Open Access Methodology article

In silico labeling reveals the time-dependent label half-life and transit-time in dynamical systems

Thomas Maiwald12*, Julie Blumberg34, Andreas Raue1, Stefan Hengl1, Marcel Schilling5, Sherwin KB Sy6, Verena Becker257, Ursula Klingmüller57 and Jens Timmer11089

Author Affiliations

1 Center for Systems Biology, Freiburg, Germany

2 Department of Systems Biology, Harvard Medical School, Boston, USA

3 Epilepsy Center, University Hospital Freiburg, Germany

4 Department of Neuroscience, Children's Hospital, Harvard Medical School, Boston, USA

5 Division Systems Biology of Signal Transduction, DKFZ-ZMBH Alliance, German Cancer Research Center, Heidelberg, Germany

6 College of Pharmacy, University of Florida, Gainesville, USA

7 Bioquant, Heidelberg University, Germany

8 Freiburg Institute for Advanced Studies, University of Freiburg, Germany

9 BIOSS Centre for Biological Signalling Studies, University of Freiburg, Germany

10 Department of Clinical and Experimental Medicine, Linköping University, Sweden

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BMC Systems Biology 2012, 6:13  doi:10.1186/1752-0509-6-13

Published: 27 February 2012



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.


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.


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 ( webcite).