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

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.