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An amplitude code transmits information at a visual synapse


Most neurons transmit information digitally using spikes that trigger the release of synaptic vesicles with low probability. The first stages of vision and hearing are distinct in that they operate with analog signals, but it is unclear how these are recoded for synaptic transmission. By imaging the release of glutamate in live zebrafish, we demonstrate that ribbon synapses of retinal bipolar cells encode contrast through changes in both the frequency and amplitude of release events. Higher contrasts caused multiple vesicles to be released within an event, and such coding by amplitude often continued after the rate code had reached a maximum frequency. Glutamate packets equivalent to five vesicles transmitted four times as many bits of information per vesicle compared with those released individually. By discretizing analog signals into sequences of numbers up to about 11, ribbon synapses can increase the dynamic range, temporal precision and efficiency with which visual information is transmitted.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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  1. 1.

    Rieke, F., Bialek, W., Warland, D. & de Ruyter van Steveninck, R. Spikes: Exploring the Neural Code (MIT Press, 1999).

  2. 2.

    Dayan, P. & Abbott, L. R. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, 2005).

  3. 3.

    Abbott, L. F. & Regehr, W. G. Synaptic computation. Nature 431, 796–803 (2004).

  4. 4.

    Del Castillo, J. & Katz, B. Quantal components of the end-plate potential. J. Physiol. 124, 560–573 (1954).

  5. 5.

    Choi, S. Y. et al. Encoding light intensity by the cone photoreceptor synapse. Neuron 48, 555–562 (2005).

  6. 6.

    Malagon, G., Miki, T., Llano, I., Neher, E. & Marty, A. Counting vesicular release events reveals binomial release statistics at single glutamatergic synapses. J. Neurosci. 36, 4010–4025 (2016).

  7. 7.

    Masland, R. H. The neuronal organization of the retina. Neuron 76, 266–280 (2012).

  8. 8.

    Fuchs, P. A. Time and intensity coding at the hair cell’s ribbon synapse. J. Physiol. 566, 7–12 (2005).

  9. 9.

    Lagnado, L. & Schmitz, F. Ribbon synapses and visual processing in the retina. Annu. Rev. Vis. Sci. 1, 235–262 (2015).

  10. 10.

    Jackman, S. L. et al. Role of the synaptic ribbon in transmitting the cone light response. Nat. Neurosci. 12, 303–310 (2009).

  11. 11.

    Freed, M. A. Quantal encoding of information in a retinal ganglion cell. J. Neurophysiol. 94, 1048–1056 (2005).

  12. 12.

    Sterling, P. & Laughlin, S. B. Principles of Neural Design (MIT Press, 2015).

  13. 13.

    Mennerick, S. & Matthews, G. Ultrafast exocytosis elicited by calcium current in synaptic terminals of retinal bipolar neurons. Neuron 17, 1241–1249 (1996).

  14. 14.

    Neves, G. & Lagnado, L. The kinetics of exocytosis and endocytosis in the synaptic terminal of goldfish retinal bipolar cells. J. Physiol. 515, 181–202 (1999).

  15. 15.

    Burrone, J. & Lagnado, L. Synaptic depression and the kinetics of exocytosis in retinal bipolar cells. J. Neurosci. 20, 568–578 (2000).

  16. 16.

    Rudolph, S., Tsai, M. C., von Gersdorff, H. & Wadiche, J. I. The ubiquitous nature of multivesicular release. Trends Neurosci. 38, 428–438 (2015).

  17. 17.

    Glowatzki, E. & Fuchs, P. A. Transmitter release at the hair cell ribbon synapse. Nat. Neurosci. 5, 147–154 (2002).

  18. 18.

    Singer, J. H., Lassova, L., Vardi, N. & Diamond, J. S. Coordinated multivesicular release at a mammalian ribbon synapse. Nat. Neurosci. 7, 826–833 (2004).

  19. 19.

    Mehta, B., Snellman, J., Chen, S., Li, W. & Zenisek, D. Synaptic ribbons influence the size and frequency of miniature-like evoked postsynaptic currents. Neuron 77, 516–527 (2013).

  20. 20.

    Li, G. L., Cho, S. & von Gersdorff, H. Phase-locking precision is enhanced by multiquantal release at an auditory hair cell ribbon synapse. Neuron 83, 1404–1417 (2014).

