The Photosensitivity of Rhodopsin Bleaching and Light-Induced Increases of Fundus Reflectance in Mice Measured In Vivo With Scanning Laser Ophthalmoscopy

Purpose To quantify bleaching-induced changes in fundus reflectance in the mouse retina. Methods Light reflected from the fundus of albino (Balb/c) and pigmented (C57Bl/6J) mice was measured with a multichannel scanning laser ophthalmoscopy optical coherence tomography (SLO-OCT) optical system. Serial scanning of small retinal regions was used for bleaching rhodopsin and measuring reflectance changes. Results Serial scanning generated a saturating reflectance increase centered at 501 nm with a photosensitivity of 1.4 × 10−8 per molecule μm2 in both strains, 2-fold higher than expected were irradiance at the rod outer segment base equal to that at the retinal surface. The action spectrum of the reflectance increase corresponds to the absorption spectrum of mouse rhodopsin in situ. Spectra obtained before and after bleaching were fitted with a model of fundus reflectance, quantifying contributions from loss of rhodopsin absorption with bleaching, absorption by oxygenated hemoglobin (HbO2) in the choroid (Balb/c), and absorption by melanin (C57Bl/6J). Both mouse strains exhibited light-induced broadband reflectance changes explained as bleaching-induced reflectivity increases at photoreceptor inner segment/outer segment (IS/OS) junctions and OS tips. Conclusions The elevated photosensitivity of rhodopsin bleaching in vivo is explained by waveguide condensing of light in propagation from rod inner segment (RIS) to rod outer segment (ROS). The similar photosensitivity of rhodopsin in the two strains reveals that little light backscattered from the sclera can enter the ROS. The bleaching-induced increases in reflectance at the IS/OS junctions and OS tips resemble results previously reported in human cones, but are ascribed to rods due to their 30/1 predominance over cones in mice and to the relatively minor amount of cone M-opsin in the regions scanned.

. Calibration of the scan field. A. Full-FOV SLO angiographic image of the retina of a mouse injected by tail vein with fluorescein. B. Image of the flat-mounted eye of the same mouse taken with a Nikon A1 confocal microscope (4X); the images in B has been arranged so as to best correspond to that in A, as illustrated in C, which presents a superposition of the two. The Nikon A1 image scale was calibrated with a 10 µm reticle grid and found to be accurate to within 1%. D. A number of retinal vessel branch-points could be unequivocally identified in both images A and B (see white lines superimposed on the images for examples), and the distances of the branch points from the center of the optic nerve head measured independently in the two images in their respective units. These measurements were plotted against one another and fitted with a straight line forced to go through the origin (red line). The slope was found to be 43.1 µm deg -1 .

