Lithium is a strange drug. It also cures bipolar disorder and nobody knows why. It also fucks up the liver over time and basically people on lithium eventually have to make a choice between dying or being insane.
High-dose lithium is extremely hard on your kidneys and may well lead to kidney failure in a decade or so. Medium-dose lithium is a lot more gentle but still requires monitoring. Many people can go down in dose after initial treatment, and good psych prescribers will attempt to do this after a while. (Or patients will request it, after the other side effects of lithium become noticable after the bipolar has settled down.) Low-dose lithium is much harder to study and may well be pretty safe. May.
It is not quite true that people have no idea how it cures bipolar disorder. It's definitely affecting the ion channels (sodium, potassium, etc), just like many other anticonvulsant drugs also used for treating bipolar. So the mechanism for action is not totally insane and unique. Now, why the ion channels are the place to go for certain people, that's an open question....
Personal theory: these things are like "global constants" for the brain's GPU. Somewhat similar to the temperature constant in an LLM. There is no real "explanation" for why they work, they just have an effect. Various chemicals have various effects, often depending on the patient (because other constants vary, training data varies...) and we pick the chemical we like the effect of most.
If you read a literature review for lithium's mechanism of action, it's a wild ride [0] that clearly demonstrates exactly how little we know. More importantly, though, is that all of this is made up ex post facto. Nobody can take a _new_ drug and tell you anything concrete about what it will do or how it will work: instead, we look at what happens and _then_ we make crude guesses. It is essentially modern miasma theory. For those who have forgotten, the application of miasma theory built our first sanitation systems, which eliminated more deaths from disease than the entirety of vaccines. That is to say: just because we are groping in the dark does not make the work useless, and indeed, our first vaccines were also constructed with very primitive methods.
I think that a more concrete understanding of the human body can only come when we start to understand all the many pathways of life in/on/around the body. Right now, our technology constrains us to investigate only individual points in mostly static ways. Give it a few decades of advancement and I bet we'll have some fascinating insights. I would also bet that, as with any complex system, there will be no simple answers to how things work.
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For what it's worth, in the specific case of lithium, the American Society of Health-System Pharmacists would agree with me that the mechanism of action is unknown: https://www.drugs.com/monograph/lithium.html
[0] https://link.springer.com/article/10.1007/s40263-013-0039-0
Lithium is one of a large class of drugs that modulate the chemical potentials of the body's voltage-gated ion channels. There are a lot of drugs in this class, and most have been used with at least some degree of success to treat bipolar disorder. This class is also first-line treatment for many forms of epilepsy. The GABA system is directly tied in here too, and GABAergic agents are generally considered part of this class... and, guess what, they often help in bipolar as well. Lithium is a unique member of this class, and it is completely obvious (to a biochemist) that adding another species of alkali metal in sufficient concentration will disrupt the chemical potentials of sodium and potassium ion transport in the ion channels.
My point is: the first-level effect of lithium is well understood, and it affects an area that is well known to be affected by other drugs that have similar effects. So it is not total voodoo. However, you are also very correct that our understanding starts to break down after this. We can come up with new ion channel modulating drugs, and can reasonably expect them to be effective candidates for helping bipolar patients. What we cannot do is predict other targets or classes of drugs that might be interesting. That is where our understanding breaks down.
Here is where we can both agree: we know a few things about the mechanism, which allow us to make some useful judgments in a few limited cases. We can also both agree that we know so little that, if a new, similar drug were proposed, with only a small change to its chemical structure, neither of us would dare make any confident statements about its action. We also cannot accurately predict what would happen if given to a patient with a well-studied but different disorder. In other words: most of the useful judgments about lithium - those that would be economically or socially interesting, for example - cannot be made from the model, because our understanding of the mechanism of action is too crude.
All of that is also, however, true about my hypothetical Corolla from my first example: we can say a few things, but most of the useful judgments that could be made from a full understanding cannot be made. It would be obvious to anyone that we do not understand the Corolla. So why, then, would we claim to understand lithium?
As a matter of fact, lithium patients aren't much worse off when it comes to kidney function. Especially with modern levels of around 0.6 to 0.8 mmols.
Lithium has many modes of action, ion channels like you said, but also GSK3 function, BDNF changes and many more. It even changes the DNA methylation.
Also, to my knowledge, we are not entirely sure why most, if not all, of the psychiatric drugs work. Plenty of hypotheses though.