Paul Fernandez, Ricard Solé
Paper #: 03-12-071
Recent models of genome-proteome evolution have shown that some of the key traits displayed by the global structure of cellular networks might be a natural result of a duplication- diversification (DD) process. One of the consequences of such evolution is the emergence of a small world architecture together with a scale-free distribution of interactions. Here we show that the domain of parameter space where such structure emerges is related to a phase transition phenomenon. At this transition point, modular architecture spontaneously emerges as a byproduct of the DD process. Although DD models lack any functionality and are thus free from meeting functional constraints, they show the observed features displayed by the real proteome maps when tuned close to a sharp transition point separating a highly connected graph from a disconnected system. Close to such a boundary, the maps are shown to display scale-free hierarchical organization, behave as small worlds, and exhibit modularity. It is conjectured that natural selection tuned the average connectivity in such a way that the network reaches a sparse graph of connections. One consequence of such a scenario is that the scaling laws and the essential ingredients for building a modular net emerge {\em for free} close to such a transition.