Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells

Optimizing SGLT inhibitor treatment for diabetes with chronic kidney diseases

Diabetes induces glomerular hyperfiltration, affects kidney function, and may lead to chronic kidney diseases. A novel therapeutic treatment for diabetic patients targets the sodium-glucose cotransporter isoform 2 (SGLT2) in the kidney. SGLT2 inhibitors enhance urinary glucose, [Formula: see text] and fluid excretion and lower hyperglycemia in diabetes by inhibiting [Formula: see text] and glucose reabsorption along the proximal convoluted tubule. A goal of this study is to predict the effects of SGLT2 inhibitors in diabetic patients with and without chronic kidney diseases. To that end, we applied computational rat kidney models to assess how SGLT2 inhibition affects renal solute transport and metabolism when nephron population are normal or reduced (the latter simulates chronic kidney disease). The model predicts that SGLT2 inhibition induces glucosuria and natriuresis, with those effects enhanced in a remnant kidney. The model also predicts that the [Formula: see text] transport load and thus oxygen consumption of the S3 segment are increased under SGLT2 inhibition, a consequence that may increase the risk of hypoxia for that segment. To protect the vulnerable S3 segment, we explore dual SGLT2/SGLT1 inhibition and seek to determine the optimal combination that would yield sufficient urinary glucose excretion while limiting the metabolic load on the S3 segment. The model predicts that the optimal combination of SGLT2/SGLT1 inhibition lowers the oxygen requirements of key tubular segments, but decreases urine flow and [Formula: see text] excretion; the latter effect may limit the cardiovascular protection of the treatment.

Decoding the regulatory mechanism of glucose and insulin induced phosphatidylinositol 3,4,5-trisphosphate dynamics in β-cells

In MIN6 pancreatic β-cells, glucose and insulin act in a synergistic manner to regulate the dynamics of Phosphatidylinositol (3,4,5)-trisphosphate (PIP₃). However, the precise regulatory mechanism behind such an experimentally observed synergy is poorly understood. In this article, we propose a phenomenological mathematical model for studying the glucose and insulin driven PIP₃ activation dynamics under various stimulatory conditions to unfold the mechanism responsible for the observed synergy. The modeling study reveals that the experimentally observed oscillation in PIP₃ dynamics with disparate time scales for different external glucose doses is mainly orchestrated by the complex dynamic regulation of cytosolic Ca²⁺ in β-cells. The model accounts for the dose-dependent activation of PIP₃ as a function of externally added insulin, and further shows that even in the absence of Ca²⁺ signaling, externally added glucose can still maintain a basal level of endogenous insulin secretion via the fatty acid metabolism pathway. Importantly, the model analysis suggests that the glucose mediated ROS (reactive oxygen species) activation often contributes considerably to the synergistic activation of PIP₃ by glucose and insulin in a context dependent manner. Under the physiological conditions that keep β-cells in an insulin responsive state, the effect of glucose induced ROS signaling plays a moderate role in PIP₃ activation. As β-cells approach an insulin resistant state, the glucose induced ROS signaling significantly affects the PIP₃ dynamics. Our findings provide a plausible mechanistic insight into the experimentally observed synergy, and can lead to novel therapeutic strategies.

Predicted consequences of diabetes and SGLT inhibition on transport and oxygen consumption along a rat nephron

Diabetes increases the reabsorption of Na(+) (TNa) and glucose via the sodium-glucose cotransporter SGLT2 in the early proximal tubule (S1-S2 segments) of the renal cortex. SGLT2 inhibitors enhance glucose excretion and lower hyperglycemia in diabetes. We aimed to investigate how diabetes and SGLT2 inhibition affect TNa and sodium transport-dependent oxygen consumption [Formula: see text] along the whole nephron. To do so, we developed a mathematical model of water and solute transport from the Bowman space to the papillary tip of a superficial nephron of the rat kidney. Model simulations indicate that, in the nondiabetic kidney, acute and chronic SGLT2 inhibition enhances active TNa in all nephron segments, thereby raising [Formula: see text] by 5-12% in the cortex and medulla. Diabetes increases overall TNa and [Formula: see text] by ∼50 and 100%, mainly because it enhances glomerular filtration rate (GFR) and transport load. In diabetes, acute and chronic SGLT2 inhibition lowers [Formula: see text] in the cortex by ∼30%, due to GFR reduction that lowers proximal tubule active TNa, but raises [Formula: see text] in the medulla by ∼7%. In the medulla specifically, chronic SGLT2 inhibition is predicted to increase [Formula: see text] by 26% in late proximal tubules (S3 segments), by 2% in medullary thick ascending limbs (mTAL), and by 9 and 21% in outer and inner medullary collecting ducts (OMCD and IMCD), respectively. Additional blockade of SGLT1 in S3 segments enhances glucose excretion, reduces [Formula: see text] by 33% in S3 segments, and raises [Formula: see text] by <1% in mTAL, OMCD, and IMCD. In summary, the model predicts that SGLT2 blockade in diabetes lowers cortical [Formula: see text] and raises medullary [Formula: see text], particularly in S3 segments.

