Wayne Hayes1, Kai Sun, Nataša Pržulj. 1. Department of Computer Science, University of California, Irvine, CA 92697-3435, USA.
Abstract
MOTIVATION: Large amounts of biological network data exist for many species. Analogous to sequence comparison, network comparison aims to provide biological insight. Graphlet-based methods are proving to be useful in this respect. Recently some doubt has arisen concerning the applicability of graphlet-based measures to low edge density networks-in particular that the methods are 'unstable'-and further that no existing network model matches the structure found in real biological networks. RESULTS: We demonstrate that it is the model networks themselves that are 'unstable' at low edge density and that graphlet-based measures correctly reflect this instability. Furthermore, while model network topology is unstable at low edge density, biological network topology is stable. In particular, one must distinguish between average density and local density. While model networks of low average edge densities also have low local edge density, that is not the case with protein-protein interaction (PPI) networks: real PPI networks have low average edge density, but high local edge densities, and hence, they (and thus graphlet-based measures) are stable on these networks. Finally, we use a recently devised non-parametric statistical test to demonstrate that PPI networks of many species are well-fit by several models not previously tested. In addition, we model several viral PPI networks for the first time and demonstrate an exceptionally good fit between the data and theoretical models.
MOTIVATION: Large amounts of biological network data exist for many species. Analogous to sequence comparison, network comparison aims to provide biological insight. Graphlet-based methods are proving to be useful in this respect. Recently some doubt has arisen concerning the applicability of graphlet-based measures to low edge density networks-in particular that the methods are 'unstable'-and further that no existing network model matches the structure found in real biological networks. RESULTS: We demonstrate that it is the model networks themselves that are 'unstable' at low edge density and that graphlet-based measures correctly reflect this instability. Furthermore, while model network topology is unstable at low edge density, biological network topology is stable. In particular, one must distinguish between average density and local density. While model networks of low average edge densities also have low local edge density, that is not the case with protein-protein interaction (PPI) networks: real PPI networks have low average edge density, but high local edge densities, and hence, they (and thus graphlet-based measures) are stable on these networks. Finally, we use a recently devised non-parametric statistical test to demonstrate that PPI networks of many species are well-fit by several models not previously tested. In addition, we model several viral PPI networks for the first time and demonstrate an exceptionally good fit between the data and theoretical models.