MODELING OF SINGLE CHANNEL AND WHOLE CELL CURRENT MEASUREMENTS WITH APPLICATION TO CALCIUM CHANNELS (NEURON, BIOPHYSICS, MARKOVIAN MODELS)
WILSON, DAVID LYNN
Doctor of Philosophy
Modern measurements of membrane, ionic channel molecules consist of whole cell current relaxations obtained using various voltage pulse protocols, current noise power spectra from small numbers of channels, and single channel intervals in the form of waiting, closed, and open time histograms. A state-variable description was developed for predicting these measurements from Markovian state models, and it was used to analyze the parameter identifiability properties of the models and measurements. Computer programs were developed for estimating model parameters; these included maximum likelihood estimation for the single channel data. In the case of the Ca channel, the parameters from a variety of models were found to be faster when obtained from whole cell rather than single channel measurements. The latter measurements were low pass filtered at 1 kHz in order to reliably detect the (TURN) 1/2 picoamp openings; the errors that resulted were elucidated by running Monte Carlo simulated channels through the threshold detection algorithm. Intervals were distorted by the absence of brief open and closed times as well as falsely prolonged open and closed times. An analytical technique was developed for computing the resulting distorted histograms, and after correction there was reasonable agreement between the measurements. Other errors found using single channel simulations included the appearance of a bimodal amplitude distribution from filtered channels having a single amplitude and the effects of noise and finite record length recording. Of six models considered for describing activation, a 4-state model best fit the whole cell relaxations resulting from simple, short pulse protocols, and it also predicted results from 2-pulse protocols and temperature experiments. Some inactivation models were eliminated because they were unable to simulate recover from inactivation and single channel failure traces. A family of models was suggested that describes the present experimental results, and possible tests for future model discrimination were evaluated using simulation. Two relatively insensitive tests were the 2-pulse test for "coupled" inactivation and the single channel Hi-Lo sort method for determining Ca-accumulation-dependent processes. It is concluded that the combination of parameter estimation and simulation is a useful tool for interpreting results and helping to plan experiments and analyses.