Regulatory curve

When R is present, we expect that the entire BI of A will change. The extent of this change will depend on Cg. We shall examine, in particular, the rate of change ofe as a function of Cj, along a line of fixed C. The resulting curve will be referred to as the regulatory curve. The choice of the fixed value of C, although arbitrary, is made as follows. 

Since kjf > 0, the regulatory function is a monotonically decreasing fimction of C j, i.e., the effector acts as an inhibitor. Figure 8.6 shows a series of BI, 0, for different values of Cg, and the corresponding regulatory curve. Note the sharp initial drop of Rg(Cg) at = 0. 

The regulatory curve is derived by again solving the equation... 

Figure 8.8. Bis and the regulatory curve for the model of Section 8.5. The parameters are (a) 1,...

Figure 8.12. Regulatory curves for the same parameters as in Fig. 8.11 but for m = 3,4,5,6. The larger m, the sharper the transition between the active and inactive enzyme. Note the shift of the transition point to lower values of Xj. ...

Figure 8.13. The slopes of the regulatory curves for the same parameters as in Figs. 8.11 and 8.12, but with m = 10, 20, 30.

We see that the correlations grow rapidly with m, leading to very sharp inverted S-shaped regulatory curves. 

Finally, we note that the BI and the regulatory curves are plotted as a function... 

Figure 8.16. Regulatory curves for the same model as in Fig. 8.15 but with m - 5, 10, 15, 20. Note that the larger is m, the sharper is the transition from an active to an inactive enzyme. The full line corresponds to m = 100.

We shall call the new function 6a b) the regulatory curve. It gives the drop, caused by adding B from the initial value of 6a = 0.8 along the vertical line at fixed A. Clearly, for any qs 0, the slope of the function is negative and its curvature positive ... 

Thus we substitute Xa = A in (3.7.19) and follow the regulatory curve defined by... 

It is easy to verify that for y < 1 the regulatory curve (3.7.23) has everywhere a negative slope and a positive curvature. This is similar to the Langmuir-type curve we have seen in section 3.7.1. The significance of the condition y < 1 in terms of the molecular parameters of the model follows from definition (3.7.18)... 

S-shaped analogue of the binding isotherm. It is clear that generalization of the model of section 3.3, where there is exactly one catalytic and one regulatory subunit, will lead to a conclusion similar to the conclusion of this section. The regulatory curve 6 (Xb) will be essentially the same as that of (3.7.23) with a different interpretation of the coefficient. Therefore in the next section we turn to examining the minimal model that shows an inverted S-shaped regulatory curve. 

Figure 3.23a and b demonstrate the regulatory behavior of this system. To meet the required conditions for this case, we chose K = 10, Ha = 100, and Hb = 0.001. Note that, initially, adding B to the system causes a small change in the binding curve (Fig. 3.23a) the spacing between the curves increases with Xb- This is also shown by the (inverted) S-shaped regulatory curve in Fig. 3.23b. 

The regulatory curve in Fig. 3.23b is clearly different from the regulatory curves in Figs. 3.21b and 3.22b. As in the model treated in section 3.4, which was modified in the present section, we cannot expect a sharp transition from active to inactive enzyme, as we would have liked e.g., see Fig. 3.20. However, it is clear that by generalization of the models treated in sections 3.5 and 3.6 we can obtain sharper transitions within a specific concentration range of the inhibitor B. Actual enzymes normally have more than three... 

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