Mitochondrial membrane potential (ΔΨM) is a central intermediate in oxidative energy metabolism. Although ΔΨM is routinely measured qualitatively or semi-quantitatively using fluorescent probes, its quantitative assay in intact cells has been limited mostly to slow, bulk-scale radioisotope distribution methods. Here we derive and verify a biophysical model of fluorescent potentiometric probe compartmentation and dynamics using a bis-oxonol-type indicator of plasma membrane potential (ΔΨP) and the ΔΨM probe tetramethylrhodamine methyl ester (TMRM) using fluorescence imaging and voltage clamp. Using this model we introduce a purely fluorescence-based quantitative assay to measure absolute values of ΔΨM in millivolts as they vary in time in individual cells in monolayer culture. The ΔΨP-dependent distribution of the probes is modelled by Eyring rate theory. Solutions of the model are used to deconvolute ΔΨP and ΔΨM in time from the probe fluorescence intensities, taking into account their slow, ΔΨP-dependent redistribution and Nernstian behaviour. The calibration accounts for matrix:cell volume ratio, high- and low-affinity binding, activity coefficients, background fluorescence and optical dilution, allowing comparisons of potentials in cells or cell types differing in these properties. In cultured rat cortical neurons, ΔΨM is -139 mV at rest, and is regulated between -108 mV and -158 mV by concerted increases in ATP demand and Ca2+-dependent metabolic activation. Sensitivity analysis showed that the standard error of the mean in the absolute calibrated values of resting ΔΨM including all biological and systematic measurement errors introduced by the calibration parameters is less than 11 mV. Between samples treated in different ways, the typical equivalent error is ~5 mV.
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