Elke Schaper

Olivier Gascuel

Maria Anisimova
email: manisimova@hotmail.com

Deep conservation of human protein tandem repeats within the eukaryotes

Keywords: Protein evolution, tandem repeats, conservation, phylogenetic analysis

Tandem repeats (TRs) are a major element of protein sequences in all domains of life. They are particularly abundant in mammals, where by conservative estimates one in three proteins contain a TR. High generation-scale duplication and deletion rates were reported for nucleic TR units. However, it is not known whether protein TR units can also be frequently lost or gained providing a source of variation for rapid adaptation of protein function, or alternatively, tend to have conserved TR unit configurations over long evolutionary times. To obtain a systematic picture for proteins TRs, we performed a proteome-wide analysis of the mode of evolution for human TRs. For this purpose, we propose a novel method for the detection of orthologous TRs based on circular profile hidden Markov models. For all detected TRs we reconstructed bi-species TR unit phylogenies across 61 eukaryotes ranging from human to yeast. Moreover, we performed additional analyses to correlate functional and structural annotations of human TRs with their mode of evolution. Surprisingly, we find that the vast majority of human TRs are ancient, with TR unit number and order preserved intact since distant speciation events. For example, ≥61% of all human TRs have been strongly conserved at least since the root of all mammals, approximately 300 Mya ago. Further, we find no human protein TR that shows evidence for strong recent duplications and deletions.

The results are in contrast to high generation-scale mutability of nucleic TRs. Presumably, most protein TRs fold into stable and conserved structures that are indispensible for the function of the TR-containing protein. All of our data and results are available for download

Introduction

Tandem repeats (TRs) are sequence repetitions that occur right next to each other. They are typically classified by the length of the tandemly repeated unit into: microsatellites (<10 base pairs or bp), minisatellites (10-100 bp), and, albeit less widely-used, megasatellites (>100 bp) [START_REF] Gondo | Human megasatellite DNA RS447: copy-number polymorphisms and interspecies conservation[END_REF][START_REF] Thierry | Megasatellites: a new class of large tandem repeats discovered in the pathogenic yeast Candida glabrata[END_REF]. Nucleic TRs are often found to be polymorphic in terms of the number of TR units as a result of high unit gains/loss rates [START_REF] Gondo | Human megasatellite DNA RS447: copy-number polymorphisms and interspecies conservation[END_REF][START_REF] Vergnaud | Minisatellites: Mutability and Genome Architecture[END_REF][START_REF] Bhargava | Mutational dynamics of microsatellites[END_REF], though these rates are highly heterogeneous among TR loci.

Protein TRs are a major element of protein sequences in all domains of life. They are typically encoded by nucleic TRs in coding regions such that a TR unit duplication\loss generally does not involve a frameshift [START_REF] Toth | Microsatellites in Different Eukaryotic Genomes: Survey and Analysis[END_REF]. However, protein TR regions may span multiple exons. Protein TRs exhibit a high sequence diversity [START_REF] Marcotte | A census of protein repeats[END_REF][START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF], reflected in an equally high structural diversity [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF]. For instance, protein TRs may fold into fibrous structures, solenoids, or, for tandem repetitions of whole domains, 'beads on a string' organizations [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF]. On the other hand, protein TRs are also often associated with unstructured regions [START_REF] Tompa | Intrinsically unstructured proteins evolve by repeat expansion[END_REF][START_REF] Simon | Tandem and cryptic amino acid repeats accumulate in disordered regions of proteins[END_REF][START_REF] Jorda | Protein tandem repeats -the more perfect, the less structured[END_REF][START_REF] Szalkowski | Markov models of amino acid substitution to study proteins with intrinsically disordered regions[END_REF].

The high gains/loss rates of nucleic TRs were proposed to be suggestive of comparable high rates for protein TRs [START_REF] Tompa | Intrinsically unstructured proteins evolve by repeat expansion[END_REF]. In particular for micro-and minisatellites, examples of highly variable protein TRs were observed in all domains of life [START_REF] Macdonald | A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington's disease chromosomes[END_REF][START_REF] Sawyer | Natural variation in a Drosophila clock gene and temperature compensation[END_REF][START_REF] Coil | Intragenic tandem repeat variation between Legionella pneumophila strains[END_REF][START_REF] Butler | Evolution of pathogenicity and sexual reproduction in eight Candida genomes[END_REF][START_REF] Chevanne | WD-repeat instability and diversification of the Podospora anserina hnwd non-self recognition gene family[END_REF]; see [START_REF] Gemayel | Variable Tandem Repeats Accelerate Evolution of Coding and Regulatory Sequences[END_REF]Riegler et al. 2012 a review). Changes in protein TRs typically affect the protein sequence and the eventual folding and functionality of the protein product, leading to changes in phenotype or fitness. For example in human, the expansion of polyQ tracts in Huntingtin leads to Huntington's disease (MacDonald 1993 TR unit length l = 1), while in fruit flies, polyQ variation in the per gene tunes its circadian clock [START_REF] Sawyer | Natural variation in a Drosophila clock gene and temperature compensation[END_REF]. Other examples were observed for minisatellite TRs: An association of TR unit gains/losses with phenotypic traits was found in S. cerevisiae, where variation in flocculin TRs (! ~ 45 amino acids or aa) resulted in modulated cell adhesion properties [START_REF] Verstrepen | Intragenic tandem repeats generate functional variability[END_REF]); a similar association was proposed for several C. albicans genes [START_REF] Butler | Evolution of pathogenicity and sexual reproduction in eight Candida genomes[END_REF] e.g. l ~ 32 aa).

It has been argued that variation in functional TRs may provide a source of genetic variability allowing for fast adaptation [START_REF] Marcotte | A census of protein repeats[END_REF][START_REF] Levdansky | Coding tandem repeats generate diversity in Aspergillus fumigatus genes[END_REF][START_REF] Richard | Comparative genomics and molecular dynamics of DNA repeats in eukaryotes[END_REF][START_REF] Chevanne | WD-repeat instability and diversification of the Podospora anserina hnwd non-self recognition gene family[END_REF][START_REF] Riegler | Tandem repeat markers as novel diagnostic tools for high resolution fingerprinting of Wolbachia[END_REF], for example in an evolutionary arms race. Conversely, conservation of TRs may also be an indicator of functional relevance.

However overall, little is known at current about the evolutionary modes and time scales of protein TRs.

To study their evolution, the sequence similarity of TR units within a single TR may be analyzed to infer gains/loss events [START_REF] Björklund | Expansion of Protein Domain Repeats[END_REF][START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF][START_REF] Light | The evolution of filamin-a protein domain repeat perspective[END_REF]. For example, Björklund et al. used patterns of TR unit similarity to show that the duplication of multiple units is more frequent than the duplication of single units for common tandemly repeated protein domains [START_REF] Björklund | Expansion of Protein Domain Repeats[END_REF]). This approach is implicitly based on the assumption that the TR units evolved from a common ancestral unit and therefore can be described by a TR unit phylogeny.

For the related problem of gene paralogs arranged in tandem, gene phylogenies (also called duplication histories in this context), were shown useful for systematic studies of gene gains/loss events [START_REF] Elemento | Reconstructing the duplication history of tandemly repeated genes[END_REF][START_REF] Lajoie | Duplication and inversion history of a tandemly repeated genes family[END_REF]). Here, we use a similar idea to study the evolution of TR units. Compared to gene phylogenies, the analysis of TR phylogenies is challenging due to shorter unit lengths introducing errors in the reconstructed phylogenies. Yet, here we show that TR phylogenies display clear patterns that shed light on their evolution. Any observed TR region may have been conserved over a long evolutionary time scale, or alternatively, it may have originated very recently through rapid evolution. Without the study of orthologous TR regions from multiple species, it is impossible to deduce whether a TR is of a recent or ancient origin. To shed light on the age of a TR, one requires a mapping of TR unit gains/losses to speciation events, based on alignments of orthologous proteins with TRs from multiple species. This approach has been used to study the evolution of TR regions according to the TR unit number, similar to the analysis of microsatellite DNA data (see Bhargava and Fuentes 2010 for a review). Here, we expand this idea to conduct a systematic phylogenetic analysis of TR units from multiple species in order to test whether TR regions evolve rapidly or are predominantly conserved. Both rapid and conserved modes of evolution may uncover different functional categories of proteins, where the evolution of TRs is presumably shaped by their contribution to the function of the whole protein. For pairs of species, we build TR unit phylogenies including all TR units from the orthologous proteins in both species. The resulting "bi-species" TR unit phylogenies reflect both the ancestral expansion of the TR units before speciation, and lineage specific gains/losses after speciation (see Fig. 1A). Thus, this approach allows us to recognize TRs that have been conserved since the speciation event. For some proteins, such as the human TORC subunit LST8 (Fig. 1B), the conservation can be traced back deep to the common ancestor of human and yeast. On the other hand, we are also able to identify TRs that have been subject to recent TR unit gains/losses (e.g. Fig. 1C). Note that besides TR units gains/losses, other mechanisms such as intragenic conversion may lead to modifications in the TR configuration (i.e. number and order of TR units). An intragenic conversion event may be approximated by a TR unit loss that is immediately followed by a TR unit gain. When referring to gains/losses, we implicitly include such alternative mechanisms in the remainder of this paper.

