A Systems Model of the Eco-physiological Response of Plants to Environmental Heavy Metal Concentrations

The ecophysiological response of plants to environmental heavy metal stress is indicated by the profile of its tissue HM concentrations (Cp) versus the concentration of the HM in the substrate (Cs). We report a systems biology approach to the modelling of the Cp-Cs profile using as loose analogy, the Verhulst model of population dynamics but formulated in the concentration domain. The HM is conceptualized as an ecological organism that ‘colonizes’ the resource zone of the plant cells driven by the potential supplied by the higher HM concentration in the substrate. The infinite occupation by the HM is limited by the eventual saturation of the cellular binding sites. The solution of the differential equation results in the logistic equation, the r-K model. The model is tested for 3 metalophillic plants T.erecta, S. vulgaris and E. splendens growing in different types of substrates, contaminated to varying extents by different copper compounds. The model fitted the experimental Cp-Cs profiles well. The r,K parameter values and secondary quantities derived from them, allowed a quantification of the number of Cu binding sites per cell at saturation, the sensitivities (affinities) of these sites for Cu in the 3 experimental systems as well as the extraction of information related to the substrate phyto-availability of the Cu. Thus even though the model operates at the systems level it permits useful insights into underlying processes that ultimately derive from the cumulative molecular processes of HM homeostasis. The chief advantages of the model are its simplicity, fewer arbitrary parameters, and the non-specification of constraints on substrate and plant type.