The main inhibitory neurotransmitters are GABA (gamma-aminobutyric acid, which is made from Glu through decarboxylation of the α-C group) and glycine. The bind to transmiitter-gated chloride channels, which when open hyperpolarize the membrane. Benzodiazepines (like Valium and Librium - anti-anxiety and muscle-relaxing agents) and barbituates (like phenobarbital-hypnotics) bind at allosteric sites and potentiate the binding of each other and GABA.
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Figure: Mechanisms of Channel Gating