In the following, we describe the multi-species analysis of TR unit phylogenies in detail, and introduce criteria to classify TRs according to their mode of evolution. We apply this approach in a proteome wide study on the evolution of human TRs with TR unit length ≥ 15 aa in comparison with orthologous TRs in 60 other eukaryotic species. For the vast majority of these human TRs, our analyses reveal a surprisingly sustained conservation of TR unit configurations (i.e. number and order of TR units) throughout the eukaryotic kingdom.

Lastly, we correlate the results with structural features of TRs, as well as functional annotations of TR-containing proteins, in order to better understand the origin and consequences of the different evolutionary modes. All material and data is available for download at http://www.atgc-montpellier.fr/TRE.

New approaches

To analyze the evolution of human TRs across the eukaryotic clade we developed a phylogenetic pipeline, which can be summarized as follows:

(1) TRs were annotated exhaustively in the human proteome using specifically devised circular profile hidden Markov models (cpHMMs).

(2) For each human TR-containing protein, orthology annotations were obtained from the complete proteomes of 60 other eukaryotic species from Ensembl Compara [START_REF] Vilella | EnsemblCompara GeneTrees: Complete, duplication-aware phylogenetic trees in vertebrates[END_REF][START_REF] Flicek | Ensembl 2013[END_REF]. For each annotated human TR, homologous TR regions in all orthologous proteins were searched using the corresponding cpHMM.

(3) The selected 60 species considered in our study are separated from the human lineage by a wide range of divergences, from chimp (the closest) and mouse, to zebrafish and baker's yeast (the furthest). Thus, comparisons of TRs in orthologous proteins in all pairs of species allowed us to describe the TR evolution since the speciation events of the species pairs. Taken together, these bi-species comparisons permitted to backtrack the conservation of human TRs throughout the eukaryotic clade. For this purpose, we reconstructed bi-species TR unit phylogenies for all pairs of TR-containing orthologs (Fig. 1). These phylogenies were evaluated to ascertain whether the human TR unit configurations have been conserved since speciation (Fig. 1B), or alternatively, became separated through gains or losses of TR units after speciation (Fig. 1C).

(4) The classification of TRs according to conserved and separated modes of evolution was correlated with functional annotations and other TR characteristics, notably the type of Pfam family.

Annotation of tandem repeats in the human proteome

To annotate consecutive repeat units in sequence data we have developed cpHMMs based on a sequence profile of a potential TR unit. In our model the match states describe the consensus positions of the TR unit (Fig. 2). In contrast to the standard profile HMM [START_REF] Eddy | Profile hidden Markov models[END_REF], we introduced transitions between the last and the first match states, so that one TR unit could be directly followed by the next, until no further match is found (pink, orange and red transitions in Fig. 2). This way, TR regions with an arbitrary number of units can be inferred. Furthermore, since TR units often do not have well-defined boundaries [START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF][START_REF] Szalkowski | Graph-based modeling of tandem repeats improves global multiple sequence alignment[END_REF], we assumed that a new TR was equally likely to start and end at any of the positions of a profile (blue transitions).

A set of potential TR unit profiles was obtained from known protein domains and de novo detection of TRs in the human proteome. Since the Pfam database [START_REF] Punta | The Pfam protein families database[END_REF][START_REF] Mistry | The challenge of increasing Pfam coverage of the human proteome[END_REF]) includes many prominent protein domains found in tandem, we used Pfam annotations to look for potential TRs. Currently, around 40% of the human proteomic sequence carry Pfam-A annotations. For all Pfam-A annotations we constructed cpHMMs, allowing the possibility that any Pfam-A domain might be repeated in tandem. As short and rare TRs are not expected to be part of the Pfam database, we additionally built cpHMMs from de novo TR detections. Due to algorithmic differences, the TR detection by existing de novo TR detection algorithms is highly disparate [START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF]. Thus, rather than using any single algorithm, we combined the TR predictions of four available algorithms

(Material & Methods).
Lastly, the cpHMMs were used to annotate human TRs. To control the number of false positive TRs, each annotation was statistically validated using a model-based likelihood ratio test [START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF]. In summary, we obtained a set of human TRs and corresponding cpHMMs.

Annotation of orthologous tandem repeats in eukaryotic species

To study the evolution of human protein TRs, we compared them to homologous TRs in orthologous proteins of eukaryotic genomes. Orthology annotations and protein-wide sequence data for 60 other eukaryotic species were obtained from Ensembl Compara [START_REF] Vilella | EnsemblCompara GeneTrees: Complete, duplication-aware phylogenetic trees in vertebrates[END_REF][START_REF] Flicek | Ensembl 2013[END_REF]. For each human TR, we applied the corresponding cpHMMs across the set of orthologous proteins to detect all homologous TRs.

Using phylogenetic patterns to study TR evolution

To systematically determine the mode of TR evolution, we studied bi-species TR unit phylogenies, assuming that all units have descended from an ancestral unit. In particular, for all human vs. non-human orthologous protein pairs in our dataset, we reconstructed phylogenetic histories of TR units similar to those in Figure 1. Compared to multi-species TR unit phylogenies, bi-species phylogenies are simpler to analyze, whilst containing sufficient information about the TR evolution in the human lineage. To ensure accurate phylogeny reconstruction, the TR units need to be informative about their gains/loss history. Therefore, we excluded from our analysis all short TRs with unit length < 15 as well as all TRs with < 4 TR units.

Reconstructed bi-species TR unit phylogenies helped us to determine whether TR unit duplications occurred before or after the speciation events separating both studied species. This permitted to classify the TR unit phylogenies according to different modes of evolution: long-standing TR unit conservation, and recent TR unit separation (Fig. 1). To analyze the phylogenetic patterns of bi-species TR unit phylogeny from species A and B, we calculated the following statistics:

• The TR unit numbers in the two orthologous proteins (A and B), ! ! and ! ! ;

• The number of cherries (i.e. pairs of leaves that share the parent node on the phylogeny; [START_REF] Mckenzie | Distributions of cherries for two models of trees[END_REF], ! ! , and the number of bi-species cherries, that is, formed by TR units of both species A and B, ! !" . For example, H2 and Y2 in Fig. 1B form a bi-species cherry, and it is ! ! = ! !" = 7 for the entire phylogeny.

• The conservation of TR unit order in bi-species cherries, measured by the Kendall rank statistic ! computed on the pairs of indices representing TR unit order. More precisely, TR units from the two species A and B were indexed by their order in the protein sequence from 1 to ! ! or to ! ! , respectively. This way, a pair of order indices was recorded for each bi-species cherry. For example, a bi-species cherry formed by the first TR unit in one species and the third unit in the other species has an index pair of !(1,3). If each of species A and B contain four TR units and their order is perfectly preserved, the index pairs will be (1,1), (2,2), (3,3) and (4,4) leading to !! = 1. For example, it is !! = 1 for the phylogeny in Fig. 1B.

• The parsimony score ! ! computed over the TR unit phylogeny on species labels A and B (see e.g. [START_REF] Felsenstein | Phylogenies from molecular sequences: inference and reliability[END_REF][START_REF] Steel | Distributions on bicoloured binary trees arising from the principle of parsimony[END_REF]. The parsimony score is equivalent to the number of splits on the phylogeny that are necessary to separate all TR units of species A from all TR units of species B, and is thus a measure for the separation of these TR units through gains and losses. For example, ! ! = 7 for the example phylogeny in Fig. 1B, where the speciation of A and B happened after the duplication of an ancestral TR unit in the ancestor of A and B. In contrast, ! ! = 1 for the example in Fig. 1C, indicating that the speciation event was followed by TR unit gains and losses in at least one lineage.

