Pressure-induced wall thickness variations in multi-layered wall of a pollen tube and Fourier decomposition of growth oscillations.

The augmented growth equation introduced by Ortega is solved for the apical portion of the pollen tube as an oscillating volume, which we approach in the framework of a two-fluid model in which the two fluids represent the constant pressure and the fluctuating features of the system. Based on routine Fourier analysis, we calculate the energy spectrum of the oscillating pollen tube, and discuss the resonant frequency problem of growth rate oscillations. We also outline a descriptive model for cell wall thickness fluctuations associated with small, yet regular variations (~ 0.01 MPa) observed in turgor pressure. We propose that pressure changes must lead to the sliding of wall layers, indirectly resulting in a wave of polarization of interlayer bonds. We conclude that pollen tube wall thickness may oscillate due to local variations in cell wall properties and relaxation processes. These oscillations become evident because of low amplitude/high frequency pressure fluctuations δP being superimposed on turgor pressure P. We also show that experimentally determined turgor pressure oscillates in a strict periodical manner. A solitary frequency f0 ≈ 0.066 Hz of these (~ 0.01 MPa in magnitude) oscillations for lily pollen tubes was established by the discrete Fourier transform and Lorentz fit.