Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Spatial Description of Biochemical Networks

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_89-1

Abstract

Many biological behaviors require that biochemical species be distributed spatially throughout the cell or across a number of cells. To explain these situations accurately requires a spatial description of the underlying network. At the continuum level, this is usually done using reaction-diffusion equations. Here we demonstrate how this class of models arises. We also show how the framework is used in two popular models proposed to explain spatial patterns during development.

Keywords

Diffusion Morphogen gradient Pattern formation Reaction-diffusion Turing instability 
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Bibliography

  1. Chen Y, Lagerholm BC, Yang B, Jacobson K (2006) Methods to measure the lateral diffusion of membrane lipids and proteins. Methods 39:147–153CrossRefGoogle Scholar
  2. Cowan AE, Moraru II, Schaff JC, Slepchenko BM, Loew LM (2012) Spatial modeling of cell signaling networks. Methods Cell Biol 110:195–221CrossRefGoogle Scholar
  3. Goehring NW, Grill SW (2013) Cell polarity: mechanochemical patterning. Trends Cell Biol 23:72–80CrossRefGoogle Scholar
  4. Holmes WR, Edelstein-Keshet L (2013) A comparison of computational models for eukaryotic cell shape and motility. PLoS Comput Biol 8:e1002793; 2012CrossRefGoogle Scholar
  5. Iglesias PA, Devreotes PN (2008) Navigating through models of chemotaxis. Curr Opin Cell Biol 20:35–40CrossRefGoogle Scholar
  6. Kondo S, Miura T (2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329:1616–1620CrossRefMATHMathSciNetGoogle Scholar
  7. Lander AD (2013) How cells know where they are. Science 339:923–927CrossRefGoogle Scholar
  8. Mahmutovic A, Fange D, Berg OG, Elf J (2012) Lost in presumption: stochastic reactions in spatial models. Nat Methods 9:1163–1166CrossRefGoogle Scholar
  9. Meyers J, Craig J, Odde DJ (2006) Potential for control of signaling pathways via cell size and shape. Curr Biol 16:1685–1693CrossRefGoogle Scholar
  10. Rogers KW, Schier AF (2011) Morphogen gradients: from generation to interpretation. Annu Rev Cell Dev Biol 27:377–407CrossRefGoogle Scholar
  11. Sheth R, Marcon L, Bastida MF, Junco M, Quintana L, Dahn R, Kmita M, Sharpe J, Ros MA (2012) Hox genes regulate digit patterning by controlling the wavelength of a turing-type mechanism. Science 338:1476–1480CrossRefGoogle Scholar
  12. Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond 237:37–72CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Electrical & Computer Engineering, The Johns Hopkins UniversityBaltimore, MDUSA