Hydrodynamics, cell wall and ion dynamics are all important properties that regulate pollen tube growth. Currently, the two main pollen tube growth models, the cell wall model and the hydrodynamic model do not appear to be reconcilable. Here we develop an integrative model for pollen tube growth and show that our model reproduces key experimental observations: (1) that the hypertonic condition leads to a much longer oscillatory period and that the hypotonic condition halves the oscillatory period; (2) that oscillations in turgor are experimentally undetectable; (3) that increasing the extracellular calcium concentration or decreasing the pH decreases the growth oscillatory amplitude; (4) that knockout of Raba4d, a member of the Rab family of small GTPase proteins, decreases pollen tube length after germination for 24 h. Using the model generated here, we reveal that (1) when cell wall extensibility is large, pollen tube may sustain growth at different volume changes and maintain relatively stable turgor; (2) turgor increases if cell wall extensibility decreases; (3) increasing turgor due to decrease in osmolarity in the media, although very small, increases volume change. However, increasing turgor due to decrease in cell wall extensibility decreases volume change. In this way regulation of pollen tube growth by turgor is context dependent. By changing the osmolarity in the media, the main regulatory points are extracellular osmolarity for water flow and turgor for the volume encompassed by the cell wall. However, if the viscosity of cell wall changes, the main regulatory points are turgor for water flow and wall extensibility for the volume encompassed by the cell wall. The novel methodology developed here reveals the underlying context-dependent regulatory principle of pollen tube growth.
Keywords: cell wall and ion dynamics; interplay of hydrodynamics; mathematical modeling; oscillatory dynamics; pollen tube growth; regulation coefficients.