Contrast adaptation in the Limulus lateral eye

Abstract

Luminance and contrast adaptation are neuronal mechanisms employed by the visual system to adjust our sensitivity to light. They are mediated by an assortment of cellular and network processes distributed across the retina and visual cortex. Both have been demonstrated in the eyes of many vertebrates, but only luminance adaptation has been shown in invertebrate eyes to date. Since the computational benefits of contrast adaptation should apply to all visual systems, we investigated whether this mechanism operates in horseshoe crab eyes, one of the best-understood neural networks in the animal kingdom. The spike trains of optic nerve fibers were recorded in response to light stimuli modulated randomly in time and delivered to single ommatidia or the whole eye. We found that the retina adapts to both the mean luminance and contrast of a white-noise stimulus, that luminance- and contrast-adaptive processes are largely independent, and that they originate within an ommatidium. Network interactions are not involved. A published computer model that simulates existing knowledge of the horseshoe crab eye did not show contrast adaptation, suggesting that a heretofore unknown mechanism may underlie the phenomenon. This mechanism does not appear to reside in photoreceptors because white-noise analysis of electroretinogram recordings did not show contrast adaptation. The likely site of origin is therefore the spike discharge mechanism of optic nerve fibers. The finding of contrast adaption in a retinal network as simple as the horseshoe crab eye underscores the broader importance of this image processing strategy to vision.

adaptation is a basic characteristic of all neural systems. Much research effort is thereby devoted to elucidating the neural mechanisms that mediate the phenomenon. Among the most studied are the mechanisms that adjust the sensitivity of the eye to light. Two primary forms of visual adaptation have been described based on the statistical features of the scene to which they respond. One is mean luminance adaptation, and the other is luminance variance (or contrast) adaptation. Through the action of these mechanisms, the retina is able to accommodate the wide input range of the visual system, which exceeds 10 orders of magnitude of illumination, within the narrow output range of its optic nerve fibers, which can fire up to hundreds of impulses per second.

The process of luminance adaptation modulates the gain and dynamics of retinal neurons so as to retain light sensitivity and avoid response saturation when mean illumination level changes (Shapley and Enroth-Cugell 1984; Walraven et al. 1990). By holding sensitivity constant, the eye can faithfully communicate contrast patterns to the brain under diverse lighting conditions (Troy and Enroth-Cugell 1993). The process has components in photoreceptor cells (Dowling 1967; Perlman and Normann 1998; Pugh et al. 1999; Schneeweis and Schnapf 1999) and every other cell in the retinal network (Cicerone and Green 1980; Green and Powers 1982; Rushton and Westheimer 1962). The various receptoral and postreceptoral mechanisms activate at distinct light levels (Dunn et al. 2007), and their adaptive effects are pooled by retinal ganglion cells over an area the size of their receptive field center (Cleland and Enroth-Cugell 1968; Green et al. 1977). Because of the wide operating range, luminance adaptation is generally considered a logarithmic process that normalizes local variations in incident light intensity by the ambient level. It is often modeled using a quasi-linear framework, wherein the retinal output is specified by convolving the visual input with a spatiotemporal filter having parameters that are fixed by the mean steady-state luminance (Purpura et al. 1990; Smith et al. 2008).

The process of contrast adaptation modulates retinal gain and dynamics according to the variance of luminance in the scene, irrespective of the mean level, to match best the output range of neurons to the range of input variation (Baccus and Meister 2002; Chander and Chichilnisky 2001; Kim and Rieke 2001; Manookin and Demb 2006; Shapley and Victor 1978; Smirnakis et al. 1997). By maximizing use of neural signaling capacity, the retina can maintain the pattern discriminability of ganglion cells as the eyes scan the scene or the animal moves between hazy and clear environments. The process has two subcomponents that differ in speed (Baccus and Meister 2002). The faster one (also called contrast gain control) is virtually instantaneous and operates outside of the classic receptive field center and surround of ganglion cells (Enroth-Cugell and Jakiela 1980; Passaglia et al. 2001, 2009). It reportedly extends inside of the receptive field as well (Beaudoin et al. 2007). The slower one has a response time of seconds to minutes and a summation area that includes the receptive field center (Demb 2008). Its spatial extent beyond the center is unclear. The processes are thought to compute contrast by integrating the outputs of many nonlinear subunits that are small in size, widely distributed in space, and rectifying in nature (Bonin et al. 2006; Shapley and Victor 1978). Their adaptive effect on ganglion cell output is traditionally modeled by feeding the neural contrast signal to a gain control that dynamically alters the spatiotemporal characteristics of the retinal filter during visual stimulation (Berry et al. 1999; Enroth-Cugell and Freeman 1987; Shapley and Victor 1979).

