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Journal of Computational Neuroscience

, Volume 17, Issue 2, pp 107–126 | Cite as

Tristate Markov Model for the Firing Statistics of Rapidly-Adapting Mechanoreceptive Fibers

  • Burak Güçlü
  • Stanley J. Bolanowski
Article

Abstract

Rapidly-adapting (RA) mechanoreceptive fibers, which are associated with Meissner corpuscles, mediate one component of the neural information that contributes to the sense of touch. Responses of cat RA fibers subject to 40-Hz sinusoidal stimulation were modeled as a Markov process. Since an RA fiber generates one, two or no spikes in each cycle of the stimulus, the fiber's activity was considered to exist in one of these three possible states. By analyzing empirically generated spike trains, the probability of each state and the probabilities of transitions between the three states were found as a function of the average firing rate of the fiber. The average firing rate depends on the stimulus amplitude. In addition, the phase of each spike with respect to the stimulus cycle was represented by a Laplace distribution. Based on empirical data, the mean and the standard deviation of this distribution decrease as the stimulus amplitude is increased. The entire stochastic model was implemented on a computer to simulate the responses of RA fibers. The post-stimulus time, inter-spike interval and period histograms generated from the simulations match the histograms obtained from the empirical data well as quantified by relative errors. This temporal model can be combined with a population model for average rate to derive a spatio-temporal description of the responses of somatosensory afferents. The effects of changing the stimulation frequency are discussed.

mechanoreceptor rapidly-adapting fiber Meissner corpuscle Markov process sinusoidal response 

