A mathematical model explains saturating axon guidance responses to molecular gradients

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


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.

Publication types

  • Retracted Publication

MeSH terms

  • Animals
  • Axons / drug effects*
  • Axons / physiology*
  • Cells, Cultured
  • Chemotaxis*
  • Growth Cones / drug effects*
  • Growth Cones / physiology*
  • Lab-On-A-Chip Devices
  • Models, Theoretical
  • Rats, Wistar

Grants and funding

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.