Luminance adaptation and contrast adaptation are image processing strategies that all visual systems should seemingly exploit. Decades of work on species across the animal kingdom have established this is true for the former, but the latter is a more recent discovery that has been demonstrated only in vertebrate retinas to date. Contrast adaptation is commonly investigated using a white-noise approach, which involves presenting a random time-varying stimulus and analyzing the neural response with a model consisting of a linear temporal filter and a static nonlinearity. Here, we apply white-noise analysis to a well-studied invertebrate visual system, the compound lateral eyes of the horseshoe crab (Limulus polyphemus). The Limulus eye offers an interesting test of the evolutionary importance of contrast adaptation because its retina is relatively simple and compact. Each of its ∼1,000 ommatidia contains just 2 types of visual neurons: retinular cells and eccentric cells. The retinular cells transduce incident light into a membrane depolarization that passively propagates through gap junctions to the eccentric cells. The eccentric cells then integrate the excitatory signal with self- and lateral-inhibitory synaptic signals and encode the result as a train of action potentials transmitted across the retina and to the brain. Moreover, after a century of research on the eye, the mechanisms of phototransduction, inhibition, and spike generation are understood in such quantitative detail that computer models can accurately simulate the retinal output of horseshoe crabs moving along the ocean floor past objects of behavioral interest to the animal (Passaglia et al. 1997, 1998). Although the simple retinal architecture and rich research history would suggest that contrast gain control mechanisms are unlikely, our results indicate that the Limulus eye does indeed show contrast adaptation like the vertebrate retina.

MATERIALS AND METHODS

Animals.

Experiments were performed during daytime hours on adult male horseshoe crabs obtained from the Marine Biological Laboratory (Woods Hole, MA). Males were studied because females are loaded with eggs that make it harder to isolate their optic nerve. The animals were housed in a 50-gal saltwater tank (Oceanariums, Daytona Beach, FL) at 17°C with a specific gravity of 1.023–1.025 and fed fresh clams every 1–2 wk. They were exposed to a 12:12-h light-dark cycle produced by a Super Bright LightPad (7,800 cd/m²; Artograph, Delano, MN) under timer control.

Electrophysiological recording.

Details of the electrophysiological techniques have been reported (Liu and Passaglia 2009). In short, a horseshoe crab was secured to a wooden platform with screws and submerged to the gills in aerated artificial seawater (Instant Ocean). For optic nerve recordings, a 2-cm hole was cut in the carapace just anterior to one lateral eye. The underlying nerve was cleared of tissue and guided into a nylon recording chamber. The chamber was mounted to the carapace with screws and filled with Limulus saline solution. A single nerve fiber was dissected free and drawn into a microsuction electrode (A-M Systems, Carlsborg, WA) connected to a multichannel bioamplifier and spike discriminator (Xcell-3x4 and APM-2; FHC, Bowdoinham, ME). For electroretinogram (ERG) recordings, an opaque plastic tube was mounted over the opposite eye with screws. The tube was sealed with petroleum jelly, filled with saline, and capped. A silver wire electrode was inserted into the saline through the cap and connected to the bioamplifier. Laboratory software acquired spike discharge times and ERG signals with a precision of 0.1 and 1 ms, respectively.

Visual stimulation.

For optic nerve recordings, the eye was stimulated with light delivered by a cathode-ray-tube (CRT) monitor (CPD-E240, 17-in. Sony Trinitron, distance: 10 cm) or by a fiber optic coupled to a digital video projector (PJD5123; ViewSonic, Walnut, CA). The CRT or a large light pipe (diameter: 4 mm) was used for whole eye stimulation, and a small light pipe (diameter: 0.2 mm) was used for single ommatidial stimulation. Figure 1A illustrates the fiber-optic setup. An optical coupler collected projector light (2,700 cd/m²) with an uncoated plano-convex lens (diameter: 40 mm, back focal length: 35.1 mm) and focused it through a ×45 microscope objective into the fiber optic. A multirotational micropositioner directed the light pipe at the eye or aligned it on the optic axis of the recorded ommatidium. The distance between the fiber optic and objective could be set at three positions, each of which attenuated the mean light output by 1 log unit (LU). Laboratory software controlled the visual display via a digital video processor (Bits⁺⁺; Cambridge Research Systems, Rochester, United Kingdom) that has a wide dynamic range and trigger signals to synchronize data collection with light stimulation. The display output was measured with a calibrated photometer (UDT Instruments, San Diego, CA) and gamma corrected by the software. The maximum output after linearization was 60 cd/m² for the CRT and 20 and 8.5 cd for the large and small light pipes, respectively. These amounts were reduced with neutral density filters or the optical coupler by a factor of 1, 10, or 100 (0, −1, or −2 LU). The eye was given at least 10 min to adjust to each step in luminance level before data collection. For ERG recordings, the eye was stimulated with an ultrabright light-emitting diode (LED; 45T9679; Newark Electronics, Palatine, IL) inserted through the cap of the opaque tube. The LED output (peak: 521 nm, range: 480–560 nm) was computer-controlled and synchronized with data collection via a data acquisition card (USB-6210; National Instruments, Austin, TX). The LED output was also linearized by software to give a maximum output of 7 cd. For both light sources, the stimulus waveform was a pseudorandom binary sequence (PRBS) that randomly alternated between two luminance values at a frame rate of 100 Hz for 180–600 s. PRBS contrast was varied across stimulus trials by setting the values to ±25, ±50, ±75, or ±100% of the mean luminance, which was half of the maximum output of the light source for a given LU setting.

