A Steady-State-Transition Model of Insulin Secretion.
Cohen, David Marshall
1981
Abstract
Secretion of insulin from pancreatic islets of Langerhans is multiphasic. The pattern of secretion varies according to the secretagogues that trigger the secretion. Previously proposed mathematical models of insulin secretion have dealt solely with glucose-stimulated release, and not with the more complex patterns of secretion in response to other secretagogues or combinations of secretagogues. A technique is described for constructing a mathematical model of the regulation of insulin secretion in response to various secretagogues. Algorithms for the fitting of experimental data to algebraic curves are used to compute the parameters of curve approximations of the insulin-secretory response to changes in the concentrations of secretagogues. A system of linear ordinary differential equations for the state vector of the mathematical model is determined from these parameters, using matrix algebra. The components of the state vector represent activity levels of the compartments of the model. The selective effects of the secretagogues on the mathematical model are inferred from the parameters of the curve approximations of the appropriate experimental data. An experimental design and mathematical technique for determining the biological equivalents of the compartments of the model are sugested. The proposed analytical technique can be used to model the simultaneous effects of secretagogues on other biological variables as well as on hormone secretion. The model has four compartments; each compartment represents an impotant, hypothetical biological energy transformation which affects the secretory rate. The activity of compartment number 4 is correlated with the insulin-secretory rate. The proposed model reproduces experimentally observed patterns of insulin secretion, such as the acute and late phases of release in response to glucose or to leucine; the "off-response" that occurs upon the removal of certain stimuli, such as leucine; and the long-term potentiating effect of repetitive administration of secretagogues. In the context of the proposed model, in the absence of glucose an increase in the concentration of L-leucine stimulates, inhibits, stimulates, and inhibits compartments 1,2,3, and 4, respectively. In the presence of glucose the effects are the same, except that compartment 4 is stimulated. Thus, the off-response to leucine, which occurs in the presence but not in the absence of glucose, is associated with a change in the actions of leucine on a single compartment. Specific perturbations of the inputs to compartments 1,2, and 3 cause an acute-phase, late-phase, and off-response, respectively, by inducing changes in the activity level of compartment 4. Raising the concentration of glucose causes the inhibition, stimulation, inhibition, and stimulation of compartments 1,2,3, and 4, respectively. Compartment 4 of the model may represent the balance of stimulatory and inhibitory forces within the pancreatic islets. It is concluded that (1)an off-response is consistent with a compartmental model; (2)the facilitating effect of a constant concentration of glucose on leucine-stimulated insulin secretion is consistent with a selective effect of glucose on a single compartment of the model; (3)Mathematical analysis of secretory responses to secretagogues can yield information about their selective effects on the compartments of a mathematical model.Types
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