Multi-timescale Analysis of Cellular Electrical Activity

Florida State University, Tallahassee FL

Investigators

Abstract

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.