The Pearson test is performed to decide whether a network (a particular choice of a set of parameters for a particular topology) shows a transient response to a step change in input or not. The starting point is at steady state under a constant input concentration

. At time

the input concentration is changed from

to

via a step function (A). Consequently the output will either (B) not sense the change and maintain the same steady state

, (C) change monotonically to a new steady state

, or (D) show a transient response followed by a relaxation to a new steady state

that might or might not be equal to the pre-step change steady state

. A network passes the test only if it is transiently responsive. (E–H)

(red) is a perfectly biochemically adaptable function and

(green) is a monotonically changing function. If The Pearson shape correlation between the computed time course (blue) and

,

, is bigger than that between it and

,

, then the test is passed (E, G, H) and the network is termed a Transiently- Responsive (TR) network, otherwise the test is failed (F) and the network is termed Non-Pearson (NP). In (E) and (F), we show two cases where a biased visual inspection would deem both networks looking similar, but in reality they are distinguished by the Pearson test. A biochemically adaptable network is one that is both transiently responsive and returns to a new steady state very close to the pre-step change steady state. For example, (G) is not biochemically adaptable as there is a large difference between the pre-step change steady state and the new one. On the other hand, (H) is perfectly biochemically adaptable as it is both transiently responsive and perfectly robust, i.e. it returns exactly to its pre-step change steady state.

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