Mathematical modelling group

Mathematical modelling of regulatory mechanisms of polar auxin flow in plants

Nowadays, mathematical modelling is used as a tool for studying auxin transport more and more often. Present models are sometimes excessively simplified and/or do not reflect the structure of the real system properly. We have focused on construction of a detailed model of auxin transport mechanisms in plant cells using experimental data to analyse particular transport mechanism separately (an analytical-synthetic approach). These data include measurements of accumulation kinetics of radiolabeled auxins in cell suspensions and HPLC analysis of radiolabeled auxin metabolism, which has both provided valuable information about auxin transport properties at cellular level. Using the mathematical model, we have succeeded to prove the effect of NAA metabolism on NAA transport, the ability of tobacco auxin efflux carrier to transport synthetic auxin 2,4-D out of the cells and also to define some of the crucial parameters of cellular auxin transport (Hošek & Kubeš et al., Journal of Experimental Botany 2012). Based on the analysis of the model and performed simulations, the model seems to have a considerable potential for further development in order to contribute to the studies of regulatory mechanisms of active auxin transport.

Construction of the mathematical model of 2,4-D accumulation in cell

Construction of the mathematical model of 2,4-D accumulation in cell. (A) Flow of 2,4-D into/out of the cell entirely by diffusion in case of active influx and efflux inhibition (B) Flow of 2,4-D into/out of the cell by diffusion and active efflux in case of active influx inhibition

Mathematical modelling of the dynamics of metabolic conversions of cytokinins

Metabolic conversions of cytokinins are a dynamical process used by the plant to respond to internal and external stimuli in order to maintain hormonal homeostasis. The first mathematical model of cytokinin metabolic conversions (Lexa et al., Annals of Botany 2003) is built upon the biosynthetic pathway of trans-zeatins that is dependent on isopentenyladenosinmonophosphate and localized in plastids. The model omits the possibility of the alternative direct pathway, where trans-zeatins are produced in cytosol with the use of a different precursor as a donor of the isopentenyl group for adenosiphosphate (Astot et al., PNAS 2000). Even though the production of zeatin-type cytokinins is entirely dependent on the activity of monooxygenases CYP735 (Takei et al., The Journal of Biological Chemistry 2004), this pathway shows only a minor significance in the model. Moreover, the metabolic network used for the construction of the model by Lexa et al. lacks the biosynthetic pathway of cis-zeatins. Six years after this model had been published, the genes coding cytokininphosphoribosylhydrolases were identified. Cytokininphosphoribosylhydrolases are responsible for the single-step production of cytokinin bases from phosphates (Kuroha et al., The Plant Cell 2009). During the following years, substrate specificities of a number of enzymes were defined in addition to what was described by the model by Lexa et al. A newly designed mathematical model of cytokinin metabolism including all metabolic pathways discovered so far would have a potential to explain the origin of cis-zeatins or dihydrozeatins, to support or deny the hypothetic cis-trans-isomerase or to assess the importance and possible regulation of the hydloxylases for the production of zeatin-based cytokins. Our first goal is to construct a multicompartmentational mathematical model of the dynamics of metabolic conversions of cytokinins upon an updated scheme of cytokinin metabolism. Then a series of experimental measurements of the conversions of exogenously applied cytokinins in Arabidopsis thaliana (Columbia-0 ecotype) seedlings will be designed and performed. Based on these data together with the known baseline cytokinin concentrations (Samsonová et al., manuscript in preparation) the parameters of the model will be optimized. The resulting calibrated model will be further analysed and its capability of hypothesis testing will be determined.

We cooperate with doc. RNDr. Ing. Marcel Jiřina, Ph.D. (department of biomedical informatics, Faculty of Biomedical Engineering, Czech Technical University in Prague).