Optical estimation of absolute membrane potential using fluorescence lifetime imaging

All lifetime images are represented as an overlay of photon count (pixel intensity) and weighted average lifetime (pixel color) throughout the text (τm + PC, Figure 1—figure supplement 1). Pixels with insufficient signal to fit a fluorescence decay are shown in black. The photon counts, as well as the lifetimes, in image sequences on the same set of cells are scaled across the same range.

Pixels with photon counts below 300 (VF2.1.Cl) or 150 (VF2.0.Cl) photons at the peak of the decay (time bin with the most signal) were omitted from analysis to ensure reproducible fits. Because the lifetime of VFs does not fully decay to baseline in a single 12.5 ns laser cycle, the incomplete multiexponentials fitting option was used, allowing the model to attribute some signal early in the decay to the previous laser cycle. Out of 256 time bins from the analog-to-digital converter (ADC), only data from time bins 23 to 240 were used in the final fit. The offset parameter (detector dark counts per ADC time bin per pixel) was set to zero. The number of iterations for the fit in SPCImage was increased to 20 to obtain converged fits. Shift between the IRF and the decay trace was fixed to 0.5 (in units of ADC time bins), which consistently gave lifetimes of standards erythrosin B (1 mg/mL in H2O) (Boens et al., 2007) and fluorescein (2 μM in 0.1 N NaOH, H2O) (Magde et al., 1999) closest to reported values (Figure 1—source data 2).

To obtain sufficient photons but keep excitation light power minimal, binning between neighboring pixels was employed during fitting. This procedure effectively takes the lifetime as a spatial moving average across the image by including adjacent pixels in the decay for a given pixel. To obtain larger photon counts, the confocal pinhole was set between 2.5 and 3.5 airy units, which corresponds to optical section thickness of approximately 2.5 µm.

Data typeAcquired pixel width (μm)Binned pixel width (μm)Acquisitiontime (s)Img size (pixels)Concentration Curve (Figure 1—figure supplement 2, Figure 2—figure supplement 4)0.443.0875–90256 × 256Vmem Distributions (Figure 3)1.248.6890–120256 × 256Electrophysiology Recording1.003.0115–3064 × 64EGF Time Series0.882.643064 × 64

All tabulated values are for an individual frame, although multiple sequential frames were recorded in both the electrophysiology and EGF experiments. For each recording type, the width of each pixel at acquisition is reported, as well as the width of the area included in the binned lifetime signal during fitting. All pixels are square. The acquisition time reflects the total time to collect the image, not the total time exposing each pixel. All FLIM images have 256 time bins in the ns regime, so a 256 × 256 spatial image size represents a 256 × 256 × 256 total dataset. Img = image.

Images were divided into cell groups, with each cell group as a single region of interest (ROI). ROIs were determined from photon count images, either manually from the cell morphology in FIJI (Schindelin et al., 2012) or automatically by sharpening and then thresholding the signal intensity with custom MATLAB code (Source code 2). Regions of images that were partially out of the optical section or contained punctate debris were omitted. Sample ROIs are shown in Figure 1—figure supplement 1.

For cells that adjoin other cells, attribution of a membrane region to one cell versus the other is not possible. As such, we chose to interpret each cell group as an independent sample (‘n’) instead of extracting Vmem values for individual cells. Adjacent cells in a group are electrically coupled to varying degrees, and their resting membrane potentials are therefore not independent (Meşe et al., 2007). While this approach did not fully utilize the spatial resolution of VF-FLIM, it prevented overestimation of biological sample size for the effect in question.

The mean τm across all pixels in an ROI was used as the lifetime for that ROI. Lifetime values were mapped to transmembrane potential via the lifetime-Vmem standard curves determined with whole-cell voltage-clamp electrophysiology. For electrophysiology measurements, the relationship between the weighted average lifetime (Equation 4) and membrane potential for each patched cell was determined by linear regression, yielding a sensitivity (m, ps/mV) and a 0 mV lifetime (b, ps) for each cell (Equation 5). The average sensitivity and 0 mV point across all cells of a given type were used to convert subsequent lifetime measurements (τ) to Vmem (Figure 2—source data 1, Equation 6). For quantifying changes in voltage (ΔVmem) from changes in lifetime (Δτ), only the average sensitivity is necessary (Equation 7).(5)τ=m*Vmem+b(6)Vmem=(τ-b)m(7)ΔVmem=(Δτ)m

