Accurate distance determination of nucleic acids via foerster resonance energy transfer: Implications of dye Linker length and rigidity

ARTICLE

pubs.acs.org/JACS

€

Accurate Distance Determination of Nucleic Acids via Forster

Resonance Energy Transfer: Implications of Dye Linker Length and

Rigidity

||

Simon Sindbert,^†,Stanislav Kalinin,*^,†,||Hien Nguyen,^‡Andrea Kienzler,^§Lilia Clima,^§Willi Bannwarth,^§

Bettina Appel,^‡Sabine M€uller,*^,‡and Claus A. M. Seidel*^,†

^†Institut f€ur Physikalische Chemie, Lehrstuhl f€ur Molekulare Physikalische Chemie, Heinrich-Heine-Universit€at, Universit€atsstrasse 1,

Geb 26.32, 40225 D€usseldorf, Germany

^‡Institut f€ur Biochemie, Bioorganische Chemie, Ernst-Moritz-Arndt-Universit€at Greifswald, Felix-Hausdorﬀ-Strasse 4, 17487,

Greifswald, Germany

^§Fakult€at f€ur Chemie und Biochemie, Albert-Ludwigs Universit€at Freiburg, AK Bannwarth, Albertstrasse 21, 79104, Freiburg, Germany

S Supporting Information

b

ABSTRACT: In F€orster resonance energy transfer (FRET) experiments, the

donor (D) and acceptor (A) ﬂuorophores are usually attached to the macro-

molecule of interest via long ﬂexible linkers of up to 15 Å in length. This causes

signiﬁcant uncertainties in quantitative distance measurements and prevents

experiments with short distances between the attachment points of the dyes

due to possible dye-dye interactions. We present two approaches to overcome

the above problems as demonstrated by FRET measurements for a series of

dsDNA and dsRNA internally labeled with Alexa488 and Cy5 as D and A dye,

respectively. First, we characterize the inﬂuence of linker length and ﬂexibility on FRET for diﬀerent dye linker types (long, inter-

mediate, short) by analyzing ﬂuorescence lifetime and anisotropy decays. For long linkers, we describe a straightforward procedure that

allows for very high accuracy of FRET-based structure determination through proper consideration of the position distribution of the

dye and of linker dynamics. The position distribution can be quickly calculated with geometric accessible volume (AV) simulations,

provided that the local structure of RNA or DNA in the proximity of the dye is known and that the dye diﬀuses freely in the sterically

allowed space. The AV approach provides results similar to molecular dynamics simulations (MD) and is fully consistent with

experimentalFRET data. Ina benchmark study for ds A-RNA, anrmsd valueof 1.3 Å is achieved. Consideringthecase of undeﬁned dye

environments or veryshort DAdistances, weintroduceshortlinkerswitha propargyl or alkenyl unit for internal labeling of nucleic acids

to minimize position uncertainties. Studies by ensemble time correlated single photon counting and single-molecule detection show

that the nature of the linker strongly aﬀects the radius of the dye’s accessible volume (6-16 Å). For short propargyl linkers, hetero-

geneous dye environments are observed on the millisecond time scale. A detailed analysis of possible orientation eﬀects (κ²problem)

indicates that, for short linkers and unknown local environments, additional κ²-related uncertainties are clearly outweighed by better

deﬁned dye positions.

However, two problems commonly arise when performing

quantitative FRET measurements. First, the ﬂuorescent dyes are

typically attached to the biomolecule via long ﬂexible linkers, for

example, the “standard” C6 (hexamethlyen) linker. The overall

length of the linkage from the attachment point to the center of

the chromophore is, thus, given by the length of the linker and

the internal chemical structure of the dye and amounts to up to

20 Å. This yields a signiﬁcant uncertainty in dye position and

quenching environment.^14-18Second, the FRET eﬃciency also

depends on the relative orientation of the transition dipole

moments of the two dyes,^3,7,8,19-21which is expressed by the

orientation factor κ². It can range from 0 to 4 and has a strong

inﬂuence on the measured FRET eﬃciencies.

1. INTRODUCTION

Measuring distances within biomolecules via F€orster reso-

nance energy transfer (FRET) has been a very useful technique

in the ﬁeld of structural biology for decades.^1-5It is based on the

fact that an excited ﬂuorescent dye (donor) can transfer energy to

another dye (acceptor) if the emission spectrum of the donor over-

laps with the excitation spectrum of the acceptor. The eﬃciency of

this energy transfer strongly depends on the distance between

the dyes^3,6-9allowing for donor-acceptor distance (R_DA) mea-

surements in the range of about 20-100 Å. In the past years,

FRET measurements on single molecules (smFRET) have

become possible.^10,11smFRET largely overcomes many problems

of ensemble FRET, including species and time averaging, incom-

plete or unspeciﬁc labeling, as well as position-dependent donor or

acceptor quenching artifacts.^12,13

Received: June 29, 2010

Published: February 3, 2011

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2011 American Chemical Society

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Journal of the American Chemical Society

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The eﬀect of long dye linkers and the problems they can cause

for quantitative FRET measurements are well-known.^2,22-24There

are approaches to circumvent this problem through modeling of

the dye and linker motions,^25-29and, thus, to calculate the ac-

cessible volume and mean position of the dye. This approach,

however, works only for well-deﬁned dye environments such as a

straight double helix of double-stranded (ds) DNA or RNA. In

many biomolecules, for example, complex RNA structures, the

local structure is unknown, which makes such simulations impos-

sible. Furthermore, there are approaches to minimize the dye

position uncertainties, thus making modeling less important.

Nucleobases can be replaced by ﬂuorescent analogues,^30,31and

ﬂuorophores can be covalently linked as end-caps of DNA dup-

lexes³²or stacked at the ends of the helices in the manner of addi-

tional base pairs.²¹However, this strongly restricts dye reorienta-

tion, and κ²cannot be assumed to be 2/3.

In this work, we suggest alternative procedures of obtaining

highly accurate FRET-based structural information using intern-

ally labeled nucleic acids with dye linkers of diﬀerent length and

ﬂexibility. Depending on whether the structure of the local envi-

ronment of the dye is known, two cases have to be considered. If a

simulation is possible, we demonstrate that an easily applicable

accessible volume (AV) simulation method^28,29provides realistic

dye position distributions, which are consistent MD data and

experimental smFRET results. For the case of an unknown local

structure, we introduce alternative short dye linkers. They signi-

ﬁcantly decrease dye position uncertainty while allowing the ﬂuo-

rophores to rotate somewhat freely. In particular, short linkers are

also expected to be more suitable for measuring short distances

because, in this range, the length of long linkers becomes com-

parable to the absolute distances between donor and acceptor dye

(R_DA). To consider the implications of using long and short dye

linkers on quantitative FRET measurements, we present systemat-

ic studies for DNA and RNA to demonstrate the inﬂuence of the

linker ﬂexibility and length on the ﬂuorescence properties of two

representative dyes.

In section 2, we introduce the new short dye linkers for

labeling of nucleic acids. We synthesized the modiﬁed nucleoside

phosphoramidites shown in Figure 1 and incorporated them into

oligonucleotides of deﬁned sequence (section S1.1 in the Support-

ing Information). The alkenyl linkers (Figure 1A and B) were

introduced by Heck chemistry,^33,34and the propargyl linkers

(Figure1CandD) were introducedbySonogashira coupling^33,35,36

starting from 5-iodo-2⁰-deoxyuridine or 5-iodoridine.

Figure 1. Modiﬁed RNA (A, B, and C) and DNA (D) building blocks

with triﬂuoroacetamide-protected amino groups, which contain linkers

of diﬀerent length and ﬂexibility.

possible positions for EPR and FRET labels.^28,29For deﬁned

environments, the AV approach provides dye position distributions

that are very similar to those obtained by molecular dynamics (MD)

simulations.²⁵However, in contrast to the previous work,^29,37we

do not assume the dye to have a ﬁxed static position within its

AV but consider all accessible dye positions as equally populated.

We demonstrate that this approach provides a far better approxima-

tion of the dye behavior. Furthermore, we account for the three

diﬀerent dimensions of the ﬂuorophores. We applied this metho-

dology in a FRET benchmark study for ds A-RNA with long C6

dye linkers, where a very good rmsd value of 1.3 Å was achieved.

This demonstrates that long dye linkers can be safely used in

FRET experiments, if three conditions are fulﬁlled: (1) the local

structure of RNA or DNA in the proximity of the dye is known,

(2) the DA distance is larger than the sum of the linkage lengths

and larger than ∼0.7 ꢀ F€orster radius (that is, R_DA> 35-40 Å for

our dyes), and (3) there are no stacking interactions between the

dye and the nucleic acid. Using a multiparameter ﬂuorescence

detection setup³⁸allows one to easily test for the presence of such

interactions.

In section 3.4, we studied the inﬂuence of the linker type on

the additional broadening of R_DAdistributions due to a very slow

(>milliseconds) interchange between distinct dye environments.

We can show that this eﬀect becomes signiﬁcant for short and

stiﬀ dye linkers.

In section 3.5, we introduce a rigorous procedure to minimize

the uncertainties in the orientation factor κ², which is necessary

because orientational distribution of both D and A is not strictly

isotropic even for the longest linkers. We used time-resolved

ﬂuorescence anisotropy decays of D-only and A-only molecules

and the FRET-sensitized acceptor anisotropy decay to determine

the residual anisotropies, which allow us to compute probability

distributions for possible values of κ²and estimate errors due to

In section 3.1, we studied the inﬂuence of the linker ﬂexibility

and length on the individual ﬂuorescence properties (ﬂuorescence

quantum yield, lifetime, and anisotropy) of Alexa488 and Cy5 dyes

for DNA and RNA.

In sections 3.2 and 3.3, we characterized experimentally and

theoretically the broadening of interdye distances due to dye

linker motions. We performed quantitative FRET distance mea-

surements using internally labeled dsDNA and dsRNA as test

systems using single-molecule multiparameter ﬂuorescence de-

tection (smMFD) and ensemble time-correlated single-photon-

counting (eTCSPC) techniques. We found that for both types of

FRET measurements the modeling of the dye position and the

R_DAdistribution is essential for the quantitative interpretation of

the observed FRET eﬃciencies. However, for short dye linkers,

these corrections are much less important. For the simulation of

the environment of ﬂuorescent dye positions, we further devel-

oped simple geometric computations to calculate the sterically

accessible volume (AV), which has been proposed to predict

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ARTICLE

Figure 2. (A) Exemplary structures of the linkers S_t(propargyl) and S_d, I, and L (all alkenyl) with the dyes (Alexa488 and Cy5) used in DNA (left) and

RNA (right). The donor and acceptor dyes are depicted in green and red color, respectively. Donor and acceptor dyes have been used in combination

with each of the shown linkers. (B,C) Duplex structures of DNA1 (B) and RNA1 (C). Labeling positions are depicted in green and red for Alexa488 and

Cy5, respectively.

uncertainties in the relative orientation of the dyes. Even if the

residual anisotropies increase signiﬁcantly for shorter linkers,

it turns out that κ²errors increase only slightly. Thus, short and

ﬂexible linkers can be recommended for unknown local environ-

ments, because additional κ²-related uncertainties are clearly

outweighed by better deﬁned dye positions.

(1.72 g, 11.3 mmol, 2.3 equiv) and 56 mL of anhydrous DMF were

added. Anhydrous argon was bubbled through this suspension for 5 min.

The apparatus was again degassed and ﬂooded with anhydrous argon.

The reaction mixture was stirred at 50 ꢀC for 17 h, and afterward cooled

to room temperature and ﬁltered over Celite. The Celite was washed

with 50 mL of CH₂Cl₂/MeOH (5:1). The solvent of the combined

organic phases was removed under reduced pressure. Remaining DMF

was removed by condensation at 40 ꢀC and 4 ꢀ 10^-2mbar. The crude

product was puriﬁed by column chromatography on a B€uchi Sepacore

chromatography system (5 ꢀ 15 cm, F1-6, 20 mL; F7-30, 10 mL;

CHCl₃/MeOH = 8.25:1.75). Fractions 7-30 were combined, and the

solvent was removed under reduced pressure. The desired product was

2. MATERIALS AND METHODS

Synthesis of Labeled DNA and RNA. General. All reactions

were carried out in dry solvents under argon atmosphere. All solvents and

reagents were purchased from commercial sources and used as supplied

unless otherwise stated. The solvents used in palladium coupling reactions

were freed from oxygen. All products were visualized on TLC plates

(aluminum sheets coated with silica gel 60 F 254, 0.2 mm thickness) at

254 nm ultraviolet light. Column chromatography was performed using

silica gel type 60 ACC 35-70 μm. ¹H, ¹³C, and ³¹P NMR spectra were

measured either on AC 250, ARX 300, AM 400, DRX 400, DRX 500, and

DRX 600 systems from Bruker or on a Mercury VX 300 system from

Varian using CDCl₃, CD₃CN, or [d₆]DMSO as solvent. UV spectra were

recorded on a Perkin-Elmer-Lambda-35-UV/vis spectrometer or on a

Varian Nano Drop ND-1000 spectrophotometer.

