The dose–response curve of the gravitropic reaction: a re‐analysis

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Abstract
The dose–response curve of the gravitropic reaction is often used to evaluate the gravisensing of plant organs. It has been proposed (Larsen 1957) that the response (curvature) varies linearly as a function of the logarithm of the dose of gravistimulus. As this model fitted correctly most of the data obtained in the literature, the presentation time (tp, minimal duration of stimulation in the gravitational field to induce a response) or the presentation dose (dp, minimal quantity in g.s of stimulation to induce a response) were estimated by extrapolating down to zero curvature the straight line representing the response as a function of the logarithm of the stimulus. This method was preferred to a direct measurement of dp or tp with minute stimulations, since very slight gravitropic response cannot be distinguished from the background oscillations of the extremity of the organs. In the present review, it is shown that generally the logarithmic model (L) does not fit the experimental data published in the literature as well as the hyperbolic model (H). The H model in its simplest form is related to a response in which a ligand‐receptor system is the limiting phase in the cascade of events leading to the response (Weyers et al. 1987). However, it is demonstrated that the differential growth, responsible for the curvature (and the angle of curvature), would vary as a hyperbolic function of the dose of stimulation, even if several steps involving ligand‐receptor systems are responsible for the gravitropic curvature. In the H model, there is theoretically no presentation time (or presentation dose) since the curve passes through the origin. The value of the derivative of the H function equals a/b and represents the slope of the cune at the origin. It could be therefore used to estimate gravisensitivity. This provides a measurement of graviresponsiveness for threshold doses of stimulation. These results imply that the presentation time (or presentation dose) derived from the L model cannot be used anymore as an estimate of gravisensitivity. On the contrary, the perception time (minimal duration of a repeated stimulation which induces a response), which is less than 1 s, should be related to the perception of gravity. The consequences of these results on the mode of action and the nature of graviperception are discussed.