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Cell Orientation by a Microgrooved Substrate Can Be Predicted by Automatic Control Theory

Ralf Kemkemer ^* , Simon Jungbauer , Dieter Kaufmann  and Hans Gruler ^*

^* Departments of Biophysics and Human Genetics, University of Ulm, Ulm, Germany; and Max-Planck-Institute for Metals Research, Stuttgart, Germany

Correspondence: Address reprint requests to Prof. Dr. Hans Gruler, Tel.: 49-731-502-3052; E-mail: hans.gruler{at}uni-ulm.de.

Cells have the ability to measure and respond to extracellular signals like chemical molecules and topographical surface features by changing their orientation. Here, we examined the orientation of cultured human melanocytes exposed to grooved topographies. To predict the cells' orientation response, we describe the cell behavior with an automatic controller model. The predicted dependence of the cell response to height and spatial frequency of the grooves is obtained by considering the symmetry of the system (cell + substrate). One basic result is that the automatic controller responds to the square of the product of groove height and spatial frequency or to the aspect ratio for symmetric grooves. This theoretical prediction was verified by the experiments, in which melanocytes were exposed to microfabricated poly(dimethylsiloxane) substrates having parallel rectangular grooves of heights (h) between 25 and 200 nm and spatial frequencies (L) between 100 and 500 mm^–1. In addition, the model of the cellular automatic controller is extended to include the case of different guiding signals acting simultaneously.