Touching the surface – how cells experience the mechanical properties of their environment – a mathematical model

It is becoming increasingly clear that the mechanical properties of their environment play a crucial role in determining cellular behaviour and coordination. Notably, the stiffness of the underlying substrate has been shown to determine the specialisation of stem cells, overriding chemical cues over an extended period of time: mesenchymal stem cells develop into brain-like cell types when cultivated on extremely soft substrates and more bone-like cell types on stiffer substrates. Throughout the body cells are influenced by the mechanical properties of their surroundings eg osteoporosis has been linked to mechanical changes in bone tissue and the ageing of stem cells within the central nervous system with the stiffening of their microenvironment. Further, understanding these differences in cell behaviour is crucial for tissue engineering applications and to understand how the mechanical microenvironment may affect cancer growth and invasion.

Cells probe the mechanical properties of their environment by the transmission of internally generated contractile forces from the cytoskeleton to the exterior. I develop an elasticity theory-based model to describe this mechanosensory mechanism, which I analyse and solve using both analytical and computational methods. I consider the distribution of adhesion throughout a cell to recreate cell shapes and deformations that are consistent with those experimentally observed.  I use the model to predict observed cellular adaptations to changes in mechanical properties of the underlying gel.  I show that the distribution of adhesion points between the cell and substrate naturally affects the resultant cellular deformation and resultant cellular stiffness sensing. Specifically, increasing the adhered area effectively increases the resistance experienced by a cell while large gaps between adhered regions reduce the resistance experienced. Further, energy considerations have significant implications for the optimisation of cell adhesion.