The Sensitivity Conferred by a Substrate Cycle

Another example in which conclusions based solely on intrinsic sensitivities may give misleading results is the sensitivity conferred by a substrate cycle. The intrinsic sensitivity for effectors of the forward reaction in the cycle is (1 -I- C/J), where C is the rate of cycling and J is the net flux across the cycle (Table I). However, this sensitivity only equals the net sensitivity if all other potential effectors of the cycle, particularly the pathway - substrate and product, remain at constant concentrations, or if oppositions due to changes in these concentrations are minimized. Changes in the concentrations of substrates and products will produce internal oppositions (see Section III,C) that result in a lower net sensitivity than that predicted from the intrinsic sensitivity. Moreover, whereas the intrinsic sensitivity increases without limit as C/J increases, the net sensitivity may reach a limiting value (9). This system has been analyzed previously (9) but in view of some criticisms of the role of substrate cycles (42) it is analyzed more extensively here. The system to be analyzed is the same as that in the previous section (Fig. 2), except that reaction E2 is replaced by a substrate cycle  

The overall response of/ to X is still described by Eq. (15), but with Ej representing the net flux across the cycle (i.e., F minus C). Using the product rule [Eq. (8)] and the elementary sensitivities given in Table I, 

To examine the effects of cycling, C, on this overall sensitivity, let us consider two extremes zero cycling (C equals zero) and infinite cy- 

All terms in this ratio are positive, except for (since this describes an inhibition) for simplicity this term may be replaced by its absolute, and therefore positive value, where The above ratio then 

Since is positive, cycling will increase the sensitivity of the flux to regulator X provided that s j r ,), that is, if the sensitivity of the subsequent reaction of the system to the concentration of the product, P, is greater than the sensitivity of the reverse reaction of the cycle to the concentration of P. This situation can be met in several ways (9). For example, in the fructose 6-phosphate/fructose bisphosphate cycle, fructose bisphosphatase (equivalent to C above) has aK for fructose 1,6-bis-phosphate of about 1 pM (or at least two orders of magnitude lower than many other glycolytic enzymes for their glycolytic substrates) so that it is probably saturated with fructose bisphosphate in vivo (equivalent to P in 

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These elementary sensitivities have all been derived previously. Although their expression in terms of elementary communications is new, it was implicit in their derivation. For example, the derivation of the sensitivity conferred by a substrate cycle (Newsholme and Crabtree (32) assumed a linear response of the enzyme to the regulator (i.e., r = 1) as well as an irreversible reaction (i.e., R = 1) under these conditions the sensitivity of the net flux to the regulator is equal to that of the elementary communication, rate of forward (or reverse) reaction net flux across cycle. Similarly, the derivation of the effects of reversibility assumed a linear response to effectors, so that the resultant sensitivities are the same as those of the communication, forward (or reverse) processrate of reaction. 

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