Optical constraints on two-photon voltage imaging

Abstract

Significance: Genetically encoded voltage indicators (GEVIs) are a valuable tool for studying neural circuits in vivo, but the relative merits and limitations of one-photon (1P) versus two-photon (2P) voltage imaging are not well characterized.

Aim: We consider the optical and biophysical constraints particular to 1P and 2P voltage imaging and compare the imaging properties of commonly used GEVIs under 1P and 2P excitation.

Approach: We measure the brightness and voltage sensitivity of voltage indicators from commonly used classes under 1P and 2P illumination. We also measure the decrease in fluorescence as a function of depth in the mouse brain. We develop a simple model of the number of measurable cells as a function of reporter properties, imaging parameters, and desired signal-to-noise ratio (SNR). We then discuss how the performance of voltage imaging would be affected by sensor improvements and by recently introduced advanced imaging modalities.

Results: Compared with 1P excitation, 2P excitation requires $\sim {10}^4$ -fold more illumination power per cell to produce similar photon count rates. For voltage imaging with JEDI-2P in the mouse cortex with a target SNR of 10 (spike height to baseline shot noise), a measurement bandwidth of 1 kHz, a thermally limited laser power of 200 mW, and an imaging depth of $>300\mu m$ , 2P voltage imaging using an 80-MHz source can record from no more than $\sim 12$ neurons simultaneously.

Conclusions: Due to the stringent photon-count requirements of voltage imaging and the modest voltage sensitivity of existing reporters, 2P voltage imaging in vivo faces a stringent tradeoff between shot noise and tissue photodamage. 2P imaging of hundreds of neurons with high SNR at a depth of $>300\mu m$ will require either major improvements in 2P GEVIs or qualitatively new approaches to imaging.

Keywords: shot noise; two-photon; voltage imaging.

Fig. 1

Comparison of 1P and 2P brightness and sensitivity of fluorescent voltage indicators. (a) Diagram of the experiment. HEK cells were sequentially illuminated with wide-field 1P light in steps of increasing intensity and then by spiral scan 2P steps of increasing intensity. (b) Example HEK cell expressing the GEVI ASAP3. The 2P spiral scan pattern is shown in red, and the analysis ROI is shown in green. $\text{Scale bars}=5\mu \mathrm{m}$. (c) Example single-trial data for a cell expressing ASAP3. (d) Top: fluorescence in panel (c) as a function of 1P intensity with a linear fit. Bottom: fluorescence as a function of 2P power with quadratic fit. (e) Log–log plot of count rate versus optical power on the cell for seven voltage indicators. 1P data, filled symbols; 2P data, empty symbols. Error bars are standard error of the mean from at least $n=8$ cells. The excitation wavelengths used for 1P (2P) excitation of each of the reporters were ASAP3 488 nm (930 nm), BeRST1 635 nm (850 nm), JEDI-2P 488 nm (930 nm), QuasAr6a 635 nm (900 nm), ${\text{Voltron}2}_{525}$ 488 nm (930 nm), ${\text{Voltron}2}_{585}$ 594 nm (1100 nm), and ${\text{Voltron}2}_{669}$ 635 nm (1220 nm). A horizontal line is shown at $1.5\times {10}^7\text{counts}/\mathrm{s}$, equivalent on our camera to ${10}^7$ impinging photons/s. (f) Whole-cell patch clamp protocol for measuring voltage sensitivity under 1P and 2P excitation. (g) Average voltage responses of JEDI-2P and ${\text{Voltron}2}_{525}$ under 1P and 2P illumination. (h) Ratio of voltage contrast under 2P versus 1P illumination for JEDI-2P and ${\text{Voltron}2}_{525}$, $n=5$ cells per construct.

Fig. 2

Depth-dependent 1P and 2P signals in the brain. (a) Experimental protocol. In a mouse expressing JEDI-2P, raster-scanned 2P ($\lambda =920\mathrm{nm}$) and DMD-patterned 1P imaging ($\lambda =488\mathrm{nm}$) were alternately applied to neurons at different depths. 1P illumination patterned to cell-free regions was used to estimate the background signal. (b) Example 1P and 2P images of cells at three depths. $\text{Scale bars}=5\mu \mathrm{m}$. (c) Estimated signal-to-background ratio for $n=43$ neurons under patterned 1P illumination. (d) Mean count rate from the membranes of $n=43$ neurons under 2P illumination. The color indicates excitation power. The inset shows the cell at $473\mu \mathrm{m}$ depth (boxed on the graph). $\text{Scale bar}=5\mu \mathrm{m}$.

