A control-theoretic law of human glucose homeostasis

Glucose homeostasis is a fundamental component of human physiology, and its failure underlies diabetes. Existing measures, such as mean glucose levels, provide limited insight into the underlying physiological processes because a quantitative law linking glycemic trajectories directly to regulatory capacity has yet to be established. We derived an equation, F = K{middle dot}G, that connects glucose inputs (F) and measurable features of glucose dynamics (G) to the systems regulatory capacity (K). K includes proportional-integral-derivative (PID)-like components from control theory, while G integrates glucose-trajectory characteristics, including area under the curve, amplitude, and temporal distortion. Analyses of clamp and continuous glucose monitoring data from more than 2,000 individuals showed that K was identifiable from glucose dynamics and explained interindividual variation in glucose tolerance and diabetes complication risks beyond conventional metrics. This framework identified four subtypes of impaired glucose regulation, including an underappreciated subtype characterized by deficient insulin-independent glucose-lowering. These results provide a mechanistic interpretation of how biological systems achieve robust glucose regulation and a practical basis for stratifying glucose tolerance and disease risk.