Protocol for analyzing emergence dynamics of diabetes with obesity using numerical continuation and bifurcation analysis

Type 2 diabetes (T2D) is a multifactorial disease that slowly and inconspicuously progresses over years. Here, we present a protocol for analyzing slow progression dynamics of T2D with obesity. We describe steps for using software to exploit the differences between the timescales of the metabolic variables and using numerical continuation and bifurcation analysis. We detail procedures to analyze bi-stable system dynamics and identify the thresholds that separate healthy and diabetic states. For complete details on the use and execution of this protocol, please refer to Yildirim et al. (2023).1</p

Gain of function mutation in K(ATP) channels and resulting upregulation of coupling conductance are partners in crime in the impairment of Ca²⁺ oscillations in pancreatic ß-cells

Gain of function mutations in the pore forming Kir6 subunits of the ATP sensitive K+ channels (K(ATP) channels) of pancreatic β-cells are the major cause of neonatal diabetes in humans. In this study, we show that in insulin secreting mouse β-cell lines, gain of function mutations in Kir6.1 result in a significant connexin36 (Cx36) overexpression, which form gap junctional connections and mediate electrical coupling between β-cells within pancreatic islets. Using computational modeling, we show that upregulation in Cx36 might play a functional role in the impairment of glucose stimulated Ca2+ oscillations in a cluster of β-cells with Kir6.1 gain of function mutations in their K(ATP) channels (GoF-K(ATP) channels). Our results show that without an increase in Cx36 expression, a gain of function mutation in Kir6.1 might not be sufficient to diminish glucose stimulated Ca2+ oscillations in a β-cell cluster. We also show that a reduced Cx36 expression, which leads to loss of coordination in a wild-type β-cell cluster, restores coordinated Ca2+ oscillations in a β-cell cluster with GoF-K(ATP) channels. Our results indicate that in a heterogenous β-cell cluster with GoF-K(ATP) channels, there is an inverted u-shaped nonmonotonic relation between the cluster activity and Cx36 expression. These results show that in a neonatal diabetic β-cell model, gain of function mutations in the Kir6.1 cause Cx36 overexpression, which aggravates the impairment of glucose stimulated Ca2+ oscillations.</p

Gain of function mutation in K(ATP) channels and resulting upregulation of coupling conductance are partners in crime in the impairment of Ca²⁺ oscillations in pancreatic ß-cells

Gain of function mutations in the pore forming Kir6 subunits of the ATP sensitive K+ channels (K(ATP) channels) of pancreatic β-cells are the major cause of neonatal diabetes in humans. In this study, we show that in insulin secreting mouse β-cell lines, gain of function mutations in Kir6.1 result in a significant connexin36 (Cx36) overexpression, which form gap junctional connections and mediate electrical coupling between β-cells within pancreatic islets. Using computational modeling, we show that upregulation in Cx36 might play a functional role in the impairment of glucose stimulated Ca2+ oscillations in a cluster of β-cells with Kir6.1 gain of function mutations in their K(ATP) channels (GoF-K(ATP) channels). Our results show that without an increase in Cx36 expression, a gain of function mutation in Kir6.1 might not be sufficient to diminish glucose stimulated Ca2+ oscillations in a β-cell cluster. We also show that a reduced Cx36 expression, which leads to loss of coordination in a wild-type β-cell cluster, restores coordinated Ca2+ oscillations in a β-cell cluster with GoF-K(ATP) channels. Our results indicate that in a heterogenous β-cell cluster with GoF-K(ATP) channels, there is an inverted u-shaped nonmonotonic relation between the cluster activity and Cx36 expression. These results show that in a neonatal diabetic β-cell model, gain of function mutations in the Kir6.1 cause Cx36 overexpression, which aggravates the impairment of glucose stimulated Ca2+ oscillations.</p

A data-driven computational model for obesity-driven diabetes onset and remission through weight loss

Obesity is a major risk factor for the development of type 2 diabetes (T2D), where a sustained weight loss may result in T2D remission in individuals with obesity. To design effective and feasible intervention strategies to prevent or reverse T2D, it is imperative to study the progression of T2D and remission together. Unfortunately, this is not possible through experimental and observational studies. To address this issue, we introduce a data-driven computational model and use human data to investigate the progression of T2D with obesity and remission through weight loss on the same timeline. We identify thresholds for the emergence of T2D and necessary conditions for remission. We explain why remission is only possible within a window of opportunity and the way that window depends on the progression history of T2D, individual's metabolic state, and calorie restrictions. These findings can help to optimize therapeutic intervention strategies for T2D prevention or treatment.</p

Bariatric surgery improves postprandial VLDL kinetics and restores insulin mediated regulation of hepatic VLDL production

