Mathematical models for insulin secretion in pancreatic β-cells

Assessing the Effect of Incretin Hormones and Other Insulin Secretagogues on Pancreatic Beta-Cell Function: Review on Mathematical Modelling Approaches

Mathematical modelling in glucose metabolism has proven very useful for different reasons. Several models have allowed deeper understanding of the relevant physiological and pathophysiological aspects and promoted new experimental activity to reach increased knowledge of the biological and physiological systems of interest. Glucose metabolism modelling has also proven useful to identify the parameters with specific physiological meaning in single individuals, this being relevant for clinical applications in terms of precision diagnostics or therapy. Among those model-based physiological parameters, an important role resides in those for the assessment of different functional aspects of the pancreatic beta cell. This study focuses on the mathematical models of incretin hormones and other endogenous substances with known effects on insulin secretion and beta-cell function, mainly amino acids, non-esterified fatty acids, and glucagon. We found that there is a relatively large number of mathematical models for the effects on the beta cells of incretin hormones, both at the cellular/organ level or at the higher, whole-body level. In contrast, very few models were identified for the assessment of the effect of other insulin secretagogues. Given the opportunities offered by mathematical modelling, we believe that novel models in the investigated field are certainly advisable.

Islet Function and Insulin Sensitivity in Latent Autoimmune Diabetes in Adults Taking Sitagliptin: A Randomized Trial

CONTEXT

The long-term effects of dipeptidyl peptidase-4 inhibitors on β-cell function and insulin sensitivity in latent autoimmune diabetes in adults (LADA) are unclear.

OBJECTIVE

To investigate the effects of sitagliptin on β-cell function and insulin sensitivity in LADA patients receiving insulin.

DESIGN AND SETTING

A randomized controlled trial at the Second Xiangya Hospital.

METHODS

Fifty-one patients with LADA were randomized to sitagliptin + insulin (SITA) group or insulin alone (CONT) group for 24 months.

MAIN OUTCOME MEASURES

Fasting C-peptide (FCP), 2-hour postprandial C-peptide (2hCP) during mixed-meal tolerance test, △CP (2hCP - FCP), and updated homeostatic model assessment of β-cell function (HOMA2-B) were determined every 6 months. In 12 subjects, hyperglycemic clamp and hyperinsulinemic euglycemic clamp (HEC) tests were further conducted at 12-month intervals.

RESULTS

During the 24-month follow-up, there were no significant changes in β-cell function in the SITA group, whereas the levels of 2hCP and △CP in the CONT group were reduced at 24 months. Meanwhile, the changes in HOMA2-B from baseline were larger in the SITA group than in the CONT group. At 24 months, first-phase insulin secretion was improved in the SITA group by hyperglycemia clamp, which was higher than in the CONT group (P < .001), while glucose metabolized (M), insulin sensitivity index, and M over logarithmical insulin ratio in HEC were increased in the SITA group (all P < .01 vs baseline), which were higher than in the CONT group.

CONCLUSION

Compared with insulin intervention alone, sitagliptin plus insulin treatment appeared to maintain β-cell function and improve insulin sensitivity in LADA to some extent.

COEXISTENCE OF THREE OSCILLATORY MODES OF INSULIN SECRETION: MATHEMATICAL MODELING AND RELEVANCE TO GLUCOSE REGULATION

Insulin secretion in pancreatic [Formula: see text]-cells exhibits three oscillatory modes with distinct period ranges, called fast, slow, and ultradian modes. To unveil the mechanism underlying such oscillatory behaviors and their roles in blood glucose regulation, we propose a combined model for the glucose–insulin regulation system, incorporating both the cell-level insulin secretion mechanism and inter-organ interactions in the blood glucose regulation. Special emphasis is placed on the identification of the mechanism of the slow oscillation and its role associated with the whole-body glucose regulation. Via extensive numerical simulations, we obtain macroscopic behaviors of the three types of insulin/glucose oscillations in the whole-body as well as microscopic behaviors of the membrane potential and the calcium concentration in the [Formula: see text]-cell. Finally, optimal regulatory strategies for the blood glucose level are discussed on the basis of the quantitative information obtained from the mathematical modeling and numerical simulations.

Role of Connexins and Pannexins in the Pancreas

The pancreas produces enzymes with a digestive function and hormones with a metabolic function, which are produced by distinct cell types of acini and islets, respectively. Within these units, secretory cells coordinate their functioning by exchanging information via signals that flow in the intercellular spaces and are generated either at distance (several neural and hormonal inputs) or nearby the pancreatic cells themselves (inputs mediated by membrane ionic-specific channels and by ionic- and metabolite-permeant pannexin channels and connexin "hemichannels"). Pancreatic secretory cells further interact via the extracellular matrix of the pancreas (inputs mediated by integrins) and directly with neighboring cells, by mechanisms that do not require extracellular mediators (inputs mediated by gap and tight junction channels). Here, we review the expression and function of the connexins and pannexins that are expressed by the main secretory cells of the exocrine and endocrine pancreatic cells. Available data show that the patterns of expression of these proteins differ in acini and islets, supporting distinct functions in the physiological secretion of pancreatic enzymes and hormones. Circumstantial evidence further suggests that alterations in the signaling provided by these proteins are involved in pancreatic diseases.

Mathematical models of electrical activity of the pancreatic β-cell: a physiological review

Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.