1

obtained as slightly brown foam. Yield: 79%. H NMR (400 MHz, in

[d₆]DMSO): δ = 2.08-2.14 (m, 2H, 2⁰-H), 3.51-3.63 (m, 2H, 5⁰-H),

3

3.78 (td, ³J_{4 ,5}= 3.4 Hz, J_{4 ,3}= 3.6 Hz, 1H, 4 -H), 4.20-4.22 (m, 3H,

0

3

NH-CH₂þ 3⁰-H), 5.06 (t, J_{5 OH,5}= 5.1 Hz, 1H, 5⁰-OH), 5.22

0

(d, ³J_{3 OH,3}= 4.3 Hz, 1H, 3⁰-OH), 6.09 (t, J_{1 ,2}= 6.7 Hz, 1H, 1⁰-H),

3

0

8.17 (s, 1H, 6-H), 10.04 (m_c, 1H, NH-CH₂),11.6 (s, 1H, 3-NH). ¹³

C

NMR (100 MHz, in [d₆]DMSO): δ = 161.5 (4-C), 156.0 (q, ³J₅F =

00

6⁰⁰

36.6 Hz, (CdO)CF₃), 149.4 (2-C), 144.1 (6-C), 115.8 (quart, ²J_{6 6}F =

00 00

288, CF₃), 97.6 (5-C), 87.6 (4⁰-C), 87.4 (1⁰⁰-C), 84.8 (1⁰-C), 75.4 (2⁰⁰-C),

70.2 (3⁰-C), 61.0 (5⁰-C), 40.2 (2⁰-C superposed by DMSO signals),

29.4 (3⁰⁰-C). MS (ESI): m/z (%) = 798.7 (13), 777.7 (11), 776.7 (37)

[2M þ Na^þ], 701.9 (14), 550.9 (12), 399.8 (100) [M þ Na^þ].

Linkers. The alkinyl linker, N-propargyltrifluoroacetamide (S_t), was

synthesized according to Stockwell;³⁹the alkenyl linkers, N-allyltrifluor-

oacetamide (S_d) and N-allyl-6-(N-trifluoroacetamido)hexanamide (L),

were synthesized as described by Dey and Sheppard³⁶and Meller and

Brown.⁴⁰See Figures 1 and 2 for the respective structures.

5-(3-Triﬂuoroacetamidopropargyl)-5⁰-O-dimethoxytrityl-2⁰-deoxy-

uridine-3⁰-[(2-cyano-ethyl)-N,N⁰-diisopropylaminophosphoramidite]

(Figure 1, D). 5-(3-Triﬂuoroacetamidopropargyl)-5⁰-O-dimethoxytrityl-

2⁰-deoxyuridine was prepared according to the standard protocol for

5⁰-O-dimethoxytritylation of 2⁰-deoxynucleosides.⁴¹5-(3-Triﬂuoroacetamido-

propinyl)-5⁰-O-dimethoxytrityl-2⁰-deoxyuridine (430 mg, 0.6 mmol) and bis-

diisopropylammonium tetrazolide (82 mg, 0.5 mmol) were dried three times

azeotropically with 5 mL of anhydrous acetonitrile each. The remainder

5-(3-Triﬂuoroacetamidopropargyl)-2⁰-deoxyuridine. A two-neck

ﬂask was charged with 5⁰-iodo-uridine (2.00 g, 5.65 mmol), Pd/C

(304 mg, 0.282 mmol), CuI (214 mg, 1.13 mmol, 20 mol %), and

Amberlite IRA 67 (5.14 g). The compounds were dried under high

vacuum and afterward kept under argon. Propargyltriﬂuoroacetamide

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was then dissolved in anhydrous CH₂Cl₂(5 mL) and treated with 2-

cyanoetoxy-bis-(N,N-diisopropylamino)phosphine (530 μL, 1.7 mmol).

The reaction mixture was stirred for 3 h under argon at room tempera-

ture. Next, the mixture was poured into a degassed saturated NaHCO₃

solution and extracted three times with degassed CH₂Cl₂. The combined

organic layers were dried over Na₂SO₄, and the solvent was removed

under reduced pressure. The crude material was puriﬁed by short column

chromatography on deactivated silica gel (1% Et₃N). The product

was eluted with cyclohexane/AcOEt (5:7) and was obtained as a slightly

beige foam. Yield: 83%. ¹H NMR (300 MHz, CDCl₃, both diastereomers):

δ = 1.01-1.25 (m, 12H, 2 ꢀ CH(CH₃)₂,) 2.34-2.61 (m, 4H, CH₂CN,

2⁰-H), 3.32-3.82 (m, 12H, 5⁰-H OCH₂, 2 ꢀ i-Pr-CH, 2 ꢀ OCH₃),

3.87-3.91 (m, 1H, 4⁰-H), 4.14 (m, 2H, 9-H), 4.57-4.59 (m, 1H, 3⁰-H),

CH(CH₃)₂), 2.77 (t, ³J = 5.8 Hz, 1H,CH₂-CN), 2.88 (t, ³J = 5.8 Hz, 1H,

CH₂-CN), 3.48-3.61 (m, 2H, CH(CH₃)₂), 3.74 (s, 6H, OCH₃), 3.97 (t,

³J = 5.7 Hz, 2H, OCH₂), 4.16-4.22 (m, 2H, H-4⁰, H-3⁰), 4.49-4.56 (m,

1H, H-2⁰), 5.78 (d, ³J = 5.7 Hz, 1H, H-1⁰), 5.84 (d, ³J = 6.3 Hz, 1H, H-1⁰),

6.87-6.92 (m, 4H, ar), 7.27-7.43 (m, 9H, ar), 7.99, 8.01 (2s, 1H, H-6),

9.97-9.99 (m, 1H, NH), 11.75 (br s, 1H, NH). ³¹P NMR (300 MHz,

[d₆]DMSO, 25 ꢀC, δ_Pof H₃PO₄at 0.0 ppm as the external reference): δ

(ppm) = 148.24, 149.27.

5-(3-Triﬂuoroacetamidopropenyl)-uridine. 5-Iodoridine (740 mg,

2 mmol) was dissolved in 7 mL of DMF. To the resulting solution were

added sodium acetate buﬀer (7.1 mL, 0.1 M, pH 5.2) and N-allyltriﬂuo-

roacetamide (2 mL, 17 mmol). A solution of Na₂[PdCl₄] (658 mg,

2.2 mmol) in DMF (7 mL) was added while stirring vigorously. The reac-

tion ﬂask was placed in an oil bath at 80 ꢀC for 8 h. The precipitated

palladium was ﬁltered oﬀ through Celite. The ﬁltrate was concentrated in

vacuo to a viscous brown oil. The crude product was puriﬁed by column

chromatography (dichloromethane/methanol 98:2) to obtain a white

powder. Yield: 58%. ¹H NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Hof the

solvent at 2.5 ppm as internal reference): δ (ppm) = 3.55-3.70 (m, 2H,

H-5⁰, H-5⁰⁰), 3.82-3.89 (m, 3H, CH₂, H-4⁰), 3.99 (1H, br s, H-3⁰), 4.07

(m, 1H, H-2⁰), 5.09 (br s, 1H, OH), 5.22 (br s, 1H, OH), 5.41 (d, 1H,

OH), 5.77 (d, ³J = 4.8 Hz, 1H, H-1⁰), 6.18 (d, ²J = 15.9 Hz, 1H, dCH),

6.46 (tt, ²J = 15.9 Hz, ³J = 6.1 Hz, 1H, dCH), 8.12 (s, 1H, H-6), 9.69 (t,

³J = 5.4 Hz, 1H, NH). ¹³C NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Cof the

solvent at 39.61 ppm as internal reference): δ (ppm) = 41.59, 60.51,

3

6.34 (t, J = 6.6 Hz, 1H, 1⁰-H), 6.76-6.91 (m, 4H, ar.), 7.61-7.70 m,

9H, ar.), 8.21, 8.22 (2 ꢀ s, 1H, 6-H). ³¹P NMR (120 MHz, CDCl₃)

δ = 149.1, 150.0. MS (ESI): m/z (%) = 303.2 (14) [DMT^þ], 901.9 (100)

[M þ 22^þ].

5-(3-Triﬂuoroacetamidopropargyl)-5⁰-O-dimethoxytrityl-2⁰-O-tert-

butyldimethylsilyl Uridine. 5-Iodoridine was 5⁰-O-tritylated and 2⁰-O-

silylated according to standard procedures described in the literature.^42,43

5-Iodo-5⁰-O-dimethoxytrityl-2⁰-O-tert-butyldimethylsilyl-uridine (300 mg,

0.38 mmol) was dissolved in 3.0 mL of DMF, and 228 μL of freshly

distilled triethylamine was added. N-Propargyltriﬂuoroacetamide (182 mg,

1.1 mmol), Pd(PPh₃)₄(44.0 mg, 0.066 mmol), and Cu(I)iodide (14.4 mg,

0.076 mmol) were added to the solution. The reaction mixture was stirred

for 8 h in the dark at room temperature, concentrated in vacuo, and a solu-

tion of 5% Na₂EDTA was added to the residue. The crude product was

extracted with ethyl acetate (3 ꢀ 20 mL). The combined organic layers

were collected, dried over Na₂SO₄, and concentrated in vacuo. The crude

product was puriﬁed by column chromatography (hexane/ethylacetate

70: 30) to give 5⁰-O-(4,4⁰-dimethoxytrityl)-2⁰-O-tert-butyldimethylsilyl-5-

(3-triﬂuoroacetamidoprop-1-ynyl)uridine as a pale yellow solid. Yield:

66%. ¹HNMR(300 MHz, [d₆]DMSO, 25ꢀC, δ_Hof the solvent at 2.5 ppm

as internal reference): δ (ppm) = 0.03, 0.05 (2s, 6H, Si(CH₃)₂), 0.88

(s, 9H, C(CH₃)₃), 3.08, (2s, 2H, H-5⁰, H-5⁰⁰), 3.74 (s, 6H, 2 ꢀ OCH₃),

3.93 (d, ³J = 5.4 Hz, 2H, N-CH₂), 4.01-4.09 (m, 2H, H-4⁰, H-3⁰), 4.34

(t, ³J = 4.6 Hz, 1H, H-2⁰), 5.17 (d, ³J = 6.0 Hz, 1H, OH-3⁰), 5.74 (d, ³J =

5.7 Hz, 1H, H-1⁰), 6.89 (dd, ²J = 9.0 Hz, ³J = 3.3 Hz, 4H,ar), 7.23-7.43

2

69.51, 73.73, 84.75, 88.13, 109.86, 115.97 (quart, J = 288 Hz, CF₃),

123.92, 124.23, 138.20, 149.90, 156.06 (quart, ³J = 36 Hz, (CdO)CF₃),

162.25.

5-[3-(6-Triﬂuoroacetylamidohexanamido)propenyl]uridine. 5-Iodor-

idine (740 mg, 2 mmol) was dissolved in 7 mL of DMF. NaOAc buﬀer (7.1

mL, 0.1 M, pH 5.2) and N-allyl-6-(N-triﬂuoroacetylamido)hexanamide

(3.85 g, 14mmol) wereaddedtothesolution, andamixtureof Na₂[PdCl₄]

(172 mg, 0.59 mmol) in DMF (2.5 mL) was added while stirring vigo-

rously. The reaction ﬂask was placed in an oil bath at 83 ꢀC. After 2 h,

another portion of Na₂[PdCl₄] was added. After 8 h, the precipitated

palladium was ﬁltered oﬀ through Celite. NaBH₄(2 ꢀ 12 mg) was added

to the ﬁltrate while vigorously stirring. The resulting yellowish solution was

ﬁltered through Celite, and the solvents were evaporated to give a viscous

yellow oil. The crude product was puriﬁed by column chromatography,

giving a white solid. Yield: 50%. ¹H NMR (300 MHz, [d₆]DMSO, 25 ꢀC,

δ_Hof the solvent at 2.5 ppm as internal reference): δ (ppm) = 1.20-1.31

(m, 2H, CH₂), 1.42-1.55 (m, 4H, CH₂-CH₂), 2.09 (t, ³J = 7.4 Hz, 2H,

CH₂), 3.13-3.19 (m, 2H, CH₂), 3.54-3.60 (m, 2H, H5⁰, H5⁰⁰), 3.74 (t,

³J = 5.4 Hz, 2H, CH₂), 3.82-3.87 (m, 1H, H4⁰), 3.99 (q, ³J = 4.7 Hz, 1H,

H-3⁰), 4.04-4.09 (m, 1H, H-2⁰),5.07(d,³J= 5.1 Hz, 1H, OH),5.2(t,³J=4.8

Hz, 1H, OH), 5.39 (d, ³J = 5.5 Hz, 1H, OH), 5.78 (d, ³J = 4.9 Hz, 1H, H-1⁰),

6.12 (d, ²J = 16.0 Hz, 1H, dCH), 6.40 (tt, ²J = 15.9 Hz, ³J = 5.8, 1H, dCH),

7.96 (t, ³J = 5.6 Hz, 1H, NH), 8.08 (s, 1H, H-6), 9.39 (br s, 1H, NH), 11.42

(br s, 1H, NH). ¹³C NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Cof the solvent

at 39.61 ppm as internal reference): δ (ppm) = 25.11, 25.79, 28.04, 35.06,

3

(m, 9H,ar), 7.97 (s, 1H, H-6⁰), 9.97 (t, J = 5.4 Hz, 1H, N-H), 11.74

(s, 1H, N-H). ¹³C NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Cof the solvent

at 39.61ppmasinternalreference):δ(ppm) =-5.14, -4.78, 17.92, 25.63,

29.31, 55.00, 59.75, 63.03, 69.62, 74.87, 75.56, 83.28, 85.92, 87.41, 88.86,

98.08, 113.22, 113.30, 115.76 (quart, ²J = 289 Hz, CF₃), 126.65, 127.42,

127.93, 129.67, 129.73, 134.96, 135.54, 143.34, 144.84, 149.46, 155.93

(quart, ³J = 37 Hz, (CdO)CF₃), 158.1, 161.41.

