Photocycle Dynamics of the Archaerhodopsin 3 Based Fluorescent Voltage Sensor QuasAr1

The retinal photocycle dynamics of the fluorescent voltage sensor QuasAr1 (Archaerhodopsin 3 P60S-T80S-D95H-D106H-F161V mutant from Halorubrum sodomense) in pH 8 Tris buffer was studied. The samples were photoexcited to the first absorption band of the protonated retinal Schiff base (PRSB) Ret_580 (absorption maximum at λmax ≈ 580 nm), and the retinal Schiff base photoisomerization and protonation state changes were followed by absorption spectra recordings during light exposure and after light exposure. Ret_580 turned out to be composed of two protonated retinal Schiff base isomers, namely Ret_580I and Ret_580II. Photoexcitation of Ret_580I resulted in barrier-involved isomerization to Ret_540 (quantum yield ≈ 0.056) and subsequent retinal proton release leading to Ret_410 deprotonated retinal Schiff base (RSB). In the dark, Ret_410 partially recovered to Ret_580I and partially stabilized to irreversible Ret_400 due to apoprotein restructuring (Ret_410 lifetime ≈ 2 h). Photoexcitation of Ret_580II resulted in barrier-involved isomerization to Ret_640 (quantum yield ≈ 0.00135) and subsequent deprotonation to Ret_370 (RSB). In the dark, Ret_370 partially recovered to Ret_580II and partially stabilized to irreversible Ret_350 due to apoprotein restructuring (Ret_370 lifetime ≈ 10 h). Photocycle schemes and reaction coordinate diagrams for Ret_580I and Ret_580II were developed and photocyle parameters were determined.

All-optical electrophysiology in neuroscience was achieved by channelrhodopsin based optical perturbation of membrane potentials and the membrane potential readout with fluorescent voltage sensing domains [26][27][28].

Results
The QuasAr1 samples in pH 8 Tris buffer were photoexcited to the first absorption band (protonated retinal Schiff base Ret_580) in the green-yellow-orange spectral range, and the retinal photoisomerization and protonation state changes were followed by absorption spectra recordings during light exposure and after light exposure. The temporal absorption coefficient development at fixed wavelengths was measured with high time resolution. Additionally, excitation wavelength dependent fluorescence emission quantum distributions were measured immediately after excitation light switch-off and after sample recovery in the dark (results presented in the Supplementary Materials). Emission wavelength dependent fluorescence excitation quantum distributions were also determined after sample recovery (results are shown in the Supplementary Materials).

Absorption Spectroscopic Photocycle Studies
QuasAr1 samples were excited with light emitting diodes LED 590 nm (excitation near absorption maximum of Ret_580) and LED 530 nm (excitation near absorption maximum of protonated retinal Schiff base photoisomer Ret_540 of Ret_580 I ) as well as with a HeNe laser at 632.8 nm (excitation near absorption maximum of protonated retinal Schiff base photoisomer Ret_640 of Ret_580 II ). For the excitation with LED 590 nm, photocycle studies with three different excitation intensities were carried out to study the dependence of the photocycle dynamics on the excitation intensity. The excitations with LED530 nm and a HeNe laser were carried out to study the influence of the excitation wavelength within the broad S 0 -S 1 absorption band of the Ret_580 chromophores and of the formed photoisomer excitations on the photocycle dynamics.
The results of the photocycle studies with LED 590 nm at high excitation intensity are presented below (Figures 1-4), while the results of the photocycle studies with LED 590 nm at medium intensity (Figures S1-S3) and at low intensity ( Figures S4 and S5) as well as the results of the photocycle studies with LED 530 nm ( Figures S6-S9) and with the HeNe laser (Figures S10-S13) are presented in the Supplementary Materials.
