The family of pentameric ligand-gated ion channels (pLGICs) includes both inhibitory and excitatory receptors. Electrophysiological methods have explored the time-dependent ion currents induced by their neurotransmitter agonists. Kinetic modeling requires a minimum of three conformational states: resting, active, and desensitized. However, current traces of inhibitory and excitatory pLGICs differ substantially. Reproducing their basic features requires different state connectivity: whether the desensitized state is accessed from the resting or active state. It is surprising that a property as fundamental as state connectivity would differ within the same family. So, we explore the possibility that the connectivity is the same, but corresponding states differ in function: Analogous states on the free energy landscape have similar structure, but differ in ion conductivity, free energies, and agonist binding affinities. This hypothesis is tested using a kinetic model in which agonist and anesthetics modulate the receptor free energy landscape by adsorbing to the membrane in which the receptor is embedded. It was previously shown that even with only three states, the complex behavior observed for GABA(A)R is reproduced, including its response to anesthetics. It is demonstrated here that this hypothesis accounts for an important difference between inhibitory and excitatory receptors: their opposite responses to inhalation anesthetics.