Intracellular ionic concentration by calibration from fluorescence indicator emission spectra, its relationship to the K_d, F_min, F_max formula, and use with Na-Green for presynaptic sodium

The emission spectra calibration curves for a fluorescence indicator and the F_min, F_max, and K_d formula were shown to be related. Using the known calibrated fluorescence emitted by Sodium Green (Na-Green) and photo-multiplier-tube quantum efficiency, we calculated the detection signal over a range of sodium concentrations. The calculated calibration curves were compared for optical filters passing a narrow band, medium band or full spectrum. We found that a method based on the full emission spectrum was the most appropriate. Given a known resting concentration of intracellular sodium, calibrated readings can be converted to concentration values. This method is applicable to any fluorescence indicator when curves for emission spectra over a range of concentrations are available. We measured sodium concentration changes during trains of action potentials (APs) at a crayfish motor axon's presynaptic terminals injected with Na-Green. During low frequency AP trains, net sodium increases asymptotically with frequency. Average net Na-flux per AP decreases for increasing terminal size. The terminals of crayfish motor axon have surface area to volume ratio which is 7700 times larger than for squid. Thus, in comparison to squid, crayfish terminals exhibit a larger change in [Na⁺]_i during equivalent AP activity.