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Elife. 2016 Feb 2;5:e12248. doi: 10.7554/eLife.12248.

A mathematical model explains saturating axon guidance responses to molecular gradients.

Author information

1
Queensland Brain Institute, The University of Queensland, St. Lucia, Australia.
2
School of Mathematics and Physics, The University of Queensland, St. Lucia, Australia.
3
Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.
4
Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, St. Lucia, Australia.

Abstract

Correct wiring is crucial for the proper functioning of the nervous system. Molecular gradients provide critical signals to guide growth cones, which are the motile tips of developing axons, to their targets. However, in vitro, growth cones trace highly stochastic trajectories, and exactly how molecular gradients bias their movement is unclear. Here, we introduce a mathematical model based on persistence, bias, and noise to describe this behaviour, constrained directly by measurements of the detailed statistics of growth cone movements in both attractive and repulsive gradients in a microfluidic device. This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values. This work introduces the most accurate predictive model of growth cone trajectories to date, and deepens our understanding of axon guidance events both in vitro and in vivo.

KEYWORDS:

Axon guidance; Mathematical model; Microfluidics; neuroscience; rat

PMID:
26830461
PMCID:
PMC4755759
DOI:
10.7554/eLife.12248
[Indexed for MEDLINE]
Free PMC Article
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