Parameter estimation in tree graph metabolic networks
- Published
- Accepted
- Subject Areas
- Agricultural Science, Computational Biology, Food Science and Technology, Mathematical Biology, Plant Science
- Keywords
- Metabolic networks, Systems biology, Kinetic models, Glycosylation, Network inference, Solanum lycopersicum
- Copyright
- © 2016 Astola et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2016. Parameter estimation in tree graph metabolic networks. PeerJ Preprints 4:e2077v2 https://doi.org/10.7287/peerj.preprints.2077v2
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 very fast compared to the usually applied methods, since it is not based on an iterative scheme. 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.
Author Comment
This has been submitted to PeerJ.
Supplemental Information
Time series measurements of metabolites
This excel file contains the concentrations of the metabolites on different time points and under different conditions.
A software program for solving the kinetic rates given the time series of concentrations
This Mathematica notebook solves the time-varying enzyme concentrations, given the time-series of concentrations and a hypothetical metabolic network.
microarray measurements of glycosyl transferases
This dataset was used to compare the estimated enzymatic rates from the mathematical model to the actual expression rates of the enzymes that are potentially involved in the reactions.