Dyslipidemia in obesity results from excessive production and impaired clearance of triglyceride-rich (TG-rich) lipoproteins, which are particularly pronounced in the postprandial state. Here, we investigated the impact of Roux-en-Y gastric bypass (RYGB) surgery on postprandial VLDL1 and VLDL2 apoB and TG kinetics and their relationship with insulin-responsiveness indices. Morbidly obese patients without diabetes who were scheduled for RYGB surgery (n = 24) underwent a lipoprotein kinetics study during a mixed-meal test and a hyperinsulinemic-euglycemic clamp study before the surgery and 1 year later. A physiologically based computational model was developed to investigate the impact of RYGB surgery and plasma insulin on postprandial VLDL kinetics. After the surgery, VLDL1 apoB and TG production rates were significantly decreased, whereas VLDL2 apoB and TG production rates remained unchanged. The TG catabolic rate was increased in both VLDL1 and VLDL2 fractions, but only the VLDL2 apoB catabolic rate tended to increase. Furthermore, postsurgery VLDL1 apoB and TG production rates, but not those of VLDL2, were positively correlated with insulin resistance. Insulin-mediated stimulation of peripheral lipoprotein lipolysis was also improved after the surgery. In summary, RYGB resulted in reduced hepatic VLDL1 production that correlated with reduced insulin resistance, elevated VLDL2 clearance, and improved insulin sensitivity in lipoprotein lipolysis pathways.</p

Calcium Oscillation Frequency-Sensitive Gene Regulation and Homeostatic Compensation in Pancreatic β -Cells

Pancreatic islet β -cells are electrically excitable cells that secrete insulin in an oscillatory fashion when the blood glucose concentration is at a stimulatory level. Insulin oscillations are the result of cytosolic Ca 2 + oscillations that accompany bursting electrical activity of β -cells and are physiologically important. ATP-sensitive K + channels (K(ATP) channels) play the key role in setting the overall activity of the cell and in driving bursting, by coupling cell metabolism to the membrane potential. In humans, when there is a defect in K(ATP) channel function, β -cells fail to respond appropriately to changes in the blood glucose level, and electrical and Ca 2 + oscillations are lost. However, mice compensate for K(ATP) channel defects in islet β -cells by employing alternative mechanisms to maintain electrical and Ca 2 + oscillations. In a recent study, we showed that in mice islets in which K(ATP) channels are genetically knocked out another K + current, provided by inward-rectifying K + channels, is increased. With mathematical modeling, we demonstrated that a sufficient upregulation in these channels can account for the paradoxical electrical bursting and Ca 2 + oscillations observed in these β -cells. However, the question of determining the correct level of upregulation that is necessary for this compensation remained unanswered, and this question motivates the current study. Ca 2 + is a well-known regulator of gene expression, and several examples have been shown of genes that are sensitive to the frequency of the Ca 2 + signal. In this mathematical modeling study, we demonstrate that a Ca 2 + oscillation frequency-sensitive gene transcription network can adjust the gene expression level of a compensating K + channel so as to rescue electrical bursting and Ca 2 + oscillations in a model β -cell in which the key K(ATP) current is removed. This is done without the prescription of a target Ca 2 + level, but evolves naturally as a consequence of the feedback between the Ca 2 +-dependent enzymes and the cell’s electrical activity. More generally, the study indicates how Ca 2 + can provide the link between gene expression and cellular electrical activity that promotes wild-type behavior in a cell following gene knockout

Protocol for analyzing emergence dynamics of diabetes with obesity using numerical continuation and bifurcation analysis

Summary: Type 2 diabetes (T2D) is a multifactorial disease that slowly and inconspicuously progresses over years. Here, we present a protocol for analyzing slow progression dynamics of T2D with obesity. We describe steps for using software to exploit the differences between the timescales of the metabolic variables and using numerical continuation and bifurcation analysis. We detail procedures to analyze bi-stable system dynamics and identify the thresholds that separate healthy and diabetic states.For complete details on the use and execution of this protocol, please refer to Yildirim et al. (2023).1 : Publisher’s note: Undertaking any experimental protocol requires adherence to local institutional guidelines for laboratory safety and ethics

The key components of the model.

<p>Green arrows are for stimulatory and red circles are for inhibitory pathways. In the wild-type cells, bursting is paced by metabolic oscillations acting on K(ATP) channels. In the KO cells, genetic disruption of K(ATP) channels leads to increased Kir2.1 current, which now drives bursting.</p

Bursting in wild-type model cells.

<p>Slow glycolytic oscillations drive bursting through actions on the K(ATP) current. (A) cAMP declines at the start of each Ca²⁺ plateau. (B) K(ATP) channel conductance. (C-D) Adenine nucleotide concentrations in the cytosol. (E) Slow glycolytic oscillations are reflected in the FBP time course.</p

Distinct model predictions of the effects of partial inhibition of SERCA pumps with thapsigargin distinguishes the two models.

<p>(A) In the model where bursting is driven by oscillations in the ER calcium concentration simulation of TG application reduces the <i>c</i>_<i>er</i> (red) and terminates slow <i>c</i> oscillations (black). (B) In this model, the z-curve and <i>c</i>_<i>er</i> nullcline are shifted far to the left and the periodic spiking branch is destabilized. The new stable periodic branch exhibits fast two-spike bursting at the value of <i>c</i>_<i>er</i> at which the trajectory settles. (C) In the model in which bursting is driven by oscillations in the Kir2.1 current, bursting continues after TG application (black) because the <i>AMP</i>_<i>c</i> oscillations (red) persist. (D) In this model, TG increases the amplitude of the <i>AMP</i>_<i>c</i> oscillations, which shifts the <i>c</i>_<i>∞</i> curve further to the right and increases the period of oscillations, but the burst mechanism is unaltered.</p