Allosteric model for cAMP oscillations

Allosteric model for cAMP oscillations Extracellular cAMP... 

To understand the reasons why it is necessary to modify the hypotheses on which the allosteric model for cAMP signalling is based, it is useful to define more precisely the mechanism that underlies oscillations in this model. 

Fig. 7.2. Developmental path of the cAMP signaUing system in the parameter space formed by adenylate cyclase and phosphodiesterase activity. The stability diagram is established by linear stability analysis of the steady state admitted by the three-variable system (5.1) governing the dynamics of the allosteric model for cAMP signalling in D. discoideum (see section 5.2). In domain C sustained oscillations occur around an unstable steady state. In domain B, the steady state is stable but excitable as it amplifies in a pulsatile manner a suprathreshold perturbation of given amplitude. Outside these domains the steady state is stable and not excitable. The arrow crossing successively domains A, B and C represents the developmental path that the system should follow in that parameter space to account for the observed sequence of developmental transitions no relay relay oscillations (Goldbeter, 1980).

Fig. 5.17. Oscillations of intracellular (j8) and extracellular (y) cAMP, accompanied by a significant periodic variation of ATP (a) in the allosteric model for the synthesis of cAMP in D. discoideum. The curves are obtained by numerical integration of eqns (5.1) for the following parameter values v = 0.1 s cr= 1.2 s , k = k, = 0.4 s L = 10, q = 100, = 10 (Goldbeter Segel, 1977).

For a first theoretical approach of the transitions between relay and oscillations, it is useful to return to the allosteric model proposed for the mechanism of cAMP synthesis in D. discoideum (Goldbeter Segel, 1980) (see section 5.2 and fig. 5.16 for a scheme of that model). Two key parameters in any model for cAMP synthesis in D. discoideum are the activity of adenylate cyclase, which catalyses the production of cAMP from ATP, and the activity of phosphodiesterase, which hydrolyses the signal in the extracellular medium. In the allosteric model governed by eqns (5.1), parameters a and k measure, respectively, the maximum rate of the cyclase and of the phosphodiesterase. 

This two-variable system (Goldbeter et al, 1978) presents the additional advantage of being formally identical with the system of eqns (2.7) studied in chapter 2 for glycolytic oscillations. This similarity stems from the basic structure common to the two models a substrate, injected at a constant rate, is transformed in a reaction catalysed by an allosteric enzyme activated by the reaction product. In the cAMP-synthesizing system in D. discoideum, activation is indirect as extracellular cAMP enhances the synthesis of intracellular cAMP, which is then transported into the extracellular medium. However, the hypothesis of a quasi-steady state for intracellular cAMP is tantamount to considering that the variation of )8 is so fast that the enzyme is, de facto, activated directly by its apparent product, extracellular cAMP. 

The numerical study of the four-variable system (5.9a-d) reveals that it is capable of sustained oscillatory behaviour. These results, developed in further detail in the following section, also indicate that ATP remains practically constant in the course of cAMP oscillations (fig. 5.30, below). Thus, in contrast with the allosteric model considered above, the model based on receptor desensitization can account for the experimental observation (fig. 5.22) on the limited variation of ATP in the course of cAMP oscillations. Once we have established that the model predicts this characteristic feature of the experimental system, we may consider, as a first approximation, that ATP remains constant in time at the value given by eqn (5.11), in view of the relative smallness of the maximum rate of adenylate cyclase compared to the accumulative rate of ATP utilization in other pathways ... 

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