Theory for durotactic axon guidance

During the development of the nervous system, neurons extend bundles of axons that grow and
meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these
bundles to migrate and reach their functional target. Directional information depends on external
cues such as chemical or mechanical gradients. Unlike chemotaxis that has been extensively studied,
the role and mechanism of durotaxis, the directed response to variations in substrate rigidity, remain
unclear. We model bundle migration and guidance by rigidity gradients by using the theory of
morphoelastic rods. We show that at a rigidity interface, the motion of axon bundles follows a
simple behavior analogous to optic ray theory and obeys Snell’s law for refraction and reflection.
We use this powerful analogy to demonstrate that axons can be guided by the equivalent of optical
lenses and fibers created by regions of different stiffnesses.