Wave-pinning and cell polarity from a bistable reaction-diffusion system
Yoichiro Mori 1, Alexandra Jilkine 1 and Leah Edelstein-Keshet 2*
1 UBC
2 University of British Columbia
* To whom correspondence should be addressed. E-mail: keshet{at}math.ubc.ca.
Submitted on August 29, 2007
Revised on October 5, 2007
Accepted on 20 December 2007
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Abstract |
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Motile eukaryotic cells polarize in response to external signals. Numerous mechanisms have been suggested to account for this symmetry breaking and for the ensuing robust polarization. Implicated in this process are various proteins that are recruited to the plasma membrane and seggregate at an emergent front or back of the polarizing cell. Among these are PI3K, PTEN, and members of the Rho family GTPases such as Cdc42, Rac, and Rho. Many such proteins, including the Rho GTPases cycle between active membrane-bound forms and inactive cytosolic forms. In previous work, we have shown that this property, together with appropriate crosstalk endows a biochemical ``circuit'' (Cdc42, Rac, and Rho) with the property of inherent polarizability. Here we show that this property is present in an even simpler system comprised of a single active/inactive protein pair with positive feedback to its own activation. The simplicity of this minimal system also allows us to explain the mechanism using insights from mathematical analysis. The basic idea resides in a well-known property of reaction-diffusion (RD) systems with bistable kinetics, namely, propagation of fronts. However, it crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation to pin the waves into a stable polar distribution. We refer to these dynamics as wave-pinning and we show that this phenomenon is distinct from Turing-instability generated pattern formation that occurs in RD systems that appear to be very similar. We explain the mathematical basis of the phenomenon, relate it to spatial segregation of Rho GTPases, and show how it can account for spatial amplification, maintainance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells.
Key Words:
Rho-GTPases, bistable reaction-diffusion, cell polarization, stationary front
