Abstract
The static discharge rate of Renshaw cells (studied in deafferented, intercollicularly decerebrate cats) has a nonlinear dependence on the frequency of trains of stimulus impulses to α-motor axons in the ventral root. This dependence is well described by a rectangular hyperbola that approaches saturation with increasing stimulus frequency. The tendency to saturate is independent of the number of motor axons exciting a Renshaw cell. On average, the stimulus frequency at which the discharge rate reaches half its saturation value lies between 10 and 15 Hz. The effect of Renshaw cell activity — measured as the antidromic inhibition of individual α-motoneurons — reflects the form of the static frequency characteristics. An electric circuit analog of the Renshaw cell membrane is presented which serves to explain the qualitative features of the static input-output relations; the nonlinearity is the result of synapses with linear properties acting together at the cell membrane.
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Alpern, A., Rushton, W.A.H., Torii, S.: Encoding of nerve signals from retinal rods. Nature 223, 1171–1172 (1969)
Baylor, D.A., Fuortes, M.G.F.: Electrical responses of single cones in the retina of the turtle. J. Physiol. (Lond.) 207, 77–92 (1970)
Beidler, L.M.: A theory of taste stimulation. J. gen. Physiol. 38, 133–139 (1954)
Benecke, R., Takano, K., Schmidt, J., Henatsch, H.-D.: Tetanus toxin induced actions on spinal Renshaw cells and Ia-inhibitory interneurones during development of local tetanus in the cat. Exp. Brain Res. 27, 271–286 (1977)
Bergmans, J., Burke, R., Lundberg, A.: Inhibition of transmission in the recurrent inhibitory pathway to motoneurones. Brain Res. 13, 600–602 (1969)
Cleveland, S., Kuschmierz, A., Ross, H.-G.: Responses of Renshaw cells to step changes in input. J. Physiol. (Lond.) 284, 76–77P (1978)
Cleveland, S., Ross, H.-G.: Dynamic properties of Renshaw cells: frequency response characteristics. Biol. Cybern. 27, 175–184 (1977)
Cornish-Bowden, A., Eisenthal, R.: Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot and other methods. Biochem. J. 139, 721–730 (1974)
Cornish-Bowden, A., Porter, W.R., Trager, W.F.: Evaluation of distribution-free confidence limits for enzyme kinetic parameters. J. theor. Biol. 74, 163–175 (1978)
Curtis, D.R., Ryall, R.W.: The synaptic excitation of Renshaw cells. Exp. Brain Res. 2, 81–96 (1966)
Eccles, J.C., Eccles, R.M., Iggo, A., Lundberg, A.: Electrophysiological investigations on Renshaw cells. J. Physiol. (Lond.) 159, 461–478 (1961)
Eccles, J.C., Fatt, P., Koketsu, K.: Cholinergic and inhibitory synapses in a pathway from motor-axon collaterals to motoneurones. J. Physiol. (Lond.) 126, 524–562 (1954)
Eisenthal, R., Cornish-Bowden, A.: The direct linear plot: a new graphical procedure for estimating enzyme kinetic parameters. Biochem. J. 139, 715–720 (1974)
Fain, G.L., Dowling, J.E.: Intracellular recordings from single rods and cones in the mudpuppy retina. Science 180, 1178–1181 (1973)
Frank, K., Fuortes, M.G.F.: Unitary activity of spinal interneurones of cats. J. Physiol. (Lond.) 131, 424–435 (1956)
Fromm, C., Haase, J., Wolf, E.: Depression of the recurrent inhibition of extensor motoneurons by the action of group II afferents. Brain Res. 120, 459–468 (1977)
Granit, R., Kernell, D., Shortess, G.K.: quantitative aspects of repetitive firing of mammalian motoneurones, caused by injected currents. J. Physiol. (Lond.) 169, 911–931 (1963)
Granit, R., Renkin, B.: Net depolarization and discharge rate of motoneurones, as measured by recurrent inhibition. J. Physiol. (Lond.) 158, 461–475 (1961)
Haase, J.: Die Transformation des Entladungsmusters der Renshaw-Zellen bei tetanischer antidromer Reizung. Pflügers Arch. ges. Physiol 276, 471–480 (1963)
Haase, J., van der Meulen, J.P.: Effects of supraspinal stimulation on Renshaw cells belonging to extensor motoneurones. J. Neurophysiol. 24, 510–520 (1961)
Haase, J., Vogel, B.: Direkte und indirekte Wirkungen supraspinaler Reizungen auf Renshaw-Zellen. Pflügers Arch. 325, 334–346 (1971)
Henatsch, H.-D., Kaese, H.J., Langrehr, D., Meyer-Lohmann, J.: Einfluß des motorischen Cortex der Katze auf die Renshaw-Rückkopplungshemmung der Motoneurone. Pflügers Arch. ges. Physiol. 274, 51 (1961)
Hultborn, H., Pierrot-Deseilligny, E.: Input-output relations in the pathway of recurrent inhibition to motoneurones in the cat. J. Physiol. (Lond.) 297, 267–287 (1979)
Kato, M., Fukushima, K.: Effect of differential blocking of motor axons on antidromic activation of Renshaw cells in the cat. Exp. Brain Res. 20, 135–143 (1974)
