Robustness-based model validation of an apoptosis signalling network model

Models of intracellular biochemical reaction networks are difficult to parameterise due to the
low number of quantitative time series experimental values. Therefore, model validation or
invalidation plays an important role, as it allows to check qualitatively whether a model structure
is suited or not to reproduce qualitatively the experimental findings.
This paper analyses the robustness of an experimentally validated polynomial differential
equation model of TNF-induced pro-and anti-apoptotic signalling. The bistability of the median
model is shown robust to large single parameter variations. Only two parameters (XIAP
and Procaspase-3 production rates) are shown to be fragile, in particular when changed
simultaneously. Therefore, the model seems valid from the point of view of robustness analysis
of the bistability.
Many biological experiments quantify average concentrations or the percentage of viable cells,
while other methods such as microscopy-based experiments observe single cells. The integration
of single cell and cell population behaviour of TNF-induced pro- and anti-apoptotic signalling
has been achieved via a cell ensemble model, whose robustness is also analysed here. We show
that within the cell population there are cells with not only quantitative differences, but also
qualitative ones. In particular, all cells are not bistable. The degree of robustness applicable
for the median cell is expanded to combine mono- and bistable models. This measure, applied
solely to the two-dimensional subspace of fragile parameters, is shown to correlate well with the
time of death. While robustness of bistability can serve for model validation of the median cell
model, it cannot for the model of the cell population.