A FLIM Microscopy Based on Acceptor-Detected Förster Resonance Energy Transfer

Abstract

Time-resolved donor-detected Förster resonance energy transfer (trDDFRET) allows the observation of molecular interactions of dye-labeled biomolecules in the ∼10–100 Å region. However, we can observe longer-range interactions when using time-resolved acceptor-detected FRET (trADFRET), since the signal/noise ratio can be improved when observing the acceptor emission. Therefore, we propose a new methodology based on trADFRET to construct a new fluorescence lifetime microscopy (FLIM-trADFRET) technique to observe biological machinery in the range of 100–300 Å in vivo, the last frontier in biomolecular medicine. The integrated trADFRET signal is extracted in such a way that noise is canceled, and more photons are collected, even though trADFRET and trDDFRET have the same rate of transfer. To assess our new methodology, proof of concept was demonstrated with a set of well-defined DNA scaffolds.

1. Introduction

Macromolecular assemblies are responsible for replication, transcription, translation, vesicular transport, viral, and parasitic infections.¹⁻⁶ Fortunately, after the elucidation of these macromolecular mechanisms, new therapeutic approaches can be created to better fight disease by repairing, halting degenerative processes, or stopping infectious machinery at the molecular level.^4,7,8 The latest microscopy technologies give molecular resolution below 300 Å (Figure 1A, orange box) and the current “fluorescence lifetime imaging microscopy” based on time-resolved donor-detected Förster resonance energy transfer (FLIM-trDDFRET) methodology (Figure 1A, yellow box)² can observe molecular activities in the 10–100 Å range. Traditional trDDFRET lifetime of D in the presence of A (τ_D(A)) gets closer to the reference donor lifetime (τ_D) at increasing D-A distances.

Figure 1.

(A) Scale of living organisms (www.microbiologyinfo.com). Fluorescence microscopy techniques (orange box) have breached Abbe′s limit and reached ∼300 Å resolution. Traditional trDDFRET (yellow box) for our FRET pairs detect molecular interaction in the 10–100 Å region (yellow box). However, our FLIM-trADFRET methodology (pink box) can detect macromolecular interaction in the remaining gap region of 100 Å–300 Å. (B) The sensitized trADFRET intensity (purple, I_trADFRET) has approximately threefold higher intensity with respect to its lifetime reference ⟨τ_Std⟩ (red) than the traditional trDDFRET (green, τ_D(A)) and its respective reference (orange, τ_D) (Database S1). (C) The FRET process initiates by an excitation pulse (blue) that excites D toward D*, which transfers its energy in the presence of an acceptor (A). The kinetic mechanism is a → b → c with some branches (black arrows), where a and b correspond to D* and A*, respectively, and c corresponds to the photons, hν_(A), emitted by the excited A*. The value of d[A*]/dt, is 0 at t₀, and it rises to a maximum (t_max) and decays exponentially to 0. D* and A* are inactivated via their respective radiative lifetimes (τ), that is, the sum of the reciprocal of the sum fluorescence rate and the nonradiative pathways (Σk_i, black arrows). (D) The fluorescein (Fl, donor) and x-rhodamine (Xr, acceptor) dyes have broad emissions (yellow and red arrows, respectively) for which signals are collected by 520- and 620-nm interference filters. The excitations were 481 and 470 nm for LaserStrobe and FluoTime, respectively. (E, F) k_t (Eq 4) and FRET efficiency (100% × (1 – τ_D(A)/τ_D)) plots as a function of mean interdye distance (R̅) for the Fl_int and Xr pair attached to the N oligo series for which R₀ is 61.8 Å and τ_D is 4.12 ns (Database S2). (G, H) The k_t as a function of lifetimes in nanoseconds (ns) and picoseconds (ps), respectively. The τ_D(A) dropped 1.5 logs from 0 to 4 ns (blue), and 3 logs from 4.0 to 4.12 ns (red). TheR̅ of 115, 125, 180, and 300 Å correspond to τ_D(A) values of 4023, 4045, 4113, and 4119.7 ps, respectively, which corresponded to energy transfers of 2.35, 1.44, 0.164 and 0.008% in the same order (Database S1). (I, J) Simulated trDDFRET lifetimes, in logarithmic and percentage scale, respectively. τ_D is 4.12 ns, and τ_D(A) varies from 0.13, 1.37, 3.40, to 4.02 ns for R̅ of 35, 55, 80, and 115 Å, respectively (Database S1). As the distance increases the lifetime difference, Δτ = τ_D – τ_D(A), approaches to zero thus making the R̅ calculation impossible. Thus, at 115 Å, τ_D and τ_D(A) (blue and brown curve, respectively) cannot be discriminated by the fitting algorithms due to curve overlapping. (K, L) The FLIM-trADFRET simulations from 35 Å up to 300 Å; our methodology utilizes the time-resolved sensitized trADFRET whose rising curve allows photon accumulation over the steady background, ⟨τ_Std⟩. For our dye pairs at distances beyond 100 Å, the trDDFRET τ_D(A) approaches to the τ_D, acting as a limiting maximum value. However, in the case of the trADFRET, the signal accumulates on top of the ⟨τ_Std⟩ thus improving S/N ratio by increasing sensitized signal strength and decreasing background noise.

