| Summary: | Actin growth is a fundamental biophysical process and it is, at the same
time, a prototypical example of diffusion-mediated surface growth. We formulate
a coupled chemo-mechanical, one-dimensional growth model encompassing both
material accretion and ablation. A solid bar composed of bound actin monomers
is fixed at one end and connected to an elastic device at the other. This
spring-like device could, for example, be the cantilever tip of an atomic force
microscope. The compressive force applied by the spring on the bar increases as
the solid grows and affects the rate of growth. The mechanical behaviour of the
bar, the diffusion of free actin monomers in a surrounding solvent and the
kinetic growth laws at the accreting/ablating ends are accounted for. The
constitutive response of actin is modeled by a convex but otherwise arbitrary
elastic strain energy density function. Treadmilling solutions, characterized
by a constant length of the continuously evolving body, are investigated.
Existence and stability results are condensed in the form of simple formulas
and their physical implications are discussed.
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