# Role of geometrical cues in neuronal growth

## TL;DR

This study investigates how geometrical cues influence neuronal growth, combining experimental measurements with stochastic modeling to understand axonal dynamics on patterned surfaces.

## Contribution

It introduces a stochastic approach to describe growth cone motion and demonstrates how surface geometry affects axonal alignment and dynamics.

## Key findings

- Axons align strongly on micro-patterned surfaces matching growth cone size.
- Growth cone dynamics follow a Langevin equation with deterministic and stochastic components.
- A transition from linear to non-linear stochastic behavior occurs with changing surface periodicity.

## Abstract

Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micro-patterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from an Ornstein-Uhlenbeck process to a non-linear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide new insight into the role of curvature sensing proteins and their interactions with geometrical cues.

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Source: https://tomesphere.com/paper/1903.01337