  Understanding the design of the universe of protein structures may provide
insights into protein evolution. We study the architecture of the protein
domain universe, which has been found to poses peculiar scale-free properties
(Dokholyan et al., Proc. Natl. Acad. Sci. USA 99: 14132-14136 (2002)). We
examine the origin of these scale-free properties of the graph of protein
domain structures (PDUG) and determine that that the PDUG is not modular, i.e.
it does not consist of modules with uniform properties. Instead, we find the
PDUG to be self-similar at all scales. We further characterize the PDUG
architecture by studying the properties of the hub nodes that are responsible
for the scale-free connectivity of the PDUG. We introduce a measure of the
betweenness centrality of protein domains in the PDUG and find a power-law
distribution of the betweenness centrality values. The scale-free distribution
of hubs in the protein universe suggests that a set of specific statistical
mechanics models, such as the self-organized criticality model, can potentially
identify the principal driving forces of molecular evolution. We also find a
gatekeeper protein domain, removal of which partitions the largest cluster into
two large sub-clusters. We suggest that the loss of such gatekeeper protein
domains in the course of evolution is responsible for the creation of new fold
families.
