Introduction

Psychophysical studies show that humans are sensitive to the ratio of negative (intensity lower than the mean) and positive (intensity higher than the mean) patches of contrast in visual scenes (Chubb et al. 1994, 2004; Graham et al. 2016). This ratio is described by the parameter known as skewness. Visual stimuli are called positively skewed if there is a predominance of negative contrasts with some infrequent patches of high positive contrast and negatively skewed when the situation is reversed. Figure 1 illustrates one's ability to discriminate visual scenes based on skewness by mimicking an experiment performed by Chubb et al. (1994, 2004). The textures were randomly drawn from two distributions equal in every aspect but skewness (Bonin et al. 2006). Yet, one can appreciate the clear difference between negatively skewed images (right upper) and positively skewed images (remaining panels). Chubb et al. (1994, 2004) showed that on a phenomenological level, the sensitivity to skewness can be described by the so-called blackshot mechanism. This blackshot mechanism does not react to skewness per se, rather its sensitivity to strong negative contrasts is simply much higher than to strong positive contrasts, hence it effectively reports the fraction of strong negative contrasts within the scene.

An example of textures used by Chubb et al. (1994) to probe psychophysically the ability of humans to discriminate textures based on skewness. The textures consisted of the either vertical (upper) or horizontal (lower) bars of alternating skewness. The participant was asked to judge the orientation of the bars. Arrows indicate the probability distribution from which the corresponding bar was drawn. The bars were drawn from the probability distributions following the approach described by Bonin et al. (2006) and differed only in terms of skewness (±0.4).

What are the neuronal correlates of the blackshot mechanism? Studies using salamander retinal ganglion cells (Tkačik et al. 2014) and cat lateral geniculate nucleus (LGN) neurons (Bonin et al. 2006) did not report any differences in response associated with changes in stimulus skewness. Therefore, both studies concluded that the discrimination between skewed stimuli occurs in the visual cortex. In contrast, it is well established that the gain of the retinal photoreceptor is asymmetric; given an equal stimulus magnitude, the response amplitude to a strong (>0.4 Weber unit) negative contrast step is greater than it is to a strong positive contrast step (Laughlin, 1981; van Hateren, 2005; Endeman & Kamermans, 2010; Baden et al. 2013; Angueyra et al. 2021). Furthermore, this responses asymmetry is observed throughout the postreceptor retinal stages (Lee et al. 2003; Zaghloul et al. 2003), the LGN (Kremkow et al. 2014) and the primary visual cortex (Zemon et al. 1988; Jin et al. 2008; Yeh et al. 2009; Kremkow et al. 2014). The asymmetric processing of positive and negative contrasts should lead to different response amplitudes to negatively and positively skewed stimuli and thus might underpin the discrimination of skewed stimuli.

A possible reason why the differences in responses to skewed stimuli were not found in retinal ganglion cell (Tkačik et al. 2014) and LGN (Bonin et al. 2006) studies was the power spectra of the stimuli used. In both cases, the researchers used band-limited white noise, whereby large proportions of the signal power are outside the photoreceptor frequency bandwidth. Thus, in both studies, temporal filtering discarded a significant portion of the signal, reducing the skewness and amplitude of the ‘effective’ light stimuli available to drive the photoreceptor non-linear gain. Consequently, Bonin et al. (2006) and Tkačik et al. (2014) might not have found significant differences in the processing of skewed stimuli because (a) their stimuli hardly differed in terms of ‘effective’ skewness, and (b) the ‘effective’ amplitudes of the stimuli used were too low to drive cone photoreceptors outside their linear response range.

Here, we stimulated goldfish cones with sets of skewed stimuli with bandwidths similar to those of the goldfish cones and found that responses to negatively skewed stimuli indeed have higher amplitude than responses to positively skewed stimuli.

Methods Ethical approval

All animal experiments were conducted under the responsibility of the ethical committee of the Royal Netherlands Academy of Arts and Sciences (KNAW), acting in accordance with the European Directive 2010/63 of the European Parliament and of the Council, under license number AVD-801002016517, issued by the Central Comity Animal Experiments of The Netherlands. In addition, every possible measure was taken to reduce any potential suffering and the number of animals used. For all experiments, retinas from 10- to 15-cm-long adult (6–18 months) goldfish (Carassius auratus) of either sex were used. The fish were supplied by Gommers-Ducheine BV (Ghent, The Netherlands) and held in tanks with a water temperature of 15°C in a 12 h–12 h light–dark cycle and were fed six times per week.