Fig. 1.

A: experimental setup. i: Video projector under computer control. ii: Optical coupler. iii: Multiaxis micropositioner. iv: Fiber-optic light pipe used for single ommatidial illumination. v: Suction electrode mounted in optic nerve recording chamber. B: model of a horseshoe crab eye ommatidium. Stimulus is passed through the lens to a phototransduction process that simulates how retinula cells transduce light fluctuations into membrane depolarizations. The excitatory light signal is then summated with self- and lateral-inhibitory signals by an electrical circuit description of the eccentric cell, and the integrated signal is encoded by a voltage-to-frequency converter as a train of spikes. Spikes fired by the eccentric cell drive the self-inhibitory process, and those fired by eccentric cells in neighboring model ommatidia drive the lateral-inhibitory process. The model consists of a 16 × 16 array of ommatidia for which behavior is determined by 10 parameters (Passaglia et al. 1998), all of which were fixed at published values except for mean light level.

Model simulations.

The same PRBS stimuli were input to a computational model that simulates how the Limulus eye transforms visual images into optic nerve spike trains. Details of the model organization and its experimental validation have been published (Passaglia et al. 1997, 1998). In short, the model consists of a 16 × 16 array of electrical circuits coupled via inhibitory interactions into a neural network. Each circuit is the cell-based equivalent of an ommatidium. Figure 1B illustrates known optical and neural processes of the eye that have been incorporated into model ommatidia. The processes include light collection by corneal lenses, phototransduction by retinular cells, spike encoding by the eccentric cell, and network interactions via self- and lateral-inhibitory synapses. The model simulates eye output by first convolving the stimulus with the point spread function of corneal optics. The light signal is then fed to a phototransduction process that modulates an excitatory conductance representing the collective response of retinular cells to single-photon events, known as quantum bumps (Dodge et al. 1968). The process is programmed to exhibit luminance adaptation by adjusting bump amplitude in accordance with the mean photon rate. The photoreceptor signal is conducted through a circuit description of the eccentric cell to a spike-generating process, where it summates with self- and lateral-inhibitory signals triggered by action potentials fired by the eccentric cell and its nearby neighbors, respectively. Finally, the spike generator encodes the combined signal as a train of action potentials, which modulate the inhibitory conductance of neighboring model ommatidia in a spatially weighted manner. The model output is governed by 10 parameters: λ̄ (mean photon rate), Δρ (optical acceptance angle), τ_B (time constant of quantum bumps), α_max (max amplitude of quantum bumps), K_SI (strength of self-inhibition), τ_SI (time constant of self-inhibition), K_LI (strength of lateral inhibition), τ_LI (time constant of lateral inhibition), σ_LI (spatial spread of lateral inhibition), and S (sensitivity of spike generator). All parameters were fixed at published values for a standard horseshoe crab eye (Passaglia et al. 1998) except for mean photon rate, which was altered to reflect the ambient light level of this study. Simulations were performed with a time step of 0.2 ms. It is important to note that contrast adaptation was not explicitly programmed into any aspect of the model.

Data analysis.

