First we asked whether different measures for asserting domain promiscuity produce similar results. We compared the following methods: number of different direct neighbours of a given domain (NN), number of domains with which a given domain occurs in the same arrangement (NCO) and number of triplets (NTRP) (Tab. 1, see Methods for details). We found that all applied measures strongly correlate with each other and with the number of occurrences of a given domain (Fig. 1). Thus, most of the variation in domain promiscuity as defined by any of the existing measures can be explained by the number of occurrences.

The data presented further were obtained using the number of neighbours (NN) as a preliminary measurement for promiscuity. However, the results are similar if other measures are selected for computation (see supplementary material).

To understand the relationship between the number of occurrences of a domain and its promiscuity, we investigated the following question in more detail. If the number of observed neighbours correlates with number of occurrences, does, for a given domain, the number of its neighbours in a given genome correlate with the number of occurrences of that domain in that genome? In other words, assume one counts the number of occurrences (N) of a certain domain in different genomes. For each genome, we compare N with the number of neighbours this domain has in the given genome. We wanted to know if there is a correlation, in a given genome, between the number of occurrences of a domain and the number of its neighbours. First, we divided the SwissPfam database in sets, each corresponding to one organism only. Secondly, we compiled a list of all domains found in SwissPfam. For each of these domains, we analysed each of the genome files separately. Given the domain and organism, we counted the number of occurrences (N) of this domain as well as the number of its neighbours (NN). For each domain, we analysed the relationship between NN and N. A comparison of this relationship for two domains and sample plots for selected domains are displayed in Fig. 2. Each of these plots corresponds to a domain or domain clan (see Methods for the description how calculations were made for domain super-families; domain clans were taken from Pfam 10).

Many domains can be found in only one or two genomes, or are always present in one or two different arrangements only. We find that 86,252 Pfam A and B domains (74%) are found only in one or two proteins in the SwissPfam data set. 77,629 domains (66%) have only two or fewer different neighbors. For Pfam A domains the corresponding numbers are 1624 (26%) and 1265 (20%), respectively. Therefore, no regression can be calculated for these domains. However, for the domains for which a correlation could be reliably calculated, all of them show a significant correlation between N and NN. In fact, the relationship between NN and N is almost perfectly log-linear for many domains (see Fig. 2 and supplementary material). We find that, for a given domain, the number of occurrences in a genome is a very good predictor of promiscuity when promiscuity is defined by NN, NCO or NTRP. The tight relationship between N and NN underlines the fact that measures such as the number of co-occurrences, neighbours or local triplets of a protein essentially only show how abundant a domain is.

According to the previously proposed random model of evolution 29, the promiscuity of a domain defined in terms of co-occurrences is tightly linked to the frequency of a domain. If this was the case, then the apparent promiscuity of domains does not necessarily depend on any inherent property of the domain itself. Instead, it may indicate that such domains had more opportunity to propagate and rearrange, for example because they are older. In other words, given the high correlation between N and NN, domain promiscuity based on NN does not give substantially more information than its abundance. To understand how domains differ in their inherent properties to form new combinations, these two factors – number of abundance and promiscuity – must be unlinked. This prompted us to search for a new measure of promiscuity that would not be correlated with domain abundance. Using this measure, it should be possible to find out which properties of domains correlate with their abundance, and which show the intrinsic ability of a domain to form new combinations.

We observed that the strengh of the relationship between N and NN differs for different domains. Fig. 2A shows an example of two domains – a methyltransferase domain and the Sushi domain. For both domains, there is a strong relationship between the number of occurrences (N) and the number of neighbours (NN). However, given the same N, the methyltransferase domain has many more neighbours than the Sushi domain.

We examined whether domains that originated early in life history have a higher number of neighbours, as predicted by the random evolution model. To get a rough estimate of the relationship between the age of a domain and its properties, we have adopted a simplified version of the approach described by Wang et. al 33 and divided domains into three groups: "old", "middle" and "new" based on their taxonomic spread. "Old" domains are present in all kingdoms; "middle" are common for all lineages in either of the Eukaryota, Archea or Bacteria and "new" are specific to one lineage within these groups (e.g. in Metazoa only).

