Encoding of luminance and contrast by linear and nonlinear synapses in the retina

Abstract

Understanding how neural circuits transmit information is technically challenging because the neural code is contained in the activity of large numbers of neurons and synapses. Here, we use genetically encoded reporters to image synaptic transmission across a population of sensory neurons-bipolar cells in the retina of live zebrafish. We demonstrate that the luminance sensitivities of these synapses varies over 10(4) with a log-normal distribution. About half the synapses made by ON and OFF cells alter their polarity of transmission as a function of luminance to generate a triphasic tuning curve with distinct maxima and minima. These nonlinear synapses signal temporal contrast with greater sensitivity than linear ones. Triphasic tuning curves increase the dynamic range over which bipolar cells signal light and improve the efficiency with which luminance information is transmitted. The most efficient synapses signaled luminance using just 1 synaptic vesicle per second per distinguishable gray level.

Figure 1

The Zebrafish ribeye a (ctbp2) Promoter Drives Expression in Neurons Containing Ribbon Synapses (A) Imaging synaptic reporters in the retina of live zebrafish using a two-photon microscope. Full-field stimuli were applied through a light guide. (B and C) A stable transgenic fish expressing membrane targeted EGFP (memEGFP) under control of 1.8 kb of the genomic sequence upstream of the ribeye a gene (Tg(−1.8ctbp2:memEGFP)lmb). At 4 dpf, all sensory organs known to express ribbon synapses were labeled, including the retina, the inner ear (white asterisk), the pineal gland (bold arrow), and the neuromasts (arrow heads). (B) Side view, (C) top view of the fish head. Additionally EGFP expression can be seen in the optic nerve and the optic tectum (black asterisk). (D) In a fish at 7 dpf, EGFP expression is driven in hair cells of the inner ear (side view) and maculae (not shown). (E and F) EGFP expression in the pineal gland and a neuromast, respectively (side view; 7 dpf). (G) In the retina, the ribeye a promoter drove expression of memEGFP in photoreceptors and bipolar cells. (H) Labeled photoreceptors in the outer nuclear layer (ONL), their terminals in the outer plexiform layer (OPL), cell bodies of bipolar cells in the inner nuclear layer (INL), and their terminals in the inner plexiform layer (IPL). (I) Expression of sypHy localized to terminals in the OPL and IPL in the stable Tg(−1.8ctbp2:sypHy)lmb line used in this study (see also Figure S1).

Figure 2

In Vivo Imaging of Synaptic Transmission in the Retina (A) Field of view showing sypHy expression in synaptic terminals of bipolar cells in the IPL of a fish at 10 dpf. (B) ROIs from the same field highlighted in different colors. When viewed at highest resolution, numbers mark ON terminals and red numbers OFF. Nonresponding terminals numbered in white. (C) Difference images highlighting the change in sypHy fluorescence in response to steps of light. Attenuation of the light source is shown in log units (ND 4 to ND 1). Darker areas show OFF terminals; brighter areas are ON. (D) Raster plot showing the relative change in fluorescence (ΔF/F) for each ROIs marked in (B). The intensity of the stimulus was increased in steps of 1 log unit, with a maximum intensity of 5.5 × 10⁵ photons/μm²/s. (E) Responses of five individual ON terminals to light steps increasing in intensity by 0.5 log units. Darker hues indicate more sensitive terminals. The black arrows highlight some examples of switches in response polarity. (F) Responses of five individual OFF terminals (see also Figure S2).

Figure 3

Calculating the Rate of Vesicle Release from sypHy Signals (A) Electron micrographs indicate that there are about 15,000 vesicles in an average bipolar cell terminal (background). The number of unquenched sypHy molecules on the surface depends on both the rate of exocytosis and the rate of endocytosis (foreground). (B) Estimating the rate of endocytosis in vivo: comparison of the sypHy signal in response to a bright step of light (ND 1) averaged from a population of 95 ON terminals (green) and 272 OFF terminals (red). In OFF terminals, the sypHy signal decayed exponentially with τ ∼10 s (black line). In ON terminals, the signal decayed at the same rate when the light step was turned off. In both channels, acceleration of vesicle release generated a sypHy signal that rose at a constant average rate for the first 2 s (black lines). (C) Estimation of the sypHy surface fraction (α_min) by acid quenching. First, responses to a step of bright light (ND 1) were measured in ON and OFF terminals at pH 7.4. Then, sypHy molecules on the surface in darkness were quenched with a solution at pH 3.2. The difference between the minimum fluorescence at pH 7.4 and pH 3.2 reflects quenching of the surface fraction (dashed lines). Traces averaged from 10 fish. α_min averaged 0.8% in ON and OFF terminals (see also Figure S3). (D) Upper traces: average fluorescence response of ON (green) and OFF (red) terminals to a 40 s light step (ND 1). The response and recovery phases could both be described as double-exponential functions (smooth lines). Lower traces: a comparison is shown of the conversion of the fluorescence response to rates of vesicle release, V_exo(t), using the raw sypHy signal (noisy trace) and the fitted traces that minimize noise. Thick black bars in upper graph show the values of F_min used for this calculation, as described in Experimental Procedures.