Recording procedures

On the day of the experiment, goldfish were first dark adapted for 5–10 min, killed by decapitation and their eyes enucleated. Retinas were isolated under dim red illumination, then placed photoreceptor side up in a recording chamber (300 μl; model RC-26G, Warner Instruments) mounted on a Nikon Eclipse 600FN microscope. The preparation was viewed on an LCD monitor by means of a ×60 water-immersion objective (NA 1.0; Nikon), a CCD camera and infrared (λ > 800 nm; Kodak wratten filter 87c, USA) differential interference contrast optics. The tissue was continuously superfused with oxygenated Ringer solution at room temperature (20°C). The composition of the Ringer solution was as follows (mM): 102.0 NaCl, 2.6 KCl, 1.0 MgCl2, 1.0 CaCl2, 28.0 NaHCO3 and 5.0 glucose, continuously gassed with 2.5% CO2 and 97.5% O2 to yield a pH of 7.8 (osmolarity 245–255 mosmol l−1). For calcium current (ICa) measurements, 5 mM of NaCl was replaced with 5 mM of CsCl, and 100 μM of niflumic acid was added.

Measurements from goldfish cones were performed in current-clamp (voltage response) and voltage-clamp (photo- and calcium current) configurations. Patch pipettes (resistance 7–8 MΩ, PG-150T-10; Harvard Apparatus, Holliston, MA, USA) were pulled with a Brown Flaming Puller (model P-87; Sutter Instruments, Novato, CA, USA). The patch pipette solution contained (mM): 96 potassium gluconate, 10 KCl, 1 MgCl2, 0.1 CaCl2, 5 EGTA, 5 HEPES, 5 ATP-K2, 1 GTP-Na3, 0.1 cGMP-Na, 20 phosphocreatine-Na2 and 50 units ml−1 creatine phosphokinase, adjusted with KOH to pH 7.27–7.3 (osmolarity 265–275 mosmol l−1). The chloride equilibrium potential (ECl) was −55 mV except when ICa was studied. Here, ECl was set at −41 mV by changing the concentrations of potassium gluconate and KCl to 87 and 19 mM, respectively. All chemicals were supplied by Sigma-Aldrich (Zwijndrecht, The Netherlands), except for NaCl (Merck Millipore, Amsterdam, The Netherlands).

Filled patch pipettes were mounted on a MP-85 Huxley/Wall-type manual micromanipulator (Sutter Instrument) and connected to a HEKA EPC-10 Dual Patch Clamp amplifier (HEKA Elektronik, Lambrecht, Germany). After obtaining a whole-cell configuration, cones were first classified spectrally based on their response amplitudes to long-, mid- or short-peak wavelength light flashes (see next subsection). Subsequent light stimuli were generated using only the light source that induced that largest light response during the spectral classification stage. Only cells with stable and fast light responses were stimulated with light skewed stimuli. Data were recorded at a sample rate of 1 kHz using the Patchmaster software package (HEKA Elektronik).

In total, we recorded from 14 cones in eight animals in voltage-clamp mode (light responses, eight cones in seven animals; ICa measurements, six cones in one animal) and from 16 cones in 14 animals in current-clamp mode (all light responses).

For the skew stimulus set 1 (see next subsection) conditions, in voltage clamp we recorded from one short-wavelength-sensitive cone (S-cones), six middle-wavelength-sensitive cones (M-cones) and one long-wavelength-sensitive cone (L-cones); and in the current-clamp mode from two S-cones, six M-cones and one L-cone. For the skew stimulus set 2 conditions, we recorded two S-cones and five M-cones in current-clamp mode only. No spectral classification of the cones was done in the experiments concerning measurements of the ICa.

Light stimuli

The light stimulator was a custom-built LED stimulator with a three-wavelength high-intensity LED (Atlas, Lamina Ceramics, Westhampton, NJ, USA). The peak wavelengths were 465, 525 and 624 nm. Bandwidth was < 25 nm. Linearity was ensured by an optical feedback loop. The output of the LED stimulator was coupled to the microscope via an optical fibre and focused on cone outer segments though a ×60 water-immersion objective. The mean light intensity of all stimuli was 1.2 × 104 photons μm−2 s−1, which is in the photopic level for goldfish (Malchow & Yazulla, 1986). Stimuli were presented at 1 kHz.