5-(3-Triﬂuoroacetamidopropargyl)-5⁰-O-dimethoxytrityl-2⁰-O-tert-

butyldimethylsilyl-uridine-3⁰-[(2-cyanoethyl)-N,N⁰-diisopropylamino-

phosphoramidite] (Figure 1, C). 5-(3-Triﬂuoroacetamidopropargyl)-5⁰-O-

dimethoxytrityl-2⁰-O-tert-butyldimethylsilyl uridine (296 mg, 0.36 mmol)

was coevaporated with 5 mL of dichloromethane containing 10% pyridine.

The nucleoside was kept under vacuum overnight. Dry ethyl diisopropyl

amine (0.32 mL, 4 ꢀ 0.36 mmol, freshly distilled just before use) was

added, followed by 2 mL of dry dichloromethane. 2-Cyanoethyl-N,N⁰-

diisopropylamino-chlorophosphoramidite (0.12 mL, 1.5 ꢀ 0.36 mmol)

was added dropwise to the solution. After 3 h, 0.2 mL of dry methanol was

added. The reaction mixture was diluted with 150 mL of ethyl acetate

containing 10% triethylamine, washed with a saturated solution of Na₂CO₃

(1 ꢀ 10 mL), and with a saturated solution of potassium chloride (1 ꢀ

10 mL), dried over Na₂SO₄, and concentrated in vacuo. After puriﬁcation

byshort column chromatography (hexane/ethylacetate/triethylamine 60:

30:10), the product was obtained as a pale yellow foam. Yield: 80%. ¹H

NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Hof the solvent at 2.5 ppm as inter-

nal reference, both diastereomers): δ (ppm) = 0.01, 0.03, 0.05, 0.09 (4s,

12H, Si-CH₃), 0.83, 0.86 (2s, 18H, C(CH₃)₃), 1.18-1.53 (m, 12H,

2

40.80, 43.20, 60.55, 69.57, 73.68, 84.75, 88.04, 110.32, 115.95 (quart, J =

3

289 Hz, CF₃), 122.09, 126.90, 137.34, 149.79, 156.10 (quart, J = 36 Hz,

(CdO)CF₃), 162.06, 171.69.

Both compounds, 5-(3-triﬂuoroacetamidopropenyl)uridine and 5-

[3-(6-triﬂuoroacetyl-aminohexanamido)propenyl)uridine, were 5⁰-O-

dimethoxytritylated and 2⁰-O-silylated with TBDMSCl according to

standard protocols.^42,43

5-(3-Triﬂuoroacetamidopropenyl-5⁰-O-dimethoxytrityl-2⁰-O-tert-

butyldimethylsilyl-uridine-3⁰-[(2-cyanoethyl)-N,N⁰-diisopropylamin-

ophosphoramidite] (Figure 1, B). 5-(3-Triﬂuoroacetamidopropenyl)-5⁰-O-

dimethoxytrityl-2⁰-O-tert-butyldimethylsilyluridine (243 mg, 0.3 mmol) was

coevaporated with dichloromethane (3 ꢀ 5 mL) containing 10% pyri-

dine. The nucleoside was kept under vacuum overnight. Dry ethyl diiso-

propyl amine (0.27 mL, 1.2 mmol, freshly distilled over CaH₂just before

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used) was added, followed by 2 mL of dry dichloromethane. 2-Cya-

noethyl-N,N⁰-diisopropylamino-chlorophosphoramidite (0.1 mL, 0.45

mmol) was added dropwise to the solution. After 3 h, 0.1 mL of dry

methanol was added. After 15 min, the reaction mixture was diluted with

100 mL of ethyl acetate (prewashed with Na₂CO₃) containing 1% NEt₃,

washedwith a saturated solution ofNa₂CO₃(20 mL), dried over Na₂SO₄,

and concentrated in vacuo to remove the solvents. The residue was puri-

ﬁed by short column chromatography (hexane/ethyl acetate 60:40 f

50:50, 1% triethylamine) to get the product as a white foam. Yield: 87%.

¹H NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Hof the solvent at 2.5 ppm as

internal reference, both diastereomers): δ (ppm) = 0.01, 0.03, 0.05, 0.08

(4s, 6H, Si-CH₃), 0.83, 0.85 (2s, 9H, C(CH₃)₃), 1.09-1.12 (m, 12H,

CH(CH₃)₂), 2.77 (t, ³J= 6.0Hz, 2H, CH₂), 3.52-3.67 (m, 4H, H5⁰, H5⁰⁰,

NCH(CH₃)₂), 3.73 (s, 6H, OCH₃), 3.76-3.80 (m, 2H, OCH₂),

4.16-4.23 (m, 2H, H-4⁰, H-3⁰), 4.48-4.55 (m, 1H, H-2⁰), 5.65, 5.66

(2d, ²J= 15.8 Hz, 1H, dCH), 5.84, 5.88 (2d, ²J= 5.96 Hz, 6.38 Hz, 1H, H-1⁰),

6.25-6.36 (m, 1H, dCH), 6.87-6.91 (m, 4H, ar), 7.24-7.42 (m, 9H,

ar), 7.68, 7.69 (2s, 1H, H-6), 9.56 (br s, 1H, NH), 11.59 (br s, 1H, NH).

³¹P NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Pof H₃PO₄at 0.0 ppm as the

external reference): δ (ppm) = 148.27, 149.23.

Procedures . Hybridization of DNA and RNA. The hybridiza-

tion buffer for the DNA samples contained 20 mM TRIS, 100 mM NaCl,

and 10 mM MgCl₂, pH 7.5. For RNA, it contained 20 mM KH₂PO₄/

K₂HPO₄, 100 mM KCl, and 10 mM MgCl₂, pH 6.5. The concentra-

tion of the DNA or RNA molecules in the buffer ranged between 2 and

10 μM. For FRET molecules, the ratio between the amount of acceptor

and donor strand ranged from 1 to 2. For donor- and acceptor-only mo-

lecules, the ratio of unlabeled to labeled strand was 3:1. The solution was

heated to a temperature of 90 ꢀC inside a water bath and was then allo-

wed to cool to room temperature overnight.

Time-Resolved Polarized Fluorescence Experiments and Data

Analysis. Ensemble time-correlated single-photon-counting (eTCSPC)

measurements were performed using pulsedlaser excitation. Fluorescence

intensity and anisotropy decay curves were fitted using the iterative re-

convolution approach.⁴⁶The fits approximately range from the maximum

of the instrument response functions (IRF) to the first time channel

with less than 100 detected photons. The fluorescence intensity decays

of FRET-labeled molecules (donor and acceptor emission) were fitted

globally with the decays of the molecules only labeled with either the

donor (donor only, D-only) or the acceptor (acceptor only, A-only) dye.

The fluorescence decays were modeled by single or double exponential

decays or by assuming a Gaussian distribution of distances (section 3.3).

Alternatively, the fluorescence decays were deconvoluted by using the

maximum entropy method.^47,48The anisotropy decays were recovered by

globally fitting the sum (F þ 2GF_^) and difference (F - GF_^) curves

(F , F_^, fluorescence signals in parallel and perpendicular polarization

planes relative to the vertically polarized excitation light, respectively; G,

ratio of the sensitivities of the detection system for vertically and hori-

zontally polarized light). The anisotropy decays r(t) were modeled by

double or triple exponential decays (rotational correlation times F₁, F₂,

and F₃) with free amplitudes (b₁, b₂, and b₃). For further details, see

section S1.5 in the Supporting Information.

Single-Molecule Fluorescence Measurements. Multiparameter

fluorescence detection (MFD) measurements were performed as des-

cribed in refs 12,13,49. Each molecule generates a brief burst of fluo-

rescence photons as it traverses the detection volume. This photon-train

is divided initially into its parallel and perpendicular components via a

polarizing beamsplitter and then into wavelength ranges using a dichroic

beamsplitter. Bursts of fluorescence photons are distinguished from the

background of 1-2 kHz by applying certain threshold intensity criteria.⁵⁰

For further details, see section S1.5 in the Supporting Information.

Measurements of Fluorescence Quantum Yields. Φ_Fdetermi-

nation was performed according to ref 7. Rhodamine 700 in ethanol

(Φ_F= 0.38)⁵¹and Rhodamine 110 (Φ_F= 0.95) were used as reference

dyes for Cy5 and Alexa488, respectively. Correction for the solvent

refractive index was performed as described in ref 7.

5-[3-(6-Triﬂuoroacetylaminohexanamido)-propenyl]-5⁰-O-dime-

thoxytrityl-2⁰-O-tert-butyldimethylsilyluridine-3⁰-[(2-cyanoethyl)-N,

N⁰-diisopropylaminophosphoramidite] (Figure 1, A). 5-[3-(6-Triﬂuoro-

acetylamidohexanamido)propenyl]-5⁰-O-dimethoxytrityl-2⁰-O-tert-butyl-

dimethylsilyluridine (278 mg, 0.3 mmol) was coevaporated with dry

pyridine (3 ꢀ 5 mL) and dichloromethane (3 ꢀ 5mL). Thenucleosidewas

kept under vacuum overnight. Dry ethyl diisopropyl amine (0.27 mL,

1.2 mmol, freshly distilled over CaH₂just before used) was added, followed

by 2 mL of dry dichloromethane. 2-Cyanoethyl-N,N⁰-diisopropylamino-

chlorophosphoramidite (0.1 mL, 0.45 mmol) was added dropwise to the

solution. After 2 h, another 0.1 equiv of phosphitylating reagent was added.

After 2 h, 0.1 mL of dry methanol was added, and after 15 min the reaction

mixture was diluted with 100 mL of ethyl acetate (prewashed with

Na₂CO₃) containing 1% triethylamine, washed with a saturated solution

of Na₂CO₃(20 mL), dried over Na₂SO₄, and concentrated in vacuo. The

residue was puriﬁed by short column chromatography (hexane/ethyl

acetate 60:40 f 50:50, 1% triethylamine) to obtain a white foam. Yield:

82%. ¹H NMR (300 MHz, [d₆]DMSO, 25 ꢀC, δ_Hof the solvent at 2.5 ppm

as internal reference, both diastereomers): δ (ppm) = 0.00, 0.02, 0.05, 0.08

(2s, 6H, Si(CH₃)₂), 0.83, 0.85 (2s, 9H, C(CH₃)₃), 1.11 (d, ³J = 6.9 Hz,

12H, CH(CH₃)₂), 1.15-1.19 (m, 2H, CH₂₃), 1.43-1.48 (m, 2H, CH₂),

1.99-2.02 (m, 2H, CH₂), 2.75, 2.86 (2t, J = 5.8 Hz, 2H, CH₂CN),

3.12-3.18 (m, 2H, CH₂), 3.24-3.30 (m, 2H, H-5⁰, H-5⁰⁰), 3.46-3.59 (m,

2H, CH), 3.72-3.74 (m, 8H, OCH₃, CH₂), 3.77-3.84 (m, 2H, OCH₂),

4.14-4.16 (m, 1H, H-4⁰), 4.20-4.26 (m, 1H, H-3⁰), 4.47-4.57 (m, 1H,

H-2⁰), 5.63, 5.65 (2d, ²J = 15.8 Hz, 1H, dCH), 5.86, 5.90 (2d, ³J = 6.4 Hz,

1H, H-1⁰), 6.17, 6.27 (m, 1H, dCH), 6.87-6.91 (m, 4H, ar), 7.23-7.43

(m, 9H, ar), 7.64, 7.67 (2s, 1H, H-6), 7.76-7.81 (m, 1H, NH), 9.39 (m,

1H, NH), 11.6 (br s, 1H, NH). ³¹PNMR(300MHz, [d₆]DMSO, 25ꢀC, δ_P

of H₃PO₄at 0.0 ppm as the external reference): δ (ppm) = 149.39, 148.22.

Oligonucleotides. Details on oligonucleotide synthesis^44,45as well

as on labeling of deoxyoligonucleotides and oligoribonucleotides with Cy5

and Alexa488 can be found in sections S1.1, S1.2, and S1.3 of the Support-

ing Information. Ultrapure labeled DNA1 with the L linker, RNA2 and

RNA3 oligonucleotides (PAGE grade), and all unlabeled counter se-

quences were purchased from Purimex (Grebenstein, Germany). DNA1

oligonucleotides with the I Linker were purchased from IBA (G€ottingen,

Germany). All sequences of the DNA and RNA strands are given in sec-

tion S1.4 of the Supporting Information. Additionally, the sequences and

labeling positions of DNA1 and RNA1 are illustrated in Figure 2B and C.

The linker types L and I for DNA and L for RNA were chosen for reasons

of commercial availability, and the RNA linker types for reasons of chemical

suitability. Throughout this work, if not stated differently, the same linker

type is used at the donor (D) and the acceptor (A) positions.

3. RESULTS AND DISCUSSION

For highly accurate FRET measurements, several linker and

dye eﬀects must be taken into account. First, the DNA and RNA

microenvironment aﬀects the dyes’ photophysics and local mo-

tions. Second, all observable FRET parameters depend on spatial

distributions of donor and acceptor positions. The ﬁnal goal is to

restrict the dye motions to achieve a well-deﬁned dye localization

in FRET experiments. If, on the other hand, the dye reorientation

is restricted, additional orientational eﬀects (κ²eﬀects) ﬁnally

inﬂuence the FRET eﬃciency, which we must learn to take into

account.

