What was Saddam Hussein supposed to have in his basement? (Rollover.)
Let's learn a little more about neurotransmitters. The brain uses many types of neurotransmitters, but the peripheral nervous systems only uses a few. Acetylcholine is the neurotransmitter for both the parasympathetic nervous system and for the somatic nerves that connect sense organs and muscles. (The sympathetic nervous system uses a series of structurally similar chemicals, epinephrine, norepinephrine, collectively called catacholamines.) [Not required reading, but here is a cute explanation of autonomic action: http://www.madsci.org/posts/archives/jan2000/947350899.An.r.html ]
Before you read the book's section, here is a simpler approach: http://faculty.washington.edu/chudler/weap.html.
After you read the section, you may be interested in this picture, Other structures, which shows the basic chemical structure of the nerve gases. You'll note that a variety of chemicals will do the same basic job, covalently binding to the active site of acetylcholinesterase (AChE). With a little imagination, you can see they have a vaguely similar structure, and they all inactivate acetylcholinesterase. Some were common agricultural chemicals, I have used one of them, myself. This is a common phenomenon, while enzymes work like a lock and key, in fact many different keys may fit, or at least jam the lock. These Structure-Activity Relationships (SAR) are often used to predict the effects of drugs and chemicals for which the actual laboratory testing is weak or nonexistent.
Why were the organophosphorus insecticides permitted at all? In fact some of them are still in wide use. The effects of the chemical are quite different in different species due to kinetics, the uptake and elimination of the chemicals. The effect at the active site of AChE is the same in bugs and bunnies, but much less of the chemical actually gets to active sites in the bunny. Hence low concentrations may have no effect on humans, but still kill bugs. Some of these chemicals biodegrade very quickly and are not a long term threat to health or the environment. Some are a threat.