Abstract

Life phenomena result from the mutual equilibrium between the living matter and the surrounding media. A network of servo-mechanisms physiologically restores the stable equilibrium between the interior matter of a living entity in the face of external perturbative agents. In particular, living cells can balance exogenous and endogenous forces using an iterative process, also known as mechano-reciprocity. Hence, not only living matter can adapt through epigenetic remodelling to the external physical cues, but it can also respond by activating gene regulatory processes, which may also drive the onset of pathologies, e.g. solid tumours. Moreover, living materials have the striking ability to change actively their micro-structural organization in order to adjust their functions to the surrounding media, developing a state of internal tension, which even persists after the removal of any external loading. This complex mechanical and biochemical interaction can finally control morphogenesis during growth and remodelling, leading to shape instabilities characterized by a complex morphological phase diagram

In this lecture, I will introduce few mathematical modelling approaches to mechanobiology and morphogenesis in living materials [1], with several applications concerning solid tumours [2,3], gastro-intestinal organogenesis [4], bacterial colonies [5] and nerve fibers [6].

[1] Ciarletta P, Preziosi L, Maugin GA.Mechanobiology of interfacial growth. JOURNAL OF
THE MECHANICS AND PHYSICS OF SOLIDS , 2013, vol. 61, p. 852-872;
[2] Giverso, C.,  Ciarletta, P. (2016). Tumour angiogenesis as a chemo-mechanical surface instability. SCIENTIFIC REPORTS , 6.
[3] Ciarletta P. Buckling instability in growing tumour spheroids. PHYSICAL REVIEW LETTERS , 2013, vol. 110.
[4] Ciarletta P., Balbi V., Kuhl, E. Pattern selection in growing tubular tissues. PHYSICAL
REVIEW LETTERS , 2014, 113, 248101.
[5] Giverso, C., Verani M., Ciarletta P. Branching instability in expanding bacterial colonies.
JOURNAL OF THE ROYAL SOCIETY INTERFACE , 2015, 12, 20141290
[6] Taffetani M., Ciarletta P. Elastocapillarity can control the formation and the morphology
of beads-on-string structures in solid fibers, PHYSICAL REVIEW E , 2015, 91, 032413