APPLIED MATHEMATICS

Unraveling Cellular Motion

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Science  10 Nov 2006:
Vol. 314, Issue 5801, pp. 897
DOI: 10.1126/science.314.5801.897a

The mechanisms whereby living cells propel themselves across various media involve a remarkably complicated set of factors. Experiments 25 years ago sought to track the wrinkle patterns induced by cell motion on an elastic film, and thus to determine the forces underlying cellular motion, but the problem proved highly nonlinear. A later proposal was to monitor the movement of fluorescent marker beads in a soft gel that remained in the linear elastic regime, but these results were highly sensitive to input data. Most recently, cells were observed on a bed of microneedles, with the degree of needle bending used to extract the force exerted by the cells as they traveled. However, in this case spatial resolution was limited and the environment somewhat unrealistic.

Calculations in such a context, which rely on incomplete data to create a model, are called inverse problems and crop up in many fields, including geophysics, medical imaging, and astronomy. Unfortunately, solving this class of ill-posed problems is often difficult on account of their high sensitivity to changes in the data. Ambrosi presents a fresh strategy for solving the inverse problem of cell traction on an elastic substrate, employing marker data to reveal the forces that cells exert on a gel. The method uses minimization followed by numerical solution of coupled partial differential equations and may also be applicable to other similar inverse problems. — DV

SIAM J. Appl. Math. 66, 2049 (2006).

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