Abstract
BackgroundMathematical 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.ResultsApplication 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.ConclusionsOur 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).
Highlights
Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally
A good tracer does not hamper the flux of the substance, one can assume that the flux of the tracer within a certain reaction is proportional to the flux of the original species. This is the key property of the in silico labeling approach, where an additional set of reactions is added to an existing mathematical model describing the kinetic behavior of a tracer, called the label
In silico labeling for linear processes we prove that the label half-life coincides with the half-life of a species x which is produced by an unknown, potentially non-linear influx vin and is consumed by a linear process
Summary
Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally. A good tracer does not hamper the flux of the substance, one can assume that the flux of the tracer within a certain reaction is proportional to the flux of the original species This is the key property of the in silico labeling approach, where an additional set of reactions is added to an existing mathematical model describing the kinetic behavior of a tracer, called the label. In contrast to real tracer experiments, the in silico method offers the opportunity to define dead-ends, avoid double-counting of cycling label, and to restrict the label to a sub-network of reactions This allows asking specific questions about the original system, like how long it takes for 50% of the molecules of a substance to travel along a certain path, while in reality an alternative path may exist. Predominant paths can be identified in deterministic models as has been done previously for stochastic systems [7]
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