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A probabilistic approach to demixing odors

Abstract

The olfactory system faces a hard problem: on the basis of noisy information from olfactory receptor neurons (the neurons that transduce chemicals to neural activity), it must figure out which odors are present in the world. Odors almost never occur in isolation, and different odors excite overlapping populations of olfactory receptor neurons, so the central challenge of the olfactory system is to demix its input. Because of noise and the large number of possible odors, demixing is fundamentally a probabilistic inference task. We propose that the early olfactory system uses approximate Bayesian inference to solve it. The computations involve a dynamical loop between the olfactory bulb and the piriform cortex, with cortex explaining incoming activity from the olfactory receptor neurons in terms of a mixture of odors. The model is compatible with known anatomy and physiology, including pattern decorrelation, and it performs better than other models at demixing odors.

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Figure 1: Circuit diagram.
Figure 2: Evolution of activity in the mean concentration cells (the ) when three odors are presented.
Figure 3: Probability of odor presence and inferred concentration.
Figure 4: Activity in response to a single odor whose concentration is equal to 3, the mean concentration of present odors.
Figure 5: Performance of the model when detecting a known odor (target) against background odors.
Figure 6: Evolution of pattern correlations in our model.
Figure 7: Generalized ROC curves.

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References

  1. Su, C.-Y., Menuz, K. & Carlson, J.R. Olfactory perception: receptors, cells, and circuits. Cell 139, 45–59 (2009).

    Article  CAS  Google Scholar 

  2. Rokni, D., Hemmelder, V., Kapoor, V. & Murthy, V.N. An olfactory cocktail party: figure-ground segregation of odorants in rodents. Nat. Neurosci. 17, 1225–1232 (2014).

    Article  CAS  Google Scholar 

  3. Malnic, B., Hirono, J., Sato, T. & Buck, L.B. Combinatorial receptor codes for odors. Cell 96, 713–723 (1999).

    Article  CAS  Google Scholar 

  4. Pouget, A., Beck, J.M., Ma, W.J. & Latham, P.E. Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16, 1170–1178 (2013).

    Article  CAS  Google Scholar 

  5. Li, Z. A model of olfactory adaptation and sensitivity enhancement in the olfactory bulb. Biol. Cybern. 62, 349–361 (1990).

    Article  CAS  Google Scholar 

  6. Hendin, O., Horn, D. & Tsodyks, M.V. Associative memory and segmentation in an oscillatory neural model of the olfactory bulb. J. Comput. Neurosci. 5, 157–169 (1998).

    Article  CAS  Google Scholar 

  7. Li, Z. & Hertz, J. Odour recognition and segmentation by a model olfactory bulb and cortex. Network 11, 83–102 (2000).

    Article  CAS  Google Scholar 

  8. Hopfield, J.J. Olfactory computation and object perception. Proc. Natl. Acad. Sci. USA 88, 6462–6466 (1991).

    Article  CAS  Google Scholar 

  9. Hendin, O., Horn, D. & Hopfield, J.J. Decomposition of a mixture of signals in a model of the olfactory bulb. Proc. Natl. Acad. Sci. USA 91, 5942–5946 (1994).

    Article  CAS  Google Scholar 

  10. Connelly, T., Savigner, A. & Ma, M. Spontaneous and sensory-evoked activity in mouse olfactory sensory neurons with defined odorant receptors. J. Neurophysiol. 110, 55–62 (2013).

    Article  CAS  Google Scholar 

  11. Beck, J., Heller, K. & Pouget, A. Complex inference in neural circuits with probabilistic population codes and topic models. in Advances in Neural Information Processing Systems 25 (Curran Associates, 2012).

  12. Grabska-Barwińska, A., Beck, J., Pouget, A. & Latham, P. Demixing odors – fast inference in olfaction. in Advances in Neural Information Processing Systems 26 (Curran Associates, 2013).

  13. Egger, V., Svoboda, K. & Mainen, Z.F. Mechanisms of lateral inhibition in the olfactory bulb: efficiency and modulation of spike-evoked calcium influx into granule cells. J. Neurosci. 23, 7551–7558 (2003).

    Article  CAS  Google Scholar 

  14. Weiss, Y., Simoncelli, E.P. & Adelson, E.H. Motion illusions as optimal percepts. Nat. Neurosci. 5, 598–604 (2002).

    Article  CAS  Google Scholar 

  15. Shepherd, G. (ed.) The Synaptic Organization of the Brain 5th edn. (Oxford Univ. Press, 2004).

  16. Fukunaga, I., Berning, M., Kollo, M., Schmaltz, A. & Schaefer, A.T. Two distinct channels of olfactory bulb output. Neuron 75, 320–329 (2012).

    Article  CAS  Google Scholar 

  17. Igarashi, K.M. et al. Parallel mitral and tufted cell pathways route distinct odor information to different targets in the olfactory cortex. J. Neurosci. 32, 7970–7985 (2012).