Skew stimulus set 1

Skewed stimuli were based on the natural time series of chromatic intensities (NTSCI) from the Van Hateren library (Van Hateren et al. 2002). Given that psychophysical studies have shown that visual scene discrimination occurs when intensities within the spatial domain are skewed (Fig. 1), one may wonder how appropriate it is to study the phenomena with time series of intensities. However, we argue that such an approach is correct for the following two reasons. Firstly, saccadic eye movements convert spatial stimuli into time series. Hence, the photoreceptors of subjects in psychophysical studies ‘perceive’ the presented skewed textures as time series of intensities. Secondly, direct light response of a photoreceptor depends only on the light intensities falling upon its outer segment and not on the spatial structure of the stimulus. Hence, one can reproduce the response of an array of cones to the presentation of a single spatial texture by recording the response of a single cone to a collection of time series of intensities that correspond to the differing retinal locations.

The NTSCI power spectrum is typical of that of ‘natural stimuli’ in that power declines as a function of frequency (Van Hateren, 1997; Van Hateren et al. 2002; Frazor & Geisler, 2006). As a result of the predominance of lower frequencies, most of the light-intensity changes throughout the NTSCI occur over time scales accessible to goldfish cones, and previously, the NTSCI has been used to unlock several non-linear performance features of cones (Endeman & Kamermans, 2010; Howlett et al. 2017). To ensure that all aspects other than skewness remained equal, we first picked short stretches from the NTSCI that were positively skewed, then simply flipped these around the mean to generate negatively skewed stimuli.

Van Hateren's NTSCI is composed of intensity profiles for three distinct chromatic channels that, although similar, are not equal. Here, we used only the ‘red’ channel intensity profile of the NTSCI to generate our skewed stimuli. These stimuli then drove the LED with the peak wavelength best matched to the spectral type of the recorded cone. The LED intensities were also adjusted such that each cone type received an equal number of quanta. In this way, we ensured that we delivered the same stimuli to cones regardless of their spectral type.

To generate stimulus set 1, we divided the NTSCI (Van Hateren et al. 2002) into 1-s-long stretches. From each stretch, we subtracted its minimum value, adjusted the mean light intensities to be equal and selected stretches with similar power spectra, root mean square (r.m.s.) and median contrasts (between 0.23 and 0.25). The r.m.s. and median contrast for each stretch was calculated, respectively, as the ratio between the standard deviation and mean of the stretch, and the ratio between its deviation from the median and its median. To ensure an absolute similarity between positively and negatively skewed stimuli, we selected only stretches where the maximum value was not larger than two times the mean. Next, we chose stretches with skewness values of 0.9, 1.6 and 2.2. The skewness was calculated with Eq. (1): (1)where N is the number of elements in the stretch, I corresponds to the light intensity of an element, Imean and σ are the mean and standard deviation within the stretch, and the angle brackets denote averaging over the period.

We narrowed our selection further to three stretches, all with similar power spectra (data not shown). Power spectra were calculated by Welch's averaged periodogram method (Welch, 1967). No window function was used; the length of the Fourier transform was same as the length of each corresponding data sequence. The total stimulus power was calculated as the integral under power spectra, and the differences in the total stimulus power were no more than 10%. Finally, an additional pink noise stimulus with zero skew and similar power spectra was added to the set. In total, skew stimulus set 1 consisted of seven 1 s stimuli.

Skew stimulus set 2

This stimulus set consisted of three 4-s-long stretches with a skewness of 2.2, 0 and −2.2. They were generated in the same way as skew stimulus set 1, but with one additional condition, i.e. the degree of skewness delivered by the stimulus remained unchanged by the temporal filtering of the cone. This was ensured by first convolving the NTSCI stretch with the mean photocurrent impulse response function (see Data Analysis) obtained from responses to skew stimulus set 1. The skew of the convolution product, representing the ‘effective’ stimulus, was then compared with the skew of the original stimulus. This was also confirmed by determining the effective skewness after convolving the stimuli with the impulse response function of each cone measured in skew stimulus set 2 conditions.

