We finally note that perfect robustness (complete insensitivity) to all protein and metabolites is an idealized feature.
Perfect robustness within a network is unlikely to occur unless the network fulfils some very specific criteria [2], and indeed such perfect robustness is probably relatively rare in biological systems.
The three groups, cross-validated in the Giordano dataset (Figure 1C), presented almost perfect robustness ( = 1) and discrepancy indices ( = 0.001).
The ideal integral control scenario that we considered above led to the perfect robustness of certain system variables with respect to certain (external or parametric) perturbations.
Such perfect robustness can be achieved when a time integrator is applied to any variation of the controlled variable (or system error).
Both synchronous and asynchronous piES achieve virtually perfect robustness regardless of the number of processors, while pLSA becomes significantly less reliable as the number of processors increases.
A specific pathway then shows perfect robustness of a system variable vis-à-vis multiple perturbations (or parameters) but perfect tracking with respect to only a limited set of parameters (e.g. a reference signal r).
For a simple, unbranched, one-stage lineage with renewal control, nearly perfect robustness of final terminal cell numbers can be observed [ 4], demonstrating that renewal control provides integral feedback in final state tissues as well as steady state ones.
We focused on the control structures leading to so-called 'perfect adaptation' , as defined by (i) complete robustness of the concentration of the pathway's end product towards perturbations in supply and demand, (ii) perfect tracking of perturbations by variables involved in the adaptation.
Analysis of steady state behavior indicates that either strategy improves parametric robustness (insensitivity to parameters), although perfect robustness exists only at the first layer.