In this work, we present the equations and experimental strategies to observe trFRET-sensitized acceptor (A), creating the basis of a new type of FLIM, herein called FLIM-trADFRET, that increases the FRET resolution up to 300 Å (Figure 1A–D, Database S1). For trDDFRET and trADFRET, the rate of transfer (k_t) and the FRET efficiency is the same in both cases (Figure 1E–J),⁹⁻¹⁶ but the latter has unlimited photon accumulation and background noise reduction (red line, Figure 1G,H) allowing better signal–noise ratio (S/N)¹⁷ (Figure 1K,L). Our new approach is based on the photon accumulation of the trADFRE ⟨τ_trADFRET^Obs⟩ over a reference lifetime ⟨τ_Std⟩ that has been acquired with a standard solution (Figure 1J,K). Therefore, our FLIM-trADFRET accumulate signals like ¹H and ¹³C NMR experiments, where nuclei relaxation is averaged in low-concentration samples.^18,19 Similarly, magnetic resonance imaging (MRI) in which T1 and T2 relaxations are collected by stacking image frames to improve resolution²⁰⁻²² or for stealth airplane detection in the military.²³

2. Materials and Methods

The single- and double-labeled N′ and N oligo series (Figure S1, Table 1) were synthesized with their corresponding unlabeled complementary strands by TriLink Biotechnologies, Inc. (San Diego, CA) followed by both HPLC and PAGE purification. All experiments were conducted at 20 ± 0.1 °C in 10 mM Tris, 100 mM KCl, 2.5 mM MgCl₂ and 1 mM CaCl₂ (pH 8). The top strand concentrations were 10–50 nM, and duplexes were formed with 10× complement concentration.

Table 1. N′ and N Oligo Sequences. The DNA Oligos Were Labeled with 5′ X-Rhodamine (5′-Xr*, Acceptor) and 3′ Fluorescein (3′-*Fl, Donor) Attached by 6-Carbon Long Linkers for the Former, and the Latter with 5′Xr and Internally Labeled Fl by a 12-Atom Long Linker (Fl_int, Donor)^a.

N′ series	double-labeled DNA sequences
14N′	5′-Xr*GGGAATAACTTGGC*Fl-3′
29 N′	5′-Xr*GGCTAATACTATATAATAGACGACTTGGC*Fl-3′
N series	double-labeled DNA sequences
24 N	5′-Xr*GCGAATAATAATGACGACTTGAA(dT-Flint)GTGGC-3′
29 N	5′-Xr*GCGAATAATAATAACGTGACGACTTGAA(dT-Flint)GTGGC-3′
34 N	5′-Xr*GCGAATAATAATAAATCGACGTGACGACTTGAA(dT-Flint)GTGGC-3′
39 N	5′-Xr*GCGGCAATAGATAATATGAACTAATTTAACTACTTGAA(dT-Flint)GTGGC-3′
44 N	5′-Xr*GCGGCATAGACTAATATTTTTATAACTAATTTAACTTCTTGAA(dT-Flint)GTGGC-3′
49 N	5′-Xr*GGGAATAATAATAAAGGGAAGAAGACTTGGCTCGACGTGACGACTTGAA(dT-Flint)GTGGC-3′
52 N	5′-Xr*GCGACAATAATAATAAAGGGAATAAGACTTGGCTCGACGTCACGACTTGAA(dT-Flint)GTGGC-3′
56 N	5′-Xr*GCGTAGTGCTATGTAATCGACGAATCGGGCAAAGCTAGTAGTTAGTAAACTTGAA(dT-Flint)GTGGC-3′
34 N complements	DNA sequences
standard	5’-GCC-ACA-TTA-AAG-TCG-TCA-CGT-CGA-TTT-ATT-ATT-ATT-CGC-3’
mismatch T at 20	5’-GCC-ACA-TTA-AAG-TCG-TCA-CTT-CGA-TTT-ATT-ATT-ATT-CGC-3’
mismatch A at 20	5’-GCC-ACA-TTA-AAG-TCG-TCA-CAT-CGA-TTT-ATT-ATT-ATT-CGC-3’
mismatch C at 20	5’-GCC-ACA-TTA-AAG-TCG-TCA-CCT-CGA-TTT-ATT-ATT-ATT-CGC-3’
d spacer (abasic) at 20	5’ GCC-ACA-TTC-AAG-TCG-TCA-C(d Spacer)T-CGA-TTT-ATT-ATT-ATT-CGC-3′
two d-spacers at 20–21	5’ GCC-ACA-TTC-AAG-TCG-TCA-(d Spacer)(d Spacer)T-CGA-TTT-ATT-ATT-ATT-CGC-3’
1st half (Flint side)	5’-GCC-ACA-TTC-AAG-TCG-TCA-C-3′
2nd half (Xr side)	5′-T-CGA-TTT-ATT-ATT-ATT-CGC-3’

^aAlso, the single-labeled D (DNA*Fl-3′ and DNA*Fl_int) and A (Xr*DNA) sequences were synthesized. The N′ series was composed of only two sequences with a 14 and 29 basepair (bp) interdye separation; and in the case of the N oligos, they have an interdye separation of 29, 34, 39, 44, 49, 52, and 56 bps without considering the extra 5 bps toward the 3′end. The standard complements and several versions of 34 N complements were synthesized to hybridized with the top strands.

