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BMC Syst Biol. 2012; 6: 13.
Published online 2012 February 27. doi:  10.1186/1752-0509-6-13
PMCID: PMC3395849
In silico labeling reveals the time-dependent label half-life and transit-time in dynamical systems
Thomas Maiwald,corresponding author#1,2 Julie Blumberg,#3,4 Andreas Raue,1 Stefan Hengl,1 Marcel Schilling,5 Sherwin KB Sy,6 Verena Becker,2,5,7 Ursula Klingmüller,5,7 and Jens Timmer1,8,9,10
1Center for Systems Biology, Freiburg, Germany
2Department of Systems Biology, Harvard Medical School, Boston, USA
3Epilepsy Center, University Hospital Freiburg, Germany
4Department of Neuroscience, Children's Hospital, Harvard Medical School, Boston, USA
5Division Systems Biology of Signal Transduction, DKFZ-ZMBH Alliance, German Cancer Research Center, Heidelberg, Germany
6College of Pharmacy, University of Florida, Gainesville, USA
7Bioquant, Heidelberg University, Germany
8Freiburg Institute for Advanced Studies, University of Freiburg, Germany
9BIOSS Centre for Biological Signalling Studies, University of Freiburg, Germany
10Department of Clinical and Experimental Medicine, Linköping University, Sweden
corresponding authorCorresponding author.
#Contributed equally.
Thomas Maiwald: tmaiwald/at/gmail.com; Julie Blumberg: blumberg.julie/at/gmail.com; Andreas Raue: andreas.raue/at/fdm.uni-freiburg.de; Stefan Hengl: stefan.hengl/at/googlemail.com; Marcel Schilling: m.schilling/at/dkfz.de; Sherwin KB Sy: sherwin.kenneth.sy/at/gmail.com; Verena Becker: Verena_Becker/at/hms.harvard.edu; Ursula Klingmüller: u.klingmueller/at/dkfz.de; Jens Timmer: jeti/at/fdm.uni-freiburg.de
Received May 10, 2011; Accepted February 27, 2012.
Abstract
Background
Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally. In cell biology, two main properties of interest are (1) the time-period a protein is accessible to other molecules in a certain state - its half-life - and (2) the time it spends when passing through a subsystem - its transit-time. We discuss two approaches to quantify the half-life, present the novel method of in silico labeling, and introduce the label half-life and label transit-time. The developed method has been motivated by laboratory tracer experiments. To investigate the kinetic properties and behavior of a substance of interest, we computationally label this species in order to track it throughout its life cycle. The corresponding mathematical model is extended by an additional set of reactions for the labeled species, avoiding any double-counting within closed circuits, correcting for the influences of upstream fluxes, and taking into account combinatorial multiplicity for complexes or reactions with several reactants or products. A profile likelihood approach is used to estimate confidence intervals on the label half-life and transit-time.
Results
Application to the JAK-STAT signaling pathway in Epo-stimulated BaF3-EpoR cells enabled the calculation of the time-dependent label half-life and transit-time of STAT species. The results were robust against parameter uncertainties.
Conclusions
Our approach renders possible the estimation of species and label half-lives and transit-times. It is applicable to large non-linear systems and an implementation is provided within the PottersWheel modeling framework (http://www.potterswheel.de).
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