Calcium homeostasis is a key factor in the regulation of cardiac excitation–contraction coupling. Calcium dynamics in cardiomyocytes is governed by ATP which depends on insulin dependent glucose concentration, via the glucose transporter type 4 (GLUT4) transporter. It would therefore be interesting to see how calcium dynamics changes in a cardiomyocyte under diabetic conditions. We proposed and analysed a four dimensional ordinary differential equation (ODE) model to capture the interdependency of calcium dynamics on glucose uptake and ATP generation. More specifically, we looked for the role of GLUT4, energy metabolism, L-type channels, RyR2 channels, SERCA2a pumps and leakage rate in the normal functioning of cardiomyocytes. To understand the system dynamics, we first obtained the stability and Hopf-bifurcation criteria of steady state and then through parameter perturbation we captured the role of different parameters in maintaining normal calcium oscillation (frequency 40 to 180 beats per minute and amplitude ≥0.4 μM) and hence normal cardiac function. We observed that any divergence in the GLUT4 activity (especially a decrease in the glucose uptake rate) might cause abnormal calcium oscillation, leading to cardiac dysfunction (CD). Our study finally hypothesizes that a regulated sarcoplasmic reticulum (SR) calcium flux could be a possible therapeutic strategy to maintain normal calcium dynamics in diabetic heart and to prevent possible CD.

中文翻译：

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恢复糖尿病心肌细胞的钙稳态：通过数学模型进行的研究

钙稳态是调节心脏兴奋与收缩耦合的关键因素。心肌细胞中的钙动力学受ATP的控制，ATP取决于胰岛素依赖的葡萄糖浓度，通过4型葡萄糖转运蛋白（GLUT4）转运蛋白。因此，有趣的是观察在糖尿病条件下心肌细胞中钙动力学的变化。我们提出并分析了一个四维常微分方程（ODE）模型，以捕获钙动力学对葡萄糖吸收和ATP生成的相互依赖性。更具体地说，我们寻找了GLUT4，能量代谢，L型通道，RyR2通道，SERCA2a泵和渗漏率在心肌细胞正常功能中的作用。为了了解系统动力学，我们首先获得了稳态的稳定性和Hopf分叉准则，然后通过参数扰动捕获了不同参数在维持正常钙振荡（频率为40至180次/分钟，振幅≥0.4μM）中的作用。因此，心脏功能正常。我们观察到，GLUT4活性的任何差异（特别是葡萄糖摄取率的降低）都可能引起异常的钙振荡，从而导致心脏功能障碍（CD）。我们的研究最后假设，调节的肌浆网（SR）钙通量可能是维持糖尿病心脏正常钙动力学并预防CD的一种可能的治疗策略。