Mathematical modelling of the gravitropic reaction in fungi and  plants

Bioinformatics is commonly understood as involving work with DNA and protein sequences. However databases and computational analysis was used by some programming biologists with large data sets long before  sequence databases became widely available. Researchers were searching for (and finding) other biological data to work with. One of many such areas was the investigation of spatial movements in fungi and plants.

This page describes several mathematical models of the gravitropic reaction that were created by the late Alvydas Stočkus and Audrius Meškauskas (Institute of Botany, Lithuania) in co-operation with David Moore in the School of Biological Sciences at The University of Manchester, United Kingdom.

The gravitropic response is a very complex phenomenon, and two general strategies can be adopted in creating mathematical 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; Stočkus & 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 gravitropically responding organs without requiring detail about how the tropic response is realised. The resultant model is an abstraction, which can be applied to a wide range of subjects. Indeed, the model groups described on this page were successfully used in simulating and predicting tropic responses in such different groups as fungi and plants. Comparison of the object behaviour, predicted by a certain model, with actual experimental data can be used to explore the processes, even those that are currently not possible or very difficult to measure directly (see example). Using inhibitor analysis, it is sometimes 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 object under the Erath-standard 1 g gravitational acceleration, they have the 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 angles of disorientation. In our demonstration programs you will be able to change such environmental parameters easily and then see the behaviour predicted by the model. The ability to make correct predictions under changed conditions can be a serious criterion when it is necessary to choose between alternative hypothesis.

Currently we have created two model groups:

The most recent model, developed by Audrius Meškauskas and David Moore, simulates the spatial organisation of the gravitropic reaction. The output is a set of hypothetical images of the bending organ, indicating how the whole shape changes in time. Hence the output of this model can be much more strictly compared with experimental data, providing the possibility of reaching more exact conclusions.
Verbal description Mathematical description Computer simulation (Java) 
The earlier models, developed by the late Alvydas Stočkus (and applied to fungi in collaboration with David Moore), simulates change of the apex angle during the gravitropic reaction (Stočkus, 1994). The output is a graphical curve, indicating how the apex angle changes with time. The models were successfully used for simulation of gravitropic reaction of various objects from plant and fungi kingdoms. These analyses provided a good foundation for development of the more recent models on the spatial development of gravitropic reaction.
Verbal description Mathematical description Computer simulation (Java)

 

Experimental data on the spatial organisation of the gravitropic curvature Scientific publications

They lift frail heads in gravity and good faith (from Derek Mahon's poem A disused shed in Co. Wexford)