  Various molecules exclusively accumulate at the front or back of migrating
eukaryotic cells in response to a shallow gradient of extracellular signals.
Directional sensing and signal amplification highlight the essential properties
in the migrating cells, known as cell polarity. In addition to these, such
properties of cell polarity involve unique determination of migrating direction
(uniqueness of axis) and localized gradient sensing at the front edge
(localization of sensitivity), both of which may be required for smooth
migration. Here we provide the mass conservation system based on the
reaction-diffusion system with two components, where the mass of the two
components is always conserved. Using two models belonging to this mass
conservation system, we demonstrate through both numerical simulation and
analytical approximations that the spatial pattern with a single peak
(uniqueness of axis) can be generally observed and that the existent peak
senses a gradient of parameters at the peak position, which guides the movement
of the peak. We extended this system with multiple components, and we developed
a multiple-component model in which cross-talk between members of the Rho
family of small GTPases is involved. This model also exhibits the essential
properties of the two models with two components. Thus, the mass conservation
system shows properties similar to those of cell polarity, such as uniqueness
of axis and localization of sensitivity, in addition to directional sensing and
signal amplification.