In Figure 1a, the development of absorption coefficient spectra of QuasAr1 in pH 8 buffer during light exposure with LED 590 nm (λ exc = 590 nm) of input intensity I exc = 64.65 mW cm −2 is displayed. The spectral light distribution g LED 590 nm (λ) of the LED 590 nm is included in the figure. The absorption coefficient curves belong to the exposure times listed in the legend. With increasing exposure time, the curves show the decrease of the absorption band around 580 nm and the dominant buildup of an absorption band around 370 nm. The triple-dotted curve belonging to t exc = 0 (named Ret_580 (t exc = 0)) shows the initial absorption coefficient spectrum of QuasAr1 deprived from retinal isomer contributions other than Ret_580 (dashed triple dotted curve named Residuals). The curves Ret_580 (t exc = 0) and Residuals were determined in [33]. The inset in Figure 1a shows the temporal development of the absorption coefficient α a (t exc ) at the probe wavelength λ pr = 620 nm (long-wavelength absorption region of Ret_580). It indicates an initially fast absorption decrease (photoconversion of Ret_580 I component) followed by a slow absorption decrease (photoconversion of Ret_580 II component). In Figure 1a, the development of absorption coefficient spectra of QuasAr1 in pH 8 buffer during light exposure with LED 590 nm (λexc = 590 nm) of input intensity Iexc = 64.65 mW cm −2 is displayed. The spectral light distribution gLED 590 nm (λ) of the LED 590 nm is included in the figure. The absorption coefficient curves belong to the exposure times listed in the legend. With increasing exposure time, the curves show the decrease of the absorption band around 580 nm and the dominant buildup of an absorption band around 370 nm. The triple-dotted curve belonging to texc = 0 (named Ret_580 (texc = 0)) shows the initial absorption coefficient spectrum of QuasAr1 deprived from retinal isomer contributions other than Ret_580 (dashed triple dotted curve named Residuals). The curves Ret_580 (texc = 0) and Residuals were determined in [33]. The inset in Figure 1a shows the temporal development of the absorption coefficient αa (texc) at the probe wavelength λpr = 620 nm (longwavelength absorption region of Ret_580). It indicates an initially fast absorption decrease (photoconversion of Ret_580I component) followed by a slow absorption decrease (photoconversion of Ret_580II component). The triple dotted curve named Ret_580 (texc = 0) in the wavelength range >310 nm shows the absorption coefficient contribution of Ret_580 to QuasAr1 before light exposure (taken from Figure 1 in [33]). The dashed triple-dotted curve named Residuals shows the absorption coefficient contribution of residual retinal isomers in QuasAr1 other than Ret_580 (taken from Figure 1 in [33]). The curve gLED 590 nm (λ) = SLED 590 nm (λ)/SLED 590 nm (λmax) shows the spectral distribution of the excitation light source LED 590 nm. The inset shows the temporal dependence of αa (620 nm) versus exposure time texc. The data points are fitted by  More detailed information on the photoinduced retinal isomerization and deprotonation dynamics of Ret_580 during light exposure was obtained by subtracting the remaining Ret_580 absorption coefficient contributions αa,Ret_580(λ,texc) at time texc and the initial residual retinal isomers The triple dotted curve named Ret_580 (t exc = 0) in the wavelength range >310 nm shows the absorption coefficient contribution of Ret_580 to QuasAr1 before light exposure (taken from Figure 1 in [33]). The dashed triple-dotted curve named Residuals shows the absorption coefficient contribution of residual retinal isomers in QuasAr1 other than Ret_580 (taken from Figure 1 in [33]). The curve g LED 590 nm (λ) = S LED 590 nm (λ)/S LED 590 nm (λ max ) shows the spectral distribution of the excitation light source LED 590 nm. The inset shows the temporal dependence of α a (620 nm) versus exposure time t exc . The data points are fitted by α a (t rec ) = α a (0 with α a (0) = 1.554 cm −1 , ∆α I = 0.436 cm −1 , τ sat,I = 0.015 min, ∆α II = 1.03 cm −1 , and τ sat,II = 8.65 min. (b) Absorption coefficient spectra of formed species of QuasAr1 in pH 8 Tris buffer due to light exposure with LED 590 nm of input intensity I exc = 64.65 mW cm −2 . The absorption contributions of Ret_580, α aRet_580 (λ, t exc ), and of the initial residuals, α a,Residuals (λ,0), from (a) are subtracted, i.e., ∆α a (λ, t exc ) = α a (λ, t exc ) − α a,Ret_580 (λ, t exc ) − α a,Residuals (λ, t exc = 0). The approximate peak wavelength positions of the retinal isomers Ret_640, Ret_540, Ret_460, Ret_410, and Ret_370 are indicated at the bottom. The inset shows the temporal development of ∆α a at λ pr = 540 nm, 460 nm, 410 nm, and 370 nm versus exposure time t exc . The corresponding absorption coefficient spectra development (scattering contributions approximately subtracted) is shown in Figure 3a. The absorption band centered at 580 nm (Ret_580) recovered partly, and the formed absorption band around 370 nm (Ret_370 including Ret_410) disappeared partly. The absorption band around 280 nm (dominant