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The Role of Photon Statistics in Visual Perception

  • Leonid KrivitskyEmail author
  • Vadim Volkov
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 217)

Abstract

We address the question of how fundamental photon fluctuations are perceived by a live visual system. The discussion is focused on specific type of photoreceptor cells within the eye, known as retinal rod cells. Rod cells provide vision under low light conditions and they are sensitive at a single photon level. We review experiments on interaction of the rod cells with light sources of different photon statistics, including coherent, pseudo-thermal, and single-photon sources. Accurate control over photon statistics of light stimuli, combined with technique for the readout of rod cells response, enable precise and unambiguous characterization of intrinsic features of the visual system at single and discrete photon levels.

References

  1. 1.
    J.E. Dowling, The Retina: An Approachable Part of the Brain (Belknap Press of Harvard University Press, Cambridge, MA, 2012). Revised EditionGoogle Scholar
  2. 2.
    C.R. Braekevelt, S.A. Smith, B.J. Smith, Fine structure of the retinal photoreceptors of the barred owl (Strix varia). Histol. Histopathol. 11(1), 79–88 (1996)Google Scholar
  3. 3.
    M. Joseph, A. Corless, Minimum diameter limit for retinal rod outer segment disks. Development of Order in the Visual System, ed. by S.R. Hilfer et al. (Springer, New York Inc., 1986), pp. 127–142Google Scholar
  4. 4.
    K. Palczewski, G protein-coupled receptor rhodopsin. Annu. Rev. Biochem. 75, 743–767 (2006)CrossRefGoogle Scholar
  5. 5.
    M.L. Woodruff, M.D. Bownds, Amplitude, kinetics, and reversibility of a light-induced decrease in guanosine 3′,5′-cyclic monophosphate in frog photoreceptor membranes. J. Gen. Physiol. 73(5), 629–653 (1979)CrossRefGoogle Scholar
  6. 6.
    H.W. Choe, Y.J. Kim, J.H. Park, T. Morizumi, E.F. Pai, N. Krauss, K.P. Hofmann, P. Scheerer, O.P. Ernst, Crystal structure of metarhodopsin II. Nature 471, 651–655 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    K. Palczewski, T. Kumasaka, T. Hori, C.A. Behnke, H. Motoshima, B.A. Fox, I. Le Trong, D.C. Teller, T. Okada, R.E. Stenkamp et al., Crystal structure of rhodopsin: a G protein-coupled receptor. Science 289, 739–745 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    L. Stryer, Exploring light and life. J. Biol. Chem. 287, 15164–15173 (2012)CrossRefGoogle Scholar
  9. 9.
    T.D. Lamb, Gain and kinetics of activation in the G-protein cascade of phototransduction. Proc. Natl. Acad. Sci. U.S.A. 93, 566–570 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    T.D. Lamb, E.N. Pugh Jr., Phototransduction, dark adaptation, and rhodopsin regeneration the proctor lecture. Invest. Ophthalmol. Vis. Sci. 47, 5138–5152 (2006)CrossRefGoogle Scholar
  11. 11.
    E.N. Pugh Jr., T.D. Lamb, Cyclic GMP and calcium: the internal messengers of excitation and adaptation in vertebrate photoreceptors. Vis. Res. 30, 1923–1948 (1990)CrossRefGoogle Scholar
  12. 12.
    R.H. Cote, M.A. Brunnock, Intracellular cGMP concentration in rod photoreceptors is regulated by binding to high and moderate affinity cGMP binding sites. Biol. Chem. 268(23), 17190–17198 (1993)Google Scholar
  13. 13.
    X. Zhang, R.H. Cote, cGMP signaling in vertebrate retinal photoreceptor cells. Front Biosci. 10, 1191–1204 (2005)CrossRefGoogle Scholar
  14. 14.
    E.E. Fesenko, S.S. Kolesnikov, A.L. Lyubarsky, Induction by cyclic GMP of cationic conductance in plasma membrane of retinal rod outer segment. Nature 313, 310–313 (1985)ADSCrossRefGoogle Scholar
  15. 15.
