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Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron

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Abstract

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.

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References

  • Av-Ron E (1994) The role of a transient potassium current in a bursting neuron model. J. Math. Biol. 33:71–87.

    Google Scholar 

  • Boekhoff I, Seifert E, Göggerle S, Lindemann M, Krüger B-W, Breer H (1993) Pheromone-induced second-messenger signaling in insect antennae. Insect Biochem. Molec. Biol. 23:757–762.

    Google Scholar 

  • Breer H (1994) Odor recognition and second messenger signaling in olfactory receptor neurons. Seminars in Cell Biol. 5:25–32.

    Google Scholar 

  • Breer H, Boekhoff I, Tareilus E (1990) Rapid kinetics of second messenger formation in olfactory transduction. Nature 345: 65–68.

    Google Scholar 

  • Bressloff, PC (1995) Dynamics of a compartmental model integrate-and-fire neuron with somatic potential reset. Physica D 80:399–412.

    Google Scholar 

  • De Kramer JJ (1985) The electrical circuitry of an olfactory sensillum in Antheraea polyphemus. J. Neurosci. 5:2484–2493.

    Google Scholar 

  • De Kramer JJ, Kaissling K-E, Keil T (1984) Passive electrical properties of insect olfactory sensilla may produce the biphasic shape of spikes. Chem. Senses 8:289–295.

    Google Scholar 

  • Duchamp-Viret P, Duchamp A, Vigouroux M (1989) Amplifying role of convergence in olfactory system: a comparative study of receptor cell and second order neuron sensitivities. J. Neurophysiol. 61:1085–1094.

    Google Scholar 

  • Ennis DM (1991) Molecular mixture models based on competitive and non-competitive agonism. Chem. Senses 16:1–17.

    Google Scholar 

  • Firestein S (1992) Electrical signals in olfactory transduction. Current Opinion Neurobiol. 2:444–448.

    Google Scholar 

  • Gerstner W, van Hemmen JL (1992) Universality in neural networks: The importance of the ‘mean firing rate’. Biol. Cybern. 67:195–205.

    Google Scholar 

  • Getchell TV, Shepherd GM (1978) Responses of olfactory receptor cells to step pulses of odour at different concentrations in the salamander. J. Physiol. Lond. 282:521–540

    Google Scholar 

  • Getz WM, Akers RP (1995) Partitioning non-linearities in the response of honey bee olfactory receptor neurons to binary odors. BioSystems 34:27–40.

    Google Scholar 

  • Hahn I, Scherer PW, Mozell MM (1994) A mass transport model of olfaction. J. Theor. Biol. 167:115–128.

    Google Scholar 

  • Kaissling K-E (1969) Kinetics of olfactory receptor potentials. In: C Pfaffman, ed. Olfaction and Taste III. Rockfeller University Press, New York. pp. 52–70.

    Google Scholar 

  • Kaissling K-E (1971) Insect olfaction. In: LM Beidler, ed. Handbook of sensory physiology. Springer-Verlag, Berlin. pp. 351–431.

    Google Scholar 

  • Kaissling K-E (1977) Structures of odour molecules and multiple activities of receptor cells. In: J Le Magnen, P MacLeod, eds. Olfaction and Taste VI. IRL, London, pp. 9–16.

    Google Scholar 

  • Kaissling K-E (1986) Chemo-electrical transduction in insect olfactory receptors. Ann. Rev. Neurosci. 9:121–145.

    Google Scholar 

  • Kaissling K-E (1987) R.H. Wright lectures on insect olfaction. In: K Colbow, ed. Simon Fraser University, Canada.

    Google Scholar 

  • Kaissling K-E (1990) Antennae and noses: their sensitivities as molecule detectors. In: Borsellino et al., eds. Sensory transduction. Plenum, New York. pp. 81–97.

    Google Scholar 

  • Kaissling K-E (1994) Elementary receptor potentials of insect olfactory cells. In: K Kurihara, N Suzuki, H Ogawa, eds. Olfaction and Taste XI, Springer Verlag, Tokyo. pp. 812–815.

    Google Scholar 

  • Kaissling K-E, Boeckoff I (1993) Transduction and intracellular messengers in pheromone receptor cell of the moth Antheraea polyphemus. In: K Wiese, FG Gribakin, AV Popov, G Renninger, eds. Sensory systems of arthropods. Birkhä user Verlag, Basel. pp. 489–502.

