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System identification of Drosophila olfactory sensory neurons


The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron’s response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.

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Bayesian Adaptive Regression Splines


Dipropylene glycol






Maximally informative dimensions


Olfactory sensory neuron


Photoionization detector


Peristimulus time histogram


Reverse correlation


Root-mean-square error


Spike-triggered average


Spike-triggered covariance


  1. Aertsen, A. M. H. J., & Johannesma, P. I. M. (1981). The spectro-temporal receptive field. A functional characteristic of auditory neurons. Biological Cybernetics, 42, 13343.

    Google Scholar 

  2. Aguera y Arcas, B., & Fairhall, A. (2003). What causes a neuron to spike? Neural Computation, 15, 1789–1807.

    Article  PubMed  Google Scholar 

  3. Bau, J., Justus, K., & Carde, R. (2002) Antennal resolution of pulsed pheromone plumes in three moth species. Journal of Insect Physiology, 48(4), 433–442.

    CAS  Article  PubMed  Google Scholar 

  4. Berry, M. J., & Meister, M. (1998). Refractoriness and neural precision. Journal of Neuroscience, 18, 2200–2211.

    CAS  PubMed  Google Scholar 

  5. Brenner, N., Bialek, W., & de Ruyter van Steveninck, R. (2000). Statistical properties of spike trains: Universal and stimulus-dependent aspects. Neuron, 26(3), 695–702.

    CAS  Article  PubMed  Google Scholar 

  6. Bussgang, J. (1952). Crosscorrelation functions of amplitude-distorted Gaussian signals (Vol. 16, p. 3). Technical Report, Research Laboratory Of Electronics, MIT.

  7. Clyne, P., Grant, A., O’Connell, R., & Carlson, J. (1997). Odorant response of individual sensilla on the Drosophila antenna. Invertebrate Neuroscience, 3(2), 127–135.

    CAS  Article  PubMed  Google Scholar 

  8. de Bruyne, M., Foster, K., & Carlson, J. (2001). Odor coding in the drosophila antenna. Neuron, 30(2), 537–552.

    Article  PubMed  Google Scholar 

  9. Dougherty, D. P., Wright, G. A., & Yew, A. C. (2005). Computational model of the cA.M.P.-mediated sensory response and calcium-dependent adaptation in vertebrate olfactory receptor neurons. PNAS, 102, 2415.

    Google Scholar 

  10. Fairhall, A. L., Burlingame, C. A., Narasimhan, R., Harris, R. A., Puchalla, J. L., & Berry, M. J. (2006). Selectivity for multiple stimulus features in retinal ganglion cells. Journal of Neurophysiology, 96(5), 2724–2738.

    Article  PubMed  Google Scholar 

  11. French, A. S., & Meisner, S. (2007). A new method for wide frequency range dynamic olfactory stimulation and characterization. Chemical Senses, 32(7), 681–688.

    CAS  Article  PubMed  Google Scholar 

  12. Geffen, M. N., Broome, B. M., Laurent, G., & Meister, M. (2009). Neural encoding of rapidly fluctuating odors. Neuron, 61(4), 570–586.

    CAS  Article  PubMed  Google Scholar 

  13. Gomez, G., Voigt, R., & Atema, J. (1999). Temporal resolution in olfaction III: Flicker fusion and concentration-dependent synchronization with stimulus pulse trains of antennular chemoreceptor cells in the American lobster. Journal of Comparative Physiology A, 185(5), 427–436.

    Article  Google Scholar 

  14. Gu, Y., Lucas, P., & Rospars, J.-P. (2009). Computational model of the insect pheromone transduction cascade. PLoS Computers in Biology, 5(3), e100321.

    Google Scholar 

  15. Halnes, G., Ulfhielm, E., Ljunggren, E. E., Kotaleski, J. H., & Rospars, J.-P. (2009). Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of Computational Neuroscience, 27, 471.

    Article  PubMed  Google Scholar 

  16. Hinterwirth, A., Zeiner, R., & Tichy, H. (2004). Olfactory receptor cells on the cockroach antennae: Responses to the direction and rate of change in food odour concentration. European Journal of Neuroscience, 19, 3389–3392.

    Article  PubMed  Google Scholar 

  17. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation. Journal of Physiology, 117, 500–557.

    CAS  PubMed  Google Scholar 

  18. Hunter, I. W., & Korenberg, M. J. (1986). The identification of nonlinear biological systems: Wiener and hammerstein cascade models. Biological Cybernetics 55(2–3), 135–144.

    CAS  PubMed  Google Scholar 

  19. Justus, K., Carde, R., & French, A. S. (2005). Dynamic properties of antennal responses to pheromone in two moth species. Journal of Neurophysiology, 93, 2233–2239.

    CAS  Article  PubMed  Google Scholar 

  20. Kaissling, K.-L. (2009). Olfactory perireceptor and receptor events in moths: A kinetic model revised. Journal of Comparative Physiology, 195, 895.

    CAS  Article  PubMed  Google Scholar 

  21. Kass, R. E., Ventura, V., & Cai, C. (2003). Statistical smoothing of neuronal data. Network: Computation in Neural Systems, 14, 5–15.

    Article  Google Scholar 

  22. Kass, R. E., Ventura, V., & Brown, E. N. (2005) Statistical issues in the analysis of neuronal data. Journal of Neurophysiology, 94, 8–25.

    Article  PubMed  Google Scholar 

  23. Keat, J., Reinagel, P., Reid, R. C., & Meister, M. (2001). Predicting every spike: A model for the responses of visual neurons. Neuron, 30(3), 803–817.

    CAS  Article  PubMed  Google Scholar 

  24. Lemon, W., & Getz, W. (1997). Temporal resolution of general odor pulses by olfactory sensory neurons in American cockroaches. Journal of Experimental Biology, 200(Pt 12), 1809–1819.