2.1. Instrumentation, Data Acquisition, and Fitting Analysis

Time-resolved decays were collected by two instruments: (1) LaserStrobe, LS (Photon Technologies, Inc., Birmingham, NJ) with 10 Hz excitation rate provided with a PLD481 dye tuned to 481 nm with emission collected through nonfluorescing 520 and 620 nm interference filter (10BPF10-520 and 10BPF10-620, full width at half maximum (FWHM) = 9 nm, Oriel Corp., Stratford, CT) preceded by a 50 mm × 50 mm aperture and 1 cm path length quartz liquid filter of 24.1 mM acetate buffered dichromate, pH 4, to remove scattered excitation light. To collect direct A lifetime, the excitation was provided by a PLD575 dye tuned to 585 nm. The emission collection was carried out in 120–150 channels in a 23–25 ns window with three successive replicate decays collected and averaged to yield one sample decay. A total of four sets of six decays were collected for a total of 72 individual curves. The instrument response function (IRF) was obtained for each set using a diluted glycogen solution for deconvolution purposes (Database S3 and Database S5). (2) FluoTime, FT (PicoQuant GmbH, Berlin, Germany), with 20 MHz pulsed excitation rate at 470 nm provided by a pulsed diode laser LDH-P-C-470 (PicoQuant, GmbH, Berlin, Germany) with emission collected through the same filters. In the case of the FluoTime, the decays were collected at 20 MHz over 6 s with a photon detection rate below 1% of the excitation repetition frequency and concentrations maintained between 20 and 50 nM to avoid pile-up error. The IRF was collected every 30–60 min using a solution of colloidal silicon dioxide (LUDOX, DuPont, Wilmington, DE) with the baseline intensity matched to the sample decays to facilitate fitting, having an FWHM of 40 picoseconds (ps) or less. A total of 350 sample decays were collected in 50 sets of 7 decays each and at least 175 decays for the standard solutions grouped in 25 sets of 7 decays each (full data set provided, Database S3, Database S6, and Database S7).

The raw curves were fitted to mono-, bi-, and tri-exponential decay models evaluated by iterative deconvolution based on the Marquardt algorithm. In the case of the LaserStrobe, the optimal model was identified using χ², the runs test normal variate, Z, and the Durbin–Watson parameter. In the case of the FluoTime instrumentation, only a global fitting χ² value is given for each set to discriminate models (Database S3, Database S6, and Database S7).

3. Results and Discussion

3.1. Dye Spectroscopy Properties

Our testing material were two families of 5′end labeled x-rhodamine (Xr) and either 3′ end (3′-Fl) and internally labeled Fl (Fl_int) duplex DNA oligomers, called N′ and N oligos, respectively (Table 1, Figure S1). We preferred DNA since it can be designed to have a well-defined straight and fixed geometry,^24,25 instead of a peptide scaffold as seen in earlier seminal work.²⁶ Our duplexes have been extensively studied in our previous trDDFRET work with two spectrometers (FluoTime and LaserStrobe) and we have characterized the in situ dye spectroscopy properties, such as maximum molar absorbances (ε), excitation ratios, absorption and emission spectra shifting, quantum yields (QY), natural lifetime (τ⁰), nonstatically quenched fraction (1 – S), dynamic lifetime (Φ), and the respective lifetimes (τ)²⁷⁻²⁹ relevant for trADFRET calculation and the Förster distance (R₀). We also report the anisotropy (r_ss) values of the dyes attached by flexible linkers to the duplexes to calculate the dipole–dipole dye orientation factor (<κ²>) lower and upper values, <κ²> _min and <κ²> _max, respectively (Database S2), to set the maximum and minimum interdye distances, R_max and R_min, in the case that <k² > is different from 2/3 when the dye depolarization isotropy condition is not achieved.³⁰

3.2. Traditional trDDFRET

We calculated trFRET-derived distance distribution (P(R)) that has a mean distance, ^–R, and a standard deviation (σ) for the double-labeled 14 N′ and 29 N′ oligos, using both traditional trDDFRET (Figure 2A–D)²⁹ and trADFRET (Figure 2E–N). In the case of the former, the D intensities of 14 N′ (orange, I_D) and D in the presence of the A (green, I_D(A)) were collected with a 520-nm interference filter for the LaserStrobe (Figure 2A) and FluoTime (Figure 2B, Database S3). Thus, the deconvoluted 14 N′ I_D and I_D(A) yielded the lifetime (Database S3) difference, Δτ = τ_D – τ_D(A), this difference is caused by the energy transfer process which provides information to calculate the P(R)′s R̅ and σ values (eq 3 supplementary text, Table 2, Database S4). While in the case of the 29 N′, the Δτ values (Database S3) were 0.105 ns (± 0.044 ns) and −0.041 ns (± 0.022 ns), for LaserStrobe and FluoTime, respectively, which overlapping impedes the P(R) determination (Table 2, Figure 2C,D, Database S4).

