Théo Falgarone

Étienne Villain

Francois Richard

Zarifa Osmanli

Andrey V Kajava
email: andrey.kajava@crbm.cnrs.fr

Census of exposed aggregation-prone regions in proteomes

Keywords: protein aggregation, bioinformatics, large-scale analysis, evolution, kingdoms of life

Loss of solubility usually leads to the detrimental elimination of protein function. In some cases, the protein aggregation is also required for beneficial functions. Given the duality of this phenomenon, it remains a fundamental question how natural selection controls the aggregation. The exponential growth of genomic sequence data and recent progress with in silico predictors of the aggregation allows approaching this problem by a large-scale bioinformatics analysis. Most of the aggregation-prone regions are hidden within the 3D structures and, therefore, they cannot realize their potential to aggregate. Thus, the most realistic census of the aggregation prone regions requires crossing aggregation prediction with information about the location of the natively unfolded regions. This allows us to detect so-called "Exposed Aggregation-prone Regions" (EARs). Here, we analyzed the occurrence and distribution of the EARs in 76 full reference proteomes from the three kingdoms of life. For this purpose, we used the TAPASS pipeline, which provides a consensual result based on several predictors of aggregation. Our analysis revealed a number of new statistically significant correlations about the presence of EARs in different organisms, their dependence on protein length, cellular localizations, co-occurrence with short linear motifs, and the level of protein expression. We also obtained a list of proteins with the conserved aggregation-prone sequences for further experimental tests. Insights gained from this work led to a deeper understanding of the functional and evolutionary relations of the protein aggregation. number of high quality whole-proteome sequencing data, made a new census of aggregation-prone regions in proteins timely. In this paper, we present the results of such a detailed analysis of 76 full reference proteomes from the UniProt databank.

INTRODUCTION

Proteins are usually soluble molecules interacting transiently with each other or the other biomolecules. After performing their functions, they are degraded by proteases. Thanks to the dynamic balance between protein synthesis and degradation, living organisms can efficiently regulate many different processes. However, occasionally, some proteins, often for not entirely clear reasons, form aggregates. Most of the aggregates have a very characteristic structure of amyloid fibrils. These fibrils are typically straight, around 10 nm in diameter, thermostable, protease resistant, and rich in β-structure [START_REF] Steven | Molecular Biology of Assemblies and Machines[END_REF]. They are completely or partially insoluble and frequently lead to a variety of age-related diseases including Alzheimer's disease, Parkinson's disease and others [START_REF] Benson | Amyloid nomenclature 2020: update and recommendations by the International Society of Amyloidosis (ISA) nomenclature committee[END_REF]. In some cases, the amyloid fibrils (named prions) can be "infectious agents". The prion fibrils, which are found themselves in another organism or a cell, can trigger the formation of similar fibrils and cause transmissible neurodegenerative diseases (3). The amyloid deposits can not only be composed of copies of the same protein, but also represent co-aggregates of two or more proteins and by doing so simultaneously impair several biological processes [START_REF] Bondarev | Protein coaggregation related to amyloids: Methods of investigation, diversity, and classification[END_REF]. At the same time, not all amyloid fibrils are linked to diseases. Increasing number of studies describe so called "functional" amyloids, which fulfill beneficial roles in the organism [START_REF] Erskine | Functional Amyloid and Other Protein Fibers in the Biofilm Matrix[END_REF][START_REF] Greenwald | Biology of amyloid: Structure, function, and regulation[END_REF]. For example, curli proteins from some gram-negative bacteria form amyloid fibrils on the bacterial surface. They are involved in biofilm formations, which is a successful strategy allowing microorganisms to resist the threats of the environment (UV radiation, oxygen, desiccation etc) [START_REF] Barnhart | Curli biogenesis and function[END_REF]. Other examples from mammals are RIP1 and RIP3 proteins whose co-aggregation into amyloid fibrils mediates a key interaction of necroptosis signaling [START_REF] Kajava | Evolutionary link between metazoan RHIM motif and prion-forming domain of fungal heterokaryon incompatibility factor HET-s/HET-s[END_REF][START_REF] Li | The RIP1/RIP3 necrosome forms a functional amyloid signaling complex required for programmed necrosis[END_REF]. Despite great interest in protein aggregation, especially regarding amyloids, scientists have focused on a few of the most devastating amyloidoses or known cases of functional amyloids. However, the overall prevalence of the protein aggregation in organisms is not yet well studied. This analysis requires computational methods for in silico prediction of the aggregation. The propensity to form aggregates is coded by the amino acid sequence, therefore, several computational programs have been developed [START_REF] Ahmed | A structure-based approach to predict predisposition to amyloidosis[END_REF][START_REF] Ahmed | Breaking the amyloidogenicity code: Methods to predict amyloids from amino acid sequence[END_REF][START_REF] Conchillo-Solé | AGGRESCAN: A server for the prediction and evaluation of 'hot spots' of aggregation in polypeptides[END_REF][START_REF] Fernandez-Escamilla | Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins[END_REF][START_REF] Tartaglia | Prediction of Aggregation-Prone Regions in Structured Proteins[END_REF][START_REF] Thompson | The 3D profile method for identifying fibril-forming segments of proteins[END_REF][START_REF] Walsh | PASTA 2.0: An improved server for protein aggregation prediction[END_REF][START_REF] Louros | Structurebased machine-guided mapping of amyloid sequence space reveals uncharted sequence clusters with higher solubilities[END_REF][START_REF] Wojciechowski | PATH -Prediction of Amyloidogenicity by Threading and Machine Learning[END_REF] Availability of the computational tools for prediction of aggregation-prone regions made it possible to obtain a more general view of this phenomenon by using in silico analysis of the whole-proteome data. Previous in silico studies revealed a number of interesting observations [START_REF] Tartaglia | Prediction of Aggregation-Prone Regions in Structured Proteins[END_REF][START_REF] Antonets | Exploring Proteins Containing Amyloidogenic Regions in the Proteomes of Bacteria of the Order Rhizobiales[END_REF][START_REF] Tartaglia | Correlation between mRNA expression levels and protein aggregation propensities in subcellular localisations[END_REF][START_REF] Antonets | Predicting amyloidogenic proteins in the proteomes of plants[END_REF][START_REF] Castillo | Prediction of the aggregation propensity of proteins from the primary sequence: Aggregation properties of proteomes[END_REF][START_REF] Chen | Natural selection against protein aggregation on self-interacting and essential proteins in yeast, fly, and worm[END_REF][START_REF] Das | Sequence complexity of amyloidogenic regions in intrinsically disordered human proteins[END_REF][START_REF] De Groot | Protein aggregation profile of the bacterial cytosol[END_REF][START_REF] Goldschmidt | Identifying the amylome, proteins capable of forming amyloid-like fibrils[END_REF][START_REF] Monsellier | Aggregation propensity of the human proteome[END_REF][START_REF] Prabakaran | Aggregation prone regions in human proteome: Insights from large-scale data analyses[END_REF]. For example, a study of six proteomes (P. tetraurelia, S. cerevisiae, C. elegans, D. melanogaster, M. musculus and H. sapiens) using a specially developed algorithm, demonstrated that the average aggregation propensity of a proteome correlates inversely with the complexity and longevity of the studied organisms [START_REF] Tartaglia | Organism complexity anti-correlates with proteomic $β$-aggregation propensity[END_REF]. In another analysis of the proteomes of D. melanogaster, S.cerevisiae and C. elegans using TANGO predictor [START_REF] Fernandez-Escamilla | Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins[END_REF] it was shown that proteins that are essential to organism fitness (knockdown of these genes leads to lethality), have a lower aggregation score than nonessential proteins [START_REF] Chen | Natural selection against protein aggregation on self-interacting and essential proteins in yeast, fly, and worm[END_REF]. Analysis of the human proteome by the Zyggregator method [START_REF] Pawar | Prediction of 'aggregation-prone' and 'aggregation-susceptible' regions in proteins associated with neurodegenerative diseases[END_REF][START_REF] Tartaglia | The Zyggregator method for predicting protein aggregation propensities[END_REF] suggested that proteins involved in the secretion pathway are more prone to aggregation compared to non-membrane proteins in general [START_REF] Monsellier | Aggregation propensity of the human proteome[END_REF]. Application of the 3D profile method to E. coli, S. cerevisiae, and H. sapiens proteomes showed that the predicted high propensity for amyloid formation does not reflect well the limited number of proteins involved in disease-related or functional amyloid deposits [START_REF] Goldschmidt | Identifying the amylome, proteins capable of forming amyloid-like fibrils[END_REF]. The same analysis of proteins from PDB suggested that most of the predicted aggregation prone regions are hidden within the 3D protein structure and, therefore, inaccessible for intermolecular interactions such as aggregation [START_REF] Villain | Porins and amyloids are coded by similar sequence motifs Etienne[END_REF]. The analysis of cytosolic bacterial (E. coli) and eukaryotic (H. sapiens) proteomes indicated that the aggregation propensity of proteins inversely-correlates with their abundance [START_REF] Antonets | Exploring Proteins Containing Amyloidogenic Regions in the Proteomes of Bacteria of the Order Rhizobiales[END_REF][START_REF] Tartaglia | Correlation between mRNA expression levels and protein aggregation propensities in subcellular localisations[END_REF][START_REF] Antonets | Predicting amyloidogenic proteins in the proteomes of plants[END_REF]. Most of these data are in agreement with the conclusion that the evolutionary pressure acts on the proteins to minimize their aggregation propensity.

Several publications have reported that proteomes contain a very high percentage of proteins with amyloidogenic or aggregation-prone regions (AR), which is in obvious conflict with a small number of the known proteins involved in amyloidoses [START_REF] Prabakaran | Aggregation prone regions in human proteome: Insights from large-scale data analyses[END_REF]. It was explained by the fact that most of the predicted ARs are hidden within the 3D structure preventing aggregation [START_REF] Falgarone | TAPASS: Tool for annotation of protein amyloidogenicity in the context of other structural states[END_REF] . Conversely, in most known cases of amyloidosis, the native conformation of the polypeptide chains that form amyloid deposits in vivo, is unfolded (or intrinsically disordered). Thus, to get a more realistic census of the aggregation prone regions in proteomes, it is necessary to cross aggregation prediction with information about the location of the intrinsically disordered regions (IDRs). IDRs are always exposed for the intermolecular interactions critical for aggregation. We used this concept to develop a computational pipeline TAPASS [START_REF] Falgarone | TAPASS: Tool for annotation of protein amyloidogenicity in the context of other structural states[END_REF], which can detect such "Exposed Amyloidogenic Regions" or, otherwise "Exposed Aggregation-prone Regions" (EARs) located within IDRs and carrying high potential to aggregate (see Figure 1). To obtain the most consensual results on the occurrence and distribution of the EARs in proteomes we selected three predictors of aggregation (TANGO, Pasta 2.0 and ArchCandy 2.0) [START_REF] Ahmed | A structure-based approach to predict predisposition to amyloidosis[END_REF][START_REF] Fernandez-Escamilla | Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins[END_REF][START_REF] Walsh | PASTA 2.0: An improved server for protein aggregation prediction[END_REF]. They were selected based on the diversity of their basic principles, their popularity, and ability to be downloaded for analysis of a large number of sequences. TAPASS also provides information about the cellular localization, post-translational modifications, and functions of aggregation-prone proteins. In addition to the advances with the predictors of aggregation, the past few years were marked by a significant increase in the number and quality of proteome sequencing data, Thus, the advances with methods predicting aggregation potential, development of the TAPASS pipeline, as well as an increasing [START_REF] Cao | Cryo-EM structures of four polymorphic TDP-43 amyloid cores[END_REF]. TAPASS predicts several ARs, which are located within the 3D structures (orange) and two EARs (magenta) located at the C-terminal IDR.