3.1. Characterization of the Local Environment of the

Dyes. As local quenching processes and restricted mobilities

will complicate FRET analysis, we investigated how the nature

and length of the linker influence the fluorescence properties of

the dye for internally labeled dsDNA and dsRNA. Throughout

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this work, we used Alexa488 as a donor and Cy5 as an acceptor

dye (Figure 2). For internal postlabeling of the nucleic acids, we

use the NHS-ester of Cy5, which, in contrast to phosphoamidite

derivatives of Cy5 (having the same name, which leads to con-

fusions; see Figure S2 in the Supporting Information), contains

two sulfonic acid groups to prevent dye sticking. Three different

linker types for the uracil or thymine base with decreasing stif-

fness and increasing length were used: (i) short stiff linkers with

four backbone atoms (S_tand S_d); (ii) a linker of intermediate

length (I) with seven backbone atoms; and (iii) long flexible

linkers (L) with 11 backbone atoms, which are most fre-

quently used in the scientific community (usually referred to as

“C6-amino linker”) (Figure 2).

3.1.1. Analysis of Local Quenching in DNA and RNA.

We analyzed local quenching by fluorescence quantum yield and

lifetime measurements. Figure 3A shows typical ensemble fluores-

cence lifetime measurements by eTCSPC (see Figure S1A and

S1B in section S2.1 of the Supporting Information for the decays

with the complementary FRET dye). We describe the fluores-

cence decays F(t) of single-labeled dsDNA and dsRNA by up to

two fluorescence lifetimes τ_iwith the species fractions x_iand a

species-averaged fluorescence lifetime Æτæ_x(eq 1).

FðtÞ ¼ x₁expð - t=τ₁Þ þ x₂expð - t=τ₂Þ with

hτi_x¼ x₁τ₁þ x₂τ₂

ð1Þ

The results of the fluorescence lifetime analysis are summarized in

Table 1. In most cases, the Æτæ_xvalues are proportional to the

fluorescence quantum yields of the donor and the acceptor

(Φ_FDand Φ_FA, respectively; see Table 1), which indicates purely

dynamic quenching (see Table S1 in the Supporting Informa-

tion).

The ﬂuorescence of the rhodamine dye Alexa488 can be in

principle quenched by nucleobases, which results in a multi-

exponential ﬂuorescence decay. Photoinduced electron transfer

(PET) or proton-coupled electron transfer between organic ﬂuo-

rophores and suitable electron-donating moieties, such as the

nucleobase guanine, can quench ﬂuorescence upon van der

Waals contact.^15,52-54PET quenching has been used as reporter

for monitoring conformational dynamics in oligonucleotides.⁵⁴It

is striking that no quenching eﬀects are observed for DNA, but

there is quenching for RNA (see Æτæ_xin Table 1). This is in line

with the spatial distribution of the dyes (see further). For RNA,

the dye is closer to the nucleobases, because it is still partially

inside the major groove, whereas in DNA it is primarily outside.

In contrast to Alexa488, Cy5 has its own additional linker with

6 atoms between the chromophore and the reactive coupling

group (Figure 2), which increases the distance to the nucleo-

bases, so that only slight ﬂuorescence lifetime diﬀerences be-

tween DNA and RNA are noticeable.

The ﬂuorescence properties of the Cyanine dye Cy5 are less

aﬀected by PET quenching⁵⁴but rather more by trans f cis

photoisomerization,^55-58which is inﬂuenced by speciﬁc solvent

eﬀects^59,60and sterical constraints set by the local environment.⁵⁸

In water, free Cy5 shows a single exponential ﬂuorescence relaxa-

tion with a lifetime of 0.9 ns,^60,61whereas our measurements

yielded for each linker biexponential ﬂuorescence decays of Cy5.

The second lifetime was usually similar to that in water, and the

ﬁrst lifetime is signiﬁcantly larger. In view of the above ﬁndings

for the photoizomerization of Cyanine dyes, the multiexponen-

tial decay of Cy5 is most likely due to the heterogeneous DNA or

RNA microenvironment and not necessarily due to signiﬁcant

Figure 3. (A,B) Exemplary presentation of DNA1 (left panel) and

RNA1 (right panel) eTCSPC measurements of single labeled nucleic

acids: (A) ﬂuorescence decay curves (weighted residuals are presented

above each plot) and (B) ﬂuorescence anisotropy decays with the re-

scaled IRFs curves. The ﬁt results are listed in Tables 1 and 2. (C,D)

Schematic sketch for the orientation of the transition dipole moments of

the dyes with respect to the linker axes. The transition dipole moment of

Alexa488 is assumed to be perpendicular to the linker axis; the linker can

wobble within a cone with the opening half angle θ_D. (D) The transition

dipole moment of Cy5 is assumed to be parallel to the linker axis; the

linker can wobble within a cone with the opening half angle θ_A.

sticking of the dye to DNA or RNA. Thisinterpretation ofmultiple

microenvironments is supported by our recent single-molecule

studies on Cy5-labeled dsDNA,⁶¹where at least two Cy5 states

with distinct ﬂuorescence lifetimes and anisotropies have been

found. The steady-state anisotropy increases with the lifetime indi-

cating a more restricted environment, which reduces the rate for

cis-trans isomerization as well as the local linker wobbling motion

(for more details, see section 3.1.2). Moreover, it is remarkable

that for all linkers with close proximity to the allyl-unit (I for DNA

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Table 1. Fluorescence Lifetimes (τ) and Quantum Yields (Φ_F) of Single Dyes Coupled to ds Nucleic Acids^a

D-only

A-only

DNA1

linker

Æτæ_x, ns

Φ_FD

τ, ns

Æτæ_x, ns

Φ_FA

τ₁, ns (x₁)

τ₂, ns (x₂)

L

I

4.13

4.16

4.20

0.92

1.03

0.98

4.13

4.16

4.20

1.16

1.29

1.17

0.38

0.40

0.21

2.34 (11%)

2.41 (16%)

2.18 (12%)

1.01 (89%)

1.08 (84%)

1.03 (88%)

S_t

RNA1

linker

Æτæ_x, ns

Φ_FD

τ₁, ns (x₁)

τ₂, ns (x₂)

Æτæ_x, ns

Φ_FA

τ₁, ns (x₁)

τ₂, ns (x₂)

L

3.70

3.28

3.60

0.83

0.70

0.84

4.08 (90%)

3.89 (81%)

3.99 (88%)

0.27 (10%)

0.67 (19%)

0.71 (12%)

1.10

1.20

1.10

0.36

0.38

0.36

1.22 (73%)

1.45 (51%)

1.21 (77%)

0.79 (27%)

0.93 (49%)

0.72 (23%)

S_d

S_t

^aTypical errors: single τ, (0.02 ns; double τ_i(major component with x_i≈ 80-90%), (0.03 ns; τ_j(minor component with x_j≈ 10-20%), (0.4 ns;

Φ_FD, (0.05; Φ_FA, (0.03.

and S_dfor RNA) the mean ﬂuorescence lifetimes Æτæ_xof Cy5

deviate from those of the other linkers, which indicates a slightly

diﬀerent mean environment.

Let us ﬁnally mention the only exception from the strict cor-

relation between the species-averaged ﬂuorescence lifetime Æτæ_x

and the ﬂuorescence quantum yield listed in Table 1 and Table

S1. We surprisingly observe additional static Cy5 quenching for

the S_tlinker in DNA, which is also clearly detectable in ensemble-

and sm-FRET experiments and will be discussed in detail in sec-

tion 3.4.

“disk” with the opening half angle θ_disk= θ_D(Figure 3C). The

second-rank order parameter S⁽_D²⁾is given by eq 3.

rﬃﬃﬃﬃﬃﬃﬃﬃ

r_¥,D

r₀

1

donor : cos²θ_disk

¼

¼ - S^ð_D^2Þ

ð3Þ

2

Thus, anisotropy senses both the linker and the dye rotations.

Even if the linker cannot wobble (i.e., is totally stiﬀ), the dye can

still rotate about the linker, and a rather low residual anisotropy

r_¥,D= 1/4(r₀) is expected.

In contrast, the transition dipole moment of the acceptor dye

Cy5 is more parallel to the linker axis (Figure 2), and the linker

together with the dye can wobble within a cone with the opening

half angle θ_cone= θ_Aas depicted in Figure 3D. The motion is

characterized by the second-rank order parameter S⁽_A²⁾in eq 4.⁸

rﬃﬃﬃﬃﬃﬃﬃﬃ

3.1.2. Linker Motions in DNA and RNA. Figure 3B shows

typical time-resolved ensemble measurements of fluorescence

anisotropies (see also Figure S1C and S1D in section S2.1 of the

Supporting Informationfor decayswiththe complementaryFRET

dye). The fluorescence anisotropy decays r(t) with the funda-

mental anisotropy r₀were formally characterized by up to three

rotational correlation times F_iwith the anisotropy amplitudes

b_i(eq 2):

r_¥,A

r₀

1

acceptor : cos θ_coneð1 þ cos θ_coneÞ ¼

¼ S^ð_A^2Þ

2

ð4Þ

rðtÞ ¼ b₁expð - t=F₁Þ þ b₂expð - t=F₂Þ

þ b₃expð - t=F₃Þ with r₀gb₁þ b₂þ b₃

Thus, anisotropy senses predominantly the linker motions as the

dye rotates about the linker producing little or no ﬂuorescence

depolarization. If the linker cannot wobble, the dye rotates only

parallel to the linker, which results in a very high residual ani-

sotropy r_¥,A≈ r₀. The approximation of the Cy5 motion by eq 4

is supported by the fact that r_¥,Ais always >0.1 (Table 2), which is

inconsistent with eq 3.

The analysis of the ﬂuorescence anisotropies together with the

rotational correlation times for D-only and A-only labeled DNA

and RNA are compiled in Table 2.

As, in contrast to Cy5, the donor dye Alexa488 has no addi-

tional internal linker between the chromophore and the reactive

coupling group, it is most suited to study the inﬂuence of the

diﬀerent nucleobase linkers. In RNA, the wobbling motion of the

propargyl linker S_tand of the propenyl linker S_dis negligible (eq 3,

θ_disk≈ 0ꢀ), because the linker is stiﬀ and short and the major

groove of the RNA is very deep and narrow. The major groove of

DNA is wider, and thus a small linker wobbling motion is ob-

served (θ_disk= 16ꢀ and 23ꢀ for the S_tand I linkers, respectively).

If the linkers become longer and more ﬂexible, the linker

wobbling should be limited not by the size of the dye but rather

by the opening angle of the groove. Because Cy5 has its own

ð2Þ

As the dye motion is partially restricted by the nucleic acids,

the longest correlation time reflects to a significant extent the

overall tumbling motion of the molecule (global motion; for

more details, see section S1.5 of the Supporting Information),

and its amplitude corresponds to the residual anisotropy r_¥,

which allows the determination of second-rank order parameters

S⁽²⁾(eqs 3 and 4). The average anisotropy corresponds to the

steady-state anisotropy r_s, which is also measured in ensemble or

single-molecule experiments by multiparameter fluorescence

detection (MFD).

To rationalize dye motion, we must consider that the orienta-

tion of the transition dipole moment with respect to the linker is

diﬀerent for D and A. On the basis of the chemical structure of

the linked donor dye Alexa488 in Figure 2, we assume the transi-

tion dipole moment to be approximately perpendicular to the

linker axis as depicted in Figure 3C. Irrespective of the linker mo-

tions, rotations of the transition dipole about the linker axis signi-

ﬁcantly depolarize the donor ﬂuorescence. In addition, if the

linker can wobble within a cone with the opening half angle θ_D,

the transition dipole of the donor can explore the space within a

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Table 2. Rotational Correlation Times F_i, Obtained for Donor-Only (r₀= 0.375) and Acceptor-Only (r₀= 0.390) DNA1 and

RNA1 Samples^a

D-only

F₂, ns (b₂)

A-only

_2(global), ns (b₂= r_¥,A

b

linker

r_S

F₁, ns (b₁)

F_3(global), ns (b₃= r_¥,D

)

θ_disk

r_S

F₁, ns (b₁)

F

)

θ_cone

DNA1

7.9 [4-¥] (0.02)

11.7 [8-25] (0.07)

8.7 [6-11] (0.08)

L

I

0.043

0.077

0.085

0.17 (0.23)

0.20 (0.21)

0.11 (0.13)

0.76 (0.12)

1.0 (0.10)

0.86 (0.16)

45ꢀ

23ꢀ

16ꢀ

0.208

0.234

0.206

0.51 (0.26)

0.57 (0.22)

0.60 (0.25)

>60 [60-¥] (0.13)

>60 [40-¥] (0.17)

>60 [20-¥] (0.12)

47ꢀ

41ꢀ

47ꢀ

S_t

RNA1

L

0.065

0.128

0.117

0.27 (0.22)

0.38 (0.14)

0.30 (0.15)

1.5 (0.09)

2.2 (0.10)

2.1 (0.09)

6.6 [4-60] (0.05)

9.5 [7-¥] (0.11)

13.0 [8-15] (0.10)

32ꢀ

∼0ꢀ

0.211

0.254

0.237

0.68 (0.26)

0.66 (0.18)

0.70 (0.21)

8.1 [5-16] (0.13)

10.9 [8-15] (0.21)

10.7 [8-19] (0.17)

47ꢀ

35ꢀ

40ꢀ

S_d

S_t

^aTypical errors: r_s, (0.002; F (major component), (0.1 ns; r_¥, (0.015. ^bFor the longest (global) correlation time, 1σ conﬁdence intervals are shown in

squared brackets.

