| Neurons have both a fast and slow mode of signaling. Fast signals are communicated by transmembrane voltage changes, while calcium levels within the cell communicate information on a much slower time scale. Calcium acts as a second messenger responsible for modulating neuronal excitability in many ways including the mediation of gene transcription in the cell and the sensitivity of the cell to further stimulus. I propose a means of determining calcium conductance density of the cell membrane from intracellular calcium concentration measurement data using a two step process. The first step is the inference of calcium current density from calcium concentration measurements using a least squares fit to the data. Once an estimate of the calcium current density is determined, the minimum value over time is used to determine the calcium conductance density. I develop a voltage model of the neuron's electrical signal with ion diffusion and drift which includes voltage-gated calcium currents and calcium-dependent potassium currents. The influx of calcium resulting from the voltage model will prime the endoplasmic reticulum with calcium. A model of the dynamics of calcium induced calcium release from the endoplasmic reticulum via IP3 receptors which includes diffusion of calcium and IP3 as well as calcium buffering by the mitochondria results in a calcium wave similar to what has been observed experimentally. Finally, I use a branch structure together with IP3 generation, calcium buffers in the cytosol and ER, cell membrane calcium transports (voltage-gated calcium channels, pumps, exchangers, and store-operated channels), and ER calcium transports (IP3 receptors, ryanodine receptors, pumps, leak channels) to show that calcium waves initiate in the apical trunk at the point where the stimulated oblique branches off. |
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