Stimulus secretion coupling in pancreatic beta-cells

胰岛素分泌受损是2型糖尿病发病机制中的关键步骤，沿着靶组织对胰岛素的低效利用。 分泌的两个主要成分是钙进入胰腺β细胞和由钙触发胰岛素颗粒胞吐。 我们对这两种成分及其对糖尿病的作用进行了建模。 我们主要集中在钙振荡的机制在一个范围内的时间，从秒到分钟。 较慢类别的振荡（5 - 10分钟周期）是循环中脉动胰岛素浓度的主要驱动因素，这已被证明是胰岛素敏感组织（尤其是肝脏）响应的最佳选择。 该模型历史发展的详细信息可参见我们前几年的报告和当前的综述文章（参考文献#1）。 我们称之为集成振荡器模型（IOM），以表明振荡的结果从一个电子振荡器（EO）和代谢振荡器（MO）的伙伴关系。 电振荡器（EO）基于钙对离子通道的负反馈，直接对钙激活的钾（K（Ca））通道的负反馈和间接对ATP依赖性钾（K（ATP））通道的负反馈，因为钙降低ATP/ADP比率。 代谢振荡器（MO）由果糖1，6二磷酸（FBP）对糖酵解中产生它的酶磷酸果糖激酶（PFK）的正反馈控制。 MO通过K（ATP）通道与EO通信，K（ATP）通道将细胞的代谢状态（ATP/ADP比率）转化为电去极化。 K（ATP）通道具有临床意义，因为它们是胰岛素刺激药物的靶点，例如磺酰脲类甲苯磺丁脲和格列本脲，它们是开发用于治疗2型糖尿病的第一类口服药物。 严重的K（ATP）功能获得性突变是新生儿糖尿病的主要原因，而在全基因组关联研究（GWAS）中，中度功能获得性突变与较轻但更常见的成人发病形式的糖尿病（2型糖尿病）有关。 相反，K（ATP）的功能丧失突变是家族性高胰岛素血症的主要原因，家族性高胰岛素血症是一种在儿童中发现的遗传性疾病，其中β细胞持续电活性并在正常或低血糖时分泌胰岛素，导致危及生命的低血糖。高胰岛素血症的另一个主要原因是葡萄糖激酶（GK）的过度活性，它在DOM中也起着关键作用。 我们在这一领域的工作历史超过四十年，结果邀请在一年两次的动力系统会议上由工业与应用数学学会主办（2023年6月）的全体会议上发表演讲。 广受欢迎的谈话导致进一步邀请写一篇简短的新闻文章，突出了谈话的一些关键信息，包括数学建模在解决胰岛素分泌中关键生物学和医学问题中的作用，以及这些生物学应用在产生新的数学知识中的作用。 尽管IOM取得了许多成功，但今年新的数据和新模式的建议对IOM提出了挑战。新的模型认为，钙和胰岛素分泌的振荡结果不通过质膜离子通道的K（ATP）通道的控制下，但从主要的细胞内储存细胞器，内质网（ER）的钙释放的钙进入。 在其他细胞类型中也发现了这种基于钙释放的振荡，但我们在参考文献#1中指出，这种机制不能解释在β细胞中进行的大量实验观察，并且可以通过经典钙进入模型很好地解释。 我们进一步证明了正则模型实际上可以解释那些声称使它失效的新观测。 我们认为，尽管如此，新的观察结果还是有价值的，因为它们引起了人们对钙释放的一个先前未被充分认识的作用以及调节振荡开始的阈值水平的相关机制的注意。这在生理学上非常重要，因为阈值将必须抑制胰岛素分泌以避免低血糖的基础（空腹）方案与必须迅速增加胰岛素分泌一个数量级以有效抑制来自摄入的碳水化合物的葡萄糖升高的餐后方案区分开。 用于治疗T2 D的高度成功的胰高血糖素样肽1（GLP-1）受体激动剂家族部分地通过介导阈值的小的向下偏移而起作用。

Impaired insulin secretion is a key step in the pathogenesis of type 2 diabetes, along with inefficient use of insulin by target tissues. The two main components of secretion are calcium entry into pancreatic beta cells and triggering of insulin granule exocytosis by that calcium. We have modeled both components and their contributions to diabetes. We have focused mainly on the mechanisms of calcium oscillations over a range of periods, from seconds to minutes. The slower class of oscillations (5 - 10 minute period) is the main driver of pulsatile insulin concentration in the circulation, which has been shown to be optimal for the response of insulin-sensitive tissues, especially the liver. Details of the historical development of the model can be found in our reports from previous years and in a current review article (ref. #1). We call the resulting model the integrated oscillator model (IOM) to indicate that the oscillations result from the partnership of an electrical oscillator (EO) and a metabolic oscillator (MO). The electrical oscillator (EO) is based on negative feedback of calcium onto ion channels, directly onto calcium-activated potassium (K(Ca)) channels and indirectly onto ATP-dependent potassium (K(ATP)) channels because calcium reduces the ATP/ADP ratio. The metabolic oscillator (MO) is governed by positive feedback of fructose 1,6 bisphosphate (FBP) on the enzyme in glycolysis that produces it, phosphofructokinase (PFK). The MO communicates with the EO via the K(ATP) channels, which transduce the metabolic state of the cell (ATP/ADP ratio) into electrical depolarization. K(ATP) channels are of clinical significance as they are a target of insulin-stimulating drugs, such as the sulfonylureas tolbutamide and glyburide, the first class of oral medications developed for the treatment of Type 2 Diabetes. Severe gain-of-function mutations of K(ATP) are a major cause of neo-natal diabetes mellitus, whereas moderate gain-of-function mutations have been linked in genome-wide association studies (GWAS) to the milder but more common adult-onset form of diabetes, type 2 diabetes. Conversely, loss-of-function mutations of K(ATP) are a major cause of familial hyperinsulinism, a hereditary disease found in children in which beta cells are persistently electrically active and secrete insulin in the face of normal or low glucose, causing life-threatening hypoglycemia. Another major cause of hyperinsulinism is excessive activity of the enzyme glucokinase (GK), which also plays a key role in the DOM. Our history of work in this area over four decades resulted in an invitation to give a plenary lecture at the biannual meeting on Dynamical Systems hosted by the Society for Industrial and Applied Mathematics (June, 2023). The well-received talk led to a further invitation to write a short news article highlighting some of the key messages of the talk, including the role of mathematical modeling in solving problems of key biological and medical interest in insulin secretion and the role of these biological applications in generating new mathematical knowledge. Though it has had many successes, the IOM was challenged this year by new data and a proposal for a new model. The new model holds that the oscillations in calcium and insulin secretion result not from calcium entry through plasma membrane ion channels under the control of K(ATP) channels but from calcium release from the primary intracellular storage organelle, the endoplasmic reticulum (ER). Such calcium release based oscillations are found in other cell types, but we argued in Ref. #1 that this mechanism cannot account for the large body of experimental observations that have been made in beta cells and are well accounted for by the canonical calcium entry model. We showed further that the canonical model can in fact account for the new observations that were claimed to invalidate it. We argued that the new observations nonetheless have value because they draw attention to a previously underappreciated role of calcium release and related mechanisms to modulate the threshold level at which oscillations begin. This is of great physiological importance because the threshold divides the basal (fasting) regime where insulin secretion must be throttled down to avoid hypoglycemia from the post-prandial regime where insulin secretion must be promptly increased by an order of magnitude to effectively restrain the rise in glucose from ingested carbohydrates. The highly successful family of glucagon-like peptide 1 (GLP-1) receptor agonists for treating T2D work in part by mediating small downward shifts in the threshold.