MATERIAL AND METHODS

TAPASS pipeline

The input file of TAPASS requires protein sequences in Fasta format and can contain additional informations from UniProt(35) (gene id, GO term, version, modification date...). The pipeline uses: IUPred [START_REF] Dosztányi | The pairwise energy content estimated from amino acid composition discriminates between folded and intrinsically unstructured proteins[END_REF] and our in-house predictor (IDRs), CATH associated with HMMER 3.3 (structural domains) [START_REF] Dawson | CATH: An expanded resource to predict protein function through structure and sequence[END_REF][START_REF] Eddy | Accelerated Profile HMM Searches[END_REF], TMHMM (transmembrane regions) [START_REF] Krogh | Predicting transmembrane protein topology with a hidden Markov model: Application to complete genomes[END_REF], SignalP (signal peptide) [START_REF] Petersen | SignalP 4.0: Discriminating signal peptides from transmembrane regions[END_REF], SLiMs (short linear motifs) [START_REF] Kumar | ELM-the eukaryotic linear motif resource in 2020[END_REF][START_REF] Ruhanen | Potential of known and short prokaryotic protein motifs as a basis for novel peptide-based antibacterial therapeutics: A computational survey[END_REF], Pfam (structural and functional domains)(43), Pasta 2.0(16), TANGO [START_REF] Fernandez-Escamilla | Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins[END_REF] and updated version of ArchCandy 2.0 (aggregation-prone regions) [START_REF] Ahmed | A structure-based approach to predict predisposition to amyloidosis[END_REF][START_REF] Falgarone | TAPASS: Tool for annotation of protein amyloidogenicity in the context of other structural states[END_REF]. The results of the three predictors of aggregation, ArchCandy 2.0, Pasta 2.0 and TANGO, were treated separately. Each predictor gives the start and end positions of ARs in protein sequences. An AR is considered as EAR if at least 80 % of an individual hit of AR predictor overlap with an IDR. Thus, our analysis led to three independent censuses of the aggregation-prone regions. If all three censuses yielded similar regularities, then these findings were considered as more reliable and treated with special attention.

Selection of proteomes for large-scale analysis 76 reference proteomes with 1 123 749 proteins in total were selected from the UniProt databank (see Supplementary data) [START_REF] Bateman | UniProt: A worldwide hub of protein knowledge[END_REF]. The proteomes belong to the three kingdoms of life: eukaryote, bacteria and archaea. The selection of species was made to have well-annotated and complete reference proteomes covering the diversity of living organisms. Viral proteomes were not considered in this analysis due to small size of their proteomes yielding very different results depending on the strains. Their analysis will be a subject of our future study.

RESULTS

Occurrence of ARs and EARs in the proteomes

Previous studies detected a very high percentage of AR-containing proteins in proteomes with almost each protein having at least one predicted AR [START_REF] Castillo | Prediction of the aggregation propensity of proteins from the primary sequence: Aggregation properties of proteomes[END_REF][START_REF] Goldschmidt | Identifying the amylome, proteins capable of forming amyloid-like fibrils[END_REF][START_REF] Monsellier | Aggregation propensity of the human proteome[END_REF]. The results of our analysis of 76 reference proteomes support this conclusion predicting 68.6 %, 79.3 % and 90.0 % of AR-containing proteins by ArchCandy 2.0, Pasta 2.0 and TANGO, respectively. The coverage of ARs, obtained by dividing the number of amino acid residues involved in ARs by the number of all residues in proteins, is equal to 12.6 %, 6.2 % and 11.3 % for ArchCandy 2.0, Pasta 2.0 and TANGO respectively. A very high percentage of AR-containing proteins is in contradiction with a small number of proteins known to be involved in different amyloidoses or functional amyloids. However, if we consider EARs, the number of potential aggregation-prone proteins is drastically reduced. EAR-containing proteins represent 9.0 %, 6.8 % and 19.5 % of all proteins with coverage of 0.8 %, 0.2 % and 0.4 % of residues according to ArchCandy 2.0, Pasta 2.0 and TANGO respectively. The low percentage of proteins with EARs, in contrast to a very high percentage of ARs, agrees better with the small number of the known proteins involved in aggregation in vivo.

Aggregation-prone regions in prokaryotic and eukaryotic organisms

Analyzing the 76 selected proteomes we observed a relatively uniform distribution of AR-containing proteins among the organisms (Figure 2). Curiously, Homo sapiens has the least number of AR-containing proteins. At the same time, we saw a large variation in the proportion of EAR-containing proteins. Among the organisms with the least number of EAR-containing proteins are thermophilic prokaryotes (6 archaea and 5 bacteria: Chloroflexus aurantiacus, Thermodesulfovibrio yellowstonii, Dictyoglomus turgidum, Nanoarchaeum equitans, Sulfolobus solfataricus, Thermotoga maritima, Archaeoglobus fulgidus, Thermococcus kodakaraensis, Methanocaldococcus jannaschii, Candidatus korarchaeum, Aquifex aeolicus). The eukaryotes with the simplest level of organization, mostly unicellular (or partially unicellular) protists such as Plasmodium falciparum, Leishmania major, Thalassiosira pseudonana, Trypanosoma cruzi, Toxoplasma gondii and Dictyostelium discoideum have the greatest numbers of EAR-containing proteins (Figure 2). High levels of EAR-containing proteins are also found in two fungi (Ustilago maydis, Neurospora crassa), fruit flies (Drosophila melanogaster), mosquitoes (Anopheles gambiae) and chickens (Gallus gallus). Most of them are known to have the greatest number of low-complexity repetitive sequences [START_REF] Mier | Disentangling the complexity of low complexity proteins[END_REF]. This is particularly the case of Trypanosoma cruzi and Dictyostelium discoideum, which have an abnormal high level of Asn/Gln rich regions, two types of amino acids frequently found in amyloids. Among analyzed mammalians, Homo sapiens has the least number of EAR-containing proteins (Figure 2). Having a global view of the dispersion of aggregation potential of the proteomes, it was interesting to analyze the tendencies associated with groups of the organisms. First, we compared prokaryotes and eukaryotes. All three predictors detect more AR-containing proteins and higher AR-coverage in prokaryotes in comparison to eukaryotes (Figure 3A and3B). The tendency is reversed when we compare the occurrence of EARs (Figure 3C). The percentage of EAR-containing proteins and coverage of EARs are noticeably higher in eukaryotic than in prokaryotic organisms (Figure 3C and3D). This can be explained by a higher number of IDRs in eukaryotes, which require the IDRs to mediate a more complex network of protein-protein interactions in comparison to prokaryotes [START_REF] Pancsa | Structural disorder in eukaryotes[END_REF][START_REF] Ward | Prediction and Functional Analysis of Native Disorder in Proteins from the Three Kingdoms of Life[END_REF]. At the same time, the coverage of EARs in IDRs is lower in eukaryotes compared to prokaryotes (Figure 3E). Thus, the eukaryotic IDRs are less aggregation-prone on average than the prokaryotic ones, suggesting a higher selective pressure on their IDRs to avoid aggregation. The more thermophilic the less aggregation-prone A unique feature of prokaryotes is the wide range of their optimal growth temperatures (OGTs), some of them reaching temperatures above 105°C [START_REF] Stetter | History of discovery of the first hyperthermophiles[END_REF]. We estimated the aggregation potential of the prokaryotic proteomes depending on the OGTs. For this purpose, we subdivided the selected reference proteomes into two groups: 20 mesophilic organisms, those with an OGT below 41°C and 11 thermophilic organisms with an OGT above 41°C. The comparison of proportion and coverage of ARs from these groups do not reach the same conclusion as ArchCandy 2.0 predicts a decrease in ARs in the thermophilic organisms, while PASTA 2.0 and TANGO show the opposite tendency (see Supplementary Figure 1). However, evaluation of EARs by all the predictors clearly demonstrated that they decrease with the increase of OGT (Figure 4). It has been also shown that the frequency of glutamine residue, which has a high amyloidogenic potential, decreases, while the total frequency of charged residues, which can block amyloid-formation, increases in thermophilic proteins [START_REF] Villain | Aspartate-phobia of thermophiles as a reaction to deleterious chemical transformations[END_REF]. At the same time, the temperature increase may favor aggregation. For example, it has been shown that the amyloidogenesis rate constant of Aβ-peptide increases and the lag time decreases with increasing temperature [START_REF] Tiiman | In vitro fibrillization of Alzheimer's amyloid-β peptide (1-42)[END_REF]. Considering all this, we can conclude that the decrease in the EARs with OGT can be a result of an evolutionary pressure on the thermophilic proteins to avoid the aggregation.

Occurrence of EARs in proteins depending on their length

In general, the longer the protein chain, the higher the probability for it to have both ARs and EARs. One would expect that if the ARs or EARs are uniformly distributed in protein sequences, their occurrence would correlate linearly with protein length. To see the tendency better, one can normalize the occurrence of ARs/EARs by dividing it by protein length. Previously, similar analyses have been done for the ARs using bacterial proteins [START_REF] De Groot | Protein aggregation profile of the bacterial cytosol[END_REF] and the human proteome [START_REF] Monsellier | Aggregation propensity of the human proteome[END_REF]. Both studies showed that the aggregation potential of a protein normalized by its length goes down with the increase of protein size. To compare this conclusion with our results from the 76 selected proteomes, we analyzed the normalized proportion of AR-containing proteins and normalized AR-coverage depending on length (Figure 5 A,C). In agreement with the previous studies, we observed a decrease in the normalized proportion of AR-containing proteins and AR coverage with length. The steady decrease starts after 500 residues. The graph of AR coverage has a sharp peak at around 350-residue length. Clustering proteins by MMseqs2 (51) at 30 % of sequence identity, we found that this peak contains a significant excess of G protein-coupled receptors having high AR coverage, explaining this anomaly. The 200-500 residue region with the highest AR coverage and proportion coincides with the length ranges where proteins are predicted to be the most structured (Figure 5E) and in general, it negatively correlates with the IDR coverage by protein length. Thus, the AR proportion and coverage curves can be explained by the fact that structured regions have a higher probability of containing ARs, and proteins of less than 500 residues are mostly structured.

