The Relationship between the Misfolding Avoidance Hypothesis and Protein Evolutionary Rates in the Light of Empirical Evidence.

For more than a decade, the misfolding avoidance hypothesis (MAH) and related theories have dominated evolutionary discussions aimed at explaining the variance of the molecular clock across cellular proteins. In this study, we use various experimental data to further investigate the consistency of the MAH predictions with empirical evidence. We also critically discuss experimental results that motivated the MAH development and that are often viewed as evidence of its major contribution to the variability of protein evolutionary rates. We demonstrate, in Escherichia coli and Homo sapiens, the lack of a substantial negative correlation between protein evolutionary rates and Gibbs free energies of unfolding, a direct measure of protein stability. We then analyze multiple new genome-scale data sets characterizing protein aggregation and interaction propensities, the properties that are likely optimized in evolution to alleviate deleterious effects associated with toxic protein misfolding and misinteractions. Our results demonstrate that the propensity of proteins to aggregate, the fraction of charged amino acids, and protein stickiness do correlate with protein abundances. Nevertheless, across multiple organisms and various data sets we do not observe substantial correlations between proteins' aggregation- and stability-related properties and evolutionary rates. Therefore, diverse empirical data support the conclusion that the MAH and similar hypotheses do not play a major role in mediating a strong negative correlation between protein expression and the molecular clock, and thus in explaining the variability of evolutionary rates across cellular proteins.

Molecular function limits divergent protein evolution on planetary timescales.

Functional conservation is known to constrain protein evolution. Nevertheless, the long-term divergence patterns of proteins maintaining the same molecular function and the possible limits of this divergence have not been explored in detail. We investigate these fundamental questions by characterizing the divergence between ancient protein orthologs with conserved molecular function. Our results demonstrate that the decline of sequence and structural similarities between such orthologs significantly slows down after ~1-2 billion years of independent evolution. As a result, the sequence and structural similarities between ancient orthologs have not substantially decreased for the past billion years. The effective divergence limit (>25% sequence identity) is not primarily due to protein sites universally conserved in all linages. Instead, less than four amino acid types are accepted, on average, per site across orthologous protein sequences. Our analysis also reveals different divergence patterns for protein sites with experimentally determined small and large fitness effects of mutations. Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

An experimental assay of the interactions of amino acids from orthologous sequences shaping a complex fitness landscape.

Characterizing the fitness landscape, a representation of fitness for a large set of genotypes, is key to understanding how genetic information is interpreted to create functional organisms. Here we determined the evolutionarily-relevant segment of the fitness landscape of His3, a gene coding for an enzyme in the histidine synthesis pathway, focusing on combinations of amino acid states found at orthologous sites of extant species. Just 15% of amino acids found in yeast His3 orthologues were always neutral while the impact on fitness of the remaining 85% depended on the genetic background. Furthermore, at 67% of sites, amino acid replacements were under sign epistasis, having both strongly positive and negative effect in different genetic backgrounds. 46% of sites were under reciprocal sign epistasis. The fitness impact of amino acid replacements was influenced by only a few genetic backgrounds but involved interaction of multiple sites, shaping a rugged fitness landscape in which many of the shortest paths between highly fit genotypes are inaccessible.

Self-consistency test reveals systematic bias in programs for prediction change of stability upon mutation.

Motivation: Computational prediction of the effect of mutations on protein stability is used by researchers in many fields. The utility of the prediction methods is affected by their accuracy and bias. Bias, a systematic shift of the predicted change of stability, has been noted as an issue for several methods, but has not been investigated systematically. Presence of the bias may lead to misleading results especially when exploring the effects of combination of different mutations. Results: Here we use a protocol to measure the bias as a function of the number of introduced mutations. It is based on a self-consistency test of the reciprocity the effect of a mutation. An advantage of the used approach is that it relies solely on crystal structures without experimentally measured stability values. We applied the protocol to four popular algorithms predicting change of protein stability upon mutation, FoldX, Eris, Rosetta and I-Mutant, and found an inherent bias. For one program, FoldX, we manage to substantially reduce the bias using additional relaxation by Modeller. Authors using algorithms for predicting effects of mutations should be aware of the bias described here. Availability and implementation: All calculations were implemented by in-house PERL scripts. Supplementary information: Supplementary data are available at Bioinformatics online. Note: The article 10.1093/bioinformatics/bty348, published alongside this paper, also addresses the problem of biases in protein stability change predictions.

Local fitness landscape of the green fluorescent protein.

Fitness landscapes depict how genotypes manifest at the phenotypic level and form the basis of our understanding of many areas of biology, yet their properties remain elusive. Previous studies have analysed specific genes, often using their function as a proxy for fitness, experimentally assessing the effect on function of single mutations and their combinations in a specific sequence or in different sequences. However, systematic high-throughput studies of the local fitness landscape of an entire protein have not yet been reported. Here we visualize an extensive region of the local fitness landscape of the green fluorescent protein from Aequorea victoria (avGFP) by measuring the native function (fluorescence) of tens of thousands of derivative genotypes of avGFP. We show that the fitness landscape of avGFP is narrow, with 3/4 of the derivatives with a single mutation showing reduced fluorescence and half of the derivatives with four mutations being completely non-fluorescent. The narrowness is enhanced by epistasis, which was detected in up to 30% of genotypes with multiple mutations and mostly occurred through the cumulative effect of slightly deleterious mutations causing a threshold-like decrease in protein stability and a concomitant loss of fluorescence. A model of orthologous sequence divergence spanning hundreds of millions of years predicted the extent of epistasis in our data, indicating congruence between the fitness landscape properties at the local and global scales. The characterization of the local fitness landscape of avGFP has important implications for several fields including molecular evolution, population genetics and protein design.

