RETRACTED: A mathematical model explains saturating axon guidance responses to molecular gradients

TLDR

Correct wiring is crucial for nervous system function, and while molecular gradients guide growth cones to their targets, the way these gradients bias the inherently stochastic trajectories of growth cones remains unclear. The study aims to develop a mathematical model that captures how persistence, bias, and noise govern growth cone behavior in attractive and repulsive gradients. The model is constrained by detailed statistics of growth cone movements measured in a microfluidic device, integrating persistence, bias, and noise parameters. The model explains the rapid saturation of average axon turning angles in vitro and represents the most accurate predictive model of growth cone trajectories to date, enhancing understanding of axon guidance in vitro and in vivo.

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.