Glucosinolates are sulphur-rich natural substances found in plants of the Brassicaceae family. Breakdown products of glucosinolates facilitate defence against plant pathogens. The distinct taste and flavour of certain Brassicaceae vegetables (broccoli, cauliflower and cabbage) and condiments (mustard, horseradish and wasabi) is due to the presence of glucosinolates. For humans, glucosinolates functions as cancer-preventive agents and flavour compounds. To fully exploit the potential of glucosinolates in agriculture and medicine, complete understanding of why and how plants synthesize glucosinolates is important.
Why build a mathematical model?
Mathematical modelling is a powerful tool for analysing complex biological systems. It is extensively used to study metabolic networks, concluding a theory called control analysis that quantitatively describes the role of metabolic enzymes in the regulation of reaction rates and metabolite concentrations. Models of metabolic processes, like every other models, are usually developed for certain pragmatic reasons. Every mathematical model is based on some simplifying assumptions to facilitate possible analytical or computational treatment and interpretation of the results. The usefulness of the model depends on the trade-off between the correctness of the representation and the simplicity. Any model from its very beginning is known to be not correct to certain extent. This could be better understood as “we build models to learn why they fail”. Of course, the iterative model-building process gradually eliminates errors and unjustified assumptions, but a certain remainder of incorrectness is deliberately accepted for the sake of simplicity.
Any scientific representation is always a simplification or, more-or-less, a distorted image of the reality.
Mathematical modelling of glucosinolate biosynthesis:
A primary difficulty in the analysis of glucosinolates is the vast diversity of their chemical structures. Apparently, developing models in which all possible structures are represented as a single variable is very challenging. Here, we developed a mathematical model of biosynthesis of glucosinolates, derived from methionine, found in our model plant Arabidopsis thaliana. The principle focus encompasses the metabolite (substrate and product) concentration (i.e. the number of moles of substance per unit volume) and the reaction rate, which is change in concentration per unit time. Our model shows how the reaction rates depend on all other metabolite concentrations, a behaviour originating from broad-range substrate specificity of the metabolic enzymes. Extensive variation is observed in both composition and total accumulation of glucosinolates across different Arabidopsis ecotypes. Addressing the observed diversity, our model explains why and how a particular class of glucosinolates with a particular frequency are produced. Furthermore, by relating the genomic differences to metabolic properties and thus adjusting model parameters, we can reproduce patterns of glucosinolate accumulation from different Arabidopsis ecotypes. Thus, our model provides a framework wherein the link between the genotypes (different plant species) and phenotypes (patterns of glucosinolate accumulation) can be investigated. The knowledge gained will be used to develop new technologies for crop-protection, which is one of the key objectives of CEPLAS.
Suraj Sharma, Institute for Quantitative and Theoretical Biology, Heinrich Heine University Düsseldorf
Under the heading Planter’s Punch we present each month one special aspect of the CEPLAS research programme. All contributions are prepared by our young researchers.