Using electroretinograms and multi-model inference to identify spectral classes of photoreceptors and relative opsin expression levels

Introduction

Animals possess a diversity of opsin proteins, one of the main genetic components underlying spectral photoreceptor classes (Porter et al., 2012). It is now possible to identify functional amino acid sequence sites of opsin proteins that determine the spectral sensitivity of photoreceptors (Arendt et al., 2004; Porter et al., 2007). The number and wavelength sensitivity of spectral photoreceptor classes an organism possesses is needed to understand whether it can discriminate natural spectra (i.e., has some form of color vision), and also to understand the mechanistic context of visually guided behavior (Kelber & Osorio, 2010). Spectral classes of photoreceptors are generally identified using a combination of extracellular and intracellular electroretinographic (ERG) techniques (Arikawa, Inokuma & Eguchi, 1987). Extracellular recordings detect a summed contribution of multiple classes of photoreceptors, including relatively rare classes that are difficult to identify using intracellular techniques. It is possible to isolate spectral photoreceptor classes using chromatic adaptation, where light of a restricted waveband is used to light-adapt single photoreceptor classes and the resulting effects on spectral sensitivity are observed in extracellular recordings. However, because visual pigments are all natively sensitive to short wavelengths (Bowmaker, 1999), this procedure is most applicable to long wavelength receptors in organisms that possess up to three spectral photoreceptor classes (Goldsmith, 1986). Intracellular techniques are the most accurate for verifying the existence of spectral classes; but they can be further supported by modeling approaches which incorporate physical parameters obtained from histological techniques (Stavenga & Arikawa, 2011).

I have developed a framework of multi-model selection using overall spectral sensitivities of the visual system. The goals of this framework were to:

1. Identify the most likely number of opsin-based spectral photoreceptor classes of visual systems from extracellular ERGs, and from known parameters of the photoreceptor array.

2. Establish whether differences between individuals in structural photoreceptor parameters affect identification of the same underlying number of opsin-based spectral photoreceptor classes found in A.

3. Map relative opsin expression levels to relative visual pigment concentrations when structural parameters and opsin identities of the photoreceptor array are known.

The framework used here employs Akaike’s information criterion (AIC_c) to select among competing alternative hypotheses (Akaike, 1974). AIC is an objective measure that imposes a realistic penalty for over-parameterization (Burnham & Anderson, 2002). For goals A) and B) the alternative hypotheses are the number and relative area in cross-section, or frequency, of spectral photoreceptor classes. For goal C), the alternative hypotheses are the number of opsins which differ in relative expression level. Others have used multi-model selection to identify the number of photoreceptors in the eyes of oceanic fish, using the relative contributions of photoreceptor classes in cross-section to absorbance (Horodysky et al., 2008, 2010). Existing models of absorptance, which use parameters of real photoreceptors (Snyder, Menzel & Laughlin, 1973), are developed here to incorporate parameters of multiple tiers, or to model absorptive layers affecting the spectral sensitivity of underlying photoreceptors.

Materials and Methods

Example selection

I used organisms which have between one and five classes of spectral photoreceptors to examine capabilities and limitations of the described framework. Four organisms were used to address goals A) and B), and spectral sensitivities from dark-adapted eyes were used to minimize effects of variation among individuals of changing visual pigment concentration, pigment migration, or varying levels of metarhodopsin (Stavenga, 2010). The fifth organism was used to address goal C) to map differences in visual pigment concentrations to relative opsin expression level for two populations of the same species.

1. The onycophoran velvet worm, Principapillatus hitoyensis (Fig. 1A) expresses a single spectral opsin class in its photoreceptors (Beckmann et al., 2015).

