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Scaling of Morphogenetic Patterns

  • Manan’Iarivo Rasolonjanahary
  • Bakhtier Vasiev
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 1863)

Abstract

Mathematical studies of morphogenetic pattern formation are commonly performed by using reaction–diffusion equations that describe the dynamics of morphogen concentration. Various features of the modeled patterns, including their ability to scale, are analyzed to justify constructed models and to understand the processes responsible for these features in nature. In this chapter, we introduce a method for evaluation of scaling for patterns arising in mathematical models and demonstrate its use by applying it to a set of different models. We introduce a quantity representing the sensitivity of a pattern to changes in the size of the domain, where it forms, and we show how to use it to perform a formal analysis of scaling for chemical patterns forming in continuous systems.

Key words

Mathematical modeling Pattern formation Robustness and scaling 

Notes

Acknowledgments

This work has been supported by the EPSRC scholarship to M.R. and BBSRC grant BB/K002430/1 to B.V.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Manan’Iarivo Rasolonjanahary
    • 1
  • Bakhtier Vasiev
    • 1
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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