Models of glucagon secretion, their application to the analysis of the defects in glucagon counterregulation and potential extension to approximate glucagon action

Mathematical Model of Glucagon Kinetics for the Assessment of Insulin-Mediated Glucagon Inhibition During an Oral Glucose Tolerance Test

Glucagon is secreted from the pancreatic alpha cells and plays an important role in the maintenance of glucose homeostasis, by interacting with insulin. The plasma glucose levels determine whether glucagon secretion or insulin secretion is activated or inhibited. Despite its relevance, some aspects of glucagon secretion and kinetics remain unclear. To gain insight into this, we aimed to develop a mathematical model of the glucagon kinetics during an oral glucose tolerance test, which is sufficiently simple to be used in the clinical practice. The proposed model included two first-order differential equations -one describing glucagon and the other describing C-peptide in a compartment remote from plasma - and yielded a parameter of possible clinical relevance (i.e., S_GLUCA(t), glucagon-inhibition sensitivity to glucose-induced insulin secretion). Model was validated on mean glucagon data derived from the scientific literature, yielding values for S_GLUCA(t) ranging from -15.03 to 2.75 (ng of glucagon·nmol of C-peptide^-1). A further validation on a total of 100 virtual subjects provided reliable results (mean residuals between -1.5 and 1.5 ng·L^-1) and a negative significant linear correlation (r = -0.74, p < 0.0001, 95% CI: -0.82 - -0.64) between S_GLUCA(t) and the ratio between the areas under the curve of suprabasal remote C-peptide and glucagon. Model reliability was also proven by the ability to capture different patterns in glucagon kinetics. In conclusion, the proposed model reliably reproduces glucagon kinetics and is characterized by sufficient simplicity to be possibly used in the clinical practice, for the estimation in the single individual of some glucagon-related parameters.

Quantification of the glycemic response to microdoses of subcutaneous glucagon at varying insulin levels

OBJECTIVE

Glucagon delivery in closed-loop control of type 1 diabetes is effective in minimizing hypoglycemia. However, high insulin concentration lowers the hyperglycemic effect of glucagon, and small doses of glucagon in this setting are ineffective. There are no studies clearly defining the relationship between insulin levels, subcutaneous glucagon, and blood glucose.

RESEARCH DESIGN AND METHODS

Using a euglycemic clamp technique in 11 subjects with type 1 diabetes, we examined endogenous glucose production (EGP) of glucagon (25, 75, 125, and 175 μg) at three insulin infusion rates (0.016, 0.032, and 0.05 units/kg/h) in a randomized, crossover study. Infused 6,6-dideuterated glucose was measured every 10 min, and EGP was determined using a validated glucoregulatory model. Area under the curve (AUC) for glucose production was the primary outcome, estimated over 60 min.

RESULTS

At low insulin levels, EGP rose proportionately with glucagon dose, from 5 ± 68 to 112 ± 152 mg/kg (P = 0.038 linear trend), whereas at high levels, there was no increase in glucose output (19 ± 53 to 26 ± 38 mg/kg, P = NS). Peak glucagon serum levels and AUC correlated well with dose (r2 = 0.63, P < 0.001), as did insulin levels with insulin infusion rates (r2 = 0.59, P < 0.001).

CONCLUSIONS

EGP increases steeply with glucagon doses between 25 and 175 μg at lower insulin infusion rates. However, high insulin infusion rates prevent these doses of glucagon from significantly increasing glucose output and may reduce glucagon effectiveness in preventing hypoglycemia when used in the artificial pancreas.

