An electrical description of the motoneurone, and its application to the analysis of synaptic potentials

Abstract

SUMMARY1. The Rall model of the motoneurone, which consists of a lumped resistance and capacitance, representing the soma, in parallel with a distributed resistance-capacitance network of finite length, representing the equivalent dendritic cable, has been used to investigate the effects of varying electrical and geometrical parameters on the time course of transients generated at the model soma.2. An analytical solution has been obtained for the voltage at the model soma, following a brief current injection at any point on the dendritic cable, in terms of the dendritic to soma conductance ratio, the electrotonic length of the cable, the membrane time constant, and the electrotonic distance between the point of current injection and the soma. This solution has been used to study the response at the soma to currents with a smooth time course, and to brief rectangular current pulses. Computations of these voltage transients are given to illustrate the effect of the above parameters on voltage time course.3. A method for determining the membrane time constant, the dendritic to soma conductance ratio, and the electrotonic length of the dendritic cable, is described. The method involves measurements from the decay time course of the transient at the soma following a brief current pulse being applied at the soma.4. A method is described whereby the time course of a synaptic potential, assumed to be generated by synaptic knobs located exclusively at the soma, may be used to determine the motoneurone parameters, and a parameter describing the time course of current injection.

Influence of dendritic location and membrane properties on the effectiveness of synapses on cat motoneurones

“…amplitudes compatible with the estimated value of the time integral of a quantal conductance change, 40 x 10-10 mho msec (see Methods). Peak amplitude values corresponding to quantal conductance pulses in the physiological range of 0-2-0-5 msec are enclosed within vertical lines (see Methods; Kuno & Miyahara, 1969a;Jack & Redman, 1971b). Thus a quantal conductance change at the distal dendritic site illustrated here would be expected to generate an e.p.s.p.…”

Slow excitatory synaptic potentials recorded from neurones of guinea‐pig submucous plexus.

“…A shift in the apparent reversal potential to levels more negative than the true equilibrium potential and a 'shunting' of the dendritic conductance change are qualitatively consistent with dendritic synaptic locations (Rall, 1967;Smith, Wuerker & Frank, 1967;Jack, Noble & Tsien, 1975). Computational experiments, making use of a compartmental model (Rall, 1964(Rall, , 1967Jack & Redman, 1971), showed that the observed shift in the slow e.p.s.p. reversal potential is also quantitatively compatible with the observed discrepancy in the conductance ratios (J.…”

Post‐natal development of ganglia in the lower lumbar sympathetic chain of the rat.

“…As the initial faster decay did not last for longer than 10 % of the final cell time constant, the cell dendrites must be electrically short, i.e. less than 0 5 space constants (Jack & Redman, 1971; see also McLachlan, 1974). The proportion of cells whose electrotonic potentials gave evidence of dendritic current spread increased during the developmental period examined.…”