Evaluating the Importance of Glucagon in the Insulin-Glucose Regulatory System: A Mechanistic Modeling Approach

Abstract

The dynamics of insulin and glucose are tightly regulated. The pancreatic islets of Langerhans contain both beta and alpha cells which produce insulin and glucagon, respectively. Insulin is the only hormone in the body that lowers blood glucose levels by acting like a key for glucose to enter cells. Without insulin, cells cannot utilize glucose, their primary source of energy. In contrast, glucagon functions as a hormone which elevates blood glucose levels by promoting the breakdown of glycogen in the liver. Maintaining blood glucose within a safe range is vital since both excessively high and low levels can be life-threatening (hyperglycemia and hypoglycemia, respectively), and these two hormones work together to achieve this balance. In this work we aim to underscore the significance of glucagon in the insulin-glucose regulatory system. We construct a three-compartment mechanistic model that includes insulin, glucose, and glucagon, which is then validated by fitting to publicly available from an intravenous glucose tolerance test (IVGTT). After model validation, we investigate how removing glucose feedback from insulin secretion, as seen in insulin-dependent diabetes, disrupts the regulation of glucose and glucagon. To do this, we simulate the model (a) when insulin secretion is reduced to mimic an insufficient dose of insulin, (b) when the peak of insulin action is delayed mimicking a dosing delay of insulin, and (c) when both occur simultaneously. Lastly, we test different half-lives of insulin to evaluate how an increased half-life of manufactured insulin may further disrupt the system. We find that when insulin secretion is decreased, glucagon still responds to high glucose levels by decreasing glucagon production. This suggests that in cases of type 2 diabetes, where glucagon secretion is elevated despite high levels of glucose, a lack of insulin response may not be the sole cause for glucagon dysfunction. We also find that delaying insulin secretion increases the risk of a hypoglycemic event through a suppression of glucagon production. Initially, the spike in glucose causes glucagon secretion to be reduced; this is then followed by the delay in insulin peak which then continues to suppress glucagon despite blood glucose levels falling, leading to a lack of response by glucagon and a subsequent hypoglycemic event. Furthermore, we find that a higher half-life of insulin causes it to remain longer in the blood stream, inhibiting glucagons response to severely low glucose levels (glucose levels less than 3.9 mmol/L). This sheds light on why patients taking exogenous insulin, which has a longer half-life than endogenous insulin, may have difficulty recovering from hypoglycemic events. Hence, our model suggests that keeping the half-life of exogenous insulin below 10 minutes and administering it immediately after meals could help reduce the risk of hypoglycemic events in patients with type 1 or insulin dependent diabetes. Overall, we highlight how a disruption in the feedback between insulin and glucose not only alters blood glucose levels, but also glucagon response, which may lead to further disruption of the system.