The dependence of EARs on protein length demonstrates that it differs from ARs (Figure 5 B,D). Proteins longer than 2000 were grouped into one subset. The predictors used have systematic biases at the terminal regions of proteins and this affects results on the short sequence lengths. To take this bias into account, we also run the predictors against a set of randomized sequences. This set contains proteins from our database with each sequence computationally shuffled, respecting the average amino acid composition of our database and having the same distribution of protein lengths. This allowed us to determine a correction coefficient which was used to adjust the values of EAR, AR and IDR.

The predictors show a plateau with the lowest EAR-coverage for the shortest proteins (less than 350 residues), which steadily goes up for longer proteins. A similar trend is observed when we plot the dependence of the proportion of EAR-containing proteins by length. The dependence of the coverage of IDRs against protein length (Figure 5E) is similar to the one of EARs, explaining the low aggregation potential of the short sequences by their tendency to be structured. Indeed, the region of 200-400 residues, which corresponds to the stable structural domains of proteins, has the lowest coverage of IDRs and EARs. To see the tendency linked only to the characteristics inherent in the IDR sequences, we analyzed the dependence between the EAR coverage in IDRs and the length of proteins. The analysis shows that for TANGO and PASTA 2.0, shorter sequences have higher EAR coverage in IDRs. In contrast, ArchCandy 2.0 predicted an increase of EAR coverage in IDRs with protein length (Figure 5F). One explanation of this discrepancy between the predictors maybe the fact that ArchCandy predicts Asn/Gln-rich regions, which are frequently found in long proteins, as aggregation prone, while TANGO and PASTA do not. Thus, we do not observe a decrease in aggregation potential with an increase of protein size when we consider EARs. The longer a protein chain, the higher its propensity to aggregate. Therefore, the question arises as to the mechanism preventing fibril formation of long proteins. One possible explanation can be that long proteins, having multiple IDRs, represent "steric brushes", preventing their intermolecular interactions and aggregation due to the high entropic barrier [START_REF] Rubinstein | Polymer Physics[END_REF].

Occurrence of EAR-containing proteins in different cellular compartments

Proteins having different cellular localizations may differ in their aggregation potential. Therefore, we analyzed the occurrence of AR-and EAR-containing proteins in 4 major subcellular localizations: secreted proteins identified by SignalP [START_REF] Petersen | SignalP 4.0: Discriminating signal peptides from transmembrane regions[END_REF], transmembrane proteins by using TMHMM [START_REF] Krogh | Predicting transmembrane protein topology with a hidden Markov model: Application to complete genomes[END_REF], nuclear proteins with NLS (nuclear localization signals) found by SLiMs [START_REF] Kumar | ELM-the eukaryotic linear motif resource in 2020[END_REF], and the remaining proteins that were considered mostly cytosolic (Figure 6). We observed similar levels of AR-containing proteins in all compartments except the transmembrane proteins, which have significantly higher levels (Supplementary Figure 2). The high level of AR-containing proteins among the transmembrane proteins was expected because their hydrophobic TM helices are detected as ARs by all predictors. The most striking observation was the high level of EAR-containing proteins in nucleus of eukaryotes, which is at least two times higher than in the other cellular localizations (Figure 6A). In line with this result, it has been shown previously that under stress conditions, proteins in the nucleus tend to form aggregates [START_REF] Karamanos | Mechanisms of amyloid formation revealed by solution NMR[END_REF]. In prokaryotes, we observed more EAR-containing proteins among those involved in the secretory pathway in comparison to those present in the transmembrane and cytosol (Figure 6B). This tendency suggests that the secreted proteins being outside of the cell are under a reduced evolutionary pressure to avoid aggregation. Formation of aggregates out of the cell may be less deleterious for unicellular prokaryotic organisms in comparison with most of the eukaryotes, which can accumulate unwanted deposits within the extracellular space of their tissues. Moreover, it is known that many prokaryotes use secreted proteins to form functional amyloids [START_REF] Erskine | Functional Amyloid and Other Protein Fibers in the Biofilm Matrix[END_REF].

Relationship between cellular abundance of proteins and ARs/EARs frequencies

The amount of genome-wide data on gene expression has drastically increased in the past few years [START_REF] Stephens | Big data: Astronomical or genomical?[END_REF]. The data comes from various technologies, organisms, and tissues (normal or disease related), making it difficult to compare them in a large-scale analysis. In this case, we find that the data from the Protein Abundance Database (PaxDb) [START_REF] Wang | Version 4.0 of PaxDb: Protein abundance data, integrated across model organisms, tissues, and cell-lines[END_REF] are the most suitable for our purposes. PaxDb represents protein abundance by "protein per million" (ppm) and by doing so, overcomes the problem of variability in cell size or dilutions in the samples used, making comparisons between them possible. The PaxDb has the protein expression level in different tissues and organs of organisms. Additionally, it provides the average abundance of a protein in the whole organism. We used this average abundance value to analyze the expression level of AR-/EAR-containing proteins, which are available both in PaxDb and in our dataset. Expression levels range from almost zero up to more than 100 000 ppm. The majority of proteins have values of less than 2 ppm. The number of proteins with the abundance more than 50 ppm drops significantly (Figure 7). Therefore, we grouped these proteins together in our analysis. The analysis revealed that the frequency of occurrence of EAR-containing proteins decreases with the ppm growth and is becoming lower than non-EAR-containing proteins. From the observed dependence of the difference between EAR-and non-EAR-containing proteins, we can conclude that highly expressed proteins are less prone to aggregate, with this finding being consistent in the three predictors used. We observed a similar tendency with the frequency of occurrence of AR-containing proteins depending on the abundance (see Supplementary Figure 3). It suggests that highly expressed proteins are under a greater selective pressure to avoid aggregation. This conclusion is in agreement with a previous study of human proteins also suggesting that aggregation-prone proteins and gene level expression are inversely correlated [START_REF] Tartaglia | Correlation between mRNA expression levels and protein aggregation propensities in subcellular localisations[END_REF].

EAR levels in essential proteins

As demonstrated previously, essential genes are subject to a greater selection pressure than non-essential genes [START_REF] Wang | Version 4.0 of PaxDb: Protein abundance data, integrated across model organisms, tissues, and cell-lines[END_REF][START_REF] Jordan | Essential Genes Are More Evolutionarily Conserved Than Are Nonessential Genes in Bacteria[END_REF]. It has also been shown that essential proteins are less prone to aggregation [START_REF] Tartaglia | Correlation between mRNA expression levels and protein aggregation propensities in subcellular localisations[END_REF][START_REF] Chen | Natural selection against protein aggregation on self-interacting and essential proteins in yeast, fly, and worm[END_REF]. In order to find essential proteins in our database, we used the DEG database of essential proteins [START_REF] Luo | DEG 15, an update of the Database of Essential Genes that includes built-in analysis tools[END_REF] and run BLAST program with E-value < 0,001 [START_REF] Altschul | Basic local alignment search tool[END_REF]. By this approach we identified 705692 essential proteins (~62,6 %) in our database. Analysis of these proteins by the three predictors showed a lower EAR coverage, and in a lesser extent, proportion of essential and non-essential EAR-containing proteins in eukaryotes (Figure 8 A,C). Our results are in agreement with previous conclusions that essential proteins have a lower aggregation score than non-essential proteins [START_REF] Chen | Natural selection against protein aggregation on self-interacting and essential proteins in yeast, fly, and worm[END_REF]. In prokaryotes, we observe the opposite tendency (Figure 8B,D). Previous analyses of ARs (not EARs) made on a smaller scale in bacteria [START_REF] De Groot | Protein aggregation profile of the bacterial cytosol[END_REF] have shown that essential proteins have less ARs. Our results of the AR analysis in prokaryotes (see Supplementary Figure 4) are in agreement with this conclusion.

Short Linear Motifs (SLiMs) in EARs

A significant portion of protein interactions are mediated by short linear motifs (SLiMs) preferentially found in IDRs [START_REF] Kumar | ELM-the eukaryotic linear motif resource in 2020[END_REF]. As EARs are also located within the IDRs, it was interesting to analyze the co-occurrence of SLiMs and EARs in proteins. Although both prokaryotes and eukaryotes have functional SLiMs, the eukaryotic linear motifs are more common, as well as better classified and documented. Most of the eukaryotic SLiMs can be found in the ELM resource (41) alongside with their descriptions, experimental evidence from the literature, and Regular Expressions (RegEx) of the recurrent patterns. Therefore, we focused our analysis on the SLiMs from eukaryotes. For this purpose, we applied the RegEx from the ELM database [START_REF] Kumar | ELM-the eukaryotic linear motif resource in 2020[END_REF] to the IDRs and EARs determined by our pipeline [START_REF] Falgarone | TAPASS: Tool for annotation of protein amyloidogenicity in the context of other structural states[END_REF]. The SLiMs are subdivided into 6 major classes: (LIG) ligand binding motifs and (DOC) docking sites both involved in protein-protein interactions of the functional complexes, (MOD) modification sites covering several post-translational modifications of proteins (e.g. phosphorylation, palmitoylation, glucosylation), (DEG) sites of proteins that are important in regulation of protein degradation rates, (TRG) targeting sites responsible for protein sorting in cellular compartments and (CLV) specific cleavage sites. The results of all three aggregation predictors showed that EAR-containing proteins are enriched in SLiMs in comparison to IDR-containing proteins without EARs (Figure 9). By using the exact Fisher test, we were able to select SLiMs, which are significantly enriched in EAR-containing proteins compared to IDRcontaining proteins alone. Interestingly, 20 of the 25 degradation motifs (proteasome pathway) from DEG class occur more frequently in EAR-containing proteins than in non-EAR-containing proteins (Figure 9). 17 of the 22 TRGs are also more frequently present in EAR-containing proteins than in IDR-containing proteins. Among them, 3 SLiMs were found to be Endosome-Lysosome-Basolateral sorting signals. These results suggest that EAR-containing proteins may be more susceptible to being degraded by proteasome and lysosome pathways compared to just IDR-containing proteins. This might be a strategy used by organisms to prevent protein aggregation by increasing the degradation of potential aggregation-prone proteins. Cleavage sites (CLV) are less prevalent in EARs, which may prevent the release of smaller amyloidogenic peptides such as the well-known Aβ-peptide (60).