tryptophan absorption) increased steadily due to thermal apoprotein restructuring [33]. The inset in Figure 3a shows the partial absorption coefficient recovery at λpr = 580 nm were the absorption is determined by Ret_580, and the partial absorption coefficient decrease at λpr = 370 nm due to reprotonation of Ret_370 to Ret_580. The only partial reconversion of Ret_370 to Ret_580 is due to a changeover from the reversible photocycle dynamics to the thermal irreversible deprotonation of Ret_580 and the Ret_370 ground-state potential energy lowering below the ground-state energy level of Ret_580 (changeover from Ret_370 to Ret_350, see discussion below) caused by the dynamic thermal apoprotein restructuring [33] during the slow recovery time of the photocycle process. More detailed information on the photoinduced retinal isomerization and deprotonation dynamics of Ret_580 during light exposure was obtained by subtracting the remaining Ret_580 absorption coefficient contributions α a,Ret_580 (λ,t exc ) at time t exc and the initial residual retinal isomers contributions Residuals from the developing absorption coefficient spectra of Figure 1a. The remaining Ret_580 absorption coefficient contributions are approximately determined by α a,Ret_580 (λ, t exc ) ≈ α a,Ret_580 (λ, t exc = 0) × α a (λ = 620 nm, t exc )/α a (λ = 620 nm, t exc = 0) (the spectral shape of α a,Ret_580 is assumed to do not change with exposure time, the magnitude of α a,Ret_580 (λ = 620 nm, t exc ) is nearly given by the magnitude of α a (λ = 620 nm, t exc ) of QuasAr1 since at λ = 620 nm absorption contributions from formed species are thought to be small). The resulting curves ∆α a (λ, t exc ) = α a (λ, t exc ) − α a,Ret_580 (λ, t exc ) − α a,Residuals (λ, t exc = 0), which are displayed in the main part of Figure 1b, show the absorption coefficient spectra development of formed species of QuasAr1 due to the light exposure. New absorption bands are seen around λ ≈ 540 nm (PRSB Ret_540), ≈ 460 nm (PRSB Ret_460), ≈ 410 nm (RSB Ret_410), and ≈ 370 nm (RSB Ret_370). There is an indication of a new absorption band around 640 nm (PRSB Ret_640). The absorption band of Ret_540 extends out beyond λ exc = 590 nm. The temporal developments of ∆α a at the probe wavelengths λ pr = 540 nm, 460 nm, 410 nm, and 370 nm are depicted in the inset of Figure 1b. The absorption band of Ret_540 decreased with continued light exposure. It is thought that Ret_540 is formed by photoisomerization of PRSB Ret_580 I (likely 13-cis isomer in specific apoprotein conformation Apoprotein I ) to PRSB Ret_540 (likely all-trans isomer in apoprotein conformation Apoprotein I ). The decrease of Ret_540 for t exc > 30 s is thought to be determined dominantly by deprotonation of Ret_540 to Ret_410. The absorption bands of Ret_460, Ret_410, and Ret_370 are overlapping. Ret_370 was built up during the whole time of light exposure. It is thought that Ret_580 II (likely all-trans isomer in specific apoprotein conformation Apoprotein II ) is converted to Ret_370 (likely formed by photoisomerization of all-trans retinal isomer to a cis isomer Ret_640 in specific apoprotein conformationApoprotein II and subsequent deprotonation, for details see discussion below). At λ pr = 460 nm the absorption changes are dominated by the short-wavelength tail of Ret_540 and the long-wavelength tails of Ret_410 and Ret_370. The build-up of Ret_460 population is small and only indicated by a small absorption structure change around 460 nm.
The attenuation coefficient spectra development of the QuasAr1 sample used in Figure 1a after excitation light switch-off over a recovery time range of nearly five days (sample in the dark at room temperature) is displayed in Figure 2. The inset in Figure 2 shows the temporal attenuation coefficient development at λ pr = 580 nm and 370 nm.    In order to see details in the absorption coefficient spectra development after excitation light switch-off in Figure  3a, Figure 3b (Ret_580 contribution and initial residual retinal contributions are subtracted from Figure 3a). The inset of Figure 3b shows the temporal development of Δαa(trec) at the probe wavelengths λpr = 540 nm, 460  Figure 1a). Immediately after the end of exposure, fluorescence emission spectra were measured. The durations of recovery t rec are listed in the figure. The absorption coefficient spectra before exposure (t exc = 0) and at the end of exposure (t exc = 25 min) are included. The inset shows the absorption coefficient recoveries α a (t rec ) at λ pr = 580 nm and 370 nm. The data points are fitted by α a (t rec ) = α a (0)  = 580 nm, 530 nm, and 370 nm are displayed in Figure 4 for a QuasAr1 sample in pH 8 Tris buffer. A fresh thawed sample was used. In the first run, the probe wavelength was set to λpr = 580 nm, the exposure time was texc = 1.5 s, and the time of recovery in the dark was set to 10 min. Then, it was followed immediately by the second run with the same exposure/dark parameters at λpr = 530 nm. Next, it was followed immediately by the third run with the same exposure/dark parameters at λpr = 370 nm. .