Figure 2.

Time-resolved DDFRET and trADFRET lifetimes. Deconvoluted time-resolved intensity for the 14 N′ (A, B) and 29 N′ (C, D) in the absence (orange, I̅_D) and presence of A (green, I̅_D(A)) with 2% added noise and respective fits (τ_D and τ_D(A), black lines) for both instruments. In contrast to 14 N′, the 29 N′ overlapping curves and lifetimes impeded P(R) calculations (Database S4). (E, F) The observed LaserStrobe trADFRET intensity (green, S̅_trADFRET) with 2% added noise for the double-labeled 14 N′ and 29 N′ collected with the 620 nm interference filter at 481 nm excitation, respectively. The leaked D intensity in the presence of A (orange, I̅_D(A)) corresponded to the trDDFRET decays (shown in figure A), is multiplied by 1/(r + 1), and the directly excited A (pink, I̅_A) is multiplied by r/(r + 1), where the “r” parameter is the I_A/I_D(A) ratio (eq 11, Database S5). The I̅_D(A) and I̅_A were acquired with the same N oligo sample with the 520-nm filter at 481 nm excitation, and the 620 nm interference filter at 585 nm excitation wavelength, respectively. The sum of I̅_D(A)·1/(r + 1) + I̅_A·r/(r + 1), contaminating signals (red) were removed to extract the sensitized I_trADFRET (light blue). The sensitized I_trADFRET for the 14 N′ and 29 N′ with the least-squares fitted curve (black) in a logarithmic scale (G) and linear scale (H, I), respectively. (J–N) The sensitized I_trADFRET, I̅_D(A) and I̅_A of 14 N′ and 29 N′ acquired with FluoTime collected with the same filters but at 470 nm excitation (Database S6). The calculated R̅ and σ values were equivalents for both instruments (Table 2).

Table 2. Calculated Inter-Dye Distances Acquired by trDDFRET and trADFRET for the N′ Series.

			14N’		29 N’
instrumentation	methodology	equationd	R̅ (Å)	σ (Å)	R̅ (Å)	σ (Å)
LaserStrobe	trDDFRETa	3	64.5 ± 1.8	7.1 ± 0.2	NA	NA
	trADFRETb	18	64.3 ± 1.1	5.3 ± 0.7	117.4 ± 1.9	4.0 ± 0.3
FluoTime	trDDFRETa	3	63.1 ± 1.9	8.5 ± 0.9	NA	NA
	trADFRETc	18	63.3 ± 1.1	5.0 ± 0.9	115.9 ± 2.4	15.2 ± 1.9
		average	63.8 ± 1.5	6.5 ± 1.6	116.6 ± 2.1	9.6 ± 7.9

^aDatabase S4.

^bDatabase S5.

^cDatabase S6.

^dValues are calculated by simplex minimization routines, and the errors correspond to the standard deviation of the univariate analysis for each parameter²⁹ assuming a <k²> = 2/3 under the isotropic condition where all dye dipole orientations are present at the energy transfer process, resulting in the R̅ value. We used long flexible linkers to tether our dye probes to the duplex DNA to maximize the possibility of the isotropic state. However, when dye isotropic conditions are not attained, there is larger uncertainty in calculating the interdye distances, which can be estimated as an R_max and R_min range by finding the upper and lower bounds of <k²> by employing anisotropy depolarization information (Database S2). For the 5′- Xr*DNA_ds and DNA_ds*Fl end-labeled duplexes (N′ series), the <k²> _max and <k²>_min were 1.787 and 0.341 respectively, and these <k²> bounds were calculated according to Dale et al.³⁰ which yielded an R_max of +19% and R_min of −11% of the reported R̅.

3.3. The trADFRET Mathematical Treatment

All relevant equations are addressed in the supplementary text materials. The trADFRET observed intensity acquired by the 620-nm interference filter, S_trADFRET^Exc/620nm (t) (eq 8) and whose deconvolution yields τ_trADFRET, contains three signals, the sensitized ADFRET (I_ADFRET), the leaked D(A) (I_D(A)), and directly excited A intensities (I_A) for the LaserStrobe (Figure 2E-I, Database S5) and FluoTime (Figure 2J–N, Database S6). The last two (I_D(A) + I_A) must be eliminated to observe the sensitized I_trADFRET whose kinetic feature is strikingly different in the time course (Figure 2G,L), compared to trDDFRET (Figure 2A–D) since it rises from zero to a maximum amplitude (Gain) at a maximum time (t_max) as the excited D* transfers energy to pump A to an excited state A* followed by subsequent τ_A decay. t_max is delayed as the inter-dye separation increases as observed from 14 N′ to the 29 N′ since the k_t decreases and t_max takes a longer time to build up a maximum A* concentration (Figure 2H,I,M,N).