Figure 4

Variations in the Intensity-Response Relation of Different Synaptic Terminals (A) Upper trace, average fluorescence response of ON terminals to light steps of three different intensities. Smooth lines show the description of these responses by a series of double exponential fits. Lower trace, conversion of the upper signal to rates of vesicle release using both original and fitted traces. (B) The rate of vesicle release in OFF terminals calculated in the same way. (C) Averaged response from the 20% most sensitive ON terminals (dark green) and the 20% least sensitive (light green). (D) Averaged response from the 20% most sensitive OFF terminals (dark red) and the 20% least sensitive (light red). (E) Peak release rate at light onset as a function of the relative intensity could be described using a Hill function. Dark green: averages of the 33% most sensitive ON terminals (n = 35, I_1/2 = 2.7 × 10⁻⁴, h = 2.8). Light green: 33% least sensitive terminals (n = 37, I_1/2 = 1.7 × 10⁻², h = 0.9). Dashed arrows show I_1/2. Error bars are SEM. (F) Hill function fit to the intensity-response relation of two subsets of OFF terminals: the 33% most sensitive (dark red; n = 65, I_1/2 = 1.1 × 10⁻⁴, h = 2.4) and 33% least sensitive (light red; n = 58, I_1/2 = 5.7 × 10⁻³, h = 5.1).

Figure 5

Nonlinearities and Sensitivity across the Population of Bipolar Cell Terminals (A) The distribution of Hill coefficients (h) across individual synaptic terminals. ON (green, n = 536), OFF (red, n = 1,218). Both distributions show a distinct population with h < 1.5 (termed “linear”), and a second population with h > 2.0 (“nonlinear”). The fitted function is the sum of two Gaussians. (B) Distribution of I_1/2 across a complete sample of ON (green) and OFF (red) terminals from 178 experiments. The fitted curves are log-normal functions with the shape $\exp \left[-{\left(\ln \left(I/I_0\right)/2\sigma \right)}^2\right]$. (C) Distribution of I_1/2 across the complete sample of ON and OFF terminals (n = 1,754). I₀, the peak of the distribution, occurs at a relative intensity of 1.47 ± 0.39 × 10⁻³, equivalent to 8.1 × 10² photons μm⁻² s⁻¹. In comparison, the threshold for activation of cones is about 10² photons μm⁻² s⁻¹ (Schnapf et al., 1990). The width of the distribution $\sqrt{2}\sigma$ was 4.2 ± 0.4 log units. There was no correlation between I_1/2 and h (see also Figure S4).