II. Absolute calibration of the broadband laser light source at the pupil
In a number of the experiments presented we employed a broadband supercontinuum light source (Fianium, SC-400) in order to measure mouse fundus spectral reflectance distributions over a wide spectral range before, during and after bleaching (Figs. 4, 6). To determine the absolute reflectances (Eq 1) in these experiments it was necessary to measure P in (λ ), the absolute spectral power density (watts nm -1 ) of the source at the pupil plane (Fig. 1D). To extract a spectrum proportional to P in (λ ) we created a model eye with a Fluorilon 99W reflecting disc (Avian Tech, Gainesville, FL); the latter acts as a Lambertian reflector with an extremely (< 0.5%) flat reflectance spectrum. We used manufacturer specifications for the SLO optical elements to correct for losses in transmission from the disc to the spectrometer, but in fact found the predicted losses to be very small (Fig. 1D). The absolute spectral density was then determined by equating the power measured with the Thorlabs power meter with the numerically integrated spectrum measured by the spectrometer from the light reflected through the optical system from the model eye, as now described.
First, consider a monochromatic laser stimulus of wavelength λ and power 1 µW, and identify the spectral power density of this stimulus as P 1µW (λ ). The Thorlabs S120C power meter uses a silicon photodiode operating in photovoltaic mode: it first converts the current generated in response to light into voltage, and then, internally converts the voltage into a power reading. The current that P 1µW (λ ) generates in the power meter is P 1µW (λ )S PM (λ ) (amps), where S PM (λ ) is the spectral sensitivity of the power meter expressed in amps/watt. The internal voltage generated is K P 1µW (λ ) S PM (λ ), where K must have the unit ohms. When using the power meter the user must select a wavelength (in this case λ itself), and the internal (digital) circuitry of the meter then generates an appropriate scale factor C PM (λ ) such that the readout is 1 µW. The internal scale factor must satisfy Eq S1 because P PM (λ) and P 1µW (λ) are both equal to 1 µW. It follows that the power meter scale factor C PM (λ) is given by i.e., the scale constant C PM (λ) is inversely proportional to S PM (λ). These relations are not surprising: they simply recapitulate the procedure by which the photodiode-based power meter converts the current generated by a monochromatic stimulus into a power reading.
Next consider an experiment with a broadband source having unknown power spectral density P in (λ) (watts/nm) at the pupil plane. With the Ocean Optics spectrometer we measure the light from this source reflected through the imaging system from the model eye. We used manufacturer specifications for the SLO optical elements to correct for spectral distortions in transmission from the model eye to the spectrometer, even though the distortion was very small -Fig. 1D). These measurements and corrections yield a measured spectral power density P ME (λ) from the model eye that is proportional to the light spectral power density entering the eye: i.e., P in (λ) = C SF P ME (λ), where C SF is a scale constant to be determined. In each experiment we took a reading with the Thorlabs power meter from the broadband distribution with the calibration wavelength set (arbitrarily) to 580 nm, so that the power meter used the internal scale factor C PM (580 nm) for its conversion. The measured power reading P PM (watts) must then satisfy the relation where in the second line of Eq S3 substitution from Eq S2 was made. It follows that the scaling factor C SF is obtained as Thus, the desired absolute spectral power density P in (λ) of light entering the eye was obtained from the measured (and transmission-corrected) spectrum P ME (λ) of the model eye and the derived scale factor as P in (λ) = C SF P ME (λ). A useful feature of Eq S4 is that the ohmic constant K in Eq S3 is eliminated, and only the relative spectral sensitivity of the power meter is needed because S PM appears as a ratio. In the determination of C SF the denominator of Eq S4 was obtained by interpolating the measured model eye !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Supplementary Material,!Zhang!et!al.,!SLO measurement of mouse rhodopsin spectrum P ME (λ) and the Thorlab power meter sensitivity spectrum S PM (λ) on a 1 nm grid and performing trapezoidal numerical integration with a Matlab TM script.
The units of the broadband spectrum P in (λ) are W/nm. We converted the latter into rhodopsin-equivalent (λ max = 498 nm) photons by converting P in (λ) into photon flux units and integrating against the absorption spectrum of mouse rhodopsin, Rho(λ): where "h" is Planck's constant and "c" is the speed of light, and Rho(λ) is the absorption spectrum derived from Lamb's 4 photopigment extinction spectrum template with λ max = 498 nm as modified by Govardovskii 5 to accommodate the pigment β-band, and converted to an absorption spectrum with axial density OD max = 0.35 at the λ max (cf.  (Table 1).