Functional domains enriched in EAR-containing proteins

With a method similar to the SliMs enrichment, we tried to identify functional Pfam domains enriched in EAR-containing proteins. Of the 15116 known Pfam domains, only 1410 are significantly more prevalent in EAR-containing proteins predicted by ArchCandy 2.0 (exact Fisher test, p-value < 0.001). 484 of them belong to 154 clans according to the classification of Pfam. The functional domains and clans that came on top are: nucleoporin FG repeat region (CL0647), RNA recognition motif domains (CL0221) and zinc-finger domains (CL0511, CL0390) (see Supplementary data 1). We searched the experimental evidence of aggregation by these domains in the literature and found that the nucleoporin proteins are known to form amyloids [START_REF] Danilov | The human nup58 nucleoporin can form amyloids in vitro and in vivo[END_REF]. EAR-containing proteins predicted by both ArchCandy 2.0 and TANGO are positively enriched in nucleoporin FG repeat region (CL0647). From the known functional amyloids described in the literature, we also found back RIPK1 and RIPK3 [START_REF] Kajava | Evolutionary link between metazoan RHIM motif and prion-forming domain of fungal heterokaryon incompatibility factor HET-s/HET-s[END_REF][START_REF] Li | The RIP1/RIP3 necrosome forms a functional amyloid signaling complex required for programmed necrosis[END_REF] and PMEL17 [START_REF] Raposo | The dark side of lysosome-related organelles: Specialization of the endocytic pathway for melanosome biogenesis[END_REF], which were conserved in 6 distinct proteins from mammalians with the prediction of ArchCandy 2.0 but not Pasta 2.0 or TANGO. Previous studies of Pfam domains and gene ontology (GO) term enrichment in amyloidogenic proteins [START_REF] Das | Sequence complexity of amyloidogenic regions in intrinsically disordered human proteins[END_REF][START_REF] Prabakaran | Aggregation prone regions in human proteome: Insights from large-scale data analyses[END_REF] pointed out the over-representation of membrane transport activity, pH and ion regulation and even cytoskeleton organization. However, they considered ARs not EARs. Therefore, we did not find most of the afore mentioned functions in our analysis.

Conservation of EARs sequences

Another approach to find new functional amyloids is to search for EARs that are conserved among different species. For this purpose, we reduced EARs predicted by either ArchCandy 2.0, TANGO or Pasta 2.0 with CD-HIT (63) at 70 % sequence identity and 90 % of coverage, to obtain a non-redundant set of the EARs (Table 1). Then, we ran BLAST [START_REF] Altschul | Basic local alignment search tool[END_REF] for each EAR sequence against all proteins from our redundant database to select only conserved EAR sequences (Figure 10). This gave us for each EAR a Multiple Sequence Alignment (MSA) of similar sequences found in other proteins. Some sequences of the MSA were EARs and the others were not according to the predictors. We selected the MSAs with EARs in more than five other proteins and further reduced the MSA number by merging those that shared at least 80 % of the same conserved EAR. This clustering results found 2218, 869 and 178 of the most conserved EAR sequences for ArchCandy 2.0, Pasta 2.0 and TANGO, respectively (Table 1). We observed that only a small number of EAR sequences are conserved out of more than one million proteins. Among them we found already known functional amyloids, such as RIPK3 and RIPK1 (8) and PMEL17 [START_REF] Raposo | The dark side of lysosome-related organelles: Specialization of the endocytic pathway for melanosome biogenesis[END_REF]. This suggests that the list of conserved EARs found by this protocol (Supplementary data 2) can be used for detection and experimental tests of new functional amyloids.

DISCUSSION

The recent progress with computational approaches predicting aggregation [START_REF] Ahmed | A structure-based approach to predict predisposition to amyloidosis[END_REF][START_REF] Conchillo-Solé | AGGRESCAN: A server for the prediction and evaluation of 'hot spots' of aggregation in polypeptides[END_REF][START_REF] Fernandez-Escamilla | Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins[END_REF][START_REF] Thompson | The 3D profile method for identifying fibril-forming segments of proteins[END_REF][START_REF] Walsh | PASTA 2.0: An improved server for protein aggregation prediction[END_REF][START_REF] Wojciechowski | PATH -Prediction of Amyloidogenicity by Threading and Machine Learning[END_REF][START_REF] Tartaglia | The Zyggregator method for predicting protein aggregation propensities[END_REF][START_REF] Falgarone | TAPASS: Tool for annotation of protein amyloidogenicity in the context of other structural states[END_REF], and an increasing number of whole-proteome sequencing data, opened an avenue for the comprehensive census of aggregation-prone regions in proteins. In this work, we performed the detailed analysis of 76 full reference proteomes from the UniProt databank. As a result, a number of interesting correlations, confirmed by all the predictors used in this work (ArchCandy 2.0, Pasta 2.0 and TANGO), were discovered. First, we detected a significantly lower percentage of EAR-containing proteins (about 10%) in comparison with a high percentage of AR-containing proteins in proteomes (about 80%). The number of EARs correlates better with a small number of the known proteins forming aggregates in vivo, and, therefore, EARs can be suggested as a more precise measure of the aggregation potential of proteins. We showed that there are more ARs in prokaryotes than in eukaryotes and that this tendency is inverted for EARs. Second, we found that the thermophilic prokaryotes have significantly less EARs and ARs in comparison to mesophilic prokaryotes. The correlation may reflect an evolutionary pressure on the thermophilic proteins, because the amyloid formation rate constant increases with temperature [START_REF] Tiiman | In vitro fibrillization of Alzheimer's amyloid-β peptide (1-42)[END_REF]. Additionally, in agreement with previous studies, we observed small decrease in the normalized AR coverage with protein length. However, we do not observe a decrease in the aggregation potential of sequences with an increase of protein size when we consider EARs. In our opinion, the mechanism of prevention of aggregation of long proteins has an entropic basis, where the other parts of the chain generate repulsive forces for intermolecular interactions similar to molecular brushes. It worth mentioning that our analysis did not confirm previously published conclusions that the average aggregation propensity of a proteome correlates inversely with the complexity and longevity of the studied organisms [START_REF] Tartaglia | Organism complexity anti-correlates with proteomic $β$-aggregation propensity[END_REF].

It was also shown that proteins having different cellular localizations differ in the aggregation potential. For example, the level of EAR-containing proteins in nuclear proteins of eukaryotes is about two times higher than in the other cellular localizations. In prokaryotes, we observed more EAR-containing proteins among those involved in the secretory pathway in comparison to the transmembrane and cytosolic proteins. This tendency suggests that the secreted proteins being outside of the cell are under a reduced evolutionary pressure to avoid aggregation. Remarkably, a great majority of EAR-containing proteins are enriched in SLiMs in comparison to IDR-containing proteins without EARs. We also noticed that highly expressed proteins are less prone to aggregate suggesting that highly expressed proteins are under a greater negative selective pressure in order to avoid the aggregation. Finally, we revealed a greater level of aggregation predicted in non-essential proteins compared to essential proteins. Thus, we performed the census of the aggregation-prone regions in proteomes. A number of new relationships found in this work led us to a better understanding of the functional and evolutionary relations of protein aggregation in organisms from the three kingdoms of life: eukaryote, bacteria and archaea. Beyond this, our study opens up new opportunities for a number of experimental tests.

Figure 1 .

 1 Figure 1. A general scheme showing mapping of ARs and EARs on a structural model of human TAR DNAbinding protein 43. This protein forms amyloid fibrils by the C-terminal Low Complexity Domain (LCD, 274-414)[START_REF] Cao | Cryo-EM structures of four polymorphic TDP-43 amyloid cores[END_REF]. TAPASS predicts several ARs, which are located within the 3D structures (orange) and two EARs (magenta) located at the C-terminal IDR.

Figure 2 .

 2 Figure 2. Proportion of (A) AR-and (B) EAR-containing proteins per organism predicted by using three predictors of aggregation, ArchCandy 2.0 (red), Pasta 2.0 (blue) and TANGO (green). Archaea, bacteria, eukaryotes and mammalian eukaryotes are outlined by yellow, orange, blue and violet respectively (made by using free options in iTOL, https://itol.embl.de/ (45)).

Figure 3 .

 3 Figure 3. Level of aggregation potential according to three amyloid predictors in prokaryotes and eukaryotes. Coverage of ARs (A), proportion of AR-containing proteins (B), coverage of EARs (C), proportion of EAR-containing proteins (D) and coverage of EARs in IDRs (E). For statistical analysis between eukaryotic and prokaryotic organisms we performed a t-test for the predictors individually (ns : non-significant; * : p-value < 0.05 ; ** : p-value < 0.01 ; *** : p-value < 0.001 ; **** : p-value < 0.0001).

Figure 4 .

 4 Figure 4. Coverage of EAR (A) and proportion of EAR-containing proteins (B) in mesophilic (blue) and thermophilic organisms (orange). The analyzed set of thermophilic organisms is: Chloroflexus aurantiacus, Thermodesulfovibrio yellowstonii, Dictyoglomus turgidum, Nanoarchaeum equitans, Sulfolobus solfataricus, Thermotoga maritima, Archaeoglobus fulgidus, Thermococcus kodakaraensis, Methanocaldococcus jannaschii, Candidatus korarchaeum, Aquifex aeolicus. For statistical analysis between mesophilic and thermophilic organisms we performed a t-test for predictors individually (ns : nonsignificant; * : p-value < 0.05 ; ** : p-value < 0.01 ; *** : p-value < 0.001 ; **** : p-value < 0.0001).

Figure 5 .

 5 Figure 5. Plots of the proportion of AR (A) and EAR (B) containing proteins depending on the protein length. Plots of coverage of AR (C) and EAR (D) in proteins according to their length. Plots of coverage of IDR (E) and EAR in IDR (F). Proteins are grouped by subsets of 50 residues (e.g. 1-50, 51-100 etc).Proteins longer than 2000 were grouped into one subset. The predictors used have systematic biases at the terminal regions of proteins and this affects results on the short sequence lengths. To take this bias into account, we also run the predictors against a set of randomized sequences. This set contains proteins from our database with each sequence computationally shuffled, respecting the average amino acid composition of our database and having the same distribution of protein lengths. This allowed us to determine a correction coefficient which was used to adjust the values of EAR, AR and IDR.

Figure 6 .

