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Biological Cybernetics

, Volume 112, Issue 5, pp 403–413 | Cite as

Nonlinearization: naturalistic stimulation and nonlinear dynamic behavior in a spider mechanoreceptor

  • Andrew S. French
  • Keram Pfeiffer
Original Article
  • 62 Downloads

Abstract

In a previous study, we used linear frequency response analysis to show that naturalistic stimulation of spider primary mechanosensory neurons produced different response dynamics than the commonly used Gaussian random noise. We isolated this difference to the production of action potentials from receptor potential and suggested that the different distribution of frequency components in the naturalistic signal increased the nonlinearity of action potential encoding. Here, we tested the relative contributions of first- and second-order processes to the action potential signal by measuring linear and quadratic coherence functions. Naturalistic stimulation shifted the linear coherence toward lower frequencies, while quadratic coherence was always higher than linear coherence and increased with naturalistic stimulation. In an initial attempt to separate the order of time-dependent and nonlinear processes, we fitted quadratic frequency response functions by two block-structured models consisting of a power-law filter and a static second-order nonlinearity in alternate cascade orders. The same cascade models were then fitted to the original time domain data by conventional numerical analysis algorithms, using a polynomial function as the static nonlinearity. Quadratic models with a linear filter followed by a static nonlinearity were favored over the reverse order, but with weak significance. Polynomial nonlinear functions indicated that rectification is a major nonlinearity. A complete quantitative description of sensory encoding in these primary mechanoreceptors remains elusive but clearly requires quadratic and higher nonlinear operations on the input signal to explain the sensitivity of dynamic behavior to different input signal patterns.

Keywords

Mechanotransduction Nonlinear Sensory coding Naturalistic Spider Action potential 

Notes

Acknowledgements

This study was supported by the Canadian Institutes for Health Research and the Natural Sciences and Engineering Council of Canada.

