A re-examination of the possibility of controlling the firing rate gain of neurons by balancing excitatory and inhibitory conductances

It has been suggested that balancing excitatory and inhibitory conductance levels can control the firing rate gain of single neurons, defined as the slope of the relation between discharge frequency and excitatory conductance. According to this view the increase in firing rate produced by an input pathway can be controlled independently of the ongoing firing rate by adjusting the mixture of excitatory and inhibitory conductances produced by other pathways converging onto the neuron. These conclusions were derived from a simple RC-neuron model with no active conductances, or firing threshold mechanism. The analysis of that model considered only the subthreshold behaviour and did not consider the relation between total trans-membrane conductance and firing rate. Similar conclusions were also derived from a simple parallel conductance based model. In this paper I consider, as an example of a repetitively firing neuron, a generic model of cat lumbar α-motoneurons with excitatory and inhibitory inputs and a second independent excitatory pathway. The excitatory and inhibitory inputs can be thought of as central descending controls while the second excitatory pathway may represent, for example, the monosynaptic Ia-afferent pathway. I have re-examined the possibility that the firing rate gain of the ‘afferent’ pathway can be controlled independently of the ongoing firing rate by balancing the excitatory and inhibitory conductances activated by the descending inputs. The steady state firing rate of the model motoneuron increased nearly linearly with the excitatory current, as it does in real motoneurons (primary firing range). The model motoneuron also showed a secondary firing range, whose slope was steeper than in primary range. The firing rate gain was measured by increasing the conductance of the ‘afferent’ pathway. The firing rate gain (in the primary and secondary firing range) of the ‘afferent’ pathway was found to be the same regardless of the particular mixture of excitatory and inhibitory conductances acting to produce the ongoing firing rate. This result was obtained for a single-compartment model, as well as for a two-compartment model consisting of an active somatic compartment and a dendritic compartment containing an L-type calcium conductance. Put simply, the firing rate gain of an input to a neuron cannot be controlled by balancing excitatory and inhibitory conductances produced by other independent input pathways, or by the spatial distribution of excitation and inhibition across the neuron. Three potential ways of controlling the firing rate gain are presented in the ‘Discussion’. Firing rate gain can be controlled by actions at the presynaptic terminal, by inhibitory feedback, which is a function of the neuron’s firing rate, or by neuromodulator substances that affect intrinsic inward or outward currents.