ﬂexible 6 atom linker, the nucleobase linker eﬀects are much

weaker. Consistently, the L linker has the largest ﬂexibility for

both DNA and RNA. In DNA, the cone angles of both dyes, θ_disk

and θ_cone, are equal, which supports the idea that the wobbling

angle is only limited by the opening angle of the major groove. In

RNA, the results still diﬀer slightly because of the diﬀerent dye

linker lengths and the greater depth of the major groove. The

experimental residual anisotropies nicely agree with the half

opening angles of approximately 45ꢀ and 30ꢀ observed for the

grooves of DNA and RNA, respectively (Table 2). As ﬂuores-

cence lifetime measurements and single-molecule studies⁶¹in-

dicate heterogeneous microenvironments of Cy5, it is important

to note that the additional state with the longer lifetime is to

some extent less mobile. The steady-state anisotropy r_sof this

state is about 0.2,⁶¹indicating that the dye is not stuck but has

suﬃcient rotational freedom (having in mind large values of

(ii) ÆR_DAæ_Eis the FRET-averaged distance between the dyes.

It is calculated from the mean FRET eﬃciency (eq 5A)

using eq 5B.

ꢀ

ꢁ

1

hEi ¼

ð5AÞ

ð5BÞ

1 þ R_D⁶_A=R₀⁶

1=6

hR_DAi_E¼ R₀ðhEi^{- 1}- 1Þ

In eq 5, R₀is the F€orster radius. ÆR_DAæ_Eis determined from

time-averaged ﬂuorescence intensity measurements on the

single-molecule (section 3.2.2) or ensemble level.

(iii) R_mpis the distance between the mean positions of the

dyes (R_mp= |ÆR_Dæ - ÆR_Aæ|) and is used for the geometric

description of FRET-based structural models.²⁵As shown

below, R_mpcannot be measured directly via FRET. The

detailed calculation of ÆR_DAæ, ÆR_DAæ_E, and R_mpis described

in section S2.2 (eqs S3-S5) in the Supporting Information.

F

_(global), r_s≈ r₀would be expected for a immobile species).

To better understand the longest (global) rotational correla-

3.2.1. Calculation of the Volume Accessible to the FRET

Dyes

tion time F_(global)(Table 2), we performed simulations of DNA1

and RNA1 rotations using the HydroPro software.⁶²For DNA1

and RNA1, respectively, three correlation times of 10, 22, and

35 ns (DNA1) and 12, 23, and 32 ns (RNA1) are predicted. In

most cases, experimentally obtained values of F_(global)(Table 2)

are similar to the shortest predicted correlation time, which

represents the rotation about the helical axis. A notable excep-

tion is Cy5 attached to DNA1, which shows systematically

longer values of F_(global). This fact suggests that the preferential

orientation of the Cy5 transition dipole is nearly parallel to the

helical axis of DNA, so that it senses the other slower rotational

motions.

3.2. FRET Benchmark Study. In this and the following

sections, we will show that it is crucial for a proper interpretation

of FRET results to consider the distributions of D and A dye

positions given by the vectors R_Dand R_A, respectively. Because

different techniques determine distinct average distances be-

tween donor and acceptor dyes, we have to define and distinguish

three different quantities.

The AV Approach. The prediction of the FRET dye positions

with respect to the macromolecule of interest is absolutely essential

for the interpretation of quantitative FRET measurements, especially

when the dyes are attached via long ﬂexible linkers. If the local

structure of a macromolecule is known or can be predicted, the dye

positions have been successfully computed by molecular dynamics

(MD) simulations.^25-27However, MD simulations are time-

consuming and too complex for everyday use. Recently, alternative

methods based on simple geometric computations have been

proposed to predict possible positions for EPR and FRET labels.^28,29

As sketched in Figure 4A, these methods approximate the

dye by a sphere with an empirical radius of R_dye, where the

central atom of the ﬂuorophore (see Table 3 for deﬁnition) is

connected by a ﬂexible linkage of a certain eﬀective length L_link

and width w_linkto the nucleobase. The overall length of the

linkage is given by the actual length of the linker and the internal

chemical structure of the dye. A geometric search algorithm

ﬁnds all dye positions within the linkage length from the

attachment point, which do not cause steric clashes with the

macromolecular surface. All allowed positions are considered as

equally probable, which allows one to deﬁne an accessible volume

for the dye (AV).

(i) ÆR_DAæ denotes the mean distance between the dyes

and can be determined by eTCSPC measurements.

ÆR_DAæ is calculated by integrating over all possible posi-

tions of the two dyes and the resulting distances (ÆR_DAæ =

Æ|R_D- R_A|æ).

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Figure 4. (A) Schematic comparison of AV and MD simulations of dye positions. For AV simulations, we used w_link= 4.5 Å, and R_dye(1)= 5 Å, R_dye(2)

=

4.5 Å, and R_dye(3)= 1.5 Å for the three dimensions of Alexa488. See Table 3 for values for L_link. (B) Molecular dynamics (left) and AV (middle, right)

simulations of possible positions of Alexa488 attached to DNA1 (B-form) (left, middle) or RNA1 (A-form) (right) via linker L. The structures are

rendered via PyMOL.⁶⁵(C) Top view of Alexa488 position distributions simulated by the AV approach for L (left) and S_t(right) linkers. The helical axis

of DNA and the mean position of the dye are shown as red and black spheres, respectively. (D) Coordinate system used to deﬁne the mean dye positions

ÆR_Dæ and ÆR_Aæ in Table 3. The red dashed arrow indicates the helical axis of the nucleic acid.

Spatial Requirements Are Better Described by a Complex

Fluorophore Shape. For RNA, AV simulations using the em-

pirical dye radius R_dye= 3.5 Å²⁹result in two separated dye clouds

(see Figure S3 in the Supporting Information). It is obvious that

the space between the obtained clouds should also be accessible

for the planar chromophores used here. This demonstrates that,

for some sterically demanding local environments, for example,

in RNA, it is important to take the three quite diﬀerent dimen-

sions of a ﬂuorophore into account.

Therefore, for each calculation of a position distribution, we

used the real physical dimensions of the ﬂuorophore and per-

formed three independent AV simulations with three diﬀerent

radii R_dye(i)and superimposed them. Thus, the obtained position

distribution represents an average weighted by the number of

allowed positions. Throughout this work, we used for Alexa488

R_dye(1)= 5 Å, R_dye(2)= 4.5 Å, and R_dye(3)= 1.5 Å and for Cy5

R_dye(1)= 11 Å, R_dye(2)= 3 Å, and R_dye(3)= 1.5 Å. It turned out that

these “mixed” AV simulations are necessary to accurately predict

dye distributions for RNA; yet for DNA, the eﬀect of the dye

radius is much less pronounced.

The fact that the dyes are assumed as spheres makes it impos-

sible to take into account aberrations due to asymmetric struc-

tures (e.g., for Cy5, Figure 2). However, in our case, this results

only in an angular shift, which is easy to correct for as we have the

possibility of comparison to MD data.

The AV method is clearly not applicable when dyes show

considerable interactions (such as sticking) with DNA or RNA.²¹

However, in this work, we employ internal labeling of DNA and

RNA, which minimizes interactions of the dyes with DNA and

RNA. We use NHS-ester of Cy5, which, in contrast to phos-

phoamidite derivatives of Cy5 (see Figure S2 in the Supporting

Information), contains two sulfonic acid groups. The negative

charges of Cy5 and Alexa488 largely prevent dye sticking. With

the exception of dyes with S_tlinkers (see section 3.4), there is no

evidence for the presence of long-lived dye heterogeneities,

which justiﬁes the use of the AV method in this work. It is worth

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Table 3. Estimation of Mean Positions for Alexa488 and Cy5 Using MD and AV Simulations

method

linker L_link, Å (D)

ÆR_Dæ, Å (x, y, z)^a

|ÆR_Dæ|, Å^a

σ_D, Å L_link, Å (A)

ÆR_Aæ, Å (x, y, z)^a

|ÆR_Aæ|, Å^a

σ_A, Å

DNA1

MD

AV^b

L

7.4 -3.8 4.4

6.9 -4.1 2.2

6.0 -4.3 3.1

4.3 -4.7 3.2

9.4

8.3

8.0

7.1

11.4

5.0 -7.1 2.7

6.5 -4.0 2.3

6.2 -4.0 2.7

6.1 -4.0 2.9

9.1

7.9

7.8

12.9

15.2

11.0

10.2

L

I

20

15

11

13.1

9.0

22

17

16

S_t

5.7

RNA1

AV^b

L

20

11

-0.1 -8.5 4.5

-4.0 -2.9 3.9

9.6

6.3

11.3

4.9

22

14

16

-0.8 -8.5 4.2

-3.9 -3.4 3.7

-2.8 -4.9 3.9

9.5

6.3

6.9

12.8

6.9

S_d

S_t

4.9

8.6

^aBetween the C5-atom of the base (origin) and for Alexa488 the O atom at position 10 of the xanthene ring or for Cy5 the C atom at position 3 of the

pentamethine chain; see Figure 4D. ^bFor all AV simulations, we used the same linkage width w_link= 4.5 Å. The distinct linkage lengths L_linkwere

determined from the most extended conformations.

mentioning that strong interactions between a dye and DNA or

RNA are probably impossible to adequately model even by MD

simulations, because millisecond time scales are currently not

accessible to MD.⁶³In this work, we developed an improved

accessible volume simulation procedure based on the algorithm

“Model Satellite Prior” implemented in the “FRETnpsTools”

program^29,37and then performed our own distance calculations

as described. The pdb ﬁles of the macromolecules were gener-

ated with the Nucleic Acid Builder (NAB) software, which is part

of AmberTools.⁶⁴

Comparison of AV with MD. We tested the suitability of the

AV approach in two steps: (i) in this section, the predictions of the

AV approach are compared to the results of the MD simulation

from;²⁵and (ii) in section 3.2.2, the AV approach is used to model

the dye position distributions in a FRET benchmark study.

Figure 4B shows distributions of possible positions of Alexa488

attached to DNA and RNA via the L linker simulated by MD (left)

and AV (middle and right). Each AV simulation needs ﬁve input

parameters: three dye radii R_dye(1,2,3)as deﬁned above, w_link, and

L_link. We used typical parameters for the linkage width (w_link= 4.5 Å)

from ref 29. The linkage lengths (L_link) were estimated from the

fully extended conformations of each linker using the Hyperchem

software⁶⁶and are listed in Table 3.

Considering the L linker, the outer border of the volume

accessible to Alexa488 attached to DNA is displayed as a green

net in Figure 4B. The volume calculated by AV closely resembles

the distribution predicted by MD. In comparison to MD data, AV

predicts the mean position (of Alexa488 (ÆR_Dæ) (O atom at

position 10 in the xanthene ring) with respect to the C5 atom of

the uracil (Figure 4D) with a deviation of 2.2 Å (Table 3). As

expected, due to the asymmetric structure of Cy5, the distribu-

tion of its positions simulated using the AV approach agrees less

well with MD data (3.5 Å deviation between the respective mean

positions ÆR_Aæ deﬁned by the C atom at position 3 in the penta-

methine chain). However, the z-displacement (2.3 Å; see Figure 4D)

and the distance from ÆR_Aæ to the helical axis (11.5 Å) are similar

to MD values (2.7 and 11.8 Å, respectively). Therefore, the main

diﬀerence between the mean positions of Cy5 predicted by MD

and AV is a small angular displacement along the xy-plane of

∼20ꢀ. Thus, in the following, we apply this additional shift for all

Cy5 positions predicted by AV.

the nucleobase (ÆR_Dæ and ÆR_Aæ) are always positive (Figure 4D).

This means that they are always shifted toward the 3⁰-end of

DNA or RNA, which has a signiﬁcant eﬀect on DA distances

(inset in Figure 5C). For L linkers, the displacement between the

dyes in z-direction due to linkers (Δz_link) is 7-8 Å (Table 3).

Thus, for structure determinations or when choosing labeling

positions, it is crucial to take this displacement into account.

Additionally, as opposed to DNA, the base pair plane in A-RNA

is not perpendicular to the helical axis so that the C5 atoms of

opposing nucleobases are displaced against each other by Δz_C5

=

1.6 Å toward the 3⁰-ends of the respective strands. In summary,

the z-displacement of the dyes is determined by three factors and

is given by Δz = Δz_bpΔn þ Δz_linkþ Δz_C5where the basepair

separation Δn is counted from D to A toward the 5⁰-end of DNA

or RNA (i.e., Δn is negative if A is closer to the 3⁰end).

For both DNA and RNA, the attached dyes point into the

major groove, and the volume follows the helical twist of the

groove, which is visible best for RNA (Figure 4B). The groove is

deeper and narrower for RNA, so that the dye motion is expected

to be more restricted. This is consistent with the experimental

anisotropy decays (Section 3.1.2).

In the case of DNA, the calculated mean dye positions are

remarkably insensitive to linkage length (Table 3), which is pro-

bably due to the fact that, with increasing linker length, the acces-

sible volume expands in all directions as illustrated in Figure 4C.

On the other hand, the distance distribution shape changes signi-

ﬁcantly with linkage length used for the simulations (Figure 4C).

As discussed below, all observable FRET parameters can strongly

depend on the width of the R_DAdistribution. In other words,

the knowledge of the mean dye positions is usually insuﬃcient to

predict the FRET eﬃciency. Thus, and to compare AV with MD

results, the standard deviations of the simulated position distribu-

tions (σ_Dand σ_A) are also included in Table 3. For the L linkers,

the height (projection to the z-axis, Figure 4D) of the accessible

volume corresponds to (5 base pairs, which results in signiﬁcant

problems for short DA distances.

