Abstract
Biological oscillation occurs at various levels, from cellular signaling to organismal behaviors. Mathematical modeling has allowed a quantitative understanding of slow oscillators requiring changes in gene expression (e.g., circadian rhythms), but few theoretical studies have focused on the rapid oscillation of cellular signaling. The tobacco pollen tube, which exhibits growth bursts every 80 s or so, is an excellent system for investigating signaling oscillation. Pollen tube growth is controlled by a tip-localized ROP1 GTPase, whose activity oscillates in a phase about 90 degrees ahead of growth. We constructed a mathematical model of ROP1 activity oscillation consisting of interlinking positive and negative feedback loops involving F-actin and calcium, ROP1-signaling targets that oscillate in a phase about 20 degrees and 110 degrees behind ROP1 activity, respectively. The model simulates the observed changes in ROP1 activity caused by F-actin disruption and predicts a role for calcium in the negative feedback regulation of the ROP1 activity. Our experimental data strongly support this role of calcium in tip growth. Thus, our findings provide insight into the mechanism of pollen tube growth and the oscillation of cellular signaling.
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