In the next sub-sections, we describe simple classification rules computed from these statistics to distinguish between TRs with conserved or separated TR configurations.

Detecting protein tandem repeat conservation

In one possible evolutionary scenario, no unit duplications or losses occurred in the TR region in neither lineage of two species after speciation: The ancestral TR unit configuration (i.e. number and order of TR units) is then fully preserved in the current day species. Directly after the speciation, the closest relative of any TR unit in the ancestral protein of species A is the (homologous) TR unit in the orthologous ancestral protein of species B (Fig. 1A). If no TR unit gains or losses occurred since speciation (Fig. 1B), the order and the number of TR units remains the same and the TR unit phylogenies fulfill ! ! = ! ! = ! ! = ! !" !and ! = 1. We call such TRs perfectly conserved between species A and B. Presumably, the numbers of perfectly conserved TRs would be underestimated in our analysis, mostly due to errors in phylogenetic reconstruction, but also in orthology annotation (see Material & Methods for details). To cushion errors in TR annotation and phylogeny reconstruction, we attributed strong TR unit conservation, if (max(! ! , ! ! ) ! -! ! !" ≤ 1), ! !" ≥ 4, and ! = 1. In comparison to perfect conservation, this classification rule allows that one TR unit may not have been detected, or that the ith TR unit in one species may not pair with the ith TR unit in the second species in one case (see examples of strongly conserved TR phylogenies in suppl. Fig. S2, Suppl. Mat.

online).

The false positive annotation of strong or perfect conservation is unlikely. For example, the probability of falsely assigning perfect conservation to a pair of random TRs with n TR units is 2.89 • 10 !! for n = 4, and as low as 7.40 • 10 !! for n = 5 (see Methods for the derivation, and Table 2 for p-values for ! ≥ 4). Thus, bi-species TR unit phylogenies displaying perfect conservation indicate that no TR unit gains or losses are likely to have occurred in either lineage since speciation. In comparison, the probability of assigning strong conservation by chance is higher with 1.88 • 10 !! for n=4 and 1.12 • 10 !! for n=5, albeit still sufficiently small for our attenuated measure to be reliable.

Based on these definitions we used multiple bi-species comparisons to backtrack the conservation of human TRs. This way, we can ascertain the conservation of a human TR up to the speciation time of human and the species most distant to human, for which perfect conservation of the TR was still observed. This speciation time should be considered as a lower boundary to the estimate of the actual time since when a human TR had been conserved. Note that we do not necessarily find the TR to be conserved among all other descendants since this speciation node. TR conservation may be obfuscated in some descendants due to errors in orthology annotation and phylogeny reconstruction. Also, some of the other descendent lineages might be subject to a different mode of TR evolution, with frequent unit gains and losses.

Detecting protein tandem repeat separation

The frequency of TR conservation in human proteome was contrasted with the frequency of TR separation, whereby all TR units from one species were more closely related to each other than to any TR unit in the other species, and vice versa. TR separation was evaluated based on the following rules. Two homologous TRs were assumed to exhibit perfect TR unit separation if ! ! = 1!(cf. Fig. 1C). As above, due to errors in tree reconstruction, TR pairs that are perfectly separated in reality might not appear separated into two clades on the inferred unit phylogeny. To account for some of these cases, we introduced the following relaxed condition: a pair of TRs exhibited strong separation when ! ! ≤ 2. In this case, the bi-species TR unit phylogeny can be partitioned into two or three monophyletic clades (see examples of strongly separated TR phylogenies in suppl. Fig. S3, Suppl. Mat. online).

In a more complex scenario, some TR units of the same TR region may be conserved, whereas others may undergo duplications and losses. To account for this case, we attributed difference in TR unit number to pairs of TRs with unit number difference ≥ 4.

Among others, the analysis of TR unit separation between closely related species allowed us to identify TRs that have undergone gains/losses recently. Potentially, such TRs might be subject to ongoing TR unit number changes. Note that errors in orthology annotation might lead to an overestimation of the numbers of separated TRs. On the other hand, overestimations due to phylogeny reconstruction errors are less likely. For example, the probability of falsely assigning perfect separation (strong separation) to a pair of random TRs with n TR units is 2.16 • 10 !! (1.88 • 10 !! ) for n = 4 and 5.44 • 10 !! (1.12 • 10 !! ) for n = 5 (see Methods for details, and Table 2 for p-values for ! ≥ 4).

Results

Distribution of TRs in human proteins and their eukaryotic orthologs

3,091 non-overlapping TRs (with ≥ 4 TR units of length ≥ 15) were detected in 2,532 (13%) of all 20,162 human proteins. Of all detected TRs, 356 were de novo annotations, 570 were zinc finger repeats, 225 were leucine rich repeats (LRRs), and 186 were WD40 repeats (Table 1A). In total, 193 different PFAM-A domains were found as repeated in tandem in at least one human protein. In the following, we refer to different TRs as of the same type if they were detected with the same cpHMM profile (describing either one of the 193 PFAM-A domains or the 356 distinct de novo detected TRs). The observed distribution of annotated TRs among the TR types was highly uneven, with 43% (70%) of all TRs described by just 1% (5%) of all TR types.

Table 1B shows the frequency of orthologous TRs and their level of conservation for prominent species and the most frequent TR types. To investigate the significance of a given TR for the TR-containing gene, we first tested whether the TR was equally old as the TRcontaining gene. For each human TR-containing gene we traced back the most distant ortholog in the other species (Fig. 3A). Similarly, for each human TR-containing gene we traced back the most distant ortholog that still contained at least four TR units (Table 1B, Fig. 3A). We found that almost all TRs were as ancient as the TR-containing gene, and were lost only in rare cases. For example, of all human TR-containing proteins, 90% had an ortholog in a non-mammal species, of which 94% also contained the homologous TR with at least 4 units. This implies that the TR is an essential component of the TR-containing protein.

The conservation of human protein TRs

To determine evolutionary ranges with evidence for TR conservation, we identified the species furthest to human for which either perfect conservation, or strong conservation was detected in the orthologous TR. For example, to establish conservation of a human TR at least to the root of the bilaterians, the human TR was compared to its orthologous TR -if presentin the non-bilaterian species available in our dataset, namely S. cerevisiae. The TR conservation between human and S. cerevisiae provided strong evidence for the conservation of the human TR since their speciation, thus beyond the first bilaterians. Further, the conservation of a human TR compared to its ortholog in any of the other 60 species indicates that it has been conserved at least since the speciation of chimp and human, thus well beyond the most recent common ancestor of all humans. This definition is cumulative, that is, the number of TRs that are conserved to the root of a given clade (e.g. bilaterians) is less than (equal to) the number of TRs conserved to the root of any nested clade (e.g. chordates). Fig. 3A summarizes the numbers of human TRs that have been conserved since different eukaryotic speciation events, ordered from the most recent (human/chimp) to the oldest (human/yeast). We found that 92% of all human protein TRs were strongly conserved, and 90% were perfectly conserved between human and at least one other species in our dataset. Surprisingly, such conservation was observed not only within closely related species: 61% of all protein human TRs were strongly conserved since the root of the mammalian clade, while 17% were strongly conserved since the root of the vertebrates. This shows that for the vast majority of TRs their mode of evolution is not marked by high rates of TR unit gain or loss.

Functional analysis of strongly conserved TRs

To better understand the functional constraints that require conservation of TRs, we contrasted the subset of human proteins containing TRs that were strongly conserved in at least one species beyond the mammals (1,896 TRs in 1,553 proteins) with all human TRcontaining proteins (3,091 TRs in 2,532 proteins). We studied the distribution of different TR types, as well as the enrichment of functional annotations for proteins with TRs using GOrilla [START_REF] Eden | GOrilla: a tool for discovery and visualization of enriched GO terms in ranked gene lists[END_REF].

TR types strongly conserved at least to the root of all mammals are diverse, spanning 81% of all annotated human TR types. The distribution of different TR types among the proteins with conserved TRs is highly biased. For example, more than half (58%) of all conserved TRs could be attributed to just 5% of all TR types. In other words, a handful of TR types were observed at very high frequencies (e.g., zinc finger, ankyrins or ANKs, LRR, WD40) while the majority of others appeared at low frequencies.