The corresponding absorption coefficient spectra development (scattering contributions approximately subtracted) is shown in Figure 3a. The absorption band centered at 580 nm (Ret_580) recovered partly, and the formed absorption band around 370 nm (Ret_370 including Ret_410) disappeared partly. The absorption band around 280 nm (dominant tryptophan absorption) increased steadily due to thermal apoprotein restructuring [33]. The inset in Figure 3a shows the partial absorption coefficient recovery at λ pr = 580 nm were the absorption is determined by Ret_580, and the partial absorption coefficient decrease at λ pr = 370 nm due to reprotonation of Ret_370 to Ret_580. The only partial reconversion of Ret_370 to Ret_580 is due to a changeover from the reversible photocycle dynamics to the thermal irreversible deprotonation of Ret_580 and the Ret_370 ground-state potential energy lowering below the ground-state energy level of Ret_580 (changeover from Ret_370 to Ret_350, see discussion below) caused by the dynamic thermal apoprotein restructuring [33] during the slow recovery time of the photocycle process.
In order to see details in the absorption coefficient spectra development after excitation light switch-off in Figure 3a, the absorption coefficient spectra development ∆α a (λ, t rec ) = α a (λ, t rec ) − α a,Ret_580 (λ, t rec ) − α a,Residuals (λ, t exc = 0) is displayed in Figure 3b (Ret_580 contribution and initial residual retinal contributions are subtracted from Figure 3a). The inset of Figure 3b shows the temporal development of ∆α a (t rec ) at the probe wavelengths λ pr = 540 nm, 460 nm, 410 nm, 370 nm, and 640 nm. The absorption of Ret_370, Ret_410, and Ret_460 decreased within the first 20 h of light switch-off and then leveled off. ∆α a (640 nm,t rec ) indicates the formation of Ret_640 by thermal activation of isomerization of Ret_580 II [33].
The temporal absorption coefficient developments with a time resolution of δt res = 12.5 ms at λ pr = 580 nm, 530 nm, and 370 nm are displayed in Figure 4 for a QuasAr1 sample in pH 8 Tris buffer. A fresh thawed sample was used. In the first run, the probe wavelength was set to λ pr = 580 nm, the exposure time was t exc = 1.5 s, and the time of recovery in the dark was set to 10 min. Then, it was followed immediately by the second run with the same exposure/dark parameters at λ pr = 530 nm. Next, it was followed immediately by the third run with the same exposure/dark parameters at λ pr = 370 nm.
The top part of Figure 4 shows the absorption development at λ pr = 580 nm during and after light exposure. During light exposure, the absorption decreased dominantly by photoisomerization of Ret_580 I to Ret_540. After excitation light switch-off, initially a minute absorption decrease is observed likely due to the conversion of Ret_540 to Ret_410 (absorption band of Ret_540 extends out to 580 nm). The following slight absorption increase is thought to be due to partial reprotonation of Ret_410 to Ret_580 I (see discussion below).
The middle part of Figure 4 shows the absorption development at λ pr = 530 nm in a second exposure of the sample. The absorption decrease during light exposure is due to the absorption decrease of the broad absorption band of Ret_580 which dominates the absorption at 530 nm. The weaker absorption decrease, as compared with λ pr = 580 nm, is due to the formation of the absorption band of Ret_540 during light exposure. After light switch-off, the absorption at 530 nm decreased because of deprotonation of Ret_540 to Ret_410 (time constant τ rel,Ret_540 ≈ 37 s, see discussion below). The spike at the position of light switch-on is thought to be an artifact caused by a photoinduced transient thermal grating [34,35] (the same effect was observed by replacing the QuasAr1 sample with a sample of rhodamine 6G in methanol).
The bottom part of Figure 4 shows the absorption development at λ pr = 370 nm in a third exposure of the sample. After excitation light switch-on, the increase of absorption is slightly time delayed (≈0.1 s). After excitation light switch-off (t exc,end = 1.5 s), the absorption continues to increase within the first 40 s, and then, levels off (time constant τ rel,Ret_640 ≈ 17 s). The absorption dynamics is thought to be dominated by the conversion of Ret_640 to Ret_370 by proton release (see discussion below).