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References

  1. Anderson DJ, Rose JE, Hind JE, Brugge JF (1971) Temporal position of discharges in single auditory nerve fibers within the cycle of sine-wave stimulus: Frequency and intensity effects. J. Acoust. Soc. Am. 49: 1131–1139.PubMedGoogle Scholar
  2. Ballard DH (1997) An Introduction to Natural Computation. MIT Press, Cambridge, MA.Google Scholar
  3. Beierholm U, Nielsen CD, Ryge J, Alstrøm P, Kiehn O (2001) Characterization of reliability of spike timing in spinal interneurons during oscillating inputs. J. Neurophysiol. 86: 1858–1868.PubMedGoogle Scholar
  4. Bell J, Holmes M(1992) Model of the dynamics of receptor potential in a mechanoreceptor. Math. Biosci. 110: 139–174.CrossRefPubMedGoogle Scholar
  5. Bensmaïa S (2002) A transduction model of the Meissner corpuscle. Math. Biosci. 176: 203–217.CrossRefPubMedGoogle Scholar
  6. Berry MJ, Warland DK, Meister M (1997) The structure and precision of retinal spike trains. Proc. Natl. Acad. Sci. USA 94: 5411–5416.CrossRefPubMedGoogle Scholar
  7. Birnbaum ZW (1952) Numerical tabulation of the distribution of Kolmogorov's statistic for finite sample size. J. Am. Statist. Assoc. 47: 425–441.Google Scholar
  8. Bolanowski SJ, Gescheider GA, Verrillo RT, Checkosky CM(1988) Four channels mediate the mechanical aspects of touch. J. Acoust.Soc. Am. 84: 1680–1694.PubMedGoogle Scholar
  9. Cohen RH, Vierck CJ Jr (1993) Population estimates for responses of cutaneous mechanoreceptors to a vertically indenting probe on the glabrous skin of monkeys. Exp. Brain Res. 94: 105–119.PubMedGoogle Scholar
  10. Freeman AW, Johnson KO (1982a) Cutaneous mechanoreceptors in macaque monkey: Temporal discharge patterns evoked by vibration, and a receptor model. J. Physiol. 323: 21–41.PubMedGoogle Scholar
  11. Freeman AW, Johnson KO(1982b)Amodel accounting for effects of vibratory amplitude on responses of cutaneous mechanoreceptors in macaque monkey. J. Physiol. 323: 43–64.PubMedGoogle Scholar
  12. Gaumond RP, Molnar CE, Kim DO (1982) Stimulus and recovery dependence of cat cochlear nerve fiber spike discharge probability. J. Neurophysiol. 48: 856–873.PubMedGoogle Scholar
  13. Goodwin AW, Macefield VG, Bisley JW (1997) Encoding of object curvature by tactile afferents from human fingers. J. Neurophysiol. 78: 2881–2888.PubMedGoogle Scholar
  14. Goodwin AW, Youl BD, Zimmerman NP (1981) Single quickly adapting mechanoreceptive afferents innervating monkey glabrous skin: Response to two vibrating probes. J. Neurophysiol. 45: 227–242.PubMedGoogle Scholar
  15. Grandori F, Pedotti A (1982) A mathematical model of the Pacinian corpuscle. Biol. Cybern. 46: 7–16.PubMedGoogle Scholar
  16. Greenspan JD, Bolanowski SJ (1996) The psychophysics of tactile perception and its peripheral physiological basis. In: L Kruger, ed. Handbook of Perception and Cognition 7: Pain and Touch. Academic Press, San Diego, pp. 25–103.Google Scholar
  17. Güclü B, Bolanowski SJ (1999) Population responses of RA mechanoreceptors with hypothetical spatial distributions. Soc. Neurosci. Abstr. 25: 407.Google Scholar
  18. Güclü B, Bolanowski SJ (2001) Statistical comparison of the intensity characteristics of monkey and cat mechanoreceptive RA fibers. Soc. Neurosci. Abstr. 27, Program No: 50.4.Google Scholar
  19. Gü clü B, Bolanowski SJ (2002) Modeling population responses of rapidly-adapting mechanoreceptive fibers. J. Comput. Neurosci. 12: 201–218.CrossRefPubMedGoogle Scholar
  20. Güclü B, Bolanowski SJ (2003a) Distribution of the intensitycharacteristic parameters of cat rapidly adapting mechanoreceptive fibers. Somatosens. Mot. Res. 20: 149–155.CrossRefPubMedGoogle Scholar
  21. Güclü B, Bolanowski SJ (2003b) Time-dependent Markov model for the sinusoidal steady-state response of rapidly-adapting fibers. Soc. Neurosci. Abstr. 29, Program No: 172.16.Google Scholar
  22. Güclü B, Bolanowski SJ (2003c) Correlation of spatial event plots with simulated population responses of mechanoreceptive fibers. Somatosens. Mot. Res. 20: 199–208.CrossRefPubMedGoogle Scholar
  23. Güclü B, Bolanowski SJ (2003d) Frequency responses of cat rapidly adapting mechanoreceptive fibers. Somatosens. Mot. Res. 20: 249–263.CrossRefPubMedGoogle Scholar
  24. Güclü B, Bolanowski SJ (2004) Probability of stimulus detection in a model population of rapidly adapting fibers. Neural Comput. 16: 39–58.CrossRefPubMedGoogle Scholar
  25. Hubbard SJ (1958) A study of rapid mechanical events in a mechanoreceptor. J. Physiol.-London 141: 198–218.PubMedGoogle Scholar