References

  1. Barth FG (2002) A spider’s world, senses and behavior. Springer, BerlinCrossRefGoogle Scholar
  2. Barth FG, Höller A (1999) Dynamics of arthropod filiform hairs. V. The response of spider trichobothria to natural stimuli. Philos Trans R Soc Lond B 354:183–192CrossRefGoogle Scholar
  3. Barth FG, Libera W (1970) Ein Atlas der Spaltsinnesorgane von Cupiennius salei Keys. Chelicerata ( Araneae). Z Morph Tiere 68:343–369CrossRefGoogle Scholar
  4. Bendat JS, Piersol AG (1980) Engineering applications of correlation and spectral analysis. Wiley, New YorkGoogle Scholar
  5. Bewick GS, Banks RW (2015) Mechanotransduction in the muscle spindle. Pflügers Arch 467:175–190CrossRefPubMedCentralPubMedGoogle Scholar
  6. Brown MC, Stein RB (1966) Quantitative studies on the slowly adapting stretch receptor of the crayfish. Kybernetik 3:175–185CrossRefPubMedCentralPubMedGoogle Scholar
  7. Catton WT (1958) Some properties of frog skin mechanoreceptors. J Physiol 141:305–322CrossRefPubMedCentralPubMedGoogle Scholar
  8. Chapman KM, Smith RS (1963) A linear transfer function underlying impulse frequency modulation in a cockroach mechanoreceptor. Nature 197:699–700CrossRefGoogle Scholar
  9. Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Math Comput 19:297–301CrossRefGoogle Scholar
  10. DiCaprio RA, Billimoria CP, Ludwar BCh (2007) Information rate and spike-timing precision of proprioceptive afferents. J Neurophysiol 98:1706–1717CrossRefPubMedCentralPubMedGoogle Scholar
  11. French AS (1980a) Phototransduction in the fly compound eye exhibits temporal resonances and a pure time delay. Nature 283:200–202CrossRefPubMedCentralPubMedGoogle Scholar
  12. French AS (1980b) Sensory transduction in an insect mechanoreceptor: linear and nonlinear properties. Biol Cybern 38:115–123CrossRefGoogle Scholar
  13. French AS, Butz EG (1973) Measuring the Wiener kernels of a non-linear system using the fast Fourier transform algorithm. Int J Control 17:529–539CrossRefGoogle Scholar
  14. French AS, Holden AV (1971) Frequency domain analysis of neurophysiological data. Comput Progr Biomed 1:219–234CrossRefGoogle Scholar
  15. French AS, Marmarelis VZ (1999) Nonlinear analysis of neuronal systems. In: Windhorst U, Johansson H (eds) Modern techniques in neuroscience research. Springer, Berlin, pp 627–640CrossRefGoogle Scholar
  16. French AS, Wong RKS (1977) Nonlinear analysis of sensory transduction in an insect mechanoreceptor. Biol Cybern 26:231–240CrossRefPubMedCentralPubMedGoogle Scholar
  17. French AS, Holden AV, Stein RB (1972) The estimation of the frequency response function of a mechanoreceptor. Kybernetik 11:15–23CrossRefPubMedCentralPubMedGoogle Scholar
  18. French AS, Höger U, Sekizawa S-i, Torkkeli PH (2001) Frequency response functions and information capacities of paired spider mechanoreceptor neurons. Biol Cybern 85:293–300CrossRefPubMedCentralPubMedGoogle Scholar
  19. Gettrup E (1963) Phasic stimulation of a thoracic stretch receptor. J Exp Biol 40:323–333Google Scholar
  20. Gorur-Shandilya S, Demir M, Long J, Clark DA, Emonet T (2017) Olfactory receptor neurons use gain control and complementary kinetics to encode intermittent odorant stimuli. Elife 6:e27670CrossRefPubMedCentralPubMedGoogle Scholar
  21. Hunter IW, Korenberg MJ (1986) The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol Cybern 55:135–144PubMedPubMedCentralGoogle Scholar
  22. Jacobs GA, Miller JP, Aldworth Z (2008) Computational mechanisms of mechanosensory processing in the cricket. J Exp Biol 211:1819–1828CrossRefPubMedCentralPubMedGoogle Scholar
  23. Juusola M, de Polavieja GG (2003) The rate of information transfer of naturalistic stimulation by graded potentials. J Gen Physiol 122:191–206CrossRefPubMedCentralPubMedGoogle Scholar
  24. Juusola M, Weckström M, Uusitalo RO, Korenberg MJ, French AS (1995) Nonlinear models of the first synapse in the light-adapted fly retina. J Neurophysiol 74:2538–2547CrossRefPubMedCentralPubMedGoogle Scholar
  25. Kelly M, Babineau D, Longtin A, Lewis JE (2008) Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs. Biol Cybern 98:479–490CrossRefPubMedCentralPubMedGoogle Scholar
  26. Kim KI (1991) On measuring the system coherency of quadratically nonlinear systems. I EEE Trans Sig Process 39:212–214CrossRefGoogle Scholar
  27. Kim YC, Wong WF, Powers EJ, Roth JR (1979) Extension of the coherence function to quadratic models. Proc IEEE 67:428–429CrossRefGoogle Scholar
  28. Kirkpatrick S, Gelatt CD, Vecchi MP (1883) Optimization by simulated annealing. Science 220:671–680CrossRefGoogle Scholar
  29. Koles ZJ, Smith RS (1974) Characteristics of the sensory discharge of the muscle spindle in Xenopus laevis. Kybernetik 15:99–110CrossRefPubMedCentralPubMedGoogle Scholar