Quantum Yield of Photoconversion
The quantum yield of photoconversion φ con of Ret_580 to other retinal isomers during light exposure is given [36] by the ratio of the number density ∆N con of converted Ret_580 molecules to the number density ∆n ph,abs of absorbed photons by Ret_580, i.e., The number density ∆N con is determined by where N 0 is the initial number density of Ret_580, α a,0 (λ pr ) is the initial absorption coefficient of Ret_580 at the probe wavelength λ pr , and ∆α a (λ pr ) is the absorption coefficient change of Ret_580 at λ pr (λ pr is selected at a wavelength region where practically only Ret_580 is absorbing). The initial number density N 0 of Ret_580 is given by where σ a (λ pr ) is the absorption cross-section of Ret_580 at λ pr . It is presented in Figure S2 of the Supplementary Materials to [33]. The number density ∆n ph,abs of absorbed photons by Ret_580 is determined by the excitation light intensity I exc at the excitation wavelength λ exc , the time interval of light exposure δt exc and the absorption coefficient α a (λ exc ) of Ret_580. It is given by where hν exc is the photon excitation energy (ν exc = c 0 /λ exc is the photon frequency, c 0 is the speed of light in vacuum, and h is the Planck constant). The determined approximate quantum yields of photoconversion of Ret_580 versus exposure time are displayed in Figure 5. The φ con (t exc ) curves give only approximate values of φ con,Ret_580 (t exc ) since α a (λ pr ,t exc ) used in the calculations is only approximately equal to α a,Ret_580 (λ pr ,t exc ), and the used α a (λ exc ,t exc ) is only approximately equal to α a,Ret_580 (λ exc ,t exc ). In the main subfigures, λ pr = 620 nm was used where α a (λ pr ,t exc ) is nearly equal to α a,Ret_580 (λ pr ,t exc ) during the whole exposure time.
In the insets of the subfigures, λ pr = 580 nm was used. There, α a (t exc ) was measured with high time resolution and for the short exposure times α a (λ pr ,t exc ) remained nearly equal to α a,Ret_580 (λ pr ,t exc ). The absorption coefficient data in the insets of Figure 1a (λ exc = 590 nm, I exc = 64.65 mW cm −2 , and λ pr = 620 nm), Figure S1a (λ exc = 590 nm, I exc = 14.07 mW cm −2 , and λ pr = 620 nm), Figure S4a (λ exc = 590 nm, I exc = 1.12 mW cm −2 , and λ pr = 620 nm), Figure S6a  All φ con (t exc ) curves in Figure 5 show an initially fast decrease and a changeover to a near exposure time independent but excitation light intensity dependent low value. As was shown in [33] and is discussed below, Ret_580 consists of two protonated retinal Schiff base isomers Ret_580 I (fraction κ Ret_580 I ≈ 0.41 [33]) and Ret_580 II (fraction κ Ret_580 II ≈ 0.59 [33]) with different ground-state isomerization dynamics [33] and photoisomerization dynamics. The initially large quantum yield of photoconversion is due to the photoisomerization of Ret_580 I to Ret_540 and subsequent deprotonation of Ret_540 to Ret_410. The low quantum yield of photoconversion after conversion of Ret_580 I is due to the low-efficient photoisomerization of Ret_580 II to Ret_640 and subsequent deprotonation to Ret_370. The excitation intensity dependent lowering of φ con (t exc ) for t exc > 0 is due to the generation of the photoisomers Ret_540 and Ret_640 and their subsequent back photoisomerization of Ret_540 to Ret_580 I and Ret_640 to Ret_580 II (see discussion below). S1a (λexc = 590 nm, Iexc = 14.07 mW cm −2 , and λpr = 620 nm), Figure S4a (λexc = 590 nm, Iexc = 1.12 mW cm −2 , and λpr = 620 nm), Figure S6a (λexc = 530 nm, Iexc = 114.2 mW cm −2 , and λpr = 620 nm), and Figure  S10a (λexc = 632.8 nm, Iexc = 15.56 mW cm −2 , and λpr = 620 nm) were employed for the main subfigures. The absorption coefficient curves in the top left parts of Figure 4 (λexc = 590 nm, Iexc = 64.65 mW cm −2 , and λpr = 580 nm), Figure S9 (λexc = 530 nm, Iexc = 114.2 mW cm −2 , and λpr = 580 nm), and Figure S13 (λexc = 632.8 nm, Iexc = 15.65 mW cm −2 , and λpr = 580 nm) were employed for the insets in the subfigures.  Figure S10a). The curves in the insets are derived from the high time resolution absorption measurements (top part of Figure 4 for λexc = 590 nm, top part of Figure S9 for λexc = 530 nm, and top part of Figure S13 for λexc = 632.8 nm). All  con(texc) curves in Figure 5 show an initially fast decrease and a changeover to a near exposure time independent but excitation light intensity dependent low value. As was shown in [33] and is discussed below, Ret_580 consists of two protonated retinal Schiff base isomers Ret_580I (fraction  Figure S10a). The curves in the insets are derived from the high time resolution absorption measurements (top part of Figure 4 for λ exc = 590 nm, top part of Figure S9 for λ exc = 530 nm, and top part of Figure S13 for λ exc = 632.8 nm).

