2 results
4 - Genetic interactions and network reliability
-
- By Edgar Delgado-Eckert, Department of Biosystems Science and Engineering, ETH Zurich, Niko Beerenwinkel, Department of Biosystems Science and Engineering
- Edited by Florian Markowetz, Michael Boutros
-
- Book:
- Systems Genetics
- Published online:
- 05 July 2015
- Print publication:
- 02 July 2015, pp 51-64
-
- Chapter
- Export citation
-
Summary
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.
Biological networks
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.
14 - Mutagenetic Tree Models
- from Part II - Studies on the four themes
- Edited by L. Pachter, University of California, Berkeley, B. Sturmfels, University of California, Berkeley
-
- Book:
- Algebraic Statistics for Computational Biology
- Published online:
- 04 August 2010
- Print publication:
- 22 August 2005, pp 278-290
-
- Chapter
- Export citation
-
Summary
Mutagenetic trees are a class of graphical models designed for accumulative evolutionary processes. The state spaces of these models form finite distributive lattices. Using this combinatorial structure, we determine the algebraic invariants of mutagenetic trees. We further discuss the geometry of mixture models. In particular, models resulting from mixing a single tree with an error model are shown to be identifiable.
Accumulative evolutionary processes
Some evolutionary processes can be described as the accumulation of non-reversible genetic changes. For example, the process of tumor development of several cancer types starts from the set of complete chromosomes and is characterized by the subsequent accumulation of chromosomal gains and losses, or by losses of heterozygosity [Vogelstein et al., 1988, Zang, 2001]. Mutagenetic trees, sometimes also called oncogenetic trees, have been applied to model tumor development in patients with different types of cancer, such as renal cancer [Desper et al., 1999, von Heydebreck et al., 2004], melanoma [Radmacher et al., 2001] and ovarian adenocarcinoma [Simon et al., 2000]. For glioblastoma and prostate cancer, tumor progression along the mutagenetic tree has been shown to be an independent cytogenetic marker of patient survival [Rahnenführer et al., 2005].
Amino acid substitutions in proteins may also be modeled as permanent under certain conditions, such as a very strong selective pressure. For example, the evolution of human immunodeficiency virus (HIV) under antiviral drug therapy exhibits this behavior.