Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

Abstract

In the Caenorhabditis elegans zygote, PAR protein patterns, driven by mutual anatagonism, determine the anterior-posterior axis and facilitate the redistribution of proteins for the first cell division. Yet, the factors that determine the selection of the polarity axis remain unclear. We present a reaction-diffusion model in realistic cell geometry, based on biomolecular reactions and accounting for the coupling between membrane and cytosolic dynamics. We find that the kinetics of the phosphorylation-dephosphorylation cycle of PARs and the diffusive protein fluxes from the cytosol towards the membrane are crucial for the robust selection of the anterior-posterior axis for polarisation. The local ratio of membrane surface to cytosolic volume is the main geometric cue that initiates pattern formation, while the choice of the long-axis for polarisation is largely determined by the length of the aPAR-pPAR interface, and mediated by processes that minimise the diffusive fluxes of PAR proteins between cytosol and membrane.

Bulk-surface coupling reconciles Min-protein pattern formationin vitroandin vivo

“…Bulk-surface coupling is inherent to many pattern-forming systems beyond the Min system. Intracellular pattern formation in general is based on cycling of proteins between cytosolic and membrane/cortex-bound states; see for example the Cdc42 system in budding yeast and fission yeast (33,58), the PAR system (46,59) in C. elegans, excitable RhoA pulses in C. elegans (60), Xenopus and starfish oocytes (61), and MARCKS dynamics in many cell types (62,63). Further examples include, intracellular signaling cascades (64)(65)(66)(67) and, potentially, intercellular signaling in tissues and biofilms.…”

“…In previous reports, various methods have been employed to enclose the bulk in all three spatial dimensions using microchambers, microwells or vesicles (17,19,21,22,24,43). In contrast to the classical in vitro setup on a large and planar membrane, patterns cannot evolve freely in such geometries because adaption to the confinement ("geometry sensing") interferes with pattern formation (38,45,46). As an illustrative example, consider a traveling wave which is the typical unconfined in vitro phenomenon.…”

Mechanochemical Control of Symmetry Breaking in the Caenorhabditis elegans Zygote

“…It is reasonable to employ computer-assisted approaches to achieve quantitative explanations from these insights. Several mathematical models have already contributed to our understanding of the basic principles in C. elegans SB (Tostevin and Howard, 2008 ; Dawes and Munro, 2011 ; Goehring et al, 2011b ; Kravtsova and Dawes, 2014 ; Gross et al, 2019 ; Geßele et al, 2020 ). Further comprehensive assessment and modeling of the concentration, diffusion, and complex composition of the actin cytoskeleton and PAR proteins will be useful to decipher the complex molecular behaviors into simple principles that govern the spatial organization of a cell.…”

CDC-42 Interactions with Par Proteins Are Critical for Proper Patterning in Polarization

“…In this study, we have reduced the geometry of the embryo to a 1D domain for computational efficiency to facilitate the exploration of a five dimensional parameter space. However, other studies have studied polarization dynamics of simplified two variable models on fully 3D domains [ 39 ] or explicitly included the geometry of the embryo [ 40 ] to investigate the spatial orientation of the polarity axis. Noting the computational demands, we leave minimal network and eFAST analysis of higher dimensional parameter spaces in more complex geometries and 3D domains for future work.…”