3.2.2. Single-Molecule FRET Measurements of RNA Prove

the Accuracy of the AV Model. For RNA (Figure 4B, right),

no MD data are available to calibrate the AV parameters. To test

the predictions of the AV approach nevertheless, we experimen-

tally determined five DA distances within two internally labeled

dsRNAs (RNA2 and RNA3, sequences and labeling positions can

be found in section S1.4 in the Supporting Information) via

Regardless of the linker and the ﬂuorophore, the z-coordinates

of the mean positions of the dyes with respect to the C5 atom of

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smFRET. Moreover, we used these two sequences to demonstrate

also the effect of a dye displacement toward the 3⁰end of the

nucleic acid caused by the linker (inset of Figure 5C). In RNA2,

both dyes are close to the 5⁰ends, so that they are displaced toward

each other (- effect). In RNA3, both dyes are close to the 3⁰ends

and are thus displaced in opposite directions (þ effect). To avoid

any possible orientational artifacts in this benchmark study, we

investigated RNAs, where the dyes were attached by L linkers.

From FRET Data ÆR_DAæ_Eto Structural Information R_mp. As

we will show in sections 3.3 and 3.4, distinct time averaging regi-

mes, from nano- to milliseconds, need to be considered for the

interpretation of FRET data acquired with diﬀerent experimental

techniques. For this section, it is suﬃcient to know that all ﬂuoro-

phore positions of molecules with L linkers will be averaged dur-

ing the millisecond dwell time of the single molecule in the con-

focal observation volume. Thus, the information on the width of

the position distribution is lost; that is, the mean FRET eﬃciency

ÆEæ is observed. Because FRET eﬃciencies and distances are

averaged diﬀerently, that is, E(|ÆR_Dæ - ÆR_Aæ|) ¼ ÆE(|R_D- R_A|)æ,

simulated mean DA position distances (R_mp) cannot be directly

compared to the experimental DA distance values ÆR_DAæ_E(eq 5).

As ÆR_DAæ_E¼ R_mp, one cannot measure R_mpdirectly. However,

for structure determination, it is necessary to obtain distances

that allow a comparison between measurement and simulation.

For solving this problem, several features must be considered.

The easiest solution (algorithm 1) is to calculate R_mpfrom measured

ÆR_DAæ_Eor E by applying a R_mpTÆR_DAæ_Econversion function (for

details, see ref 25). However, especially for small distances, this

function can be ambiguous because the slope becomes very small

(Figure S4 in the Supporting Information). Moreover, ÆR_{DA E}

æ

depends not only on R_mpbut also to some extent on the mutual

orientation of dye clouds. Thus, for a safe solution (algorithm 2),

it is generally advantageous to calculate the theoretical ÆR_{DA E}

æ

values and directly compare with experimental data. Because the

R_DAdistribution is directly obtained from AV simulations, theo-

retical ÆR_DAæ_Ecan be calculated according to eq 5. On the other

hand, due to its high speed, the easy approach with the R_mpT

ÆR_DAæ_Econversion function is more practical for structure model-

ing. For instance, if an iterative algorithm is applied to structure

optimization, remodeling of the dyes’ AVs and calculating ÆR_{DA E}

æ

at each iteration step may become very time-consuming, so that

this cannot be done in all steps.

Figure 5. (A) Sketch illustrating the dynamic orientation averaging of

FRET: the diﬀusion of the dyes in the accessible volume with the character-

istic diﬀusion rate constant k_dand the reorientation ﬂuctuations with the rate

k_R(k_R= 1/F₁); k_R. k_FT. k_d(k_FT: FRET rate constant). (B) PDA of

RNA2(19-) (selected bursts). FRET eﬃciency histogram of experimental

data (gray area) is ﬁtted (black solid line) using the following parameters:

ÆR_DAæ_E= 48.8 Å; σ_app= 1.9 Å; 12.5% of D-only; 1.6% of impurities with

apparent R_DA= 68.8 Å (also present in D-only samples); χ²_r=0.91. Weighted

residuals are shown in the upper plot. PDA parameters: time window Δt =

1 ms; mean background intensities in the green and red detection channels

ÆB_Gæ = 1.23 kHz; ÆB_Ræ = 0.49 kHz; spectral crosstalk, 1.7%; Φ_FD(0)= 0.8;

Φ_FA= 0.29; Alexa488-Cy5 F€orster radius R₀= 52 Å; green/red detection

In eq 5A, two assumptions are made, which are sketched in

Figure 5A and referred to as dynamic orientation averaging of

FRET. First, the diﬀusion of the dyes in the sterically allowed

volume with the characteristic diﬀusion rate constant k_dis much

slower than the FRET rate constant k_FT. Here, by FRET rate, we

mean the formal overall kinetic rate of donor quenching via FRET

(typically some ns^-1), which can be directly measured using

TCSPC. In other words, the distribution of individual DA dis-

tances R_DA,iis quasi-static on the FRET time scale. Second, the

local reorientation ﬂuctuations with the rate constant of k_R= 1/F₁

are fast so that a mean eﬀective orientation factor κ²(due to the

restriction of dye motions it is not necessarily equal to 2/3) can be

used. In this work, we will experimentally check the validity and

error limits of assuming the “standard” case, that is, isotropic ave-

rage with fast and unrestricted dye rotation (k_R. k_FT. k_dand

the wobble half angle 90ꢀ, resulting in κ²= 2/3).

eﬃciency ratio: 0.78. (C) DA distances ÆR_DAæ_Emeasured by smFRET

(compiled also in Table S2 in section S2.5 of the Supporting Information)

plotted versus expected (simulated using AV) distances ÆR_DAæ_E(9) and R_mp

(0). The following polynomial approximation of a R_mpTÆR_DAæ_E-conversion

3

2

function was used: ÆR_DAæ_E= -2.68 ꢀ 10^-5R_mpþ 7.53 ꢀ 10^-3R_mp

þ

0.272R_mpþ 23.1. The solid line represents equal expected and measured

distances. The statistical experimental errors are smaller than the symbol size.

The dashed lines represent the expected uncertainties due to possible errors of

κ²(section 3.5) given by the typical precision of 5.1% in Table 5. Inset: Sketch

illustrating that for a given basepair separation between D and A, the linker ori-

Photon Distribution Analysis (PDA). When photon bursts of

freely diﬀusing molecules are analyzed, it is mandatory to take

into account that the obtained FRET eﬃciency histograms are

aﬀected by the stochastic nature of photon emission and detection

entation may lead to a decrease (-, blue) or an increase (þ, orange) in R_DA

.

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(shot noise) and other sources of dynamic or static hetero-

geneities. The use of an exact description for the theoretical shot

noise distribution, photon distribution analysis (PDA),^67,68allows

us to separate shot noise from inhomogeneous broadening and

calculate the FRET-averaged DA distances ÆR_DAæ_E(for further

details on PDA, see section S2.4 in the Supporting Information). A

F€orster Radius R₀= 52 Å of Alexa488-Cy5 (assuming an orien-

tation factor κ²= 2/3, justiﬁcation given in section 3.5) is used to

calculate the DA distances with eq 5B. As an example, we present

a smFRET histogram of the labeled sample RNA2(19-) in

Figure 5B. The PDA analysis clearly shows the presence of the

three species: (I) major population (85.9%) of the expected FRET

species with ÆR_DAæ_E= 48.8 Å (orange line); (II) 12.5% of D-only

to consider as the accuracy of FRET increases to angstr€om

resolution.

3.3. Influence of DA Distance Distributions on Ensemble

Time-Resolved FRET Measurements. In the case of short DA

distances with high FRET, uncertainties in dye position repre-

sent a large fraction of the absolute R_DAvalues, which may lead to

significant systematic errors. As shown in Table 3, the “effective”

linkage lengths (|ÆR_Dæ| and |ÆR_Aæ|) are expected to range

typically between 8 and 10 Å. Moreover, distance distribution

half widths become comparable to R_DA. To characterize the

resulting R_DAdistributions also experimentally, we measured

donor and acceptor fluorescence decays in the presence of FRET

for labeled DNA and RNA samples with small separations

between the dyes (10 and 11 bps for DNA1 and RNA1,

respectively), by using eTCSPC. Experimental eTCSPC data

in Figure 6 obtained for DNA1 samples could not be fitted using

a single FRET rate, that is, with a single fluorescence lifetime

to describe the FRET state (see Figure 6, upper residuals plot).

We attribute the complex donor decay to a distribution of

donor-acceptor distances, which is likely mainly due to the

flexibility of the dye linkers. In view of the averaging regime,

which has been discussed in section 3.2.2, fluorescence lifetime

measurements allow one to obtain snapshots of heterogeneities,

which live longer than the fluorescence lifetime (in our case 4 ns).

In other words, due to its high time resolution, TCSPC can be

used to characterize DA distance distributions p(R_DA). For

example, the analysis of donor fluorescence decays F_D(t) (D

decay) by eq 6 recovers p(R_DA).^7,24,71

(green line); and (III) 1.6% of impurities with an apparent R_DA

=

68.8 Å (blue line; also present in donor-only samples). Moreover, a

ﬁxed DA distance is not suﬃcient for the FRET species, and a

Gaussian distance distribution with an apparent distribution half

width (σ_app) has to be used instead. The recovered σ_appis about

4-5% of the mean distance ÆR_DAæ_Eand can be attributed mainly to

acceptor photophysics.⁶¹Thus, σ_appmust not be confused with real

physical distance distributions (modeled or recovered by donor

ﬂuorescence lifetime analysis of eTCSPC). However, additional

broadening leading to considerably larger values for σ_appcan be due

to distance heterogeneities as seen later (section 3.4).

In Figure 5C, the experimental FRET-averaged distances ÆR_{DA E}

æ

of all ﬁve molecules are plotted versus the calculated values for R_mp

(open symbols) and ÆR_DAæ_E(full symbols). We assumed a perfect

A-RNA (parameters are given in Table S3 in the Supporting Infor-

mation) for the AV model. As we do not need to ﬁnd an unknown

!

Z

t

6

target structure, it is suﬃcient to calculate theoretical values of ÆR_{DA E}

æ

F_DðtÞ ¼

pðR_DAÞ exp

-

½1 þ ðR₀=R_DAÞ ꢁ dR_DA

τ_Dð0Þ

by an R_mpTÆR_DAæ_Econversion function (algorithm 1).

R_DA

We ﬁrst calculated the coordinates of the mean D- and A-

positions, which are given in Table 3 (alternative representations

of ÆR_Dæ and ÆR_Aæ are given in Table S3B in the Supporting In-

formation). Next, R_mpvalues were calculated and converted to

ÆR_DAæ_Eby using the R_mpTÆR_DAæ_Econversion function given in the

caption shown in Figure S4 (Supporting Information). In Figure 5C,

the solid line with a slope of 1 indicates perfect agreement between

theory and experiment. Notably, only FRET-averaged (eq 5) DA

distances ÆR_DAæ_Edescribe the FRET experiment correctly for the

whole distance range; that is, the theory must include the distri-

bution of dye positions. Especially for short distances, there are

large deviations between the measured FRET distances (ÆR_DAæ_E)

and the distances between the modeled mean positions of the

dyes (R_mp, 0), whereas the theoretical and experimental values

for ÆR_DAæ_Eagree very well, which is also indicated by an rmsd

value of 1.3 Å. The agreement is even better than expected for the

given position and orientational uncertainties (dashed lines in

Figure 5C; see Table 3 and section 3.5), which suggests that

for the ﬁve samples studied here κ²is very close to 2/3, as

discussed in section 3.5. Moreover, the speciﬁc linker displace-

ment eﬀect of the dye relative to C5 of the pyrimidine base is

described correctly. This eﬀect results in an average z-shift of the

mean position of the dye of ∼4.3 Å (=1/2Δz_linkþ 1/2Δz_C5)

toward the 3⁰end (Figure 5C). Thus, simpliﬁed modeling of

dye positions by the AV method and the described correction

for systematic errors is usually suﬃcient and agrees well with

both MD and our experimental data obtained for DNA and

RNA.

ð6Þ

where τ_D(0)is the donor fluorescence lifetime without acceptor.

For simplicity, the distribution p(R_DA) can be assumed to be

Gaussian. Considering also the presence of donor-only mole-

cules, the fitting parameters of eq 7 are then the mean DA

distance ÆR_DAæ, the half-width σ_DAof the R_DAdistribution, and

also the fraction of donor-only molecules x_D(in our measure-

ments typically below 10%):

!

Z

2

1

ðR_DA- hR_DAiÞ

pﬃﬃﬃﬃﬃ

F_DðtÞ ¼ ð1 - x_DÞ

exp

-

2σ²_DA

2πσ_DA

R_DA

!

t

6

exp

-

½1 þ ðR₀=R_DAÞ ꢁ dR_DAþ x_Dexp

-

τ_Dð0Þ

ð7Þ

To test the accuracy of the AV model, we compared the mean

and the half-width of the distribution p(R_DA) obtained by

fitting eq 7 to experimental TCSPC data, with those predicted

by the AV simulations. A good agreement between experi-

mental and simulated data was found (see section 3.3.1). To

justify the use of a Gaussian distribution in eq 7, we simulated

a DA distribution of a FRET experiment using two AV

position distributions (see Figure S5A in the Supporting

Information). Interestingly, this DA distribution p(R_DA) is

very well described by a Gaussian distribution. The validity

of the approximation of p(R_DA) by a single Gaussian distri-

bution can be checked experimentally as demonstrated in

section 3.4.

