Mechanisms and Measurements of Scale Invariance of Morphogen Gradients

  • Yan Huang
  • David UmulisEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1863)


Morphogen gradients provide positional information to underlying cells that translate the information into differential gene expression and eventually different cell fates. Scale invariance is the property where the gradients of the morphogen adjust proportionately to the size of the domain. Scale invariance of morphogen gradients or patterns of differentiation is a common phenomenon observed between individuals within the same species and between homologous tissues or structures in different species. To determine whether or not a pattern is scale invariant, others and we have developed definitions and measurements of gradient scaling. These include point-wise and global scaling errors as well as global scaling power. Furthermore, there are a number of mathematical conditions for scale invariance of advection–diffusion–reaction models that inform mechanisms of scaling. Herein we provide a deeper perspective on modeling and measurement of scale invariance of morphogen gradients.

Key words

Scale invariance Morphogen gradient Reaction–diffusion Mathematical model Morphogenesis 


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

Authors and Affiliations

  1. 1.Agricultural and Biological EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA

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