The biochemical and molecular mechanisms underlying epistatic gene interactions observed in various living organisms are poorly understood. In this chapter, we introduce a mathematical framework linking epistasis to the redundancy of biological networks. The approach is based on network reliability, an engineering concept that allows for computing the probability of functional network operation under different network perturbations, such as the failure of specific components, which, in a genetic system, correspond to the knock-out or knock-down of specific genes. Using this framework, we provide a formal definition of epistasis in terms of network reliability and we show how this concept can be used to infer functional constraints in biological networks from observed genetic interactions. This formalism might help increase our understanding of the systemic properties of the cell that give rise to observed epistatic patterns.
A major goal of post genomic biomedical research consists in understanding how the genetic components interact with each other to form living cells and organisms. The systems-wide approach requires both novel experimental techniques for mapping out such interactions and new mathematical models to describe and to analyze them. Interacting biological systems are often represented as networks (or graphs), where vertices correspond to components (e.g., genes, proteins, or metabolites) and edges correspond to pair wise interactions (e.g., activation, molecular binding, or chemical reaction). This abstract representation provides the conceptual basis for network biology, which aims at understanding the cell's functional organization and the complex behavior of living systems through biological network analysis (Strogatz 2001, Barabási & Oltvai 2004).
Various experimental methods have been developed to measure physical interactions (molecular binding events) among proteins and several computational methods exist for predicting such interactions. These data give rise to protein–protein interaction (PPI) networks which are available from dedicated databases (Schwikowski et al. 2000, Xenarios et al. 2000, Jensen et al. 2009). Genetic interactions, or epistasis, refers to functional relationships between genes.