Recorded and computed responses to PRBS stimuli were subjected to white-noise analysis (Chichilnisky 2001), yielding a linear-nonlinear (LN) model for each luminance and contrast condition. For spike discharge records, the linear element was estimated by binning spike-time data at 10 ms, extracting the 500-ms stimulus segment that preceded each time bin in which spikes were fired, weighting the segments by the spike count in those bins, averaging over all segments, and normalizing the average by its absolute maximum. For voltage records, the linear element was estimated by downsampling the voltage data to 10-ms bins, extracting the 500-ms stimulus segment that preceded each data point, weighting the segment by the voltage difference at that point from the overall mean voltage, averaging over time, and normalizing the average by its absolute maximum. Since all cells in the Limulus eye are excited by light, the linear element always had a peak value of +1. The nonlinear element was estimated by convolving the PRBS stimulus with the linear element, binning the amplitude of the resultant signal into 20 buckets spaced evenly between the signal peak and trough, and averaging the recorded spike rate for all times in which the signal fell within each bucket. To assess effects of stimulus luminance and contrast, LN model waveforms were respectively parameterized in terms of a difference-of-exponentials function and piecewise linear function and least-squares fit using a Levenberg-Marquardt algorithm (MATLAB; The MathWorks, Natick, MA). The difference of exponentials function L(t) was given by:

$$L(t)={({\alpha }_{1}t/{\tau }_1)}^{{\kappa }_1}{e}^{-{\kappa }_{1}t\hspace{0.17em}/{\tau }_1}-{({\alpha }_{2}t/{\tau }_2)}^{{\kappa }_2}\hspace{0.17em}{e}^{-{\kappa }_{2}t\hspace{0.17em}/{\tau }_2}$$

where α, τ, and κ are the strength, time constant, and order of the positive and negative filter elements. The piecewise linear function N[x(t)] was given by:

$$N\hspace{0.17em}\left[x\left(t\right)\right]=\max \{0,\mathrm{\beta }[x\left(t\right)-\gamma ]\}\text{,}\hspace{0.17em}\hspace{0.17em}x\left(t\right)=\text{PRBS}\cdot L\left(t\right)$$

where γ and β are the threshold and gain of the static nonlinearity. The quality of LN model descriptions and eye model simulations was evaluated by presenting a novel PRBS stimulus that repeated every 5.12 s for 180–600 s and averaging the recorded response to the repeated noise sequence. The fraction of response variance captured by the models was specified by the coefficient of determination (r²):

$$r^2=1-\frac{{\sum }_t{\left[n\left(t\right)-m\left(t\right)\right]}^2}{{\sum }_t{\left[n\left(t\right)-\overline{n}\right]}^2}$$

where n(t) and n̄ are the time-varying and time-averaged neural response, respectively, and m(t) is the model response. The statistical significance of parameter variations across data sets was assessed by one- and two-way ANOVA with a 95% criterion.

RESULTS

LN modeling of Limulus spike trains.

Figure 2A illustrates a short (0.2 s) segment of the PRBS stimulus and the spike train that was recorded from a single fiber in the horseshoe crab optic nerve. From the spike response, a LN model was constructed by reverse correlation with the stimulus. Figure 2B gives the linear filter and static nonlinearity of the LN model estimated from a representative neuron. The linear filter was biphasic in shape for the mean luminance levels tested, which indicates that optic nerve fibers tended to fire a spike when a bright sequence followed a longer dark sequence. The static nonlinearity was piecewise linear to a first approximation since spike rate cannot go negative. The LN model data were fit with a difference-of-exponentials function and a linear rectification function, respectively, to provide smooth waveforms for model simulations and parameters for quantifying changes in waveform shape across animals and stimulus conditions. The quality of LN models of Limulus spike trains was evaluated by repeatedly presenting a PRBS to the eye. Figure 2C displays a 1.5-s segment of the recoded spike train for successive stimulus repeats. The discharges were organized into firing events that often contained a single reliably timed spike, implying that the neuron responded to specific temporal features within the PRBS. The patterning of spike events was highly reproducible except for a few trials in which the pattern was disrupted by the cell's selection of a different trigger feature midway through the stimulus. The standard deviation of spike-time jitter for high probability (>0.4) events was 19.4 ms on average (N = 6). Figure 2D shows that LN model simulations tracked the spike rate modulation fairly well (mean r² = 0.53 for 100% contrast, N = 6), but the model routinely underestimated the peak rate, owing to the high temporal precision of optic nerve spike events, and it responded to some PRBS features the eye did not see. As a result, the goodness of fit is slightly less than what was reported for vertebrate ganglion cell spike trains (r² = 0.62; Beaudoin et al. 2007).

Fig. 2.