2. Homo sapiens possesses one rod and three cone (S, M, and L) photoreceptor classes. Normal human scotopic sensitivity (Fig. 1B) is represented by S-class cone and rod photoreceptor sensitivities (Bowmaker & Dartnall, 1980; Wyszecki & Stiles, 2000). In contrast, scotopic sensitivity of patients with enhanced S-cone syndrome (Fig. 1C) is a condition in which S-cone frequency is increased due to mutations in a transcription factor that controls photoreceptor expression (Haider et al., 2000). Human absorptance models are corrected here for transmittance through the lens and a distal macula tier protecting the retina that affects spectral sensitivity (Wyszecki & Stiles, 1982).

3. The branchiopod crustacean water flea, Daphnia magna (Fig. 1D) possesses four spectral photoreceptor classes (Smith & Macagno, 1990).

4. The swallowtail butterfly, Papilio xuthus (Figs. 1E and 1F) possesses at least five main spectral classes of photoreceptor type (Arikawa, Inokuma & Eguchi, 1987), in several classes of ommatidia with specialized filtering pigments (Stavenga & Arikawa, 2011).

5. The bluefin killifish, Lucania goodei, possesses five cone photoreceptor classes based on known opsins (SWS1, SWS2B, SWS2A, RH2-1, and LWS). Separate populations of this species have been shown to regulate opsin expression depending on their photic environments (Fuller et al., 2004). Killifish absorptance models are corrected here for transmittance through a tier of distal ellipsosomes associated with cone classes found in the related killifish Fundulus heteroclitus (Flamarique & Harosi, 2000), and through the lens of the Nile tilapia Oreochromis niloticus (Lisney, Studd & Hawryshyn, 2010). The relative frequency of the cones cone classes that express SWS2B, RH2-1, and LWS were corrected to take into account that they are double cones.

Results and Discussion

Visual physiologists have long used inferences from thin sections to identify the wavelength of peak absorbance for visual pigments. The reason is the absorbance of visual pigments can be predicted very accurately once the wavelength of peak absorbance, λ_max, is identified. In practice, this is achieved by excising a portion of the retina, taking sections of the photoreceptors, and measuring the fraction of light which is transmitted or absorbed. Ideally, this is performed on single photoreceptors, using a range of narrow-bandwidth light to infer the wavelength of peak absorbance. Vision researchers found that peak absorbance can be used to normalize the rest of the absorbance curve to create a template curve (Dartnall, 1953). Then, using just the wavelength of peak absorbance, it was found that the rest of the curve can be predicted using mathematical expressions. These nomograms correspond closely to visual pigment that is extracted in solution (Govardovskii et al., 2000). Therefore, the idea of a “universal visual pigment template” is very useful when the wavelength of peak absorbance is known, referred to as “normalized absorption templates”. And because λ_max of a visual pigment is primarily determined by the particular opsin amino acids in opsin–chromophore interactions, it is now possible to specify which amino acids determine a specific absorbance profile (Arendt et al., 2004; Porter et al., 2007). However, a normalized absorption template can be misleading when placing the function of a single photoreceptor class in context of other photoreceptors, or the overall spectral sensitivity of the eye. Therefore, absorptance models were used here with the assumption that they are a more realistic approximation for overall sensitivity estimated from extracellular ERGs, and to incorporate multiple layers of filtering.

The first goal of the framework presented here was to find whether overall sensitivity can be used to identify the most likely number of underlying spectral classes of photoreceptors. As can be seen from the fit of each best model to the data (Fig. 1), and from the evidence ratios (Tables 1 and 2), the framework described here is generally able to resolve the number and relative cross-sectional area or frequency of the photoreceptors in the visual systems I have modeled. It is important to note that AIC avoids over-parameterization with the clearest example shown here for velvet worm Principapillatus hitoyensis. Though one to five spectral classes were considered (Table 1; Table S1), to add parameters (i.e., more complex models), the likelihood of those models, given the data, must outweigh the penalty imposed by additional parameters. Principapillatus hitoyensis sensitivity (Fig. 1A, points) is represented by a single spectral opsin class expressed in its photoreceptors with an estimated λ_max of 484 nm, and the best-supported model here was a single receptor GFKRD absorptance model with λ_max of 481 nm (Fig. 1A, black curve).

