Mechanotransduction mechanisms in growing spherically structured tissues

There is increasing experimental interest in mechanotransduction in multi-cellular tissues as opposed to single cells. This is driven by a growing awareness of the importance of physiologically relevant three-dimensional culture and of cell-cell and cell-gel interactions in directing growth and development. The paradigm biophysical technique for investigating tissue level mechanobiology in this context is to grow model tissues in artificial gels with well-defined mechanical properties. These studies often indicate that the sti↵ness of the encapsulating gel can significantly alter cellular behaviours. We demonstrate here potential mechanisms linking tissue growth with sti↵ness-mediated mechanotransduction. We show how tissue growth in gel systems generates points at which there is a significant qualitative change in the cellular stress and strain experienced. We show analytically how these potential switching points depend on the mechanical properties of the constraining gel and predict when they will occur. Significantly, we identify distinct mechanisms that act separately in each of the stress and strain fields at di↵erent times. These observations suggest growth as a potential physical mechanism coupling gel sti↵ness with cellular mechanotransduction in three-dimensional tissues. We additionally show that non-proliferating areas, in the case that the constraining gel is soft compared with the tissue, will expand and contract passively as a result of growth. Central compartment size is thus seen to not be a reliable indicator on its own for growth initiation or active behaviour.