In vivo studies have investigated the role of β-cell dysfunction in type 2 diabetes (T2D), whereas in vitro research on islets has elucidated key mechanisms that control the insulin secretion rate. However, the relevance of the cellular mechanisms identified in vitro (i.e., the triggering and amplifying pathways) has not been established in vivo. Furthermore, the mechanisms underpinning β-cell dysfunction in T2D remain undetermined. We propose a unifying explanation of several characteristic features of insulin secretion both in vitro and in vivo by using a mathematical model. The model describes the triggering and amplifying pathways and reproduces a variety of in vitro and in vivo tests in subjects with and without T2D, identifies the mechanisms modulating first-phase insulin secretion rate in response to basal hyperglycemia or insulin resistance, and shows that β-cell dysfunction in T2D can be explained by an impaired amplifying pathway with no need to postulate defects in intracellular calcium handling.

The effect of endurance exercise on enhancing insulin sensitivity and glucose flux has been well established with techniques such as the hyperinsulinemic clamp. Although informative, such techniques do not emulate the physiological postprandial state, and it remains unclear how exercise improves postprandial glycaemia. Accordingly, combining mixed-meal tolerance testing and the triple-stable isotope glucose tracer approach, glucose fluxes [rates of meal glucose appearance (Ra), disposal (Rd), and endogenous glucose production (EGP)] were determined following acute endurance exercise (1 h cycling; ~70% V̇o) and 4 wk of endurance training (cycling 5 days/wk). Training was associated with a modest increase in V̇o (~7%, P < 0.001). Postprandial glucose and insulin responses were reduced to the same extent following acute and chronic training. Interestingly, this was not accompanied by changes to rates of meal Ra, Rd, or degree of EGP suppression. Glucose clearance (Rd relative to prevailing glucose) was, however, enhanced with acute and chronic exercise. Furthermore, the duration of EGP suppression was shorter with acute and chronic exercise, with EGP returning toward fasting levels more rapidly than pretraining conditions. These findings suggest that endurance exercise influences the efficiency of the glucoregulatory system, where pretraining rates of glucose disposal and production were achieved at lower glucose and insulin levels. Notably, there was no influence of chronic training over and above that of a single exercise bout, providing further evidence that glucoregulatory benefits of endurance exercise are largely attributed to the residual effects of the last exercise bout.

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Mechanical stimuli and geometrical constraints transmitted across the cytoskeleton to the nucleus affect the nuclear morphology and cell function. Human pluripotent stem cells (hPSCs) represent an effective tool for evaluating transitions in nuclear deformability from the pluripotent to differentiated stage, and for deciphering the underlying mechanisms. We report the first study that investigates the nuclear deformability induced by geometrical constraints of hPSCs both in the pluripotent stage and during early germ layer specification. We specifically developed micro-structured surfaces coupled with high-content imaging analysis algorithms to quantitatively characterize nuclear deformability. Our results show that hPSCs possess high nuclear deformability, which does not alter pluripotency. We observed nuclear deformability transition along early germ layer specification: during early ectoderm differentiation nuclear deformability is strongly reduced, during early endoderm differentiation nuclei keep a deformed shape and during early mesoderm specification they show an intermediate behaviour. Different mRNA expressions between hPSCs differentiated on flat and micro-structured surfaces have been observed along early mesoderm and early endoderm specification. In order to better understand the mechanisms of the nuclear deformability transition observed during early ectoderm differentiation, we also employed cytoskeletal and nuclear protein inhibitors to evaluate their role in determining the nuclear shape. Actin and nesprin are essential for maintaining deformed nuclei, while lamin A/C and intermediate filaments confer rigidity to the nucleus. This study suggests that nuclear deformability is highly regulated during differentiation.