For example, domain PF00001 (a transmembrane receptor from the rhodopsin family) is found in all domains of life, while the Kringle domain (PF00051) can be found only in the eukaryotes. While the former would be defined as 'old,' the latter would be defined as 'new' and nodes in-between as 'middle.' Indeed, domains that originated early have, on average, a higher number of neighbours. For example, domains that are found in all main three life forms (Bacteria, Archea and Eukaryota) have on average 12.51 neighbours, while the respective values for Eukaryota and Metazoa are 5.72 and 3.69. This does not mean that all ancient domains are very widely spread or have a high number of neighbours. In fact, the variance of these properties also increases with domain age, and thus there are domains that probably are very ancient, but do not form many combinations. For example, the RNA polymerase domain PF04983 occurs in many clades altogether 89 times, but has only 9 different neighbours.

However, we expect that truly versatile domains should have equal chance of arising during the course evolution. That is, a young domain that recently appeared can also be versatile, albeit in a limited clade. For example, a novel transcription related domain that recently evolved in mammals is not expected to be different in its ability to form new domain combinations from a domain shared throughout the tree of life, although it will not have yet as many connections formed. Given the random model, the number of connections is a function of time, however not necessarily dependent on an inherent property different in older and in younger domains. We observe a strong correlation between the age of a domain and its observed number of occurrences, as well as the number of neighbours (p < 10^-15 in a one-way ANOVA for three age categories). Therefore, older domains seem to be more promiscuous if measured using previously described units of promiscuity such as the NN or NCO. This is possibly due to the fact that these domains had more time to spread, in accordance with the model presented by Vogel et al. 29.

We wanted, however, to know, whether older domains are intrinsically more versatile than younger domains. Specifically, we ask whether domains that originated at the root of the tree of life have a significantly different DV I from domains that originated later. We did not find any significant differences (p = 0.16 in a one-way ANOVA). Since the domains that are specific to a clade are generally younger than domains spread throughout the tree of life, this finding shows that the average DV I does not depend on the age of a domain (Fig. 4). This means that domains arising at any time during the evolution have the same chance of becoming versatile.

We further asked whether the domain versatility differed significantly between Bacteria, Eukaryotes and Archea. We expected that due to the fact that eukaryotic proteins tend to contain more domains, the versatility in eukaryotic proteins will be higher. To test this hypothesis, for each of the genomes in one of the three forms of life (Bacteria, Archea and Eukaryota) we calculated the average DV I of all domains that are contained in that genome.

We find a small, but statistically highly significant difference between prokaryotic (bacterial and archeal) and eukaryotic genomes. The average DV I for bacterial, archeal and eukaryotic genomes were, respectively, 0.64 ± 0.0003, 0.65 ± 0.0012, and 0.58 ± 0.0002. Thus eukaryotic domains tend to be even slightly less versatile, although though they may form, on average, more connections in a domain co-occurrence network than a prokaryotic domain. This is in contrast with previously reported findings based on domain versatility measures correlated with domain abundance 12. There are two possible explanations for this phenomenon. First, it may be that the apparent decrease in DVI corresponds to a higher rate of gene expansion by gene and genome duplications. We have tested this by correcting the DVI by gene expansion through removal of redundant domain arrangements and found that results are robust. A second possibility is based on the fact that eukaryotic proteins have, on average, more domains than prokaryotic protein. Furthermore, it has been previously reported that domain rearrangements most frequently involve protein termini 18. Since in Eukaryota, there are proportionally fewer terminal domains and since the non-terminal domains are less likely to acquire new neighbors, on the average, an eukaryotic domain will form fewer connections (acquire new neighbors) than expected from its abundance, and therefore has a relatively low DV I. On the same hand, due to the larger genomes and gene expansion in Eukaryotes, domains are more abundant and domain rearrangements more frequent in terms of absolute numbers. This makes the domains appear more versatile if one applies one of the measures of promiscuity that is correlated with domain abundance.

