Abstract
We study the glycosylation processes that convert initially toxic substrates to nutritionally valuable metabolites in the flavonoid biosynthesis pathway of tomato (Solanum lycopersicum) seedlings. To estimate the reaction rates we use ordinary differential equations (ODEs) to model the enzyme kinetics. A popular choice is to use a system of linear ODEs with constant kinetic rates or to use Michaelis–Menten kinetics. In reality, the catalytic rates, which are affected among other factors by kinetic constants and enzyme concentrations, are changing in time and with the approaches just mentioned, this phenomenon cannot be described. Another problem is that, in general these kinetic coefficients are not always identifiable. A third problem is that, it is not precisely known which enzymes are catalyzing the observed glycosylation processes. With several hundred potential gene candidates, experimental validation using purified target proteins is expensive and time consuming. We aim at reducing this task via mathematical modeling to allow for the pre-selection of most potential gene candidates. In this article we discuss a fast and relatively simple approach to estimate time varying kinetic rates, with three favorable properties: firstly, it allows for identifiable estimation of time dependent parameters in networks with a tree-like structure. Secondly, it is relatively fast compared to usually applied methods that estimate the model derivatives together with the network parameters. Thirdly, by combining the metabolite concentration data with a corresponding microarray data, it can help in detecting the genes related to the enzymatic processes. By comparing the estimated time dynamics of the catalytic rates with time series gene expression data we may assess potential candidate genes behind enzymatic reactions. As an example, we show how to apply this method to select prominent glycosyltransferase genes in tomato seedlings.
Highlights
In this paper we study metabolic network inference from given biological time-series data
This paper focuses on the mathematical modeling of tree structured metabolic networks in general, the original motivation rose from biological questions concerning the specific networks in flavonol biosynthesis
Throughout this article we use as a model example data the time series of the concentrations of the metabolites involved in a putative quercetin glycosylation pathway (PlantCyc, 2016)
Summary
In this paper we study metabolic network inference from given biological time-series data. The two main ingredients in general metabolic pathway inference are the reconstruction of the network topology and the estimation of the parameters involved. When the network is large and the concentrations of intermediates are unknown, or when there are no time series data available, one may still study the fluxes by setting up stoichiometric models for flux balance analysis (Varma & Palsson, 1995; Stelling et al, 2002; Orth, Thiele & Palsson, 2010). If time-series data of metabolites are available ordinary differential equations (ODEs) can often provide a suitable model (Chen, Niepel & Sorger, 2010; Chou & Voit, 2009; Srinath & Gunawan, 2010; Hatzimanikatis, Floudas & Bailey, 1996). We will test our models and data on both conditions
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