title: In silico labeling reveals the time-dependent label half-life and transit-time in dynamical systems.
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).
authors.affiliation: Center for Systems Biology, Freiburg, Germany. tmaiwald@gmail.com
authors.forename: Thomas
authors.initials: T
authors.lastname: Maiwald
authors.forename: Julie
authors.initials: J
authors.lastname: Blumberg
authors.forename: Andreas
authors.initials: A
authors.lastname: Raue
authors.forename: Stefan
authors.initials: S
authors.lastname: Hengl
authors.forename: Marcel
authors.initials: M
authors.lastname: Schilling
authors.forename: Sherwin Kb
authors.initials: SK
authors.lastname: Sy
authors.forename: Verena
authors.initials: V
authors.lastname: Becker
authors.forename: Ursula
authors.initials: U
authors.lastname: Klingmüller
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer
mesh_terms: D019295:Computational Biology / Q000379:methods*; D053612:Janus Kinases / Q000378:metabolism; D016013:Likelihood Functions; D050791:STAT Transcription Factors / Q000378:metabolism; D015398:Signal Transduction; D009626:Terminology as Topic; D013997:Time Factors
chemical_list: D050791:STAT Transcription Factors; D053612:Janus Kinases