Casey Bennett with Peter J. Thomas, Dept. of Mathematics, and David Friel, Dept. of Neurosciences

Consequences of random ion channel gating for irregularity of Purkinje cell firing patterns

Purkinje cells (PC) are neurons located in the cerebellum, which are understood to play a fundamental role in motor control in humans and mice. Like other nerve cells in the brain, they have cell membranes that act as RC circuit elements that can temporarily hold a small electric charge; once the electrical potential across the cell membrane exceeds a threshold voltage, the PC fires or “spikes”: experimental recordings of cell voltage versus time show rapid increases in voltage, followed by a reset to a lower starting voltage, with the cycle continuing approximately periodically. The capacity to sustain regenerative spiking is referred to as membrane excitability. It is known that membrane excitability is a consequence of ion channel proteins embedded in the cell membrane, which fluctuate stochastically between conducting and nonconducting states, in a manner that is sensitive to the voltage difference across the cell membrane. The ion channel states in turn affect membrane voltage by increasing or decreasing the number of current pathways to redistribute charge. Due to currents flowing spontaneously through particular ion channels, Purkinje cells spontaneously spike at regular intervals, and this regular spiking activity is believed to play an important role in motor control in neural circuits within the cerebellum.

The basic mechanisms that generate spiking in neurons are well understood, and so is the function of collections of ion channels. However, the way in which multiple ion channels jointly contribute to excitability, and how excitability is modified by mutation of the underlying channel protein genes, remains a mystery. This project explores the relationship between ion channels and single neuron dynamics in two stages by first implementing a noisy differential equation, and then generating large numbers of computer experiments. The final task of the first stage will identify the mathematical property(s), which the simple noisy differential equation model lacks, in comparison to data collected experimentally.