Biotinis synthesized by by micororganisms in the gut. Pantothenic acid is also synthesized by microorganisms in the gut. Biotin and pantohenic acid are involved in bipolar depression. See the page on Bipolar depression. Changes is gut microbiota could, by affecting biotin synthesis and pantothenic acid synthesis and have an effect on bipolar depression.
If supplements are not available in the gastrointestinal tract this cannot but affect gut microbiota differently compared to supplements that are available in the gastrointestinal tract. I am open to the possibility that differences in gut microbiota can play a big role in mental states, however, the gut could also be set up so the gut has to use nutrients when nutients first pass through the gut. Use of nutrients by the gut could be a necessary first step in the use of nutrients systematically.
There is a lot of talk about how the diet of our very distant ancestors is the diet that is appropriate for us. One thing is certain about the diet of our very distant ancestors. Our very distant ancestors did not take nutrients than were formulated not to be available in the gut.
Only taking supplements that are available in the gut, when taking supplements, is one way to address to address gut microbiota positively. As an example EPA + DHA combinations are frequently supplied in enteric coated softgels to avoid ‘fishy smells’. However, biting on the softgels, swallowing the contents and then throwing the softgels away works much better for depression. And what is more even given EPA + DHA work in clinical trials EPA + DHA will not work in the field as EPA + DHA supplements sold in stores are very frequently enteric coated.