A note on dynamical compensation and its relation to parameter identifiability

We recently identified a motif for dynamical compensation (DC) – a property where a system maintains the dynamics and steady-state of a regulated variable robust in the face of fluctuations in key parameters. Such parameters are therefore unidentifiable from measurements of the regulated variable at steady-state. On the other hand, since the models showing dynamical compensation are typically non-redundant, their parameters are identifiable from experimental data. We clarify this apparent discrepancy by requiring that the parameters of DC circuits be identifiable both away from steady-state and when measuring other system variables. We use this observation to provide a definition for DC in terms of parameter identifiability and discuss its relevance for the examples provided in Karin et al.