Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones

Expositions of quantitative methods and algorithms for biological data tend to be scattered through the technical literature, often across different fields, and are thus awkward to assimilate. This book documents one example of this: the relationship between the cell biology idea of metabolic networks and the mathematical idea of polyhedral cones. Such cones can be used to describe the set of steady\-state admissible fluxes through metabolic networks, and consequently have become important constructs in the field of microbiology. \nVia convex cone concepts, fundamental objects called elementary flux modes (EFMs) can be described mathematically. The fundamental algorithm of this relationship is the double description method, which has an extended history in the field of computational geometry. This monograph addresses its relatively recent use in the context of cellular metabolism. \n\nMetabolic Networks, Elementary Flux Modes, and Polyhedral Cones\n•\taddresses important topics in the mathematical description of metabolic activity that have not previously appeared in unified form,\n•\tintroduces a central topic of mathematical systems biology in a manner accessible to nonmathematicians with some mathematical and computational experience, and\n•\tpresents a careful study of the double description method, a fundamental algorithm of computational geometry, in the context of metabolic analysis.\nThe core audience for this book includes mathematicians, engineers, and biologists interested in cell metabolism. Computational geometers will also find it of interest.

Isaac Klapper is a professor of mathematics at Temple University. He studies physical and ecological mathematical models of microbial communities including biofilms. Daniel B. Szyld is a professor of mathematics at Temple University. He has worked on many aspects of numerical linear algebra and matrix computations, including eigenvalue problems, sparse matrix techniques, Schwarz preconditioning and domain decomposition, and Krylov subspace methods. He is an AMS and SIAM fellow. Kai Zhao is an assistant professor of instruction at Temple University. He studies probability and stochastic processes including quantum random walks on fractals.