Dynamics of glucose and insulin concentration connected to the β‐cell cycle: model development and analysis

Abstract

BackgroundDiabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β‐cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β‐cell cycle for the development of diabetes mellitus.MethodsThis paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the β‐cell cycle. The interplay of glucose, insulin, and β‐cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability.ResultsOur model shows the connection of glucose and insulin concentrations to the β‐cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the β‐cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose‐insulin regulatory system showed in biological experiments.ConclusionsThis work focusses on modeling the physiological situation of the glucose‐insulin regulatory system with a detailed consideration of the β‐cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

Development, growth and maintenance of β-cell mass: Models are also part of the story

“…The direct effect of glucose on the dynamics of β-cell mass was also analyzed quantitatively by developing a compartmental model coupling insulin storage and glucose regulation with the slow dynamics of β-cell cycle (Gallenberger et al, 2012). In this model, glucose is assumed to stimulate the transition from the G 1 to the S phase of the cell cycle, which is an important checkpoint in β-cell replication (Cozar-Castellano et al, 2006; Cozar-Castellano et al, 2008).…”

“…Given that insulin metabolizes glucose, we would expect insulin to affect β-cell cycle indirectly in this model. Gallenberger et al's (Gallenberger et al, 2012) model reconfirms the observed β-cell mass adaptability to metabolic demand, but it cannot explain how insulin induces anti-apoptotic signal in β-cells (Johnson et al, 2006). The balance between cell cycle replication and β-cell mass, and how it is affected by moderate and prolonged hyperglycemia, remains an open question that can be investigated quantitatively.…”

A closed-loop multi-level model of glucose homeostasis

“…Recent applications of multi-level models have been proposed to describe the pathophysiology of beta-cells in the endocrine pancreas [ 17 ], and the whole body effects of the altered insulin signaling cascade in adipocytes [ 18 ], while other applications described the effects of inflammation on the onset of T2DM and its complications [ 19 ]. The holistic approach of hierarchical modeling identifies subcellular processes, specific cell subtypes and tissues, organs and the whole body as strictly interconnected layers, where physiological variations occurring at any level would affect the dynamics elsewhere in the stacked constitutive elements.…”

Mathematical Modelling and Simulation of <i>β</i>-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes

“…Using a mathematical model similar to the model of Topp et al, De Gaetano and collaborators introduced the concept of pancreatic reserve [14]. Gallenberger et al proposed a model on the dynamics of glucose and insulin concentration connected to the β-cell cycle [15]. More generally and for modelling details, the reader is referred to recent reviews that dealt explicitly with different models using differential equations, delayed differential equations, integro-differential equations, stochastic differential equations, optimal control and other methods for glycaemic control, blood glucose monitoring and devices devoted to diabetic prevention [16]- [22].…”