A: schematic of white-noise approach. Pseudorandom binary sequence (PRBS) stimulus (left) is presented to a horseshoe crab eye, and a spike train (right) is recorded from a single optic nerve fiber. A linear-nonlinear (LN) model of the crab eye is then constructed from the stimulus and spike response. B: linear filter (left) estimated by reverse correlation and static nonlinearity (right) estimated by mapping the filtered stimulus onto the response. Solid lines are a difference-of-exponentials fit of the linear filter data and a piecewise linear fit of the static nonlinearity data. norm., Normalized. C: raster plot of the times of spike discharge of the recorded nerve fiber for repeated full-field presentation of the same PRBS stimulus. The vertical bands indicate repeated firing events. Arrowhead points to trials in which the pattern of firing events was altered due to the recorded neuron responding to a different stimulus feature midway through the stimulus. D: time-varying firing rate of the recorded nerve fiber across all trials (thick line) and the rate estimate produced by the LN model (thin line). Asterisks indicate firing events that were misrepresented by the LN model. ips, Impulses per second.

Effect of PRBS luminance and contrast: whole eye stimulation.

We evaluated the suitability of the white-noise approach for horseshoe crab eyes by varying the mean luminance of the PRBS. Figure 3A shows the linear filter and static nonlinearity of a representative neuron for whole eye stimulation of fixed contrast at three luminance levels. It can be seen that filter dynamics are faster at brighter light levels and that the slope of the nonlinearity is steeper. The increase in response speed and contrast gain (slope) is consistent with known effects of luminance adaptation on the eye (Dodge et al. 1968). Table 1 summarizes the effect of mean PRBS luminance on LN model parameters across neurons (N = 8). Many parameters showed a dependence on mean light level, but the changes were statistically significant only for the filter time constants, τ₁ and τ₂, and the static nonlinearity gain, β. On average, the time constants both lengthened by a factor of 1.5 and contrast gain decreased by a factor of 3.1 over 3 LU of light attenuation.

Fig. 3.

A: linear filter (left) and static nonlinearity (right) estimated from an optic nerve fiber for PRBS stimulation of the whole eye at different mean luminance levels [0 log units (LU): black, −1 LU: red, −2 LU: blue]. B: linear filter (left) and static nonlinearity (right) from an optic nerve fiber for PRBS stimulation of the whole eye at different contrasts (25%: green, 50%: blue, 75%: red, 100%: black).

Table 1.

Average parameter values of LN model fits of whole eye stimulation data as a function of mean PRBS luminance

	0 LU	−1 LU	−2 LU
α1	2.80 ± 0.09	2.80 ± 0.12	2.76 ± 0.07
τ1, s(*)	0.07 ± 0.01	0.09 ± 0.01	0.11 ± 0.03
κ1	9.8 ± 2.9	9.3 ± 2.0	9.4 ± 3.7
α2	2.31 ± 0.20	2.13 ± 0.41	1.98 ± 0.32
τ2, s(*)	0.12 ± 0.02	0.16 ± 0.03	0.19 ± 0.04
κ2	4.3 ± 2.5	4.3 ± 2.1	4.2 ± 2.4
γ	−0.7 ± 0.4	−0.7 ± 0.5	−0.7 ± 0.8
β, ips(*)	11.7 ± 4.2	6.6 ± 1.7	3.8 ± 2.2

N = 8. Parameters marked by asterisks showed a statistically significant dependence on luminance level. LN, linear-nonlinear; PRBS, pseudorandom binary sequence; LU, log unit; ips, impulses per second.

We tested for contrast adaptation by holding mean PRBS luminance constant and varying PRBS contrast. Figure 3B shows the linear filter and static nonlinearity of a representative neuron for whole eye stimulation at four contrast levels. It can be seen that filter dynamics are unchanged, except perhaps for the 25% condition, whereas the slope of the nonlinearity becomes shallower with increasing contrast. The inverse relation between response gain and luminance variance defines the phenomenon of contrast adaptation in vertebrate eyes. Table 2 summarizes the effect of PRBS contrast on LN model analysis across neurons (N = 9). None of the filter parameters was significantly altered, but there was a tendency for the filter to look slightly more biphasic in shape at lower contrasts as reflected by changes in κ. Gain changes were evident in every cell, increasing β by a factor of 2.2 on average as contrast was reduced from 100 to 25%.

Table 2.

