Modeling pollen tube growth: Feeling the pressure to deliver testifiable predictions

Abstract

T he frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step toward understanding the dynamics of the growth behavior in walled cells.Plant cell growth and expansion is driven by the turgor pressure which provides the physical force necessary to expand the rigid cell wall. While turgor is an essential prerequisite for growth, no direct correlation was found between the magnitude of the turgor pressure and the growth rate of the cell in the pollen tube, a unidirectionally expanding cell.1 This observation seems counterintuitive given that a simple physical relation, formulated by Lockhart's equation, predicts a linear relationship between turgor and growth rate.2 The question of whether and how turgor and

Pressure–Induced Cell Wall Instability and Growth Oscillations in Pollen Tubes

“…The oscillation frequency can be estimated from Fig. 5 to be a value of approximately Hz, which is in accord with the main observed periodical mode [5] in the longitudinal power spectrum of pollen tube oscillatory motion, and presumably also with the rate of exocytosis and new cell wall assembly in Nicotiana tabacum pollen tubes [4] . This periodical growth activity, can in turn be related to the stress-relaxation rate at the – interface ( Fig.…”

“…Oscillations take place between and potential energy level (compare with [60] , Fig. 2 ), by tunneling through symmetry change, yielding , while the amplitude is determined by the actual pressure level, in accord with experiments ( [4] , [9] ). The source of the potential: pressure – induced (residual) internal stress field in the wall.…”

“…Fig. 4 in [9] ; [4] ). Wall expansion is allowed by stress relaxation (molecular separation for – values exceeding those of harmonic potential).…”

“…We also showed that cellular turgor pressure does not need to undergo changes during these repeated growth phases to display periodicity in growth. However, turgor pressure is still central in controlling the dynamics of pollen tube growth because of its ability to change wall stress and hence oscillation frequencies in the different osmotic environments [4] .…”

“…Pollen tube growth is a critical process in the life cycle of higher plants (Winship et al, 2010). It has garnered a lot of attention and is at the center of considerable controversy (Kroeger and Geitmann, 2011a). The pollen tube is the carrier of the male gametes in flowering plants.…”