(A–B) Long time trajectories showing transitions between low- and high-FRET states (efficiencies of 0 and 0.45). The top panel shows calculated FRET efficiency in blue and two-state Hidden Markov Model fit in green (McKinney et al., 2006). The bottom panels show Cy3 and Cy5 fluorescence emission in green and red respectively. At low DNA concentration (A), the low FRET state predominates. As DNA concentration is increased (B), more time is spent in the high FRET state, because the dwell times in the low FRET state are shorter. At low DNA concentrations, there appears to be long- and short-lived high-FRET states. Likewise, at near-saturating DNA concentrations, there appear to be long and short-lived low FRET states. (C, D) Cumulative distributions of low- and high-FRET dwell times (blue circles). Fits to single-exponentials (black) show large nonrandom residuals (lower panels), consistent with the heterogeneity noted in (A) and (B). Double-exponentials (red) give smaller, more uniform residuals. (E) Apparent association rate constants as a function of DNA concentration. The apparent rate constant for the fast phase depends on DNA concentration (blue circles), indicating a bimolecular step binding event. The apparent rate constant for the slow phase does not depend on DNA-concentration (blue triangles), suggesting an isomerization event. (F) Apparent dissociation rate constants as a function of DNA concentration (phase one shown in blue circles, and phase two shown in blue triangles). Neither phase shows a DNA concentration dependence, indicating a dissociation and/or isomerization events. 68% confidence intervals are estimated using the conf_interval function of lmfit by performing F-tests (Newville et al., 2014). Conditions: 20 mM Tris pH 8.0, 200 mM KCl.