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METHODS IN CELL PHYSIOLOGY

An Excel-based model of Ca²⁺ diffusion and fura 2 measurements in a spherical cell

Department of Physiology and Cell Biology, University of Nevada School of Medicine, Reno, Nevada 89557

Submitted 30 June 2003 ; accepted in final form 22 September 2003

We wrote a program that runs as a Microsoft Excel spreadsheet to calculate the diffusion of Ca²⁺ in a spherical cell in the presence of a fixed Ca²⁺ buffer and two diffusible Ca²⁺ buffers, one of which is considered to be a fluorescent Ca²⁺ indicator. We modeled Ca²⁺ diffusion during and after Ca²⁺ influx across the plasma membrane with parameters chosen to approximate amphibian sympathetic neurons, mammalian adrenal chromaffin cells, and rat dorsal root ganglion neurons. In each of these cell types, the model predicts that spatially averaged intracellular Ca²⁺ activity ([Ca²⁺]_avg) rises to a high peak and starts to decline promptly on the termination of Ca²⁺ influx. We compared [Ca²⁺]_avg with predictions of ratiometric Ca²⁺ measurements analyzed in two ways. Method 1 sums the fluorescence at each of the two excitation or emission wavelengths over the N compartments of the model, calculates the ratio of the summed signals, and converts this ratio to Ca²⁺ ([Ca²⁺]_avg,M1). Method 2 sums the measured number of moles of Ca²⁺ in each of the N compartments and divides by the volume of the cell ([Ca²⁺]_avg,M2). [Ca²⁺]_avg,M1 peaks well after the termination of Ca²⁺ influx at a value substantially less than [Ca²⁺]_avg because the summed signals do not reflect the averaged free Ca²⁺ if the signals come from compartments containing gradients in free Ca²⁺ spanning nonlinear regions of the relationship between free Ca²⁺ and the fluorescence signals. In contrast, [Ca²⁺]_avg,M2 follows [Ca²⁺]_avg closely.

intracellular calcium; kinetic model; diffusion coefficient; fura 2ff; furaptra

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