Multiscale modelling of axon durotaxis

Thesis

During development, axons navigate to their targets in part by responding to spatial variation in substrate stiffness, a phenomenon termed durotaxis. Yet, existing theories of axon guidance lack a framework that connects environmental stiffness, focal-adhesion-mediated traction generation, and the deformation and reorientation of the axon shaft. This thesis develops such a framework, built on the hypothesis that guidance cues act by modulating growth cone traction, which in turn reorients the axon through its mechanical response.

Our analysis proceeds from the microscale upwards. The motor–clutch system on a deformable substrate is formulated as a differential Chapman–Kolmogorov equation for the full linker-extension distribution. The single-linker steady state is solved exactly, giving a statistical characterisation of dynamical regimes previously identified only from simulated trajectories; a mean-field treatment of the many-linker case yields an explicit expression for the optimal substrate stiffness and the conditions under which it exists. Coupling this traction law to a remodelling beam model of the axon shaft gives the Axon-Beam-Clutch model, which produces both positive and negative durotaxis and predicts a guidance mode not previously described: convergence onto trajectories parallel to lines of optimal stiffness, a behaviour that depends on the finite spatial extent of the axon and therefore on long-range mechanical sensing by the shaft.

The bending stiffness of the axon, a parameter required by the model, is inferred from pulling experiments using an extensible beam description in place of the conventional elastic string. The same data are shown to support either of the two estimates reported in the literature, B ∼ 10−21Nm2 and B ∼ 10−19 Nm2, depending on whether the axon is treated as isotropic.

The Axon-Beam-Clutch framework is then applied to neurite interaction with sharp stiffness interfaces, guidance of Xenopus retinal ganglion cell axons along the optic tract, and segmented outgrowth of motor axons in the peripheral nervous system, in each case identifying what traction-based guidance can account for in isolation.

Authors: Kassianides, C

• DOI: 10.5287/ora-6gzp5n671
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: modelling; mechanics; simulation; bending stiffness; bending rigidity; development; traction; optic tract; beam; mean field; focal adhesion; durotaxis; axon
• Subjects: Mathematical models