Accurate FRET measurements within single diffusing biomolecules using alternating-laser excitation

Abstract

Fluorescence resonance energy transfer (FRET) between a donor (D) and an acceptor (A) at the single-molecule level currently provides qualitative information about distance, and quantitative information about kinetics of distance changes. Here, we used the sorting ability of confocal microscopy equipped with alternating-laser excitation (ALEX) to measure accurate FRET efficiencies and distances from single molecules, using corrections that account for cross-talk terms that contaminate the FRET-induced signal, and for differences in the detection efficiency and quantum yield of the probes. ALEX yields accurate FRET independent of instrumental factors, such as excitation intensity or detector alignment. Using DNA fragments, we showed that ALEX-based distances agree well with predictions from a cylindrical model of DNA; ALEX-based distances fit better to theory than distances obtained at the ensemble level. Distance measurements within transcription complexes agreed well with ensemble-FRET measurements, and with structural models based on ensemble-FRET and x-ray crystallography. ALEX can benefit structural analysis of biomolecules, especially when such molecules are inaccessible to conventional structural methods due to heterogeneity or transient nature.

FIGURE 1

Alternating-laser excitation microscopy. (A) Microscope setup for ALEX. EOM, electrooptical modulator; P, polarizer; DM, dichroic mirror; OBJ, objective; PH, pinhole; F, filter; APD, avalanche photodiode. Modulators combined with polarizers result in alternating-laser excitation. After spatial and spectral filtering, emitted fluorescence photons were detected on APDs. (B) Time traces for a high-E DNA. The emission streams are and where represents the emission rate in the Y emission detection channel while X-excitation is on. Burst a is due to a high-E D-A species (low and high ). Burst b is due to a D-only species (high and very low ). D-only species (stars); D-A species (solid circles).

FIGURE 2

Sorting single molecules using ALEX-based E_PR-S histograms. (A) Expected location of labeled molecules depending on D-A stoichiometry and D-A distance. (B) Species required for recovering all corrections factor needed for accurate-E measurements using the method that depends on laser-alternation characteristics. D-only species provides the D-leakage factor l, A-only species provides the A-direct-excitation factor d, and two D-A species with large difference in E provide the γ-factor. (C) Species required for recovering all corrections needed for accurate-E measurements using the method that is independent of laser-alternation characteristics. D-only species provides the D-leakage factor l, a D-A species with E ∼ 0 (“simple-coincidence” control) provides the modified A-direct-excitation factor d′, and a D-A species with appreciable E provides the γ-factor. Use of A-only species is not necessary.

FIGURE 3

ALEX-based E_PR-S histograms for DNA fragments used for the determination of accurate-E. Light and dark gray curves in E_PR and S histograms: individual and sum of Gaussian fits to the one-dimensional histograms. (A–E) Histogram for T1B28, T1B23, T1B18, T1B13, and T1B8 DNA, respectively. The thick solid lines correspond to E_PR, S-values as predicted for D-A species using γ = 0.71 and β = 1.25.

FIGURE 4

ALEX-based distance measurement and its dependence on detection-correction factor-γ. (A) E_PR-1/S plot for the DNA of Fig. 3 and its dependence on alignment. Mean E_PR-1/S values and linear fit for optimal alignment (solid circles and solid line); mean E_PR-1/S values and linear fit for suboptimal alignment (open circles and dotted line). Error bars are the standard deviations of three measurements; error bars for E_PR are not visible (<0.01). With optimal alignment, the linear fit yields γ = 0.71, and β = 1.25. Suboptimal alignment changes the correction factors (γ = 1.05; β = 1.30), leading to changes in E_PR and 1/S; however, corrected values of E are identical to the one obtained by optimal alignment (Table 1; Fig. 4 B). (B) Relation between E_PR and E, and its dependence on γ. Optimal alignment (•); suboptimal alignment (○). (Gray lines) E_PR − E correction curves for γ = 0.71, and γ = 1.05. (Dotted lines) E_PR − E correction curves for 0.25 < γ < 4. Differences between E_PR and E are maximal for intermediate values of E, and for γ ≫ 1 and γ ≪ 1. (C) Relation between R_PR and R, and its dependence on factor-γ . The differences between R_PR and R increase linearly with increasing R.

FIGURE 5

A single ALEX measurement can recover accurate-E. E_PR-S histogram for a mixture of D-only, A-only, T1B28, and T1B13 DNA. (Dotted rectangle) Area of histogram shown in the E_PR histogram. D-only species were used for D-leakage correction, A-only species for A-direct-excitation correction, and the T1B28/T1B13 pair for determination of γ.

FIGURE 6

Comparison of E-values measured for DNA fragments with values predicted from cylindrical models of DNA. ALEX-based E (E_sm) (•). Ensemble E (E_ens) (○). Theoretical E (E_the) was calculated (Clegg et al., 1993; Norman et al., 2000) using where n is the interprobe separation (in bp), L is the rise of the terminal probe along the helix axis, d is the radial distance of the center of the donor probe from the helix axis (in Å), a is the radial distance of the center of the acceptor probe from the helix axis (in Å), θ is the rotation angle for fluorophores separated by n bp (calculated using θ = 34 (n − 1)), ϕ is the cylindrical angle between radially extended donor and acceptor when spaced by 1 bp, and R_o is the Förster radius (in Å). The solid curve represents E_the for a DNA model with the donor probe proximal to the DNA helical axis (L = 4 Å, a = 25 Å, d = 0 Å, ϕ = 232°, and R_o = 69 Å), whereas the dotted curve represents E_the for a DNA model with the donor probe distal from the DNA helical axis (L = 4 Å, a = 25 Å, d = 15 Å, ϕ = 232°, and R_o = 69 Å). Error bars are the standard deviations of three measurements. In all cases, E_sm-values fit better to theoretical values than E_ens.

FIGURE 7

E_PR-S histograms for RNAPσ^TMR,366 complexed with DNA carrying an acceptor at various positions, and γ-determination. Histograms display only the D-A species; D-only and A-only species were removed using > 20 photons and > 20 photons, respectively. (A–D) Complexes with acceptor at +64, +29, +28, and +25, respectively. (E) Linear relation between E_PR and 1/S allows extraction of β- and γ-factors; each point reflects the averages and standard deviations of three experiments.