General anesthetics bind reversibly to ion channels, modifying their global conformational distributions, but the underlying atomic mechanisms are not completely known. We examine this issue by way of the model protein Gloeobacter violaceous ligand-gated ion channel (GLIC) using computational molecular dynamics, with a coarse-grained model to enhance sampling. We find that in flooding simulations, both propofol and a generic particle localize to the crystallographic transmembrane anesthetic binding region, and that propofol also localizes to an extracellular region shared with the crystallographic ketamine binding site. Subsequent simulations to probe these binding modes in greater detail demonstrate that ligand binding induces structural asymmetry in GLIC. Consequently, we employ residue interaction correlation analysis to describe the internal allosteric network underlying the coupling of ligand and distant effector sites necessary for conformational change. Overall, the results suggest that the same allosteric network may underlie the actions of various anesthetics, regardless of binding site.