Cells on a Bed of Micro-Needles: Modeling of the Scaling of the Response

The behavior of a cell attached to a bed of micro-needles is investigated using a bio-chemo-mechanical model. In experiments, the cell is spread on the tips of the micro-needles to which it is attached by focal adhesions bonded to ligands in the fibronectin on the posts. Actin stress-fibers form and attach to the focal adhesion plaques and exert contractile force on the micro-needles. As a result, the posts deflect and their displacements are measured and used to calculate the applied forces. This step is straightforward, because the cells do not adhere to the flanks of the micro-needles, and Euler-Bernoulli beam theory can be used to convert the bending displacements to applied loads. The bio-chemo-mechanical model for the cytoskeleton incorporates a signal, the tension-stabilized formation of actomyosin stress fibers, and their myosin motor driven contractility. In conjunction, the focal adhesions are modeled to account for their mechanosensitivity, in which loads transmitted to them from the stress-fibers encourage the development of plaques attached to the fibronectin on the micro-needle tips. These features have been programmed into a finite element code (ABAQUS) and used to simulate the behavior of cells attached to a bed of micro-posts. The micro-needles themselves are modeled as elastic structures and, consequently, the contractile force applied by the cells causes them to bend. The model of a cell on micro-needles successfully reproduces the characteristics of the data from the experiments. The scaling of the behavior in terms of micro-needle height, diameter, spacing, and elastic stiffness is investigated. In addition, the parameters of the bio-chemo-mechanical model of the cytoskeleton and the focal adhesions are varied (contractile tension, rate of stress-fiber contraction, persistence time for the signal and the effective stiffness of the focal adhesions) and their effect on scaling of the response also investigated. The results provide insight into the bio-chemo-mechanical response of cells to biological stimuli. The scaling simulations also give guidance on how experiments utilizing cells on micro-needles can be designed to extend the understanding of the mechanosensitivity of cells.