Calcium current isolation

To measure ICa, we used the mean voltage response (seven cells, 69 repeats in total) of cone photoreceptors to stimulus set 2 as the command voltages for the voltage-clamp experiments.

To isolate ICa, we followed the approach described by Fahrenfort et al. (1999). Briefly, to eliminate the calcium-dependent chloride current, ECl was set at −41 mV, and 100 μM niflumic acid was added to the Ringer solution; delayed rectifying and hyperpolarization-activated potassium currents were blocked by replacing 5 mM NaCl in the Ringer solution with 5 mM CsCl; light-activated conductances were saturated by a 20 μm spot of bright white light focused on the cone outer segment; linear leak currents were removed by subtraction. The leak current was estimated by clamping cones at −70 mV, stepping to potentials between −100 and 20 mV in 5 mV steps for 100 ms, calculating the mean current between 20 and 60 ms after the step onset, then determining the linear fit of the current–voltage relationship between −100 and −60 mV (Vroman et al. 2014; Kamar et al. 2019).

Data analysis

For each cell, the skewness of its mean response to each stimulus was determined using Eq. (1). In Figs 2, 3D and 8A, data were fitted using built-in Matlab least-square methods. All data analysis was performed in Matlab and Python.

Left panel, voltage responses as z-scores to skew stimulus set 2 for a representative recorded cone (black line) and for the simulated cone (orange line). The coefficient of determination (R2) between these two traces was 0.96. Right panel, examples of the impulse response functions obtained from the simulated responses to negatively (red) and positively (blue) skewed stimuli. Similar to the impulse response functions estimated from the recorded responses (Fig. 8B and C), the simulated impulse response functions peaked 3 ms [8.5 (2.64)%, n = 7, P = 0.00039, Student's paired t-test] later for the negatively skewed stimulus compared with the positively skewed stimulus and showed no statistically significant difference in their full width at half-maximum [FWHM; Δ = 0.006 (0.019)%, n = 7, P = 0.447, Student's paired t-test] or integration time [Δ = −2.6 (2.53)%, n = 7 P = 0.0512, Student's paired t-test]. Parameters for the simulation are listed in the Table 1.

Parallel cascade identification is the most rigorous method to describe the signal-processing properties of cone responses to naturalistic stimuli (Korenberg, 1991). However, for practical reasons our analysis focuses only on the estimation of the first parallel cascade, which is effectively a linear filter followed by a static non-linearity. Apart from the computational and descriptive simplicity, this approach is also justifiable because it describes cone responses accurately, accounting for >95% of the variance.

The linear temporal filtering properties of a cone were described by its impulse response function. Impulse response functions were estimated as the inverse Fourier transform of the ratio between the stimulus–response cross-power and stimulus–power spectra (Wiener, 1964; Kim & Rieke, 2001). The spectra were calculated using Welch's averaged periodogram method (Welch, 1967). Stimuli and responses were detrended, divided into 500-ms-long stretches with 50% overlap, and windowed with a Hamming function. The length of the Fourier transform was 1024 ms. For Figs 3-5 and 7, impulse response functions were averaged across the entire skew stimuli sets to avoid biases in their estimate associated with skewness of the individual stretches (Chichilnisky, 2001; Simoncelli et al. 2004; Bonin et al. 2006; Tkačik et al. 2014).

To estimate the ‘effective’ stimuli, we convolved the impulse response functions of the cone with the ‘original’ light stimuli. Skews of these ‘effective’ stimuli were calculated with Eq. (1). Discrepancies between the skewness of the ‘effective’ stimuli and the skewness of the responses of the cone were considered to be a result of non-linear cone properties.

For ‘effective’ Weber contrast steps (Figs 7 and 8A), light stimuli were first converted into Weber contrast steps (Fig. 7) with Eq. (2): (2)

These Weber contrast steps (C) were then convolved with a mean impulse response function to obtain the ‘effective’ Weber contrast steps. The mean impulse response function used here was the averaged voltage response-derived impulse response function of all 16 cones measured in current clamp, which was subsequently scaled such that the integral under its curve yielded one (Fig. 7; Howlett et al. 2017).

