The question is kind of broad, and I decided to give four notable examples from credible sources of long-term potentiation of inhibitory responses (iLTP) below. Upregulation of postsynaptic GABAA and GABAB currents are the predominant effectors responsible for iLTP. The mechanism through which these effects are initiated are, however, variable between the various systems described. As far as I can see, non of the examples are Hebbian (i.e., non of the examples below are dependent on spike-timing).
Repetitive firing of interneurons has been shown to enhance the spike-mediated inhibitory postsynaptic currents in CA1 pyramidal neurons in the hippocampus. this enhancement was mediated by GABAB receptors. The hippocampus is a brain structure where most of the research in long-term potentiation has been done in the past decades. It is a hot spot of learning and synaptic plasticiy where long-term potentiation is also induced by repetitive (tetanic) stimulation. The enhanced inhibitory responses were mediated by astrocytes that in turn affected the inhibitory responses in the pyramidal neurons. Astrocytes may therefore be a necessary intermediary in activity-dependent modulation of inhibitory synapses in the hippocampus. The mechanism through which the glial cells did this was not described in the paper. It was not mediated via Cl- or K+ (Kang et al., 1998).
In hippocampal neurons it has been shown that prolonged depolarization of cultured cells leads to increased expression of inhibitory GABAA receptors that ultimately decrease the artificially-induced high spike rate activity to normal levels (Rannals & Kapur, 2011). This increase in GABAA activity was accompanied by a larger activity of GABA syntheszing enzyme GAD, likely showing increased GABA release.
In the thalamus, postsynaptic thalamocortical (TC) cells show inhibitory long-term potentiation (iLTP). This iLTP was explicitly shown to be non-Hebbian, because it did not depend on the timing between presynaptic and postsynaptic activity. Instead, it was shown to be induced by postsynaptic burst activity alone. iLTP required postsynaptic dendritic Ca2+ influx that triggered the synthesis of nitric oxide that retrogradely activated presynaptic guanylyl cyclase, in turn resulting in the presynaptic expression of iLTP (Sieber et al., 2013).
A last example of iLTP was described in the visual cortex. When blocking excitatory postsynaptoc potentials, tetanic stimulation of layer IV neurons resulted in iLTP of layer V neurons postsynaptically mediated by increased GABAA receptor currents. Interestingly, the tetanic stimuli used were much like the stimuli used to evoked excitatory LTP (eLTP) in hippocampus as described above, and conditions favoring iLTP were much the same as the conditions needed to establish eLTP in the hippocampus (Komatsu, 1994).
- Kang et al., Nature Neurosci (1998); 1(8):683-92
- Komatsu, J Neurosci (1994); 14(11): 6489-99
- Rannals & Kapur, J Neurosci (2011); 31(48): 17701–12
- Sieber et al., J Neurosci (2013); 33(40): 15675-85
- How do neurons decide how to alter their output signals?