    PubMed  Google Scholar 

  25. Lindemann, B. (2001). Predicted profiles of ion concentrations in olfactory cilia in the steady state Biophysical Journal, 80, 1712.

    CAS  Article  PubMed  Google Scholar 

  26. Loftus, R. (1969). Differential thermal components in the response of the antennal cold receptor of Periplaneta americana to slowly changing temperature. Journal of Comparative Physiology A, 63(4), 415–433.

    Google Scholar 

  27. Marmarelis, V. (2004). Nonlinear dynamic modeling of physiological systems. Wiley-IEEE Press.

  28. Marmarelis, P. Z., & Naka, K. (1972). White-noise analysis of a neuron chain: An application of the Wiener theory. Science, 175(27), 1276–1278

    CAS  Article  PubMed  Google Scholar 

  29. Paninski, L. (2003). Convergence properties of three spike-triggered analysis techniques. Network: Computation in Neural Systems, 14(3), 437–464.

    Article  Google Scholar 

  30. Paninski, L., Lau, B., & Reyes, A. (2003) Noise-driven adaptation: In vitro and mathematical analysis. Neurocomputing, 52, 877–883.

    Article  Google Scholar 

  31. Pillow, J. (2007). Likelihood-based approaches to modeling the neural code. In: Bayesian brain: Probabilistic approaches to neural coding (chap. 3). MIT Press.

  32. Pillow, J., & Simoncelli, E. (2006). Dimensionality reduction in neural models: An information-theoretic generalization of the spike-triggered average and covariance analysis. Journal of Vision, 6, 414–428.

    Article  PubMed  Google Scholar 

  33. Reich, D., Victor, J., & Knight, B. (1998). The power ratio and the interval map: Spiking models and extracellular recordings. Journal of Neuroscience, 18, 10,090–10,104.

    Google Scholar 

  34. Reidl, J., Borowski, P., Sensse, A., Starke, J., Zapotocky, M., & Eiswirth, M. (2006). Model of calcium oscillations due to negative feedback in olfactory cilia. Biophysical Journal, 90, 1147.

    CAS  Article  PubMed  Google Scholar 

  35. Rospars, J.-P., Lansky, P., Duchamp, A., & Duchamp-Viret, P. (2003). Relation between stimulus and response in frog olfactory receptor neurons in vivo. European Journal of Neuroscience, 18, 1135.

    Article  PubMed  Google Scholar 

  36. Rust, N. C., Mante, V., Simoncelli, E. P., & Movshon, J. A. (2006). How MT cells analyze the motion of visual patterns. Nature Neuroscience, 9(11), 1421–1431.

    CAS  Article  PubMed  Google Scholar 

  37. Schuckel, J., Meisner, S., Torkkeli, P., & French, A. S. (2008). Dynamic properties of Drosophila olfactory electroantennograms. Journal of Comparative Physiology A, 194, 483–489.

    Article  Google Scholar 

  38. Schwartz, O., Pillow, J. W., Rust, N. C., & Simoncelli, E. P. (2006). Spike-triggered neural characterization. Journal of Vision 6(4), 484–507.

    Article  PubMed  Google Scholar 

  39. Sharpee, T., Rust, N. C., & Bialek, W. (2004). Analyzing neural responses to natural signals: Maximally informative dimensions. Neural Computation 16(2), 223–250.

    Article  PubMed  Google Scholar 

  40. Slee, S., Higgs, M., Fairhall, A., & Spain, W. (2005). Two-dimensional time coding in the auditory brainstem. Journal of Neuroscience, 25(43), 9978–9988.

    CAS  Article  PubMed  Google Scholar 

  41. Steveninck, R. V., & Bialek, W. (1988). Real-time performance of a movement-sensitive neuron in the blowfly visual system: Coding and information transfer in short spike sequences. Proceedings of the Royal Society of London Series B, 24, 379–414.

    Article  Google Scholar 

  42. Tichy, H. (2003). Low rates of change enhance effect of humidity on the activity of insect hygroreceptors. Journal of Comparative Physiology A, 189, 175–179.

    CAS  Google Scholar 

  43. Tichy, H., Hinterwirth, A., & Gingl, E. (2005). Olfactory receptors on the cockroach antenna signal odour ON and odour OFF by excitation. European Journal of Neuroscience, 22, 3147–3160.

    Article  PubMed  Google Scholar 

  44. Victor, J. D. (2005). Analyzing receptive fields, classification images and functional images: Challenges with opportunities for synergy. Nature Neuroscience, 8, 1651–1656.

    CAS  Article  PubMed  Google Scholar 

  45. Victor, J., & Shapley, R. (1980). A. method of nonlinear analysis in the frequency domain. Biophysical Journal, 29, 459–484.

    CAS  Article  PubMed  Google Scholar 

  46. Wiener, N. (1958). Nonlinear problems in random theory. MIT Press.

  47. Wu, M., David, S., & Gallant, J. (2006). Complete functional characterization of sensory neurons by system identification. Annual Review of Neuroscience, 29, 477–505.

    CAS  Article  PubMed  Google Scholar 

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The work presented here was supported by NIH under grant number R01DC008701-01 and was conducted in the Axel laboratory at Columbia University. The authors would like to thank Dr. Richard Axel for insightful discussions and for his outstanding support. The authors would like to also thank the reviewers for their suggestions for improving the presentation of the paper.

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Correspondence to Aurel A. Lazar.

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Kim, A.J., Lazar, A.A. & Slutskiy, Y.B. System identification of Drosophila olfactory sensory neurons. J Comput Neurosci 30, 143–161 (2011).

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  • System identification
  • Olfactory sensory neurons
  • White noise analysis
  • I/O modeling