Defining the limits of single-molecule FRET resolution in TIRF microscopy

Abstract

Single-molecule FRET (smFRET) has long been used as a molecular ruler for the study of biology on the nanoscale (∼2-10 nm); smFRET in total-internal reflection fluorescence (TIRF) Förster resonance energy transfer (TIRF-FRET) microscopy allows multiple biomolecules to be simultaneously studied with high temporal and spatial resolution. To operate at the limits of resolution of the technique, it is essential to investigate and rigorously quantify the major sources of noise and error; we used theoretical predictions, simulations, advanced image analysis, and detailed characterization of DNA standards to quantify the limits of TIRF-FRET resolution. We present a theoretical description of the major sources of noise, which was in excellent agreement with results for short-timescale smFRET measurements (<200 ms) on individual molecules (as opposed to measurements on an ensemble of single molecules). For longer timescales (>200 ms) on individual molecules, and for FRET distributions obtained from an ensemble of single molecules, we observed significant broadening beyond theoretical predictions; we investigated the causes of this broadening. For measurements on individual molecules, analysis of the experimental noise allows us to predict a maximum resolution of a FRET change of 0.08 with 20-ms temporal resolution, sufficient to directly resolve distance differences equivalent to one DNA basepair separation (0.34 nm). For measurements on ensembles of single molecules, we demonstrate resolution of distance differences of one basepair with 1000-ms temporal resolution, and differences of two basepairs with 80-ms temporal resolution. Our work paves the way for ultra-high-resolution TIRF-FRET studies on many biomolecules, including DNA processing machinery (DNA and RNA polymerases, helicases, etc.), the mechanisms of which are often characterized by distance changes on the scale of one DNA basepair.

Figure 1

DNA FRET standards used for heterogeneity analysis. D, donor fluorophore; A, Acceptor fluorophore; B, biotin. T1B16, T1B17, T1B18: 15-, 16-, and 17-bp donor-acceptor separation, respectively, with an end-labeled donor, and an internally labeled acceptor. T1B18GC: 17-bp donor-acceptor separation, sequence adjacent to donor changed to CCG, as shown. T1B18INT: 17-bp donor-acceptor separation, internally labeled donor, modified sequence as shown. Full sequences included in the Supporting Material.

Figure 2

(A and B) Simulated datasets (blue line, simulation) compared to theoretical predictions for a wide range of number of collected photons N (A) and mean FRET efficiencies E₀ (B). Theoretical predictions presented for numerical integration of full theoretical prediction (theory (exact), green line); for analytic result, Eq. 6, with approximations discussed in main text (theory (approximate), red line); and for analytic result, neglecting background noise in the prediction (theory, no background (approximate), black line). Results in panel A for E₀ = 0.50, results in panel B for N = 2000 photons per molecule per frame. (C) Heterogeneity analysis for 17-bp donor-acceptor separation dsDNA (T1B18, E₀ = 0.45). Results of dynamic heterogeneity analysis (dynamic, black circles) and static heterogeneity analysis (static, red circles) compared to predictions from simulation (blue dashed line) and theory (green line). Heterogeneity σ < 0.04 is required for 1-bp resolution (see text). Integration time at acquisition was 20 ms; duration of each measurement, 20 s. Each data point combines results for all molecules observed for >5 frames at that integration time in a 648-molecule dataset from 18 combined FOVs. Simulation parameters matched experimentally observed values at the original 20 ms integration time. Simulation values for longer integration times, τ, were calculated as ${\sigma }_{\text{sim}}\left(\tau \right)={\sigma }_{\text{sim}}\left(20\text{ms}\right)\sqrt{20\text{ms}/\tau }$.

Figure 3

Excess dynamic heterogeneity investigated by manual analysis and classification of molecular subpopulations. Example of single-molecule time-traces from 648-molecule dataset used for heterogeneity analysis (T1B18, Fig. 2C). A set of 119 molecules with too few above-threshold frames were excluded from manual analysis. (Top) Apparent FRET (E, red line) and stoichiometry (S, black line). (Middle) D, donor excitation donor emission (green); A, donor excitation acceptor emission (red); AA, acceptor excitation acceptor emission (black); and total emission during donor excitation, N, (cyan). (Bottom) Observed Allan deviation, σ_AD (black circles); predictions from simulation (blue dashed line). (A) A set of 227 molecules (43%) show stable fluorescence, FRET, and stoichiometry for the duration of the measurement. (B) A set of 191 molecules (36%) show steplike E fluctuations with a corresponding sharp change in AA emission and without a corresponding change in N emission, characteristic of acceptor photophysics. (C) A set of 58 molecules (11%) show slow E fluctuations with corresponding slow change in total emission intensity under donor excitation, characteristic of focal drift. Fifty-three molecules (10%) could not be clearly classified into any of the three populations.

Figure 4

Sources of static heterogeneity. (A) Sources of static heterogeneity on T1B18 dsDNA standard probed in the presence of different heterogeneity sources. Single position: static heterogeneity on a single molecule in a single position on the FOV. Multiple positions: single molecule moved between multiple different positions on the field of view (FOV) using a scanning stage. Multiple molecules: multiple molecules from a single FOV only. Multiple FOV: multiple molecules from multiple FOVs. Measurement parameters: Integration time, 100 ms; duration of measurement, 5 s; 80 photons/ms per molecule. Results for multiple molecules and multiple FOV from three separately prepared samples, >400 molecules per sample, ∼20 FOV per sample. Results for single position and multiple positions are from 19 molecules, each measured for 5 s in ≥4 different positions within an area of ∼1 FOV, yielding in total 84 distinct, randomly distributed positions across the FOV. This dataset is necessarily small, because only molecules within a small area could be used, and all molecules retained in the analysis were excited for >20 s without bleaching. (B) Magnitudes of static heterogeneity sources calculated using results from panel A. (C) Intermolecular heterogeneity investigated using dsDNA FRET standards shown in Fig. 1. Measurement parameters: Integration time, 100 ms; duration of measurement, 5 s; 80 photons/ms per molecule; three sample repeats for each measurement; >20 FOV per sample; >190 molecules per sample.

Figure 5

High-resolution static heterogeneity analysis. (A) One-basepair resolution with 1000-ms time resolution. Measured FRET distributions for dsDNA with 15-bp (T1B16) and 16-bp (T1B17) donor-acceptor separation, and for an equimolar mixture of each (T1B16-T1B17 mix). (B) Two-basepair resolution with 80-ms time resolution. Measured FRET distribution at increasing integration times for an equimolar mixture of dsDNA with 15-bp and 17-bp D-A separation (T1B16-T1B18 mix). Measurement parameters, 1-bp data: integration time at acquisition, 100 ms; duration of measurement, 5 s; ∼50 photons/ms per molecule; >1200 molecules; ∼45 combined FOV. Measurement parameters, 2-bp data: integration time at acquisition, 20 ms; duration of measurement, 20 s; 55 photons/ms per molecule; 335 molecules; 11 combined FOV.