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Cells are highly sensitive to mechanical cues in their microenvironment, which play a fundamental role in regulating orientation, cytoskeletal organization, and growth dynamics. In particular, cells and neurons seeded on cyclically stretched substrates have been shown to reorient toward well-defined equilibrium angles with respect to the principal strain direction \cite{lucci:review}
Cell reorientation can be mathematically described by a linear viscoelastic model that captures the coupled evolution of intracellular stress and orientation under periodic stretching \cite{lucci:2021}. The model predicts oscillatory reorientation dynamics converging toward a stable equilibrium angle, which can be interpreted as the minimizer of a general orthotropic elastic energy. Bifurcation analysis and numerical simulations reveal a transition in reorientation dynamics governed by the interplay between stretching frequency and the characteristic turnover time of cytoskeletal and adhesion components, with faster reorientation occurring at higher frequencies.
Building on this approach, the modeling framework is extended to neurons by coupling a viscoelastic reorientation model of the growth cone with a moving-boundary description of tubulin-driven neuron growth \cite{Colombi_neurons}. Numerical simulations across a range of stretching frequencies and strain amplitudes reproduce experimentally observed equilibrium orientations and demonstrate that both the directionality and speed of axonal growth are strongly modulated by mechanical stimulation. In particular, higher stretching frequencies and amplitudes lead to faster reorientation and more directed pathfinding.
Overall, the proposed models highlight common physical principles underlying mechanosensitive orientation in cells and neurons and provide a quantitative link between substrate mechanics, viscoelastic cellular response, and long-term growth behavior.
Bibliography
@article{lucci:review,
author = "Giverso, C. and Loy, N. and Lucci, G. and Preziosi, L.",
title = "Cell orientation under stretch: A review of experimental findings and mathematical modelling",
journal = {Journal of Theoretical Biology},
volume = {572},
pages = {111564},
year = {2023},
doi ={10.1016/j.jtbi.2023.111564}
}
@article{lucci:2021,
title = {Cell orientation under stretch: Stability of a linear viscoelastic model},
journal = {Mathematical Biosciences},
volume = {337},
pages = {108630},
year = {2021},
issn = {0025-5564},
doi = {https://doi.org/10.1016/j.mbs.2021.108630},
author = {Giulio Lucci and Chiara Giverso and Luigi Preziosi},
}
@article{Colombi_neurons,
author = {Colombi, Annachiara and Battaglia, Andrea and Giverso, Chiara},
title = {A Mathematical Model for Neuron Reorientation and Axonal Growth on a Cyclically Stretched Substrate},
journal = {Studies in Applied Mathematics},
volume = {155},
number = {3},
pages = {e70103},
year = {2025}
}
