Complex networks and simple models in biology

Abstract

The analysis of molecular networks, such as transcriptional, metabolic and protein interaction networks, has progressed substantially because of the power of models from statistical physics. Increasingly, the data are becoming so detailed--though not always complete or correct--that the simple models are reaching the limits of their usefulness. Here, we will discuss how network information can be described and to some extent quantified. In particular statistics offers a range of tools, such as model selection, which have not yet been widely applied in the analysis of biological networks. We will also outline a number of present challenges posed by biological network data in systems biology, and the extent to which these can be addressed by new developments in statistics, physics and applied mathematics.

Figure 1

Protein interaction network data is collected in different organisms. Orthologous proteins are indicated by vertical lines, interactions between proteins by lines within the planes. Individual proteins are also related through their joined phylogeny.

Figure 2

(a) all possible motifs defined by three nodes in a directed network. (b) All motifs possible defined by four nodes in an undirected network.

Figure 3

Degree distribution of the yeast protein interaction network (black circles) and best-fit power-law (red) and log–normal (blue) models (see Stumpf & Ingram 2005; Stumpf et al. 2005; Stumpf et al. in press for details).

Figure 4

Two potential sampling schemes: under neighbourhood sampling, nodes connected to some initially chosen nodes (red) are more likely to be included in the set of nodes (blue) investigated. Under random sampling nodes are chosen (approximately) at random for the interaction studies. Lightblue nodes are not included in the experimental analysis.