It has been shown that domain rearrangement events very often involve whole terminal fragments 173435. Such rearrangement events, which are predominantly protein fusion and fission events 1636, very often involve single domain proteins that are fused to or split from another protein. We observed that domains which also occur as single-domain proteins have, on average, a higher DV I (0.62 ± 0.01 vs 0.53 ± 0.01; p < 10^-7 in a two-tailed t-test with equal variances). We further supported this finding as follows. For a given domain, we considered all proteins in SwissPfam that contain this domain, and calculated the fraction of single-domain proteins (that is, fraction of proteins in SwissProt that harbour only this given domain). The proportion of single-domain proteins is correlated with the DV I of the domains (Pearson r = 0.25, p < 10^-5). Therefore, if a domain occurs frequently as a single domain protein, it is likely to have a high DV I.

Some domains may be more prone to be rearranged by a specific genomic mechanism. For example, retrotransposons are abundant in many eukaryotic genomes and may play a condsiderable role in their evolution 37383940. It has be suggested that retrotransposons may promote recombination 374142 and thus may also have an impact on domain rearrangements in turn facilitating a higher DV I. To test whether domains that are included in retrotransposition events tend to have a higher DV I, we used the LTR detection method described by Rho et al. 43. We scanned genomic DNA from Mus musculus for long terminal repeats, translated the nucleic acid sequence flanked by LTRs into all six reading frames and detected Pfam A domains by running HMMPFAM from the HMMER package 44 against Pfam A HMM models. Using an E-value cut-off of 10^-5 and removing common viral domains such as Transposases, RVTs or Gag-related domains, ~180 mostly non-viral domains were obtained. We were able to calculate the DV I for 53 domains, but did not detect any significant difference between domains found within LTR boundaries and other 'non-LTR' domains.

Previously, we have shown that domains in terminal indels differ with respect to their number of neighbours from domains found on non-terminal positions. We now asked, whether domains found at the termini are more often partaking in fusion/fission events simply because they are more abundant, or whether they tend to be more versatile. We found that the latter is the case. The average DV I for terminal domains is 0.61 as opposed to 0.49 for the non-terminal domains (p < 10^-15 for a one-way ANOVA). This means that, on average, terminal domains are more versatile.

Furthermore, the DV I correlates with average length of a domain: longer domains have a higher DV I (r = 0.25, p < 10^-6). This is in variance with previous investigations, which were based on other versatility measures such as the number of triplets (NTRP) formed 12. We interpret this contradiction as follows. Number of triplets correlates strongly with domain abundance (N). It is therefore possible that domain length primarily correlates with domain abundance. Indeed, we see a statistically significant, negative correlation between the number of occurrences of a domain and the domain length (r = -0.14, p = 0.005). We also explored the link between domain structure and versatility, but did not find any correlation.

Next, we asked what the functional properties of domains with different DVI values are. A manual investigation of the domain functions has shown that domains with low DV I are very often repeats. Note that the combinatorial effect of the repeats (that is, that several occurrences of a domain in a row give a high number of occurrences and a very low number of neighbours) have been accounted for as described in the previous section.

Among the domains with the highest DV I (see supplementary table 1) there are several domains that bind to various nucleotides such as DNA, RNA and ATP binding domains. For example, we find several Zinc finger domains, the PAS fold or the Helicase domain. On the other hand, among the domains with low DV I we see numerous structural domains and domain repeats, such as the cap region of the leucine rich repeat (LRRNT), collagen triple helix (Collagen) or the Ankyrin repeat (ANK). We wanted to know whether these observations can be quantified and if they are statistically significant.

To quantitatively test the differences, we analysed the GO terms that are associated with different domains. A GO term was associated with a domain, if it was shared by all proteins containing the given domain, as defined in the Interpro database 45. We calculated the average DV I for different GO terms and compared them using analysis of variance (ANOVA). We were not able to find any significant differences in average DV I between the different GO terms.

