A notable feature of the PPI networks is their property of power-law and scale-freeness. The differential degree of connectivity distribution has been ascribed to the preferential attachment of hub proteins (Barabasi and Albert 1999; (Barabasi and Oltvai 2004). According to this model, the probability of connecting to a new node in the network is proportional to the connectivity density (i.e., vertex degree) of the existing node. Thus, a highly connected node has greater chances of attracting a new node compared to the ‘connectivity potential’ of a sparsely connected node, i.e., rich gets richer. Interestingly, enzymes that are candidates for horizontal gene transfer seem to have higher average connectivity than other enzymes (Light et al. 2005). Furthermore, protein age seems to correlate with the network connectivity (Eisenberg and Levanon 2003). Saturation and viability have also been reported as properties of networks showing preferential attachment (D’Souza et al. 2007). Though preferential attachment of hub proteins has been studied in the past, the reasons of its origin and the functional implications of ‘rich-gets-richer’ are unclear. Interestingly, Pagel et al. (2007) propose a variable rate of attachment model according to which power-scaling can be achieved without preferential attachment.

The InParanoid algorithm (O’Brien et al. 2005) with BLOSUM45 substitution matrix for prokaryote and BLOSUM60 for eukaryote was used to identify orthologs. The pair wise orthologs were combined into multi-species cluster using MultiParanoid algorithm (Alexeyenko et al. 2006). To separate orthologs from spurious matches, a 50 bits cut-off was used. The matching segment of the longer sequence exceeded 50% of its total length. The ortholog data were also examined using COG and KOG protein family classification.

We selected fold change definition for connectivity, k_fc = k/k, and appropriate cutoff to identify hubs in different PPI networks. For Prokaryotes, a node with k_fc ≥ 2 was considered as hub (cutoff, P < 0.03 using distribution of standard normalized kfc values in Ortho_Pk). For eukaryotes the criterion was, k_fc ≥ 10 (with P < 0.001). A higher cutoff of 10-fold change was used for eukaryotes in order to minimize the effect of false positives, especially in data from S. cerevisiae. Of the orthologs identified in each category (Ortho_PkEk, Ortho_Pk and Ortho_Ek), only those satisfying stringent hub criteria in at least one species were selected. A hub was considered ‘converted to non-hub’ when its kfc value crossed the cutoff. In order to define the nature of this hub convertibility, we observed trends along the complexity profile of six species (H. pylori, E. coli, S. cerevisiae, C. elegans, D. melanogaster and Homo sapiens).

Originally introduced by Barabasi and Albert (1999) and followed by several interesting papers (Barabasi and Oltvai 2004; Nacher and Akutsu 2007), scale freeness has been widely accepted as a generic model of networks exhibiting power law distributions. However, there are some reports of protein interaction networks not conforming to the power law (Khanin and Wit 2006; Tanaka et al. 2005). It is further argued that some published PPI networks are better described by an exponential function and proponents of this approach recommend using rank plots instead of frequency-degree plots (Tanaka et al. 2005). Furthermore, it has been demonstrated that power law degree distribution is equivalent to a power law degree-rank function only if scaling exponent is greater than 2 (Wu et al. 2008). It is important to recognize that rich getting richer paradigm is not the only mechanism leading to scale free networks (Li et al. 2005). Finaly, the scale-free topology of existing protein-protein interaction networks may not be confidently extrapolated to complete interactomes (Han et al. 2005).

We addressed the paradigm of ‘rich-getting-richer’ from a different perspective. Our aim was to see if rich always get richer. If no, what would happen if hub proteins lost most of the links? As a first step, the data were integrated from six protein-protein interaction databases to create a reasonably large size and variety of the sample. Sequence homology was used to eliminate redundancy among hub proteins. A protein node was classified as a hub or non-hub based on the extent of its connectivity. People have used several criteria to define hubness based on the type of network analysis. For example, Barabasi and Albert (1999) suggest that, hub nodes in scale free networks generally exhibit connectivity, k, an order of magnitude higher than average vertex degree k of the network. Unfortunately, such measures cannot be generalized to biological networks exhibiting modularity. Han et al. (2004) used hub node criterion of k ≥ 5 (in a network with average vertex degree k = 3.6). Such arbitrary cutoff measures can lead to misclassification of nodes in large networks with potential false positive interactions. Single criterion, based on k cutoff is misleading as even a non-hub node in dense network might have edges more than hub node in less denser network. The Z score cutoff (≥2.5), based on the standardized normal distribution of connectivity values (k) has also been used to establish significant hub nodes (Ekman et al. 2006; Guimera and Nunes Amaral 2005). The Z scores definition is inappropriate in our study, since different networks exhibit different degree distributions with varying k.

One of the confounding factors in studying PPI networks is the low quality of experimental data (Gentleman and Huber 2007; Jensen and Bork 2008). This can be particularly worrying if one relies too much on a particular database or attempts to integrate several independently constructed databases (Alexeyenko and Sonnhammer 2009). To address the issue of data integrity, we adopted a stringent metric of 10-fold change to identify hubs and minimize false positives, mainly for eukaryotes. Thus, in theory even if 50% edges turn out to be false positives, the protein will still show a significantly high vertex degree to qualify for the standard definition of hubness. A smaller cutoff was, however, used for prokaryotic hub proteins given the relatively smaller k and smaller size of networks.

The current dataset includes proteins representing both physical and functional interactions to reduce data bias (Han et al. 2004). To ensure that we were studying the same protein in different organisms, a set of conserved proteins (orthologs) were extracted in all the six species. A stringent threshold of 50 bits and matching segment exceeding 50% of its total length was adopted. The ortholog data were also examined using COG and KOG protein family classification.

Our observation of proteins “getting rich” supports the preferential attachment model for all scale free networks (Barabasi and Albert 1999; Qian et al. 2001). However, we also found incidences of rich-proteins-getting-poor. Interestingly, the existing network growth models do not consider the possibility of fluctuating connectivity in hub proteins. Even if we take into account the yeast, S. cerevisiae where average connectivity score is higher, the results are still significant at 10-fold change cutoff. Our findings support the concept of hub convertibility i.e., loss, retention and gain of hubness based on the context.

We further asked if the getting-rich or getting-poor hub proteins retain their core protein partners across all the species? A total of 380 protein-partners were found to exhibit significant similarity by way of their sequence identity (e-value 0.001). Among them, 24 partners shared more than two species. Although statically non-significant (P-value = 0.13), the getting-rich proteins tend to maintain their interacting partners, thereby reflecting “an intrinsic scale-free design” of larger networks. However from this data, we could not identify an interaction partner that was ortholog in all six species. Interestingly, the functional-spread of the hub proteins shows a decrease as their partners gradually downsize in number. The present hub convertibility data suggests that several ancient proteins (hub nodes in Prokaryotes) are conserved i.e., remain as orthologs in eukaryotes despite the loss of hubness. One reason for this observation could be their key roles (Kunin et al. 2004) in the cell, irrespective of their observed connectivity patterns.

Kyaw Tun, Email: kyawtun/at/gsc.riken.jp.

Raghuraj Keshava Rao, Email: raghuraj/at/nus.edu.sg.

Lakshminarayanan Samavedham, Email: chels/at/nus.edu.sg.

Hiroshi Tanaka, Email: tanaka/at/cim.tmd.ac.jp.

Pawan K. Dhar, Email: pkdhar/at/riken.jp.