Average parameter values of LN model fits of whole eye and single ommatidial stimulation data as a function of PRBS contrast

	Whole Eye Stimulation				Single Ommatidial Stimulation
	25%	50%	75%	100%	25%	50%	75%	100%
α1	2.8 ± 0.1	2.8 ± 0.2	2.8 ± 0.1	2.8 ± 0.1	2.7 ± 0.1	2.8 ± 0.1	2.8 ± 0.1	2.7 ± 0.1
τ1, s	0.07 ± 0.01	0.07 ± 0.01	0.07 ± 0.01	0.07 ± 0.01	0.08 ± 0.02	0.08 ± 0.02	0.08 ± 0.02	0.08 ± 0.02
κ1	12.7 ± 7.5	10.9 ± 6.0	11.0 ± 4.8	11.2 ± 5.0	10.2 ± 3.7	10.4 ± 2.3	10.1 ± 2.9	8.4 ± 2.5
α2	2.7 ± 0.1	2.6 ± 0.2	2.6 ± 0.2	2.5 ± 0.1	2.5 ± 0.1	2.4 ± 0.4	2.3 ± 0.3	2.1 ± 0.3
τ2, s	0.14 ± 0.04	0.14 ± 0.05	0.14 ± 0.04	0.15 ± 0.05	0.17 ± 0.05	0.17 ± 0.06	0.18 ± 0.08	0.15 ± 0.04
κ2	6.1 ± 2.1	5.8 ± 2.6	5.6 ± 2.4	5.0 ± 2.4	7.1 ± 1.4	5.7 ± 2.7	6.1 ± 3.9	4.5 ± 2.4
γ	−0.2 ± 0.1	−0.3 ± 0.2	−0.5 ± 0.4	−0.5 ± 0.6	−0.4 ± 0.4	−0.4 ± 0.7	−0.8 ± 1.0	−0.7 ± 1.1
β, ips(*)	24.2 ± 6.8	16.6 ± 5.5	13.3 ± 6.3	10.9 ± 5.0	20.6 ± 5.1	15.2 ± 3.0	9.5 ± 3.3	6.8 ± 2.1

N = 12. Parameter with an asterisk showed a statistically significant dependence on luminance level.

We looked for an interaction of the contrast-adaptive phenomenon with mean luminance. Figure 4 shows the linear filter and static nonlinearity of a neuron from which contrast responses were measured for whole eye stimulation at three light levels. A contrast-dependent change in the static nonlinearity slope was observed at each LU level of similar amount. This amount coincided with luminance-dependent gain changes such that the 100% contrast slope at 0 and −1 LU paralleled the 50% contrast slope at −1 and −2 LU, respectively. Figure 5 summarizes the behavior for all recorded neurons together with their mean firing rate properties. The data were combined across animals by normalizing to the 100% contrast condition. Contrast gain changes were statistically significant at each level tested and indistinguishable in magnitude across mean luminance. They were also independent of the mean firing rate, which did not vary markedly with contrast.

Fig. 4.

Linear filter (left) and static nonlinearity (right) estimated at different mean luminance levels (A: 0 LU, B: −1 LU, C: −2 LU) from the same optic nerve fiber for whole eye stimulation with different PRBS contrasts (50%: thick line, 100%: thin line).

Fig. 5.

Average change in gain (β) of the static nonlinearity (A) and in the mean firing rate (MFR; B) of the population of recorded cells for PRBS stimuli of different contrast (25%: black bars, 50%: gray bars, 75%: white bars) and mean luminance (0, −1, and −2 LU). The changes are expressed relative to the 100% contrast condition to normalize for differences in overall gain and mean rate between cells. Error bars give standard deviations.

Effect of PRBS luminance and contrast: model simulations.

The finding of contrast adaptation was unexpected given the history of vision research on horseshoe crabs. We therefore examined whether a realistic cell-based computer model of the Limulus eye (Passaglia et al. 1997, 1998), published before the discovery of contrast adaption in vertebrate eyes, would exhibit the phenomenon as well. That model was configured to simulate optic nerve responses under ambient light levels different from these experiments, so the mean photon rate was adjusted via bump rate parameter λ̄ to give maximal correlation between recorded and computed spike trains. All other model parameters were set at published values. Figure 6A shows the times of spike discharge of a model optic nerve fiber during a 1.5-s segment of the same repeated PRBS stimulus. Unlike the LN model, the eye model responded with single-spike-firing events. Figure 6B shows that many of the events coincided precisely in time with those of recorded nerve fibers even though the model was never tested with such a dynamic stimulus. Other events, however, were encoded more reliably by the model than the eye and vice versa. The increased fidelity carried a heightened cost of event misalignment, and goodness-of-fit measures suffered as a result (mean r² = 0.35, N = 100 simulations). Variation of model parameter values improved the representation of some firing events at the expense of others, and no combination of values was found within a factor of 2 that produced a better match. More important than the degree of matching was whether the eye model output exhibited contrast adaptation. Figure 6C shows the linear filter and static nonlinearity estimated from model spike trains. Neither element was significantly affected by PRBS contrast, indicating the phenomenon is not explained by existing knowledge implemented in the model. A novel mechanism appears involved. This mechanism is presumably responsible for mismatches in computed and recorded firing patterns to a white-noise input.

