  A key problem of eukaryotic cell motility is the signaling mechanism of
chemoattractant gradient sensing. Recent experiments have revealed the
molecular correlate of gradient sensing: Frontness molecules, such as PI3P and
Rac, localize at the front end of the cell, and backness molecules, such as Rho
and myosin II, accumulate at the back of the cell. Importantly, this
frontness-backness polarization occurs "spontaneously" even if the cells are
exposed to uniform chemoattractant profiles. The spontaneous polarization
suggests that the gradient sensing machinery undergoes a Turing bifurcation.
This has led to several classical activator-inhibitor and activator-substrate
models which identify the frontness molecules with the activator. Conspicuously
absent from these models is any accounting of the backness molecules. This
stands in sharp contrast to experiments which show that the backness pathways
inhibit the frontness pathways. Here, we formulate a model based on the
mutually inhibitory interaction between the frontness and backness pathways.
The model builds upon the mutual inhibition model proposed by Bourne and
coworkers (Xu et al, Cell, 114, 201--214, 2003). We show that mutual inhibition
alone, without the help of any positive feedback, can trigger spontaneous
polarization of the frontness and backness pathways. The spatial distribution
of the frontness and backness molecules in response to inhbition and activation
of the frontness and backness pathways are consistent with those observed in
experiments. Furthermore, depending on the parameter values, the model yields
spatial distributions corresponding to chemoattraction (frontness pathways
in-phase with the external gradient) and chemorepulsion (frontness pathways
out-of-phase with the external gradient).
