Topological Analysis of Cellular Networks

The description of the molecular world conforming living cells has been a long standing enterprise since Biochemistry foundation. The elucidation of biochemical pathways in the early-middle twenty century gave way to a more complete picture of genes, proteins and metabolites by the beginning of Molecular Biology. Nowadays, the ultimate deciphering of such a molecular world is now becoming to be reality by the huge biotechnological advance on high throughput analysis. Genomic, proteomic and metabolomic tools have provided a revolution of the molecular biology and biomedicine expectations in very few years, as well as, the emergence of novel disciplines such as Systems and Synthetic Biology. One of the first conclusions of such large-scale analyses is that molecular species are networked in giant interconnected entities. The so-called cellular networks, -consisting of protein maps, metabolism, and gene regulatory networksbut also other systems such as food webs, internet, or social relations constitute a sort of complex networks. Contrasting with the initial thought, it was observed that their organisation strongly departs from simple random homogeneous metaphors. Interestingly, their internal organization reveals common traits that can be analysed from the perspective of modern graph theory. In this theoretical framework, a graph is a mathematical abstraction of reality that can be tackled from statistical physics and computation science perspectives. In this chapter we will present a repertoire of methods for a standard graph analysis, particularly oriented to the study of cellular networks. These tools allow us to measure and compare different networks in order to uncover their internal organization from a statistical point of view. We will show that the network approach provides a suitable framework to explore the organisation of the biomolecular world.