Fluorescence Behavior
The excitation wavelength dependent fluorescence emission quantum distributions were measured immediately after excitation light switch-off and after sample recovery in the dark. Obtained fluorescence quantum distributions are shown in Figure S14a,b and fluorescence quantum yields are shown in Figure S15 of Section S2 of the Supplementary Materials for the QuasAr1 sample used in the photocycle experiments of Figure 1a (λ exc = 590 nm, I exc = 64.65 mW cm −2 , and t exc = 25 min). Immediately after photoexcitation, the fluorescence quantum efficiency in the fluorescence wavelength region of the photoconversion products turned out to be reduced. After long-time recovery in the dark at room temperature, the fluorescence behavior changed over to the fluorescence behavior of the unexposed samples stored for a long time in the dark at room temperature [33].
The emission wavelength dependent fluorescence excitation quantum distributions of photoexcited QuasAr1 samples were determined after sample recovery in the dark at room temperature. Results are shown in Figure S16 of Section S3 of the Supplementary Materials. The fluorescence excitation spectra behaved similar to the unexposed samples stored for a long time in the dark at room temperature.

Discussion
The absorption and emission spectroscopic investigation of the thermal dynamics of the Archaerhodopsin 3 based fluorescent voltage sensor QuasAr1 [33] revealed that fresh thawed samples contained, as covalently bound chromophore, dominantly protonated retinal Schiff base (PRSB) Ret_580 (absorption maximum around 580 nm) with minor amounts of a PRSB isomer absorbing around 450 nm and deprotonated retinal Schiff base (RSB) isomers absorbing below 420 nm. Ret_580 was found to be composed of two isomers, Ret_580 I of mole fraction κ Ret_580 I ≈ 0.41 (likely having the 13-cis conformation in a specific Apoprotein I structure) and Ret_580 II of mole fraction κ Ret_580 II ≈ 0.59 (likely having the all-trans conformation in a specific Apoprotein II structure). The photocycle dynamics of Ret_580 were studied experimentally above in Section 2 and in Section S1 of the Supplementary Materials by observing the absorption spectra development during light exposure and after light exposure. The light excitation wavelength and the light excitation intensity were varied.
From the experimental results, we try to resolve the photocycle dynamics of Ret_580 I and Ret_580 II and to extract photocycle parameters in the following: The photoexcitation dynamics and the recovery dynamics of Ret_580 I were faster than the photoexcitation dynamics and the recovery dynamics of Ret_580 II . These dynamics differences allow the separate characterization of the photocycle dynamics of Ret_580 I and Ret_580 II .

Photocycle Dynamics of Ret_580 I
In Figure 6a, a proposed scheme of the photocycle dynamics of the PRSB component Ret_580 I is shown, and in Figure 7a the corresponding schematic reaction coordinate diagram is depicted. Light absorption excites Ret_580 I in its S 0 ground state (likely PRSB cis ) to a local excited state position LE in the S 1 first excited state (Ret_580 I *). From there, the S 1 state cis-trans isomerization begins along a torsional reaction coordinate via the stationary point SP (Ret_580 I,SP *), and the funnel state Fu (Ret_580 I,Fu *) with S 1 -S 0 internal conversion (IC) to the S 0 transition state TS 0 (Ret_580 I,TS 0 ) and further torsion towards the ground-state isomer Ret_540 (likely PRSB trans ). At the TS 0 transition state, there occurs forward trans isomerization to Ret_540 with quantum yield of φ iso,Ret_580 I and cis back isomerization with quantum yield φ back,Ret_580 I = 1 − φ iso,Ret_580 I . Continued light exposure causes Ret_540 photoisomerization with excitation to Ret_540*, S 1 state twisting to Ret_540 Fu *, S 1 -S 0 internal conversion IC to Ret_580 TS 0 , forward isomerization to Ret_580 I (quantum yield φ iso,Ret_540 ) and back isomerization to Ret_540 (quantum yield φ back,Ret_540 = 1 − φ iso,Ret_540 ). Ret_540 (PRSB trans ) deprotonates to Ret_410 (RSB trans ) with a relaxation time constant of τ rel,Ret_540 . Ret_410 partly recovers back to Ret_580 I by reprotonation and trans-cis isomerization (recovery time τ rec,Ret_410→Ret_580 I and quantum yield of back recovery φ rec,Ret_410→Ret_580 I ) and it partly relaxes to permanently stable Ret_400 (RSB trans ) caused by thermal apoprotein I restructuring [33]. The quantum yield of Ret_400 formation is φ therm,Ret_410→Ret_400 = 1 − φ rec,Ret_410→Ret_580 I .
