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The spatial structure of a nonlinear receptive field

Nature Neuroscience volume 15, pages 1572–1580 (2012)Cite this article

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Abstract

Understanding a sensory system implies the ability to predict responses to a variety of inputs from a common model. In the retina, this includes predicting how the integration of signals across visual space shapes the outputs of retinal ganglion cells. Existing models of this process generalize poorly to predict responses to new stimuli. This failure arises in part from properties of the ganglion cell response that are not well captured by standard receptive-field mapping techniques: nonlinear spatial integration and fine-scale heterogeneities in spatial sampling. Here we characterize a ganglion cell's spatial receptive field using a mechanistic model based on measurements of the physiological properties and connectivity of only the primary excitatory circuitry of the retina. The resulting simplified circuit model successfully predicts ganglion-cell responses to a variety of spatial patterns and thus provides a direct correspondence between circuit connectivity and retinal output.

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Figure 1: Receptive fields of On alpha-like RGCs have heterogeneous structure and nonlinear subunits.
Figure 2: Nonlinear and heterogeneous receptive-field properties cause unique responses to stimuli with fine spatial structure.
Figure 3: Excitatory inputs and spike responses have similar sensitivity to rotation.
Figure 4: Type 6 bipolar cells contact the majority of excitatory postsynaptic sites on the On alpha-like RGC.
Figure 5: Nonlinear spatial interactions in the receptive field are aligned to the locations of type 6 bipolar cells.
Figure 6: Construction of the bipolar cell weight map from anatomical measurements.
Figure 7: A predictive model of RGC responses to two-dimensional patterns of light.
Figure 8: Tests of the predictive power of simplified receptive-field models.

References

  1. Chichilnisky, E.J. A simple white noise analysis of neuronal light responses. Network 12, 199–213 (2001).

    CAS  PubMed  Google Scholar 

  2. Pillow, J.W. et al. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454, 995–999 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Pillow, J.W., Paninski, L., Uzzell, V.J., Simoncelli, E.P. & Chichilnisky, E.J. Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. J. Neurosci. 25, 11003–11013 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  4. Enroth-Cugell, C. & Robson, J.G. The contrast sensitivity of retinal ganglion cells of the cat. J. Physiol. (Lond.) 187, 517–552 (1966).

    CAS  Google Scholar 

  5. Caldwell, J.H. & Daw, N.W. New properties of rabbit retinal ganglion cells. J. Physiol. (Lond.) 276, 257–276 (1978).

    CAS  Google Scholar 

  6. Stone, C. & Pinto, L.H. Response properties of ganglion cells in the isolated mouse retina. Vis. Neurosci. 10, 31–39 (1993).

    CAS  PubMed  Google Scholar 

  7. Petrusca, D. et al. Identification and characterization of a Y-like primate retinal ganglion cell type. J. Neurosci. 27, 11019–11027 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. Demb, J.B., Haarsma, L., Freed, M.A. & Sterling, P. Functional circuitry of the retinal ganglion cell's nonlinear receptive field. J. Neurosci. 19, 9756–9767 (1999).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Hochstein, S. & Shapley, R.M. Linear and nonlinear spatial subunits in Y cat retinal ganglion cells. J. Physiol. (Lond.) 262, 265–284 (1976).

    CAS  Google Scholar 

  10. Victor, J.D. & Shapley, R.M. The nonlinear pathway of Y ganglion cells in the cat retina. J. Gen. Physiol. 74, 671–689 (1979).

    CAS  PubMed  Google Scholar 

  11. Demb, J.B., Zaghloul, K., Haarsma, L. & Sterling, P. Bipolar cells contribute to nonlinear spatial summation in the brisk-transient (Y) ganglion cell in mammalian retina. J. Neurosci. 21, 7447–7454 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. Gauthier, J.L. et al. Receptive fields in primate retina are coordinated to sample visual space more uniformly. PLoS Biol. 7, e1000063 (2009).