  21. 21.

    DeWeese, M. R. & Meister, M. How to measure the information gained from one symbol. Netw. Comput. Neural Syst. 10, 325–340 (1999).

  22. 22.

    Marvin, J. S. et al. An optimized fluorescent probe for visualizing glutamate neurotransmission. Nat. Methods 10, 162–170 (2013).

  23. 23.

    Odermatt, B., Nikolaev, A. & Lagnado, L. Encoding of luminance and contrast by linear and nonlinear synapses in the retina. Neuron 73, 758–773 (2012).

  24. 24.

    Dreosti, E., Esposti, F., Baden, T. & Lagnado, L. In vivo evidence that retinal bipolar cells generate spikes modulated by light. Nat. Neurosci. 14, 951–952 (2011).

  25. 25.

    Baden, T., Esposti, F., Nikolaev, A. & Lagnado, L. Spikes in retinal bipolar cells phase-lock to visual stimuli with millisecond precision. Curr. Biol. 21, 1859–1869 (2011).

  26. 26.

    Baden, T., Berens, P., Bethge, M. & Euler, T. Spikes in mammalian bipolar cells support temporal layering of the inner retina. Curr. Biol. 23, 48–52 (2013).

  27. 27.

    Taylor, W. R., Mittman, S. & Copenhagen, D. R. Passive electrical cable properties and synaptic excitation of tiger salamander retinal ganglion cells. Vis. Neurosci. 13, 979–990 (1996).

  28. 28.

    Robinson, D. W. & Chalupa, L. M. The intrinsic temporal properties of alpha and beta retinal ganglion cells are equivalent. Curr. Biol. 7, 366–374 (1997).

  29. 29.

    O’Brien, B. J., Isayama, T., Richardson, R. & Berson, D. M. Intrinsic physiological properties of cat retinal ganglion cells. J. Physiol. 538, 787–802 (2002).

  30. 30.

    Meister, M. & Berry, M. J. II. The neural code of the retina. Neuron 22, 435–450 (1999).

  31. 31.

    Srinivasan, M. V., Laughlin, S. B. & Dubs, A. Predictive coding: a fresh view of inhibition in the retina. Proc. R. Soc. Lond. Ser. B Biol. Sci. 216, 427–459 (1982).

  32. 32.

    Berry, M. J., Warland, D. K. & Meister, M. The structure and precision of retinal spike trains. Proc. Natl Acad. Sci. USA 94, 5411–5416 (1997).

  33. 33.

    Stone, J. V. Principles of Neural Information Theory: Computational Neuroscience and Metabolic Efficiency (Sebtel Press, 2018).

  34. 34.

    Strong, S. P., Koberle, R., de Ruyter van Steveninck, R. & Bialek, W. Entropy and information in neural spike trains. Phys. Rev. Lett. 80, 197–200 (1998).

  35. 35.

    Koch, K. et al. How much the eye tells the brain. Curr. Biol. 16, 1428–1434 (2006).

  36. 36.

    Sagdullaev, B. T., McCall, M. A. & Lukasiewicz, P. D. Presynaptic inhibition modulates spillover, creating distinct dynamic response ranges of sensory output. Neuron 50, 923–935 (2006).

  37. 37.

    Chen, S. & Diamond, J. S. Synaptically released glutamate activates extrasynaptic NMDA receptors on cells in the ganglion cell layer of rat retina. J. Neurosci. 22, 2165–2173 (2002).

  38. 38.

    Holt, M., Cooke, A., Neef, A. & Lagnado, L. High mobility of vesicles supports continuous exocytosis at a ribbon synapse. Curr. Biol. 14, 173–183 (2004).

  39. 39.

    Laughlin, S. B., de Ruyter van Steveninck, R. & Anderson, J. C. The metabolic cost of neural information. Nat. Neurosci. 1, 36–41 (1998).

  40. 40.

    Attwell, D. & Laughlin, S. B. An energy budget for signaling in the grey matter of the brain. J. Cereb. Blood Flow. Metab. 21, 1133–1145 (2001).

  41. 41.

    Barlow, H. B. in Sensory Communication (ed. Rosenblith, W. A.) 217–234 (MIT Press, 1961).

