Parameter estimation in tree graph metabolic networks.
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.
Department of Biomedical Engineering, Eindhoven University of Technology , Eindhoven , Netherlands.
Laura
L
Astola
Biometris, Department for Mathematical and Statistical Methods, Wageningen University and Research Centre , Wageningen , Netherlands.
Hans
H
Stigter
Institute of Plant Sciences Paris-Saclay , Gif-sur-Yvette , France.
Maria Victoria
MV
Gomez Roldan
Biometris, Department for Mathematical and Statistical Methods, Wageningen University and Research Centre , Wageningen , Netherlands.
Fred
F
van Eeuwijk
Plant Research Intenational-Bioscience, Wageningen University and Research Centre , Wageningen , Netherlands.
Robert D
RD
Hall
Biometris, Department for Mathematical and Statistical Methods, Wageningen University and Research Centre , Wageningen , Netherlands.
Marian
M
Groenenboom
Biometris, Department for Mathematical and Statistical Methods, Wageningen University and Research Centre , Wageningen , Netherlands.
Jaap J
JJ
Molenaar
Glycosylation; Kinetic models; Metabolic networks; Network inference; Solanum lycopersicum; Systems biology
Nature. 2002 Nov 14;420(6912):190-3
12432396
Theor Biol Med Model. 2006 Dec 15;3:41
17173669
Toxicol In Vitro. 2006 Mar;20(2):187-210
16289744
Bioinformatics. 2009 Aug 1;25(15):1923-9
19505944
Math Biosci. 2009 Jun;219(2):57-83
19327372
Phys Biol. 2011 Oct;8(5):055011
21832805
BMC Syst Biol. 2011 Jan 24;5:14
21255466
Plant Physiol. 2010 Apr;152(4):1763-71
20118273
J Biotechnol. 2010 Sep 1;149(3):132-40
20197073
Biotechnol Bioeng. 1995 Jan 5;45(1):69-79
18623053
Metabolomics. 2007;3:399-412
25653576
In Silico Biol. 2005;5(2):83-92
15972008
Genes Dev. 2010 Sep 1;24(17 ):1861-75
20810646
FEBS J. 2005 May;272(9):2141-51
15853799
Mol Cell Biochem. 1977 May 3;15(3):173-8
887080
Nat Biotechnol. 2010 Mar;28(3):245-8
20212490
J Nutr. 2006 Sep;136(9):2331-7
16920850
Fundam Clin Pharmacol. 2008 Dec;22(6):633-48
19049668