We elucidated three methodologies to find the I_D(A)/I_A ratio or “r” value for each of the N′ and N series (Supporting Information; Method a, Figure S2, Database S7; Method b, Figure S3, Database S8; and Method c, Figure S4, Table S1, Database S9). For the former, the “r” values were 1.891 ± 0.066 and 3.433 ± 0.292 for the LaserStrobe and FluoTime (Table S2, Database S9), and these values impact the Gain values which were 2.524 ± 0.046 (Database S5) and 2.785 ± 0.091 (Database S6), respectively since the excitation and photon detection systems are not the same. Notably, the 14 N′ P(R) values calculated with trDDFRET (Figure 2A,B) and trADFRET are statistically indistinguishable (Table 2, Database S5, and Database S6), thus validating our novel approach. As anticipated, the 29 N′ trDDFRET did not provide distance information (Figure 2C,D); however, we obtained the trADFRET P(R) (Eq 18) despite that energy transfer was 2.35% (Table 2, Database S1).

3.4. Time-Resolved ADFRET Simplification

At inter-dye distances of 100–120 Å, t_max converges while Gain steadily declines and is highly correlated with the P(R) parameters, which complicates the determination of ^–R and σ (Table 2, Figure S5, Database S10). Therefore, we sought to simplify the calculation by setting the P(R) integration equal to 1 (Eq 18) resulting in a novel equation that yields a time-resolved derived distance, ^trR_SS that in principle equates to a steady-state (ss) measurement (Eq 29 and Eq 30). Remarkably, the 29 N′ ^trR_SS values for the LaserStrobe and FluoTime were 119.1 ± 8.6 Å and 117.6 ± 3.3 Å, overlapping in the error, with S/N ratios of 0.8 ± 0.3 and 18.4 ± 02, respectively. The difference in S/N is expected since the FluoTime has higher collection rates than LaserStrobe (Database S11).

3.5. Long trADFRET Interactions

The ⟨τ_Std⟩ values can be subtracted from τ_trADFRET^Obs (Figure 3A,B) to yield the sensitized I_trADFRET whose integration is the number of trADFRET photons collected (Figure 3C) that at the current experimental settings has ∼3-fold stronger signal than the trDDFRET signal, calculated by 100% × (1 – τ_D/τ_D(A)) (Figure 3D). Consequently, the trADFRET acquisition regime is analogous to the NMR³¹ and MRI³² accumulation principles as the sensitized trADFRET signal stack up from a steady reference like adding icing to a cake in multiple layers. In contrast, the trDDFRET cannot be beneficiated from this method since the τ_D(A) approaches toward the reference τ_D, which acts as a limiting ceiling.

Figure 3.

Time-resolved ADFRET. (A) Deconvoluted τ_trADFRET^Obs for the N′ and N series (Database S12). (B) Each oligo has a respective ⟨τ_Std⟩, which contains deconvoluted τ_D and τ_A under no FRET conditions, at an “r” ratio. The ⟨τ_Std⟩ needs to be removed from τ_trADFRET (figure A minus figure B) to yield the sensitized I_trADFRET, which is fitted to obtain the R̅ and σ (eq 18) and ^trR_SS (eq 29) (C). (D) The trADFRET integration values as a function of R̅ have ∼3-fold more photons collected than trDDFRET since the former accumulates signal over the ⟨τ_Std⟩, and in contrast to the τ_D(A) of trDDFRET that cannot get higher than τ_D thus acting as a top limit (blue, 2D). (E) The trADFRET plot of ^trR_SS (Eq 29) vs basepairs for the N′ (blue, eq 30) and N (brown eq 29) oligo series (Database S12) were fitted to lines whose slopes corresponded to the nucleotide rise of 3.5 ± 0.1 Å and 3.3 ± 0.1 Å, respectively, which are in excellent accord with predictions for B-DNA.³³ Also, the intercepts yielded the length of linkers toward the dyes′ dipole moment with values of 15.8 ± 4.4 Å and 7.7 ± 2.4 Å, respectively. (F) The 34 N trADFRET ^trR_SS acquired with a standard complement and several complements with noncanonical basepairs; such as, A, C, T, and an abasic spacer at position 17, and double abasic spacers at 17 and 18 positions, complement fragments divided into two halves, which were added separately (half1 or half2) or collectively (half1 + half2) (Database S12).

