Back in 1995, Wolf & Burrows published a report on presynaptic inhibition in a somatosensory neuron in locust, where the efference copy signal is mediated via, precisely, metabotropic GABA receptors:
"Proprioceptive sensory neurons of a locust leg receive rhythmic presynpatic inhibition during walking", Wolf & Burrows 1995
https://www.jneurosci.org/content/15/8/5623.short
This paper is remarkable, and memorable, in what it teaches us about axo-axonic synapses:
1. A GABAergic neuron synapses onto the axon of an excitatory somatosensory neuron (a chordotonal proprioceptive neuron);
2. The somatosensory neuron receives the signal via GABA B receptors, which are metabotropic;
3. The effect on the receiving axon is a subthreshold depolarization (!);
4. The effect on the function of the receiving axon is inhibition after all.
What happens is: a subthreshold depolarization is a reduction of the membrane voltage potential. When the action potential reaches the axon, the reduced voltage potential results in a smaller depolarization, so the somatosensory axon releases less neurotransmitter to its own postsynaptic partners.
In summary: presynaptic inhibition (axo-axonic GABA synapses) does not participate of the integration function of the postsynaptic neuron – does not interfere with whether the neuron will spike or not.
Instead, presynaptic inhibition, via metabotropic GABA receptors, is a form of modulation of the postsynaptic neuron: how strongly will it pass on the signal. And that is, precisely, what's needed to implement the efference copy.
[Update: GABA B receptor is the metabotropic!]
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