The dynamics of quantifiable homeostasis. III: a linear model of certain metrical diseases.
A generalization of the linear, lagged, homeostatic process shows that whether a displacement of the trait function dies out with time, continues indefinitely, or shows a steadily amplifying (wild) oscillation depends on the value assumed by the product of the lag time and the restoration constant. Moreover, it is shown that if a steady displacing force is used rather than an instantaneous displacement, a new homing value results which is given by the ratio of the displacing force to the restoration coefficient. Combining these two developments furnishes grounds for determining whether or not an overshoot will occur when administration of a drug is stopped (for instance, the rebound thrombosis on discontinuing heparin). Further developments of these ideas show how the diabetes that begins in mature patients can be wholly accounted for by the well-known prolongation of the lag in insulin response that occurs in that disorder. If wild oscillation is to be avoided as the lag time increases, the restoration constant must be weakened (evidently by a systematic reduction in insulin receptors) and this weakening means that the homing value is displaced. Thus the hyperglycemia in this diabetes is to be seen as the price paid for avoiding wild oscillation. Provided that the therapeutic use of exogenous insulin is systematic and regular, rather than cybernetic, its success where endogenous (cybernetic) insulin secretion has failed is readily understood. The point is illustrated by a familiar analogy of a car driver with slow responses. The genetic and evolutionary implications of these ideas are outlined.