Yes, muscarinic receptors do play a role as you say, and with Parkinson’s as well. There is a need to explore and know more about this, and Anavex may be taking one of the first steps in doing so with the PDD study. If I may add, this:
AVXL 2-73 is an orally available drug candidate that restores cellular homeostasis by targeting sigma-1 and muscarinic receptors. It is a mixed ligand for sigma1/muscarinic receptors. SEE: https://www.alzforum.org/therapeutics/blarcamesine
I have located a couple of references, but only about M1.
Roles of the M1 Muscarinic Acetylcholine Receptor Subtype in the Regulation of Basal Ganglia Function and Implications for the Treatment of Parkinson's Disease
Hypothesis: We believe that small molecules that affect the function of the M1 mAChR in a highly selective manner have the potential to deliver novel, well-tolerated and efficacious drugs to treat learning and memory deficits in individuals with PDD.
Study Design: We have generated small molecules of novel chemical classes that are positive allosteric modulators of the M1 mAChR and have a good understanding of the structure-activity relationship of these molecules. Based on this knowledge, we will synthesize these molecules and optimize them for target engagement in the brain and safety.