III. Correction of the photosensitivity for pigment axial density
In this work we characterized serial bleaching scan data (Figs. 2, 4) with an exponential function of the integrated energy density (Eq 4), and used this latter formula to estimate the photosensitivity (1/Q e ) of rhodopsin in vivo (Table 1; Fig. 3). As discussed in METHODS, this formula implicitly assumes that pigment is present in "low density" in rods, i.e., that the optical density for light propagating axially in the outer segment is less than about 0.2. However, abundant microspectrophotometric literature [6][7][8] and other arguments 9 have established that the specific axial density of rhodopsin in rods is 0.014 to 0.018 OD/µm, so an average length mouse rod outer segment of 22 µm (ref 10 ) will have OD max = 0.31 to 0.40, in conflict with the "low density" assumption. Thus, it seems problematic to employ the exponential decay formula (Eqs 4, 12) to quantify bleaching dependence on energy density.
In METHODS, we present the rate equation (Eq 3) appropriate for bleaching when the pigment is present "in density". As noted, the solutions to Eq 3 for OD λ > 0.2 are not separable in p, the fraction pigment present after the bleaching exposure, but can be obtained by numerical analysis so that p, the fraction pigment present, can be plotted However, a consequence of using the exponential form is that the value of Q e will be overestimated by the shift factor that brings the curve corresponding to the true value of OD max into best correspondence with the exponential ("low density") case. This follows, because the original black curves are plotted with an abscissa scaled by Q e : for OD max = 0.35 the abscissa value Q/Q e = 1 corresponds not to p = 1/e = 0.37, but rather to p = 0.457. Thus, if the true value of OD max is 0.35, the values of log 10 (Q e ) in Table 1 should all be decreased by 0.107 log 10 units. We have not made this correction, however, for the following reasons. First, the exponential form provides a readily used parametric description of bleaching data. Second, comparison between photosensitivity investigations from different labs may be facilitated by use of the simpler, exponential decay formula. Third, at least two other parameters -f wg and OD max --need to be known to use Q e to estimate α max γ, the intrinsic photosensitivity. While we provide an argument Figure S2.
Effect of rhodopsin axial density on the bleaching function. Black traces plot solutions of Eq 3, i.e., the fraction of rhodopsin remaining after exposure of the retina to a bleaching stimulus whose energy density is expressed in units of Q e = 1/(αγf wg ): the black curve at right is the solution for OD max =0.35, while that at left is for OD max ! 0. The red curve is the curve for OD max =0.35 shifted leftward by 0.107 log 10 units.
for the estimate f wg ≈ 2 (Discussion) and also show that the value OD max = 0.35 is consistent with our reflectance data (Fig. 6) and microspectrophotometry, these values may not definitive, and certainly may be different in different species (f wg ) and in different mouse strains, different parts of the retina, and different rearing conditions, which are know to alter the outer segment length and thus OD max . Finally, we note when serial bleaching data (Fig. 2) are fitted with the "univariant" exponential formula (Eq 4, 12), the resultant action spectrum 1/Q e (λ) will be proportional the absorption spectrum (Eq 14). In contrast, if bleaching data for a series of different wavelengths simultaneously fitted with solutions to Eq 3 with the "true" value of OD max the resultant action spectrum 1/Q e (λ) should be proportional the extinction (low density) spectrum of rhodopsin. This follows because solutions to Eq 3 automatically adjust for the "top flattening" effect of optical density on the absorption spectrum.

IV. Reflectance model of albino and pigmented mouse eyes
Albino and pigmented mice have qualitatively different fundus spectral reflectance distributions, which also are altered in distinctive ways by bleaching (Fig. 6).
To explain these differences we developed a model along the lines of those previously developed by Delori and Pflibsen 11 and van de Kraats et al. 12,13 and recently applied to SLO measurement of human rhodopsin 14 . Schematics of the light flow paths identifying some of the major reflective and absorptive components of the fundus are illustrated in  Table S1 and their role in equations described below.
Absorbing components. The model formally included four spectrally varying absorbing components: the lens, melanin in the RPE and sclera (C57Bl/6J only), oxygenated hemoglobin (HbO 2 ) in the choroid, and rhodopsin in the outer segment layer.
These components are associated with wavelength-dependent optical density spectra !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Supplementary Material,!Zhang!et!al.,!SLO measurement of mouse rhodopsin D lens (λ), D mela (λ), D blood (λ) and D Rho (λ). A lens absorption spectrum was extracted from published transmission spectra of the rat lens 15 (blue curve in Fig. 6C). These data strongly confirm that the rodent lens is highly transmissive in the near UV (and throughout the visible spectrum), as would be expected 15 from the fact that the dominant mouse and rat cone opsin, Opn1sw, has a λ max of 360 nm. As the rat lens is 4 mm in axial length, while that of the mouse is ~ 2 mm, we used Beer's Law to adjust for the difference in length. Because the resultant spectrum has a transmission coefficient greater than 97% above 425 nm (the lowermost wavelength of reliability of our reflectance data - Fig. 6), for simplicity we set D lens (λ) = 0 in the model calculations, but for completeness retained the symbol in the equations to follow. Rhodopsin absorption only applies to the dark adapted state; in the fully bleached state D Rho = 0. The spectral form of D mela (λ) was that used by Kraats!et*al. 9 ,!but!scaled!by!a!free!!(i.e.,!to:be: estimated)!scale:factor!Sfmela.!! D blood (λ) was assumed to have the extinction spectrum of oxygenated hemoglobin, ε HbO2 (λ), as tabulated by Scott Prahl adjusted for an end-on axial absorbance of rhodopsin in situ OD max = 0.35 (Fig. 1D). The "1-pass" spectral density functions obtained from the fitting of the model to the reflectance data are provided in Fig. 6C. (Here "1-pass" refers to propagation of light through a single layer with the respective density function: thus, for rhodopsin, one pass through a layer of the thickness of the rod outer segment; and for hemoglobin one pass through a 45 µm thick choroid.) Reflective components. As illustrated by the OCT data (Fig.5A, B), backscattering can occur from many fundus layers, with the most potent reflectance in the posterior eye. In the NIR OCT data, back-scattering from pre-outer segment layers has discrete peaks at the NFL, OPL and ELM, but as these show no obvious "bleachdependence" we lumped the reflectance from all pre-outer segment elements into one spectrally neutral parameter, ρ pre-PR . As suggested by the OCT data, back-reflectance from rods was assumed to occur from two specific axial sites: the outer segment base or IS/OS junction (ρ IS/OS ), the outer segment tip (ρ tip ). (A weak reflectance distributed throughout the outer segment that was included in cone reflectance model of van de Kraats et al. 9 was not used in the modeling.) In keeping with the model of van de Kraats et al. the only reflecting layer deeper than the photoreceptors was assumed to be the sclera, with reflectance distribution 9 given by In modeling ρ sclera (675) was taken as a free parameter to be estimated. (Although our reflectance data only extend to ~ 650 nm, we nonetheless elected to use ρ sclera (675) as the free parameter for consistency with the van de Kraats et al. formulation.)

