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Docking kinetics and equilibrium of fluorescently labeled RNA molecules are studied with single-molecule FRET methods. Time- resolved FRET is used to monitor docking/undocking transitions for RNAs containing a single GAAA tetraloop-receptor tertiary inter- action connected by a flexible single-stranded linker. The rate constants for docking and undocking are measured as a function of Mg2+ revealing a complex dependence on metal ion concentration. Despite the simplicity of this model system, conformational heterogeneity similar to that noted in more complex RNA systems is observed; relatively rapid docking/undocking transitions are detected for approximately two-thirds of the RNA molecules, with significant subpopulations exhibiting few or no transitions on the 10- to 30-s time scale for photobleaching. The rate constants are determined from analysis of probability densities, which allows a much wider range of time scales to be analyzed than standard histogram procedures. The data for the GAAA tetraloop receptor are compared with kinetic and equilibrium data for other RNA tertiary interactions. [ABSTRACT FROM AUTHOR]