Accordingly, we successfully calculated the ^trR_SS for both oligo series (Table 3, Database S12) with the smallest value of 84.4 ± 2.4 Å and the longest of 193.2 ± 6.0 Å for the 24 N and 56 N duplexes_, respectively (Figure 3E). The N series plot of ^trR_SS values vs the number of nucleotides (Figure 3E) resulted in a slope of 3.3 ± 0.1 Å, which is in excellent agreement with the nucleotide increase observed in crystallographic studies.³³ The intercept yielded a length of the linkers and dyes of 7.7 ± 2.4 Å. In the case of the N′ series, the slope was 3.5 ± 0.2 Å and the intercept was 15.8 ± 4.4 Å (Database S12). The intercepts were not similar for these two series since the 3′Fl-linker is extended outward, and the Fl_int-linker is perpendicular to the duplex (Figure 3E). Interestingly, at these longer distances, we did not observe the helicity of B-DNA since the linkers are long and bring the dyes to the water environment and away from the DNA structure, further justifying a κ² = 0.667 ± 0.083 (Database S2). However, the helicity can be observed when the dyes are sitting with very short linkers on the end termini in shorter duplexes, 10, and 24 nucleotides.³⁴

Table 3. Simplified trADFRET Inter-Dye Distance ^trR_SS.

oligoa	τtrADFRETObs, (ns)b	⟨τStd⟩ (ns)	⟨τDiff⟩ (ns)	“r” ratioc	gain	signal/noised	trRSSe (Å)
29 N′ (LaserStrobe)	4.644	4.423	0.220	1.891	2.523	0.8	119.1
	(± 0.013)	(± 0.166)	(± 0.087)	(± 0.065)	(± 0.100)	(± 0.3)	(± 8.6)
29 N′ (FluoTime)	4.991	4.729	0.262	3.433	2.785	18.4	117.6
	(± 0.014)	(± 0.001)	(± 0.003)	(±0.292)	(± 0.185)	(± 0.2)	(± 3.3)
24 N (FluoTime)	7.245	4.553	2.691	0.662	4.298	35.889	86.3
	(± 0.074)	(± 0.001)	(± 0.010)	(± 0.016)	(± 1.296)	(± 0.393)	(± 2.4)
29 N (FluoTime)	5.529	4.553	0.976	0.662	4.298	217.911	102.2
	(± 0.004)	(± 0.001)	(± 0.001)	(±0.016)	(± 1.296)	(± 0.257)	(± 2.8)
34 N (FluoTime)	4.958	4.553	0.404	0.662	4.298	58.314	118.3
	(± 0.007)	(± 0.001)	(± 0.001)	(±0.016)	(± 1.296)	(± 0.216)	(± 3.3)
39 N (FluoTime)	4.662	4.493	0.169	0.523	3.705	18.268	132.8
	(± 0.009)	(± 0.001)	(± 0.002)	(± 0.013)	(± 1.116)	(± 0.214)	(± 3.7)
44 N (FluoTime)	4.605	4.528	0.077	0.600	4.048	5.649	154.1
	(± 0.013)	(± 0.001)	(± 0.003)	(± 0.015)	(± 1.220)	(±0.213)	(± 4.4)
50 N (FluoTime)	4.585	4.528	0.039	0.643	4.221	4.102	173.9
	(± 0.009)	(± 0.001)	(± 0.002)	(± 0.016)	(± 1.273)	(± 0.214)	(± 5.1)
52 N (FluoTime)	4.584	4.550	0.034	0.654	4.265	4.378	178.5
	(± 0.007)	(± 0.001)	(± 0.002)	(± 0.016)	(± 1.286)	(± 0.287)	(± 5.3)
56 N (FluoTime)	4.565	4.544	0.021	0.640	4.209	4.865	193.4
	(± 0.004)	(± 0.007)	(± 0.002)	(± 0.016)	(± 1.269)	(± 0.407)	(± 6.0)
56 Nf (+1/3f) (FluoTime)	4.559	4.544	0.015	0.640	4.209	3.883	213.1
	(± 0.004)	(± 0.007)	(± 0.002)	(± 0.016)	(± 1.269)	(± 0.438)	(± 6.9)
56Nf (+2/3f) (FluoTime)	4.555	4.544	0.011	0.640	4.209	2.623	226.9
	(± 0.004)	(± 0.007)	(± 0.002)	(± 0.016)	(± 1.269)	(± 0.428)	(± 8.5)
56Nf (+1f) (FluoTime)	4.550	4.544	0.006	0.640	4.209	1.266	254.3
	(± 0.004)	(± 0.007)	(± 0.002)	(± 0.016)	(± 1.269)	(± 0.405)	(± 14.6)

^aSee Table 1. The 14′N distance is better described by eq 18 (Database S6). The lifetime errors are the standard deviation of fits (Database S12).

^bThe observed τ_trADFRET^Obs is the deconvoluted lifetime of S_trADFRET (t) intensity collected at 620 nm at excitations of 470 and 481 nm for the FluoTime and LaserStrobe, respectively.

^cThe “r” ratio is calculated according to Method a for each oligomer.