Interestingly, for a range of TR types such as the Armadillo repeat (ARM), the HEAT repeat and the PHD-finger, all human TRs have been conserved since the ancestor of mammals. Likely, the unit configuration of these TR types is essential to maintain protein function, be it for structural reasons, or due to the function of certain amino acids on specific TR units.

The high diversity of TR types found for conserved TRs was reflected in the diversity of functions performed by proteins with conserved TR types. A GO-term analysis of these proteins revealed enrichment in diverse biological processes, including prominently, stimuli response, cell adhesion, protein ubiquitination, locomotion, and regulation of development, particularly nervous system development. In terms of molecular function, proteins with conserved TR are enriched in particular in protein binding and catalytic activities (Fig. 4A).

To reveal the correlation of TR type and protein function, we linked the results of the GOenrichment analysis to the TR types found in the protein with enriched functions, as summarized in Fig. 4A.

The TR type with the largest number of conserved TRs was WD40 (Table 2). WD40 repeats are thought to form a !-propeller structure that serves as a rigid scaffold to mediate the assembly of multi-protein or protein-DNA complexes [START_REF] Stirnimann | WD40 proteins propel cellular networks[END_REF][START_REF] Xu | Structure and function of WD40 domain proteins[END_REF]. WD40 repeats interact with a wide variety of proteins, peptides and DNA, and are involved in diverse cellular functions facilitated by the large sequence diversity in the TR region [START_REF] Stirnimann | WD40 proteins propel cellular networks[END_REF]. At the same time, no WD40 repeat has been annotated with enzymatic function [START_REF] Stirnimann | WD40 proteins propel cellular networks[END_REF]. Accordingly, 50% (88/177) of all human WD40 repeat containing proteins with conserved WD40 repeats are involved in protein binding (GO:0005515).

Next to WD40 repeats, TRs with !-helical TR units of 20-40 aa including large groups such as LRRs, ANKs, ARMs, HEAT and tetratricopeptide repeats are thought to be involved in protein binding [START_REF] Groves | Topological characteristics of helical repeat protein[END_REF]. The suprahelical structure of the TR region of such TRs is thought to form the scaffold for the assembly of multi-protein complexes [START_REF] Groves | Topological characteristics of helical repeat protein[END_REF][START_REF] Barford | The Role of Multiple Sequence Repeat Motifs in the Assembly of Multi-protein Complexes[END_REF][START_REF] Javadi | Tandem-repeat proteins: regularity plus modularity equals design-ability[END_REF] which in return mediates protein binding. Gains/losses of TR units in the TR region are likely to cause changes in the scaffold structure of TRs mediating molecular interactions. Any such changes would consequently affect the interaction properties. These observations were consistent with our GO-term analysis showing that conserved TRs in particular were significantly enriched with protein binding (60%, Fig. 4A).

Further, more than a third of all conserved TRs were part of membrane proteins (40%, Fig. 4A). Among the most common TR types in this group were cadherins, ANKs, LRRs and WD40 repeats (Fig. 4A). Structurally, these TRs are mostly located in the extracellular matrix, or the cytosol, but not within the membrane [START_REF] Angst | The cadherin superfamily: diversity in form and function[END_REF][START_REF] Hulpiau | New insights into the evolution of metazoan cadherins and by guest on February 12, 2014 http://mbe.oxfordjournals.org/ Downloaded from catenins[END_REF].

Functionally, these TRs may be involved in protein binding outside the membrane (de [START_REF] De Wit | Role of Leucine-Rich Repeat Proteins in the Development and Function of Neural Circuits[END_REF][START_REF] Hulpiau | New insights into the evolution of metazoan cadherins and by guest on February 12, 2014 http://mbe.oxfordjournals.org/ Downloaded from catenins[END_REF][START_REF] Mou | Functional Analysis and Expressional Characterization of Rice Ankyrin Repeat-Containing Protein, OsPIANK1, in Basal Defense against Magnaporthe oryzae Attack[END_REF]. The most frequent conserved transmembrane TRs are transmembrane helices (TMH; PF00520) in ion channels.

Human proteins with evidence for TR separation

To determine evolutionary ranges with evidence for TR unit gains/losses, we identified the species closest to human for which either a difference in TR unit number, strong or perfect separation was detected in the orthologous TR. For example, a difference in TR unit number in orthologs of human and chimp would suggest that TR unit changes occurred in at least one of the two lineages since speciation, indicating that the TR is mutable on the time scale of the speciation of the hominines. Perfect separation indicates that gains or losses of units had occurred repeatedly, affecting all TR units within the TRs.

For different eukaryotic clades, we calculated the number of TRs that have undergone unit changes in at least one species within this clade (summarized in Fig. 3B). Using this approach, for each TR we assessed when it was subjected to different degrees of unit gain/loss. Consequently we found that 5% (or 8%) of all human TRs were completely (or strongly) separated from at least one orthologous mammalian TR. In contrast, 61% of all human TRs were strongly conserved at least since the root of mammals. Note that it is possible that a TR was conserved in the human lineage beyond the ancestor of all mammals, while at the same time strong gains/losses leading to strong separation occurred on the lineage of another mammal after the separation from the human lineage. However, this is expected to be rare (0.5% of human TRs in our data), showing that within a given clade TRs consistently evolve by one single evolutionary mode, but not in a mixed-mode fashion.

Of particular interest is evidence for TR unit gains/losses in orthologous TRs within hominines, which would indicate that TR unit gains/losses might also occur on even shorter time scales, perhaps even on the population scale. However in our data, no human TR showed perfect separation compared to the orthologous TR in chimp or gorilla. In this range, only four TRs showed strong separation, including the TAPE repeat in a tumor necrosis factor (O14798, ENSP00000349324), and a de novo TR in the NAC-alpha domain-containing protein 1 (O15069, ENSP00000420477). In both examples, the TR consisted of almost identical TR units.

One other possibility is that TR unit gains/losses do occur, but do not affect the entire TR region. To account for this case, we also annotated pairs of TRs that exhibited a difference in TR unit number: 235 or 8% of all human TRs showed a difference in TR unit number compared to their orthologous TRs in chimp or gorilla, corresponding to 34% of all human TRs that had not been strongly conserved in the same range. In comparison, only 4 or 0.001% of all human TRs showed strong separation compared to their orthologous TR in chimp or gorilla. Thus in non-conserved TRs, unit mutations often lead to a change in the number of TR units without affecting the entire TR region.

Functional analysis of strongly separated TRs

To shed light on TR characteristics that correlate with strong unit gains/losses, we contrasted the subset of proteins with perfectly or strongly separated TRs in at least one species within the mammals (236 TRs in 230 proteins) with all human TR-containing proteins (3,091 TRs in 2,532 proteins). Similarly to strongly conserved TRs, we analyzed separated TRs with respect to the distribution of TR types and the GO-term enrichment (Fig. 4B).

More than half of all strongly separated TRs were formed by zinc finger motifs coordinating one eponymous zinc ion (Table 1, suppl. Fig. S6, Suppl. Mat. online). The family of zinc finger genes has been subject to a massive expansion in vertebrates, accounting for ~2% of all human genes [START_REF] Tadepally | Evolution of C2H2-zinc finger genes and subfamilies in mammals: Species-specific duplication and loss of clusters, genes and effector domains[END_REF]. The sheer number of zinc finger proteins suggests that correct orthology annotation might be particularly difficult in this group, potentially leading to an overestimation of the number of not-conserved TRs. The majority of the zinc-finger proteins bind to DNA, acting as highly specific transcription factors. More recently, binding to RNA and protein structures has also been observed [START_REF] Gamsjaeger | Sticky fingers: zinc-fingers as protein-recognition motifs[END_REF]. Taken together, proteins with zinc fingers TRs can explain most of the enriched GO terms for strongly separated TRs (Fig. 4B). Most of the zinc-finger-containing genes are arranged in clusters, and evolve through tandem gene duplications and losses [START_REF] Tadepally | Evolution of C2H2-zinc finger genes and subfamilies in mammals: Species-specific duplication and loss of clusters, genes and effector domains[END_REF]). Thus, possibly, the same evolutionary gain/loss mechanisms promote the evolution of the zinc finger TRs. Moreover, we noted that single zinc finger TR units often occupied exactly one exon. Whereas such zinc fingers clearly are repeated in tandem within the protein sequence, the TR units appear disconnected on the DNA sequence.