So far, we have neglected that the refractive index of the

macromolecule should be taken into account for F€orster radius

calculations.^69,70This small eﬀect may become necessary

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ARTICLE

Table 4. DA Distance Distribution Parameters Calculated

from eTCSPC and smFRET Data in Comparison with AV

Simulations^a

eTCSPC experiment

PDA

AV simulation

ÆR_DAæ (σ_DA), ÆR_DAæ (σ_DA),

ÆR_{DA E}

æ

R_mp, Å

ÆR_DA

æ

linker Å (D decay)

Å (A rise)

(σ_app), Å

(σ_DA), Å

DNA1

L

I

39.5 (7.5) 42.3 (6.8) 42.5 (1.5) 35.5 39.9 (8.8)

40.8 (5.9) 40.8 (8.2) 41.5 (1.5) 33.9 36.3 (6.0)

38.4 (11.2) 45.6 (7.7) 45.9 (2.9) 32.7 35.6 (4.8)

S_t

RNA1

L

41.5 (7.3) 43.2 (6.3) 42.8 (1.6) 27.5 31.6 (6.3)

35.1 (6.0) 34.5 (6.8) 36.6 (1.0) 22.7 23.9 (5.1)

34.4 (7.6) 34.6 (11.2) 36.5 (4.7) 23.0 24.4 (5.3)

S_d

S_t

Figure 6. eTCSPC measurement of the ﬂuorescence decay of Alexa488

obtained for the DNA1 FRET sample with L linker. Experimental data

(magenta 9), instrument response function (IRF, O), and the ﬁt

assuming a Gaussian distribution of distances (eq 7; bottom panel, solid

black line) are shown. Weighted residuals are presented in the upper

plots; (top) formal biexponential ﬂuorescence decay with a single FRET

state corresponding to τ_D(A)= 1.0 ns (87.5%), and a donor-only decay

with τ_D(0)= 4.1 ns (12.5%); χ²_r= 10.3; (middle) Gaussian distribution of

distances (parameters are given in Table 4) and donor-only decay (eq 7)

with τ_D(0)= 4.1 ns (6.7%); χ²_r= 1.35. The ﬁt ranges from the maximum

of the IRF to the ﬁrst time channel with less than 100 detected photons.

^aThe dye-dye separation is 10 and 11 basepairs for DNA and RNA,

respectively.

the values calculated from donor and acceptor decay curves shows

that donor quenching is indeed due to FRET and not due to, for

example, local quenching artifacts. For S_tlinkers, systematic

deviations are seen, and the R_DAdistributions are surprisingly

broad (σ_DA= 11.2 Å), which is clearly unexpected for the shor-

test linker. We will show below that a rather irregular distribution

of stable conformations of one or both dyes must exist for S_t

linkers, which cannot be described with a single Gaussian peak as

assumed in eq 7.

The extension of eqs 6 and 7 to the case of multiexponential

ﬂuorescence relaxation of D-only can be easily made (see ref 72

and section S2.6 in the Supporting Information).

Analysis of RNA. In the case of RNA, a similarly broad R_DA

distribution can be observed for the acceptor rise for the S_tlinker.

Furthermore, the agreement between theory and experiment is

generally worse than for DNA. The main reason is that the DA

distances are quite short (less than one-half of the F€orster radius

of 52 Å). At such short distances, the point dipole approximation

does not hold^8,20,75,76and should be replaced accordingly, which

is beyond the scope of the work. Furthermore, dye-dye inter-

actions⁷⁷cannot be excluded. However, let us point out that the

measurements with short linkers (S_dor S_t) provide distances that

are much closer to the structurally relevant distance between the

C5 atoms of the labeled nucleobases (30 Å) than for L linkers.

3.3.2. Translational Linker Movements Are Slow on the

Time Scale of FRET. eTCSPC data provide additional evi-

dence for quasi-static distance distributions on the time scale of

FRET as has been postulated before.²⁵Considering L, I, and S_d

linkers, the fit of R_DAdistributions to experimental fluorescence

decays typically yields distribution half-widths σ_DAcomparable to

simulated ones (Table 4). This indicates that DA distributions due

to linker motions are not significantly averaged out on the nano-

second time scale. There is no contradiction between this finding

and subns anisotropy decay times: for example, Alexa488 readily

rotates about the linker axis, which involves strong fluorescence

depolarization but very little distance fluctuations. In the case of

low FRET, there might be more averaging of distances; however,

taking into account large absolute values of R_DA, only minor rela-

tive errors could be expected because the differences in E for

dynamic and static averaging are small for large distances (for low

FRET, ÆR_DAæ ≈ R_mpirrespective of the averaging regime).

3.4. FRET Broadening on the Millisecond Time Scale. To

understand the surprisingly broad R_DAdistributions for the S_t

Moreover, the characteristic rise time of the acceptor ﬂuores-

cence (A rise) also contains information on the FRET rates^72-74

(for details, see section S2.6 and Figure S5B in the Supporting

Information).

3.3.1. Measured ÆR_DAæ Distances Do Not Compare to

Simulated R_mp. The simulated and measured distances are

presented in Table 4. Clearly, the values for distances between

mean dye positions (R_mp) simulated by the AV method do not

agree with the distances measured by eTCSPC and PDA. To

explain these deviations, one should note that, like for ÆR_{DA E}

æ

(section 3.2.2), the mean distance ÆR_DAæ measured by eTCSPC

(eqs 6 and 7) is not equal to R_mpbut is rather given by eq 8:

hR_DAi ¼ hjR_D- R_AjigjhR_Di - hR_Aij

ð8Þ

In other words, ÆR_DAæ g R_mp, so that a difference of >5 Å can be

seen for broader distance distributions (Table 4). For instance,

the distance between the centers of completely overlapping dye

clouds is zero (R_mp= 0), whereas the average distance between

individual dye positions is not (ÆR_DAæ > 0). Thus, a realistic

modeling of dye position distributions is needed not only for

PDA but also for a proper interpretation of time-resolved fluo-

rescence decays. If one compares ÆR_DAæ with ÆR_DAæ_E, the latter is

typically weighted toward R₀, that is, ÆR_DAæ_Eg ÆR_DAæ for ÆR_DAæ <

R₀and ÆR_DAæ_Ee ÆR_DAæ for ÆR_DAæ > R₀.

Analysis of DNA. For DNA samples with L and I linker, the

agreement between the simulated and experimental ÆR_DAæ values

obtained by eTCSPC and PDA is good, and remaining devia-

tions are well within the expected position (Table 3) and the

κ²-related errors (section 3.5). ÆR_DAæ and σ_DAwere also extracted by

ﬁtting the acceptor rises (Table 4). The good agreement between

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Journal of the American Chemical Society

ARTICLE

linkers (section 3.3), we performed single-molecule experiments

on freely diffusing DNA1 and RNA1 molecules to check whether

the distributions are averaged out on the millisecond time scale.

Figure 7A-D shows 2D probability histograms of FRET efficiency

E versus the donor lifetime τ_D(A), where the corresponding 1D

parameter histograms are given as projections. The number of

molecules (fluorescence bursts) in each bin is gray scale shaded

from white (lowest) to black (highest). All 2D plots show two

distinct peaks: (I) at E ≈ 0 and τ_D(A)≈ 4 ns, due to D-only popu-

lations, and (II) at E ≈ 0.7-0.8 and τ_D(A)≈ 1-2 ns attributed to

FRET subpopulations. In all plots, solid lines indicate the expec-

ted E versus τ

dependence for dynamic FRET taking fast

D(A)

linker dynamics into account⁷⁸(eqs S12 and S13 in section S2.6

of the Supporting Information). DNA and RNA samples with L

linkers show homogeneous uncorrelated E-τ_D(A)distributions

of the FRET population (Figure 7A and B), which are distributed

approximately horizontally due to independent shot noise dis-

79

tributions of E⁶⁸and τ_D(A)

.

All samples with I and S_dlinkers

exhibit similar patterns (see Figure S6 for RNA1 with S_dlinker in

section S2.7 of the Supporting Information).

On the contrary, DNA1 and RNA1 with S_tlinkers have broad

and asymmetric 2D distributions of E-τ_D(A)(Figure 7C and D).

Moreover, for S_tlinkers, a correlation between E and τ_D(A)within

the FRET subpopulation is apparent from 2D plots, indicating a

heterogeneous distribution of DA distances on the millisecond

time scale. This fact is consistent with the eTCSPC data (Table 4),

which show unexpectedly broad R_DAdistributions obtained ex-

clusively for S_tlinkers. The comparison of two complementary ds

RNA1 FRET samples with diﬀerent linkers for D and A, respec-

tively, yields that this is mainly caused by the donor. Only the

sample labeled with linker S_tat the donor and linker L at the accep-

tor position shows E broadening, whereas E is narrow for the

RNA1 sample with the opposite linker combination of the dyes

(Figure S7 in section S2.7 of the Supporting Information).

PDA. To quantify these visual effects, we performed PDA of the

smFRET data shown in Figure 7A-D. The mean FRET-averaged

DA distances ÆR_DAæ_Erecovered by PDA are typically similar to

ÆR_DAæ values found by eTCSPC (Table 4). A large deviation is ob-

served only for DNA1 with S_tlinkers, indicating distinct dye subpo-

pulations. Moreover, the apparent R_DAdistribution half-widths

found by PDA(σ_app) are significantly larger for S_tlinkers (Table 4).

For instance, for RNA1, σ_appamounts ∼13% of ÆR_DAæ_Efor S_t

linkers, whereas for other linkers σ_appdoes not exceed 3-4% of

ÆR_DAæ_E. This fact indicates the presence of FRET heterogeneities

in addition to the complex acceptor’s photophysics, which is

responsible for theminimal broadening of few percentof ÆR_DAæ_E.⁶¹

Maximum Entropy Deconvolution. To further support

this conclusion, we reanalyzed all data with S_tlinkers and used an

unbiased model-free DA distance distribution instead of the assu-

med Gaussian distribution. We performed a maximum entropy

(ME) deconvolution^47,48of R_DAdistributions observed for S_t

linkers on different time scales (Figure 7E and F): eTCSPC data

for thenanosecondtime scale(dashed lines) and PDA of smFRET

intensity data for the millisecond time scale (solid lines). ME de-

convolutions of both experiment types indicate the presence of

multiple FRET states. eTCSPC data show that S_tlinkers have two

stable conformations (corresponding to two major “stable” peaks

“s1” and “s2” in Figure 7E and F) possibly with some additional

flexibility leading to broadening of these peaks. For RNA1, PDA

data show a peak between the two DA distances found by eTCSPC

(“mixing” peak “m” in Figure 7F), which suggests that additional

averaging takes place on a time scale faster than the dwell time

Figure 7. (A-D) 2D probability histograms of FRET eﬃciency E

versus the donor lifetime τ_D(A)generated from smFRET data obtained

for (A) DNA1, L linkers; (B) RNA1, L linkers; (C) DNA1, S_tlinkers;

and (D) RNA1, S_tlinkers. The number of molecules (ﬂuorescence

bursts) in each bin is gray scale shaded from white (lowest) to black

(highest). The corresponding 1D parameter histograms are given as

projections. In all plots, solid lines indicate the E versus τ_D(A)depen-

dence given by eqs S12 and S13 in section S2.6 of the Supporting

Information. (E,F) Maximum entropy deconvolution of donor-acceptor

distance distributions for (E) DNA1, S_tlinkers and (F) RNA1, S_tlinkers.

The solid and dashed lines represent deconvolutions of single-molecule

intensity data and donor decays measured by eTCSPC, respectively. The

ME method allows one to extract distributions of ﬂuorescence lifetimes

from eTCSPC data,⁴⁸which can be converted into distributions of R_DA

.

In PDA,⁶⁸distance ME distributions are directly used to calculate FRET

eﬃciency distributions. The shaded areas indicate the region where

the observed peaks may represent multimolecular and photobleaching

events. The peaks “s1” and “s2” correspond to stable dye conformations,

whereas the peak “m” is likely due to averaging of the states s1 and s2 on

the millisecond time scale.

(ms). Dynamic PDA^78,80provides no indication for “mixing”

with millisecond characteristic times (see Figure S8 in the

Supporting Information). Thus, transitions responsible for the

“mixing” peak occur on a significantly faster time scale, whereas

the “s1” and “s2” peaks are stable during the burst duration.

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ARTICLE

For DNA1, a signiﬁcantdiscrepancy between PDA andeTCSPC

data is observed (cf., Figure 7E and Tables 1 and 4). This eﬀect

could be due to a static quenching of the acceptor in the state cor-

responding to the shorter R_DA(peak “s1” in Figure 7E). If so, the s1

state would be nearly invisible in SMD measurements because both

dyes are quenched in this state (D is quenched by high FRET),

which also explains the disagreement between donor decay and

acceptor rise data (Table 4). This explanation is supported by en-

semble measurements of the acceptor ﬂuorescence quantum yield

Φ_FA, which is reduced for the S_tlinker (Φ_FA= 0.21) as compared

to the L linker (Φ_FA= 0.38, Table 1).

In summary, complex distributions of DA distances found for S_t

linkers severely complicate their use in quantitative FRET studies.

Thus, an optimal linker must always allow for free diﬀusion within

the dye’s accessible volume. On the other hand, to minimize position

uncertainties and to prevent dye-dye interactions, linkers should

not be longer than necessary. For DNA and Alexa488, the I linker

seems to ﬁt best to these requirements. For Cy5, shorter S_dand S_t

linkers work equally well because the dye has an extra 6-atom

linker between the chromophore and the reactive coupling group

(Figure 2). Hence, for undeﬁned dye environments, where

modeling of dye positions is impossible, I and S_dare well suitable

linkers as they provide better absolute distance estimations.