^dThe signal-to-noise ratio (S/N)³⁵ was calculated according to: , where σ_τADFRET² and σ_⟨τstd⟩ are variances of τ_trADFRET^Obs and ⟨τ_std⟩, respectively.

^eThe ^trR_SS errors are calculated with propagation analysis (Database S11 and Database S12) assuming a <k²> = 2/3 at the isotropic condition in which all dye dipole orientations are present at the time of the energy transfer process. We used flexible linkers to tether our dye probes to the duplex DNA to maximize the isotropic state. However, when dye isotropic conditions are not attained, there is larger uncertainty in calculating the interdye distances, which can be estimated as upper and lower R values, R_max and R_min, respectively, by finding the upper and lower bounds of <k²>. For the 5′-Xr and Fl_int labeled probes (N series), the <k²> _max and <k²>_min were 1.611 and 0.375, respectively, and these values were calculated according to Dale et al.³⁰ with the dye anisotropy values of the Xr*DNA_ds and DNA_ds*Fl_int duplexes (Database S2). The resulted R_max and R_min were + 17 and −10% of the reported R̅ at isotropic conditions. In the case of the 5′-Xr and 3′-Fl end-labeled duplexes (N′ series), the R_max and R_min were + 19 and −11%, respectively, for which the <k²> _max and <k²>_min were 1.787 and 0.341, respectively.

^fStandard-solution aliquots addition in terms of mole fraction (f) to the 56 N.

Also, we have calculated the 34 N ^trR_SS values (eq 29) hybridized with standard and noncanonical complements (Figure 3F, Database S12). The 34 N distance was ∼120.5 ± 3.4 Å, which was not possible to detect by trDDFRET. In contrast, we observed a shorter ^trR_SS value of 103.7 ± 2.9 Å when the 34 N duplex was hybridized with two complement halves, non-interconnected with respect to the canonical complement since a kink is formed between nucleotide 19 and 20 of the top stand. In contrast, when only the left- and the right-half fragments were hybridized the ^trR_SS values were 90.4 ± 2.5 Å, and 73.7 ± 2.1 Å, respectively (Figure 3F, Database S12) since for each case the overhangs are not straight.

3.6. Time-Resolved ADFRET Limits

We designed an experiment to mask and overwhelm the sensitized I_ADFRET to determine the upper limit by adding aliquots (f) of the standard solution, made of a mix of 1:1 single-labeled A and D duplexes, (Xr*DNA_ds, DNA_ds*Fl, or DNA_ds*Fl_int) that are not attached to the same DNA_ds, to its respective 29 N′ (Figure 4A, Database S13) and 34 N (Figure 4E, Database S14). By adding the (f) standard solution to the double-labeled duplex (29 N′ or 34 N) more donor and acceptor background (Figure 1B, yellow and red curves, respectively) that does not contain FRET distance information is detected with respect to the distance-containing information of I_ADFRET”. Indeed, the τ_trADFRET^Obs plotted as a function of normalized aliquot, f/(f + 1), was fitted to a line with a slope “m” that yielded the dynamic range for both series, and the intercept “b” corresponded to the initial τ_trADFRET (Figure 4B,F). Similarly, the plot of τ_trADFRET^Obs × (1 + f) vs f, was fitted to a line whose slope was equal to ⟨τ_Std⟩ and the intercept yielded the initial optimal τ_trADFRET for the 29 N′ (Figure 4C) and 34 N (Figure 4G). The maximum ^trR_SS for the 29 N′ and 34 N masking experiments were 242.0 ± 6.8 Å (Figure 4D, Database S13) and 275.3 ± 7.7 Å (Figure 4H, Database S14), whose S/N ratios were 0.92 ± 0.20 and 0.85 ± 0.07, and FRET efficiencies were 0.028 and 0.013% (Database S1), respectively.

Figure 4.

Time-resolved ADFRET limits of each series were found by adding aliquots of the standard mixture solution, in molar basics (f), to simulate FRET at longer R̅ as the observed S_trADFRET is being overwhelmed by a stronger background intensity. (A) For the 29 N′, the τ_trADFRET^Obs dynamic range was 4.991 ± 0.007 ns to 4.729 ± 0.005 ns from 0 f to 40 f (standard solution), respectively, and further aliquot addition did not result in τ_trADFRET change (Database S13). (B) The τ_trADFRET^Obs vs normalized dilution factor, f/(f + 1), yielded a line with a slope (m = −0.262 ns ± 0.018 ns) that corresponds to the dynamic range. The intercept (b = 4.986 ns ± 0.014 ns) is the initial τ_trADFRET of the 29 N′. (C) The τ_trADFRET^Obs × (1 + f) vs f plot yielded a straight line with a slope that corresponds to ⟨τ_Std⟩ = 4.726 ns ± 0.001 ns, and the intercept (b = 4.982 ns ± 0.042 ns) yielded also the initial τ_trADFRET. (D) The corresponding 29 N^trR_SS was 117.7 Å ± 3.3 Å (S/N = 35.9 ± 0.2) and 242 ± 6.8 Å (S/N = 0.92 ± 0.20) for the last dilution. (E) A similar approach was carried out for 34 N, which resulted in a dynamic range of 4.915 ± 0.032 ns to 4.553 ± 0.011 ns from 0 f to 100 f, respectively (Database S14). (F) The τ_trADFRET^Obs vs normalized dilution factor, f/(f + 1), yielded a line with a slope (m = −0.381 ± 0.008 ns) that corresponds to the dynamic range, and the intercept (b = 4.940 ± 0.006 ns) was the initial τ_trADFRET for the 34 N. (G) The τ_trADFRET^Obs × (1 + f) vs f plot yielded a straight line with a slope that corresponded to ⟨τ_Std⟩= 4.553 ± 0.001 ns, and the intercept (b = 4.984 ± 0.025 ns) yielded also the initial τ_trADFRET. (H) The corresponding 34 N^trR_SS was 120.5 ± 3.4 Å (S/N = 11.1 ± 0.1) and 275.3 ± 7.7 Å (S/N = 0.85 ± 0.07) for the last dilution.