Among the other TRs strongly separated in at least one mammal were the neuroblastoma breakpoint family (NBPF or DUF1220, PF06758), immunoglobulin I-set (PF07679), the calcium-binding EGF (PF07645), and an EGF-like (PF00008) domain repeats.

In total, 52 distinct TR types were subject to strong separation in at least one human protein, with 30 of these being de novo annotations. The abundance of de novo detected TRs might imply that the TR types that undergo strong gains/losses in many cases may be relatively rare types, which have possibly appeared recently.

Discussion

In our proteome-wide analyses, most of the TRs were remarkably informative about their duplication history, despite their short sequence. As a result, we were able to classify the majority of human TRs as conserved (68%) with well-preserved TR unit configurations over long evolutionary distances (at least to the root of all mammals), while only few TRs were separated (8%) with clear evidence of configuration changes in the same range. Below we discuss these sets of TRs, as well as the correlation of their evolutionary mode with TR characteristics including the TR unit number, length, between-unit divergence, as well as the exon structure underlying the TR region.

Rapid evolution of protein tandem repeats is rare

Very few TRs appear to undergo rapid TR unit gains/losses. However, these few identified examples of separated TRs might exhibit variation within populations. Indeed, they include the zinc finger repeat in PRDM9, which carries strong variation in both chimp and human populations [START_REF] Hinch | The landscape of recombination in African Americans[END_REF][START_REF] Auton | A fine-scale chimpanzee genetic map from population sequencing[END_REF], and strongly influences the location of meiotic recombination hotspots [START_REF] Baudat | PRDM9 is a major determinant of meiotic recombination hotspots in humans and mice[END_REF][START_REF] Berg | Variants of the protein PRDM9 differentially regulate a set of human meiotic recombination hotspots highly active in African populations[END_REF]. Further, 12 (of 14) NBPF repeats involved in higher cognitive functions show a difference in TR unit number between human and chimp and gorilla. The majority of NBPF repeats were not strongly conserved between human and any other species, with none of them strongly conserved beyond the Catarrhines. Similar to zinc fingers, frequent NBPF unit gains/losses coincide with the recent expansion of TR-containing genes, particularly in the human lineage [START_REF] Popesco | Human lineage-specific amplification, selection, and neuronal expression of DUF1220 domains[END_REF] where gene copy number variation correlates to neurodevelopmental disorders [START_REF] Dumas | DUF1220-Domain Copy Number Implicated in Human Brain-Size Pathology and Evolution[END_REF]) and brain cancer [START_REF] Diskin | Copy number variation at 1q21.1 associated with neuroblastoma[END_REF].

Beyond these (few) examples our analysis shows that separation of TR units is extremely rare. Strikingly, no case of perfect separation was found between human and chimp or gorilla. In comparison, other types of sequence changes are much more common in this range: ~70% of all proteins were subject to substitutions (median of 2 non-synonymous substitutions per protein), and ~5% were subject to in-frame indels in a comparison of the human and chimp proteomes (Chimpanzee Sequencing and Analysis Consortium 2005). In summary, the vast majority of analyzed TRs cannot present potential for population level variability in terms of tandem repeat unit gains/losses, and so this process is unlikely to facilitate rapid adaptation to changes as has been proposed (e.g. [START_REF] Chevanne | WD-repeat instability and diversification of the Podospora anserina hnwd non-self recognition gene family[END_REF] for a WD40 TR in P. anserina).

Interestingly, more TRs with difference in TR unit number were annotated de novo compared to all TRs (e.g., within hominines this was 22% vs. 12% respectively). Having fewer Pfam annotations among variable TRs might indicate that de novo TRs are rare (otherwise they should be represented in Pfam), and therefore likely recent. Indeed, 75% of those variable de novo TRs had no ortholog TR outside mammals, compared to 15% in the complete TR set. Our findings are consistent with a recent hypothesis that TRs may function as a substrate for the formation of new domains and subsequently new genes (Bornberg-Bauer and Albà 2013).

The majority of human protein TRs are highly conserved

The majority of all human TRs are conserved at least within mammals or further back in time -in stark contrast with the rarity of separated TRs. Most likely, these conserved TRs had avoided any recent TR unit changes, with a unit configuration conserved deep into the eukaryotic tree. Thus the TR duplications that had lead to the original expansion of the TR should be ancient. Indeed, 52 TRs were conserved even between human and yeast, amounting to 13% of all human TRs that have a detectable ortholog in yeast. These ancient, highly conserved TRs include a range of TR types: for example, domain repeats such as the calponin homology (PF00307) and the prenyltransferase (PF00432), solenoid repeats such as WD40 (PF00400) (Fig. 1B), armadillo (PF00514), but also repeats with other structural configurations such as the EF hand (PF00036) (see Kajava 2012 for a structural classification of TRs). With such structural diversity at hand, there must be more than one guiding principle to explain the structural importance of ancient conserved TRs.

To investigate whether the conservation of a TR unit configuration is generally accompanied by the conservation of the TR unit sequence, we estimated the relative substitution rates in the TR and flanking regions (see Material & Methods). We found that the substitution rates in the TR region of strongly conserved repeats were on average 2.3 times lower than the rates in the protein sequence flanking the TR, both of which were by an order of magnitude below the respective rates for strongly separated TRs (suppl. Table S7, Suppl.

Mat. online). This shows that the majority of TRs are conserved both in terms of the TR sequence and in terms of their unit configuration (allowing accurate reconstruction of TR unit phylogenies over long evolutionary time-scales). Such sequence conservation on two levels is likely to be accompanied by an equally sustained structural conservation of TR regions, which is presumably required to maintain the function of the TR-containing protein.

TR conservation and TR type

Many more human TRs are conserved rather than separated (e.g., ~ 8:1 in mammals).

Conserved TRs clearly encompass more distinct TR types compared to separated TRs (~ 3:1), although the ratio is lower due to the relatively large number of de novo TRs among the separated repeats. Interestingly, TRs of the same type may be found in proteins with either conserved or separated TRs (such as zinc finger, Ca-binding EGF and the Immunoglobin I-set domains in Fig. 4). For example, among the zinc finger TRs 121 were strongly conserved to the root of all mammals, while 117 were strongly separated in the same range. Generally however, different TR types dominated the sets of conserved and separated TRs, with a clearly larger variety among the conserved TRs (Fig. 4, Suppl. Fig. S5-6, Suppl. Mat. online).

Similarly, the proteins containing either conserved or separated TRs differed in their functional annotations. Proteins with conserved TRs were enriched in a vast variety of molecular functions, related for example to cell-cell communication and cell adhesion, regulation of (nervous system) development, protein binding, but also catalytic activity. On the other hand, functions of separated TRs were dominated by DNA binding and gene expression regulation (largely due to zinc finger TRs).

TR conservation and substitution rates

In our dataset the mode of evolution of a given TR was best predicted by its between-unit sequence divergence (Fig. 5A). TR units in strongly separated TRs clearly had a lower divergence compared to TR units in strongly conserved TRs. At the same time, we found that substitution rates in the TR regions of strongly separated repeats were on average 10 times higher than those for strongly conserved TRs (in a comparison of human/mouse TR containing orthologs. Details in Material & Methods. Results in Suppl. Table S7, Suppl. Mat. online). Taken together, strongly separated TRs had lower between-unit sequence divergence, despite higher substitution rates in the whole TR regions. The following may explain these apparently contradictory results. In strongly separated TRs, due to the elevated rates of TR unit gain/loss, some TR units repeatedly get lost, while others duplicate in identical copies. As long as the substitution rates do not exceed the unit gain/loss rates, the TR units within the TR region will preserve high similarity (or low divergence) with each other [START_REF] Chevanne | WD-repeat instability and diversification of the Podospora anserina hnwd non-self recognition gene family[END_REF]. Despite the similarity of TR units between each other, the effective substitution rate still appears high when comparing orthologous TR regions: When substitutions occur on the propagating TR unit in one ortholog, these will spread over the entire TR region, leading to the divergence of the orthologous TR regions. Moreover, the accumulation of substitutions/indels in the repeat unit sequence is thought to decrease the rate of TR unit gain/loss by lowering the sequence mispairing probability [START_REF] Schug | The distribution and frequency of microsatellite loci in Drosophila melanogaster[END_REF][START_REF] Faux | RCPdb: An evolutionary classification and codon usage database for repeat-containing proteins[END_REF]). Therefore, low TR unit divergence within a TR region may be likewise a consequence and a requirement for TR unit gains/losses. Speaking now of conserved TRs, their high dissimilarity level is explained by their ancient origins that outweigh their low evolutionary rates.