    PubMed  PubMed Central  Google Scholar 

  13. Thibos, L.N. & Levick, W.R. Bimodal receptive fields of cat retinal ganglion cells. Vision Res. 23, 1561–1572 (1983).

    CAS  PubMed  Google Scholar 

  14. Passaglia, C.L., Troy, J.B., Ruttiger, L. & Lee, B.B. Orientation sensitivity of ganglion cells in primate retina. Vision Res. 42, 683–694 (2002).

    PubMed  PubMed Central  Google Scholar 

  15. Brown, S.P., He, S. & Masland, R.H. Receptive field microstructure and dendritic geometry of retinal ganglion cells. Neuron 27, 371–383 (2000).

    CAS  PubMed  Google Scholar 

  16. Soo, F.S., Schwartz, G.W., Sadeghi, K. & Berry, M.J. II. Fine spatial information represented in a population of retinal ganglion cells. J. Neurosci. 31, 2145–2155 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Volgyi, B., Chheda, S. & Bloomfield, S.A. Tracer coupling patterns of the ganglion cell subtypes in the mouse retina. J. Comp. Neurol. 512, 664–687 (2009).

    PubMed  PubMed Central  Google Scholar 

  18. Pang, J.J., Gao, F. & Wu, S.M. Light-evoked excitatory and inhibitory synaptic inputs to ON and OFF alpha ganglion cells in the mouse retina. J. Neurosci. 23, 6063–6073 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Murphy, G.J. & Rieke, F. Network variability limits stimulus-evoked spike timing precision in retinal ganglion cells. Neuron 52, 511–524 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Gollisch, T. & Meister, M. Eye smarter than scientists believed: neural computations in circuits of the retina. Neuron 65, 150–164 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Schwartz, G.W. & Rieke, F. Nonlinear spatial encoding by retinal ganglion cells: when 1 + 1 ≠ 2. J. Gen. Physiol. 138, 283–290 (2011).

    PubMed  PubMed Central  Google Scholar 

  22. Wassle, H., Puller, C., Muller, F. & Haverkamp, S. Cone contacts, mosaics, and territories of bipolar cells in the mouse retina. J. Neurosci. 29, 106–117 (2009).

    PubMed  PubMed Central  Google Scholar 

  23. Yamagata, M. & Sanes, J.R. Dscam and Sidekick proteins direct lamina-specific synaptic connections in vertebrate retina. Nature 451, 465–469 (2008).

    CAS  PubMed  Google Scholar 

  24. Morgan, J.L., Soto, F., Wong, R.O. & Kerschensteiner, D. Development of cell type-specific connectivity patterns of converging excitatory axons in the retina. Neuron 71, 1014–1021 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. Morgan, J.L., Schubert, T. & Wong, R.O. Developmental patterning of glutamatergic synapses onto retinal ganglion cells. Neural Dev. 3, 8 (2008).

    PubMed  PubMed Central  Google Scholar 

  26. Lin, B. & Masland, R.H. Synaptic contacts between an identified type of ON cone bipolar cell and ganglion cells in the mouse retina. Eur. J. Neurosci. 21, 1257–1270 (2005).

    PubMed  Google Scholar 

  27. Kerschensteiner, D., Morgan, J.L., Parker, E.D., Lewis, R.M. & Wong, R.O. Neurotransmission selectively regulates synapse formation in parallel circuits in vivo. Nature 460, 1016–1020 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  28. Berntson, A. & Taylor, W.R. Response characteristics and receptive field widths of on-bipolar cells in the mouse retina. J. Physiol. (Lond.) 524, 879–889 (2000).

    CAS  Google Scholar 

  29. Dacey, D. et al. Center surround receptive field structure of cone bipolar cells in primate retina. Vision Res. 40, 1801–1811 (2000).

    CAS  PubMed  Google Scholar 

  30. Mills, S.L. & Massey, S.C. Differential properties of two gap junctional pathways made by AII amacrine cells. Nature 377, 734–737 (1995).