The photodynamics of Ret_580 I is described in Section S4.1 of the Supplementary Materials. The parameters of the Ret_580 I photocycle dynamics derived in the analysis are collected in Table 1.
The speed of Ret_580 I cis-trans photoisomerization to Ret_540 is slowed down by a potential energy barrier along the S 1 state torsional path from the local excited state LE to the funnel state Fu of internal conversion. The time constant of Ret_580 I cis-trans photoisomerization to Ret_540, τ iso,Ret_580 I →Ret_540 is of the order of the Ret_580 average Strickler-Berg based fluorescence lifetime [43][44][45] of τ F,SB,Ret_580 ≈ 61.5 ps [33] (separate fluorescence lifetimes for Ret_580 I and Ret_580 II were not determined).

Photocycle Dynamics of Ret_580 II
In Figure 6b, a proposed scheme of the photocycle dynamics the PRSB component Ret_580 II is shown. In Figure 7b, the corresponding schematic reaction coordinate diagram is depicted. Light absorption excites Ret_580 II in its S 0 ground state (likely PRSB trans ) to a local excited state position LE in the S 1 first excited state (Ret_580 II *). From there, begins the S 1 state trans-cis isomerization along a torsional reaction coordinate via the stationary point SP (Ret_580 II,SP *), and the funnel state Fu (Ret_580 II,Fu *). It follows S 1 -S 0 internal conversion IC to the S 0 transition state TS 0 (Ret_580 II,TS 0 ) and continued torsion towards the ground-state isomer Ret_640 (likely PRSB cis ). At the TS 0 transition state, there occurs forward cis isomerization to Ret_640 with a quantum yield of φ iso,Ret_580 II and trans back isomerization with quantum yield of φ back,Ret_580 II = 1 − φ iso,Ret_580 II . The continued light exposure causes Ret_640 photoisomerization with excitation to Ret_640*, S 1 state twisting to Ret_640 Fu *¸S 1 -S 0 internal conversion IC to Ret_640 TS 0 , forward isomerization to Ret_580 II (quantum yield φ iso,Ret_640 ), and back isomerization to Ret_640 (quantum yield φ back,Ret_640 = 1 − φ iso,Ret_640 ). Ret_640 (PRSB cis ) deprotonates to Ret_370 (RSB cis ) with a relaxation time constant of τ rel,Ret_640 . Ret_370 partly recovers back to Ret_580 II by reprotonation and cis-trans isomerization (recovery time τ rec,Ret_370→Ret_580 II , quantum yield φ rec,Ret_370→Ret_580 II ), and it partly relaxes to permanently stable Ret_350 (RSB cis ) caused by thermal apoprotein II restructuring [33]. The quantum yield of Ret_350 formation is φ therm,Ret_370→Ret_350 = 1 − φ rec,Ret_370→Ret_580 II .
The photodynamics of Ret_580 II is described in Section S4.2 of the Supplementary Materials. The parameters of the Ret_580 II photocycle dynamics derived in the analysis there are collected in Table 1.
The speed of Ret_580 II trans-cis photoisomerization to Ret_640 slowed down by a potential energy barrier along the S 1 state torsional path from the local excited state LE to the funnel state Fu of internal conversion. The time constant of Ret_580 II trans-cis photoisomerization to Ret_640, τ iso,Ret_580 II →Ret_640 is of the order of the Ret_580 average Strickler-Berg based fluorescence lifetime [43][44][45] of τ F,SB,Ret_580 ≈ 61.5 ps [33].