TR conservation and the number of TR units

Separated TRs tended to contain more TR units than conserved TRs (Fig. 5B). The tendency of separated TRs to contain more units may be grounded in molecular biases: For nucleic tandem repeats it has been observed that TRs with more units are subject to increased duplication rates [START_REF] Schlötterer | Evolutionary dynamics of microsatellite DNA[END_REF][START_REF] Ellegren | Microsatellites: simple sequences with complex evolution[END_REF][START_REF] Bhargava | Mutational dynamics of microsatellites[END_REF], presumably due to a larger number of potential slippage sites. Similarly, protein TRs with a higher number of units may be more likely to undergo TR unit number changes.

In general, it is interesting to understand why for the majority of TRs the number of TR units is constant throughout large evolutionary time scales. Most likely, the protein function, and in turn its structure necessitate a fixed number of TR units. Interestingly, conserved TRs of the same type may appear in different (non-orthologous) proteins with widely varying numbers of TR units. For example, in conserved human zinc finger TRs unit numbers ranged from (the minimum of) 4 to 39. This holds for TRs that fold into the 'beads on a string' structure such as the zinc finger TRs [START_REF] Kajava | Tandem repeats in proteins: from sequence to structure[END_REF]), but also for TRs where the individual TR units do not fold independently, such as the EGF-like laminins (up to 31 units),

the linear/open solenoid LRRs (up to 27 units), and the circular/closed solenoid WD40 repeats (up to 37 units). Interestingly, WD40 repeats were also shown to be highly mutable in one fungi gene family and still functional for different numbers of TR units (Chevanne et al. structure to mediate protein binding (see Results).

TR conservation and the TR unit length

Separated TRs exhibited shorter repeat units compared to conserved TRs (Fig. 5C). For nucleic microsatellite and minisatellite TRs, for example, TRs with shorter units also have higher TR unit duplication rate [START_REF] Schlötterer | Evolutionary dynamics of microsatellite DNA[END_REF][START_REF] Leclercq | DNA slippage occurs at microsatellite loci without minimal threshold length in humans: a comparative genomic approach[END_REF]. If this were applied to protein TRs, those with shorter TR units would be expected to undergo more TR unit changes and are thus more likely to become separated.

In light of the above, it does not seem surprising that for minisatellite type TRs with shorter units (10-15aa) we observed a clear decrease in unit conservation, as well as an increase in the relative proportion of strongly separated TRs, compared to TR regions with longer units (suppl. Fig. S4, Suppl. Mat. online). Possibly, as the TR unit length decreases there would be a transition from observing mostly conserved TRs to gradually observing more and more separated TRs. Indeed, frequent insertions/deletions have been observed for homorepeats and dipeptide repeats among primates, including human [START_REF] Loire | Evolution of Coding Microsatellites in Primate Genomes[END_REF]. In particular, variation in the number of TR units in protein homorepeats has been reported within human populations, and is known to be associated with various human diseases [START_REF] Orr | Trinucleotide repeat disorders[END_REF]. On the other hand, human homorepeats were shown to be more conserved than corresponding trinucleotide TRs in non-coding sequence [START_REF] Mularoni | Natural selection drives the accumulation of amino acid tandem repeats in human proteins[END_REF]). Note that with shorter TR units, phylogeny reconstruction becomes increasingly prone to errors, which may obscure TR phylogeny-driven results for such ranges.

TR conservation and the exon structure

Frequently, exons in TR-containing proteins span multiples of whole TR units [START_REF] Street | The Role of Introns in Repeat Protein Gene Formation[END_REF][START_REF] Björklund | Nebulin: a study of protein repeat evolution[END_REF]. TRs may evolve by a mechanism of tandem gains/losses of repeat units such as replication slippage, or alternatively by duplication of whole exons, which does not necessarily occur in tandem, such as exon shuffling [START_REF] Björklund | Expansion of Protein Domain Repeats[END_REF].

To distinguish between these mechanisms, we measured the number of exons spanned by the TR region, as well as the maximum number of adjacent TR units found in a single exon (Fig. 5D-E).

In our data 31% of all separated TRs were contained within a single exon. For these, we can exclude the exon-shuffling-like process to explain TR unit changes. On the other hand, for 26% of all separated TRs, one exon corresponded to at most one TR unit. Lacking proximity of the protein TR units in the nucleic sequence, these TRs most likely evolve through an exon shuffling-like process. Another indicator for the mechanism of TR units gains/losses can be derived from the exon structures of multiple TRs of the same TR type. For example, we found that whilst the number of NBPF TR units varied widely (up to 55) in all 14 NBPF-containing proteins, the number of TR units per exon stayed constant (2 or 3). This indicates that NBPF TRs evolve through an exon-shuffling-like process.

Altogether, both mechanisms of unit gains/loss seem to play an important role during the TR evolution. Interestingly, many of the separated TRs either were found to occupy one exon per TR unit, or contained many TR units per exon, exhibiting a roughly bimodal distribution in terms of the maximum number of TR units per exon (Fig. 5E), whereas the conserved TRs did not show this behavior. Possibly, for some conserved TRs the presence of multiple exon boundaries rupturing the TR unit structure on the nucleic level may prevent duplications/losses of TR units.

Conclusion

Our genome-wide study of the evolution of human protein TRs demonstrates that despite the common belief that TRs evolve rapidly, large numbers of protein TRs (l ≥ 15 aa) exhibit sustained conservation deep into the eukaryotic tree, with many TR regions preserved even since the common ancestor of human and yeast. Surprisingly, TR regions are frequently the most conserved part of the protein sequence. Conserved TRs can be found in proteins performing a wide variety of key functions. All together, our observations suggest a pronounced role of protein TRs in the function of the TR-containing protein, indicating that the functional significance of TRs has been underestimated. On the other hand, we found only few TRs with evidence for recent and strong TR unit gains/losses. To better understand the functional and potentially adaptive relevance of this small set of fast evolving protein TRs in the future, a case-wise analysis of their function may be of interest.

Cross-species studies of tandem repeat unit phylogenies, like the one presented here, appear to be a powerful tool to gain insights on TR evolution. We found that human TR sequences are for the majority of TRs remarkably informative about its duplication history. This opens the door to more detailed studies of TR unit gains/losses. Possibly, unique events can be pinpointed to specific lineages within the gene phylogeny, but also within the TR region.

Future research on the association of specific 3D structures and functions to TRs in proteins could use the analyses of TR unit phylogenies to provide insights to the impact of specific TR unit gains/losses.

Material and Methods

Annotation of TRs in human proteins with circular HMM

The complete set of 20,240 gene trees with associated protein sequences from 61 eukaryotic species including human were obtained from Ensembl Compara v69. For all human sequences, TRs were annotated based on: a) tandemly repeated PFAM A domains and b) de novo detections.

For each PFAM A domain annotated in the Ensembl human proteins, the corresponding sequence profile hidden Markov model (HMM) was obtained from the PFAM database [START_REF] Punta | The Pfam protein families database[END_REF]. To detect PFAM domains that occurred as TRs, their profile HMMs were transformed into circular profile HMMs, or cpHMMs (Fig. 2), so that one motif (described by its sequence profile) could be repeated in tandem via a circular transition from the final to the starting state of the HMM. TRs corresponding to PFAM A domains were annotated in human sequences using the Viterbi algorithm applied to cpHMMs (S1, Suppl.

Mat. online). Annotated this way TRs were retained for further analyses if they had at least four TR units (! ≥ 3.5).

To include TRs that were not represented among PFAM A, additional TRs were predicted de novo on the human proteome with HHrepID v1.1.0 [START_REF] Biegert | De novo identification of highly diverged protein repeats by probabilistic consistency[END_REF], T-REKS v1.3 [START_REF] Jorda | T-REKS: identification of Tandem REpeats in sequences with a K-meanS based algorithm[END_REF], TRUST v1.0 [START_REF] Szklarczyk | Tracking repeats using significance and transitivity[END_REF]) and XSTREAM v1.72 [START_REF] Newman | XSTREAM: a practical algorithm for identification and architecture modeling of tandem repeats in protein sequences[END_REF] and subsequently filtered for minimal requirements (! !"!!"#$% ≤ 0.8; ! ≥ 2.5; ! ≥ 10) (see below for exact definitions of ! !"!!"#$% , l and n) and statistical significance (! = 0.01). Statistical significance of TR predictions was assessed using the likelihood ratio tests as in [START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF], for details see Suppl. Mat. S1. De novo predicted TRs overlapping with PFAM-based TR annotations were discarded.