    W.H. Cobbs, E.N. Pugh Jr., Cyclic GMP can increase rod outer-segment light-sensitive current 10-fold without delay of excitation. Nature 313, 585–587 (1985)ADSCrossRefGoogle Scholar
  16. 16.
    K. Matulef, W.N. Zagotta, Cyclic nucleotide-gated ion channels. Annu. Rev. Cell Dev. Biol. 19, 23–44 (2003)CrossRefGoogle Scholar
  17. 17.
    R.R. Birge, Nature of the primary photochemical events in rhodopsin and bacteriorhodopsin. Biochim. Biophys. Acta 1016, 293–327 (1990)CrossRefGoogle Scholar
  18. 18.
    B.K.-K. Fung, J.B. Hurley, L. Stryer, Flow of information in the light-triggered cyclic nucleotide cascade of vision. Proc. Natl. Acad. Sci. U.S.A. 78, 152–156 (1981)ADSCrossRefGoogle Scholar
  19. 19.
    N. Sim, M.F. Cheng, D. Bessarab, C.M. Jones, L.A. Krivitsky, Measurement of photon statistics with live photoreceptor cells. Phys. Rev. Lett. 109, 113601 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    M.E. Burns, E.N. Pugh Jr., Lessons from photoreceptors: turning off G-protein signaling in living cells. Physiology (Bethesda) 25, 72–84 (2010)Google Scholar
  21. 21.
    C.M. Krispel, D. Chen, N. Melling, Y.J. Chen, K.A. Martemyanov, N. Quillinan, V.Y. Arshavsky, T.G. Wensel, C.K. Chen, M.E. Burns, RGS expression rate-limits recovery of rod photoresponses. Neuron 51, 409–416 (2006)CrossRefGoogle Scholar
  22. 22.
    C.K. Chen, M.L. Woodruff, F.S. Chen, D. Chen, G.L. Fain, Background light produces a recoverin-dependent modulation of activated-rhodopsin lifetime in mouse rods. J. Neurosci. 30, 1213–1220 (2010)CrossRefGoogle Scholar
  23. 23.
    W.H. Cobbs, E.N. Pugh Jr., Kinetics and components of the flash photocurrent of isolated retinal rods of the larval salamander, Ambystoma tigrinum. J. Physiol. 394, 529–572 (1987)CrossRefGoogle Scholar
  24. 24.
    P. Bisegna, G. Caruso, D. Andreucci, L. Shen, V.V. Gurevich, H.E. Hamm, E. DiBenedetto, Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys. J. 94, 3363–3383 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    F. Rieke, D.A. Baylor, Origin of reproducibility in the responses of retinal rods to single photons. Biophys. J. 75, 1836–1857 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    U.B. Kaupp, R. Seifert, Cyclic nucleotide-gated ion channels. Physiol. Rev. 82(3), 769–824 (2002)CrossRefGoogle Scholar
  27. 27.
    E. Eismann, F. Müller, S.H. Heinemann, U.B. Kaupp, A single negative charge within the pore region of a cGMP-gated channel controls rectification, Ca2+ blockage, and ionic selectivity. Proc. Natl. Acad. Sci. U.S.A. 91(3), 1109–1113 (1994)ADSCrossRefGoogle Scholar
  28. 28.
    K.W. Yau, D.A. Baylor, Cyclic GMP activated conductance of retinal photoreceptor cells. Annu. Rev. Neurosci. 12, 289–327 (1989)CrossRefGoogle Scholar
  29. 29.
    F. Rieke, D.A. Baylor, Single photon detection by rod cells of the retina. Rev. Mod. Phys. 70, 1027–1036 (1998)ADSCrossRefGoogle Scholar
  30. 30.
    T. Doan, A. Mendez, P.B. Detwiler, J. Chen, F. Rieke, Multiple phosphorylation sites confer reproducibility of the rod’s single-photon responses. Science 313, 530–533 (2006). PMID: 16873665, http://dx.doi.org/10.1126/science.1126612ADSCrossRefGoogle Scholar
  31. 31.