  26. Jänig W, Schmidt RF, Zimmermann M (1968) Single unit responses and the total afferent outflow from the cat's foot pad upon mechanical stimulation. Exp. Brain Res. 6: 100–115.PubMedGoogle Scholar
  27. Johansson RS, Vallbo AB (1979) Tactile sensibility in the human hand: Relative and absolute densities of four types of mechanoreceptive units in glabrous skin. J. Physiol.-London 286: 283–300.PubMedGoogle Scholar
  28. Johnson KO (1974) Reconstruction of population response to a vibratory stimulus in quickly adapting mechanoreceptive afferent fiber population innervating glabrous skin of the monkey. J. Neurophysiol. 37: 48–72.PubMedGoogle Scholar
  29. Lindblom U (1965) Properties of touch receptors in distal glabrous skin of the monkey. J. Neurophysiol. 28: 966–985.PubMedGoogle Scholar
  30. Loewenstein WR, Skalak R (1966) Mechanical tranmission in a Pacinian corpuscle. An analysis and a theory. J. Physiol.-London 182: 346–378.PubMedGoogle Scholar
  31. Looft FJ (1994) Response of monkey glabrous skin mechanoreceptors to random-noise sequences: I. Temporal response characteristics. Somatosens. Mot. Res. 11: 327–344.PubMedGoogle Scholar
  32. Looft FJ (1996a) Response of monkey glabrous skin mechanoreceptors to random noise sequences: II. Dynamic stimulus state analysis. Somatosens. Mot. Res. 13: 11–28.PubMedGoogle Scholar
  33. Looft FJ (1996b) Response of monkey glabrous skin mechanoreceptors to random noise sequences: III. Spectral analysis. Somatosens. Mot. Res. 13: 235–244.PubMedGoogle Scholar
  34. Massey FJ, Jr. (1951) The Kolmogorov-Smirnov test for goodness of fit. J. Am. Statist. Assoc. 46: 68–78.Google Scholar
  35. Mountcastle VB, Talbot WH, Sakata H, Hyvärinen J (1969) Cortical neuronal mechanisms in flutter-vibration studied in unanesthetized monkeys. Neuronal periodicity and frequency discrimination. J. Neurophysiol. 32: 452–484.PubMedGoogle Scholar
  36. Phillips JR, Johnson KO, Hsiao SS (1988) Spatial pattern representation and transformation in monkey somatosensory cortex. Proc. Natl. Acad. Sci. USA 85: 1317–1321.PubMedGoogle Scholar
  37. Reich DS, Victor JD, Knight BW, Ozaki T, Kaplan E(1997) Response variability and timing precision of neuronal spike trains in vivo. J. Neurophysiol. 77: 2836–2841.PubMedGoogle Scholar
  38. Ritter T (1998) Normal, Chi-Square and Kolmogorov-Smirnov statistics functions in JavaScript. http://www.ciphersbyritter. com/JAVASCRP/NORMCHIK.HTM.Google Scholar
  39. Rose JE, Brugge JF, Anderson DJ, Hind JE (1967) Phase-locked response to low-frequency tones in single auditory nerve fibers of the squirrel monkey. J. Neurophysiol. 30: 769–793.PubMedGoogle Scholar
  40. Rozanov YA (1969) Probability Theory: A Concise Course. Dover, New York.Google Scholar
  41. Srinivasan MA, LaMotte RH (1987) Tactile discrimination of shape: Responses of slowly and rapidly adapting mechanoreceptive afferents to a step indented into the monkey fingerpad. J. Neurosci. 7: 1682–1697.PubMedGoogle Scholar
  42. Talbot WH, Darian-Smith I, Kornhuber HH, Mountcastle VB (1968) The sense of flutter-vibration: Comparison of the human capacity with response patterns of mechanoreceptive afferents from the monkey hand. J. Neurophysiol. 31: 301–334.PubMedGoogle Scholar
  43. Tiesinga PHE, José JV (2000) Synchronous clusters in a noisy inhibitory neural network. J. Comput. Neurosci. 9: 49–65.CrossRefPubMedGoogle Scholar
  44. Tiesinga PHE, Fellous J-M, Sejnowski TJ (2002a) Spike-time reliability of periodically driven integrate-and-fire neurons. Neurocomputing 44-46: 195–200.CrossRefGoogle Scholar
  45. Tiesinga PHE, Fellous J-M, Sejnowski TJ (2002b) Attractor reliability reveals deterministic structure in neuronal spike trains. Neural Comput. 14: 1629–1650.CrossRefPubMedGoogle Scholar
  46. Whitsel BL, Kelly EF, Xu M, Tommerdahl M, Quibrera M (2001) Frequency-dependent response of SI RA-class neurons to vibrotactile stimulation of the receptive field. Somatosens. Mot. Res. 18: 263–285.CrossRefPubMedGoogle Scholar
  47. Whitsel BL, Kelly EF, Quibrera M, Tommerdahl M, Li Y, Favorov OV, Xu M, Metz CB (2003) Time-dependence of SI RA neuron response to cutaneous flutter stimulation. Somatosens. Mot. Res. 20: 45–69.CrossRefPubMedGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Burak Güçlü
    • 1
    • 2
  • Stanley J. Bolanowski
    • 1
    • 2
  1. 1.Institute for Sensory ResearchSyracuse
  2. 2.Department of Bioengineering and NeuroscienceSyracuse UniversitySyracuseUSA

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