Multi-timescale Analysis of Cellular Electrical Activity

该项目将使用数学和计算分析来了解激素分泌内分泌和心脏细胞的活动模式。人体内有许多细胞具有电活性。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，肌肉细胞启动收缩。了解这些细胞的电活动是理解它们行为的基础。这不是一件容易的事，因为电活动是由离子流介导的，离子流通过细胞膜上的几种离子通道以非线性的方式通过膜电位相互作用。更复杂的是，有许多细胞内信号分子作用于这些通道并改变它们的行为。本项目重点研究胰腺胰岛素分泌细胞、应激激素分泌垂体细胞和心室细胞的膜电位振荡。这些振荡可能是有益的，也可能是病理性的，这取决于细胞类型。这个项目的一个目标是理解振荡发生的原因，在它们是病态的情况下，确定如何终止它们。另一个目标是培养本科生和研究生直接适用于生物系统的复杂数学技术的理论和应用。通过与几个实验实验室的互动，促进了这种培训。描述电可兴奋细胞的变量通常在不同的时间尺度上发生显著变化。有些变量能迅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子系统的水平上，也可以发生在慢变量子系统的水平上，或者发生在涉及两个子系统的变量的某个中间水平上。为了理解振荡的基础，应该以适当的方式划分系统变量，便于使用几何奇异摄动分析或快/慢分析。本项目采用快速/慢速分析方法检查垂体促肾上腺皮质激素和胰腺β细胞的爆发振荡，以及心室肌细胞去极化后病理早期（EADs）。前者驱动激素分泌，而后者在组织水平上可导致室性心动过速。对不同模型的快速/慢速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）的作用机制，使细胞在不同的行为之间移动，有些有节奏，有些没有。它还将用于了解不同刺激频率对心室肌细胞产生EAD的影响，心室肌细胞通常接受来自窦房结原位的周期性刺激。该项目由数学科学部/数学生物学和分子与细胞生物学/细胞动力学和功能项目共同支持。该奖项反映了美国国家科学基金会的法定使命，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.