    A.W. Azevedo, T. Doan, H. Moaven, I. Sokal, F. Baameur, S.A. Vishnivetskiy, K.T. Homan, J.J. Tesmer, V.V. Gurevich, J. Chen, F. Rieke, C-terminal threonines and serines play distinct roles in the desensitization of rhodopsin, a G protein-coupled receptor. Elife 4 (2015).  https://doi.org/10.7554/elife.05981
  32. 32.
    V. Torre, H.R. Matthews, T.D. Lamb, Role of calcium in regulating the cyclic GMP cascade of phototransduction in retinal rods. Proc. Natl. Acad. Sci. U.S.A. 83(18), 7109–7113 (1986)ADSCrossRefGoogle Scholar
  33. 33.
    M. Capovilla, L. Cervetto, V. Torre, The effect of phosphodiesterase inhibitors on the electrical activity of toad rods. J. Physiol. 343, 277–294 (1983)CrossRefGoogle Scholar
  34. 34.
    M. Capovilla, L. Cervetto, V. Torre, Effects of changing external potassium and chloride concentrations on the photoresponses of Bufo bufo rods. J. Physiol. 307, 529–551 (1980)CrossRefGoogle Scholar
  35. 35.
    E.N. Pugh Jr., T.D. Lamb, Amplification and kinetics of the activation steps in phototransduction. Biochim. Biophys. Acta 1141(2–3), 111–149 (1993)CrossRefGoogle Scholar
  36. 36.
    D.A. Baylor, B.J. Nunn, J.L. Schnapf, The photocurrent, noise and spectral sensitivity of rods of the monkey Macaca fascicularis. J. Physiol. 357, 575–607 (1984)CrossRefGoogle Scholar
  37. 37.
    S. Asteriti, S. Grillner, L. Cangiano, A Cambrian origin for vertebrate rods. eLife 4, e07166 (2015).  https://doi.org/10.7554/elife.07166
  38. 38.
    J.R. Sanes, S.L. Zipursky, Design principles of insect and vertebrate visual systems. Neuron 66(1), 15–36 (2010).  https://doi.org/10.1016/j.neuron.2010.01.018CrossRefGoogle Scholar
  39. 39.
    C. Montell, Visual transduction in Drosophila. Annu. Rev. Cell Dev. Biol. 15, 231–268 (1999)CrossRefGoogle Scholar
  40. 40.
    C. Montell, Drosophila visual transduction. Trends Neurosci. 35, 356–363 (2012)CrossRefGoogle Scholar
  41. 41.
    R.C. Hardie, M. Juusola, Phototransduction in Drosophila. Curr. Opin. Neurobiol. 34C, 37–45 (2015)CrossRefGoogle Scholar
  42. 42.
    R.C. Hardie, Phototransduction in Drosophila melanogaster. J. Exp. Biol. 204(Pt 20), 3403–3409 (2001)Google Scholar
  43. 43.
    A. Auerbach, F. Sachs, Flickering of a nicotinic ion channel to a subconductance state. Biophys. J. 42(1), 1–10 (1983)ADSCrossRefGoogle Scholar
  44. 44.
    O. Alvarez, C. Gonzalez, R. Latorre, Counting channels: a tutorial guide on ion channel fluctuation analysis. Adv. Physiol. Educ. 26(1–4), 327–341 (2002)CrossRefGoogle Scholar
  45. 45.
    I. Lestas, G. Vinnicombe, J. Paulsson, Fundamental limits on the suppression of molecular fluctuations. Nature 467, 174–178 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    D.G. Spiller, C.D. Wood, D.A. Rand, M.R. White, Measurement of single-cell dynamics. Nature 465, 736–745 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    P.N. Steinmetz, R.L. Winslow, Optimal detection of flash intensity differences using rod photocurrent observations. Neural Comput. 11(5), 1097–1111 (1999)CrossRefGoogle Scholar
  48. 48.