 6 Figure 6. Plots of proportion of EAR-containing proteins according to the protein localization in eukaryotic (A) and prokaryotic (B) organisms. Proteins are splitted in four groups: cytosolic proteins, extracellular ones with signal peptides (SP), transmembrane proteins (TM) and nuclear proteins having nuclear localization signals (NLS). The proportions of the analyzed proteins are: in eukaryotes, 58.5% are cytosolic, 6.2% have SPs, 21.4% are transmembrane proteins and 13.9% have NLS. In prokaryotes, 71.9 % are cytosolic, 4.3% have SPs and 23.7% are transmembrane proteins. For statistical analysis between the different cell compartments we performed an anova test for the predictors individually (ns : non-significant; * : p-value < 0.05 ; ** : p-value < 0.01 ; *** : p-value < 0.001 ; **** : p-value < 0.0001).

Figure 7 .

 7 Figure 7. Frequency of occurrence of EAR -containing proteins predicted by ArchCandy 2.0 (A), Pasta 2.0 (B) and TANGO (C). Proteins are grouped based on their abundance in three groups : less than 5 ppm, 5-50 ppm, and more than 50 ppm.

Figure 8 .

 8 Figure 8. Coverage of EARs in essential and non-essential proteins in eukaryote (A) and prokaryote (B) organisms. Proportion of EAR-containing proteins known as essential or non-essential in eukaryote (C) and prokaryote (D) organisms. For statistical analysis between essential and non-essential proteins we performed a t-test for amyloidogenic predictors individually (ns : non-significant; * : p-value < 0.05 ; ** : pvalue < 0.01 ; *** : p-value < 0.001 ; **** : p-value < 0.0001).

Figure 9 .

 9 Figure 9. Ratio of proportions of SLiMs in EAR-containing proteins and in IDR-containing proteins without EAR, predicted by three predictors. Each dot represents a given SLiMs grouped in 6 classes denoted by different colors. The majority of the SLiMs have their ratios greater than 1.0 (red dotted line), meaning that they are enriched in EAR-containing proteins.

Figure 10 .

 10 Figure 10. Protocol for the evaluation of EAR sequence conservation.

Table 1 .

 1 Number of EARs at each step of the protocol.

	Predictor	Number of non-	EARs	found	EARs found 2	EARs	found	Number of clusters
		redundant EARs	one time in	to 5 times in	more than 5	with	the	most
			MSA		MSA	times in MSA	conserved EARs
	ArchCandy 2.0 93229	72153 (77.4%) 16124	4952 (5.3%)	2218
					(17.3%)
	Pasta 2.0	42997	35412 (82.4%) 5683 (13.2%) 1902 (4.4%) 869
	TANGO	13816	12342 (89.3%) 1219 (8.8%) 255 (1.8%)	178

FUNDING

This work was supported by REFRACT project with Latin America in RISE program (2018-2023) H2020-MSCA-RISE-2018 to A.V.K.; Azerbaijan National Academy of Sciences and The Ministry of Science and Education of Azerbaijan to Z.O.; the Ministère de l'Education Nationale de la Recherche et de Technologie (MENRT) to E.V. and F.R.; by a CNRS PhD fellowship to T.F.

ACKNOWLEDGMENT

The authors thank Priya Amin for her assistance with the English.

Author Contributions: Conceptualization, A.V.K., T.F. and E.V.; methodology, A.V.K., T.F. and E.V.; software, T.F. and E.V.; data curation, T.F., F.R. and Z.O.; writing-original draft preparation, T.F. and A.V.K.; writing-review and editing, A.V.K., T.F., Z.O, F.R, E.V.; supervision, A.V.K.

CONFLICT OF INTEREST:


Alexander Miguel Monzon

Paula N Arrías

Arne Elofsson

Pablo Mier

Miguel A Andrade- Navarro

Martina Bevilacqua

Damiano Clementel

Alex Bateman

Layla Hirsh

Maria Silvina Fornasari

Gustavo Parisi

Damiano Piovesan

Andrey V Kajava

Silvio C E Tosatto
email: silvio.tosatto@unipd.it

A STRiP-ed definition of Structured Tandem Repeats in Proteins

Keywords: Structured tandem repeats, protein repeats, TRP dichotomies

Tandem Repeat Proteins (TRPs) are a class of proteins with repetitive amino acid sequences that have been studied extensively for over two decades. Different features at the level of sequence, structure, function and evolution have been attributed to them by various authors. And yet many of its salient features appear only when looking at specific subclasses of protein tandem repeats. Here, we attempt to rationalize the existing knowledge on Tandem Repeat Proteins (TRPs) by pointing out several dichotomies. The emerging picture is more nuanced than generally assumed and allows us to draw some boundaries of what is not a "proper" TRP. We conclude with an operational definition of a specific subset, which we have denominated STRPs (Structural Tandem Repeat Proteins), which separates a subclass of tandem repeats with distinctive features from several other less well-defined types of repeats. We believe that this definition will help researchers in the field to better characterize the biological meaning of this large yet largely understudied group of proteins.

Introduction

Since the advent of modern biochemistry, a considerable amount of work has been devoted to understanding proteins in all their different facets. Classifications have been established to describe proteins at the evolutionary [START_REF] Mistry | Pfam: The protein families database in 2021[END_REF][START_REF] Blum | The InterPro protein families and domains database: 20 years on[END_REF] and structural [START_REF] Sillitoe | CATH: increased structural coverage of functional space[END_REF] level. While these work well for globular proteins, the underlying domain paradigm has increasingly shown its limitations [START_REF] Parisi | Protein" no longer means what it used to[END_REF]. A particular area of difficulty are tandem repeat proteins (TRPs). Tandem repeats in proteins are generally defined as contiguous stretches of duplicated amino acid sequences [START_REF] Kajava | Editorial for special issue "Proteins with tandem repeats: sequences, structures and functions[END_REF]. TRPs have been studied in terms of sequence -structure relationship [START_REF] Kobe | When protein folding is simplified to protein coiling: the continuum of solenoid protein structures[END_REF]. A strong dependence of the protein fold on the length of the sequence repeat has been used to build a classification of TRPs [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF]. Similarly, studies trying to establish the evolutionary history of TRPs have found duplication events as the predominant mechanism for TRP expansion [START_REF] Lang | Structural Evidence for Evolution of the β/α Barrel Scaffold by Gene Duplication and Fusion[END_REF]. At the same time, most of the functional knowledge about TRPs is limited to a handful of protein families, most notably solenoids [START_REF] Kobe | When protein folding is simplified to protein coiling: the continuum of solenoid protein structures[END_REF]Andrade et al., 2001a). It is currently unclear how far these concepts can be generalized. We argue that this is largely due to the presence of variability within multiple TRP attributes, which make it difficult to place TRPs all in the same box. In the following, we will try to address each of these as dichotomies, even though we are aware that not all of them can be simplified to either one of two options, before presenting an attempt to derive an operational definition of TRPs that encompasses their most salient features.

TRP dichotomies

Sequence dichotomies

The first and most obvious dichotomy in TRPs is at the sequence level. Here, we can establish differences at the DNA level as well as repeat evolution and protein coverage.

Protein repeats at the DNA level

Repeats at the DNA level are very common. A recent study puts the fraction of the repetitive human genome at 53.9% of the genome sequence [START_REF] Hoyt | From telomere to telomere: The transcriptional and epigenetic state of human repeat elements[END_REF]. Initially thought of as "junk", repetitive DNA regions have been recognized as important sites for innovation in genomes [START_REF] Makałowski | Genomic scrap yard: how genomes utilize all that junk[END_REF], carrying out various important structural and functional roles [START_REF] Shapiro | Why repetitive DNA is essential to genome function[END_REF]. Repetitive DNA can be further distinguished into tandem and interspersed repeats, with many sub-classes captured in the manually curated Dfam database [START_REF] Storer | The Dfam community resource of transposable element families, sequence models, and genome annotations[END_REF]. Protein repeats are not necessarily translated from repeats at the DNA level. The degeneracy of the genetic code implies that even the most simple repeats, homorepeats (stretches of consecutive repetitions of a single amino acid [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF], also known as polyX [START_REF] Mier | Context characterization of amino acid homorepeats using evolution, position, and order: Characterization of Amino Acid Homorepeats[END_REF]), are not always codified by pure codon repeats. However, in most cases, the DNA replication slippage mechanism, causative of the generation of homorepeats, produces DNA repeats that simply translate to homorepeat sequences [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF] ). Synonymous point mutations within DNA repeats translating to homorepeats have been described to be evolutionarily selected in some cases to hamper the DNA slippage mechanism and to maintain a controlled non-toxic length [START_REF] Rolfsmeier | Stabilizing effects of interruptions on trinucleotide repeat expansions in Saccharomyces cerevisiae[END_REF][START_REF] Mier | Glutamine Codon Usage and polyQ Evolution in Primates Depend on the Q Stretch Length[END_REF].

Longer and less perfect repeats forming 3D structures do not necessarily translate from repeated DNA. For example, TIM-barrels have evolved by gene duplication and fusion [START_REF] Lang | Structural Evidence for Evolution of the β/α Barrel Scaffold by Gene Duplication and Fusion[END_REF], and are assembled by repeats at the secondary structure level, in this case, and an eightfold repeat of (alpha/beta) units [START_REF] Wierenga | The TIM-barrel fold: a versatile framework for efficient enzymes[END_REF].

Sequence complexity

At the amino acid level, regions with tandem repeats can be formed by sequences of very different complexity. Sequence complexity is defined as the divergence of the residues forming a sequence or region from the expected background in a complete dataset in terms of usage and periodicity. There is a full range of examples from low to high complexity, from homorepeats to globular proteins. The shorter the repeats the lower the complexity of the resulting sequence. Repeats of length one exemplify this perfectly. Homorepeats (polyX) represent the sequence with the lowest possible complexity. Repeats of short lengths bias the sequence as well because the repetition of the pattern only allows for a few amino acids. Only when the repeat length is large enough to accommodate a rich composition of amino acids can repeats eventually be formed by complex sequences. The complexity of the repeats suggests disorder. It has been observed that perfect repeats tend to be disordered [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF]. This is because perfect repeats reflect a recent duplication event, and generally, repeat duplications are easier to accommodate in disordered regions. However, when the lengths of the repeats become very short (and complexity reduces), this correlation vanishes because the structural properties of the repeat region depend more on the properties of the dominant amino acid. For repeats of length one, even though they all have the same level of sequence complexity, the polyQ region of human Huntingtin (UniProtKB acc.:P42858) has alpha-helical conformation [START_REF] Urbanek | Flanking regions determine the structure of the poly-glutamine in Huntingtin through mechanisms common among glutamine-rich human proteins[END_REF], while the polyS region of the bovine protein FAM193B (UniProtKB acc.:A7MB40) is disordered.