Where standard error of the mean of a voltage determination (δVmem) is given, error was propagated to include the standard errors of the slope (δm) and y-intercept (δb) of the voltage calibration, as well as the standard error of the lifetime measurements (δτ) in the condition of interest (Equation 8). For error in a voltage change (δΔVmem), only error in the calibration slope was included in the propagated error (Equation 9). Where standard deviation of VF-FLIM derived Vmem values is shown, a similar error propagation procedure was applied, using the standard deviation of the average sensitivity and 0 mV lifetime for that cell line.(8)δVmem=Vmemδτ2+δb2τ-b2+δmm2(9)δΔVmem=ΔVmemδΔτΔτ2+δmm2

The intrinsic nature of fluorescence lifetime introduces a point of reference into the voltage measurement, from which a single lifetime image can be interpreted as resting membrane potential. Differences in this reference point (reported here as the 0 mV lifetime) over time and across cells provides an estimate of the voltage-independent noise in VF-FLIM. We report resolution as the root-mean-square deviation (RMSD) between the optically calculated voltage (VFLIM) and the voltage set by whole-cell voltage clamp (Vephys), which is analogous to the resolution calculations described previously by Cohen and co-workers (Hou et al., 2014). The RMSD of n measurements (Equation 10) can be determined from the variance σ (Cone and Cone, 1976) (Equation 11) and the bias (Equation 12) of the estimator (in this case, VF-FLIM) relative to the ‘true’ value (in this case, electrophysiology). These calculations are described graphically in Scheme 2 below.(10)RMSD=σ2+Bias2(11)σ2=1n∑i=1n(VFLIM,i-Vephys,i)2(12)Bias=1n∑i=1nVFLIM,i-1n∑i=1nVephys,i

The voltage-independent variations in lifetime are much larger between cells than within a cell. Therefore, the error in measuring absolute voltage changes on a given cell (‘intra-cell’ comparisons) is lower than the error in determining the absolute Vmem of that cell (‘inter-cell’ comparisons, since the calibration used is from another cell). We can therefore determine an ‘intra-cell’ RMSD and an ‘inter-cell’ RMSD to reflect the voltage resolution of these two types of measurements. To calculate ‘intra-cell’ error, we look at the RMSD between Vephys and VFLIM using the τfl-Vmem relationship for that specific cell. Phrased another way, we are looking at the amount of error that would be expected in estimating Vmem of a cell if its exact τfl-Vmem relationship were known. This ‘intra cell’ RMSD estimates the error expected in quantifying changes in Vmem on a given cell. We calculate an intra cell error for each cellular recording, so intra cell errors are reported throughout the text as a mean ± SEM of the intra cell errors for all individual cells of a given type. The average intra cell error was at or below 5 mV for all cell lines tested (Figure 2—source data 1).

The error in the absolute membrane potential determination (‘inter-cell’) is calculated here as the RMSD between the y-intercept (0 mV lifetime) of all of the individual cells’ lifetime-voltage relationships and the 0 mV value for the averaged calibration for all cells of a given type. This metric quantifies how well the lifetime-Vmem relationship for a given cell line represents an individual cell’s lifetime-Vmem relationship. This ‘inter cell’ RMSD ranged from 10 to 23 mV for the tested cell lines (Figure 2—source data 1). Much smaller errors for a population value of Vmem can be obtained by averaging Vmem recordings from multiple cells.

This method of calculating error assumes that the electrophysiology measurement is perfectly accurate and precise. Realistically, it is likely that some of the variation seen is due to the quality of the voltage clamp. As a result, these RMSD values provide a conservative upper bound for the voltage errors in VF-FLIM.

For sample images of CAESR in HEK293T (Figure 1—figure supplement 4), fluorescence decays were fit using SPCImage to a biexponential decay model as described for VF2.1.Cl above, using a peak photon threshold of 150 and a bin of 2 (binned pixel width of 5 μm). To better match the studies by Cohen and co-workers (Brinks et al., 2015), which isolated the membrane fluorescence from cytosolic fluorescence by directing the laser path, the lifetime-voltage relationships were not determined with these square-binned images. Instead, membranes were manually identified, and the fluorescence decays from all membrane pixels were summed together before fitting once per cell. (This is in contrast to the processing of VoltageFluor data, where the superior signal to noise and localization enables fitting and analysis of the lifetime on a pixel by pixel basis). This ‘one fit per membrane’ analysis of CAESR was performed in custom MATLAB code implementing a Nelder-Mead algorithm (Source code 1, adapted from Enderlein and Erdmann, 1997). CAESR data were fit to a biexponential model with the offset fixed to 0 and the color shift as a free parameter.