Targeting SUR1/Abcc8-type neuroendocrine KATP channels in pancreatic islet cells

ATP-sensitive K⁺ (K_ATP) channels play a regulatory role in hormone-secreting pancreatic islet α-, β- and δ-cells. Targeted channel deletion would assist analysis and dissection of the intraislet regulatory network. Toward this end Abcc8/Sur1 flox mice were generated and tested by crossing with glucagon-(GCG)-cre mice to target α-cell K_ATP channels selectively. Agonist resistance was used to quantify the percent of α-cells lacking channels. 41% of Sur1^loxP/loxP;GCG-cre⁺ and ∼64% of Sur1^loxP/−;GCG-cre⁺ α-cells lacked K_ATP channels, while ∼65% of α-cells expressed enhanced yellow fluorescent protein (EYFP) in ROSA-EYFP/GCG-cre matings. The results are consistent with a stochastic two-recombination event mechanism and a requirement that both floxed alleles are deleted.

Treating type 1 diabetes: from strategies for insulin delivery to dual hormonal control

Type 1 diabetes is a disorder where slow destruction of pancreatic β-cells occurs through autoimmune mechanisms. The result is a progressive and ultimately complete lack of endogenous insulin. Due to β-cell lack, secondary abnormalities in glucagon and likely in incretins occur. These multiple hormonal abnormalities cause metabolic instability and extreme glycemic variability, which is the primary phenotype. As the disease progresses patients often develop hypoglycemia unawareness and defects in their counterregulatory defenses. Intensive insulin therapy may thus lead to 3-fold excess of severe hypoglycemia and severely hinder the effective and safe control of hyperglycemia. The main goal of the therapy for type 1 diabetes has long been physiological mimicry of normal insulin secretion based on monitoring which requires considerable effort and understanding of the underlying physiology. Attainment of this goal is challenged by the nature of the disease and our current lack of means to fully repair the abnormal endocrine pancreas interactive functions. As a result, various insulin preparations have been developed to partially compensate for the inability to deliver timely exogenous insulin directly to the portal/intrapancreatic circulation. It remains an ongoing task to identify the ideal routes and regimens of their delivery and potentially that of other hormones to restore the deficient and disordered hormonal environment of the pancreas to achieve a near normal metabolic state. Several recent technological advances help addressing these goals, including the rapid progress in insulin pumps, continuous glucose sensors, and ultimately the artificial pancreas closed-loop technology and the recent start of dual-hormone therapies.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Insulin therapy and hypoglycemia

Hypoglycemia is the most important and common side effect of insulin therapy. It is also the rate limiting factor in safely achieving excellent glycemic control. A three-fold increased risk of severe hypoglycemia occurs in both type 1 and type 2 diabetes with tight glucose control. This dictates a need to individualize therapy and glycemia goals to minimize this risk. Several ways to reduce hypoglycemia risk are recognized and discussed. They include frequent monitoring of blood sugars with home blood glucose tests and sometimes continuous glucose monitoring (CGM) in order to identify hypoglycemia particularly in hypoglycemia unawareness. Considerations include prompt measured hypoglycemia treatment, attempts to reduce glycemic variability, balancing basal and meal insulin therapy, a pattern therapy approach and use of a physiological mimicry with insulin analogues in a flexible manner. Methods to achieve adequate control while focusing on minimizing the risk of hypoglycemia are delineated in this article.

Association of Basal hyperglucagonemia with impaired glucagon counterregulation in type 1 diabetes

Glucagon counterregulation (GCR) protects against hypoglycemia, but is impaired in type 1 diabetes (T1DM). A model-based analysis of in vivo animal data predicts that the GCR defects are linked to basal hyperglucagonemia. To test this hypothesis we studied the relationship between basal glucagon (BasG) and the GCR response to hypoglycemia in 29 hyperinsulinemic clamps in T1DM patients. Glucose levels were stabilized in euglycemia and then steadily lowered to 50 mg/dL. Glucagon was measured before induction of hypoglycemia and at 10 min intervals after glucose reached levels below 70 mg/dL. GCR was assessed by CumG, the cumulative glucagon levels above basal; MaxG, the maximum glucagon response; and RIG, the relative increase in glucagon over basal. Analysis of the results was performed with our mathematical model of GCR. The model describes interactions between islet peptides and glucose, reproduces the normal GCR axis and its impairment in diabetes. It was used to identify a control mechanism consistent with the observed link between BasG and GCR. Analysis of the clinical data showed that higher BasG was associated with lower GCR response. In particular, CumG and RIG correlated negatively with BasG (r = −0.46, p = 0.012 and r = −0.74, p < 0.0001 respectively) and MaxG increased linearly with BasG at a rate less than unity (p < 0.001). Consistent with these results was a model of GCR in which the secretion of glucagon has two components. The first is under (auto) feedback control and drives a pulsatile GCR and the second is feedback independent (basal secretion) and its increase suppresses the GCR. Our simulations showed that this model explains the observed relationships between BasG and GCR during a three-fold simulated increase in BasG. Our findings support the hypothesis that basal hyperglucagonemia contributes to the GCR impairment in T1DM and show that the predictive power of our GCR animal model applies to human pathophysiology in T1DM.

