Mathematical Analysis of Electrical Oscillations in Anterior Pituitary Cells

Florida State University, Tallahassee FL

Investigators

Abstract

This project is a hybrid mathematical/experimental approach to the analysis of the behavior of hormone-secreting pituitary cells. We record a cell's electrical activity and use features of this to calibrate a mathematical model. This calibration is done with the aid of a graphics processing unit (GPU) for fast optimization of a fitness function that compares features of the model voltage trace to those of the experimental recording. Once calibrated, the model is used to make predictions about the effects of changes in biological parameters, such as the conductances of various types of ionic currents. These predictions are then tested on the same cell that was used to calibrate the model, using the dynamic clamp technique to inject a model-based ionic current into a real cell. To help with our understanding of the model, and thus to make more useful predictions, we use geometric singular perturbation methods to understand the basis for spiking and bursting patterns of electrical activity, and the parameter ranges where different types of activity occur. The ultimate goal of mathematical models for biological systems is to generate hypotheses that can be tested in the lab. If the model is well calibrated, then testing a prediction made by the model is the best way to determine if our understanding of the biology that is reflected in the model is correct. In particular, if a test of a model prediction fails, then it means that something is wrong with our understanding of the biology that was the basis for the model. However, this is only true if the model is well calibrated, since a model that is correct in its formulation, but incorrect in its parameterization, can lead to incorrect predictions. This caveat is particularly important given the great degree of cell-to-cell heterogeneity that exists in many biological systems. For example, a cell may exhibit one type of pattern of activity, while a neighboring cell of the same type may exhibit a very different pattern of activity, reflecting differences in biological parameter values. In this project, we combine fast model calibration with the dynamic clamp technique to calibrate a model based on a single cell's activity, and then test predictions made by the model on the same cell, overcoming problems associated with cellular heterogeneity.