Abstract
Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.
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References
Bayly, E.J.: Spectral analysis of pulse frequency modulation in the nervous system. I.E.E.E. Trans. Bio-Med. Engng. 15, 257 (1968).
Bendat, J.S., Piersol, A.G.: Measurement and analysis of random data. New York: John Wiley 1966.
Benignus, V.A.: Estimation of the coherence spectrum and its confidence interval using the fast Fourier transform. I.E.E.E. Trans. Audio and Electroacoustics AU-17, 145 (1969).
Borsellino, A., Poppele, R.E., Terzuolo, C.A.: Transfer functions of the slowly adapting stretch receptor organ of Crustacea. Cold Spr. Harb. Symp. quant. Biol. 30, 581 (1965).
Brown, M.C., Stein, R.B.: Quantitative studies on the slowly adapting stretch receptor of the crayfish. Kybernetik 3, 175 (1966).
Chapman, K.M., Nichols, T.R.: Electrophysiological evidence that cockroach tibial tactile spines have separate sensory axons. J. Insect Physiol. 15, 2103 (1969).
—, Smith, R.S.: A linear transfer function underlying impulse frequency modulation in a cockroach mechanoreceptor. Nature (Lond.) 197, 699 (1963).
Crowe, A.: Studies on the transfer function of a cockroach mechanoreceptor. Comp. Biochem. Physiol. 20, 13 (1967).
D'Azzo, J.J., Houpis, C.H.: Feedback control system analysis and synthesis. New York: McGraw Hill 1966.
French, A.S.: PULSE, an event/time histogramming program for the Digital Equipment Corp. LAB-8 computer and FNEW-pulse, a function generating routine for use with PULSE and FOCAL. Comp. Progr. Bio-Med. 1, 105 (1970).
—, Holden, A.V.: Alias-free sampling of neuronal spike trains. Kybernetik 8, 165 (1971)
— Frequency domain analysis of neurophysiological data. Comp. Progr. Bio-Med. 1, 219 (1971).
— Semi-on-line implementation of an alias-free sampling system for neuronal signals. Comp. Progr. Bio-Med. 2, 1 (1971).
—, Stein, R.B.: A flexible neural analog using integrated circuits. I.E.E.E. Trans. Bio-Med. Engng. BME-17, 248 (1970).
Holden, A.V., French, A.S.: Spectral analysis of receptor dynamics. Canad. Physiol. 2, 14 (1971).
Houk, J., Simon, W.: Response of Golgi tendon organs to forces applied to muscle tendon. J. Neurophysiol. 30, 466 (1967).
Hughes, G.W., Maffei, L.: Retinal ganglion cell response to sinusoidal light stimulation. J. Neurophysiol. 29, 333 (1966).
Jenkins, G.M., Watts, D.G.: Spectral analysis and its applications. San Francisco: Holden-Day 1968.
Kiang, N.Y.-S., Watanabe, T., Thomas, E.C., Clark, L.F.: Discharge patterns of single fibers in the cat's auditory nerve. Cambridge: M.I.T. 1965.
Knight, W.: Frequency response for sampling integrator and for voltage to frequency convenor. In: Systems analysis in neurophysiology. Ed. C.A. Terzuolo, University of Minnesota, Minneapolis 1969.
—, Toyoda, J.-I., Dodge, F.A.: A quantitative description of the dynamics of excitation and inhibitation in the eye of Limulus. J. gen. Physiol. 56, 421 (1970).
Matthews, P.B.C., Stein, R.B.: The sensitivity of muscle spindle afferents to small sinusoidal changes of length. J. Physiol. (Lond.) 200, 723 (1969).
Melvill Jones, G., Milsum, J.H.: Characteristics of neural transmission from the semicircular canal to the vestibular nuclei of cats. J. Physiol. (Lond.) 209, 295 (1970).
Pearson, T.R., Holden, A.V.: Describing functions of two insect mechanoreceptors. Proc. Canad. Fed. Biol. Soc. 13, 38 (1970).
Pinter, R.B.: Sinusoidal and delta function responses of visual cells in the Limulus eye. J. gen. Physiol. 49, 565 (1966).
Poppele, R.E., Bowman, R.J.: Quantitative description of linear behaviour of mammalian muscle spindles. J. Neurophysiol. 33, 59 (1970).
Pringle, J.W., Wilson, V.J.: The response of a sense organ to a harmonic stimulus. J. exp. Biol. 29, 220 (1952).
Resigno, A., Stein, R.B., Purple, R.L., Poppele, R.E.: A neuronal model for the discharge patterns produced by cyclic inputs. Bull. Math. Biophys. 32, 337 (1970).
Rosenthal, N. P., McKean, T.A., Roberts, W.J., Terzuolo, C.A.: Frequency analysis of stretch reflex and its main subsystems in triceps surea muscles of the cat. J. Neurophysiol. 33, 713 (1970).
Shapley, R.: Fluctuations of the impulse rate in Limulus eccentric cells. J. gen. Physiol. 57, 539 (1971).
Smith, H.W.: Approximate analysis of randomly excited controls. Cambridge: M.I.T. 1966.
Sokolnikoff, I.S., Redheffer, R.M.: Mathematics of Physics and modern engineering. New York: McGraw Hill 1958.
Spekreijse, H.: Rectification in the goldfish retina: analysis by sinusoidal and auxiliary stimulation. Vision Res. 9, 1461 (1969).
—, Oosting, H.: Linearizing: A method for analysing and synthesiz-ing non-linear systems. Kybernetik 7, 22 (1970).
Stein, R.B., French, A.S., Holden, A.V.: The frequency response, coherence and information capacity of two neuronal models. Biophys. J. (in press 1972).
van der Tweel, L.H., Spekreijse, H.: Signal transport and rectification in the human evoked-response system. Ann. N.Y. Acad. Sci. 156, 678 (1969).
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French, A.S., Holden, A.V. & Stein, R.B. The estimation of the frequency response function of a mechanoreceptor. Kybernetik 11, 15–23 (1972). https://doi.org/10.1007/BF00267761
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DOI: https://doi.org/10.1007/BF00267761