Global sensitivity and identifiability implications in systems biology

In systems biology, a common approach to model biological processes is to use large systems of differential equations. The associated parameter estimation problem requires to prior handle identifiability and sensitivity issues in a practical biological framework. The lack of method to assess global practical identifiability has leaded us to analyze and establish bridges between global sensitivity and identifiability measures. Specifically, we are interested in deriving conditions of global practical non-identifiability in association with global sensitivity results. Two cases are considered: i) insensitive (or non-observable) parameters; ii) two (or more) correlated sensitivity measures of the model output with respect to model parameters. Propositions of relationships between sensitivity and identifiability, and their proofs are developped herein. Academic examples are also treated in order to illustrate contents of these propositions.