  42. 42.

    Niven, J. E. & Laughlin, S. B. Energy limitation as a selective pressure on the evolution of sensory systems. J. Exp. Biol. 211, 1792–1804 (2008).

  43. 43.

    de Ruyter van Steveninck, R. & Laughlin, S. B. The rate of information transfer at graded-potential synapses. Nature 379, 642 (1996).

  44. 44.

    Harris, J. J., Jolivet, R. & Attwell, D. Synaptic energy use and supply. Neuron 75, 762–777 (2012).

  45. 45.

    Harris, J. J., Jolivet, R., Engl, E. & Attwell, D. Energy-efficient information transfer by visual pathway synapses. Curr. Biol. 25, 3151–3160 (2015).

  46. 46.

    Chapochnikov, N. M. et al. Uniquantal release through a dynamic fusion pore is a candidate mechanism of hair cell exocytosis. Neuron 83, 1389–1403 (2014).

  47. 47.

    Llobet, A., Beaumont, V. & Lagnado, L. Real-time measurement of exocytosis and endocytosis using interference of light. Neuron 40, 1075–1086 (2003).

  48. 48.

    Zenisek, D., Davila, V., Wan, L. & Almers, W. Imaging calcium entry sites and ribbon structures in two presynaptic cells. J. Neurosci. 23, 2538–2548 (2003).

  49. 49.

    Lagnado, L., Gomis, A. & Job, C. Continuous vesicle cycling in the synaptic terminal of retinal bipolar cells. Neuron 17, 957–967 (1996).

  50. 50.

    Pologruto, T. A., Sabatini, B. L. & Svoboda, K. ScanImage: flexible software for operating laser scanning microscopes. Biomed. Eng. Online 2, 13 (2003).

  51. 51.

    Pola, G., Schultz, S. R., Petersen, R. S. & Panzeri, S. in Neuroscience Databases: A Practical Guide (ed. Kötter, R.) 139–154 (Springer, 2003).

  52. 52.

    Budisantoso, T. et al. Evaluation of glutamate concentration transient in the synaptic cleft of the rat calyx of Held. J. Physiol. 591, 219–239 (2013).

  53. 53.

    Zenisek, D., Horst, N. K., Merrifield, C., Sterling, P. & Matthews, G. Visualizing synaptic ribbons in the living cell. J. Neurosci. 4, 9752–9759 (2004).

  54. 54.

    Gilles, J. F., Dos Santos, M., Boudier, T., Bolte, S. & Heck, N. DiAna, an ImageJ tool for object-based 3D co-localization and distance analysis. Methods 115, 55–64 (2017).

  55. 55.

    Zipfel, W. R., Williams, R. M. & Webb, W. W. Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369 (2003).

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The authors express many thanks to J. Johnston for discussions and to H. Smulders and N. Bashford for looking after the zebrafish. Thanks are also given to M. Meyer for the gift of the constructs. This work was supported by grants to L.L. from the Wellcome Trust (102905/Z/13/Z) and an EU International Training Network (H2020-MSCA-ITN-2015-674901).

Author information

B.J. wrote software, conceived and designed the experiments and helped prepare the manuscript. L.D. performed experiments and analyses. J.M.-D. carried out two-photon imaging experiments and analyses and helped prepare the manuscript. S.-H.S. performed molecular biology experiments, fish transgenesis and initial functional analyses. L.L. conceived the project, designed experiments, wrote software, analyzed results and prepared the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to Leon Lagnado.

Integrated supplementary information

Supplementary Figure 1 Overview of major steps in analysis.

a) A linescan showing changes in iGluSnFR fluorescence in a synaptic terminal in response to a full-field stimulus modulated at 5 Hz (sine wave). The left-hand side shows the profile of two active zones of a terminal stimulated at 30% contrast and the right-hand side the profile of the same terminal stimulated at 100% contrast. This is one of 187 independent experiments in which the analysis procedure was applied. b) Traces extracted from the linescans shown in a. c) Expansion of the period shown boxed in b. Note that at 30% contrast there are events at one active zone that do not coincide with events at the other (highlighted by arrowheads), whereas 100% contrast drives responses in both active zones reliably over all cycles of the 5 Hz stimulus. Analysis shown in d and e were extracted from the boxed area. d) Deconvolved trace using the estimated Wiener filter. e) Estimation of the number of quanta per event. The stimulation protocol is represented below.

