As it is known for everybody, when we turn a vertically growing plant into horizontal position, the plant bends upward, restoring the orientation, necessary for its normal life. This is also characteristic for mushrooms and many other objects. This page is about detailed, computer-based analysis of this phenomenon.

Hence

Mathematical modelling of gravitropic reaction in plant and fungi

This page describes the mathematical models of gravitropic reaction, created by Audrius Meskauskas (Gediminas Technical University, Lithuania) and Alvydas Stockus (Institute of Botany, Lithuania) in co-operation with David Moore (Manchester University, United Kingdom).

The gravitropic response is very complex phenomenon, and two general strategies can be adopted in creating the models. In one approach the specific characteristic of particular parts of the biological system are used as modelling parameters. The alternative approach (Johnson & Israelson, 1968; Brown & Chapman, 1977; Stockus & Moore, 1996) differs in that the basis of the model is independent of the real processes. It is dependent on the informational content of those processes for an organism. These imitational models use abstract terms such as "physiological signal" rather than exact parameters like "substance concentration".

The advantage of such an approach is that it can mimic the overall picture of events in gravitropicaly responding organs without going into detail about how the tropic response is realised. The resultant model is an abstraction, which can be applied to a wider range of subjects. Indeed, the model groups, described in this WWW page, were successfully used in simulating and predicting tropic responses in such different groups as plant and fungi. Comparing of the object behaviour, predicted by a certain model, with actual experimental data can be used to explore the processes, that are currently not possible of very difficult to measure directly (see example). Using inhibitor analysis, sometimes it is possible to establish closer relations between abstract model parameters and actual components of the biological system.

As a rule, the models, created in this way, are predictive. For example, fitted into the gravitropic reaction of a certain object under 1 g, they have a potential ability to predict, how the bending process would develop under 2 or 0.5 g. The models can also be used to simulate the gravitropic bending from different initial angle of reorientation. In our demonstration programs you will be able to change such environmental parameters easily and to see the predicted behaviour. The ability for a correct prediction under the changed conditions can be a serious criteria when it is necessary to choose between alternative hypothesis.

Currently we have created two model groups:

The most recent model, developed by A.Meskauskas and D.Moore, simulates the spatial organisation of the gravitropic reaction. The output is a set of the images of the bending organ, indicating, how does the whole shape changes in time. Hence the output of this model can be much more strictly compared with the experimental data, giving possibility to get more exact conclusions.
Verbal description		Mathematical description	Computer simulation Java applet C++ download (177k)
The earlier models, developed by A.Stockus, simulates the changing of the apex angle during the gravitropic reaction (Stockus, 1994). The output is a certain curve, indicating, how does the apex angle changes in time. The models were successfully used for simulation of gravitropic reaction of various objects from plant and fungi kingdoms. These works were a good base to develop the more recent models on the spatial development of gravitropic reaction.
Verbal description		Mathematical description	Computer simulation (Java applet)

 If you have any questions or suggestions, please contact Audrius.Meskauskas@fm.vtu.lt