Repeats with high complexity assemble to form entire domains, such as the beta-barrel structure in which protein CymA (UniProtKB:Q48391) folds into (PDB code: 4D51, van den [START_REF] Van Den Berg | Outer-membrane translocation of bulky small molecules by passive diffusion[END_REF], or the betapropeller formed by WD repeats in the bovine protein GNB1 (UniProtKB acc.:P62871), (PDB code: 1A0R; [START_REF] Loew | Phosducin induces a structural change in transducin beta gamma[END_REF]. In these two examples, each of the repeats is long enough (about 40 amino acids), so they can have a rich amino acid composition and gain beta structure.

Conservation

Tandem repeat variation by means of unit gain/loss has been proposed as a source of the genetic variability needed for fast adaptation (Marcotte et al., 1999), which implies that conserved repeats might be a telltale sign of functional importance. Sequence conservation between units of the same protein has been proposed to infer events of unit gain through duplication of a single unit [START_REF] Björklund | Expansion of protein domain repeats[END_REF].

In terms of repeat conservation across species, there seems to exist a variability in the degree of global conservation, which is organism-dependent. A study about human tandem repeat evolution by unit phylogeny [START_REF] Schaper | Deep conservation of human protein tandem repeats within the eukaryotes[END_REF], shows that 61% of human repeats are conserved, i.e. there is no evidence of unit acquisition/loss, at least from the root of mammals, while perfect separation occurs in only a few cases and seems to be more associated with certain types of repeats, such as zinc-finger proteins. However, in plants, although repeats are also highly conserved, there is evidence of highly mutable tandem repeats, and interestingly, these sometimes appear on proteins that are involved in pathogen defense, such as some LRRs belonging to R genes [START_REF] Schaper | The evolution and function of protein tandem repeats in plants[END_REF].

Exon-bordered and not

In Eukaryotes, it has been suggested that the evolution of tandem repeat folds could be driven by exon duplication and reshuffling [START_REF] Street | The Role of Introns in Repeat Protein Gene Formation[END_REF][START_REF] Björklund | Expansion of protein domain repeats[END_REF][START_REF] Schaper | The evolution and function of protein tandem repeats in plants[END_REF]. In this scenario, a single exon encodes for one structural repeat, thus, in cases of duplication or shuffling the new segment is usually structurally compatible with the old one. Proteins where multiple consecutive exons of similar length encode for structures that are similar and symmetric [START_REF] Haigis | Evolution of ribonuclease inhibitor by exon duplication[END_REF][START_REF] Light | The evolution of filamin-a protein domain repeat perspective[END_REF] support the hypothesis of evolution through exon duplication [START_REF] Paladin | A novel approach to investigate the evolution of structured tandem repeat protein families by exon duplication[END_REF], but no unique conclusion can be drawn for all repeat folds [START_REF] Street | The Role of Introns in Repeat Protein Gene Formation[END_REF][START_REF] Schaper | Deep conservation of human protein tandem repeats within the eukaryotes[END_REF] as this is the case for some repeat families and not for others. In line with this observation, it was established that structural domains tend to be exon-bordered while disordered regions do not [START_REF] Smithers | Why genes in pieces?'-revisited[END_REF]. In terms of stability, repeat domains fall in-between these two categories due to their cooperative folding pathways.

Even within the same repeat topology [START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF], ⍺ -solenoids, some repeat families, such as Ankyrin repeats, were demonstrated to be exon-bordered while others such as Tetratricopeptide repeats, are encoded by a unique exon spanning the entire repeat array [START_REF] Paladin | A novel approach to investigate the evolution of structured tandem repeat protein families by exon duplication[END_REF]. Other cases of repeat proteins show a complex repeat/exon pattern where the phasing is maintained, but different exons correspond to a different number of repeats [START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF]. Comparative analysis of the known isoforms generated by alternative splicing of TR-containing proteins shows that, as a rule, their different regions have an integer number of repeats and these changes do not cause serious perturbations in the overall 3D structure [START_REF] Osmanli | The Difference in Structural States between Canonical Proteins and Their Isoforms Established by Proteome-Wide Bioinformatics Analysis[END_REF]. At the same time, these structural changes create patches of new surfaces that can lead to the modification of protein functions.

Structure dichotomies

Flexibility

There have been reports of an overlap between proteins predicted to contain intrinsically disordered regions and proteins with tandem repeats. One reason is that tandem repeats are enriched in disorderpromoting residues, such as Gly and Ser [START_REF] Delucchi | A New Census of Protein Tandem Repeats and Their Relationship with Intrinsic Disorder[END_REF]. This is especially true for homorepeats, predominantly composed of hydrophilic and small residues, while large aliphatic, aromatic residues and Cys are rare [START_REF] Chavali | Amino acid homorepeats in proteins[END_REF][START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF]. Analysis of the human proteome in Swiss-Prot reveals that structured and unstructured repeat proteins are different in terms of repeat unit length and the number of repetitions. Unstructured repeat proteins, detected by overlapping the repeat annotation by Swiss-Prot and the disorder prediction from MobiDB-lite [START_REF] Necci | MobiDB-lite 3.0: fast consensus annotation of intrinsic disorder flavors in proteins[END_REF], mostly feature units of very short length and are repeated several times. The length of disordered repeat units varies considerably, ranging from less than ten amino acids to more than 60. STRiPs instead, identified in the human Swiss-Prot proteome from the repeat structures database RepeatsDB [START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF], usually have longer (between 20 and 60 residues long) and the number of repetitions corresponding to the different length does not vary as much as for disordered repeats. These observations are coherent with the structural classification of repeats proposed in [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF]. Furthermore, it was shown that increasing perfection of tandem repeat repetitiveness correlates with a stronger tendency to be unstructured [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF]. There are interesting counter-examples such as the microbial cell surface protein SasG, which has perfect repeats of G5 and E domains and, from a sequence perspective, are predicted as disordered repeats. Although they are unstable in isolation, these repeats fold cooperatively into globular domains when expressed in tandem arrays [START_REF] Gruszka | Cooperative folding of intrinsically disordered domains drives assembly of a strong elongated protein[END_REF].

One highly disordered repeat protein with low complexity is Mucin-16, which forms a protective barrier in the mucosa. It is also used as the antigen in a serum assay for monitoring ovarian epithelial cancer. The protein consists of one long extracellular region rich in Thr and Ser, which is heavily glycosylated, a single transmembrane domain and an intracellular domain. The extracellular region contains 16 SEA (Pfam ID: PF01390) domains linked by low complexity/disordered regions. Another protein with repeated low complexity regions is the Huntingtin (HD_HUMAN) protein [START_REF] Martin | Identification of a post-translationally myristoylated autophagy-inducing domain released by caspase cleavage of huntingtin[END_REF]. This protein has one 21 residue long polyQ region at the N-termini, and two shorter polyP regions. In addition, it contains more than 30 HEAT tandem repeats. The structure of this protein has been solved in complex with HAP1 [START_REF] Guo | The cryo-electron microscopy structure of huntingtin[END_REF].

A repeat protein where the lines between structure and disorder are blurry is nebulin [START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF][START_REF] Yuen | Nebulin: big protein with big responsibilities[END_REF]. Nebulin has a very interesting repeat structure, where seven domains, often covering four exons, are repeated in tandem [START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF]. These seven domains comprise one binding domain to an actin filament. The human nebulin protein contains about 35 of these sevendomain repeats, while other proteins, such as nebulette, contain fewer repeats. The nebulin protein is not predicted to be disordered, and secondary structure predictions predict one or two helices per domain. However, no nebulin structure is available and attempts to predict the structure have proven fruitless [START_REF] Vlassi | Short tandem repeats in the inhibitory domain of the mineralocorticoid receptor: prediction of a β-solenoid structure[END_REF].

A number of proteins with tandem repeats fold in stable 3D structures [START_REF] Wierenga | The TIM-barrel fold: a versatile framework for efficient enzymes[END_REF][START_REF] Björklund | Expansion of protein domain repeats[END_REF][START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF]. Typically, these proteins have long (more than ten residues) and imperfect repeats with high-complexity sequences.

Shape

Most proteins with aperiodic sequences have globular shapes. In contrast, proteins containing tandem repeats fold into structures having a variety of different shapes, which includes, in addition to globular shapes, elongated shapes and ring-like shapes (Figure 1A). The elongated molecules, which are predominantly formed by solenoid structures, are especially varied in shapes ranging from straight (Figure 1B) and twisted (Figure 1C) to curved (Figure 1D) rods [START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF]. Among these varieties of shapes, one can distinguish two major arrangements: ( 1) an open arrangement with, in principle, an unlimited number of repeats and (2) a closed one with a defined number of repeats. A typical example of an open shape would be a beta-solenoid and of closed one would be a beta-propeller (Figure 1A).

Long and short repeats

Analysis of the known 3D structures of proteins with repeats suggested a classification that subdivides them based on their repeat length and this classification allows streamlining this high diversity of the structures [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF][START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF]. Based on repeat length, the structures with repeats can be broadly divided into five classes. Class I includes repeat lengths of 1-2 residues, and these proteins can form crystalline aggregates. Class II with repeat units of 3-5 residues covers fibrous structures such as collagen or alpha-helical coiled-coils; Class IIIelongated structures where the repetitive units require each other for structural stability such as solenoid proteins; Class IVclosed repetitive structures, which include TIM-barrels and b-propellers and Class Vbead on a string structure.

Folding

Short tandem repeats with 1 or 2 residue units (Class I) are frequently composed of hydrophilic amino acids coding for intrinsically disordered regions. However, when these tandem repeats have potential to form 3D structures, they self-assemble together in aggregates [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF]. Known fibrous proteins (Class II), such as collagen or 𝛼-helical coiled-coils, fold into regular structures upon oligomerization. In some cases, for example for collagen, folding represents a multistep process. This behaviour is functionally relevant, allowing the collagen triple-helix to be formed only after transportation through the cytoplasm to the extracellular matrix [START_REF] Ishikawa | A molecular ensemble in the rER for procollagen maturation[END_REF]. The folding paradigm for Class III TRPs, especially solenoids, has been addressed by different authors in the literature [START_REF] Kajander | A new folding paradigm for repeat proteins[END_REF][START_REF] Barrick | Folding landscapes of ankyrin repeat proteins: experiments meet theory[END_REF]. Different studies, both computational and experimental, show that the folding mechanisms of these proteins are very diverse and cannot be generalized [START_REF] Galpern | Evolution and folding of repeat proteins[END_REF][START_REF] Espada | Repeat proteins challenge the concept of structural domains[END_REF]. For example, both the Ankyrin domain of Drosophila melanogaster Notch protein and the LRR of Internalin B of Lysteria monocytogenes display fully cooperative (all-or-none transitions) folding behaviour [START_REF] Courtemanche | Folding thermodynamics and kinetics of the leucine-rich repeat domain of the virulence factor Internalin B[END_REF][START_REF] Bradley | Limits of Cooperativity in a Structurally Modular Protein: Response of the Notch Ankyrin Domain to Analogous Alanine Substitutions in Each Repeat[END_REF]. However, within the LRR domain of PP32, the folding process begins with the C-terminus, potentially acting as a catalyst for the subsequent folding of the remaining structure [START_REF] Dao | Capping motifs stabilize the leucine-rich repeat protein PP32 and rigidify adjacent repeats[END_REF].