3.5. Minimizing Uncertainties Due to the Orientational

Factor K². For accurate FRET analysis, we must consider not

only translational linker diffusion, which is usually slower than ns,

but also orientational dynamics. Given subnanosecond local rota-

tional correlation times in Table 2, dynamic orientational averaging

can be assumed at least to some extent. Dye reorientation dynamics

on the time scale of FRET (k_FT, see section 3.2.2)⁸¹could, thus, be

relevant only for very short distances, which is beyond the scope of

this Article. The anisotropy measurements indicate, however, that

the orientational distribution of both D and A is not strictly isotropic

even for L-linkers (Table 2), contrary to the MD data from²⁵(for

details, see section S2.8 in the Supporting Information). Therefore,

detailed analysis of related κ²effects for all linkers must be performed.

As mentioned above, the modeling of the accessible space of a

dye is much less important for short linkers, making them more

suitable for quantitative FRET measurements in the case of unde-

ﬁned environments. One potential problem when using short linkers,

however, is the estimation of the orientation factor κ². The assump-

tion of κ²= 2/3 might not be justiﬁed for short linkers as their

movement is more restricted. In this section, we estimate the range of

possible values for κ^{2 19,82,83}for the diﬀerent linkers of DNA1 and

RNA1 and determine potential errors for FRET distance measure-

ments if κ²= 2/3 is assumed in the calculation of R₀.

Figure 8. (A) FRET-sensitized acceptor anisotropy decays (dots), the

rescaled instrument response functions (IRF, dashed line), and the

anisotropy decays (black solid lines) of DNA (left) and RNA (right) (ﬁt

results, see Table 5). (B) Sketch showing angles that deﬁne the

orientational factor κ²in eq 9: β₁and β₂are the angles between the

To minimize the uncertainty in κ², we use the residual ani-

sotropies that result from the measurements of the donor-only,

the acceptor-only (Figure 3B in Section 3.1.2.), and the FRET-

symmetry axes of the rotations of the dyes and the distance vector R_DA

,

and δ is the angle between the symmetry axes. (C) Calculated prob-

ability distributions for possible values of κ²in RNA1: (top) for linker L,

sensitized acceptor (Figure 8A) anisotropy decays (r_¥,D, r_¥,A

,

and r_¥.A(D), respectively), to calculate the range of all possible

(middle) for linker S_tand in both cases taking into account r_¥,A(D)

(bottom) for linker S_tand only using the oﬀsets from the anisotropy

decays of the donor and acceptor molecules r_¥,Dand r_¥,A

;

values for κ²by eq 9:

.

2

^ð2Þðβ₁Þ þ S^ð_A^2Þ

3

2

k²¼ þ S^ð_D^2Þ

S

^ð2Þðβ₂Þ þ S^ð_D^2ÞS^ð_A^2ÞðS^ð2ÞðδÞ

The necessary second-rank order parameters S⁽²⁾are deﬁned

in eq 3 (S⁽_D²⁾) and eq 4 (S⁽_A²⁾) and formally by:

3

þ 6S^ð2Þðβ₁ÞS^ð2Þðβ₂Þ þ 1 þ 2S^ð2Þðβ₁Þ þ 2S^ð2Þðβ₂Þ

- 9 cos β₁cos β₂cos δÞ

r_¥,AðDÞ

1

ð9Þ

S

^ð2ÞðδÞ ¼ ð3 cos²δ - 1Þ ¼

_ð2Þ, S^ð2Þðβ₁Þ

r₀S^ð2ÞS_A

2

D

In eq 9, β₁and β₂are the angles between the symmetry axes of

the rotations of the dyes and the distance vector R_DA, while δ is

the angle between the symmetry axes (Figure 8B).

1

¼

ð3 cos²β₁- 1Þ ; and S^ð2Þðβ₂Þ ¼ ð3 cos²β₂- 1Þ ð10Þ

2

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Table 5. Fit Parameters for FRET-Sensitized Acceptor Anisotropy Decay (r₀= 0.38) and Results for κ²Probability Distributions

Taking into Account r_¥,D, r_¥,A(Table ²), and r_¥,A(D)

sensitized anisotropy

F₁, ns (b₁) _2(global), ns (b₂= r_¥,DA

border values: worst cases

mean value: typical case

linker

r_S

F

)

κ²

ΔR_DA

κ²

mean

accuracy of R_DA

precision ΔR_DA

min

max

DNA1

I

0.005

0.002

0.012

0.605 (0.042)

0.400 (0.080)

0.227 (0.056)

>60 (-0.003)

>60 (-0.007)

10 (0.010)

0.25

0.22

0.42

0.94

0.92

-6%...þ15%

-6%...þ17%

-6%...þ 7%

0.6

þ3.1%

þ2.6%

þ1.7%

7.0%

5.9%

4.4%

S_t

L

0.59

0.67

RNA1

S_d

S_t

L

0.012

0.038

0.016

0.260 (0.045)

0.258 (0.069)

0.246 (0.047)

>60 (0.007)

>60 (0.031)

>60 (0.012)

0.10

0.09

0.38

1.57

1.1

-13%...þ37%

-9%...þ28%

-6%...þ 9%

0.64

0.57

0.62

þ0.8%

þ3.9%

þ2.2%

8.4%

8.9%

5.1%

0.93

κ²values (eq 9) cannot be calculated unambiguously because, in

general, the angles β₁and β₂are not experimentally accessible.

However, for an experimentally determined δ (eq 10), it is

possible to deﬁne a range of possible values for β₁and β₂(eqs

S16A and S16B in section S2.8 of the Supporting Information),

which allows one to calculate the range of κ²values (eq 9)

compatible with the experimental data (r_¥,D, r_¥,A, and r_¥,A(D)).

Note that κ²does not explicitly depend on the cone opening

half angles θ_Dand θ_A(section 3.1.2) and the assumption of dye

reorientation within a cone/disk (Figure 3C and D); that is, even

if this approximation is considered as unrealistic, it is not needed

to obtain eq 9. However, axially symmetric transition dipole ori-

entation distributions are usually assumed for κ²estimation,¹⁹

which might be not exactly the case here (Figure 4). Therefore, it

is absolutely reasonable to expect that additional averaging of mutual

orientations of D and A by diﬀusion along the DNA or RNA groove

would bring the eﬀective κ²even closer to 2/3 than given by eq 9.

This might be one of the reasons for the (unexpected) high accuracy

of our FRET benchmark study using RNA2 and RNA3 (Figure 5C

in section 3.2.2). Thus, the κ²estimations given below represent the

worst case scenario. Moreover, in this study, we cannot investigate

a possible correlation between R_DAand κ²as proposed in a few

recent theoretical works^20,75,76for the case that the dye exhibits a

slow exchange between diﬀerent microenvironments. Our simpli-

ﬁed (AV) simulations do not allow us to discuss this eﬀect.

3.5.1. Estimation of κ²Using r_¥,A(D). The residual aniso-

tropies r_¥,D, r_¥,A, and r_¥,A(D)can be used to calculate a prob-

ability distribution of κ²values. For the estimation of r_¥,A(D), the

FRET-sensitized acceptor anisotropy decays were studied for all

linkers of DNA1 and RNA1 (see section 2 for the measurement

and analysis procedures). The data and the results of the analysis

are shown in Figure 8A and Table 5, respectively. In all cases, the

decays could be fitted by a biexponential decay consisting of a fast

decay time F₁≈ 0.4 ns (resulting from fast FRET (k_FT) and local

reorientations (k_R)) and a slow decay time F₂(global motion).

As in section 3.1, the slow component is approximated by a time-

independent offset r_¥,A(D)and considered to be the residual

anisotropy. It is largest for the linker S_tin RNA and is negative for

the linkers I and S_tin DNA, which indicates that the transition

dipole moments of the dyes are preferentially orientated per-

pendicular to each other. Indeed, the differences between all

anisotropy decays indicate distinct mean dye orientations. More-

over, smFRET measurements were analyzed by inspecting 2D

probability histograms of steady state anisotropy r_sversus the

donor lifetime τ_D(A)to make sure that the resulting residual

anisotropies r_¥,A(D)are due to restricted reorientation of the dyes

and not due to a fraction of molecules where the dye is immobile.

For linkers L, the FRET populations in the r_s-τ _D(A)2D plots

appear to be symmetric at r_s≈ 0.1 and τ_D(A)≈ 1.3 ns. Thus,

there is only one anisotropy population for each lifetime popula-

tion. For shorter linkers, the anisotropy distributions become less

symmetric. The existence of additional donor populations is

most pronounced for S_tlinkers with a fraction of a 2-fold

increased steady-state anisotropy, which amounts to less than

29% (see Figure S9 in section S2.8 of the Supporting Information

for all FRET pairs). However, in no case could a completely

immobile dye species be detected.

Three distributions of possible κ²values are presented in Figure 8C

with the corresponding parameters compiled in Table 5. The smallest

and the largest possible values κ²_minand κ²_maxrepresent the worst

case scenario for a FRETdistancemeasurement for whichκ²= 2/3

is assumed. The resulting range of potential relative errors (worst

case) for distance measurements ΔR_DAtypically vary from -6%

to þ15% (Table 5). For a range of possible κ²values, one can

deﬁne an accuracy (systematic error) and a precision (uncertainty;

eqs S17A and S17B in section S2.8 of the Supporting Informa-

tion), which would result in a typical uncertainty of κ²in the FRET

distance measurements presented here. These parameters are

shown in Table 5, and it is obvious that the errors and deviations

are relatively small in all cases, although they become larger for

short linkers (see also Figure 8C). Nevertheless, the distances

measured using short linkers are reasonably accurate.

3.5.2. Estimation of κ²with Unknown r_¥,A(D). For the

estimation of κ², many groups only use r_¥,Dand r_¥,A,⁷which

result from the anisotropy decays of the D-only and the A-only

molecules, respectively, and do not measure the FRET sensitized

acceptor anisotropy decay. Hence, r_¥,A(D)is unknown, and δ must

be allowed to be every value between 0ꢀ and 90ꢀ. For compar-

ison, theprobabilitydistributions for κ²for all linkersof DNA1 and

RNA1 were also calculated accordingly; that is, only r_¥,Dand r_¥,A

were taken into account. The results are shown in Table S4 in

section S2.8 of the Supporting Information. There are only slight

changes in accuracy and precision, but the range of possible κ²

values nearly doubles. Thus, the worst-case ΔR_DAincreases

especially toward smaller distance values from typically ∼ -6%

for known r_¥,A(D)(section 3.5.1) to typically -15% for unknown

r_¥,A(D). Figure 8C shows the probability distributions for the RNA

molecules for the linkers L and S_tin case all three residual

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Journal of the American Chemical Society

ARTICLE

anisotropies are taken into account (top and middle, respectively)

and for linker S_twhen only r_¥,Dand r_¥,Aare used (bottom).

It is worth mentioning that for the estimation of κ²the steady-

state anisotropy r_sis commonly used instead of the residual ani-

sotropy r_¥.^7,29This method, however, overestimates κ²-related

errors even further as r_sis usually larger than r_¥.

’ ACKNOWLEDGMENT

C.A.M.S., S.M., H.N., and S.K. thank the German Science

foundation (DFG) in the priority program SPP 1258 “Sensory and

regulatory RNAs in prokaryotes” for funding this work. S.S. thanks

the NRW Research School Biostruct for funding. We are grateful

to Hayk Vardanyan for help in single-molecule measurements.

We thank Evangelos Sisamakis, Hugo Sanabria, Ralf K€uhnemuth,

and Suren Felekyan for very fruitful discussions. We thank Anna

K. Woꢀzniak for providing the cartoon for the TOC graphic.

4. CONCLUSION

In this work, we introduce new short dye linkers for labeling of

DNA and RNA. FRET measurements on dsDNA and dsRNA

model systems test their suitability for quantitative studies. For

well-deﬁned environments and if the dye diﬀuses freely in the

sterically allowed, mean positions of the dyes and R_DAdistribu-

tions can be accurately modeled using relatively simple and fast

accessible volume simulations. The translational motions of the

dyes appear to be slow on the time scale of the ﬂuorescence

lifetimes and depend on linker size and structure. For L, I, and S_d

linkers, the motions are completely averaged out on the milli-

second time scale, whereas S_tlinkers exhibit a complex distribu-

tion of R_DAdue to inhibited diﬀusion through the accessible

volume. It became also clear that experimentally measured

distances, especially for long linkers, cannot be directly compared

to the structurally relevant mean position distance R_mpor the

distance between C5 atoms of uracil. Because of broad distribu-

tions of DA distances, there is a large discrepancy between R_mp

and ÆR_DAæ_E(measured by smFRET) or ÆR_DAæ (measured by

eTCSPC), which must be always taken into account. When

doing so, high precision distance measurements are possible.

This correction and, therefore, modeling of dye positions is less

important for short linkers. This makes them particularly suitable

for undeﬁned environments. However, due to the inhomogene-

ities of DA distances observable for S_tas a linker for Alexa488, we

advise against its use and recommend the S_dor the I linker

instead.

It became clear that, when calculating a probability distribu-

tion for possible values of κ², its width can be further reduced

when taking into account not only the residual anisotropies of the

donor and acceptor r_¥,Dand r_¥,Abut also r_¥,A(D), which results

from the FRET-sensitized acceptor anisotropy decay. Further-

more, for short and intermediate linkers, κ²-related errors are

only slightly higher than for long linkers. When using them for

quantitative FRET measurements of internally labeled nucleic

acids with Alexa488 and Cy5 as a FRET pair, it is, therefore, safe

to assume κ²to be 2/3. For unknown local environments, long

linkers increase uncertainties signiﬁcantly more.

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Accurate distance determination of nucleic acids via foerster resonance energy transfer: Implications of dye Linker length and rigidity

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