Multi-timescale Analysis of Cellular Electrical Activity

该项目将使用数学和计算分析来了解分泌唾液的内分泌细胞和心脏细胞的活动模式。身体中的许多细胞都是电活性的。它们产生电脉冲，神经细胞通过这些脉冲编码和传递信息，内分泌细胞分泌激素，肌肉细胞开始收缩。了解这些细胞的电活动是了解它们行为的基础。这不是一件容易的任务，因为电活动是由通过细胞膜中的几种类型的离子通道的离子流介导的，这些离子通道通过膜电位以非线性方式相互作用。除了这种复杂性之外，还有许多细胞内信号分子作用于这些通道中的一些并改变它们的行为。本计画主要研究胰脏分泌胰岛素细胞、分泌压力荷尔蒙之脑下垂体细胞及心室细胞之膜电位振荡。这些振荡可能是有益的或病理性的，这取决于细胞类型。该项目的一个目标是了解为什么振荡会发生，如果它们是病理性的，则确定如何终止它们。另一个目标是培养本科生和研究生的理论和应用复杂的数学技术，直接适用于生物系统。这种训练是通过与几个实验室的互动来促进的。描述电可兴奋细胞的变量通常在显著不同的时间尺度上变化。一些变量能快速适应细胞膜电位的变化，而另一些则适应得较慢。在这种情况下，膜电位的振荡可以发生在快变量的子系统水平，或在慢子系统水平，或在涉及两个子系统变量的中间水平。为了理解振荡的基础，系统变量应该以适当的方式划分，以便于使用几何奇异摄动分析或快速/慢速分析。本项目采用快/慢分析法检查垂体促肾上腺皮质激素细胞和胰腺β细胞的爆发振荡，以及心室肌细胞的病理性早期后去极化（埃兹）。 前者驱动激素的分泌，而后者可在组织水平上导致室性心动过速。对不同模型的快/慢分析将揭示细胞行为调节剂（如皮质类固醇、葡萄糖或低钾血症）在不同行为之间移动细胞的机制，这些行为有些是有节奏的，有些不是。它也将用于了解不同的刺激频率对心室肌细胞EAD产生的影响，心室肌细胞通常接受来自原位窦房结的周期性刺激。该项目得到了数学科学/数学生物学和分子与细胞生物学/细胞动力学和功能计划的支持。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will use mathematical and computational analysis to understand patterns of activity in hormone-secreting endocrine and cardiac cells. Numerous cells in the body are electrically active. They produce electrical impulses, and these impulses through which nerve cells code and transmit information, endocrine cells secrete hormones, and muscle cells initiate contraction. Understanding the electrical activity of these cells is fundamental to understanding their behavior. This is, no easy task, since the electrical activity is mediated by ion flow through several types of ion channels in the cell membrane interacting in nonlinear ways through the membrane potential. Adding to this complexity, there are numerous intracellular signaling molecules acting on some of these channels and modifying their behavior. This project focuses on oscillations in the membrane potential of insulin-secreting cells of the pancreas, stress-hormone-secreting pituitary cells, and cells of the cardiac ventricles. These oscillations can be beneficial or pathological, depending on the cell type. One objective of this project is to understand why the oscillations happen and, in the case that they are pathological, to determine how they can be terminated. Another objective is to train undergraduate and graduate students in the theory and application of sophisticated mathematical techniques that are directly applicable to biological systems. This training is facilitated through the interaction with several experimental labs.The variables that describe an electrically excitable cell often vary on significantly different times scales. Some variables adapt quickly to changes in the cell's membrane potential, while others adapt more slowly. In such cases, oscillations in the membrane potential can occur at the level of the subsystem of fast variables, or at the level of the slow subsystem, or at some intermediate level that involves variables from both subsystems. To understand the basis of the oscillations, system variables should be partitioned in an appropriate way, facilitating the use of geometric singular perturbation analysis, or fast/slow analysis. This project employs fast/slow analysis in the examination of bursting oscillations in pituitary corticotrophs and pancreatic beta-cells, and pathological early after depolarizations (EADs) in ventricular myocytes. The former drive the secretion of hormones, while the latter can lead to, at the tissue level, ventricular tachycardia. The fast/slow analysis of the different models will uncover the mechanisms through which modulators of cell behavior, such as corticosteroids or glucose or hypokalemia, act to move the cell among distinct behaviors, some rhythmic and some not. It will also be used to understand the effects of different stimulus frequencies on EAD production in ventricular myocytes, which normally receive periodic stimulation from the sinoatrial node in situ. This project is supported by both Division of Mathematical Sciences/Mathematical Biology and Molecular and Cellular Biology/Cellular Dynamics and Function programs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.