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。人体内的许多细胞都有电活动。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了解它们行为的基础。这并不是一件容易的事情，因为电活动是通过细胞膜中几种类型的离子通道以非线性的方式通过膜电位相互作用而调节的。除了这种复杂性，还有许多细胞内的信号分子作用于其中一些通道并改变它们的行为。该项目主要研究胰腺胰岛素分泌细胞、应激激素分泌的脑下垂体细胞和心室细胞的膜电位的振荡。这些振荡可能是有益的，也可能是病态的，这取决于细胞类型。这个项目的一个目标是了解振荡为什么会发生，并在它们是病态的情况下，确定如何终止它们。另一个目标是对本科生和研究生进行直接适用于生物系统的复杂数学技术的理论和应用方面的培训。这种训练是通过与几个实验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。一些变量对细胞膜电位的变化适应得很快，而另一些变量则适应得更慢。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，或者发生在慢子系统的水平上，或者发生在涉及来自两个子系统的变量的某个中间水平上。为了了解振荡的基础，应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。该项目使用快速/慢速分析来检查垂体促肾上腺皮质激素细胞和胰岛β细胞的爆发性振荡，以及心室肌细胞的病理性早期后去极化(EADS)。前者驱动荷尔蒙的分泌，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的调节剂，如皮质类固醇或葡萄糖或低钾，通过这些机制在不同的行为之间移动，一些行为是有节奏的，另一些则不是。它还将被用来了解不同刺激频率对心室肌细胞EAD产生的影响，这些细胞通常从原位窦房结接受周期性刺激。该项目由数学科学/数学生物学和分子与细胞生物学/细胞动力学和功能计划两个部门支持。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为是值得支持的。

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.