    R.A. Yotter, D.M. Wilson, A review of photodetectors for sensing light-emitting reporters in biological systems. IEEE Sens. J. 3, 288–303 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    G.N. Gol’tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, Picosecond superconducting single-photon optical detector. Appl. Phys. Lett. 79(6), 705–707 (2001)ADSCrossRefGoogle Scholar
  50. 50.
    M. Dandin, P. Abshire, High signal-to-noise ratio avalanche photodiodes with perimeter field gate and active readout. IEEE Electron Device Lett. 33(4), 570–572 (2012)ADSCrossRefGoogle Scholar
  51. 51.
    K. Kolb, Signal-to-noise ratio of Geiger-mode avalanche photodiode single-photon counting detectors. Opt. Eng. 53(8), 081904 (2014)ADSCrossRefGoogle Scholar
  52. 52.
    J.E. Sulston, E. Schierenberg, J.G. White, J.N. Thomson, The embryonic cell lineage of the nematode Caenorhabditis elegans. Dev. Biol. 100(1), 64–119 (1983)CrossRefGoogle Scholar
  53. 53.
    A.S. Chiang, C.Y. Lin, C.C. Chuang, H.M. Chang, C.H. Hsieh, C.W. Yeh, C.T. Shih, J.J. Wu, G.T. Wang, Y.C. Chen, C.C. Wu, G.Y. Chen, Y.T. Ching, P.C. Lee, C.Y. Lin, H.H. Lin, C.C. Wu, H.W. Hsu, Y.A. Huang, J.Y. Chen, H.J. Chiang, C.F. Lu, R.F. Ni, C.Y. Yeh, J.K. Hwang, Three-dimensional reconstruction of brain-wide wiring networks in Drosophila at single-cell resolution. Curr. Biol. 21(1), 1–11 (2011)CrossRefGoogle Scholar
  54. 54.
    L. Chittka, J. Niven, Are bigger brains better? Curr. Biol. 19, R995–R1008 (2009)CrossRefGoogle Scholar
  55. 55.
    S. Herculano-Houzel, The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost. Proc. Natl. Acad. Sci. U.S.A. 109(Suppl 1), 10661–10668 (2012)CrossRefGoogle Scholar
  56. 56.
    S.M. Wu, Synaptic transmission in the outer retina. Annu. Rev. Physiol. 56, 141–168 (1994)CrossRefGoogle Scholar
  57. 57.
    W. Bialek, W.G. Owen, Temporal filtering in retinal bipolar cells. Elements of an optimal computation? Biophys. J. 58(5), 1227–1233 (1990)ADSCrossRefGoogle Scholar
  58. 58.
    H. Markram, E. Muller, S. Ramaswamy, M.W. Reimann, M. Abdellah, C.A. Sanchez, A. Ailamaki, L. Alonso-Nanclares, N. Antille, S. Arsever, G.A. Kahou, T.K. Berger, A. Bilgili, N. Buncic, A. Chalimourda, G. Chindemi, J.D. Courcol, F. Delalondre, V. Delattre, S. Druckmann, R. Dumusc, J. Dynes, S. Eilemann, E. Gal, M.E. Gevaert, J.P. Ghobril, A. Gidon, J.W. Graham, A. Gupta, V. Haenel, E. Hay, T. Heinis, J.B. Hernando, M. Hines, L. Kanari, D. Keller, J. Kenyon, G. Khazen, Y. Kim, J.G. King, Z. Kisvarday, P. Kumbhar, S. Lasserre, J.V. Le Bé, B.R. Magalhães, A. Merchán-Pérez, J. Meystre, B.R. Morrice, J. Muller, A. Muñoz-Céspedes, S. Muralidhar, K. Muthurasa, D. Nachbaur, T.H. Newton, M. Nolte, A. Ovcharenko, J. Palacios, L. Pastor, R. Perin, R. Ranjan, I. Riachi, J.R. Rodríguez, J.L. Riquelme, C. Rössert, K. Sfyrakis, Y. Shi, J.C. Shillcock, G. Silberberg, R. Silva, F. Tauheed, M. Telefont, M. Toledo-Rodriguez, T. Tränkler, W. Van Geit, J.V. Díaz, R. Walker, Y. Wang, S.M. Zaninetta, J. DeFelipe, S.L. Hill, I. Segev, F. Schürmann, Reconstruction and simulation of neocortical microcircuitry. Cell 163(2), 456–492 (2015)CrossRefGoogle Scholar
  59. 59.
