Stability and roughness of interfaces in mechanically-regulated tissues

Abstract

Cell division and death can be regulated by the mechanical forces within a tissue. We study the consequences for the stability and roughness of a propagating interface, by analysing a model of mechanically-regulated tissue growth in the regime of small driving forces. For an interface driven by homeostatic pressure imbalance or leader-cell motility, long and intermediate-wavelength instabilities arise, depending respectively on an effective viscosity of cell number change, and on substrate friction. A further mechanism depends on the strength of directed motility forces acting in the bulk. We analyse the fluctuations of a stable interface subjected to cell-level stochasticity, and find that mechanical feedback can help preserve reproducibility at the tissue scale. Our results elucidate mechanisms that could be important for orderly interface motion in developing tissues.

Final author version, In press at Phys. Rev. Lett., supplement is available at: https://www.dropbox.com/s/p5mwzdxlw40eglv/supplement_28Nov.pdf?dl=0 or contact authors

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• On BIBO stability of systems with irrational transfer function

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