Thioflavin T (ThT) is a fluorescent dye commonly used to stain amyloid plaques, but the binding sites of this dye onto fibrils are poorly characterized. We present molecular dynamics simulations of the binding of ThT and its neutral analog BTA-1 [2-(4'-methylaminophenyl)benzothiazole] to model protofibrils of the Alzheimer's disease Abeta(16-22) (amyloid beta) peptide. Our simulations reveal two binding modes located at the grooves of the beta-sheet surfaces and at the ends of the beta-sheet. These simulations provide new insight into recent experimental work and allow us to characterize the high-capacity, micromolar-affinity site seen in experiment as binding to the beta-sheet surface grooves and the low-capacity, nanomolar-affinity site seen as binding to the beta-sheet extremities of the fibril. The structure-activity relationship upon mutating charged ThT to neutral BTA-1 in terms of increased lipophilicity and binding affinity was studied, with calculated solvation free energies and binding energies found to be in qualitative agreement with the experimental measurements.