    R.G. Boothe, Perception of the Visual Environmen. Psychology (Springer Science & Business Media, 2001), 408 pages. ISBN: 978-0-387-98790-3 (Print) 978-0-387-21650-8 (Online)Google Scholar
  60. 60.
    A.P. Sampath, F. Rieke, Selective transmission of single photon responses by saturation at the rod-to-rod bipolar synapse. Neuron 41(3), 431–443 (2004)CrossRefGoogle Scholar
  61. 61.
    D. Attwell, S. Borges, S.M. Wu, M. Wilson, Signal clipping by the rod output synapse. Nature 328(6130), 522–524 (1987)ADSCrossRefGoogle Scholar
  62. 62.
    S. Barnes, V. Merchant, F. Mahmud, Modulation of transmission gain by protons at the photoreceptor output synapse. Proc. Natl. Acad. Sci. U.S.A. 90(21), 10081–10085 (1993)ADSCrossRefGoogle Scholar
  63. 63.
    A.J. Mercer, W.B. Thoreson, The dynamic architecture of photoreceptor ribbon synapses: cytoskeletal, extracellular matrix, and intramembrane proteins. Vis. Neurosci. 28(6), 453–471 (2011)CrossRefGoogle Scholar
  64. 64.
    A. Bharioke, D.B. Chklovskii, Automatic adaptation to fast input changes in a time-invariant neural circuit. PLoS Comput. Biol. 11(8), e1004315 (2015).  https://doi.org/10.1371/journal.pcbi.1004315ADSCrossRefGoogle Scholar
  65. 65.
    S.P. Langley, The bolometer and radiant energy, in Proceedings of the American Academy of Arts and Science, vol. 16 (American Academy of Arts & Sciences, May 1880–Jun 1881), pp. 342–358.  https://doi.org/10.2307/25138616, http://www.jstor.org/stable/25138616CrossRefGoogle Scholar
  66. 66.
    J. von Kries, J.A.E. Eyster, Über die zur Erregung des Sehorgans efforderlichen Energiemenzen. Z. Sinnesphysiol. 41, 373–394 (1907)Google Scholar
  67. 67.
    A. Verkhratsky, O.A. Krishtal, O.H. Petersen, From Galvani to patch clamp: the development of electrophysiology. Pflugers Arch. 453(3), 233–247 (2006)CrossRefGoogle Scholar
  68. 68.
    T. Tomita, A. Funaishi, Studies on intraretinal action potential with low-resistance microelectrode. J. Neurophysiol. 15(1), 75–84 (1952)CrossRefGoogle Scholar
  69. 69.
    G.S. Brindley, Responses to illumination recorded by microelectrodes from the frog’s retina. J. Physiol. 134(2), 360–384 (1956)MathSciNetCrossRefGoogle Scholar
  70. 70.
    A.L. Byzov, Functional properties of different cells in the retina of cold-blooded vertebrates. Cold Spring Harb. Symp. Quant. Biol. 30, 547–558 (1965)CrossRefGoogle Scholar
  71. 71.
    S.R. Grabowski, L.H. Pinto, W.L. Pak, Adaptation in retinal rods of axolotl: intracellular recordings. Science 176(4040), 1240–1243 (1972)ADSCrossRefGoogle Scholar
  72. 72.
    R.D. Penn, W.A. Hagins, Signal transmission along retinal rods and the origin of the electroretinographic a-wave. Nature 223(5202), 201–204 (1969)ADSCrossRefGoogle Scholar
  73. 73.