    CAS  PubMed  Google Scholar 

  31. Freed, M.A., Smith, R.G. & Sterling, P. Computational model of the on-alpha ganglion cell receptive field based on bipolar cell circuitry. Proc. Natl. Acad. Sci. USA 89, 236–240 (1992).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. Cohen, E. & Sterling, P. Microcircuitry related to the receptive field center of the on-beta ganglion cell. J. Neurophysiol. 65, 352–359 (1991).

    CAS  PubMed  Google Scholar 

  33. Jakobs, T.C., Koizumi, A. & Masland, R.H. The spatial distribution of glutamatergic inputs to dendrites of retinal ganglion cells. J. Comp. Neurol. 510, 221–236 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  34. Koizumi, A., Jakobs, T.C. & Masland, R.H. Regular mosaic of synaptic contacts among three retinal neurons. J. Comp. Neurol. 519, 341–357 (2011).

    PubMed  PubMed Central  Google Scholar 

  35. Zeck, G.M., Xiao, Q. & Masland, R.H. The spatial filtering properties of local edge detectors and brisk-sustained retinal ganglion cells. Eur. J. Neurosci. 22, 2016–2026 (2005).

    PubMed  Google Scholar 

  36. Creutzfeldt, O.D., Sakmann, B., Scheich, H. & Korn, A. Sensitivity distribution and spatial summation within receptive-field center of retinal on-center ganglion cells and transfer function of the retina. J. Neurophysiol. 33, 654–671 (1970).

    CAS  PubMed  Google Scholar 

  37. Kier, C.K., Buchsbaum, G. & Sterling, P. How retinal microcircuits scale for ganglion cells of different size. J. Neurosci. 15, 7673–7683 (1995).

    CAS  PubMed  PubMed Central  Google Scholar 

  38. Koch, C., Poggio, T. & Torre, V. Retinal ganglion cells: a functional interpretation of dendritic morphology. Phil. Trans. R. Soc. Lond. B 298, 227–263 (1982).

    CAS  Google Scholar 

  39. Bock, D.D. et al. Network anatomy and in vivo physiology of visual cortical neurons. Nature 471, 177–182 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  40. Helmstaedter, M., Briggman, K.L. & Denk, W. High-accuracy neurite reconstruction for high-throughput neuroanatomy. Nat. Neurosci. 14, 1081–1088 (2011).

    CAS  PubMed  Google Scholar 

  41. Hochstein, S. & Shapley, R.M. Quantitative analysis of retinal ganglion cell classifications. J. Physiol. (Lond.) 262, 237–264 (1976).

    CAS  Google Scholar 

  42. Badea, T.C. & Nathans, J. Quantitative analysis of neuronal morphologies in the mouse retina visualized by using a genetically directed reporter. J. Comp. Neurol. 480, 331–351 (2004).

    PubMed  Google Scholar 

  43. Sun, W., Li, N. & He, S. Large-scale morphological survey of mouse retinal ganglion cells. J. Comp. Neurol. 451, 115–126 (2002).

    PubMed  Google Scholar 

  44. Kong, J.H., Fish, D.R., Rockhill, R.L. & Masland, R.H. Diversity of ganglion cells in the mouse retina: unsupervised morphological classification and its limits. J. Comp. Neurol. 489, 293–310 (2005).

    PubMed  Google Scholar 

  45. Coombs, J., van der List, D., Wang, G.Y. & Chalupa, L.M. Morphological properties of mouse retinal ganglion cells. Neuroscience 140, 123–136 (2006).

    CAS  PubMed  Google Scholar 

  46. Masland, R.H. The fundamental plan of the retina. Nat. Neurosci. 4, 877–886 (2001).

    CAS  PubMed  Google Scholar 

  47. Amthor, F.R., Takahashi, E.S. & Oyster, C.W. Morphologies of rabbit retinal ganglion cells with complex receptive fields. J. Comp. Neurol. 280, 97–121 (1989).

