A new MOX report entitled “Mathematical modelling of axonal cortex contractility” by Andrini, D.; Balbi, V.; Bevilacqua, G.; Lucci, G.; Pozzi, G.; Riccobelli, D. has appeared in the MOX Report Collection.
The report can be donwloaded at the following link:
https://www.mate.polimi.it/biblioteca/add/qmox/70/2022.pdf
Abstract: The axonal cortex is composed of a regular structure of F-actin and spectrin able to contract thanks to myosin II motors. Such an active tension is of fundamental importance in controlling the physiological shape of axons. Recent experiments show that axons modulate the contraction of the cortex when subject to mechanical deformations, exhibiting a non-trivial coupling between the hoop and the axial active tension. However, the underlying mechanisms are still poorly understood. In this paper, we propose a continuum model of the axon based on the active strain theory. By using the Coleman-Noll procedure, we shed light on the coupling between the hoop and the axial active strain through the Mandel stress tensor. We propose a qualitative analysis of the system under the simplifying assumption of incompressibility, showing the existence of a stable equilibrium solution. In particular, our results show that the axon regulates the active contraction ! to mainta in a homeostatic stress state. Finally, we propose numerical simulations of the model, using a more suitable compressible constitutive law. The results are compared with experimental data, showing an excellent quantitative agreement.
