Insulin is secreted by pancreatic $\beta$-cells that are electrically coupled into micro-organs called islets of Langerhans. The secretion is due to the influx of Ca²⁺ ions that accompany electrical impulses, which are clustered into bursts. So-called “medium bursting” occurs in many $\beta$-cells in intact islets, while in other islets the $\beta$-cells exhibit “slow bursting”, with a much longer period. Each burst brings in Ca²⁺ that, through exocytosis, results in insulin secretion. When isolated from an islet, $\beta$-cells behave very differently. The electrical activity is much noisier, and consists primarily of trains of irregularly-timed spikes, or fast or slow bursting. Medium bursting, so often seen in intact islets, is rarely if ever observed. In this study, we examine what the isolated cell behavior can tell us about the mechanism for bursting in intact islets. A previous mathematical study concluded that the slow bursting observed in isolated $\beta$-cells, and therefore most likely in islets, must be due to intrinsic glycolytic oscillations, since this mechanism for bursting is robust to noise. It was demonstrated that an alternate mechanism, phantom bursting, was very sensitive to noise, and therefore could not account for the slow bursting in single cells. We re-examine these conclusions, motivated by recent experimental and mathematical modeling evidence that slow bursting in intact islets is, at least in many cases, driven by the phantom bursting mechanism and not endogenous glycolytic oscillations. We employ two phantom bursting models, one minimal and the other more biophysical, to determine the sensitivity of medium and slow bursting to electrical current noise. In the minimal model, both forms of bursting are highly sensitive to noise. In the biophysical model, while medium bursting is sensitive to noise, slow bursting is much less sensitive. This suggests that the slow bursting seen in isolated $\beta$-cells may be due to a phantom bursting mechanism, and by extension, slow bursting in intact islets may also be driven by this mechanism.

胰岛素是胰腺分泌的 $\beta$电耦合到称为朗格罕岛的微器官的微细胞。分泌是由于 伴随电脉冲聚集的Ca ²⁺离子大量涌入。所谓的“中等爆发”$\beta$-完整胰岛中的细胞，而在其他胰岛中 $\beta$-细胞表现出“缓慢爆发”，并且具有更长的时间。每次爆发都会引起Ca ²⁺，通过胞吐作用会导致胰岛素分泌。与小岛隔离后，$\beta$-单元的行为非常不同。电活动噪声较大，并且主要由定时不定时的尖峰或快速或慢速脉冲串组成。在完整的胰岛中经常见到的中等爆裂，很少观察到。在这项研究中，我们研究了孤立的细胞行为可以告诉我们完整胰岛破裂的机制的原因。先前的数学研究得出结论，在孤立的情况下观察到缓慢的爆发$\beta$-细胞，因此最有可能出现在胰岛中，必须归因于内在的糖酵解振荡，因为这种爆发机制对噪声具有鲁棒性。已证明，幻像爆发的另一种机制对噪声非常敏感，因此无法解释单个细胞中的缓慢爆发。我们根据最近的实验和数学建模证据重新检验这些结论，即至少在许多情况下，完整胰岛的缓慢爆发是由幻像爆发机制而非内源性糖酵解振荡驱动的。我们采用两种幻像爆发模型，一种是最小的，另一种是生物物理的，以确定中等和缓慢爆发对电流噪声的敏感性。在最小模型中，两种形式的猝发对噪声都非常敏感。在生物物理模型中 中等爆发对噪声敏感，而慢爆发对敏感度低得多。这表明在孤立的环境中看到的缓慢爆发$\beta$-细胞可能归因于幻影爆发机制，并且通过扩展，完整胰岛中的缓慢爆发也可以由该机制驱动。