    D.A. Baylor, T.D. Lamb, K.W. Yau, The membrane current of single rod outer segments. J. Physiol. 288, 589–611 (1979)Google Scholar
  74. 74.
    D.A. Baylor, T.D. Lamb, K.W. Yau, Responses of retinal rods to single photons. J. Physiol. 288, 613–634 (1979)Google Scholar
  75. 75.
    R.B. Barnes, M. Czerny, Läßt sich ein Schroteffekt der Photonen mit dem Auge beobachten? Zeitschrift für Physik 79(7), 436–449 (1932)ADSCrossRefGoogle Scholar
  76. 76.
    S. Hecht, S. Shlaer, M.H. Pirenne, Energy, quanta, and vision. J. Gen. Physiol. 25(6), 819–840 (1942)CrossRefGoogle Scholar
  77. 77.
    E. Brumberg, S. Vavilov, Visuelle Messungen der statistischen Photonenschwankungen. Bull. Acad. Sci. U.R.S.S. 7, 919–941 (1933)Google Scholar
  78. 78.
    E.M. Brumberg, S.I. Vavilov, Z.M. Sverdlov, Visual measurements of quantum fluctuations. I. The threshold of vision as compared with the results of fluctuation measurements. J. Phys. 7(1), 1–8 (1943)Google Scholar
  79. 79.
    S.I. Vavilov, T.V. Timofeeva, Visual measurements of quantum fluctuations. II. Fluctuations when the eye is light-adapted. J. Phys. 7(1), 9–11 (1943)Google Scholar
  80. 80.
    S.I. Vavilov, T.V. Timofeeva, Visual measurements of quantum fluctuations. III. The dependence of the visual fluctuations on the wave-length. J. Phys. 7(1), 12–17 (1943)Google Scholar
  81. 81.
    S.I. Vavilov, The Microstructure of Light (Academy of Sciences, Moscow, 1950), p. 198. (in Russian)Google Scholar
  82. 82.
    S. Hecht, S. Shlaer, M.H. Pirenne, Energy at the threshold of vision. Science 93(2425), 585–587 (1941)ADSCrossRefGoogle Scholar
  83. 83.
    R. Gunter, The absolute threshold for vision in the cat. J. Physiol. 114(1–2), 8–15 (1951)CrossRefGoogle Scholar
  84. 84.
    S. Hecht, M.H. Pirenne, The sensibility of the nocturnal long-eared owl in the spectrum. J. Gen. Physiol. 23(6), 709–717 (1940)CrossRefGoogle Scholar
  85. 85.
    M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, W.J. McGill, Multiplication noise in the human visual system at threshold: 1. Quantum fluctuations and minimum detectable energy. J. Opt. Soc. Am. 72, 419–431 (1982)ADSCrossRefGoogle Scholar
  86. 86.
    P.R. Prucnal, M.C. Teich, Multiplication noise in the human visual system at threshold: 2. Probit estimation of parameters. Biol. Cybern. 43, 87–96 (1982)CrossRefGoogle Scholar
  87. 87.
    M.C. Teich, P.R. Prucnal, G. Vannucci, M.E. Breton, W.J. McGill, Multiplication noise in the human visual system at threshold: 3. The role of non-poisson quantum fluctuations. Biol. Cybern. 44, 157–165 (1982)CrossRefGoogle Scholar
  88. 88.
    K.W. Yau, T.D. Lamb, D.A. Baylor, Light-induced fluctuations in membrane current of single toad rod outer segments. Nature 269(5623), 78–80 (1977)ADSCrossRefGoogle Scholar
  89. 89.
    P.B. Detwiler, J.D. Conner, R.D. Bodoia, Gigaseal patch clamp recordings from outer segments of intact retinal rods. Nature 300(5887), 59–61 (1982)ADSCrossRefGoogle Scholar
  90. 90.
    R.D. Bodoia, P.B. Detwiler, Patch-clamp recordings of the light-sensitive dark noise in retinal rods from the lizard and frog. J. Physiol. 367, 183–216 (1985)CrossRefGoogle Scholar
  91. 91.
