Fig. 4: Handover from cue-driven to mechanochemically self-organized dynamics.
From: Guiding self-organized pattern formation in cell polarity establishment
a, Evolution of the total numbers of cortical PAR-2, PAR-6 and NMY-2 with both cues active, as determined by numerical evaluation of equations (1)–(6). Black arrows denote an increase in protein numbers by 104. Arrowheads indicate projections of time-rate changes induced by guidance (dark blue) and self-organization (light blue) onto the tangent of the trajectory (see Methods). Guidance release (red point at T ≈ 260 s) occurs when the guiding cue component of the evolution dynamics switches from assisting (that is, pulling forwards along the trajectory) to impeding (pulling backwards along the trajectory). Guiding cues need to be active only up to the transition point at T ≈ 60 s (green dot) to achieve polarization (Supplementary Fig. 8). b, Stability diagram of the homogeneous aPAR-high state as a function of both the contractility strength C*/γ and the aPAR-myosin coupling coefficient kAM. The system is unable to polarize in response to the actomyosin cue (cM1 together with cM2) in the grey region, polarizes in response to the actomyosin cue in the yellow region, and undergoes spontaneous pattern formation in the absence of any cue in the white region. c–e, Schematic of the mechanisms of pattern formation via guided mechanochemical self-organization.
