Much more complex models of this system could be constructed, and for some stages, many detailed models already exist. For example, there are a number of models describing intracellular calcium fluctuations in response to agonists applied in the extracellular environment (15,16). Models are also available of the exocytosis of hormone or neurotransmitter in response to a rise in intracellular calcium (17). Therefore, it would be possible, to assemble these models into an overall model describing somatotroph growth hormone output as a function of GRF or artificial secretagogue stimulation. This would still leave the inhibitory input of SRIF and its interaction with GRF to be included. However, the resulting complete model would be very complex. Goldbeter (18) discusses a four differential equation model for the response of pituitary cells to luteinizing hormone-releasing hormone, which is essentially a more complex version of the authors' model here (without any somatostatin terms). The extra variables are desensitized releasing hormone receptors in their free and bound states. The authors began their modeling studies assuming that at least three differential equations (including a desensitized bound receptor state) would be necessary, but found that just two closely related differential equations (in f and u) were all that was needed to explain the experimental behavior. Somatostatin appears to exert its effect on the system only when present, and apart from its resensitizing effect on the receptors, little residual memory of its presence remains. Therefore, no further differential equations are needed to cater for its effects.
As well as its likely greater robustness, the particular value of simplicity in our present model is threefold. First, it is a relatively simple matter to determine the model's properties requiring only straightforward analytical techniques. Second, the model can be much more easily tested against experimental data and parameters estimated. Finally, as indicated in the previous section, it can be used to infer the pattern of input of GRF/GHRP from observations of the pattern of growth hormone output from the pituitary if the somatostatin concentrations are known, or to infer the input patterns of GRF and soma-tostatin if neither are known, but the nature of their interdependence is.
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