Inferring repeat-protein energetics from evolutionary information

Conserved and divergent signals in 5' splice site sequences across fungi, metazoa and plants

In eukaryotic organisms the ensemble of 5' splice site sequences reflects the balance between natural nucleotide variability and minimal molecular constraints necessary to ensure splicing fidelity. This compromise shapes the underlying statistical patterns in the composition of donor splice site sequences. The scope of this study was to mine conserved and divergent signals in the composition of 5' splice site sequences. Because 5' donor sequences are a major cue for proper recognition of splice sites, we reasoned that statistical regularities in their composition could reflect the biological functionality and evolutionary history associated with splicing mechanisms. Results: We considered a regularized maximum entropy modeling framework to mine for non-trivial two-site correlations in donor sequence datasets corresponding to 30 different eukaryotes. For each analyzed species, we identified minimal sets of two-site coupling patterns that were able to replicate, at a given regularization level, the observed one-site and two-site frequencies in donor sequences. By performing a systematic and comparative analysis of 5'splice sites we showed that lineage information could be traced from joint di-nucleotide probabilities. We were able to identify characteristic two-site coupling patterns for plants and animals, and propose that they may echo differences in splicing regulation previously reported between these groups.

Evolution and folding of repeat proteins

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. These proteins constitute excellent model systems to investigate how evolution relates to structure, folding, and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat proteins. We model the energetics by a combination of an inverse Potts-model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at the single-residue level. These parameters are used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence, and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrin repeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transitions are obtained for arrays with enough sequence-similar elements and strong interactions between them, while noncooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. Additionally, we characterized nucleation-propagation and multidomain folding mechanisms. We show that the global stability and cooperativity of the repeating arrays can be predicted from simple sequence scores.

The Effect of Mutations in the TPR and Ankyrin Families of Alpha Solenoid Repeat Proteins

Protein repeats are short, highly similar peptide motifs that occur several times within a single protein, for example the TPR and Ankyrin repeats. Understanding the role of mutation in these proteins is complicated by the competing facts that 1) the repeats are much more restricted to a set sequence than non-repeat proteins, so mutations should be harmful much more often because there are more residues that are heavily restricted due to the need of the sequence to repeat and 2) the symmetry of the repeats in allows the distribution of functional contributions over a number of residues so that sometimes no specific site is singularly responsible for function (unlike enzymatic active site catalytic residues). To address this issue, we review the effects of mutations in a number of natural repeat proteins from the tetratricopeptide and Ankyrin repeat families. We find that mutations are context dependent. Some mutations are indeed highly disruptive to the function of the protein repeats while mutations in identical positions in other repeats in the same protein have little to no effect on structure or function.

Large Ankyrin repeat proteins are formed with similar and energetically favorable units

Ankyrin containing proteins are one of the most abundant repeat protein families present in all extant organisms. They are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Here, we built and curated a dataset of 200 thousand proteins that contain 1.2 million Ankyrin regions and characterize the abundance, structure and energetics of the repetitive regions in natural proteins. We found that there is a continuous roughly exponential variety of array lengths with an exceptional frequency at 24 repeats. We described that individual repeats are seldom interrupted with long insertions and accept few deletions, in line with the known tertiary structures. We found that longer arrays are made up of repeats that are more similar to each other than shorter arrays, and display more favourable folding energy, hinting at their evolutionary origin. The array distributions show that there is a physical upper limit to the size of an array of repeats of about 120 copies, consistent with the limit found in nature. The identity patterns within the arrays suggest that they may have originated by sequential copies of more than one Ankyrin unit.

Size and structure of the sequence space of repeat proteins

The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family—the total number of sequences in that family—can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occuring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of ∼30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of fustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family, and suggests new strategies for protein design.

Natural protein molecules are only a small subset of the possible strings of amino acids. This naturally calls the question of how many protein sequences theoretically exist that are functional, and how many have already been explored by nature. To help answer this question, we developed a statistical method to calculate the total potential number of protein sequences of a given family, focusing on three families of repeat proteins, which play important roles in a variety of cellular processes. The number of sequences that we compute is limited by functional interactions between the residues of the protein, as well as its evolutionary history. Applying techniques from the physics of disordered systems, we show that the space of sequences has a rugged structure, which could hinder their evolution. Individual proteins can be organised into distinct clusters corresponding to basins of attraction of the landscape, suggesting the existence of subfamilies within each family.