Googling for "voltage-independent" ion channels neurons doesn't give a good overview over the topic (and yields only approx. 50,000 hits, compared to 500,000 hits when searching for "voltage-dependent" ion channels neurons).
What I want to learn:
How many voltage-independent ion channels are there in the brain (or in specific parts of the brain, e.g. cortex) compared to voltage-dependent ion channels? (Rough estimate, order of magnitude: a tenth, a percent, ...?)
Which functional role do they play (compared to voltage-dependent channels which are mainly (?) concerned with the propagation of action potentials along the axon)?
Are there other (and possibly more concise) references than the one I found: ROLES OF THE ION CHANNEL NALCN IN NEURONAL EXCITABILITY CONTROL (which states, that NALCN is "widely expressed in the nervous system")?
(I guess voltage-independent channels could support the mechanisms of Rall's model which doesn't pressume voltage-dependent ion channels but only modifiable membrane resistances, possibly realized by voltage-independent ion channels, right?)
Addendum: I made a bad mistake not pointing out, that I meant ion channels that are neither voltage- nor ligand-gated but just influence the membrane resistance passively. (Ligand-gated ion channels are of course examples of voltage-independent ion channels, but not the ones I wanted to ask for.) Are the voltage-independent ion channels I wanted to ask for possibly just what is called leak channels?