Where de novo TRs overlapped, only the best prediction (with the highest statistical significance and the lowest TR unit divergence) was used for further analyses. Profile HMMs of de novo TRs were built using HMMER [START_REF] Eddy | Profile hidden Markov models[END_REF], and are available at http://www.atgcmontpellier.fr/TRE. Again, we refined the de novo based TR annotation of human proteins using cpHMM, and statistically validated all refined TRs (! = 0.1) retaining those with at least four TR units (! ≥ 3.5) and unit length ! ≥ 15. Note that due to the Markovian property of the cpHMM, the annotated TRs will not be biased to a particular number of TR units.

Phylogenetic analysis of TRs within the eukaryotic clade

For every human TR, we used its cpHMM to annotate homologous TRs in all orthologous (including 1:1, 1:many and many:many orthologs) genes from other eukaryotes as represented by the Ensembl Compara gene trees. Next, we built MSAs (Multiple Sequence Alignments) for each ortholog pair (S1, Suppl. Mat. online). For each TR MSA that contained at least four TR units in both orthologs, we reconstructed bi-species maximum likelihood TR unit phylogenies using PhyML 3.0 [START_REF] Guindon | A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood[END_REF][START_REF] Guindon | New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0[END_REF]) with default options (LG+ Γ model; examples in Fig. 1).

TR characteristics

We correlated TR classification with a range of TR characteristics (Fig. 5). For this purpose we considered TRs that were classified as strongly conserved since the root of all mammals, or as strongly separated between human and at least one other mammal. For each single TR we calculated the following characteristics:

• TR unit length !, defined as the number of non-insertion sites of the TR unit, parsimoniously assuming an insertion if at this site (in the respective column of the TR MSA) the observed amino acid characters are at least as many as gaps;

• (effective) number of TR units !, as the total number of non-insertion amino acid sites in the TR-MSA divided by !;

• TR unit divergence ! !"!!"#$% , maximum likelihood estimate of the TR unit divergence obtained as a by-product of the model-based TR significance test [START_REF] Schaper | Repeat or not repeat?--Statistical validation of tandem repeat prediction in genomic sequences[END_REF]): ! !"!!"#$% is measured in expected number of aa substitutions per site since the most recent common TR unit ancestor;

• the number of exons spanning the TR region at least partly;

• the maximum number of complete TR units in a single exon. The last two statistics relied on the exon structure of the human TR-containing proteins according to Ensembl v.69.

Function enrichment analysis

Ensembl protein identifiers were mapped to HGNC symbols. The mapping of HGNC symbols species B. Assume ! ! ≥ ! ! without loss of generality. For ! = ! ! = ! ! > 2, the probability of drawing a random phylogeny with perfectly conserved TR units under the uniform tree model is

! !"#$"%&!!"#$ ! = ! ! ! !!!! ! !!!! ! !!!! ! !!! ! .
(1)

Proof. In a phylogeny with perfectly conserved TR units a) all leaves are paired in cherries and b) each cherry groups TR units one from each of A and B so that Kendall's !! = !1 (i.e.

the !th TR unit in A is always paired with the !th TR unit in B).

a) The probability distribution of ! ! !cherries in a random phylogeny with ! = 2! leaves drawn from the uniform tree model is [START_REF] Hendy | Branch and bound algorithms to determine minimal evolutionary trees[END_REF][START_REF] Mckenzie | Distributions of cherries for two models of trees[END_REF])

ℙ ! ! = ! = ! ! !!! ! !!! !! !!!! !!!! ! !!!! !!! !!! ! . (2)
Thus, the probability that all leaves are paired in cherries (so the number of cherries is exactly

n c = n) is: ! !!!! [! ! = !] = !! ! !!!! ! !!!! ! !!!! !!! !!! ! . (2')
b) The probability of !! = !1 for a given topology with ! ! = ! cherries is

! ! = 1; ! !" = ! = ! !!! ! !! ! . ( 3
)
Here, we first used that the value of ! is independent of the order of cherries and assumed the cherries to be ordered. The probability is then given by the number of leaf assignments such that ! = 1, i.e. !!, divided by the total number of distinct leaf assignments, i.e. !! ! ! ! . Finally,

! !"#$"%&!!"#$ ! = ! ! = 1; ! !" = ! • ! !!!! ! ! = ! . ∎
Table 2 shows these probabilities for a range of !.

Formula. For ! ! !and!! ! > 2 the probability of drawing a random phylogeny with strongly conserved TR units under the uniform tree model is

! !"#$%&!!"#$ ! ! , ! ! = ! ! !!!! ! !!!! ! !!!! ! !!! ! + ! ! !!!! ! !!!! !! !!! !!!! ! !!! ! , ! = ! ! = ! ! ! !!!! ! !!!! !! ! !!!! ! !!! ! , ! = ! ! = ! ! + 1 . (3) Proof. Strong conservation is assigned if (max(! ! , ! ! ) ! -! ! !" ≤ and ! = 1.
Thus, either a) the TR is perfectly conserved for ! ! = ! ! , with probabilities derived above, or b)

! ! = ! !" = ! -1 and ! = 1 for ! = ! ! = ! ! , or c) ! ! = ! !" = ! ! = !! ! -1 = ! -1
and ! = 1. The probabilities for (b) and (c) can be derived by adapting ( 2) and (3):

b) Assumed is a topology with 2! leaves so that there are ! -1 perfectly conserved cherries.

The probability that the two leaves that are not part of a cherry hold TR units from both A and B is ! !!!! , so that the total probability of case c) is

! !!!! ! ! = ! -1 • ! ! = 1; ! !" = ! -1 • ! !!!! = ! ! !!!! ! !!!! !! !!! !!!! ! !!! ! . c
) Assumed is a topology with 2! -1 leaves and ! -1 perfectly conserved cherries.

Analogous to b), we consider that the probability that the one leaf that is not part of a cherry holds a TR unit from A is ! !!!! , so that the total probability of case c) is

! !!!!!! ! ! = ! -1 • ! ! = 1; ! !" = ! -1 • ! !!!! = ! !!!! ! !!!! !! ! !!!! ! !!! ! .
The formula follows.

Statistical significance of assigning TRs as separated from bi-species TR unit phylogenies

The probability of falsely assigning perfect separation to a pair of random TRs with n TR units is 2.16 • 10 !! (5.44 • 10 !! ) for n = 4 (5) (see derivation below), which is elevated compared to the probability of falsely assigning perfect conservation. Inference errors in phylogeny reconstruction may still tend to cause an underestimation of the number of separated TRs. On the other hand, errors in sequencing and orthology annotation are expected to lead to an overestimation of the number of TRs that are separated or show a difference in TR unit number.

Derivation of the probability of randomly drawing separated TR unit phylogenies

Any perfectly separated bi-sample TR unit phylogeny has exactly one bipartition separating the tree into two subtrees each of which with leaves representing TR units from only one species either A or B (see Fig. 1C for one such configuration). The parsimony score of such a phylogeny is

! ! ! = !1.
Formula. Let ! ! and!!! ! be numbers of TR units in species A and B, so that N = ! ! + ! ! is the number of leaves in the unrooted binary tree of all TR units. The probability of drawing a random phylogeny with perfectly separated TR units under uniform model is

! !"#$"%&!!"# ! ! , ! ! = !! ! !! ‼ !! ! !! ‼ !!!! ‼ (5)
Proof. Since the number of distinct rooted binary trees with

! ! !leaves is (2! ! -3)!! (Schröder 1870
) the number of distinct perfectly separated trees connected at their roots is

then! 2! ! -3 !!! 2! ! -3 !!!.
Given that the distinct unrooted binary trees with ! leaves is 2! -5 !!!, the probability of drawing a random tree with perfectly separated TR units from a uniform tree distribution is

! !"#$"%&!!"# ! ! , ! ! = !(! ! , ! ! ) !(!) = 2! ! -3 ‼ 2! ! -3 ‼ 2! -5 ‼ . ∎
With the results of [START_REF] Carter | On the Distribution of Lengths of Evolutionary Trees[END_REF] and [START_REF] Steel | Distributions on bicoloured binary trees arising from the principle of parsimony[END_REF] on the equivalent minimal coloring problem, it can additionally be shown that the probability of strong separation is

P !"#$%&!!"# n ! , n ! -P !"#$"%&!!"# n ! , n ! = ! ! (! ! ,! ! ) !(!) = !"!! !! ! !! ! !! ! !! ! ! !!! ! ! !! ! ! ! !! ! !"!! ‼ (6).
For Eq. 5-6 calculated probabilities for a range of ! ! = ! ! = ! are shown in Table 2.