    J. Toyoda, H. Hashimoto, H. Anno, T. Tomita, The rod response in the frog and studies by intracellular recording. Vis. Res. 10(11), 1093–1100 (1970)CrossRefGoogle Scholar
  92. 92.
    T. Tomita, Electrical activity of vertebrate photoreceptors. Q. Rev. Biophys. 3(2), 179–222 (1970)CrossRefGoogle Scholar
  93. 93.
    J.E. Brown, L.H. Pinto, Ionic mechanism for the photoreceptor potential of the retina of Bufo marinus. J. Physiol. 236(3), 575–591 (1974)CrossRefGoogle Scholar
  94. 94.
    R.R. Birge, R.B. Barlow, On the molecular origins of thermal noise in vertebrate and invertebrate photoreceptors. Biophys. Chem. 55, 115–126 (1995)CrossRefGoogle Scholar
  95. 95.
    N.M. Phan, M.F. Cheng, D.A. Bessarab, L.A. Krivitsky, Interaction of fixed number of photons with retinal rod cells. Phys. Rev. Lett. 112, 213601 (2014)ADSCrossRefGoogle Scholar
  96. 96.
    L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England, 1995)CrossRefGoogle Scholar
  97. 97.
    F.T. Arecchi, Measurement of the statistical distribution of Gaussian and laser sources. Phys. Rev. Lett. 15, 912 (1965)ADSCrossRefGoogle Scholar
  98. 98.
    D.N. Klyshko, Physical Foundations of Quantum Electronics (World Scientific, Singapore, 2011)zbMATHGoogle Scholar
  99. 99.
    N. Sim, D. Bessarab, C.M. Jones, L. Krivitsky, Method of targeted delivery of laser beam to isolated retinal rods by fiber optics. Biomed. Opt. Express 2, 2926–2933 (2011)CrossRefGoogle Scholar
  100. 100.
    A.A. Malygin, A.N. Penin, A.V. Sergienko, Absolute calibration of the sensitivity of photodetectors using a biphotonic field. Sov. Phys. JETP Lett. 33, 477–481 (1981)Google Scholar
  101. 101.
    H. Mutoh, W. Akemann, T. Knöpfel, Genetically engineered fluorescent voltage reporters. ACS Chem. Neurosci. 3, 585–592 (2012)CrossRefGoogle Scholar
  102. 102.
    K.D. Piatkevich, F.V. Subach, V.V. Verkhusha, Engineering of bacterial phytochromes for near-infrared imaging, sensing, and light-control in mammals. Chem. Soc. Rev. 42(8), 3441–3452 (2013)CrossRefGoogle Scholar
  103. 103.
    T. Tolmachova, O.E. Tolmachov, A.R. Barnard, S.R. de Silva, D.M. Lipinski, N.J. Walker, R.E. Maclaren, M.C. Seabra, Functional expression of Rab escort protein 1 following AAV2-mediated gene delivery in the retina of choroideremia mice and human cells ex vivo. J. Mol. Med. (Berl) 91(7), 825–837 (2013)CrossRefGoogle Scholar
  104. 104.
    E. Pomarico, B. Sanguinetti, N. Gisin, R. Thew, H. Zbinden, G. Schreiber, A. Thomas, W. Sohler, Waveguide-based OPO source of entangled photon pairs. New J. Phys. 11, 113042 (2009)ADSCrossRefGoogle Scholar
  105. 105.
    V. Volkov, Discovering electrophysiology in photobiology: a brief overview of several photobiological processes with an emphasis on electrophysiology. Commun. Integr. Biol. 7, e28423 (2014)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Materials Research and EngineeringAgency for Science Technology and Research (A*STAR)SingaporeSingapore
  2. 2.Faculty of Life Sciences and ComputingLondon Metropolitan UniversityLondonUK
  3. 3.Department of Plant SciencesUniversity of CaliforniaDavisUSA

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