Figure 1.

(a) The Hechtian Oscillator ion fluxes regulate growth. Depicts a simplified version of the Hechtian Oscillator in [2]. This figure shows stills from the animation in Supplemental Data. Membrane and ion fluxes are analogous to a molecular “pin-ball machine.” KEY: protons: red, Ca²⁺ ions: yellow, auxin: green, stretch-activated Ca²⁺ channels; Ca²⁺ trickle initiates proton pump activity: (b) Phase I. Quiescent: [7s] Proton pump minimally active; Ca²⁺ channels closed with minimal Ca²⁺ influx. Phase II. Activation: [6s] Turgor increases cell expansion and thus wall stress that increases demand for auxin and opens stretch-activated Ca²⁺ channels; Ca²⁺ trickle initiates auxin binding by the proton pump, initiating low-level oscillator activity leading to Phase III. Phase III. Fully Activated: [12s] high auxin levels fully activate proton pump. Proton extrusion dissociates periplasmic glycomodule AGP-Ca²⁺. Entry via Ca²⁺ channels generates cytosolic Ca²⁺ waves that activate: exocytosis of: cell wall precursors, wall plasticizers and redirect auxin efflux “PIN” proteins. Phase IV: [9s] Returns to Quiescent state: Stress relaxation closes Ca²⁺ channels. Auxin dissociates from proton pump; cytosolic Ca²⁺ recycles to recharge glycomodules and determine phyllotaxis periodicity as follows.