Geometric Considerations of Micro- to Nanoscale Elastomeric Post Arrays to Study Cellular Traction Forces

Mechanical interactions between cells and their surrounding extracellular matrix (ECM) play an important role in regulating many cellular functions, such as migration, proliferation and differentiation. Cells adhere to a substrate through an integrated process that involves binding and clustering of integrins to ECM ligands, actin polymerizationdriven plasma membrane extension, and contraction of the actomyosin cytoskeleton which transmits traction forces to the substrate through sites of adhesion. Interestingly, mechanical properties of the substrate, such as stiffness and ECM ligand topology, feedback to affect the ability of cells to exert these forces and spread across the substrate. To elucidate the relationship between substrate mechanics, cell adhesion and traction forces, several approaches have been developed and continually refined. The first approach was to engineer soft materials such as partially crosslinked silicone elastomers and polyacrylamide gels. Cells cultured on these substrates generated deformations that could be mapped by the displacement of embedded fluorescent markers and used to calculate traction forces. In contrast to the continuous elastic substrata method, we pioneered another approach using microfabrication tools to develop an elastomeric micropost array (mPADs). Cells cultured on this substrate deflect underlying posts as they contract. Traction forces could be calculated from these post deflections using a simple force-displacement relationship for pure bending of an elastic cylindrical beam (Eq. 1),