There is also evidence of parallel folding pathways for consensus ankyrin repeats in which the nuclei of folding can start in different places, increasing the folding rate with chain length [START_REF] Aksel | Direct Observation of Parallel Folding Pathways Revealed Using a Symmetric Repeat Protein System[END_REF]. Closed (Class IV) TRPs are also thought to fold in a similar way. Beads on a string TRPs (class V) are different, in that they are composed of consecutive globular domains. From a folding perspective, these TRPs can be both structurally autonomous, i.e. they can fold individually and do not require the neighboring repeats for stabilization, or they might be able to fold individually but are stabilized through inter-domain interactions, as for example in the Spectrin protein [START_REF] Petersen | Analysis of Tandem Repeat Protein Folding Using Nearest-Neighbor Models[END_REF][START_REF] Batey | Apparent cooperativity in the folding of multidomain proteins depends on the relative rates of folding of the constituent domains[END_REF]. of sequence identity between the repeat units in E is similar to or higher than the examples shown in panels A-D, but the structures of the repeat units are more variable (e.g., the length of the beta strands changes from unit to unit).

Repetitiveness dichotomies

Feature

Protein coverage

Protein structural tandem repeats fold into repeated structural units that pack against each other forming compact domains (Andrade et al., 2001a). As such, one could say that the properties that apply in general to domains being units of evolution, function and structure apply also to domains formed by tandem repeats. Therefore, it is not too difficult to find examples of proteins entirely formed by a domain of tandem repeats, multiple domains with only some being tandem repeats, and even those combining more than one domain formed by tandem repeats (either of the same type or of different types). A particularity of these domains is their flexibility and evolutionary adaptability, which made them very appropriate for interactions with other proteins. The ribonuclease inhibitor is a protein of around 450 amino acids entirely composed of Leucine-rich repeats (LRRs) and its structure solved in complex with ribonuclease A shows how the beta-sheet formed by consecutive repeats coils around the targeted protein [START_REF] Kobe | A structural basis of the interactions between leucine-rich repeats and protein ligands[END_REF]. Huntingtin is an example of a very large multidomain protein that alternates several domains composed of HEAT repeats, covering approximately 75% of the sequence, with non-repeatcontaining domains [START_REF] Guo | The cryo-electron microscopy structure of huntingtin[END_REF]. In such a protein, the function of flexible tandem repeat domains, protein interaction, is dominant. Huntingtin is known to interact with hundreds of proteins, in a multiplicity of interaction sites modulated by post-translational modifications and compositionally biased regions [START_REF] Harjes | The hunt for huntingtin function: interaction partners tell many different stories[END_REF][START_REF] Kastano | The Role of Low Complexity Regions in Protein Interaction Modes: An Illustration in Huntingtin[END_REF]. In contrast, there are large proteins with a small fraction composed of tandem repeats, where protein interaction function is not dominant. One example is the mineralocorticoid receptor, which contains a domain of about 150 amino acids composed of repeats of approximately 10 amino acids [START_REF] Vlassi | Short tandem repeats in the inhibitory domain of the mineralocorticoid receptor: prediction of a β-solenoid structure[END_REF]. This protein has other domains, for example, to interact with DNA for transcriptional control and to respond to a hormone, and the structure of these globular domains is known but not that of the tandem repeats. In this case, the tandem repeat domain holds many serine residues that are the target of phosphorylation. It was hypothesized that the domain is structured in the de-phosphorylated state and becomes unstructured upon phosphorylation. In this case, the tandem repeat domain could have a function in protein interaction regulated by phosphorylation. Evolutionary analyses suggest that, while tandem repeats ensembles are propitious to increase or decrease by addition of extra repeats or by their removal, respectively, examination of homologs suggests little flexibility once the tandem repeat domain is established [START_REF] Kamel | REP2: A Web Server to Detect Common Tandem Repeats in Protein Sequences[END_REF]. Therefore, the examples above of proteins that include tandem repeat domains are stable when different family members are compared, with respect to the fraction of the protein covered by tandem repeats.

Variability in the number of repeats

There are repeats that form elongated structures (e.g. TPRs, LRRs, alpha-solenoids, etc). Those have great variability in the number of repeat units since there is no constraint of the length they can reach. In contrast, repeats that form closed structures (like barrels or propellers) have a tendency to be much more constrained in the number of units. This feature is so definitory that in theory, even in the absence of any structural information, it should be possible to know if a repeat is forming open or closed structures by analyzing the distribution of the number of repeat units observed in many proteins: repeats forming open structures have a distribution in the number of repeats that decreases continuously versus the number of units, whereas repeats forming closed structures tend to occur in multiples of the canonical number of units of the repeat domain since sometimes more than one of these closed structures can occur within a protein sequence (Andrade et al., 2001a).

Insertions

The modularity and symmetry of tandem repeat structures can be sometimes interrupted by non-repetitive segments. These segments are commonly referred to as "insertions", and can be found either inside or inbetween units. Structurally, insertions serve no purpose in maintaining the stability of the repeat fold, but instead, they might provide the ability to perform specific functions, such as binding. For example, some alpha integrins have a von Willebrand factor type A domain inserted in their propeller regions, which contains a metal-ion-dependent adhesion site (MIDAS) [START_REF] Takada | The integrins[END_REF]. Another example of functional insertions inside a repeat unit is the insertion of a helix or a bigger domain in beta-barrels, which regulate their opening and closing, like in the case of Retinol-binding protein 2 (P50120, PDB code: 4ZGU) [START_REF] Chen | Crystal structure of apo-cellular retinoic acid-binding protein type II (R111M) suggests a mechanism of ligand entry11Edited by I. A. Wilson[END_REF] or the bacterial porin oprP (P05695, PDB code: 2O4V). Smaller insertions, like those composed of longer loops, can also be functional. For example, it has been proposed that the longer loops present in the beta-helix protein Pertactin of Bordetella pertussis can help in immune evasion by epitope masking [START_REF] Hijnen | The role of peptide loops of the Bordetella pertussis protein P.69 pertactin in antibody recognition[END_REF].

Repeat perfection

Proteins that are able to fold and have the same amino acid sequence usually adopt the same 3D structure.

Similarly, if a protein has an array of perfect tandem repeats in its sequence, i.e. every repeat has exactly the same sequence, each repetitive unit usually has the same 3D structure (examples, PDB code: 1NA0 designed TPR structure and PDB code: 3UGM TAL effector with HEAT-like repeats and PDB code: 4YCW, P. anserina TPR containing protein [START_REF] Marold | A Naturally Occurring Repeat Protein with High Internal Sequence Identity Defines a New Class of TPR-like Proteins[END_REF]). Repeat perfection can be estimated by a parameter called Psim [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF], in which Psim= 1 represents total perfection, and values of 0.7 ≤ Psim<1 represent nearly perfect repeats. However, protein tandem repeats are frequently not perfect, containing a number of mutations (substitutions, insertions, deletions) accumulated during evolution. In reality, naturally occuring perfect tandem repeats seem to be very rare, with only a very low percentage of them having a Psim= 1 [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF], and most of which adopt disordered conformations. Most of the time, the decrease of the amino acid sequence similarity between repeat units leads to the increase of the difference in their 3D structure, but the conservation of specific amino acids highlights their importance for the maintenance of the repeat fold. (Example, PDB code: 1DAB, pertactin). However, an interesting case is the Pumilio family (PFAM Identifier: PF0806), also known as PUF repeats, composed of proteins that regulate translation and mRNA stability of eukaryotic organisms including mammals, flies, worms, slime mold, and yeast [START_REF] Zamore | The Pumilio protein binds RNA through a conserved domain that defines a new class of RNA-binding proteins[END_REF]. This is a good example of structure perfection and sequence degeneration. On one hand, the repeat units show a high structural similarity (average TM-Score of 0.75) and, on another hand, the average sequence identity between units is 26 percent (Supplementary Figure 1).

Discussion

Repeat evolution

By tracing the similarity between repeat units it is possible to learn more about the evolutionary processes for a particular repeat family. At the moment of duplication, two repeats are identical both at DNA and amino acid levels, but then by time, they will diverge. This means that two repeats that are more similar have a more recent ancestry than repeats that are more different. When comparing the similarity of repeats, it was found that for most families adjacent repeats are, on average, less similar to each other than repeats separated by a few repeats [START_REF] Björklund | Expansion of protein domain repeats[END_REF]. However, repeats further away are even less similar, and the exact patterns vary from family to family. The most intriguing family is nebulin, which almost exclusively seems to be duplicated in groups of seven repeats [START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF]. We have interpreted this as the most likely mechanism is a tandem duplication that favours duplication of identical (or highly similar) DNA segments.

Structure/unstructured

One of the first questions to answer when approaching a repetitive protein to predict its 3D structure is whether it is structured or not. Today, thanks to a number of methods for prediction of IDRs we can answer this question with some accuracy [START_REF] Necci | Critical assessment of protein intrinsic disorder prediction[END_REF]. In addition, proteins with tandem repeats have several supplementary correlations, which can improve this prediction. For example, the increasing perfection of repetitiveness correlates with a stronger tendency of tandem repeats to be unstructured [START_REF] Jorda | Protein Homorepeats: Sequences, Structures, Evolution, and Functions[END_REF]. Our analysis based on Human repeat proteins in Swiss-Prot also suggests that the shorter the length of the repeats, the less structured the tandem repeats are. At the same time, the shorter the repeat length, the lower is their complexity [START_REF] Mier | Disentangling the complexity of low complexity proteins[END_REF]. Thus, we can also assert that the tandem repeats with low-complexity sequences are most probably unstructured.

Future perspectives repeats and structure prediction

In December 2020 DeepMind demonstrated at CASP14 that the structure of virtually all, well folded single domain, proteins can be predicted at an accuracy close to what can be obtained experimentally [START_REF] Laine | Protein sequence-to-structure learning: Is this the end(-to-end revolution)[END_REF][START_REF] Alquraishi | Machine learning in protein structure prediction[END_REF]. For a long time, it was believed that repeat proteins caused special challenges for co-evolution based structure prediction methods. However, recently it was shown that the latest, deeplearning-based methods, can predict the structure of many repeat proteins [START_REF] Bassot | Accurate contact-based modelling of repeat proteins predicts the structure of new repeats protein families[END_REF].