Figure 6

Linear and Nonlinear Tuning Curves Encoding Luminance (A) SypHy responses from two ON terminals elicited by a series of light steps increasing in intensity by one log unit. Lower intensities caused a decrease in vesicle release. The right hand example shows suppression of release at the highest intensity, where there is a rebound burst of exocytosis at light offset (i.e., an OFF response; black arrow). (B) Responses from two OFF terminals. Lower intensities caused an increase in vesicle release. (C) The average shape of the intensity-response function for ON terminals. Linear (thin line) and nonlinear (bold) were averaged separately after normalizing the relation measured in each terminal to the intensity producing the half-maximal response, I′. The function fitted to both curves is of the form$V_{exo}=A+Int\left(\frac{I^{\prime h}}{I^{\prime h}+1}\right)+\frac{Antag}{\sigma \sqrt{2\pi }}\underset{0}{\overset{I^{\prime }}{\int }}\text{exp}\left[-{\left(\frac{\text{ln}\left(I^{\prime }\right)}{2\sigma }\right)}^2\right]d{I}^{\prime }$where A is an offset, Int is a scaling factor for the “intrinsic” component described by the Hill equation, Antag is the scaling factor for the “antagonistic” component described by the cumulative density function of a log-normal distribution, and $\sqrt{2}\sigma$ is the width of that distribution in log units. For linear synapses, A = 3.4 vesicles s⁻¹, Int = 76.1 vesicles s⁻¹, h = 0.6, Antag = −52.23, width = 3.11. For nonlinear synapses, A = 7.7 vesicles s⁻¹, Int = 67.7 vesicles s⁻¹, h = 1.3, Antag = −56.34, width = 3.23. The way the intrinsic and antagonistic components sum to generate the nonlinear tuning curve is shown in (E). (D) The average shape of the intensity-response function for OFF terminals at light onset. For linear synapses (thin line), A = 49 vesicles s⁻¹, Int = −57.8 vesicles s⁻¹, h = 0.85, Antag = 37.3, width = 2.1. For nonlinear synapses (bold line), A = 43.3 vesicles s⁻¹, Int = −64.3 vesicles s⁻¹, h = 2.11, Antag = −59.2, width = 4.46. The summation of the intrinsic and antagonistic components to generate the nonlinear tuning curve is shown in (F). (G) A comparison with luminance tuning assessed using SyGCaMP2 to monitor the presynaptic calcium signal. Each trace shows responses of individual terminals. Arrows point to examples of switches in the polarity of the response to dim or bright lights (see also Figure S5). The average shape of the intensity-response function are shown in (H) for ON terminals and (I) for OFF. The response was quantified as the initial rate of change of the SyGCaMP2 signal relative to fluorescence in the dark. Linear (thin line) and nonlinear (bold line) terminals were distinguished in the same way as for sypHy measurements, according to the Hill coefficient best describing the major part of the response. The luminance tuning curves are very similar to those measured using sypHy (C and D). All error bars are SEM.

Figure 7

Nonlinear Tuning Curves Improve Performance (A) The tuning curves of ON terminals showing the average number of vesicles released over a 0.2 s time window (green line, left axis), and the number of gray levels distinguishable by counting vesicles over this interval using an ideal observer model (black line, right axis). Thin lines are the linear synapses, and bold lines nonlinear. (B) A similar comparison for OFF terminals. (C and D) Predicted contrast sensitivity functions derived from the luminance tuning curves of ON terminals in (A) and OFF terminals in (B).

Figure 8

Nonlinear Synapses Display Higher Contrast Sensitivity (A) Assessing contrast sensitivity at different mean luminances. Contrast steps varied between 20% and 100% (5 Hz square wave) and mean luminances increased in steps of one log unit. Traces averaged from 360 ON terminals and 450 OFF. (B) Average contrast-response functions of ON terminals, measured at different mean luminances. Curves are fits of the Hill equation with values of C_1/2 as follows: I = 10⁻³, C_1/2 = 39 ± 13%; I = 10⁻² (bold trace), C_1/2 = 34% ± 10%; I = 10⁻¹, C_1/2 = 64% ± 7%; I = 10⁰, C_1/2 = 74% ± 8%. (C) Average contrast-response functions of OFF terminals, measured at different mean luminances. Curves are fits of the Hill equation with the following parameters: I = 10⁻³, C_1/2 = 72% ± 6%; I = 10⁻² (bold trace), C_1/2 = 68% ± 2%; I = 10⁻¹, C_1/2 = 71% ± 3%; I = 10⁰, C_1/2 = 83% ± 17%. (D and E) Average contrast-response functions in linear and nonlinear terminals. For each individual terminal, contrast steps were applied at the mean light intensity closest to I_1/2. (D) ON terminals. Fits of the Hill equation with C_1/2 = 76% ± 8% linear (thin line) and C_1/2 = 54% ± 7% (nonlinear, bold line). (E) OFF terminals. Fits of the Hill equation with C_1/2 = 75% ± 9% (linear, thin line) and C_1/2 = 20% ± 4% (nonlinear, bold line). (F) The relation between C_1/2 and the Hill coefficient describing luminance tuning in ON terminals (n = 560). These points are superimposed on the distribution of Hill coefficients describing luminance tuning in the same population of terminals (cf. Figure 5A). C_1/2 was systematically lower in nonlinear terminals. (G) A similar comparison for OFF terminals (n = 890). C_1/2 was systematically lower in nonlinear terminals. Error bars are SEM (see also Figure S6).