For Figs 2 and 8, we calculated impulse response functions using responses to individual skewed stretches. In this instance, the impulse response functions estimated might differ from the ‘true’ impulse response function of the system because of the biases associated with the skewness of stimuli. Nevertheless, given that the positively and negatively skewed stimuli in skew stimulus set 2 differed only in terms of skewness, the comparison of corresponding impulse response functions still enables any potential differential effect of stimulus skewness on cone signal-processing properties to be assessed. From these data, the cone integration time was calculated as the integral of the initial polarization lobe of the impulse response function (Daly & Normann, 1985).

To estimate the non-linear gain function parameters of the cone, we fitted the relationship between all the mean cone voltage responses and the ‘effective’ Weber contrast steps (Fig. 8A; 19,000 data points) as the power function of input contrast (Van Hateren & Snippe, 2006) with Eq. (3): (3)Here, V denotes the voltage response, C is the ‘effective’ Weber contrast, and a, b, d and e are fit parameters. At the biophysical level, b corresponds to the baseline rate of phosphodiesterase activity (PDE), d describes the interdependence between the PDE activity rate and the voltage response, e is proportional to the baseline concentration of cyclic guanosine monophosphate (cGMP), and a is a scaling factor (Van Hateren & Snippe, 2006). The quality of the fit was quantified with the adjusted coefficient of determination (R2). The highest R2 (0.95) was obtained using the following parameter values (value ± 95% confidence interval): a = 0.05138 ± 0.03506, b = 1.166 ± 0.072, d = −0.1251 ± 0.0959 and e = −0.05046 ± 0.03552. Our estimation of the power function (d) was close to that obtained by Van Hateren & Snippe (2006) in their theoretical study. Model

Photoreceptor responses were modelled in Matlab using Van Hateren's model of vertebrate photoreceptors (van Hateren & Snippe, 2007), which was shown to be remarkably precise in capturing the processing steps involved in generating the signal of a cone. Apart from activation of the hyperpolarization-activated current (Ih; Howlett et al. 2017; Kamermans et al. 2017), the model closely simulates all the biophysical processing steps of the cone, from the photon-initiated activation of conopsins to the cGMP-regulated changes in the photocurrent, followed by generation of the voltage response. The model simulates cone photoreceptors as a cascade of low-pass filters, a static (instantaneous and memoryless) non-linearity and two divisive feedback loops (van Hateren, 2005; Van Hateren & Snippe, 2007). The low-pass filters correspond to the kinetics of the different biophysical processing steps. The non-linearity describes the inverse proportional dependence between light intensity and changes in the cGMP concentration. The first feedback loop describes the regulation of the rate of cGMP production by calcium influx through cGMP-gated channels. The second feedback loop corresponds to the regulation of the membrane voltage by voltage-sensitive channels in the cone inner segment. The non-linear gain of the cone (Fig. 8A) originates from the interplay between the hydrolysis of cGMP by PDE and the calcium-regulated (feedback loop) production of cGMP by guanylyl cyclase (GC).

We verified that Van Hateren's model could capture responses to skewed stimuli. For this, we fitted the model to the voltage responses of seven goldfish cones recorded under skew stimulus set 2 conditions. The model parameters were modulated within the ranges determined by Endeman & Kamermans (2010) and are shown in Table 1. On average, the correlation coefficient between modelled and recorded voltage responses was 0.97 (0.037), with a coefficient of determination of 0.95 (0.007) (Fig. 2). Moreover, the impulse response functions estimated from the simulated responses to positively and negatively skewed stimuli retained features of the impulse response functions derived from the recorded voltage responses. For example, for both recorded and simulated cone voltage responses, impulse response functions peaked 3 ms [8.5 (2.64)%, P = 0.00013, Student's paired t-test] later under the negatively skewed stimulus compared with the positively skewed conditions, but showed no statistically significant difference in their full width at half-maximum (FWHM) or in integration time (Fig. 2). Thus, Van Hateren's model reproduces cone responses to skewed stimuli accurately.