Tables

Table 1. TR summary. (A) Characteristics for all analyzed human TRs, averaged over the six most frequent TR types, and de novo annotated TRs: ! denotes the TR unit length, !!the number of TR units per TR, ! !"!!"#$% the ML estimate of substitution rates per site separating the TR units within one TR, ! !"!!"#$%& the ML estimate of substitution rates per site separating the TR regions in human and mouse (Material & Methods). (B) The total number of orthologous TRs for selected eukaryotic species. p.c. and c.s are the numbers of perfectly conserved and perfectly separated TRs, respectively. For every TR we derived the probability of falling into either of these categories by random chance (Material & Methods). Bold font indicates that many more cases were found than expected by random chance (! = !0.01). or perfect separation (Eq. 5), strong separation (Eq. 6) to a pair of random TRs with ! TR units each. positions. The probability to enter the TR is equal for all match states (blue). Similarly, for all match states it is assumed to be equally likely to stay in the TR or leave the TR (blue).

! ! !"#$"%&!!"#$ ! ! !"#$%&!!"#$ !, ! ! !"#$"%&!!"# !, ! ! !"#$%&!!"# !, ! 4 2.89 • !! 1.88 • 10 !! 2.16 • 10 !! 2.16 • 10 !! 5 7.40 • 10 !! 1.12 • 10 !! 5.44 • 10 !! 7.61 • 10 !! 6 1.60 • 10 !! 4.63 • 10 !! 1.36 • 10 !! 2.46 • 10 !! 7 2.99 • 10 !! 1.47 • 10 !! 3.42 • 10 !! 7.52 • 10 !! 8 4.87 • 10 !!! 3.74 • 10 !! 8.56 • 10 !! 2.22 • 10 !!
W D 4 0 L R R A N K Z in c f in g e r C a d h e r in K e lc h I Im m . I- s e t K e lc h m o t if II F ib r o n e c t in II I T P R I Im m . V - s e t C a - b in d in g E G F T P R II E G F - li k e II E G F - li k e I # < 3 0 d e n o v o Z in c f in g e r N B P F J A Z Z in c f in g e r C a

Fig. 1 .

 1 Fig. 1. Tandem repeat unit evolution. (A) A scenario of TR unit evolution for species A and

Fig. 2 .

 2 Fig. 2. Circular TR sequence profile HMM. Shown is an example of a profile HMM

Fig. 3 .Fig. 4 .

 34 Fig. 3. Conservation and separation of 3091 human protein Tandem repeats (TRs)

Fig. 5 .

 5 Fig. 5. Characteristics of separated vs. conserved tandem repeats. Shown are frequency

  Figures

  Figure4

Table 2 . Probability of assigning perfect conservation (Eq. 1), strong conservation (Eq. 4)

 2

	All TRs	Zn finger LRR	WD40	ANK	Cadherin	I-set	de novo
	A: Human
	count 3091 570	225	186	166	107	72	356
	!! 48.5	27.9	24.0	42.2	33.2	104.8	90.9	28.4
	! 8.8	11.2	10.7	6.8	7.7	6.9	7.8	8.0
	std(!) 8.2	5.6	5.6	3.6	4.9	5.8	9.2	7.0
	! !"!!"#$% 0.96	0.50	1.14	1.35	1.03	1.13	1.30	0.64
	! !"!!"#$%& ! 0.4	0.5	0.2	0.1	0.1	0.2	0.2	1.4
	PFAM ID	-	PF00096	PF00560 PF00400 PF00023 PF00028	PF07679 -
	B: Other eukaryotes
	Chimp 2718 502	209	163	155	78	67	308
	p.c. 2134 379	164	145	134	62	55	177
	c.s. 0		0	0	0	0	0	0	0
	Mouse 1935 643	121	96	72	59	38	138
	p.c. 833	86	46	71	49	49	27	47
	c.s. 91	85	0	0	0	0	0	5
	Rat 1485 289	117	80	69	68	37	127
	p.c. 751	81	40	57	44	55	30	40
	c.s. 34	28	0	0	0	0	0	5
	Xenopus 1882 110	153	126	136	166	46	82
	p.c. 820	50	24	66	49	152	20	19
	c.s. 16	11	0	0	0	0	4	1
	Fugu 2074 162	215	157	150	95	68	112
	p.c. 808	56	29	81	54	62	44	22
	c.s. 42	39	0	0	0	0	0	0
	Zebrafish 2991 484	243	158	166	378	88	127
	p.c. 1198 59	34	93	65	351	46	26
	c.s. 293	283	0	0	0	0	0	8
	Fruitfly 1221 129	174	128	79	18	45	45
	p.c. 203	15	2	50	11	2	0	4
	c.s. 36	25	0	0	0	0	0	5
	Roundworm 722	21	54	72	63	17	28	78

by guest on February 12, 2014 http://mbe.oxfordjournals.org/ Downloaded from

2010). All in all, for many TR types, a fixed number of TR units is not per se crucial to guarantee the functioning of the TR-containing proteins, in agreement with results by other authors {e.g.[START_REF] Abraham | Alternative to Homo-oligomerisation: The Creation of Local Symmetry in Proteins by Internal Amplification[END_REF]). There must be additional reasons to explain the high conservation of the majority of TRs, such as the necessity to provide a defined scaffold by guest on February 12, 2014 http://mbe.oxfordjournals.org/ Downloaded from

Acknowledgements

We thank Erich Bornberg-Bauer, Andreas Schüler, and Gil McVean for insightful discussions and Nives Škunca, Stefan Zoller, and three anonymous reviewers for their invaluable feedback on the earlier version of this manuscript. This work was supported by the Swiss National Science Foundation (SNF) grant 31003A_127325/1 to M.A., and the SNF doctoral mobility grant to E.S.. Both E.S. and M.A. were also supported by the ETH Zürich. E.S. was invited at the "Institut de Biologie Computationnelle" (IBC) to realize the phylogenetic studies. O.G. is supported by CNRS and IBC.

to GO functional annotations, and the enrichment analysis assuming a hypergeometrical model was conducted with Gorilla [START_REF] Eden | GOrilla: a tool for discovery and visualization of enriched GO terms in ranked gene lists[END_REF]. All TR-containing human proteins constituted the background distribution, which was independently contrasted with distributions of functions within strongly separated and strongly conserved sets of TRs. The complete enrichment data set including directed acyclic graphs of enriched GO terms is available at http://www.atgc-montpellier.fr/TRE.

Substitution rates in TR regions and in flanking protein sequence

For all pairwise alignments of human-mouse TR-containing orthologs in Ensembl Compara, the evolutionary distances between the TR regions in both species (! !"!!"#$%& ), and the corresponding flanking protein regions in both species (! !"#$%& ) were computed separately (using LG+Γ in PhyML 3.0). For this purpose, the flanks on either side of the TR region were concatenated. The computed evolutionary distances are equivalent to estimates of substitution rates per site. The boundaries of TR region and flanking region were taken as the mean of the predicted TR boundaries in both species (if different).

Statistical significance of assigning TRs as conserved based on TR unit phylogenies

The probability of falsely assigning perfect conservation to a pair of random TRs with n units is as low as 2.9 • 10 !! (7.4 • 10 !! ) for n = 4 (5), rendering an overestimation of TR conservation unlikely (see derivation below). In comparison, inference errors in orthology annotation and phylogeny reconstruction are disproportionally more likely to obscure a perfectly conserved TR. Thus, the observed number of conserved TRs is presumably a lower boundary to the actual number of conserved TRs.

Derivation of the probability of randomly drawing conserved TR unit phylogenies

Formula. Let ! = ! ! + ! ! be the total number of leaves in an unrooted binary tree, with ! ! leaves representing TR units from species A, and ! ! leaves representing TR units from