This framework is also able to resolve the presence of more photoreceptors, if the data support them. Daphnia magna sensitivity (Fig. 1D) is represented by four spectral photoreceptor classes with a distal UV receptor (Smith & Macagno, 1990), and the best-supported model here was a four receptor SSH absorptance model (Table 2; Table S2). The results strongly support the presence of a UV sensitive photoreceptor in the compound eye of D. magna. Though it was poorly supported in comparison to the best model (evidence ratio > 2.0), the second best-supported model for D. magna is a three receptor SSH model, rather than a four receptor GFKRD model (Table 2). This finding can be explained by better performance of the SSH template in the UV range, which has been documented (Stavenga, 2010). Future modeling efforts for organisms with UV photoreceptors should expect stronger cumulative performance of absorptance models based on the SSH template.

Results for Principapillatus hitoyensis and D. magna indicate that this technique resolves a range of opsin-based photoreceptor classes in visual systems. In comparison to more traditional null-hypothesis testing (Table 3), AIC results were similar, with the exception of humans, in which an F-test of non-linear regression results would identify three spectral photoreceptor classes. Table 3 also shows how the penalty imposed by AIC for unneeded parameters provides similar results to comparisons of non-linear regression models. Intuitively, this type of multi-model selection should make sense in terms of natural selection, as maintaining photoreceptors is costly, and if they do not match natural spectra, there is an inarguable cost. It should also be emphasized that, to date, P. hitoyensis and D. magna have not been found to possess specialized optical filtering in their visual systems (Smith & Macagno, 1990; Martin, 1992; Beckmann et al., 2015).

To establish whether this framework can identify the same number and photoreceptor λ_max of a visual system when the frequency of the spectral photoreceptor classes is known to differ between individuals, this framework was applied to scotopic human spectral sensitivities. Normal and enhanced S-cone human scotopic sensitivities (Figs. 1B and 1C) are represented by S-cone and rod photoreceptors, with a higher frequency of S cones in patients with enhanced S-cone syndrome (Jacobson et al., 1990; Hood et al., 1995; Haider et al., 2000). Although the full width half-maximum (FWHM) of normal, dark-adapted humans is 20 nm narrower than Principapillatus hitoyensis (Fig. 1), the best-supported model using this technique is a two receptor GFKRD absorptance model (Table 1). The narrow bandwidth of normal dark-adapted humans can be explained primarily by the presence of the macula, and illustrates that overlooking absorptive layers which affect spectral sensitivity of underlying photoreceptors leads to erroneous interpretation of the number of spectral photoreceptor classes they possess. As can be seen from Table 1 and Fig. 1, the framework presented here identifies increased frequency of S cones in individuals with enhanced S-cone syndrome, and also identifies two primary spectral photoreceptor classes.

To identify limitations of model over-simplification, I applied this technique to P. xuthus sensitivity (Figs. 1E and 1F). Absorptance models (Fig. 1E, dashed lines) illustrate poor results with this technique for P. xuthus: as can be seen by the very broad (>100 μm at FWHM) sensitivity of each modeled photoreceptor in the “best” model, self-screening has been over-estimated. P. xuthus is known to use specialized filtering pigments in part to sharpen the spectral sensitivity of its receptors (Arikawa, 2003). Opsins are expressed heterogeneously in separate classes of ommatidia leading to regions of their compound eyes differing in spectral sensitivity (Arikawa, Inokuma & Eguchi, 1987; Arikawa & Stavenga, 1997). However, absorbance (Fig. 1F) at cross-section two-thirds from the distal tip of the rhabdom of an ommatidium selects a five spectral photoreceptor GFKRD absorbance model. P. xuthus possesses filtering pigments in the peak spectral regions of the photoreceptor classes with the largest deviations identified by this technique (λ_max1, λ_max2, and λ_max5, Table 2). P. xuthus is not known to possess filtering pigments in the peak bandwidths of the remaining spectral classes (λ_max3 and λ_max4, Table 2) (Wakakuwa, Stavenga & Arikawa, 2007). The comparison of P. xuthus absorbance and absorptance results serves to illustrate that multi-model selection must be used judiciously based on what is known for a given visual system. Absorbance results presented here fail to identify the diversity of receptors, and ommatidial spectral classes of organisms where fine-scale spectral discrimination is essential to their visual ecology (Koshitaka et al., 2008). The modeling framework is still useful for incorporating both electrophysiology and histology to compare the effects on overall spectral sensitivity. Deviations from these models can identify the presence of previously unknown spectral filters for an organism, or can provide objective multi-model inference to validate what is known of their visual system.