  30. Kondoh Y, Okuma J, Newland PL (1995) Dynamics of neurons controlling movements of a locust hind leg: Wiener kernel analysis of the responses of proprioceptive afferents. J Neurophysiol 73:1829–1842CrossRefPubMedCentralPubMedGoogle Scholar
  31. Korenberg MJ (1990) The identification of nonlinear biological systems: Wiener kernel approaches. Ann Biomed Eng 18:629–654CrossRefPubMedCentralPubMedGoogle Scholar
  32. Korenberg MJ, French AS, Voo SKL (1988) White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches. Biol Cybern 58:313–320CrossRefPubMedCentralPubMedGoogle Scholar
  33. Landgren S (1952) On the excitation mechanism of the carotid baroreceptors. Acta Physiol Scand 26:1–34CrossRefPubMedCentralPubMedGoogle Scholar
  34. Levin JE, Miller JP (1996) Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance. Nature 380:165–168CrossRefPubMedCentralPubMedGoogle Scholar
  35. Lewen GD, Bialek W, de Ruyter van Steveninck R (2001) Neural coding of naturalistic motion stimuli. Network 12:317–329CrossRefPubMedCentralPubMedGoogle Scholar
  36. Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441CrossRefGoogle Scholar
  37. Matthews PBC, Stein RB (1969) The sensitivity of muscle spindle afferents to small sinusoidal changes in length. J Physiol 200:723–743CrossRefPubMedCentralPubMedGoogle Scholar
  38. Miller JP, Jacobs GA, Theunissen FE (1991) Representation of sensory information in the cricket cercal sensory system. I. Response properties of the primary interneurons. J Neurophysiol 66:1680–1689CrossRefPubMedCentralPubMedGoogle Scholar
  39. Molina J, Schaber CF, Barth FG (2009) In search of differences between the two types of sensory cells innervating spider slit sensilla (Cupiennius salei Keys). J Comp Physiol A 195:1031–1041CrossRefGoogle Scholar
  40. Moss F, Pierson D, O’gorman D (1994) Stochastic resonance: tutorial and update. Int J Bifurc Chaos 4:1383–1397CrossRefGoogle Scholar
  41. Pfeiffer K, French AS (2015) Naturalistic stimulation changes the dynamic response of action potential encoding in a mechanoreceptor. Front Physiol 6:303CrossRefPubMedCentralPubMedGoogle Scholar
  42. Poppele RE (1981) An analysis of muscle spindle behaviour using randomly applied stretches. Neuroscience 6:1157–1165CrossRefPubMedCentralPubMedGoogle Scholar
  43. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1990) Numerical recipes in C. The art of scientific computing. Cambridge University Press, CambridgeGoogle Scholar
  44. Pringle JW, Wilson VJ (1952) The response of a sense organ to a harmonic stimulus. J Exp Biol 29:220–234Google Scholar
  45. Rieke F, Bodnar DA, Bialek W (1995) Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents. Proc R Soc Lond B 262:259–265CrossRefGoogle Scholar
  46. Rien D, Kern R, Kurtz R (2013) Octopaminergic modulation of a fly visual motion-sensitive neuron during stimulation with naturalistic optic flow. Front Behav Neurosci 7:155CrossRefPubMedCentralPubMedGoogle Scholar
  47. Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, UrbanaGoogle Scholar
  48. Spekreijse H, Oosting H (1970) Linearizing: a method for analysing and synthesizing nonlinear systems. Kybernetik 7:22–31CrossRefPubMedCentralPubMedGoogle Scholar
  49. Stein RB, French AS, Holden AV (1972) The frequency response, coherence and information capacity of two neural models. Biophys J 12:295–322CrossRefPubMedCentralPubMedGoogle Scholar
  50. Tolhurst DJ, Tadmor Y, Chao T (1992) Amplitude spectra of natural images. Ophthalmic Physiol Opt 12:229–232CrossRefPubMedCentralPubMedGoogle Scholar
  51. Torkkeli PH, French AS (2002) Simulation of different firing patterns in paired spider mechanoreceptor neurons: the role of Na\(^{+}\) channel inactivation. J Neurophysiol 87:1363–1368CrossRefPubMedGoogle Scholar
  52. Torkkeli PH, Meisner S, Pfeiffer K, French AS (2012) GABA and glutamate receptors have different effects on excitability and are differentially regulated by calcium in spider mechanosensory neurons. Eur J Neurosci 36:3602–3614CrossRefPubMedCentralPubMedGoogle Scholar
  53. van Hateren JH (1997) Processing of natural time series of intensities by the visual system of the blowfly. Vis Res 37:3407–3416CrossRefPubMedCentralPubMedGoogle Scholar
  54. van der Schaaf A, van Hateren JH (1996) Modelling the power spectra of natural images: statistics and information. Vis Res 36:2759–2770CrossRefPubMedCentralPubMedGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physiology and BiophysicsDalhousie UniversityHalifaxCanada
  2. 2.Department of Behavioral Physiology and SociobiologyUniversity of WürzburgWürzburgGermany

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