Katz, B.: Depolarization of sensory terminals and the initiation of impulses in the muscle spindle. J. Physiol. (Lond.) 111, 261–282 (1950)
van Keulen, L.C.M.: Relations between individual motoneurones and individual Renshaw cells. Neurosci. Letters Suppl. 3, S 313 (1979)
Knibestöl, M.: Stimulus-response functions of slowly adapting mechanoreceptors in the human glabrous skin area. J. Physiol. (Lond.) 245, 63–80 (1975)
Koehler, W., Windhorst, U., Schmidt, J., Meyer-Lohmann, J., Henatsch, H.-D.: Diverging influences on Renshaw cell responses and monosynaptic reflexes from stimulation of capsula interna. Neurosci. Lett. 8, 35–39 (1978)
Lloyd, D.P.C.: Reflex action in relation to pattern and peripheral source of afferent stimulation. J. Neurophysiol. 6, 111–119 (1943)
Lloyd, D.P.C.: Monosynaptic reflex response of individual motoneurons as a function of frequency. J. gen. Physiol. 40, 435–450 (1957)
Lloyd, D.P.C., McIntyre, A.K.: Monosynaptic reflex responses of individual motoneurons. J. gen. Physiol. 38, 771–787 (1955)
Loewenstein, W.R.: The generation of electric activity in a nerve ending. Ann. N.Y. Acad. Sci. 81, 367–387 (1959)
MacLean, J.B., Leffman, H.: Supraspinal control of Renshaw cells. Exp. Neurol. 18, 94–104 (1967)
Martin, A.R.: The effect of membrane capacitance on non-linear summation of synaptic potentials. J. theor. Biol. 59, 179–187 (1976)
Martin, B.R.: Statistics for physicists. London: Academic Press 1971
Naka, K.I., Rushton, W.A.H.: An attempt to analyse colour reception by electrophysiology. J. Physiol. (Lond.) 185, 556–586 (1966)
Piercey, M.F., Goldfarb, J.: Discharge patterns of Renshaw cells evoked by volleys in ipsilateral cutaneous and high-threshold muscle afferents and their relationship to reflexes recorded in ventral roots. J. Neurophysiol. 37, 274–302 (1974)
Pompeiano, O., Wand, P., Sontag, K.-H.: The relative sensitivity of Renshaw cells to orthodromic group Ia volleys caused by static stretch and vibration of extensor muscles. Arch. ital. Biol. 113, 238–279 (1975)
Porter, W.R., Trager, W.F.: Improved non-parametric statistical methods for the estimation of Michaelis-Menten kinetic parameters by the direct linear plot. Biochem. J. 161, 293–302 (1977)
Rall, W.: Theoretical significance of dendritic trees for neuronal input-output relations. In: Neural theory and modelling, pp. 73–97. Reiss, R.F. (ed.). Stanford: Stanford University Press 1964
Redman, S.J., Lampard, D.G., Annal, P.: Monosynaptic stochastic stimulation of cat spinal motoneurons. II. Frequency transfer characteristic of tonically discharging motoneurons. J. Neurophysiol. 31, 499–508 (1968)
Renshaw, B.: Central effects of centripetal impulses in axons of spinal ventral roots. J. Neurophysiol. 9, 191–204 (1946)
Ross, H.-G.: Experimentelle Untersuchungen und Modellvorstellungen zur quantitativen Charakterisierung der rekurrenten Inhibition spinaler Alpha-Motoneurone. Habilitationsschrift, Düsseldorf 1976
Ross, H.-G., Cleveland, S., Wolf, E., Haase, J.: Changes in the excitability of Renshaw cells due to orthodromic tetanic stimuli. Pflügers Arch. 344, 299–307 (1973)
Ross, H.-G., Cleveland, S., Haase, J.: Contribution of single motoneurons to Renshaw cell activity. Neurosci. Lett. 1, 105–108 (1975a)
Ross, H.-G., Cleveland, S., Haase, J.: Response of Renshaw cells to minimal antidromic input at various frequencies. Pflügers Arch. 355, R91 (1975b)
Ross, H.-G., Cleveland, S., Haase, J.: Quantitative relation between discharge frequencies of a Renshaw cell and an intracellularly depolarized motoneuron. Neurosci. Lett. 3, 129–132 (1976)
Ryall, R.W., Piercey, M.F.: Excitation and inhibition of Renshaw cells by impulses in peripheral afferent nerve fibers. J. Neurophysiol. 34, 242–251 (1971)
Tucker, D.: Physical variables in the olfactory stimulation process. J. gen. Physiol. 46, 453–489 (1963)
Wilkinson, G.N.: Statistical estimations in enzyme kinetics. Biochem. J. 80, 324–332 (1961)
Wilson, V.J.: Regulation and function of Renshaw cell discharge. In: Muscular afferents and motor control. Nobel Symposium 1, pp. 317–329. Granit, R. (ed.). Stockholm: Almquist u. Wiksell 1966
Wilson, V.J., Talbot, W.H., Kato, M.: Inhibitory convergence upon Renshaw cells. J. Neurophysiol. 27, 1063–1079 (1964)
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Dedicated to Professor R. Granit, Stockholm, on the occasion of his 80th birthday
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Cleveland, S., Kuschmierz, A. & Ross, HG. Static input-output relations in the spinal recurrent inhibitory pathway. Biol. Cybern. 40, 223–231 (1981). https://doi.org/10.1007/BF00453372
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DOI: https://doi.org/10.1007/BF00453372