Abstract
Homeostatic control of blood glucose is regulated by a complex feedback loop between glucose and insulin, of which failure leads to diabetes mellitus. However, physiological and pathological nature of the feedback loop is not fully understood. We made a mathematical model of the feedback loop between glucose and insulin using time course of blood glucose and insulin during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps in 113 subjects with variety of glucose tolerance including normal glucose tolerance (NGT), impaired glucose tolerance (IGT) and type 2 diabetes mellitus (T2DM). We analyzed the correlation of the parameters in the model with the progression of glucose intolerance and the conserved relationship between parameters. The model parameters of insulin sensitivity and insulin secretion significantly declined from NGT to IGT, and from IGT to T2DM, respectively, consistent with previous clinical observations. Importantly, insulin clearance, an insulin degradation rate, significantly declined from NGT, IGT to T2DM along the progression of glucose intolerance in the mathematical model. Insulin clearance was positively correlated with a product of insulin sensitivity and secretion assessed by the clamp analysis or determined with the mathematical model. Insulin clearance was correlated negatively with postprandial glucose at 2h after oral glucose tolerance test. We also inferred a square-law between the rate constant of insulin clearance and a product of rate constants of insulin sensitivity and secretion in the model, which is also conserved among NGT, IGT and T2DM subjects. Insulin clearance shows a conserved relationship with the capacity of glucose disposal among the NGT, IGT and T2DM subjects. The decrease of insulin clearance predicts the progression of glucose intolerance.
Highlights
A feedback loop linking insulin and glucose plays an essential role in glucose homeostasis [1]
We developed a mathematical model of the feedback loop that links glucose and insulin with the use of time series data of blood glucose and insulin concentrations during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps (Fig 1A)
Fluxes that regulate insulin secretion are flux 5, flux 6, and flux 7, where flux 5 depends on Y and corresponds to insulin secretion in response to an effective glucose concentration, and whose parameter k5 corresponds to the rate constant of insulin secretion; flux 6 depends on X and corresponds to systemic circulation of insulin from the pancreas to target organs; and flux 7 depends on I and corresponds to insulin clearance, and whose parameter k7 corresponds to the rate constant of insulin clearance
Summary
A feedback loop linking insulin and glucose plays an essential role in glucose homeostasis [1]. A number of clinical indices that reflect these two aspects have been proposed and shown to be of use for analysis of glucose homeostasis and the pathology of glucose intolerance [3] Given that these indices are usually determined by blood parameters under specific conditions [3], it is unclear whether they reflect all aspects of insulin secretion and insulin sensitivity. Mathematical models based on time series data of an oral glucose tolerance test (OGTT) have been developed and shown to be of clinical utility [21,22,23,24,25,26,27,28,29,30]. Given that blood glucose and insulin levels during an FSIVGTT or OGTT are mutually influenced via the negative feedback loop, it is difficult to accurately determine parameters for insulin sensitivity and insulin secretion, and a key feature of the negative feedback loop may remain to be uncovered
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