    Article  CAS  Google Scholar 

  18. Spors, H. et al. Illuminating vertebrate olfactory processing. J. Neurosci. 32, 14102–14108 (2012).

    Article  CAS  Google Scholar 

  19. Koulakov, A.A. & Rinberg, D. Sparse incomplete representations: a potential role of olfactory granule cells. Neuron 72, 124–136 (2011).

    Article  CAS  Google Scholar 

  20. Fuentes, R.A., Aguilar, M.I., Aylwin, M.L. & Maldonado, P.E. Neuronal activity of mitral-tufted cells in awake rats during passive and active odorant stimulation. J. Neurophysiol. 100, 422–430 (2008).

    Article  Google Scholar 

  21. Cury, K.M. & Uchida, N. Robust odor coding via inhalation-coupled transient activity in the mammalian olfactory bulb. Neuron 68, 570–585 (2010).

    Article  CAS  Google Scholar 

  22. Shusterman, R., Smear, M.C., Koulakov, A.A. & Rinberg, D. Precise olfactory responses tile the sniff cycle. Nat. Neurosci. 14, 1039–1044 (2011).

    Article  CAS  Google Scholar 

  23. Gschwend, O. et al. Neuronal pattern separation in the olfactory bulb improves odor discrimination learning. Nat. Neurosci. 18, 1474–1482 (2015).

    Article  CAS  Google Scholar 

  24. Moulton, D. Electrical activity in the olfactory system of rabbits with indwelling electrodes. in Wenner-Gren Center International Symposium Series vol. 1, 71–84 (Pergamon, 1963).

  25. Otazu, G.H., Chae, H., Davis, M.B. & Albeanu, D.F. Cortical feedback decorrelates olfactory bulb output in awake mice. Neuron 86, 1461–1477 (2015).

    Article  CAS  Google Scholar 

  26. Jinks, A. & Laing, D.G. A limit in the processing of components in odour mixtures. Perception 28, 395–404 (1999).

    Article  CAS  Google Scholar 

  27. Mathis, A., Rokni, D., Kapoor, V., Bethge, M. & Murthy, V.N. Reading out olfactory receptors: Feedforward circuits detect odors in mixtures without demixing. Neuron 91, 1110–1123 (2016).

    Article  CAS  Google Scholar 

  28. Friedrich, R.W. & Laurent, G. Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science 291, 889–894 (2001).

    Article  CAS  Google Scholar 

  29. Gschwend, O., Beroud, J. & Carleton, A. Encoding odorant identity by spiking packets of rate-invariant neurons in awake mice. PLoS One 7, e30155 (2012).

    Article  CAS  Google Scholar 

  30. Uchida, N. & Mainen, Z.F. Speed and accuracy of olfactory discrimination in the rat. Nat. Neurosci. 6, 1224–1229 (2003).

    Article  CAS  Google Scholar 

  31. Shen, K., Tootoonian, S. & Laurent, G. Encoding of mixtures in a simple olfactory system. Neuron 80, 1246–1262 (2013).

    Article  CAS  Google Scholar 

  32. Luo, S.X., Axel, R. & Abbott, L.F. Generating sparse and selective third-order responses in the olfactory system of the fly. Proc. Natl. Acad. Sci. USA 107, 10713–10718 (2010).

    Article  CAS  Google Scholar 

  33. Druckmann, S., Hu, T. & Chklovskii, D.B. A mechanistic model of early sensory processing based on subtracting sparse representations. in Advances in Neural Information Processing Systems 25, 1979–1987 (Curran Associates, 2012).

    Google Scholar 

  34. Tootoonian, S. & Lengyel, M. A dual algorithm for olfactory computation in the locust brain. In Advances in Neural Information Processing Systems 27, 2276–2284 (Curran Associates, 2014).

    Google Scholar 

  35. Baird, B. Nonlinear dynamics of pattern formation and pattern recognition in rabbit olfactory bulb. Physica 22D, 150–175 (1986).

    Google Scholar 

  36. Erdi, P., Gröbler, T., Barna, G. & Kaski, K. Dynamics of the olfactory bulb: bifurcations, learning, and memory. Biol. Cybern. 69, 57–66 (1993).

    Article  CAS  Google Scholar 

  37. Freeman, W.J. Nonlinear dynamics of paleocortex manifested in the olfactory EEG. Biol. Cybern. 35, 21–37 (1979).

    Article  CAS  Google Scholar 

  38. Freeman, W.J. EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb. Biol. Cybern. 35, 221–234 (1979).

    Article  CAS  Google Scholar 

  39. Li, Z. & Hopfield, J.J. Modeling the olfactory bulb and its neural oscillatory processings. Biol. Cybern. 61, 379–392 (1989).