Since the calculation of a DV I is limited to domains that occur in multiple instances in several genomes, only a small fraction of Pfam A domains could be associated with a DV I. To alleviate this problem we calculated the DV I for the 263 Pfam clans. For example, instead of calculating the DV I separately for SH3_1, SH3_2, SH3_3, SH3_4 and SH3_5 domains, we treated each occurrence of such a domain as the occurrence of its respective clan ID "CL0010". In summary, we were able to calculate the DV I for 115 clans. Furthermore, we calculated the average DV I of Pfam domains that belong to a given Pfam clans and found that both measures are significantly correlated (r = 0.6, p < 10^-12). While the latter (averaging DV I over members of Pfam clan) seems to be a more straightforward approach, the former (substituting domain names in SwissPfam by the respective Pfam clan IDs) allows a calculation of the DV I for a larger number of Pfam clans. We see that, for most of the Pfam clans, the correlation between N and NN is equally strong as for Pfam domains (see supplementary material).

We further repeated the GO analysis for Pfam clans. Again, we do not find a clear connection between the GO functions associated with a Pfam clan and the calculated DV I.

While we could see that protein domains from the same Pfam clan do indeed have similar DV I values, we were not able to show that domains that have either a low or a high DV I have a particular functional assignment, i.e. common GO annotations. Potentially, there could be a problem with the way GO annotations are assigned to proteins and protein domains; for example, automatically assigning GO terms to a domain by taking over the GO terms of the proteins that share the given domain may introduce a systematic error. On the other hand, there is maybe no general functional link between protein domain versatility and its function (e.g. some transcription factors are specialised and non-versatile whereas some others are versatile).

We calculated the following previously described indices of domain versatility: number of co-occurrences (NCO; 29), number of direct neighbours (NN) and number of triplets (NTRP; 12). For each domain, we calculated the number of co-occurrences as follows. For a given domain, all proteins containing this domain were identified. NCO is the total number of different domains in these proteins minus one. Number of immediate neighbours was calculated as the number of different domains that occur directly at the N- or C-terminus of the given domain. If a domain was found at a terminus, the number of neighbors was increased by one (terminal position of a domain was considered to be a valid domain combination). Triplets are defined as unique combinations of either: three domains, with the given domain in the middle, two domains and a letter if the domain occurs at either N- or C-terminus (e.g. N-PF00001–PF00002 means that the given domain PF00001 occurs at the N-terminus of the protein) or three letters, if the domain occurs in a single domain protein (e.g. N-PF00001-C). We calculated the number of triplets as the number of unique triplet combination in which a domain occurs. These calculations were done for all domains in the data set.

We calculated the domain versatility index (DV I) as follows. For each domain, we considered the number of occurrences (N) of this domain in a genome as well as the number of immediate neighbours (NN). We define DV I as the coefficient of logarithmic regression of NN over N with its respective error.

Furthermore, we calculated and compared both, logarithmic and linear regression coefficient of NCO, NN and NTRP over N. We have chosen the logarithmic regression coefficient for further analysis, because it follows the logarithmic model of Vogel et al. 29. The DV I has been computed in R using the following models: NN = a log(N) + b for logarythmic regression and NN = aN + b for linear regresion (N – number of occurences, NN – number of neighbors, a and b – regression coefficients). The DV I was then defined as the a coefficient from the regression model.

To correct for domain expansion, we have removed domain repeats from the data set. Similarily, to correct for gene expansion, we have removed identical domain arrangements from the data set.

To test whether the use of SwissPfam introduces a significant bias to the observed data, we have recalculated the DVI using proteins from 749 full Eukaryotic, Bacterial and Archeal genomes from the Integr8 database, release 84 (50; see supplementary materials for the full data set). Overlapping domains were removed, with PFAM domains given precedence over other annotations. In this data set we obtained DVIs for 980 domains, including 727 Pfam A domains. These DVI values correlate significantly with the values obtained for the SwissPfam data set (r = 0.91, p < 10^-15).

To compare different approaches for the DVI calculation and the index described in 32, we used the R² statistic to evaluate the goodness of fit for each domain and for different models applied. The equation used by Basu et al. 32 corresponds to a model given by the equation NN log(NN) = log(N); consequently, we define NN' = NN log(NN) and use the following regression model in R: NN' = a log(N) + b. We have calculated the average R²value for each of the three models applied.