Safe glycemic management during closed-loop treatment of type 1 diabetes: the role of glucagon, use of multiple sensors, and compensation for stress hyperglycemia

Patients with type 1 diabetes mellitus (T1DM) must make frequent decisions and lifestyle adjustments in order to manage their disorder. Automated treatment would reduce the need for these self-management decisions and reduce the risk for long-term complications. Investigators in the field of closed-loop glycemic control systems are now moving from inpatient to outpatient testing of such systems. As outpatient systems are developed, the element of safety increases in importance. One such concern is the risk for hypoglycemia, due in part to the delayed onset and prolonged action duration of currently available subcutaneous insulin preparations. We found that, as compared to an insulin-only closed-loop system, a system that also delivers glucagon when needed led to substantially less hypoglycemia. Though the capability of glucagon delivery would mandate the need for a second hormone chamber, glucagon in small doses is tolerated very well. People with T1DM often develop hyperglycemia from emotional stress or medical stress. Automated closed-loop systems should be able to detect such changes in insulin sensitivity and adapt insulin delivery accordingly. We recently verified the adaptability of a model-based closed-loop system in which the gain factors that govern a proportional-integral-derivative-like system are adjusted according to frequently measured insulin sensitivity. Automated systems can be tested by physical exercise to increase glucose uptake and insulin sensitivity or by administering corticosteroids to reduce insulin sensitivity. Another source of risk in closed-loop systems is suboptimal performance of amperometric glucose sensors. Inaccuracy can result from calibration error, biofouling, and current drift. We found that concurrent use of more than one sensor typically leads to better sensor accuracy than use of a single sensor. For example, using the average of two sensors substantially reduces the proportion of large sensor errors. The use of more than two allows the use of voting algorithms, which can temporarily exclude a sensor whose signal is outlying. Elements such as the use of glucagon to minimize hypoglycemia, adaptation to changes in insulin sensitivity, and sensor redundancy will likely increase safety during outpatient use of closed-loop glycemic control systems.

Optimizing reduction in basal hyperglucagonaemia to repair defective glucagon counterregulation in insulin deficiency

In health, the pancreatic islet cells work as a network with highly co-ordinated signals over time to balance glycaemia within a narrow range. In type 1 diabetes (T1DM), with autoimmune destruction of the β-cells, lack of insulin is considered the primary abnormality and is the primary therapy target. However, replacing insulin alone does not achieve adequate glucose control and recent studies have focused on controlling the endogenous glucagon release as well. In T1DM, glucagon secretion is disordered but not absolutely deficient; it may be excessive postprandially yet it is characteristically insufficient and delayed in response to hypoglycaemia. We review our system-level analysis of the pancreatic endocrine network mechanisms of glucagon counterregulation (GCR) and their dysregulation in T1DM and focus on possible use of α-cell inhibitors (ACIs) to manipulate the glucagon axis to repair the defective GCR. Our results indicate that the GCR abnormalities are of 'network origin'. The lack of β-cell signalling is the primary deficiency that contributes to two separate network abnormalities: (i) absence of a β-cell switch-off trigger and (ii) increased intraislet basal glucagon. A strategy to repair these abnormalities with ACI is proposed, which could achieve better control of glycaemia with reduced hypoglycaemia risk.