of dispersion (that is, ratio of variance to mean) substantially larger than one. This observation has been termed the overdispersed molecular clock. On the basis of in silico protein-evolution experiments, Bastolla and coworkers recently proposed an explanation for this observation: Proteins drift in neutral space, and can temporarily get trapped in regions of substantially reduced neutrality. In these regions, substitution rates are suppressed, which results in an overall substitution process that is not Poissonian. However, the simulation method of Bastolla et al. is representative only for cases in which the product of mutation rate micro and population size Ne is small. How the substitution process behaves when micro Ne is large is not known.

RESULTS

Here, I study the behavior of the molecular clock in in silico protein evolution as a function of mutation rate and population size. I find that the index of dispersion decays with increasing micro Ne, and approaches 1 for large micro Ne. This observation can be explained with the selective pressure for mutational robustness, which is effective when micro Ne is large. This pressure keeps the population out of low-neutrality traps, and thus steadies the ticking of the molecular clock.

CONCLUSIONS

The molecular clock in neutral protein evolution can fall into two distinct regimes, a strongly overdispersed one for small micro Ne, and a mostly Poissonian one for large micro Ne. The former is relevant for the majority of organisms in the plant and animal kingdom, and the latter may be relevant for RNA viruses.

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.

Correlation between sequence hydrophobicity and surface-exposure pattern of database proteins

Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tend to occur at the surface of a folded protein. By analyzing the known protein structures, we quantify the degree to which the hydrophobicity sequence of a protein correlates with its pattern of surface exposure. We have assessed the statistical significance of this correlation for several hydrophobicity scales in the literature, and find that the computed correlations are significant but far from optimal. We show that this less than optimal correlation arises primarily from the large degree of mutations that naturally occurring proteins can tolerate. Lesser effects are due in part to forces other than hydrophobicity, and we quantify this by analyzing the surface-exposure distributions of all amino acids. Lastly, we show that our database findings are consistent with those found from an off-lattice hydrophobic-polar model of protein folding.

The ribbon of hydrogen bonds in globular proteins. IV. The example of the papain family

A study of the role of the hydrogen-bonding side chains in the ribbon of hydrogen bonds in globular proteins, using the papain family as an example, suggests that these side chains may be divided into three categories depending on their position in the molecule. In the first category, they form part of the local ribbon, in the second they form part of the ribbon at a site remote along the main chain, and in the third they play no role in the formation of the ribbon. The second case is particularly interesting because it provides a natural mechanism for the formation of the tertiary structure of the globular proteins. The results suggest that the robustness of the globular proteins towards mutations arises from the fact that many mutations that involve hydrogen-bonding side chains either leave the hydrogen bonding of the ribbon essentially unchanged or their hydrogen bonding plays no part in the formation of the ribbon in the first place. The results show that it is possible to obtain the ribbon of hydrogen bonds for a family of proteins whose data set's are of intermediate quality by studying the ribbons of several members of such a family and then taking an average over the different partial ribbons to create a standard ribbon of hydrogen bonds for the family as a whole. This method is used here to derive the standard ribbon for the papain family with papain itself, actinidin, and human liver cathepsin B as the representatives of the family. All three members of the family fit the standard ribbon with an accuracy of 85-91%. This result opens up the use of this technique for the study of a large number of globular proteins whose recorded data sets are of intermediate quality.

Solution stability and variability in a simple model of globular proteins

It is well known among molecular biologists that proteins with a common ancestor and that perform the same function in similar organisms, can have rather different amino-acid sequences. Mutations have altered the amino-acid sequences without affecting the function. A simple model of a protein in which the interactions are encoded by sequences of bits is introduced, and used to study how mutations can change these bits, and hence the interactions, while maintaining the stability of the protein solution. This stability is a simple minimal requirement on our model proteins which mimics part of the requirement on a real protein to be functional. The properties of our model protein, such as its second virial coefficient, are found to vary significantly from one model protein to another. It is suggested that this may also be the case for real proteins in vivo.

Sequence optimization for native state stability determines the evolution and folding kinetics of a small protein

Investigating the relative importance of protein stability, function, and folding kinetics in driving protein evolution has long been hindered by the fact that we can only compare modern natural proteins, the products of the very process we seek to understand, to each other, with no external references or baselines. Through a large-scale all-atom simulation of protein evolution, we have created a large diverse alignment of SH3 domain sequences which have been selected only for native state stability, with no other influencing factors. Although the average pairwise identity between computationally evolved and natural sequences is only 17%, the residue frequency distributions of the computationally evolved sequences are similar to natural SH3 sequences at 86% of the positions in the domain, suggesting that optimization for the native state structure has dominated the evolution of natural SH3 domains. Additionally, the positions which play a consistent role in the transition state of three well-characterized SH3 domains (by phi-value analysis) are structurally optimized for the native state, and vice versa. Indeed, we see a specific and significant correlation between sequence optimization for native state stability and conservation of transition state structure.