In this study, we show that about 90% of the repeat proteins can be accurately predicted. Further, we also provide novel, most likely correct, multiple repeat models for 41 out of 48 PFAM families lacking a protein structure. The seven families where no reliable structure is predicted include two families with short motifs C_tripleX (PF02363) and Lipoprotein_15 (PF03640), (Baker model), two membrane-associated families SVM_repeat (PF13753), Ish1 (PF10281), two short families, Nebulin (PF00880), INT_rpt (PF14882) and one longer the WD repeat and coiled-coil-containing protein family (PF15390). Models for all these seven families are available from Pfam for single repeat units.

As mentioned above many repeat proteins contain disorder, if these proteins have a structure in some physiologically relevant environments and if such structures can be predicted remains to be seen.

Likely the latest progress by DeepMind will make these early attempts to model these repeat proteins outdated, once they are applied to repeat proteins en masse. It is likely that the main challenge will not be to model the individual proteins but to model the interaction of repeat proteins. Here some progress has been made both for homomeric [START_REF] Quadir | Predicting interchain contacts for homodimeric and homomultimeric protein complexes using multiple sequence alignments of monomers and deep learning[END_REF] and heteromeric interactions [START_REF] Baek | Accurate prediction of protein structures and interactions using a 3-track network[END_REF]. However, these have not yet been applied to repeat proteins, but we see no major reason for these strategies not to work on at least some repeat proteins, promising a bright future for the structural analysis of repeat proteins. The regularity, modularity and linearly arrayed structures of TRPs make them attractive targets for protein design [START_REF] Javadi | Tandem-repeat proteins: regularity plus modularity equals designability[END_REF][START_REF] Brunette | Exploring the repeat protein universe through computational protein design[END_REF]. However, there are several challenges in protein design involving TRPs such uas inefficient self-assembly, control of repeat-protein curvature, stability, diverse inter-repeat geometry, folding kinetics and undesired higher-order structures that have to be addressed [START_REF] Doyle | Rational design of α-helical tandem repeat proteins with closed architectures[END_REF][START_REF] Hallinan | Design of functionalised circular tandem repeat proteins with longer repeat topologies and enhanced subunit contact surfaces[END_REF][START_REF] Brunette | Exploring the repeat protein universe through computational protein design[END_REF]. The improvements in structure prediction methods have the potential to greatly facilitate the design of tandem repeat proteins with desired properties. This could lead to more efficient design processes and the development of novel proteins for various applications in biotechnology, medicine, and research. In recent work, proteins with repeating units were designed to bind peptides with repeating sequences, and geometric hashing was used to identify compatible protein backbones and peptide-docking arrangements [START_REF] Wu | De novo design of modular peptide-binding proteins by superhelical matching[END_REF]. Furthermore, the progress made in natural language processing has enabled the development of protein language models, with ProGPT2 being one example [START_REF] Ferruz | ProtGPT2 is a deep unsupervised language model for protein design[END_REF]. These models have the capability to produce sequences that exhibit distant relationships to natural protein sequences and possess structures that resemble those found within the known structural space, even including non-idealized complex structures.

Improve repeat annotation

As it has been mentioned throughout this work, repeat proteins present multiple dichotomies. These dichotomies represent a challenge when it comes to repeat annotation. RepeatsDB [START_REF] Paladin | RepeatsDB in 2021: improved data and extended classification for protein tandem repeat structures[END_REF] is a structured tandem repeat proteins database that serves as an important source of both manually and automatically annotated experimental protein structures for the scientific community. The database provides the user with information about start and end of regions, units and insertions, as well as classification. Currently, computational methods to automatically detect STRPs lack accuracy, and their long execution times defy their application on big structural databases. Consequently, manual curation of repeat protein structures is a time consuming task, which requires human inspection of every structure, even those belonging to the same protein. Expanding the annotation of the repeat folds is of utmost importance for developing and improving automatic detection methods, as well as for broadening the classification of repeats, among other tasks.

Disease

Since tandem repeats offer easy to evolve, large and flexible structures very appropriate for interacting with other proteins (Andrade et al., 2001b), and many disease-causing mutations involve modifications of the protein interaction network (Yeger-Lotem and Sharan, 2015), it can be expected that many tandem repeat proteins will be associated with genetic diseases. However, there does not seem to be a significant enrichment of disease association in tandem repeat proteins. For example, a query of the human reviewed proteins in the current version of UniProt (2023_03) returns 20,423 proteins of which 5,006 are annotated as involved in disease (24.6%). For comparison, of the 1,957 human reviewed proteins annotated as having a repeat, 580 were involved in disease (29.6%), which is a higher value but not terribly different. More specifically, the fraction of disease-related proteins can be even lower for some types of tandem repeats, e.g. 62 of 312 (19.9%) proteins annotated as having LRR tandem repeats. One could hypothesize that while the folding of some TRPs seems more unstable than that of globular proteins, this flexibility could allow them to accommodate more mutations, which is actually observed in the inter-repeat variability of many TRPs, which would mean them being less associated with genetic disease than other proteins. For example, 17 disease-causing mutations have been discussed recently in the ANKRD11 protein, and none of them fall in the domain of Ankyrin repeats contained by this protein [START_REF] Parenti | ANKRD11 variants: KBG syndrome and beyond[END_REF].

Conclusion

In this review we have shown how TRPs cover a wide range of different properties, making them difficult to pigeonhole into a single class with specific characteristics. Rather, TRPs should be seen as a mixed bag of different sub-phenomena which are partially contradicting each other. This plasticity is however in contrast with a subset of TRPs which can be considered "well-behaved", in the sense that they share a common set of identifying features. This subset however is of interest, as it will allow us to draw some biological conclusions on the underlying phenomena. We will therefore now endeavour to define this subset, which we will tentatively call "structured tandem repeat proteins" or "STRPs", as an operational definition (Figure 3 and Table 4). STRPs are tandem repeat proteins whosefor which their structure can be solved bywith structural biology experiments, such as X-ray crystallography or electron microscopy, or likely well predicted by state-of-theart structure prediction methods like AlphaFold [START_REF] Jumper | Highly accurate protein structure prediction with AlphaFold[END_REF]. STRPs have clear secondary structure propensities and form regular tertiary structures, which can be part of large molecular assemblies. Typically, these proteins fall into Classes III (i.e. elongated) and IV (i.e. closed) of Kajava's classification of protein tandem repeats. They fold non-independently, but their folding patterns cannot be generalized beyond this characteristic. As such, there is little room for flexibility or intrinsic disorder, which is limited to partial folding of certain units as in the case of Ankyrin repeats (e.g. IKBalpha). The sequence features of STRPs are repeat units of at least five residues which also exhibit high sequence complexity.

STRPs can be highly degenerate in sequence while maintaining a similar structure and exhibit a variable number of repeat units, suggesting a decoupling between structural size and protein function.

STRPs can be thought of as the complement to low complexity regions (LCRs) in proteins [START_REF] Mier | Disentangling the complexity of low complexity proteins[END_REF]. Where the latter is defined primarily through a set of sequence features, STRPs are predominantly defined from their structural features. What both LCRs and STRPs have in common, is their difference in behaviour from regular globular domains. The operational definition proposed for STRPs opens the door for further research in order to better understand their function and biological implications.

Figure 1 .

 1 Figure 1. Examples of shapes adopted by domains of tandem repeats. Identifiers, definition and classification correspond to entries in RepeatsDB. (A) Closed ring. 5eamA. WD repeat-containing protein 5 (aa 47-333), 7 units. Hierarchical classification: 4 Closed repeats, 4 Propeller, 1 Beta propeller with flat blades, 1 WD40 repeat. (B) Straight rod. 1ezgA. Crystal structure of antifreeze protein from the beetle, Tenebrio molitor (aa 8-79), 6 units. Hierarchical classification: 3 Elongated repeat, 1 Beta-solenoid. (C) Curved rod. 4u09A. Lic12759 (aa 44-417), 16 units. Hierarchical classification: 3 Elongated repeat, 2 Alpha/beta solenoid, 1 High curvature alpha/beta solenoid, 1 Leucine Rich Repeat. (D) Twisted rod. 4by2A. Spindle assembly abnormal 4 (Sas-4) (aa 73-203), 7 units. Hierarchical classification: 3 Elongated repeat, 4 Beta hairpins, 2 Single-layer beta-hairpin, 5 High curvature singlelayer beta-hairpin. (E) Structure with imperfect structural alignment. 2r19B. Protein yhbn (aa 35-165), 4 units. Hierarchical classification: 3 Elongated repeat, 4 Beta hairpins, 2 Single-layer beta hairpin, 1 Beta-burrito. The level

Figure 2 .

 2 Figure 2. Insertions. A) Propeller of Integrin alpha-L (P20701, PDB code: 5E6U) with a von Willebrand factor type A domain (in dark gray) inserted between its blades. B) Beta-barrel of Retinol-binding protein 2 (P50120, PDB code: 4ZGU) with an alpha-hairpin insertion (in dark gray).

Figure 3 .

 3 Figure 3. Overview of STRP features. Single protein chain definition

Table 1 -

 1 Table 1 summarizes TRP sequence dichotomies and provides examples of repeat proteins representing each feature. TRP sequence dichotomies. Examples of TRPs for each dichotomy.

	Feature	Dichotomy	Sample protein	UniProtKB
				accession number
	DNA	Repetitive	TBP_HUMAN;	P20226;
			PolyQ in MEF2A_HUMAN	Q02078
		Non-repetitive	LPTA_ECOLI;	P0ADV1;
			E0RU15_SPITD	E0RU15
	Complexity	Low	S in PolyQ in HD_HUMAN	P42858;
			PolyF193B_BOVIN	A7MB40
		High	GBB1_BOVIN;	P62871;
			Q48391_KLEOX	Q48391
	Conservation	High	LST8_HUMAN;	Q9BVC4;
			PUM5_ARATH	Q9LJX4
		Low	TR10C_HUMAN;	O14798;
			FIP2_ARATH	Q9SE95
	Exons	Matching repeats	RINI_MOUSE;	Q91VI7;
			RCC1_HUMAN	P18754

Table 2 -

 2 TRP structure dichotomies. Examples of TRPs for each dichotomy.

Table 3 -

 3 TRP repetitiveness dichotomies. Examples of TRPs for each dichotomy.

Acknowledgements

The authors are grateful to Lisanna Paladin for initial help in the manuscript, and Jiachen Lu for helping in the manual curation of RepeatsDB. This work was supported by European Union's Horizon 2020 research and innovation programme under grant agreement No 823886 (H2020 MSCA-RISE "REFRACT") and based upon work from COST Action ML4NGP, CA21160, supported by COST (European Cooperation in Science and Technology).