Scattering losses. Spectrally neutral scattering losses of incoming and reflected
light were assumed to occur in two layers or media ("med"): the pre-outer segment retina (D pre-PR ) and the "deep" layers, including RPE and choroid (D deep ).

Bleaching-induced increment in rod reflectances.
A unique feature of the mouse model was the inclusion of a factor for increased back-scattering at the rod IS/OS junction or OS base, and at the rod tips, a feature rationalize by OCT data (Fig. 5). Thus, the reflectances of the rod base and tip were assumed to be ρ IS/OS and ρ tip in the dark adapted state, and (1+Sf Blinc ) × ρ IS/OS and (1+Sf Blinc ) × ρ tip in the fully bleached state, with Sf Blinc ≥ 0 estimated by fitting the model to the reflectance data. The inclusion of this factor was motivated by both OCT data (Fig. 5C, D), and the spectral reflectance data in the long wavelength portion of the spectrum, where rhodopsin absorption is negligible, and thus in which reflectance increases cannot arise from loss of light absorption by rhodopsin bleaching. (Fig. 6A, B). (The term "bleaching-induced" was adopted to identify photoactivation of rhodopsin, rather than light in general, as the cause of the increased reflectance. In this context "bleaching" physically equivalent to isomerization of the 11-cis chromophore of rhodopsin and its structural change to the enzymatically active Metarhodopsin II (λ max = 380 nm), well established to be the form of the protein that activates phototransduction 16 .) We have treated these ρ IS/OS and ρ tip as spectrally flat and equal for simplicity, but emphasize that they could have spectral dependence -e.g., if Raleigh scattering was involved, and need not be equal.

Mathematical formulation of the model.
In the following description wavelength-dependent factors such as density spectra are indicated as functions of λ, e.g., D Rho (λ). When not so indicated, the factors are assumed to be spectrally flat, i.e., have a single value not dependent on λ.
Pre-rod outer segment layers. Transmission of reflected light through the layers anterior to the rod IS/OS junction is given by The factor 2 is present because light passes through the pre-photoreceptor media once on its incoming path and again on its outgoing path. Reflectance from pre-photoreceptor layers is treated as occurring at a single depth with a reflectivity ρ prePR after one-way transmission through the pre-photoreceptor layers.
Rod layer. Reflectance at the rod outer segment base or IS/OS junctions and at the rod tips are described by In the second line of Eq M3, α (λ) represents the normalized Lamb-Govardovskii mouse rhodopsin extinction template, and p is the fraction rhodopsin present (1 for the dark adapted state; 0 for the fully bleached state). As previously noted, for simplification we omitted a weak, diffuse back reflection by the discs that is included in the van de Kraats Cones constitute only 3% of the photoreceptors of the mouse retina, and although their inner segments are larger than those of rods, their outer segments are considerably smaller in width and length, and in the middle portion of the retina typically express only 10% or less M-opsin 18, 19 whose λ max , 508 nm, is close to that of mouse rhodopsin. Thus, their contribution to the midwave light absorption in the dark adapted central retina is predictably only a few percent of that by rhodopsin, and can be neglected. It follows that the forward-propagating light transmitted past the outer segment layer is given by Post-receptor layers. In keeping with the van de Kraats et al. formulation, the model assumes that all reflection from post-receptor layers is of light that passes through the RPE and choroid and is back-reflected by the sclera. This "deep" reflectance is given

