Novel global sensitivity analysis methodology accounting for the crucial role of the distribution of input parameters: application to systems biology models

Abstract

The reliability of model predictions is affected by multiple sources of uncertainty; therefore, most of the efforts for modeling biological systems include a sensitivity analysis step aiming to identify the key contributors to uncertainty. This generates insight about the robustness of the model to variations in environmental conditions, kinetic parameters, initial concentration of the species, or any other source of uncertainty. Local sensitivities measure the robustness of the model to small perturbations on the inputs around their nominal value. There are several numerical methods for the calculation of local sensitivities, but the calculated values should be identical within the numerical accuracy of the method used. In contrast, as will be shown in this contribution, the results of different global sensitivity analysis methods can be very different and highly dependent on the distribution considered for the inputs under evaluation. In this work, derivative-based global sensitivities are extended to be able to consider an accurate probability density function for the parameters based on the likelihood function. This strategy enforces the areas of the parameter space most likely to reproduce the desired behavior, minimizing the importance of parameter sets with low probability of being optimal to dominate the sensitivity ranking. A model of a biochemical pathway with three enzymatic steps is used here to illustrate the performance of several relevant global sensitivity analysis methods considering different probability density functions for the parameters and revealing important hints about which method and distribution to choose for each type of model and purpose of the analysis