Abstract
Tissue stiffness (Young's modulus) is a key control parameter in cell behavior and bioengineered gels where defined mechanical properties have become an essential part of the toolkit for interrogating mechanotransduction. Here, we show using a mechanical cell model that the effective substrate stiffness experienced by a cell depends, not just on the engineered mechanical properties of the substrate but critically also on the particular arrangement of adhesions between cell and substrate. In particular, we find that cells with different adhesion patterns can experience two different gel stiffnesses as equivalent and will generate the same mean cell deformations. In considering small patches of adhesion, which mimic focal adhesion complexes, we show how the experimentally observed focal adhesion growth and elongation on stiff substrates can be explained by energy considerations. Relatedly, energy arguments also provide a reason why nascent adhesions do not establish into focal adhesions on soft substrates, as has been commonly observed. Fewer and larger adhesions are predicted to be preferred over more and smaller, an effect enhanced by random spot placing with the simulations predicting qualitatively realistic cell shapes in this case.