Table 1. Parameters of Van Hateren's model used to simulate the responses of goldfish, salamander and cat cones Parameter Goldfish cones Cat cones Salamander cones Lifetime of activated conopsin (ms) 8–31 8 88 Lifetime of activated transducin (ms) 16–30 12 101 Dark phosphodiesterase activity (ms−1) 0.003 0.0028 0.003 Constant of the dependence of phosphodiesterase activity on transducin activation 0.00004–0.00023 0.00016 0.0002 Apparent Hill coefficient of CNG channels 1 1 1 Hill coefficient of guanylyl cyclase activation 4 4 4 Time constant of calcium extrusion (ms) 12–28 9 24 Guanylyl cyclase activation constant 0.1 0.09 0.1 Capacitive membrane time constant (ms) 15 6 15 Parameter of membrane non-linearity 0.7–1.1 0.8 0.85 Constant of membrane non-linearity 0.03–0.07 0.07 0.085 Time constant of membrane non-linearity (ms) 300 120 300 For the goldfish, model parameters were obtained by fitting cone responses (n = 7) to skew stimulus set 2 while constraining the range of the parameters varied to within that determined by Endeman & Kamermans (2010). For the cat and salamander, parameters were adjusted such that the impulse response function time to peak of the simulated cone approximately matched that estimated, respectively, by Donner & Hemila (1996) and by Rieke (2001) and Baccus & Meister (2002).

Next, we used Van Hateren's model to estimate the ‘effective’ stimuli in the salamander (Tkačik et al. 2014) and cat (Bonin et al. 2006) studies. To model salamander cones, we adjusted the parameters of Van Hateren's model such that the time course of the impulse response functions of simulated cones resembled those of salamander cones reported by Rieke (2001) and Baccus & Meister (2002). The exact simulation parameters are reported in Table 1. Likewise, to model cat cones Van Hateren's model parameters were adjusted such that the impulse response function time course resembled the estimates made by Donner & Hemila (1996). For the cat, exact parameters of the simulation are reported in the Table 1.

‘Light’ stimuli mimicking those used by Bonin et al. (2006) and Tkačik et al. (2014) were used to study the responses of the modelled cat (Fig. 9) and salamander (Fig. 10) cones, respectively, to changes in skewness. The only difference was that, for illustrative ease, the positively and negatively skewed stimuli were mirror copies of each other. Cat stimuli had an r.m.s. contrast of 0.7, skews of ±0.4 and a flat power spectrum band-limited to 124 Hz. Salamander stimuli had an r.m.s. contrast of 0.2, skews of ±2 and a flat power spectrum band-limited to 30 Hz.

Statistics

All data are presented as the mean (SD), unless otherwise stated. Statistical significance was tested with Student's paired or unpaired t-test or Welch's t-test, as appropriate. The reported P-values were adjusted for multiple comparisons with the Benjamini–Hochberg procedure (Benjamini & Hochberg, 1995).

Results Cone responses vary with skewness

Direct light responses of photoreceptors are not affected by the spatial structure of stimuli and instead depend only on the intensity of light falling on the photoreceptor outer segment (see ‘Light stimuli’ in the Methods section). Hence, to assess the contribution of the photoreceptor to skew discrimination, we exposed goldfish cones to a series of modified NTSCI from the Van Hateren library (Van Hateren et al. 2002; skew stimulus set 1) and recorded their photocurrent and voltage responses (Fig. 3A). Stimuli were equal in terms of mean intensity, r.m.s. and median contrast, and had similar power spectra, and their skewness varied from −2.2 to +2.2. Positively and negatively skewed stimuli were mirror copies of each other; therefore, any asymmetries between corresponding responses would reflect an asymmetry in processing by the cone.