    Article  CAS  Google Scholar 

  40. Yao, Y. & Freeman, W.J. Model of biological pattern recognition with spatially chaotic dynamics. Neural Netw. 3, 153–170 (1990).

    Article  Google Scholar 

  41. Hendin, O., Horn, D. & Tsodyks, M.V. The role of inhibition in an associative memory model of the olfactory bulb. J. Comput. Neurosci. 4, 173–182 (1997).

    Article  CAS  Google Scholar 

  42. Brody, C.D. & Hopfield, J.J. Simple networks for spike-timing-based computation, with application to olfactory processing. Neuron 37, 843–852 (2003).

    Article  CAS  Google Scholar 

  43. Polese, D., Martinelli, E., Marco, S., Di Natale, C. & Gutierrez-Galvez, A. Understanding odor information segregation in the olfactory bulb by means of mitral and tufted cells. PLoS One 9, e109716 (2014).

    Article  Google Scholar 

  44. Arevian, A.C., Kapoor, V. & Urban, N.N. Activity-dependent gating of lateral inhibition in the mouse olfactory bulb. Nat. Neurosci. 11, 80–87 (2008).

    Article  CAS  Google Scholar 

  45. Cleland, T.A. Early transformations in odor representation. Trends Neurosci. 33, 130–139 (2010).

    Article  CAS  Google Scholar 

  46. Cleland, T.A. & Linster, C. On-center/inhibitory-surround decorrelation via intraglomerular inhibition in the olfactory bulb glomerular layer. Front. Integr. Neurosci. 6, 5 (2012).

    Article  Google Scholar 

  47. Wiechert, M.T., Judkewitz, B., Riecke, H. & Friedrich, R.W. Mechanisms of pattern decorrelation by recurrent neuronal circuits. Nat. Neurosci. 13, 1003–1010 (2010).

    Article  CAS  Google Scholar 

  48. Hopfield, J.J. Odor space and olfactory processing: collective algorithms and neural implementation. Proc. Natl. Acad. Sci. USA 96, 12506–12511 (1999).

    Article  CAS  Google Scholar 

  49. Kato, H.K., Chu, M.W., Isaacson, J.S. & Komiyama, T. Dynamic sensory representations in the olfactory bulb: modulation by wakefulness and experience. Neuron 76, 962–975 (2012).

    Article  CAS  Google Scholar 

  50. Zhaoping, L. Olfactory object recognition, segmentation, adaptation, target seeking, and discrimination by the network of the olfactory bulb and cortex: computational model and experimental data. Curr. Opin. Behav. Sci. 11, 30–39 (2016).

    Article  Google Scholar 

  51. Firestein, S. & Werblin, F. Odor-induced membrane currents in vertebrate-olfactory receptor neurons. Science 244, 79–82 (1989).

    Article  CAS  Google Scholar 

  52. Wachowiak, M. & Cohen, L.B. Representation of odorants by receptor neuron input to the mouse olfactory bulb. Neuron 32, 723–735 (2001).

    Article  CAS  Google Scholar 

  53. Bozza, T., Feinstein, P., Zheng, C. & Mombaerts, P. Odorant receptor expression defines functional units in the mouse olfactory system. J. Neurosci. 22, 3033–3043 (2002).

    Article  CAS  Google Scholar 

  54. Grosmaitre, X., Vassalli, A., Mombaerts, P., Shepherd, G.M. & Ma, M. Odorant responses of olfactory sensory neurons expressing the odorant receptor MOR23: a patch clamp analysis in gene-targeted mice. Proc. Natl. Acad. Sci. USA 103, 1970–1975 (2006).

    Article  CAS  Google Scholar 

  55. Mitchell, T. & Beauchamp, J. Bayesian variable selection in linear regression. J. Am. Stat. Assoc. 83, 1023–1032 (1988).

    Article  Google Scholar 

  56. Wainwright, M.J. & Jordan, M.I. Graphical Models, Exponential Families, and Variational Inference, Foundations and Trends Machine Learning (Now Publishers, 2008).

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Acknowledgements

Funding for A.G.-B. and P.E.L. was provided by the Gatsby Charitable Foundation; for Z.F.M. and A.P., by the Human Frontiers Science Programme (RGP0027/2010) and the Simons Foundation (325057); for A.P., by the Swiss National Foundation (31003A_143707).

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A.G.-B., Z.F.M., A.P. and P.E.L conceived the project. A.G.-B., S.B., J.B., A.P. and P.E.L. developed the theory. A.G.-B., S.B., A.P. and P.E.L. wrote the manuscript. A.G.-B. performed the simulations.

Corresponding author

Correspondence to Peter E Latham.

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Grabska-Barwińska, A., Barthelmé, S., Beck, J. et al. A probabilistic approach to demixing odors. Nat Neurosci 20, 98–106 (2017). https://doi.org/10.1038/nn.4444

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