Figure 3.

FRET-induced donor decay directly visualizes FRET rate constants and donor–acceptor distances. Fluorescence intensity decays of a donor f_D|D(t) (top row) in the absence (green) and in the presence (blue, magenta, and orange) of FRET. The corresponding FRET-induced donor decays, ε_D(t)’s, are shown in the lower two rows. The fluorescence decays were calculated by eq 13 (single FRET-active species), eq 16 (mixture of FRET-active and FRET-inactive species), and eq 18 (mixture of FRET species and distribution of FRET species) (R₀ = 50 Å and k_D^–1 = 4.0 ns). Information on FRET is obtained by comparing the fluorescence decay of the donor in the presence of an acceptor (blue or magenta) to its reference given by the fluorescence decay in the absence of FRET (green). ε_D(t) contains the reference implicitly. In the middle row, ε_D(t) is shown in linear scale. In the lower row, ε_D(t) is shown with a logarithmic time axis, and the time t between excitation and detection of fluorescence was converted into a critical donor–acceptor distance axis R_DA,C by eq 15. This allows for the determination of the characteristic times of FRET k_RET^–1 and distances graphically at the point where ε_D(t) decayed to the value 1/e (shown as vertical lines). The time t corresponds to the DA distance of the FRET process. (A) Single distance of R_DA = 40 Å (magenta) and R_DA = 65 Å (blue), respectively. (B) Mixture of a FRET-active R_DA = 40 Å (magenta) and R_DA = 65 Å (blue) and a FRET-inactive species (fraction, x_noFRET = 0.1). (C) Mixture of two FRET-active species R_DA⁽¹⁾ = 40 Å (50%) and R_DA⁽²⁾ = 65 Å (50%) (orange). The position and the height of the “steps” in the lowest plot relate to the FRET rate constant and the species fractions of the individual species. For comparison, the components (dotted blue and magenta lines) of the individual species are overlaid. (D) Normal distributed distance with a mean of ⟨R_DA⟩ = 40 Å and a distribution width varying from 0 to 32 Å (black to magenta).