Characteristics necessary for an interconvertible enzyme cascade to generate a highly sensitive response to an effector.

A monocyclic interconvertible enzyme cascade, in which active and inactive states of an enzyme are interconverted by two opposing enzyme-catalysed reactions, does not necessarily produce a greater degree of sensitivity to an effector than one could expect from direct interaction between effector and target reaction. On the contrary, a cascade in which an effector acts on one of the enzymes catalysing the interconversion reactions by altering the apparent value of its specificity constant will always generate a less sensitive response than direct interaction would give. Nonetheless, even if both interconversion reactions obey Michaelis-Menten kinetics with the ordinary types of inhibition and activation, one can easily generate an enormous sensitivity in which a 0.5% change in concentration can increase the proportion of target enzyme in the active state from 10% to 90%: this corresponds approximately to a Hill coefficient of 800. To maximize the sensitivity, the following conditions must be satisfied: (1) both modifier enzymes must act under conditions of near saturation; (2) the effector must act on both of them in opposite directions; (3) it must alter the apparent values of their catalytic constants; (4) the enzyme subject to inhibition by the effector must respond at much lower effector concentrations than the enzyme subject to activation. As the last of these conditions appears to be counter-intuitive, it suggests that feeble activation of modifier enzymes in real systems may have passed unnoticed, or been dismissed as physiologically insignificant, although in reality crucial to the effective response of the system.