Stochastic model decodes axonal guidance for nerve repair scaffolds

In a new review and modeling paper on arXiv (arXiv:2205.10723, published in AppliedMath 2025), physicist Cristian Staii tackles a fundamental puzzle in neuroscience: how do axons — the long projections of neurons — navigate through complex tissue to form precise circuits? The work combines established stochastic frameworks with a novel mechanochemical model to explain how deterministic guidance from substrate mechanics and geometry interacts with random fluctuations from molecular signaling and cytoskeletal assembly.

Staii uses Langevin dynamics and the associated Fokker-Planck equation to describe axonal motion and turning under combined biases and noise. Paired with experiments, these models yield measurable parameters like effective diffusion coefficients, speed and angle distributions, and mean-square displacement. The paper then goes further: coupling the Fokker-Planck description to an actin-myosin-clutch model and performing a linear stability analysis using Routh–Hurwitz criteria. This analysis reveals three regimes: steady extension, damped oscillations, and sustained limit cycles generated by Hopf bifurcations. By linking single-cell biophysics to collective growth statistics, the work provides a quantitative framework for understanding axonal guidance and connectivity. The ultimate payoff: better design of engineered substrates and neuroprosthetic scaffolds to enhance nerve repair and regeneration after injury.