Fig. 6.

A: raster plot of the times of optic nerve fiber discharge of a realistic model of the horseshoe crab eye for repeated presentation of the same PRBS stimulus. The vertical bands show that the eye model also produces repeated firing events. B: average time-varying firing rate of a recorded nerve fiber (thick line) and model nerve fiber (thin line). Asterisks indicate firing events that were misrepresented by the model. C and D: linear filter and static nonlinearity of the model eye estimated from model spike trains for different PRBS contrasts. Solid lines are difference-of-exponential and piecewise linear fits of the respective data (25%: thick line, 50%: medium thick line, 75%: medium thin line, 100%: thin line).

Effect of PRBS contrast: single ommatidial stimulation.

To pinpoint the cellular origins of contrast adaptation, the PRBS stimulus was delivered to individual ommatidia via an optical fiber the size of corneal lenses. This separated contributions of receptor and network mechanisms (Barlow 1969) since fiber-optic illumination of adjacent ommatidia does not elicit spikes from recorded optic nerve fibers (data not shown). Figure 7 shows the linear filter and static nonlinearity for single ommatidial stimulation of varying PRBS contrast, with the rest of the eye exposed to either room light or darkness. Contrast gain changes were observed in every neuron tested (N = 12). The magnitude of gain change was not significantly different for the two background conditions so the data were combined. Table 2 summarizes the effect of PRBS contrast on LN model parameters for single ommatidial stimulation. Once again, only β depended measurably on contrast. The gain values were slightly smaller than those for whole eye stimulation because the lower light output of the small fiber optic placed the eye in more dark-adapted state (Fig. 3A). These results indicate that the lateral-inhibitory plexus that interconnects the retinal network is not the source of contrast adaptation. The mechanism must reside within individual ommatidia of the Limulus eye.

Fig. 7.

Linear filter (left) and static nonlinearity (right) estimated from the same optic nerve fiber for single ommatidial stimulation with different PRBS contrasts (50%: thick line, 100%: thin line). The rest of the eye was exposed to steady uniform light of the same mean luminance as the PRBS (A) or to darkness (B).

Effect of PRBS contrast: ERG.

The possible sites of contrast adaptation within an ommatidium are the retinula cells that collectively transduce light into a neural signal and the eccentric cell that encodes the signal in a train of optic nerve impulses. An intracellular investigation of these cells was beyond the scope of this report, but the retinula cell contribution could be indirectly evaluated by applying white-noise analysis to ERG recordings. Figure 8A shows the full-field ERG of the horseshoe crab eye to flashes delivered in darkness. The waveform is monophasic with a time to peak of ∼85 ms. Figure 8B shows the linear filter and static nonlinearity computed from ERG records of the same animal to full-field PRBS stimuli of varying contrast. It can be seen that the linear filter approximates the flash ERG except for an electrical artifact at stimulus onset. The filter is also monophasic with a similar time to peak and is shorter in duration, consistent with the expected effect of prolonged PRBS illumination on the state of luminance adaptation. Hence, the linear component estimates the temporal filtering properties of the Limulus eye quite well. It can also be seen that PRBS contrast had little to no impact on the filter shape or nonlinearity slope. This implies that the phototransduction mechanism of retinula cells, which is primarily responsible for the ERG, does not play a role in contrast adaptation. Comparable results were obtained from all animals tested (N = 3), so the phenomenon seems to originate within eccentric cells.

Fig. 8.

A: full-field electroretinogram (ERG) of a horseshoe crab eye for a 50-ms flash. B: linear filter (left) and static nonlinearity (right) estimated from ERG recordings elicited by PRBS stimuli of different contrasts (25%: thick line, 50%: medium thick line, 75%: medium thin line, 100%: thin line). Dashed line gives the shifted and rescaled flash ERG in A for purpose of comparison.