Fig. 3

Scaling of 2P voltage measurements with depth and with GEVI properties. (a) Predicted number of simultaneously measurable cells as a function of depth, based on brightness derived from HEK cells expressing JEDI-2P (Fig. 1). We assumed a spike contrast of $\beta =0.2$; target SNRs of 3 (green dotted), 5 (blue dashed), or 10 (red solid) in an integration time $\tau =1\mathrm{ms}$; a total power $P_0=200\mathrm{mW}$, targeting fraction $\varphi =1$, scattering length $l_{\mathrm{e}}=112\mu \mathrm{m}$, and a detector with perfect quantum efficiency. (b) Predicted number of simultaneously measurable cells at $\mathrm{SNR}=10$ and 200 mW power for each experimentally measured single-cell count rate reported in Fig. 2(d). (c) Number of simultaneously measurable cells under 2P illumination at a depth of $500\mu \mathrm{m}$, assuming brightness and contrast improvements of future GEVIs, target SNR of 10, and all other parameters as in panel (a).

Fig. 4

Effect of reporter kinetics on signal. (a) Response of a reporter to a 1-ms voltage pulse. An exponential rise with time constant ${\tau }_{\text{on}}$ reaches a maximum of $\beta$ followed by an exponential decay with time constant ${\tau }_{\text{off}}$. The signal comprises the total area under both response phases (cross-hatched). (b) Area under the curve in panel (a) as a function of ${\tau }_{\text{on}}$ and ${\tau }_{\text{off}}$, keeping constant pulse duration (1 ms) and steady-state voltage sensitivity (${\beta }_{\mathrm{ss}}=0.2$). Increasing ${\tau }_{\text{off}}$ allows longer integration time, whereas increasing ${\tau }_{\text{on}}$ truncates the response. (c) Effects on SNR of changing ${\tau }_{\text{on}}$ or ${\tau }_{\text{off}}$ while keeping the other fixed. The fixed parameter is shown in the legend, and variable 1 is indicated by the $x$-axis. At large ${\tau }_{\text{on}}$, $\mathrm{SNR}\sim 1/{\tau }_{\text{on}}$. At large ${\tau }_{\text{off}}$, $\mathrm{SNR}\sim {\tau }_{\text{off}}^{1/2}$.

Fig. 5

Scaling of fluorescence with numerical aperture, sample geometry, and excitation modality. (a) Geometry of a Gaussian beam, showing the width ($W_0\sim 1/\mathrm{NA}$) and waist ($b\sim {1/\mathrm{NA}}^2$). (b) Scaling of total 2P fluorescence as a function of excitation ${\mathrm{NA}}_e$ for different sample geometries. All slender dimensions are assumed to be $\ll W_0$, and all extended dimensions are assumed to be $\gg b$. In a planar raster scan, the fraction of time that a subwavelength structure is excited, $\varphi$, depends on the focus width and hence the ${\mathrm{NA}}_e$. In cases (iii), (v), and (vi), we assume that the object is perfectly in focus, i.e., in the axial plane where focus size is minimum. The collection efficiency for all geometries depends on the collection solid angle $\sim N{A}_c^2$. To calculate the total signal for targeted illumination, multiply the first and third lines; for a raster scan, multiply all three lines. (c) Total fluorescence evoked by the intersection of a laser focus and a spherical membrane, $10\mu \mathrm{m}$ diameter. We compared 1P and 2P excitations with equal ${\mathrm{NA}}_c$ and ${\mathrm{NA}}_e$, with powers adjusted to match per-molecule excitation rates at the focus at NA = 1.2. The much smaller 2P focal volume led to a 5.3-fold smaller maximum fluorescence at the highest NA (and even greater discrepancy at lower NA) and a 3-fold greater sensitivity to misalignment compared with 1P excitation.

Fig. 6

Optimal temporal and spatial splitting. (a) At fixed total power, the per-spot pulse energy is inversely proportional to the effective repetition rate, $f_{\mathrm{eff}}=f\times N_{\text{spots}}$. SNR is increased by increasing focal pulse energy up to the threshold (1-nJ horizontal line shown). Therefore, the optimal effective repetition rate lies at the intersection of the iso-power line with the threshold (circled in red). At a nonzero depth (dotted lines, $l_e$ = attenuation length), a lower repetition rate is needed to produce the same focal pulse energy. (b) For a single diffraction-limited focal spot, a total power of 200 mW, and a pulse energy threshold of 1 nJ, the optimal $f_{\mathrm{eff}}$ goes beneath 80 MHz (horizonal line) at $\sim 100\mu \mathrm{m}$ depth. Decreasing the threshold focal energy (e.g., to 0.5 nJ) increases the optimal repetition rate at a given depth. (c) For a fixed $f_{\mathrm{eff}}$, the focal pulse energy decays exponentially with depth. At $f_{\mathrm{eff}}=250\mathrm{MHz}$, a 1-nJ pulse is not achievable at any depth. At $f_{\mathrm{eff}}=40\mathrm{MHz}$, the pulse energy crosses the 1 nJ threshold at $\sim 200\mu \mathrm{m}$ depth.