In preparation for imaging, HEK293T cells were plated as described above for electrophysiology. 1 µM di-8-ANEPPS was loaded for ten minutes in HBSS at room temperature and atmospheric CO2. Coverslips were washed twice in HBSS and transferred to fresh HBSS for imaging. No surfactants were used in the loading (e.g. Pluronic F-127) because their presence worsened cell robustness for whole-cell patch-clamp electrophysiology. All recordings were made with HBSS as an extracellular solution; no cells were kept for more than 30 min after dye loading due to the increasing presence of internalized dye.

Epifluorescence imaging was performed with an inverted Observer.Z1 (Carl Zeiss Microscopy) controlled with µManager 1.4 (Open Imaging) (Edelstein et al., 2014). Images were acquired with an Orca Flash 4 Digital CMOS camera (Hamamatsu Corporation; San Jose, CA). Excitation light was provided with a Spectra X light engine (Lumencor, Inc.; Beaverton, OR). Excitation wavelengths were selected with built-in filters in the Spectra X (440/20 bandpass filter for blue and 550/15 bandpass filter for green). Blue-excited images were obtained with an excitation power of 71 mW/mm2 and an exposure time of 50 ms. Green-excited images were obtained with an excitation power of 136 mW/mm2 and an exposure time of 500 ms. Emission light was collected with a 40x magnification oil immersion objective lens using Immersol 518F immersion oil (Zeiss). Fluorescence emission was selected with a 562 nm long pass dichroic mirror and further filtered by a 593/40 bandpass filter (Semrock). Excitation and emission wavelengths were selected to match previous work with this probe as closely as possible (Zhang et al., 1998) (current excitation [blue]: 440 ± 10 nm; reported excitation [blue]: 440 ± 15 nm; current excitation [green]: 550 ± 7.5 nm; reported excitation [green]: 530 ± 15 nm; current dichroic: 562 nm long-pass; reported dichroic: 565 nm; current emission: 593 ± 20 nm; reported emission: 570 nm long pass).

Single color (e.g. blue excited or green excited) fluorescence images were background subtracted at each pixel before ratios were calculated. The background value was determined from a region of interest near the center of the image that contained no cells and minimal fluorescent debris. Excitation ratios (‘R’, blue signal divided by green signal, B/G) were then calculated pixelwise from the background subtracted fluorescence images. Pixels with less than 100 arbitrary units of signal in either the blue or the green channel were excluded from analysis and are depicted in black. Regions of interest (ROIs) were manually selected in FIJI to include only area corresponding to the cell membrane. The ratio was averaged across all pixels in a given ROI (similar to the treatment for VF-FLIM, as described in Figure 1—figure supplement 1). The ratio values per value of Vmem (set by whole cell patch clamp electrophysiology) in Figure 1—figure supplement 5E,F are the average of these cell-averaged ratios obtained in 6 or 7 sequential images acquired while the Vmem was held at the indicated value.

Where normalized R values are discussed, these values were calculated by dividing the ratio at a given potential (averaged for an ROI as discussed above) by the ratio at 0 mV, as reported previously (Zhang et al., 1998). This normalization procedure requires electrode-based calibration for every individual recording and cannot be stably extended to all cells from a particular cell line. Therefore, it is not analogous to VF-FLIM and is not the point of comparison for voltage resolution.

Mean ± standard error of the mean (SEM) of data is reported throughout the text. Hypothesis testing was performed as indicated with either analysis of variance (ANOVA) followed by appropriate post hoc tests or two-sided, unpaired, unequal variances t-tests. Statistical tests were performed in Python 2 or 3 with the SciPy, pandas and Pingouin (Vallat, 2018) packages. Unless otherwise noted, all data shown reflect at least three biological replicates (independent cultures measured on different days). Each of these biological replicates contained between 1 and 5 technical replicates (different samples of cells that were measured on the same day and had been prepared from the same cell stock). For tandem electrophysiology-FLIM measurements, each τfl-Vmem calibration includes at least three biological replicates to capture the variability expected during applications of VF-FLIM. No power analyses were performed before data were collected. Sample sizes throughout the text refer to the total number of cells or cell groups of a given type analyzed across all biological and technical replicates. Cell group identification is discussed in Methods. For experiments where resting membrane potential or resting membrane potential changes are compared to a baseline (Figures 3–5 and supplements), both control measurements and their physiologically or pharmacologically altered counterparts were recorded on each experimental day. Masking was not used during data collection or analysis.