Inferring repeat-protein energetics from evolutionary information

Espada

et al. 2019

Preprint

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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.

Section: B Statistical Energy Vs Unfolding Energysupporting

confidence: 60%

Size and structure of the sequence space of repeat proteins

Marchi

Espada

et al. 2019

Preprint

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“…Thus longer arrays are expected to break into folding 26 subdomains of different stability [17], [18]. Moreover, good approximations to the 27 folding energy can be constructed from statistical analysis of the extant 28 sequences [19], [20]. We studied here the abundance, length distribution and energetics 29 of ANK arrays in natural polypeptides.…”

mentioning

confidence: 99%

“…It was 32 recently suggested that this horizontal evolution is accelerated compared to their 33 vertical divergence in related species [24]. The internal sequence similarity in each 34 protein suggested that the domain repeats are often expanded through duplications of 35 several domains at a time, while the duplication of one domain is less common, 36 although no common mechanism for the expansion of repeats was found [23]. Here we 37 re-examine the correlations of sequence similarity in ANKs and describe the occurrence 38 of multiple types of duplication mechanisms within this family.…”

mentioning

confidence: 99%

“…Energetic characterization of the arrays 246 In order to analyze the folding energy distribution of the natural arrays found in protein 247 sequences, we define a simple energetic model based on the per-site occurrence of amino 248 acids (see Methods). This model is a simplification of a previously reported one [19] 249 that captures the most salient energetic features. We then split the Ankyrin repeat sequences.…”

mentioning

confidence: 99%

“…If extrapolated to conform an 297 array of identical repeats, this trend implies an upper limit for the array length that we 298 estimate to be (124 ± 4) repeats, which is compatible with the longest arrays found in 299 natural proteins. Considering a simple site-independent model to approximate the 300 folding energy [35], we calculated the energy distributions of the arrays and found that 301 longer arrays are made with more favorable repeats than shorter arrays (Fig 7A). At the 302 same time, longer arrays are found to be more energetically homogeneous than shorter 303 ones ( Fig 7B).…”

mentioning

confidence: 99%

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

Freiberger

Ferreiro

2019

Preprint

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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 build 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 describe that individual repeats are seldom interrupted with long insertions and accept few deletions, consistently with the know 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 Ankyrin repeats of about 120 copies, consistent with the limit found in nature. Analysis of the identity patterns within the arrays suggest that they may have originated by sequential copies of more than one Ankyrin unit. Author summaryRepeat proteins are coded in tandem copies of similar amino acid stretches. We built and curated a large dataset of Ankyrin containing proteins, one of the most abundant families of repeat proteins, and characterized the structure of the arrays formed by the repetitions. We found that large arrays are constructed with repetitions that are more similar to each other than shorter arrays. Also, the largest the array, the more energetically favourable its folding energy is. We speculate about the mechanistic origin of large arrays and hint into their evolutionary dynamics.Natural proteins that are formed with repetitions of stretches of amino-acids are 2 abundant in extant organisms [1]. Some proteins contain repetitions of short stretches, 3 forming fibrillate structures like collagen, and some contain longer repetitions of 4 globular domains like beads on a string. In between, there is a class of proteins that is 5 formed with tandem repetitions of similar stretches of about 30∼40 residues. These kind 6 of proteins (from now on repeat proteins) are present in all organisms and are believed 7 to be ancient systems [2]. Typically these polypeptides form elongated structures where 8 November 25, 2019 1/23 each repeat motifs packs against its nearest neighbors, stabilizing an overall 9super-helical fold [3]. Since most of the structural characterization of these proteins 10 were performed on model systems of short arrays that are experimentally amenable, we 11 aim at characterizing the overall structures of an abundant family of proteins. 12Ankyrin repeat proteins (ANKs) are usually described as formed with linear arrays 13 of tandem copies of a 33 residues length motif that fold to a α-loop-α − β-hairpin/loop. 14 Being one of the most common repeat proteins in nature, these molecules are believed 15 to function as sp...

Evolution and folding of repeat proteins

Proc. Natl. Acad. Sci. U.S.A.

Marchi

Mora

et al. 2022

Self Cite

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.