### On the origin and implications of scaling in biological networks

17 June 2005

Eric Deeds

Shakhnovich Lab

Department of Chemistry and Chemical Biology

Harvard University

#### Abstract

It has recently been demonstrated that many biological networks exhibit a "scale-free" topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^{-gamma}. This observation has been explained in terms of dynamical evolutionary models of duplication and divergence broadly based on the principle of "preferential attachment". In this talk I will discuss recent work exploring alternative, non-dynamic, physical models for these networks. I will specifically consider the protein-protein interaction (PPI) network. I will demonstrate that the two published independent measurements of these interactions using the yeast-2-hybrid (Y2H) methodology produce graphs that are only weakly correlated with one another despite their strikingly similar scale-free topology. I will then discuss a physical model that can explain the observation of scale-free networks of such interactions based on the fundamental principle that (de)solvation is a major physical factor in protein-protein interactions. This simple physical model reproduces not only the scale-free nature of such graphs but also their "modular" and "hierarchical" organization as empirically observed in higher-order features of these networks. A key support for this model is provided by the discovery of significant correlation between number of interactions made by a protein (its node degree k in the network) and fraction of hydrophobic residues on its surface. These results have profound implications not only for protein-protein interaction networks but also for scale-free networks in other systems.

#### References

E Deeds and E I Shakhnovich, *"The emergence of scaling in sequence-based physical models of protein evolution"*, Biophysical Journal 88:3905-3911 2005. Abstract

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