    CAS  PubMed  Google Scholar 

  48. Kim, I.J., Zhang, Y., Yamagata, M., Meister, M. & Sanes, J.R. Molecular identification of a retinal cell type that responds to upward motion. Nature 452, 478–482 (2008).

    CAS  PubMed  Google Scholar 

  49. Wassle, H., Peichl, L. & Boycott, B.B. Dendritic territories of cat retinal ganglion cells. Nature 292, 344–345 (1981).

    CAS  PubMed  Google Scholar 

  50. Ala-Laurila, P., Greschner, M., Chichilnisky, E.J. & Rieke, F. Cone photoreceptor contributions to noise and correlations in the retinal output. Nat. Neurosci. 14, 1309–1316 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  51. Abbott, L.F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999).

    CAS  PubMed  Google Scholar 

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Acknowledgements

We thank D. Perkel, G. Field, M. Berry and W. Bair for helpful comments on the manuscript. This research was made possible by support from the US National Institutes of Health (EY11850 to F.R., EY10699 and EY017101 to R.O.W. and the Vision Core Grant EY 01730), the Howard Hughes Medical Institute (F.R.) and the Helen Hay Whitney Foundation (G.W.S.).

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Authors and Affiliations

  1. Department of Physiology and Biophysics, University of Washington, Seattle, Seattle, Washington, USA.,

    Gregory W Schwartz, Haruhisa Okawa, Felice A Dunn, Rachel O Wong & Fred Rieke

  2. Department of Molecular and Cell Biology, Harvard University, Cambridge, Massachusetts, USA

    Josh L Morgan

  3. Department of Ophthalmolgy and Visual Sciences, and Department of Anatomy and Neurobiology, Washington University, St. Louis, Missouri, USA

    Daniel Kerschensteiner

  4. Howard Hughes Medical Institute, Seattle, Washington, USA

    Fred Rieke

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Contributions

G.W.S. performed ganglion cell recordings, analysis and designed receptive-field models. H.O. performed imaging experiments and analyses (Figs. 4 and 6). F.A.D. performed bipolar cell recordings (Fig. 7b). J.L.M. and D.K. performed imaging experiments analyzed in Figure 6. G.W.S., R.O.W. and F.R. conceived of experiments and analyses. G.W.S., H.O., F.A.D., R.O.W. and F.R. wrote the paper.

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Correspondence to Gregory W Schwartz.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–6, Supplementary Tables 1–3, Supplementary Discussion (PDF 3773 kb)

Supplementary Movie 1

Identifying appositions of PSD95 puncta with type 6 bipolar axon terminals. The dendritic segment shown in Figure 4c–e is zoomed in and rotated in three dimensions to demonstrate the identification of appositions with type 6 bipolar axon terminals. PSD95-CFP puncta, tdTomato filled alpha-like On RGC dendrites, On bipolar axons labeled by YFP and Syt2 immunoreactivity are shown in green, blue, red and white, respectively. The first set of flashing white dots represent all the identified PSD95 puncta and the second set show those apposed to On bipolar axon terminals. The red flashing dots represent PSD95 puncta classified as apposed to type 6 bipolar cells. (MOV 17179 kb)

Supplementary Movie 2

Identifying appositions of PSD95 puncta with type 7 bipolar axon terminals. The identification of the apposition of PSD95 puncta with type 7 bipolar cells is demonstrated in three dimensions in the same way as in Supplementary Movie 1 using the dendritic segment enlarged in Figure 4i,j. PSD95-CFP puncta, tdTomato filled alpha-like On RGC dendrites, type 7 bipolar axons labeled by GFP are shown in green, blue and red, respectively. The first set of flashing white dots represents all the identified PSD95 puncta and the second set represents those apposed to type 7 bipolar cells. (MOV 15646 kb)

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Schwartz, G., Okawa, H., Dunn, F. et al. The spatial structure of a nonlinear receptive field. Nat Neurosci 15, 1572–1580 (2012). https://doi.org/10.1038/nn.3225

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