    Google Scholar 

  • Kaissling K-E, Priesner E (1970) Die Riechschwelle des Seidenspinners. Naturwissenschaften 57:23–28.

    Google Scholar 

  • Kaissling K-E, Thornson J (1980) Insect olfactory sensilla: Structural, chemical and electrical aspects of the functional organization. In: DB Sattelle, LM Hall, JG Hildebrand, eds. Receptors for neurotransmitters, hormones and pheromones in insects. Elsevier/North-Holland, Amsterdam, pp. 261–282.

    Google Scholar 

  • Keil T (1984) Reconstruction and morphometry of silkmoth olfactory hairs: A comparative study of sensilla trichodea on the antennae of male Antheraea polyphemus and Antheraea pernyi (Insecta, Lepidoptera). Zoomorphology 104:147–156.

    Google Scholar 

  • Lamb TD, Pugh EN (1992) G-protein cascades: Gain and kinetics. Trends in Neurosci. 15:291–298.

    Google Scholar 

  • Lánský P, Rospars J-P (1993) Coding of odor intensity. BioSystems 31:15–38.

    Google Scholar 

  • Lánský P, Rospars J-P (1995) Ornstein-Uhlenbeck neuron revisited. Biol. Cybern. 72:397–406.

    Google Scholar 

  • Lánský P, Rospars J-P, Vermeulen A (1994) Basic mechanisms of coding stimulus intensity in the olfactory sensory neuron. Neural Processing Letters 1:9–13.

    Google Scholar 

  • Lowe G, Gold GH (1995) Olfactory transduction is intrinsically noisy. Proc. Natl. Acad. Sci. 92:7864–7868.

    Google Scholar 

  • Lundström KI, Karlsson JOG, Svensson SPS, Mårtensson LGE, Elwing H, Ödman S, Andersson RGG (1993) Local and non-local receptor signalling. J. Theor. Biol. 164:135–148.

    Google Scholar 

  • Lynch JW, Barry PH (1989) Action potentials initiated by single channels opening in a small neuron (rat olfactory receptor). Biophys. J. 55:755–768.

    Google Scholar 

  • Malaka R, Ragg T, Hammer M (1995) A model of chemosensory reception. In: G Tesawo, D Touretzky, J Alspector, eds. Advances in neural information processing systems, Vol. 7, Morgan Kaufmann, San Mateo.

    Google Scholar 

  • Menini A, Picco C, Firestein S (1995) Quantal-like current fluctuations induced by odorants in olfactory receptor cells. Nature 373:435–437.

    Google Scholar 

  • Nicolis G, Prigogine I (1977) Selforganization in nonequilibrium systems. Wiley, New York.

    Google Scholar 

  • O'Connel RJ, Mozell MM (1969) Quantitative stimulation of frog olfactory receptors. J. Neurophysiol. 32:51–63.

    Google Scholar 

  • Pongracz F, Firestein S, Shepherd GM (1991) Electrotonic structure of olfactory sensory neurons analyzed by intracellular and whole cell patch techniques. J. Neurophysiol. 65:747–758.

    Google Scholar 

  • Rall W (1977) Core conductor theory and cable properties of neurons. In: ER Kandel, JM Brookhardt, VB Mountcastle, eds. Handbook of physiology: The nervous system, Vol. 1. Williams and Wilkins, Baltimore, pp. 39–98.

    Google Scholar 

  • Rall W (1989) Cable theory for dendritic neurons. In: C Koch, I Segev, eds. Methods in neuronal modeling. MIT Press, Cambridge. pp. 9–62.

    Google Scholar 

  • Rospars J-P, Lánský P (1993) Stochastic model neuron without re-setting of dendritic potential: application to the olfactory system. Biol. Cyb. 69:283–294.

    Google Scholar 

  • Rospars J-P, Lánský P, Vaillant J, Duchamp-Viret P, Duchamp A (1994) Spontaneous activity of first- and second-order neurons in the frog olfactory system. Brain Res. 662:31–44.

    Google Scholar 

  • Rovinsky A, Menzinger M (1993) Dynamics of analog-to-frequency transduction by excitable systems: Sensory receptors. J. Chem. Phys. 98:9155–9166.

    Google Scholar 

  • Schwaber JS, Graves EB, Paton JFR (1993) Computational modeling of neuronal dynamics for systems analysis: application to neurons of the cardiorespiratory NTS in the rat. Brain Res. 604: 126–141.

