A very simple, one-dimensional, discrete, autonomous model of cell crawling is proposed; the model involves only three or four coupled first-order differential equations. This form is sufficient to describe many general features of cell migration, including both steady forward motion and oscillatory progress. Closed-form expressions for crawling speeds and internal forces are obtained in terms of dimensionless parameters that characterize active intracellular processes and the passive mechanical properties of the cell. Two versions of the model are described: a basic cell model with simple elastic coupling between front and rear, which exhibits stable, steady forward crawling after initial transient oscillations have decayed, and a poroelastic model, which can exhibit oscillatory crawling in the steady state.
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