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. 1996 Apr 15;492(Pt 2):597–628. doi: 10.1113/jphysiol.1996.sp021332

Relationship of firing intervals of human motor units to the trajectory of post-spike after-hyperpolarization and synaptic noise.

P B Matthews 1
PMCID: PMC1158851  PMID: 9019553

Abstract

1. Interspike interval distributions from human motor units of a variety of muscles were analysed to assess the role of synaptic noise in excitation. The time course of the underlying post-spike after-hyperpolarization (AHP) was deduced by applying a specially developed transform to the interval data. Different firing rates were studied both by varying the firing voluntarily, and by selecting subpopulations of spikes for a given firing rate from long recordings with slight variations in frequency. 2. At low firing rates the interval histograms had an exponential tail. Thus at long intervals, the motoneurone was randomly excited by noise and its post-spike AHP was complete. This contrasts with the firing produced by intracellular current injection in the cat, when the membrane potential increases linearly until threshold is reached. The interval histogram was therefore analysed with the aid of a model of synaptic excitation to deduce the mean 'trajectory' of membrane voltage in the last part of the interspike interval. 3. The computer model, described in the Appendix, was used to determine the effect of the mean level of membrane potential on the probability of a spike being excited, per unit time, during an on-going interspike interval. All variables were treated as voltages, with synaptic noise simulated by time-smoothed Gaussian noise. This enabled an interval distribution to be transformed into a segment of the underlying trajectory of the membrane potential; the potential was expressed in terms of the noise amplitude and the spike threshold. 4. At low firing rates, the equilibrium value of the membrane voltage trajectory lay well below threshold; the deviation typically corresponded to the standard deviation of the noise or more. The noise standard deviation was estimated to be about 2 mV. 5. With increasing mean firing rate, the near-threshold portion of the trajectory obtainable from the histogram occurred earlier, was steeper and rose to a higher level. Trajectories for different firing rates fell on the same curve after shifting them vertically by varying amounts. The curve was taken to represent the AHP of the motoneurone and was closely exponential. The shift of the trajectory gave its mean synaptic drive. The duration of the AHP varied between units and was longer than average for units from soleus muscle. 6. Further modelling showed that summation of noise with the AHP can explain the well-known changes in discharge variability that occur as firing rate increases. 7. It is concluded that synaptic noise plays a major role in the excitation of tonically firing human motoneurones and that the noiseless motoneurone with a linear trajectory provides an inadequate model for the conscious human. This is of interest in relation to various standard measures of human motor unit activity such as short-term synchronization.

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Selected References

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