    Google Scholar 

  • Segev I (1992) Single neurone models: oversimple, complex and reduced. Trends in Neurosci. 15:414–421.

    Google Scholar 

  • Segundo JP, Vibert J-F, Pakdaman K, Stiber M, Diez Martínez O (1994) Noise and the neurosciences: a long history, a recent revival and some theory. In: K Pribram, ed. Origins: brain and self-organization. Lawrence Erlbaum, Hillsdale, NJ, pp. 300–331.

    Google Scholar 

  • Selzer R (1984) On the specificities of antennal olfactory receptor cells of Periplaneta americana. Chem. Senses 8:375–395.

    Google Scholar 

  • Shepherd GM (1994) Discrimination of molecular signals by the olfactory receptor neuron. Neuron 13:771–790.

    Google Scholar 

  • Shirsat N, Siddiqi O (1993) Olfaction in invertebrates. Current Opinion Neurobiol. 3:553–557.

    Google Scholar 

  • Stengl M, Hatt H, Breer H (1992) Peripheral processes in insect olfaction. Ann. Rev. Physiol. 54:665–681.

    Google Scholar 

  • Tateda H (1967) Sugar receptor and α-amino acid in the rat. In: T Hayashi, ed. Olfaction and Taste II, Pergamon Press. pp. 383–397.

  • Tuckwell HC (1988) Introduction to theoretical Neurobiology. Cambridge University Press, New York.

    Google Scholar 

  • Tuckwell HC, Rospars J-P, Vermeulen A, Lánský P (1995) Time-dependent solutions for a cable model of an olfactory receptor neuron. Submitted.

  • Vareschi E (1971) Duftunterscheidung bei der Honigbiene. Einzelzell-Ableitungen und Verhaltensreaktionen. Z. Vergl. Physiol. 75:143–173.

    Google Scholar 

  • Vermeulen A, Rospars J-P, Lánský P, Tuckwell HC (1995) Coding of stimulus intensity in an olfactory receptor neuron: role of neuron spatial extension and dendritic backpropagation of action potentials. Bull. Math. Biol. In press.

  • Wilson MA, Bower JM (1989) The simulation of large-scale neural networks. In: C Koch, I Segev, eds. Methods in neuronal modeling. MIT Press, Cambridge, MA. pp. 291–333.

    Google Scholar 

  • Yamada WM, Koch C, Adams PR (1989) Multiple channels and calcium dynamics. In: C Koch, I Segev, eds. Methods in neuronal modeling. MIT Press, Cambridge, MA. pp. 97–133.

    Google Scholar 

  • Yu X, Lewis ER (1989) Studies with spike initiators: linearizations by noise allows continuous signal modulation in neural networks. IEEE Trans. Biomed. Eng. 36:36–43.

    Google Scholar 

  • Zufall F, Stengl M, Franke C, Hildebrand JG, Hatt H (1991) Ionic currents of cultured olfactory receptor neurons from antennae of male Manduca sexta. J. Neurosci. 11:956–965.

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Biométrie, Institut National de la Recherche Agronomique, 78026, Versailles Cedex, France

    Jean-Pierre Rospars

  2. Institute of Physiology and Center for Theoretical Study, Academy of Sciences of the Czech Republic, 4, Prague, Czech Republic

    Petr Lánský

  3. School of Mathematical Sciences, Institute for Advanced Studies, Australian National University, 0200, Canberra, ACT, Australia

    Henry C. Tuckwell

  4. Laboratoire de Biométrie, Institut National de la Recherche Agronomique, 78026, Versailles Cedex, France

    Henry C. Tuckwell

  5. Laboratoire de Biométrie, Institut National de la Recherche Agronomique, 78026, Versailles Cedex, France

    Arthur Vermeulen

  6. Laboratoire de Traitement d'Images et Reconnaissance de Formes, Institut National Polytechnique, 38031, Grenoble Cedex, France

    Arthur Vermeulen

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  1. Jean-Pierre Rospars
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  3. Henry C. Tuckwell
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  4. Arthur Vermeulen
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Rospars, JP., Lánský, P., Tuckwell, H.C. et al. Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron. J Comput Neurosci 3, 51–72 (1996). https://doi.org/10.1007/BF00158337

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  • DOI: https://doi.org/10.1007/BF00158337

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