Eq M6
Total reflection from the eye. The total reflectance of the eye combines the various terms described above as follows: The absolute magnitudes of the reflectances found for the mouse eye (Fig. 6) are notably lower than those obtained in human studies 11,12 . A key instrumental difference between the human reflectometry studies and ours of mice is that to deliver and collect light we employed a scanning laser ophthalmoscope, which acts confocally and thus restricts light collection to the limiting aperture of the imaging system 20 . We thus introduced a "confocal attenuation scale factor", Sf confocal , which scales the entire predicted reflectance function (Eq M7).
Summary. In the simplest terms, the ocular reflectance model is basically

Fitting the model to the reflectance data
The model was fitted to the spectral reflectance data of dark adapted and fully bleached albino and pigmented mice (Fig. 6) by least-squares minimization of a "chisquare" function: Here i = 1, 2 refer to the dark adapted and fully bleached states. Minimization was effected with a Matlab TM script employing the Nelder-Meade "fminsearch" algorithm.
The values of eight parameters were extracted by searching over a continuous range (Table 2) The end-on density of rhodopsin, OD max , was fixed at a value (0.35) estimated from independent observations in the literature. We attempted to maintain the identical values of key parameters between the two strains of mice with the obvious exception that melanin density was set to zero (Sfmela!=!0)!in fitting the albino mouse reflectance data.
The almost 10-fold lower absolute reflectance of the C57Bl/6J mice, however, could not be accomodated without greater overall spectrally neutral attenuation, as expressed in the lower value of Sf confocal and higher value of D prePR for the model describing the pigmented mouse data (Table S1).
Though the model is necessarily complex and the parameter value combinations that generate reasonable descriptions of the data not unique, the model nonetheless serves to explain (i) a number of distinctive qualitative features of the reflectance data (Fig. 6), (ii) the dominant role of rhodopsin absorption loss in light-induced increases in reflectance in the middle wavelength portion of the spectrum (Fig. 7), and (iii) the necessary and sufficient role of including bleaching-induced increments in the reflectance Comparison of the OCT depth profile data of albino and pigment mice (Fig. 5) suggests that melanin back-scattering plays a key role in C57Bl/6J mice, but as the wavelength dependence of this scattering has not been determined, we did not attempt to incorporate it. We acknowledge that the reflectance model is very much "a work in progress", but think that further refinements that incorporate insights from OCT, and that apply to data of both albino and pigmented mice (including mice with varied levels of pigmentation) hold much promise for extending the information obtained from mouse fundus imaging. !  (Fig. 5); necessary and sufficient for good fitting of model (Fig. 6) Reflectance of rod tips( ρ tip ( 0.001& 0.02& 0.02 − 0.05 0.02 − 0.05 Motivated by OCT data (Fig. 5); necessary and sufficient for good fitting of model ( Fig. 6)(  (Fig. 6A) and C57Bl/6J (Fig. 6B). The fifth and six columns present ranges of parameter values for which "good fits" of the model to the data of each strain could be obtained when all other parameters were free to vary. ("Good fit" means that the Chisq value of the fit was within ~ 15% of the minimum.) All the factors in the table with the exception of ρ sclera (675) are spectrally neutral. The spectral dependence of the reflectance model arises from the absorption of light by the rhodopsin, melanin and oxygenated hemoglobin and from the spectral dependence of the scleral reflectance, as explained in the presentation of the model (see