The examples used until this point are from dark-adapted eyes, and k, the peak absorption coefficient in Eq. (2), remained constant. In these examples λ_max, the wavelength of peak absorbance of each photoreceptor, and A_i/A, the relative area or frequency in cross-section of each photoreceptor, were allowed to vary for optimization. However, relative opsin gene expression levels can vary over short time scales (Fuller & Claricoates, 2011), or can change depending on light environment (Fuller, Noa & Strellner, 2010). Therefore, an additional goal of the modeling framework presented here was to use overall sensitivity to map relative opsin expression levels to visual pigment concentration in an organism with well-characterized photoreceptor classes, by allowing k to vary. The bluefin killifish, L. goodei, was used as two populations found in spring (broad wavelength) and swamp (red-shifted) light environments have been shown to differ in relative opsin expression level for multiple cone photoreceptor classes. The first two rows of Table 4 show the known values of λ_max, and A_i/A which were entered as constants into this framework, and the final two rows show the expression level of each opsin in proportion to all other opsins which were measured in a real-time PCR study (Fuller et al., 2004).

The alternative hypotheses in this example pertained to the number of photoreceptors that had visual pigments with absorption coefficients k < 0.001/μm. The three best models for the spring population are all well supported by the data (evidence ratio < 2.0), indicating that the framework presented here will select the presence of photoreceptors with three or four visual pigments in meaningful concentrations; the model with three visual pigments is supported for the swamp population (Table 5). Though killifish are known to have at least five main spectral cone photoreceptor classes, relative expression levels of class SWS2A reported to date for this species are not found at meaningful expression levels (Table 4) (Fuller et al., 2004). The relative frequency of UV photoreceptors (which express opsin SWS) for swamp populations is less than 0.01 (Table 4), indicating that three visual pigments are likely the main contributors to overall sensitivity. The best SSH models and transmittance through the lens and ellipsosomes are shown in Fig. 2. The optimized values of k for each visual pigment were also informative. Though they tended to individually be less than values typically found in vertebrate photoreceptors, the sum of these ranges from 0.0163 in the best four SSH model, to ∼0.0455 in one of three GFKRD models. These are all within the range of k typically found in vertebrate photoreceptors (Cronin et al., 2014). These values are informative for two reasons: first, they mean that there are most likely physiological limits to visual pigment concentrations because they are near saturation in photoreceptors, and second, when modeling k it is assumed to be at the peak wavelength of each visual pigment, which is not possible at all wavelengths, which has been addressed by Warrant & Nilsson (1998). Further, when k is compared to the sum of all k values in Fig. 3, it becomes apparent that the main opsin expression results have been reproduced by these optimized models. This indicates that future opsin expression studies, which are often difficult to place in context of either overall sensitivity or behavior (Fuller & Noa, 2010) could use the framework suggested here, and models of overall sensitivity inferred from extracellular ERGS.

Currently, empirical studies which identify the spectral properties of individual photoreceptor cells or visual pigments are difficult to place in the larger context of the visual system if all the organism’s spectral classes are not identified. The framework I have presented here can be informative for future opsin expression studies and for objectively guiding extracellular or intracellular electroretinography.

Supplemental Information