Modeling oxygen consumption in the proximal tubule: effects of NHE and SGLT2 inhibition

The objective of this study was to investigate how physiological, pharmacological, and pathological conditions that alter sodium reabsorption (TNa) in the proximal tubule affect oxygen consumption (QO2 ) and Na(+) transport efficiency (TNa/QO2 ). To do so, we expanded a mathematical model of solute transport in the proximal tubule of the rat kidney. The model represents compliant S1, S2, and S3 segments and accounts for their specific apical and basolateral transporters. Sodium is reabsorbed transcellularly, via apical Na(+)/H(+) exchangers (NHE) and Na(+)-glucose (SGLT) cotransporters, and paracellularly. Our results suggest that TNa/QO2 is 80% higher in S3 than in S1-S2 segments, due to the greater contribution of the passive paracellular pathway to TNa in the former segment. Inhibition of NHE or Na-K-ATPase reduced TNa and QO2 , as well as Na(+) transport efficiency. SGLT2 inhibition also reduced proximal tubular TNa but increased QO2 ; these effects were relatively more pronounced in the S3 vs. the S1-S2 segments. Diabetes increased TNa and QO2 and reduced TNa/QO2 , owing mostly to hyperfiltration. Since SGLT2 inhibition lowers diabetic hyperfiltration, the net effect on TNa, QO2 , and Na(+) transport efficiency in the proximal tubule will largely depend on the individual extent to which glomerular filtration rate is lowered.

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.

Glucose metabolism and oscillatory behavior of pancreatic islets

A variety of oscillations are observed in pancreatic islets. We establish a model incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic cells and the other is the glucose-insulin feedback model which considers direct and indirect feedback of secreted insulin. These two are coupled to interact with each other in the combined model, and two basic assumptions are made on the basis of biological observations: The conductance gK(ATP) for the ATP-dependent potassium current is a decreasing function of the glucose concentration whereas the insulin secretion rate is given by a function of the intracellular calcium concentration. Obtained via extensive numerical simulations are complex oscillations including clusters of bursts, slow and fast calcium oscillations, and so on. We also consider how the intracellular glucose concentration depends upon the extracellular glucose concentration, and examine the inhibitory effects of insulin.

Substrate effects on oscillations in metabolism, calcium and secretion in single mouse islets of Langerhans

Glucose induces complex patterns of oscillations in intracellular Ca2+ concentration ([Ca2+]i), metabolism and secretion in islets of Langerhans including "slow" and "fast" pulses with period of 2-5 min and 10-20 s respectively. In an effort to elucidate the origin of slow oscillations, individual mouse islets were exposed to different fuels including glyceraldehyde, pyruvate, methyl pyruvate and alpha-ketoisocaproate (KIC), all of which bypass key steps of glycolytic metabolism, while monitoring [Ca2+]i, oxygen consumption and secretion. Glyceraldehyde gave rise to slow oscillations only when substimulatory glucose was also added to the media. Glucosamine, an inhibitor of glucokinase, blocked these slow oscillations. KIC, pyruvate, and methyl pyruvate did not give rise to slow oscillations alone or with glucose present. The addition of glucose to islets bathed in nutrient-rich cell culture media accelerated metabolism and initiated slow oscillations while glyceraldehyde did not. It is concluded that glucose has a special role in accelerating metabolism and generating slow oscillations in isolated islets of Langerhans from mice. Combined with previous observations of Ca2+ dependency for all oscillations in islets, we propose that interactions between Ca2+ influx and glycolysis are responsible for the slow oscillations. In contrast, fast oscillations can occur independent of glycolytic flux.

Targeted reduction of complex models with time scale hierarchy--a case study

With the increasing flow of biological data there is a growing demand for mathematical tools whereby essential aspects of complex causal dynamic models can be captured and detected by simpler mathematical models without sacrificing too much of the realism provided by the original ones. Given the presence of a time scale hierarchy, singular perturbation techniques represent an elegant method for making such minimised mathematical representations. Any reduction of a complex model by singular perturbation methods is a targeted reduction by the fact that one has to pick certain mechanisms, processes or aspects thought to be essential in a given explanatory context. Here we illustrate how such a targeted reduction of a complex model of melanogenesis in mammals recently developed by the authors provides a way to improve the understanding of how the melanogenic system may behave in a switch-like manner between production of the two major types of melanins. The reduced model is shown by numerical means to be in good quantitative agreement with the original model. Furthermore, it is shown how the reduced model discloses hidden robustness features of the full model, and how the making of a reduced model represents an efficient analytical sensitivity analysis. In addition to yielding new insights concerning the melanogenic system, the paper provides an illustration of a protocol that could be followed to make validated simplifications of complex biological models possessing time scale hierarchies.

Computational approaches to cellular rhythms

Oscillations arise in genetic and metabolic networks as a result of various modes of cellular regulation. In view of the large number of variables involved and of the complexity of feedback processes that generate oscillations, mathematical models and numerical simulations are needed to fully grasp the molecular mechanisms and functions of biological rhythms. Models are also necessary to comprehend the transition from simple to complex oscillatory behaviour and to delineate the conditions under which they arise. Examples ranging from calcium oscillations to pulsatile intercellular communication and circadian rhythms illustrate how computational biology contributes to clarify the molecular and dynamical bases of cellular rhythms.