Verbal description of the apex angle-based models of 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 "physiological signal" 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 Coprinus cinereus stems) the the physiological signal at the stage of perception is proportional to the sine of the angle between apex and vertical position. If the organ grows in other certain angle (from horizontal), this signal is proportional to the sine of the difference between the apex angle and the .

During the transmission of the signal the usual paths of for signal transduction are used (i.e. no special constraints are impose by the model). The time, required for transduction of the signal is the main reason for a time delay between the onset of gravitroic stimulation and start of tropic bending. However, this time may also include the time delays required for signal perception and realisation as well; at the present stage of modelling these times are not separable. Hence the signal level in 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 realization site. The level of second factor is proportional to the bending speed. It may be related to the some internal systems of the regulation of the gravitropic response. You can easily ensure in necessity of to suppose such regulation by switching Kw, so-called signal weakening parameter, to zero in the simulation program.

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

P.S. indicates hyperlink to mathematical description.