Supplementary Figure 2 Spatial demixing of iGluSnFR signals from neighboring active zones.

The temporal average (black trace) is fit with the sum of two Gaussians (red trace). Dashed blue line shows individual components. The FWHM values were 1.1 μm (left) and 0.96 μm (right).

Supplementary Figure 3 The Wiener kernel used for deconvolution.

Representative example of raw events overlayed with a Wiener kernel given by equation 6. Note that the time decay constant of the fluorescence signal is approximately 50 ms. A total number of 101 raw events were averaged for estimating the Wiener kernel filter.

Supplementary Figure 4 Distinguishing events from noise.

a. The kymograph (top) shows the intensity profile along a line through a single terminal. The red and black traces (middle) show the time-course of the iGluSnFR signal over the two active zones marked to the right of the kymograph and the stimulus is shown immediately below. After 2 s there was a switch from constant illumination to full field modulation at 20% contrast, 5 Hz. The signals were demixed using a weighted sum of two Gaussians fit to the intensity profile along the line-scan, as described above. Two sections of the record (green boxes) are expanded in Supplementary Fig. 5. Note variations in the amplitude of glutamate transients. This example is one of 187 independent experiments in which this analysis was applied. b. The results of Wiener deconvolution applied to the traces in a using the kernel shown in Supplementary Fig. 3. The dashed red line shows an event in active zone 1 that did not coincide with an event in active zone 2, and the dashed black lines highlight events in active zone 2. c. The distribution of values in the traces shown in b (active zone 1 in red to the top and active zone 2 below in black) together with a fitted Gaussian (blue). The threshold of 3 sd above the baseline is indicated by the dashed blue arrow.

Supplementary Figure 5 Examples of events detected.

a. Activity in active zone 1 (red) and active zone 2 (black), with deconvolved traces immediately below the iGluSnFR signals. The period of activity corresponds to the large green box in Supplementary Fig. 4a. Thresholds for differentiating events from noise are shown by dashed blue lines, and the dashed vertical lines link the event in the deconvolved trace to the iGluSnFR trace. Note the burst of one large and then three smaller events around 43 s in active zone 1. Note also the deviation in the iGluSnFR signal from active zone 2 at 43 s which was not counted as event because it was small and slowly rising. This example is one of 187 independent experiments in which this analysis was applied. b. Activity in active zone 2 over the period shown by the small green box in Supplementary Fig. 4a. Note that of the three small upward deviations in the iGluSnFR signal after 29.2 s, only the second was counted as an event. c. A histogram of event amplitudes from active zone 1. The black trace is a fitted sum of six Gaussians.

Supplementary Figure 6 Estimating the SNR within a recording.

Representative raw trace in response to a 5 Hz sinusoidal stimulus. The SNR value calculated for this terminal was 3.95. Top: Representative recording of the raw trace. Note that red arrows show uniquantal events. Bottom: Distribution of fluorescence values from the above recording. The red line indicates the Gaussian fit with mean 0.04, and amplitude 0.74. The black line shows the experimental data. The SNR is calculated by dividing the mean uniquantal amplitude (ΔF/F = 0.8, highlighted by gray line) by the standard deviation of the noise (0.2), represented by the Gaussian. This example is one of 187 independent experiments in which this analysis was applied.

Supplementary Figure 7 Example of simulations used to estimate the temporal discrimination window.

Left: Two uniquantal events separated by 10 ms. Note that at this IEI, these events are incorrectly classified as a single 2-quanta event (bottom). Middle: Two events separated by 12 ms generate two distinguishable maxima in the deconvolved trace counted as two distinct events, the amplitude and timing of which is shown by the vertical red bars (bottom). Right: Two uniquantal events separated by 15 ms are distinguished relatively easily. In all these simulations, the SNR was 4.05. This example is one of 20 independent simulations in which similar results were observed.

Supplementary Figure 8 Scatter plot of temporal discrimination windows vs SNR values.

These simulations suggest that in low noise conditions (SNR > 5) we can reliably distinguish events separated in time by 10–15 ms. The mean temporal discrimination window value is 12.6 ms.

