## Dynamical compensation and structural unidentifiability in the *β*IG model.

The first row reproduces the last row of Fig 2 and illustrates the phenomenon of dynamical compensation: after the system has adapted to the new value of *s*_{i}, the time-evolution of the glucose concentration (G) for the new value of (*s*_{i}/2) is the same as it was with the old value before adaptation (*s*_{i}). The second row illustrates the phenomenon of structural unidentifiability: without the need for any adaptation, the time-evolution of the glucose concentration (G) is the same for any value of the parameter *s*_{i}, as long as any deviations from the original value are compensated by changes in the parameter *p*. Note that, since the upper and lower plots of G are identical, if glucose is the only measured quantity both phenomena cannot be distinguished. However, the behaviour of the other state variables (I, *β*) can be very different, as can be noticed from the third and fourth columns.