Modelling Ca2+ Oscillations in Plants

Abstract

To interpret the physiological functions of Ca2+ oscillations in plants cells, one has to understand how Ca2+ oscillations are generated and how they are modified by internal as well as external stimuli. Yet, oscillations result from nonlinear interactions of different components, which makes it impossible to intuitively predict how a certain stimulus might affect the frequency or amplitude of a Ca2+ oscillation. Usually, it is not even possible to explain why certain conditions result in Ca2+ oscillations whereas others do not. The only way to try to explain intracellular Ca2+ oscillations is by a mathematical model. Here, we give an introduction on how such a mathematical model can be derived. To start with, a general scheme of the Ca2+ fluxes in a plant cell is translated into a set of simple differential equations. Using Sr2+-induced Ca2+ oscillations in the unicellular green alga Eremosphaera viridis as an example, this general scheme is then developed into a complete mathematical model. For this, the different Ca2+ fluxes driving the Ca2+ oscillations are discussed and, term by term, integrated into two coupled, nonlinear differential equations. Where possible, the mathematical description of the transmembrane Ca2+ fluxes is based on experimental results obtained with E. viridis. In some cases, assumptions based on models of Ca2+ oscillations in animal cells are introduced. A couple of simplifications are made to prevent the mathematical model from becoming excessively complex. Despite these limitations, the derived mathematical model qualitatively reproduces the dose dependence of frequency and amplitude of Sr2+-induced Ca2+ oscillations in E. viridis. Finally, it is discussed how Ca2+ oscillations in other plant cells – such as Nod factor-induced Ca2+ oscillations in root hairs or Ca2+ oscillations in stomatal guard cells – might be described mathematically. S. Mancuso and S. Shabala (Eds.) Rhythms in Plants: Phenomenology, Mechanisms, and Adaptive Significance © Springer-Verlag Berlin Heidelberg 2007 1Department of Botany, Oklahoma State University, Stillwater, OK 74078, USA 2Department of Biomedical Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK *Corresponding author, e-mail: gerald.schoenknecht@okstate.edu Ch14.qxd 18/12/06 12:07 PM Page 295