Comparison with Other Rhodopsins
The photocycle dynamics of QuasAr1 turned out to be slow and the quantum yield of photoizmerization was found to be low. In Table S1 of the Supplementary Materials (Section S5) quantum yields of primary photoisomerization of some rhodopsins are collected for comparization. The optimization of QuasAr1 for high fluorescence efficiency and high membrane voltage sensitivity lowered the speed of photocycle dynamics and the efficiency of photoisomerization.

Sample Preparation
The sample preparation of QuasAr1 was described in [33]. The buffer contained 50 mM Tris-HCl (pH 8), 150 mM NaCl, 0.02% DDM, 0.004% CHS, 0.1 mM PMSF, and 5% glycerol. The expressed QuasAr1 solution was aliquoted to amounts of 30 µL in Eppendorf tubes, shock-frozen, and stored at −80 • C until they were thawed for experimental investigations. The experiments were carried out at room temperature.
For the absorption spectroscopic photocycle experiments, QuasAr1 samples were excited with light emitting diodes (LED 590 nm and LED 530 nm from Thorlabs Inc., Newton, NJ, United States) or with a He-Ne laser emitting at 632.8 nm (Model OEM4P, Aerotech Inc., 101 Zeta Drive, Pittsburgh, PA, USA). The sample cell in the spectrophotometer was irradiated transverse to the transmission detection path (exposed area 3 × 5 mm 2 , sample thickness along excitation path 1.5 mm, and transmission detection path length 3 mm). The excitation power P exc was measured with a power meter (model PD 300-UV-SH photodiode detector head with NOVA power monitor, Ophir Optronics LTD., Science-based Industrial Park, Hartom St 6, Jerusalem, Israel). In the study of the absorption coefficient spectra development, transmission spectra T(λ) were recorded repeatedly during the period of light exposure and after light switch-off (data interval 1 nm, averaging time 0.0125 s, recording time for a spectrum from 1100 nm to 200 nm was 11.25 s, the spectra repeating time was set to 18 or 30 s during light exposure and to longer intervals in the observation of the absorption recovery after excitation light switch-off). The temporal development of the absorption behavior of QuasAr1 at selected wavelengths was carried out with a temporal resolution of 12.5 ms.
Fluorescence spectroscopic measurements immediately after the end of photoexcitation and after excitation recovery were carried out with a spectrophotometer (Cary Eclipse, Varian Australia Pty Ltd., Mulgrave, Victoria, Australia). Details of the determination of the fluorescence quantum distributions E F (λ), the fluorescence quantum yields φ F , and the fluorescence excitation quantum distributions E ex (λ) are given in [33]. The fluorescence spectroscopic results are presented in Sections S2 and S3 of the Supplementary Materials.

Conclusions
The photocycle dynamics of the Archaerhodopsin 3 based fluorescent voltage sensor QuasAr1 from Halorubrum sodomense was studied in detail. Its dominant protonated retinal Schiff base Ret_580 absorption band around 580 nm was found to consist of two isomers Ret_580 I (likely a cis isomer) and Ret_580 II (likely a trans isomer) stabilized by different adjacent apoprotein amino acid arrangements. Their slow barrier-involved photoisomerization dynamics in the tens of picosecond regime and the low quantum efficiency of photoisomerization are thought to be responsible for the high fluorescence efficiency and high membrane voltage sensitivity of QuasAr1.
The primary photoisomerization products, Ret_540 (likely PRSB trans ) from the educt Ret_580 I, and Ret_640 (likely PRSB cis ) from the educt Ret_580 II , deprotonate slowly on a time scale of tens of seconds to the neutral retinal Schiff bases Ret_410 and Ret_370, respectively. The long lifetimes of the metastable photoisomers Ret_540 and Ret_640 cause strong excitation intensity dependent back photoisomerization to the primary isomers Ret_580 I and Ret_580 II .
The reprotonation and back isomerization of the deprotonated retinal Schiff bases Ret_410 Ret_370 to the original isomers Ret_580 I and Ret_580 II occurred on a timescale of several hours. During this long time period, thermal apoprotein restructuring led to a stabilization of the deprotonated retinal Schiff base isomers, Ret_410 to Ret_400 and Ret_370 to Ret_350, leading to an incomplete recovery to the originals Ret_580 I and Ret_580 II in the photocycle process.
The performed photocycle studies on QuasAr1 are hoped to be of value for the application of this fluorescent voltage sensor in cell membrane and neuronal function studies.

Author Contributions:
The study was initiated by A.S. and P.H. who expressed, purified and delivered the protein; A.S. carried out initial measurements of the photocycle; A.P. carried out the measurements presented in this paper; The manuscript was written by A.P.; and commented and improved by A.S. and P.H. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.