A, skew stimulus set 1 (left) and examples of voltage (middle) and photocurrent (right) responses from cone photoreceptors. B, photocurrent skewness as a function of stimulus skewness for skew stimulus set 1 (n = 8). The grey line indicates equal response and stimulus skewness. The graph shows that cone responses to positively skewed stimuli were less skewed than their stimuli and that this effect was weaker for the negatively skewed stimuli [|Δ positive skew| − |Δ negative skew|: ±0.9, 0.97 (0.436), P = 0.002; ±1.6, 0.76 (0.419), P = 0.004; and ±2.2, 0.97 (0.537), P = 0.003; n = 8, Student's paired t-test]. Also note the zero-skewed stimulus elicited skewed responses. C, voltage response skewness as a function of stimulus skewness (n = 9). Note that the voltage responses and stimuli skews have different signs owing to the signal sign inversion. The grey line indicates equal response and stimulus skews. As was the case in B, cone responses to positively skewed stimuli were less skewed than their stimuli, the effect was weaker for the negatively skewed stimuli, and the zero-skewed stimulus led to a skewed response [|Δ positive skew| − |Δ negative skew|: ±0.9, 0.84 (0.235), P = 0.00003; ±1.6, 0.54 (0.341), P = 0.004; and ±2.2, 0.77 (0.280), P = 0.0001; n = 9, Student's paired t-test]. D, mean (±SD) skewness of the voltage response as a function of the mean (±SD) photocurrent skewness. The grey line indicates equal voltage and photocurrent skews. No statistically significant differences were observed between the absolute magnitude of skewness of photocurrent and the voltage response (P-values of 0.78, 0.60, 0.14, 0.45, 0.10, 0.23 and 0.30 for the stimulus skew values of −2.2, −1.6, −0.9, 0, 0.9, 1.6 and 2.2, respectively, Welch's test). E, ‘effective’ skewness as the function of the stimulus skewness. ‘Effective’ skews were estimated from the convolution product of the light stimuli with the impulse response function of the cone (Fig. 4A and B). The grey line indicates equal ‘effective’ and response skews. This graph shows that cone temporal filtering leads to a reduction of the stimuli skewness (0, ±0.9, ±1.6 and ±2.2) in both photocurrent [respectively, 0.10 (0.05), P = 0.003; ± 0.11 (0.03), PPPt-test] and voltage response [respectively, 0.03 (0.06), P = 0.2; ±0.02 (0.06), PPPt-test].

To determine whether cones process negatively and positively skewed light stimuli in a different manner, we plotted the skews of the photocurrent (Fig. 3B) and voltage responses (Fig. 3C) against the skews of the light stimuli. If there is no difference in processing, the skewness of the response will be equal to the light stimulus skewness, and thus the data points will fall along a straight slope. However, if there is an asymmetry in the processing of positive and negative contrasts it would necessarily lead to a deviation of the data points from the grey line. Figure 3B and C shows that, for positively skewed stimuli, the photocurrent and voltage responses are skewed to a lesser degree than are the light stimuli, whereas for the negatively skewed stimuli they are almost as equally skewed as the light stimuli (note that the signal sign inversion of the voltage response also sign inverts its skewness).

To quantify this difference in response to positively and negatively skewed stimuli, for each of the three stimuli pairs (i.e. ±0.9, ±1.6 and ±2.2), we determined, for each cone, the absolute difference in skew between the stimulus and response in the positively skewed conditions (|Δ positive skew|) and in the negatively skewed conditions (|Δ negative skew|) and then subtracted the negative skew term from the positive skew term (|Δ positive skew| − |Δ negative skew|). This showed that cone responses were significantly less skewed, relative to their stimulus, when positively skewed stimuli were used in comparison to when using negatively skewed stimuli for both the photocurrent [|Δ positive skew| − |Δ negative skew|: ±0.9, 0.97 (0.436), P = 0.002; ±1.6, 0.76 (0.419), P = 0.004; and ±2.2, 0.97 (0.537), P = 0.003; n = 8, Student's paired t-test] and voltage response [|Δ positive skew| − |Δ negative skew|: ±0.9, 0.84 (0.235), P = 0.00003; ±1.6, 0.54 (0.341), P = 0.004; and ±2.2, 0.77 (0.280), P = 0.0001; n = 9, Student's paired t-test]. Thus, Fig. 3B and C indicates an asymmetry in the processing of negatively and positively skewed stimuli by cone photoreceptors.

The processing asymmetry originates exclusively within the phototransduction cascade

What are the cellular mechanisms leading to the differences in the processing of negatively and positively skewed stimuli? To tease apart the relative contributions of the phototransduction cascade and the voltage-activated membrane conductances, we plotted the skewness of the voltage responses and photocurrent against each other in Fig. 3D. The grey line depicts the conditions in which photocurrent and voltage response skews are equal in magnitude. All data points fell on this line, and the degree of photocurrent and voltage response skewness did not differ statistically at any stimulus skew level (respectively, for stimulus skew values −2.2, −1.6, −0.9, 0, 0.9, 1.6 and 2.2, Welch's t-test P-values = 0.78, 0.56, 0.09, 0.40, 0.06, 0.16 and 0.25). This means that the phototransduction cascade is the primary source of the asymmetric processing of the positively and negatively skewed stimuli.

