3:00 p.m., Friday (Feb. 15)
Math Annex 1100
University of California at Davis
How mathematics help us understand cell motion
The motion of animal cells is a complex and important process
that affects growth, development, wound healing, as well as
disease processes (such as cancer). Cell motility is known
to depend on protrusion, adhesion, and retraction of parts
of the cell, which, in turn, stem from both chemical and
mechanical changes in a structure called the cytoskeleton.
Polymerization of components of this structure (usually actin)
is one of the important processes underlying motility.
Generation of force by "molecular motors" such as myosin is
also important. Mathematical models (ordinary and partial
differential equations) and simulations (in 2D and 3D) can
help to understand the roles of the components, their
interactions, and how they are controlled to produce motion
in the cell.
I will present a mechanochemical analysis of a crawling cell
and describe a finite element model wherein (a) localized
protein polymerization and bundling generate the force for
extension, and (b) energy stored in the gel formed from the
polymers at the leading edge is subsequently used to produce
the contraction that pulls the rear of the cell forward. While
this model has features of general interest, I apply it to a
specific example, the crawling of the nematode sperm cell.
These cells crawl using a specialized "major sperm protein",
rather than actin, in their cytoskeleton. Their simplicity
provides a 'stripped down' version of a crawling cell
in which to examine the basic mechanism of cell locomotion,
independent of other cellular functions. I show how results
of the models and simulations, based on realistic values
of known biological parameters agree with the experimental