4. Conclusions

Our FLIM-trADFRET technique allows distance calculations up to ∼275 Å, an approximately threefold improvement over traditional trDDFRET. To achieve success, we have accomplished the following: (1) developing the trADFRET requisite equations; (2) simplifying the trADFRET analysis to obtain a single ^trR_SS value; (3) devising dependable experimental methods to extract the sensitized I_trADFRET that self-corrects for any dye ratio; (4) understanding clearly how to account for leaked I_D(A) and direct excited I_A through the parameter “r” ratio; and (5) lastly, determining the relevant dye spectroscopic parameters that impact trADFRET.

The FLIM-trADFRET technology will be able to monitor macromolecular assemblies (Figure 1) since they are responsible for the most relevant functions for life, such as replication, transcription, translation, vesicular transport, and viral and parasitic infection. A detailed understanding of these macromolecular mechanisms in diseased and healthy tissue can result in new therapies to stop cancer,³⁶ fight malaria,³⁷ HIV,³⁸ or even SARS-CoV19,³⁹ as discussed by Dr. Stephan Hell, Dr. William Moerner, and Dr. Eric Betzig at the Nobel Prize talk in 2014.⁴⁰⁻⁴⁸

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.analchem.0c04492.

• FLIM-trADFRET mathematical analysis, structure of the double-labeled N′ oligos, standard mixture preparation and “r” ratio by Method a, the “r” value calculated by Method b and Method c, gain, and t_max dependence for sensitized I_trADFRET as a function of R̅ and σ, the “r” ratio was acquired with “Method c” for both series, and, The “r” ratio of the three methodologies for N′ series and the respective crosstalking I_A/I_D(A) ratio of leaked intensities (PDF)

• DatabaseS1_(trADFRET_and_trDDFRET_simulations) (XLSX)

• DatabaseS2_(R0_anisotropy_kappasquared) (XLSX)

• DatabaseS3_(trDDFRET_Lifetime_both_instruments) (XLSX)

• DatabaseS4_(trDDFRET_fits_both_instruments) (XLSX)

• DatabaseS5_(trADFRET_LaserStrobe) (XLSX)

• DatabaseS6_(trADFRET_FluoTime_Table2) (XLSX)

• DatabaseS7_(FigS2_r_value_Method_a) (XLSX)

• DatabaseS8_(FigS3_Method_b) (XLSX)

• DatabaseS9_(FigS4_r_value_Method_c) (XLSX)

• DatabaseS10_(FigS5_P(R)_and_Gain_correlation) (XLSX)

• DatabaseS11_trRss(eqn30)_and_signal-noise (XLSX)

• DatabaseS12_trRss_Nseries_and_Table2 (XLSX)

• DatabaseS13_Limit_dilution_N′series (XLSX)

• DatabaseS14_Limit_dilution_Nseries (XLSX)

Author Contributions

Conceptualization: R.F.D., L.J.P. Data curation: R.F.D. Formal analysis: R.F.D. Funding acquisition: R.F.D., O.O., L.J.P. Investigation: R.F.D. Methodology: R.F.D., L.J.P. Project administration: R.F.D., L.J.P. Resources: R.F.D., L.J.P. Software: R.F.D., L.J.P. Supervision: R.F.D., K.Z.R., K.A.C., L.J.P. Validation: R.F.D., K.Z.R., K.A.C., L.J.P. Visualization: R.F.D. Writing – original draft: R.F.D. Writing – review & editing: R.F.D., K.A.C., K.Z.R., L.J.P.

The authors declare no competing financial interest.

Notes

The work was supported by National Institutes of Health Grants GM59346 and RR015468 to LJP; CONACYT-Mexico postdoctoral, SNI fellowships (130994,162809, SNI75487), and the Government of Veracruz-Mexico fellowships to R.F.D.

Notes

All data is available in the main text or the supplementary materials.