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Exploring the Control Circuit of Cell Migration by Mathematical Modeling

Javier Satulovsky ^*, Roger Lui  and Yu-li Wang ^*

^* Department of Physiology, University of Massachusetts Medical School, Worcester, Massachusetts; and Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts

Correspondence: Address reprint requests to Yu-li Wang, University of Massachusetts Medical School, 377 Plantation St., Ste. 327, Worcester, MA 01605. Tel.: 508-856-8781; Fax: 508-856-8774; E-mail: yuli.wang{at}umassmed.edu.

We have developed a top-down, rule-based mathematical model to explore the basic principles that coordinate mechanochemical events during animal cell migration, particularly the local-stimulation-global-inhibition model suggested originally for chemotaxis. Cells were modeled as a shape machine that protrudes or retracts in response to a combination of local protrusion and global retraction signals. Using an optimization algorithm to identify parameters that generate specific shapes and migration patterns, we show that the mechanism of local stimulation global inhibition can readily account for the behavior of Dictyostelium under a large collection of conditions. Within this collection, some parameters showed strong correlation, indicating that a normal phenotype may be maintained by complementation among functional modules. In addition, comparison of parameters for control and nocodazole-treated Dictyostelium identified the most prominent effect of microtubules as regulating the rates of retraction and protrusion signal decay, and the extent of global inhibition. Other changes in parameters can lead to profound transformations from amoeboid cells into cells mimicking keratocytes, neurons, or fibroblasts. Thus, a simple circuit of local stimulation-global inhibition can account for a wide range of cell behaviors. A similar top-down approach may be applied to other complex problems and combined with molecular manipulations to define specific protein functions.

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