Verbal description of the apex angle-based models of the gravitropic reaction

The difference in growth rates between opposite flanks of an axial organ is the cause of gravitropic curvature. In fact, such a specific definition is not necessary for imitational modelling. For modelling purposes, it is usually enough to assume that curvature just occurs in response to some signal. The factor (or factors) which code the delivery and intensity of this curvature in the modelling were considered to be the "physiological signals" for tropic bending.

The basic scheme of the model was derived from those of Rawitscher (1932) and Merkys et al. (1972). This group of models assume only one gravitropic signal. It is generated in the perception stage and then carried to the site of its realisation, where it is used to generate the growth differential.

For strictly positively or negatively gravitropic organs (such as fungus mushroom fruit body stems) the physiological signal at the stage of perception is proportional to the sine of the angle between the apex and the true vertical. If the organ grows in another particular angle (from the horizontal), this signal is proportional to the sine of the difference between the apex angle and the angle .

During the transmission of the signal the usual paths for transduction of physiological signals are used (that is, no special constraints are imposed by the model). The time, required for transduction of the signal is the main reason for any time delay between the onset of gravitroic stimulation and the start of tropic bending. However, this time may also include those time delays required for signal perception and realisation as well, because, at the present stage of modelling, these times are not separable. Hence, the signal level at the realisation site is proportional to the signal level in the apex as it was a certain time before.

During the realisation of gravitropic response, the bending acceleration (not speed) is proportional to the difference of two factors. The first factor is the level of gravitropic signal in the realisation site. The level of the second factor is proportional to the bending speed. It may be related to some internal system(s) for regulation of the gravitropic response. You can easily appreciate the necessity of supposing such a regulation factor by switching Kw (the so-called signal weakening parameter) to zero in the simulation program.

This model can be successfully fitted to the gravitropic reaction of many objects from both plant and fungal kingdoms. More information about this and other apex-angle based models, created in our research, can be found in our list of publications.

NOTE: indicates a hyperlink to a mathematical description.

Mathematical description

Simulation program