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Published in final edited form as: Methods. 2013 Jul 23;66(2):168–179. doi: 10.1016/j.ymeth.2013.07.026

Hidden Markov model analysis of FRET-labeled Pgp. (A) 4-state HMM with transitions between four states S_i, with i= 1, 2, 3, 4, transition probabilities k_i,i and k_i,j, and the corresponding transition probability matrix K. (B, C) FRET state assignments by two HMMs in two photon bursts of FRET-labeled Pgp during 'cyclosporin transport' conditions. FRET donor fluorescence (Alexa 488) is shown in the lower panels as green time traces with 1 ms binning. FRET acceptor fluorescence (Atto 610) is shown as red trace. Intensities are backgound and detection efficiency corrected. Direct excitation of Atto 610 results in fluorescence intensities shown as grey time traces. In the middle and upper panels, the blue traces are the calculated FRET distances from FRET efficiencies E_FRET=I_A/(I_A+ I_D), with I_A, I_D, background and cross-talk corrected intensities of FRET acceptor or donor fluorophore, and, correction factor for the different detection efficiencies and quantum yields of the two fluorophores. FRET distances r_t were obtained per data point using E_FRET=_R0⁶ / (R₀⁶ + r_t⁶) according to the Förster theory of FRET [20]. Red lines with steps are the assigned FRET levels using a 4-state HMM (middle panels) or a 9-state HMM (upper panels), respectively. Light-red colored areas are the variance ( ²) limits for the assigned FRET levels using the new estimators that include the information of sum intensities of both fluorophores at each data point (eq. (10)).

Hidden Markov model analysis of FRET-labeled Pgp. (A) 4-state HMM with transitions between four states S_i, with i= 1, 2, 3, 4, transition probabilities k_i,i and k_i,j, and the corresponding transition probability matrix K. (B, C) FRET state assignments by two HMMs in two photon bursts of FRET-labeled Pgp during 'cyclosporin transport' conditions. FRET donor fluorescence (Alexa 488) is shown in the lower panels as green time traces with 1 ms binning. FRET acceptor fluorescence (Atto 610) is shown as red trace. Intensities are backgound and detection efficiency corrected. Direct excitation of Atto 610 results in fluorescence intensities shown as grey time traces. In the middle and upper panels, the blue traces are the calculated FRET distances from FRET efficiencies E_FRET=I_A/(I_A+ I_D), with I_A, I_D, background and cross-talk corrected intensities of FRET acceptor or donor fluorophore, and, correction factor for the different detection efficiencies and quantum yields of the two fluorophores. FRET distances r_t were obtained per data point using E_FRET=_R0⁶ / (R₀⁶ + r_t⁶) according to the Förster theory of FRET [20]. Red lines with steps are the assigned FRET levels using a 4-state HMM (middle panels) or a 9-state HMM (upper panels), respectively. Light-red colored areas are the variance ( ²) limits for the assigned FRET levels using the new estimators that include the information of sum intensities of both fluorophores at each data point (eq. (10)).