DISCUSSION

The horseshoe crab eye is considered to behave as a fairly linear system at a given light level, with the spatiotemporal properties of the system varying systematically across light levels due to the action of luminance-adaptive processes (Brodie et al. 1978a,b). The eye is understood with sufficient quantitative detail that the retinal output to real-world inputs can be predicted with an accuracy limited only by spike discharge variability (Passaglia et al. 1997, 1998). White-noise analysis of optic nerve spike trains produced results consistent with known effects of luminance adaptation on the Limulus eye such as decreased response latency and response gain at brighter illumination levels. The analysis also produced the unexpected finding of contrast adaptation in the eye. Computationally similar processes have been described in downstream networks of the invertebrate visual system. For example, large monopolar cells in the fly lamina are thought to perform contrast normalization on the retinal output by reshaping the signal distribution to fit the transmission range of the cells (Laughlin 1981; van Hateren 1997), and H1 cells deeper in the fly visual system are thought to maximize information transmission by adapting over multiple time scales to higher-order features of a visual scene like the variance in image motion (Brenner et al. 2000; Fairhall et al. 2001; Harris et al. 2000). Our results provide the first demonstration of contrast adaptation in an invertebrate retina. The phenomenon presumably escaped detection during a century of vision research on horseshoe crabs because most studies stimulated the eye with light flashes, drifting periodic patterns, or underwater video collected from slow-moving crabs. Few have used a persistently exciting input like a PRBS stimulus.

A major attribute of horseshoe crabs for vision research is the simple structure of their compound eyes. This simplicity offers a test bed for evaluating the extent to which sophisticated neural circuits are needed to produce seemingly complex physiological phenomena like contrast adaptation. In the vertebrate retina, application of white-noise analysis to all major cell types has revealed multiple independent mechanisms of contrast gain control. The identified sites of action include bipolar cells, bipolar cell synapses, amacrine cells, ganglion cell dendrites, and ganglion cell spike generation (Baccus and Meister 2002; Beaudoin et al. 2007; Demb 2008; Kim and Rieke 2001, 2003; Manookin and Demb 2006; Rieke 2001; Zaghloul et al. 2005). A subtractive form was described in some bipolar cells and most amacrine and ganglion cells (Baccus and Meister 2002) and attributed in ganglion cells to a slow (>1 s) hyperpolarization due to reduced release of glutamate from bipolar cells (Manookin and Demb 2006). Slow and fast multiplicative forms were also described, with the former being attributed to slow inactivation of spike-generating currents in ganglion cells (Kim and Rieke 2001, 2003) and the latter to a fast (<1 s) change of gain or kinetics in all inner retinal neurons (Baccus and Meister 2002; Beaudoin et al. 2007). The horseshoe crab retina lacks these cell types and synaptic connections, yet its output also exhibits contrast-dependent gain changes. It will be interesting to learn from future research what is the cellular basis for this feat and its role in Limulus vision. This might, in turn, yield broader insights into what is the added value of the various contrast-adaptive mechanisms in the vertebrate retina.

With just retinular cells and eccentric cells and no excitatory synapses, there are few possible sites of origin for contrast adaptation in the Limulus eye. One possibility is that the phenomenon arises in photoreceptors, perhaps as a byproduct of luminance adaptation. Both processes reduce response gain and latency as stimulus mean and variance increase, so it stands to reason that an asymmetry in adaptation to luminance increments and decrements might cause a net gain change for white-noise stimulation like that attributed to contrast adaptation. Such an asymmetry has been shown in the vertebrate retina (He and MacLeod 1998; Saito and Fukada 1975, 1986; Yeh et al. 1996). Asymmetric luminance adaptation does not, however, appear to explain contrast adaptation in the horseshoe crab retina since white-noise analysis of ERG records indicated no effect of PRBS contrast. The phenomenon is more likely to originate within eccentric cells, presumably as the signal propagates to the cells through gap junctions, gets encoded into trains of action potentials, or drives self- and lateral-inhibitory synapses across the retinal network. A contribution from lateral inhibition can be eliminated because effects of contrast adaptation were unaltered by changes in background illumination and by confining the stimulus to the recorded ommatidium. Self-inhibition does not appear to offer a viable explanation either since it was implemented in the eye model and the model did not show contrast adaptation. Our results therefore imply that contrast adaptation either is a property of the eccentric cell spike generator or is mediated by a heretofore unknown cellular mechanism that modulates signal propagation from retinular cells to eccentric cells. The former is an attractive candidate because there is some evidence for a very slow form of adaptation in spike-firing dynamics (Fohlmeister et al. 1977), which was not implemented in the eye model. White-noise analysis of intracellular voltage records from retinal neurons in the horseshoe crab eye is now needed to affirm and extend these findings.

GRANTS

This work was supported in part by National Science Foundation CAREER Award BES-0547457.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

C.L.P. conception and design of research; T.M.V. performed experiments; T.M.V. and C.L.P. analyzed data; T.M.V. and C.L.P. interpreted results of experiments; T.M.V. and C.L.P. prepared figures; T.M.V. drafted manuscript; C.L.P. edited and revised manuscript; C.L.P. approved final version of manuscript.