Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Semin Cell Dev Biol. 2014 Nov:35:189-202. doi: 10.1016/j.semcdb.2014.08.015. Epub 2014 Sep 4.

Abstract

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Keywords: Axon guidance; Boundary formation; Morphogenetic gradient; Patterning; Reaction–diffusion equations; Retinotopic map.

Publication types

  • Review

MeSH terms

  • Algorithms*
  • Animals
  • Axons / metabolism
  • Axons / physiology
  • Brain / growth & development
  • Brain / metabolism
  • Brain / physiology
  • Computational Biology / methods*
  • Homeodomain Proteins / metabolism
  • Homeodomain Proteins / physiology
  • Humans
  • Models, Neurological*
  • Morphogenesis / physiology*
  • Otx Transcription Factors / metabolism
  • Otx Transcription Factors / physiology

Substances

  • GBX2 protein, human
  • Homeodomain Proteins
  • OTX2 protein, human
  • Otx Transcription Factors