Machine Learning: How Much Does It Tell about Protein Folding Rates?

The prediction of protein folding rates is a necessary step towards understanding the principles of protein folding. Due to the increasing amount of experimental data, numerous protein folding models and predictors of protein folding rates have been developed in the last decade. The problem has also attracted the attention of scientists from computational fields, which led to the publication of several machine learning-based models to predict the rate of protein folding. Some of them claim to predict the logarithm of protein folding rate with an accuracy greater than 90%. However, there are reasons to believe that such claims are exaggerated due to large fluctuations and overfitting of the estimates. When we confronted three selected published models with new data, we found a much lower predictive power than reported in the original publications. Overly optimistic predictive powers appear from violations of the basic principles of machine-learning. We highlight common misconceptions in the studies claiming excessive predictive power and propose to use learning curves as a safeguard against those mistakes. As an example, we show that the current amount of experimental data is insufficient to build a linear predictor of logarithms of folding rates based on protein amino acid composition.

A model of substitution trajectories in sequence space and long-term protein evolution.

The nature of factors governing the tempo and mode of protein evolution is a fundamental issue in evolutionary biology. Specifically, whether or not interactions between different sites, or epistasis, are important in directing the course of evolution became one of the central questions. Several recent reports have scrutinized patterns of long-term protein evolution claiming them to be compatible only with an epistatic fitness landscape. However, these claims have not yet been substantiated with a formal model of protein evolution. Here, we formulate a simple covarion-like model of protein evolution focusing on the rate at which the fitness impact of amino acids at a site changes with time. We then apply the model to the data on convergent and divergent protein evolution to test whether or not the incorporation of epistatic interactions is necessary to explain the data. We find that convergent evolution cannot be explained without the incorporation of epistasis and the rate at which an amino acid state switches from being acceptable at a site to being deleterious is faster than the rate of amino acid substitution. Specifically, for proteins that have persisted in modern prokaryotic organisms since the last universal common ancestor for one amino acid substitution approximately ten amino acid states switch from being accessible to being deleterious, or vice versa. Thus, molecular evolution can only be perceived in the context of rapid turnover of which amino acids are available for evolution.

Structural similarity between defense peptide from wheat and scorpion neurotoxin permits rational functional design.

In this study, we present the spatial structure of the wheat antimicrobial peptide (AMP) Tk-AMP-X2 studied using NMR spectroscopy. This peptide was found to adopt a disulfide-stabilized α-helical hairpin fold and therefore belongs to the α-hairpinin family of plant defense peptides. Based on Tk-AMP-X2 structural similarity to cone snail and scorpion potassium channel blockers, a mutant molecule, Tk-hefu, was engineered by incorporating the functionally important residues from κ-hefutoxin 1 onto the Tk-AMP-X2 scaffold. The designed peptide contained the so-called essential dyad of amino acid residues significant for channel-blocking activity. Electrophysiological studies showed that although the parent peptide Tk-AMP-X2 did not present any activity against potassium channels, Tk-hefu blocked Kv1.3 channels with similar potency (IC50 ∼ 35 µm) to κ-hefutoxin 1 (IC50 ∼ 40 µm). We conclude that α-hairpinins are attractive in their simplicity as structural templates, which may be used for functional engineering and drug design.

NMR-based approach to measure the free energy of transmembrane helix-helix interactions.

Knowledge of the energetic parameters of transmembrane helix-helix interactions is necessary for the establishment of a structure-energy relationship for α-helical membrane domains. A number of techniques have been developed to measure the free energies of dimerization and oligomerization of transmembrane α-helices, and all of these have their advantages and drawbacks. In this study we propose a methodology to determine the magnitudes of the free energy of interactions between transmembrane helices in detergent micelles. The suggested approach employs solution nuclear magnetic resonance (NMR) spectroscopy to determine the population of the oligomeric states of the transmembrane domains and introduces a new formalism to describe the oligomerization equilibrium, which is based on the assumption that both the dimerization of the transmembrane domains and the dissociation of the dimer can occur only upon the collision of detergent micelles. The technique has three major advantages compared with other existing approaches: it may be used to analyze both weak and relatively strong dimerization/oligomerization processes, it works well for the analysis of complex equilibria, e.g. when monomer, dimer and high-order oligomer populations are simultaneously present in the solution, and it can simultaneously yield both structural and energetic characteristics of the helix-helix interaction under study. The proposed methodology was applied to investigate the oligomerization process of transmembrane domains of fibroblast growth factor receptor 3 (FGFR3) and vascular endothelium growth factor receptor 2 (VEGFR2), and allowed the measurement of the free energy of dimerization of both of these objects. In addition the proposed method was able to describe the multi-state oligomerization process of the VEGFR2 transmembrane domain.