Feedback-Driven Dynamical Model for Axonal Extension on Parallel Micropatterns

TL;DR

This paper introduces a comprehensive biophysical model that integrates intracellular and environmental factors to predict and control axonal growth and alignment on micropatterned substrates, aiding neural repair strategies.

Contribution

It presents a novel unified dynamical model combining mechanochemical processes and substrate cues to explain axonal extension and alignment, supported by analytical and simulation results.

Findings

Model accurately predicts axonal elongation speed.

Identifies bifurcations driving alignment transitions.

Provides design rules for biomaterial optimization.

Abstract

Despite significant advances in understanding neuronal development, a fully quantitative framework that integrates intracellular mechanisms with environmental cues during axonal growth remains incomplete. Here, we present a unified biophysical model that captures key mechanochemical processes governing axonal extension on micropatterned substrates. In these environments, axons preferentially align with the pattern direction, form bundles, and advance at constant speed. The model integrates four core components: (i) actin-adhesion traction coupling, (ii) lateral inhibition between neighboring axons, (iii) tubulin transport from soma to the growth cone, and (4) orientation dynamics guided by the substrate anisotropy. Dynamical systems analysis reveals that the saddle-node bifurcation in the actin adhesion subsystem drives a transition to a high-traction motile state, while traction feedback shifts a pitchfork bifurcation in the signaling loop, promoting symmetry breaking and robust alignment. An exact linear solution in the tubulin transport subsystem functions as a built-in speed regulator, ensuring stable elongation rates. Simulations using experimentally inferred parameters accurately reproduce elongation speed, alignment variance, and bundle spacing. The model provides explicit design rules for enhancing axonal alignment through modulation of substrate stiffness and adhesion dynamics. By identifying key control parameters, this work enables rational design of biomaterials for neural repair and engineered tissue systems.