Supplementary Figure 9 Evidence against glutamate spillover from nearby cells.

a. Expression of iGluSnFR on two nearby bipolar cells b. After laser ablation of the soma of cell 1, the terminal does not show responses to a stimulus of high contrast (100%, 5 Hz), while the responses in the terminal of cell 2 remain. Scale bar: 5 µm. This example is one of 187 independent experiments in which this analysis was applied. This example is one of 4 independent experiments in which similar results were observed.

Supplementary Figure 10 Counting ribbons.

a. Confocal image of a bipolar cell expressing iGuSnFR (green) and synaptic ribbons labelled with a ribeye a antibody (red). Note the ribbons scattered throughout the inner plexiform layer. This example is one of 27 terminals in which ribbons could be counted. Scale bar 5 μm. b. In all three panels, the green image is a maximum intensity projection of the iGluSFR signal through a volume of 34 μm3 containing the terminal of the cell shown in a. A threshold was then applied to mask out fluorescence beyond the terminal. Superimposed in the top panel is a maximum intensity projection of the red signal through three planes (each separated by 0.25 μm) centred towards one side of the terminal. Two ribbons can be seen. The middle panel shows a similar projection of the red signal at a z distance of 3 μm from the first, where three ribbons can be seen. In the bottom panel, the red channel shows a maximum intensity projection through the entire volume of the terminal. Scale bar 1 μm (top panel).

Supplementary Figure 11 Model for calculating the probability of conflating signals from two ribbons.

a) Example sphere (grey line) and ellipsoid volumes (black line). The spherical cap of their intersection is defined from the radius of the sphere m (using the average nearest distance between ribbons), the circle radius at the z-value of the two volumes intersection a, and the height of the cap h. b) Top: The probability of collapse as a function of m (black line) overlayed with the values computed from the data (black circles). The mean probability is 8% (red dashed line). Bottom), the distribution of distances between ribbons. Red dashed line indicates mean nearest distance of 0.96 μm.

Supplementary information

Supplementary Figures 1–11 and Supplementary Table 1

Reporting Summary

Supplementary Video 1

iGluSnFR activity at bipolar cell synapses. Imaging bipolar cell terminals expressing iGluSnFR. Video begins with 5 s constant illumination followed by modulation at 1 Hz 100% contrast (5 s), 3 Hz (5 s), 5 Hz (5 s) and 10 Hz (5 s), ending with 5 s constant illumination. Field of view: 73 µm, framerate 10 Hz. Qualitatively similar responses were observed in 187 independent experiments.

Supplementary Video 2

Glutamate release imaged in individual synaptic terminals. A linescan across a terminal showing changes in iGluSnFr fluorescence. Each frame shows a 100 ms interval (100 scans of the line with time proceeding upwards). After 10 s there was a switch from constant uniform illumination to modulation at 100% contrast (sine wave). There are two sources of glutamate and at ~6 s, spontaneous events can be seen in the left-hand active zone. Real time. Similar iGluSFR signals were observed in 187 independent experiments.

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Fig. 1: Glutamate transients of varying amplitude imaged at individual active zones.
Fig. 2: Glutamatergic events of different amplitudes were composed of varying numbers of quanta.
Fig. 3: The TTA depends on the number of quanta in a release event.
Fig. 4: The relative contributions of coding by rate and amplitude.
Fig. 5: Multivesicular events increased the temporal precision of synaptic transmission.
Fig. 6: Multivesicular events increased the efficiency of the vesicle code.
Supplementary Figure 1: Overview of major steps in analysis.
Supplementary Figure 2: Spatial demixing of iGluSnFR signals from neighboring active zones.
Supplementary Figure 3: The Wiener kernel used for deconvolution.
Supplementary Figure 4: Distinguishing events from noise.
Supplementary Figure 5: Examples of events detected.
Supplementary Figure 6: Estimating the SNR within a recording.
Supplementary Figure 7: Example of simulations used to estimate the temporal discrimination window.
Supplementary Figure 8: Scatter plot of temporal discrimination windows vs SNR values.
Supplementary Figure 9: Evidence against glutamate spillover from nearby cells.
Supplementary Figure 10: Counting ribbons.
Supplementary Figure 11: Model for calculating the probability of conflating signals from two ribbons.