Cones perform a non-linear transformation on natural stimuli

Abstract

Visual information in natural scenes is distributed over a broad range of intensities and contrasts. This distribution has to be compressed in the retina to match the dynamic range of retinal neurons. In this study we examined how cones perform this compression and investigated which physiological processes contribute to this operation. M- and L-cones of the goldfish were stimulated with a natural time series of intensities (NTSI) and their responses were recorded. The NTSI displays an intensity distribution which is skewed towards the lower intensities and has a long tail into the high intensity region. Cones transform this skewed distribution into a more symmetrical one. The voltage responses of the goldfish cones were compared to those of a linear filter and a non-linear biophysical model of the photoreceptor. The results show that the linear filter under-represents contrasts at low intensities compared to the actual cone whereas the non-linear biophysical model performs well over the whole intensity range used. Quantitative analysis of the two approaches indicates that the non-linear biophysical model can capture 91 +/- 5% of the coherence rate (a biased measure of information rate) of the actual cone, where the linear filter only reaches 48 +/- 8%. These results demonstrate that cone photoreceptors transform an NTSI in a non-linear fashion. The comparison between current clamp and voltage clamp recordings and analysis of the behaviour of the biophysical model indicates that both the calcium feedback loop in the outer segment and the hydrolysis of cGMP are the major components that introduce the specific non-linear response properties found in the goldfish cones.

Figure 3. Responses of a cone photoreceptor and the phototransduction model to sinusoids

The panels show the voltage responses of a cone (dots) and the photoreceptor model (red line) to sinusoidal light stimulation of four different frequencies as indicated within each panel. Shown are the responses for two periods of stimulation, which are illustrated below the panels. For these responses, stimuli had a Michelson contrast of 50% (filled dots) and 100% (open dots). Note the different y-axis scaling for each stimulation frequency. The dashed line is the response level produced by the mean light intensity. The same parameter values are used for all model responses. Recordings are from a different cone than in Fig. 2.

Figure 1. Photoreceptor model

Boxes containing a τ represent first-order low-pass filters of unit DC-gain. Other boxes represent linear or non-linear transformations of variables. Photopigment excited by light (I) has a lifetime τ_R and excites a G-protein that quickly forms a complex E* (with lifetime τ_E) with phosphodiesterase (PDE). PDE can hydrolyse cGMP at a rate β, which consists of a dark activity c_β by unexcited PDE, and a light-dependent part k_βE*. The cGMP concentration (X) opens transduction channels (with apparent cooperativity n_X) producing current I_os into the cone's outer segment. Part of the current consists of calcium (C, extruded with a time constant τ_C), which drives cGMP synthesis (with cooperativity n_C) and thus produces a feedback. I_os drives the non-linear membrane of the inner segment, with a gain dependent on the membrane potential V_is. For more details see van Hateren (2005).

Figure 2. Responses of a cone photoreceptor and the phototransduction model to flashes

The four panels show the responses of a cone (dots) and the phototransduction model (red lines) to light flashes at three different light levels as indicated above the panels with 1 log unit steps. Flashes were of a Weber contrast of 2 (open dots and red line) or 8 (filled dots and red line), which is indicated near the traces in the panels. The stimulation period is marked by the thick black line below the responses. For A–C the flash lasted 500 ms. The stimulus of D had a duration of 10 ms and was performed at the same light level as C. For all panels the voltage axis has different scaling as indicated within each panel. The same parameter values are used for all model responses.

Figure 4. Voltage and current responses of a cone photoreceptor

A, current (top) and voltage (bottom) responses of a cone when stimulated with a 500 ms flash of 8 Weber. Both responses show a biphasic nature. However, the biphasaic nature in the voltage response is much stronger than for the current response. B, current (top) and voltage (bottom) responses of a cone when stimulated with a 2 Hz 100% contrast sinusoid. The ‘flattening’ and the ‘sawtooth’ non-linearities are visible in both traces to the same extent, indicating that these two non-linearities originate in the phototransduction cascade.

Figure 5. Responses of a cone photoreceptor and different models to a natural time series of intensities

A, the recorded natural time series of intensities (NTSI). On the right side of this panel, its corresponding probability density function (pdf) is plotted. B, the response (average of 5 individual responses) and resulting pdf of a cone photoreceptor where the NTSI was used as stimulus. C, the response and pdf of the phototransduction model when fitted to the cone of B. D, the response and pdf to the NTSI when using the linear filter that optimally transforms the stimulus into the measured response. E, detailed view of stimulus and responses around time = 6.0 s. F, detailed view of stimulus and responses around time = 17.5 s. Recordings are from a different cone than in Figs 2 and 3.

Figure 6. Coherence of a cone photoreceptor and different models

The coherences calculated for the same cone photoreceptor as in Fig. 3 (continuous line, expected coherence), the photoreceptor model (dashed line), and the optimal linear filter (dash–dot line) over the frequency range. The inset displays the amplitude transfer function of the linear filter.