Systematic variation of amino acid substitutions for stringent assessment of pairwise covariation

During protein evolution, amino acids change due to a combination of functional constraints and genetic drift. Proteins frequently contain pairs of amino acids that appear to change together (covariation). Analysis of covariation from naturally occurring sets of orthologs cannot distinguish between residue pairs retained by functional requirements of the protein and those pairs existing due to changes along a common evolutionary path. Here, we have separated the two types of covariation by independently recombining every naturally occurring amino acid variant within a set of 15 subtilisin orthologs. Our analysis shows that in this family of subtilisin orthologs, almost all possible pairwise combinations of amino acids can coexist. This suggests that amino acid covariation found in the subtilisin orthologs is almost entirely due to common ancestral origin of the changes rather than functional constraints. We conclude that naturally occurring sequence diversity can be used to identify positions that can vary independently without destroying protein function.

Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding

BACKGROUND

The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.

RESULTS

We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances.

CONCLUSIONS

Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

Different evolutionary constraints on chemotaxis proteins CheW and CheY revealed by heterologous expression studies and protein sequence analysis

CheW and CheY are single-domain proteins from a signal transduction pathway that transmits information from transmembrane receptors to flagellar motors in bacterial chemotaxis. In various bacterial and archaeal species, the cheW and cheY genes are usually encoded within homologous chemotaxis operons. We examined evolutionary changes in these two proteins from distantly related proteobacterial species, Escherichia coli and Azospirillum brasilense. We analyzed the functions of divergent CheW and CheY proteins from A. brasilense by heterologous expression in E. coli wild-type and mutant strains. Both proteins were able to specifically inhibit chemotaxis of a wild-type E. coli strain; however, only CheW from A. brasilense was able to restore signal transduction in a corresponding mutant of E. coli. Detailed protein sequence analysis of CheW and CheY homologs from the two species revealed substantial differences in the types of amino acid substitutions in the two proteins. Multiple, but conservative, substitutions were found in CheW homologs. No severe mismatches were found between the CheW homologs in positions that are known to be structurally or functionally important. Substitutions in CheY homologs were found to be less conservative and occurred in positions that are critical for interactions with other components of the signal transduction pathway. Our findings suggest that proteins from the same cellular pathway encoded by genes from the same operon have different evolutionary constraints on their structures that reflect differences in their functions.

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.

Roles of mutation and recombination in the evolution of protein thermodynamics

We present a comprehensive study of the evolutionary origin of the thermodynamic behavior of proteins. With the use of a simplified model, we exhaustively enumerate the space of all sequences and the space of all structures, simulate the evolutionary relationship between sequences and structures, and characterize the steady-state sequence distribution for all structures in terms of several thermodynamic variables. We assess the effects of two major forces of evolution: mutation and recombination. Three simplifications are made. First, a two-dimensional lattice model is used to represent protein sequences and structures. Second, proteins undergo neutral evolution so that the fitness landscape has a flat allowed region inside of which all sequences are equally fit. Third, we ignore otherwise important factors such as finite population size and evolutionary time. Two scenarios emerge from our study. The first occurs when evolution is dominated by mutation events. Even though the prototype sequence that is most mutationally robust is preferred by evolution, the preference is not strong enough to offset the huge size of sequence space. Most native sequences are located near the boundary of the fitness region and are marginally compatible with the native structure. The second scenario occurs when evolution is dominated by recombination events. Now evolutionary preference for prototype sequence is strong enough to overcome the size of sequence space so that most native sequences are located near the center of sequence-structure compatibility. We conclude that the relative frequency of mutation and recombination events is a major determinant of how optimal protein sequences are for their structures.

SNPs on human chromosomes 21 and 22 -- analysis in terms of protein features and pseudogenes

SNPs are useful for genome-wide mapping and the study of disease genes. Previous studies have focused on SNPs in specific genes or SNPs pooled from a variety of different sources. Here, a systematic approach to the analysis of SNPs in relation to various features on a genome-wide scale, with emphasis on protein features and pseudogenes, is presented. We have performed a comprehensive analysis of 39,408 SNPs on human chromosomes 21 and 22 from the SNP consortium (TSC) database, where SNPs are obtained by random sequencing using consistent and uniform methods. Our study indicates that the occurrence of SNPs is lowest in exons and higher in repeats, introns and pseudogenes. Moreover, in comparing genes and pseudogenes, we find that the SNP density is higher in pseudogenes and the ratio of nonsynonymous to synonymous changes is also much higher. These observations may be explained by the increased rate of SNP accumulation in pseudogenes, which presumably are not under selective pressure. We have also performed secondary structure prediction on all coding regions and found that there is no preferential distribution of SNPs in a -helices, b -sheets or coils. This could imply that protein structures, in general, can tolerate a wide degree of substitutions. Tables relating to our results are available from http://genecensus.org/pseudogene.