Temporal filtering affects stimulus skewness

The finite kinetics of a cone act as a linear temporal filter, attenuating the faster changes of light intensities in a stimulus more than the slower changes, which might in itself contribute to the cone response skewness being different from that of the stimulus (Fig. 3B and C). Aspects of the stimulus changing on time scales unavailable or barely accessible to drive cone responses are still included when calculating stimulus skewness. Hence, the skewness calculated for the stimulus and for the portion of the stimulus able to elicit a cone response can differ. A similar issue occurs when calculating contrast (Howlett et al. 2017). Importantly, the major part of the linear temporal filtering occurs before the conversion of the chemical signal into changes of the photocurrent, where the literature suggests the asymmetric gain of cone responses originate (van Hateren, 2005). In this subsection, we estimate the stimuli available to drive cone responses after the linear filtering stage, which we term ‘effective’ stimuli. An ‘effective’ stimulus can also be thought of as the linear prediction of the response of a cone to the light stimulus.

To determine the ‘effective’ stimuli skews, we first estimated the temporal filters of the photocurrent and voltage responses of a cone to skew stimulus set 1, following the Wiener approach (Wiener, 1964; Rieke, 2001; Fig. 4). Next, we convolved the estimated filters with the skewed stimuli to obtain the ‘effective’ stimuli. Then we calculated the skews of the ‘effective’ stimuli and plotted them against the skews of the original light stimuli in Fig. 3E, where the grey line describes the situation where the ‘effective’ skew is equal to the original skew. Given that, for each skew value, corresponding positively and negatively skewed stimuli were mirror copies of each other, hence temporal filtering affected the magnitude of their skewness equally. Data points for the positively skewed light stimuli are lower than the grey line and higher for the negatively skewed light stimuli. Hence, in all cases, the skewness of the light stimuli (0, ±0.9, ±1.6 and ±2.2) was greater than the ‘effective’ skew estimated using either the cone photocurrent [respectively, 0.10 (0.05), P = 0.003; ±0.11 (0.03), P < 0.0001; ±0.63 (0.07), P < 0.0001; and ±1.54 (± 0.13), P < 0.0001] or voltage response [respectively, 0.03 (0.06), P = 0.2; ±0.02 (0.06), P < 0.0001; ±0.61 (0.07), P < 0.0001; and ±1.57 (0.16), P < 0.0001]. The adjusted P-values describe the significance of the difference between ‘effective’ and ‘original’ skew stimulus estimated with Student's unpaired t-test.

Asymmetry in the responses to ‘effective’ stimuli

How do goldfish cones process these ‘effective’ stimuli? Figure 3E shows the ‘effective’ skew dynamic range available to cone processes after the initial linear temporal filtering stages was reduced by almost 30%, relative to the light stimuli (from ±2.2 to ±1.6). Therefore, we first completed our data set by recording the voltage responses of a cone to stimuli with ‘effective’ skews of ±2.2 (Figs 4B and 5A).

A, the mean cone impulse response functions (±SD) estimated from the photocurrent responses (violet, n = 8) and from the voltage responses (green, n = 9) to skew stimulus set 1. Individual impulse response functions calculated for each cone were used to estimate the levels of ‘effective’ skew delivered by skew stimulus set 1 (Fig. 3E). The mean impulse response function of the photocurrent was used during the selection process for skew stimulus set 2. B, left panel, the mean cone impulse response function (±SD) estimated from the voltage responses to for skew stimulus set 2 (n = 7). Right panel, skewness of the ‘effective’ stimuli as a function of the skewness of the light stimuli for skew stimulus set 2. Violet squares correspond to the ‘effective’ skewness obtained by convolving the light stimuli with the mean photocurrent impulse response function estimated from responses to skew stimulus set 1 shown in A. Black squares depict the ‘effective’ skewness of each cone response recorded under skew stimulus set 2. This was estimated by convolving each skew stimulus set 2 stimulus with the cone impulse response functions used to calculate B, left panel. Note that to simplify the visualization of the right panel of B, the cone response ‘effective’ skews (black) were multiplied by minus one. The grey line describes the condition wher