The multi-element probabilistic collocation method (ME-PCM) as a tool for sensitivity analysis of differential equation models as applied to cellular signalling networks is formulated. This method utilises a simple, efficient sampling algorithm to quantify local sensitivities throughout the parameter space. The application of the ME-PCM to a previously published ordinary differential equation model of the apoptosis signalling network is presented. The authors verify agreement with the previously identified regions of sensitivity and then go on to analyse this region in greater detail with the ME-PCM. The authors demonstrate the generality of the ME-PCM by studying sensitivity of the system using a variety of biologically relevant markers in the system such as variation in one (or many) chemical species as a function of time, and total exposure of a single chemical species.