  Control of the cytoskeleton and mechanical contacts with the extracellular
environment are essential component of motility in eukaryotic cells. In the
absence of signals, cells continuously rebuild the cytoskeleton and
periodically extend pseudopods or other protrusions at random membrane
locations. Extracellular signals bias the direction of movement by biasing the
extension of protrusions, but this involves another layer of biochemical
networks for signal detection, transduction, and control of the rebuilding of
the cytoskeleton. Here we develop a model for the latter processes that centers
on a Ras-based module that adapts to constant extracellular signals and
controls the downstream PI3K-PIP3-based module responsible for amplifying a
spatial gradient of the signal. The resulting spatial gradient can lead to
polarization, which enables cells to move in the preferred direction (up
gradient for attractants and down-gradient for repellents). We show that the
model can replicate many of the observed characteristics of the responses to
cAMP stimulation for Dictyostelium, and analyze how cell geometry and signaling
interact to produce the observed localization of some of the key components of
the amplification module. We show how polarization can emerge without
directional cues, and how it interacts with directional signals and leads to
directional persistence. Since other cells such as neutrophils use similar
pathways, the model is a generic one for a large class of eukaryotic cells.
