Abstract
A stochastic version of Kernell's (1968, 1972) model with cumulative afterhyperpolarization (AHP) was simulated. A characteristic of the model is that the AHP is the result of an increased potassium conductance (g K) that is time-dependent but not voltage-dependent. Quantal synaptic inputs are assumed to be the only source of interspike interval variability. The model reproduces many features of the steady-state discharge of peripheral vestibular afferents, provided that firing rates are higher than 40 spikes/s. Among the results accounted for are the interspike interval statistics occurring during natural stimulation, their alteration by externally applied galvanic currents and the increase in the interspike interval following an interposed shock. Empirical studies show that some vestibular afferents have a regular spacing of action potentials, others an irregular spacing (Goldberg and Fernández 1971b; Fernández and Goldberg 1976). Irregularly discharging afferents have a higher sensitivity to externally applied galvanic currents than do regular afferents (Goldberg et al. 1984). To explain the relation between galvanic sensitivity and discharge regularity requires the assumption that neurons differ in both their synaptic noise (σv) and the slopes of their postspike voltage trajectories (dμ v/dt). The more irregular the neuron's discharge at a given firing frequency, the greater is σv and the smaller is dμ v/dt. Of the two factors, dμ v/dt is estimated to be four times more influential in determining discharge regularity across the afferent population. The shortcomings of the model are considered, as are possible remedies. Our conclusions are compared to previous discussions of mechanisms responsible for differences in the discharge regularity of vestibular afferents.
Similar content being viewed by others
References
Baldissera F, Gustafsson B (1974) Firing behaviour of a neurone model based on the afterhyperpolarization conductance time course and algebraic sumation. Adaptation and steady state firing. Acta Physiol Scand 92:27–47
Baldissera F, Gustafsson B, Parmiggiani F (1976) A model for refractoriness accumulation and secondary range firing in spinal motoneurons. Biol Cybern 24:61–65
Barrett EF, Barrett JN (1976) Separation of two voltage-sensitive potassium currents and demonstration of a tetrodotoxinresistant calcium current in frog motoneurones. J Physiol (Lond) 255:737–774
Bean CP (1974) A theory of microstimulation of myelinated axons. Appendix to Abzug C, Maeda M, Peterson BW, Wilson VJ: Cervical branching of lumbar vestibulospinal axons. J Physiol (Lond) 243:499–522
BeMent SL, Ranck JB Jr (1969) A model for electrical stimulation of central myelinated fibers with monopolar electrodes. Exp Neurol 24:171–186
Connor JA (1978) Slow repetitive activity from fast conductance changes in neurons. Fed Proc 37:2139–2145
Connor JA, Stevens CF (1971) Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J Physiol (Lond) 213:31–53
Crill WE, Schwindt PC (1983) Active currents in mammalian central neurons. Trends Neurosci 6:236–240
Fernández C, Goldberg JM (1976) Physiology of peripheral neurons innervating otolith neurons of the squirrel monkey. I. Response to static tilts and to long-duration centrifugal force. J Neurophysiol 39:970–984
Furukawa T, Hayashida Y, Matsuura S (1978) Quantal analysis of the size of excitatory post-synaptic potentials of synapses between hair cells and afferent nerve fibres in goldfish. J Physiol (Lond) 276:211–226
Goldberg JM, Fernández C (1971a) Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. I. Resting discharge and response to constant angular accelerations. J Neurophysiol 34:635–660
Goldberg JM, Fernández C (1971b) Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. III. Variations among units in their discharge properties. J Neurophysiol 34:676–684
Goldberg JM, Fernández C (1977) Conduction times and background discharge of vestibular afferents. Brain Res 122:545–550
Goldberg JM, Smith CE, Fernández C (1984) Relation between discharge regularity and responses to externally applied galvanic currents in vestibular nerve afferents of the squirrel monkey. J Neurophysiol 51:1236–1256
Goldberg JM, Baird RA, Fernández C (1985) Morphophysiological studies of the mammalian vestibular labyrinth. In: Correia MJ, Perachio AA (eds) Contemporary sensory neurobiology. Alan R. Liss, New York, pp 231–245
Gustafsson B, Zangger P (1978) Effect of repetitive activation on the afterhyperpolarization in dorsal spinocerebellar tract neurones. J Physiol (Lond) 275:303–319
Gustafsson B, Lindström S, Zangger P (1978) Firing behaviour of dorsal spinocerebellar tract neurones. J Physiol (Lond) 275:321–343
Gustafsson B, Galvan M, Grafe P, Wigstrom H (1982) A transient outward current in a mammalian central neurone blocked by 4-aminopyridine. Nature 299:252–254
Highstein SM, Politoff AL (1978) Relation of interspike baseline activity to spontaneous discharges of primary afferents from the labyrinth of the toadfish, Opsanus tau. Brain Res 150:182–187
Hudspeth AJ, Corey DP (1977) Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc Natl Acad Sci USA 74:2407–2411
International Mathematics and Statistical Library Reference Manual, 8th edition, vol 2 (1980) International Mathematics and Statistical Library, Inc., Houston, Texas
Ishii Y, Matsuura S, Furukawa T (1971) Quantal nature of transmission at the synapse between hair cells and eighth nerve fibers. Jpn J Physiol 21:79–89
Kernell D (1968) The repetitive impulse discharge of a simple neurone model compared to that of spinal motoneurones. Brain Res 11:685–687
Kernell D (1972) The early phase of adaptation in repetitive impulse discharges of cat spinal motoneurones. Brain Res 41:184–186
MacGregor RJ, Oliver RM (1974) A model for repetitive firing in neurons. Kybernetik 16:53–64
Rall W (1962) Theory of physiological properties of dendrites. Ann NY Acad Sci 96:1071–1092
Rice SO (1944) Mathematical analysis of random noise. Bell Sys Tech J 23:282–332
Rossi ML, Valli P, Casella C (1977) Post-synaptic potentials recorded from afferent nerve fibers of the posterior semicircular canal in the frog. Brain Res 135:67–75
Rossi ML, Prigioni I, Valli P, Casella C (1980) Activation of the efferent system in the isolated frog labyrinth: effects on the afferent EPSPs and spike discharge recorded from single fibres of the posterior nerve. Brain Res 185:125–137
Schessel DA (1982) Chemical synaptic transmission between type I vestibular hair cells and the primary afferent nerve chalice: an intracellular study utilizing horseradish peroxidase. Ph. D. Dissertation, Bronx, NY, Albert Einstein College of Medicine
Stein RB (1967) Some models of neuronal variability. Biophys J 7:37–68
Tasaki I (1955) New measurements of the capacity and resistance of the myelin sheath and the nodal membrane of the isolated frog nerve fiber. Am J Physiol 181:639–650
Walsh BT, Miller JB, Gacek RR, Kiang NYS (1972) Spontaneous activity in the eighth cranial nerve of the cat. Int J Neurosci 3:221–236
Yagi T, Simpson NE, Markham CH (1977) The relationship of conduction velocity to other physiological properties of the cat's horizontal canal neurons. Exp Brain Res 30:587–600
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smith, C.E., Goldberg, J.M. A stochastic afterhyperpolarization model of repetitive activity in vestibular afferents. Biol. Cybern. 54, 41–51 (1986). https://doi.org/10.1007/BF00337114
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00337114