Supplementary Figure 5: Estimation of action potential initiation times to within ±12 ms (s.d.). via 1-kHz-two-photon Ca²⁺ imaging.

(a) Trans-membrane potentials of individual cortical pyramidal cells monitored in live brain tissue slices via whole-cell patch clamp electrophysiological recording (black trace; 1–5 spikes evoked with 2-ms-long current pulses of 0.5–1.7 nA at a rate of 150 Hz) during simultaneous monitoring of the cell’s somatic Ca²⁺ dynamics (red trace) with 1-kHz-two-photon imaging (100 kHz laser repetition rate; 0.7 mW per beamlet at the specimen) and the fluorescent Ca²⁺ indicator Calbryte-590. Data in panels a–i were acquired in 8 cells in neocortical slices from 3 mice. (b) Red trace: Mean Ca²⁺ transient time course, computed as the mean Ca²⁺ transient waveform (ΔF(t)/F₀) evoked in response to 80 isolated spikes or 150-Hz bursts of spikes, averaged over 8 cells (10 traces per cell). Purple trace: A parametric fit of the form \(f\left( t \right) = \frac{{Ae^{ - (t - t_0)/\tau _1}}}{{1 + e^{ - (t - t_0)/\tau _2}}}\), used in panels c–i as a matched filter for the estimation of spike or spike burst initiation times, where A, t₀, τ₁, τ₂, are, respectively, the waveform’s amplitude, time of half-rise, decay-time constant and logistic-growth-rate constant (Methods). Fit parameter values: A = 12 ± 1.2%, t₀ = 11 ± 2.0 ms, τ₁ = 766 ± 80 ms, and τ₂ = 5.6 ± 1.9 ms. (c) Black traces: Whole-cell patch clamp electrophysiological recordings of neuronal trans-membrane potentials, illustrating one, three or five spikes. Red traces: Simultaneously recorded somatic Ca²⁺ activity traces (ΔF(t)/F₀). A purple dot marks the estimated occurrence time of each spike or spike burst, determined as the time bin at which application of the matched filter, determined as in panel b, yielded its maximum output value. (d–f) Trials with individual spikes, d, bursts of 3 spikes evoked at 150 Hz, e, or bursts of 3 spikes evoked at 10 Hz, f. Dotted vertical lines indicate the spike or spike burst times obtained from the electrophysiological recordings (black traces). Purple dots indicate the occurrence times estimated from the Ca²⁺ transient waveforms (red traces) by using the matched filter. (g) Histogram of timing errors, computed as the difference between the estimated spike or spike burst initiation times as determined using an unbiased estimator and the corresponding times directly observed in the electrophysiological recordings. RMS timing estimation error was 11.6 ms, aggregated across individual spikes and spike bursts. (h) Histogram of timing errors for spike bursts. Unlike in panel g, the timing errors plotted in h and i include the systematic mean biases in timing estimation. For spike bursts, the estimation bias was –0.3 ms, and the s.d. around the bias was 11.7 ms. (i) Histogram of timing errors for individual spikes, revealing a systematic mean bias of –6.9 ms and a s.d of 10.1 ms. (j) Assessments of how fluorescence scattering might have affected the Ca²⁺ imaging data in our dual optical-electrical recordings, performed by quantifying how the fluorescence signals, ΔF(t)/F₀, during a somatic Ca²⁺ transient declined as a function of the lateral displacement from the neural cell body. The graph shows example ΔF(t)/F₀ traces determined within individual regions-of-interest (ROIs), which either match the cell body (black trace) or are 1.6-μm-diameter circles centered within different ranges away from the edge of the cell’s ROI (colored traces). Each empirical curve is shown together with a parametric fit of the same form, \(f\left( t \right) = \frac{{Ae^{ - (t - t_0)/\tau _1}}}{{1 + e^{ - (t - t_0)/\tau _2}}}\), used in panel b to characterize somatic Ca²⁺ transients. These examples are representative of the data from a total of 418 ROIs studied in the vicinity of 3 different cells. (k) Plots of the amplitudes of Ca²⁺ transient signals (mean ± s.d.) from the fit parameters, A, determined as in panel j for 1.6-μm-diameter-ROIs centered at different distances from the edge of the cell’s ROI. The values of the Ca²⁺ transient amplitudes are normalized to those observed at the cell body. Solid blue curve is a fit to the data (418 total ROIs in the vicinity of 3 different neurons) using a declining exponential function (length constant: 1.4 ± 0.2 μm). Dashed black curve is a theoretical prediction for the distance-dependent decline of fluorescence Ca²⁺ signals, computed by convolving the experimentally measured optical point spread function (Supplementary Fig. 8a) with the cell body ROI, performing the same analysis using 1.6-μm-diameter-ROIs as applied to the real data, and then fitting a declining exponential curve (length constant: 3.4 ± 0.06 μm) to the results. Ca²⁺ transient waveforms in c–f are shown after median-filtering (30 ms window) of the ΔF(t)/F₀ traces. The ΔF(t)/F₀ traces in j were median-filtered over a 100 ms window. Uncertainties to fit parameters in b and k are 95% confidence intervals.