The common explanation as to what the primary mechanism of action for organophosphates (and carbamates) is is the inhibition of the enzyme acetylcholinesterase and resulting buildup of acetylcholine at neuromuscular junctions, which ultimately results in respiratory failure. However, there is evidence that this may not be the case.
Firstly, a study reported that the nerve agent VX has been found to attack at least 132 different proteins, some of which were associated with metabolism. Source: https://www.ncbi.nlm.nih.gov/pubmed/28267914
Also, another study showed that, even when the enzyme was protected against the action of organophosphates, nerve agents still exhibited toxicity. Source: (http://www.rand.org/publications/MR/MR1018.5/MR1018.5.chap5.html) (Found in the Chapter 5 PDF, under "Non-AchE Effects")
Also also, another study was conducted on the matter. The test subjects were mice genetically engineered to lack acetylcholinesterase. The study found that the mice that totally lacked the enzyme not only lived (For over 34 days, no less), but were also twice as susceptible to OP poisoning as mice with the enzyme and exhibited the same symptoms. Source:https://www.ncbi.nlm.nih.gov/pubmed/11602663
So, how do organophoshates actually act to cause the symptoms associated with OP poisoning? What proteins do they affect? There seems to be a great abundance of evidence that the effects of poisoning are not due to AchE inhibition.