Recovery of neuronal channel densities from calcium fluorescence
Cox, Steven J.
Doctor of Philosophy
Neurons have the ability to dynamically adjust their own membrane channel densities to modulate the strength of communication with other neurons. This process is integral to such neuronal functions as spatial recognition and memory but has been difficult to measure experimentally. Historically, neuroscientists have used changes in voltage to infer changes in neuronal channel densities. However, voltage is difficult to measure away from the soma. Many important functions in the neuron, like synaptic integration, take place in the dendritic tree where traditional voltage measurements can not be taken. To interrogate the neuron in the dendrites, experimentalists have come to rely on calcium fluorescence based microscopy to infer qualitative information about voltage changes in the dendrites. In these experiments, intracellular calcium changes due to voltage depolarizations are recorded at spatially distributed sites on the dendrites through the binding of calcium to a fluorescent buffer. The recovery of channel densities can be posed as a parameter identification problem in a coupled nonlinear partial differential equation that relates the responses of calcium, the fluorescent buffer and voltage to neuronal stimulation. We convert temporally and spatially distributed fluorescence data into quantitative measurements of voltage sensitive channel densities by inverting slow time-scaled calcium data into fast time-scaled voltage data. Our approach is to solve four interrelated inverse problems corresponding to three different proposed experiments to go from calcium fluorescence to channel densities. In the first experiment, we use subthreshold calcium dynamics to infer the reaction kinetics between calcium arid fluorescent buffer. From these kinetics, we can use suprathreshold voltage stimulation to infer calcium channel densities and recover distributed voltage data. Finally we use the voltage data to infer potassium channel densities in the dendrites. Our algorithm has been shown to recover channel densities for several different calcium channel models and the delayed rectifying potassium channel from simulated noisy fluorescence data in morphologically realistic neurons.