PT  - JOURNAL ARTICLE
AU  - Geßele, Raphaela
AU  - Halatek, Jacob
AU  - Frey, Erwin
TI  - PAR protein activation-deactivation cycles stabilize long-axis polarization in <em>C. elegans</em>
AID  - 10.1101/451880
DP  - 2018 Jan 01
TA  - bioRxiv
PG  - 451880
4099  - http://biorxiv.org/content/early/2018/10/25/451880.short
4100  - http://biorxiv.org/content/early/2018/10/25/451880.full
AB  - Cell polarity endows cells with a reference frame that guides cellular organization and division. In the Caenorhabditis elegans zygote, PAR protein patterns determine the anterior-posterior axis and facilitate the redistribution of proteins for the first asymmetric cell division. While previous theoretical work has shown that mutual antagonism between (anterior) aPAR and (posterior) pPAR proteins is the key to polarity maintenance, what factors determine the selection of the polarity axis remains unclear. Here we formulate a reaction-diffusion model in a realistic cell geometry, based on bimolecular reactions and fully accounting for the coupling between membrane and cytosolic dynamics. We find that the kinetics of the phosphorylation-dephosphorylation cycle of PAR proteins is crucial for the selection of the long (anterior-posterior) axis for polarization. Biochemical cycles based on mutual exclusion alone, without a delay in dephosphorylation, would lead to short (dorsal-ventral) axis polarization. Our analysis shows that the local ratio of membrane surface to cytosolic bulk volume is the main geometric cue to which patterns adapt, and the decisive parameter that determines axis selection is given by the ratio of the diffusive length of the phosphorylated (inactive) phase to the cell length. We quantify the effect of relative protein numbers and find that they primarily affect the robustness of protein pattern formation. In particular, robustness to variations in the phosphorylation rates increases if scaffold proteins like PAR-3 are more abundant than PKC-3, which phosphorylates pPARs. Together, our theoretical study reveals the crucial role of geometry in self-organized protein pattern formation: axis selection is based on the generic dependence of intracellular pattern-forming processes on the local ratio of membrane surface to cytosolic volume.