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Applications in Biology

  • Peter Schuster
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Stochastic phenomena are central to biological modeling. Small numbers of molecules regulate and control genetics, epigenetics, and cellular metabolism, and small numbers of well-adapted individuals drive evolution. As far as processes are concerned, the relation between chemistry and biology is a tight one. Reproduction, the basis of all processes in evolution, is understood as autocatalysis with an exceedingly complex mechanism in the language of chemists, and replication of the genetic molecules, DNA and RNA, builds the bridge between chemistry and biology. The earliest stochastic models in biology applied branching processes in order to give answers to genealogical questions like, for example, the fate of family names in pedigrees. Branching processes, birth-and-death processes, and related stochastic models are frequently used in biology and they are defined, analyzed, and applied to typical problems. Although the master equation is not so dominant in biology as it is in chemistry, it is a very useful tool for deriving analytical solutions, and most birth-and-death processes can be analyzed successfully by means of master equations. Kimura’s neutral theory of evolution makes use of a Fokker–Planck equation and describes population dynamics in the absence of fitness differences. A section on coalescent theory demonstrates the applicability of backwards modeling to the problem of reconstruction of phylogenies. Unlike in the previous chapter we shall present and discuss numerical simulations here together with the analytical approaches. Simulations of stochastic reaction networks in systems biology are a rapidly growing field and several new monographs have come out during the last few years. Therefore only a brief account and a collection of references are given.

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Schuster
    • 1
  1. 1.Institut für Theoretische ChemieUniversität WienWienAustria

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