Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.
Bibliographical noteFunding Information:
We thank P. Janmey and Z. Kam for helpful discussions. U.S.S. thanks the Minerva Foundation and the Emmy-Noether program of the German Science Foundation for support. S.A.S. thanks the Schmidt Minerva Center and the Center on Self-Assembly sponsored by the Israel Science Foundation.