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Biophys J, September 2002, p. 1237-1258, Vol. 83, No. 3
*Department of Mathematics and Institute of Theoretical Dynamics,
University of California, Davis, California 95616 USA; and
Department of Mathematics, University of British
Columbia, Vancouver, British Columbia V6T 1Z2, Canada
We develop a mathematical model that describes key
details of actin dynamics in protrusion associated with cell motility. The model is based on the dendritic-nucleation hypothesis for lamellipodial protrusion in nonmuscle cells such as keratocytes. We
consider a set of partial differential equations for diffusion and
reactions of sequestered actin complexes, nucleation, and growth by
polymerization of barbed ends of actin filaments, as well as capping
and depolymerization of the filaments. The mechanical aspect of
protrusion is based on an elastic polymerization ratchet mechanism. An
output of the model is a relationship between the protrusion velocity
and the number of filament barbed ends pushing the membrane.
Significantly, this relationship has a local maximum: too many
barbed ends deplete the available monomer pool, too few are
insufficient to generate protrusive force, so motility is stalled at
either extreme. Our results suggest that to achieve rapid motility,
some tuning of parameters affecting actin dynamics must be operating in
the cell.
Biophys J, September 2002, p. 1237-1258, Vol. 83, No. 3
© 2002 by the Biophysical Society 0006-3495/02/09/1237/22 $2.00
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