FRET - Förster Resonance Energy Transfer || How to Apply FRET: From Experimental Design to Data...

5How to Apply FRET: From Experimental Design to Data AnalysisNiko Hildebrandt

5.1Introduction: FRET – More Than a Four-Letter Word!

F€orster resonance energy transfer (FRET) is a very special scientific topic because itinspires and challenges many theoretical and experimental scientists from differentresearch disciplines ranging from the fundamental life sciences over theoreticalphysics and chemistry up to applied technology in physics, electronics, chemistry,medicine, and biology. Almost as versatile as the topic itself is the discussion aboutthe acronym FRET or rather about the first letter “F.” Should it be “F” likefluorescence, which is most often involved in FRET experiments (although FRETis a nonradiative energy transfer)? Or “F” like F€orster, who was the first person todevelop a theory relating spectroscopic data such as absorption and emission spectrato the energy transfer efficiency, donor–acceptor molecule distances and orienta-tions (although many other scientists were involved in the discovery of FRET)? Orshould the “F” be completely erased in order to circumvent the discussion (or toavoid four-letter words)? Personally, I prefer to use “F€orster” in acknowledgment ofhis achievements and in order to avoid the term fluorescence, but probably the mostimportant aspect of this discussion is the fact that it is not an important discussion.FRET is a very useful and interesting technology and its experimental applicationand theoretical treatment for the many possible FRET systems should be investi-gated, discussed, and developed. Although the main theory was contributed byF€orster in the 1940s, FRET is a very modern technology because the r�6 distancedependence over approximately 1–20 nm fits extremely well into the recent discov-eries and investigations in nanoscience and nanobiotechnology [1]. The ever-increasing number of donor–acceptor pairs (cf. Chapter 14) is another evidencefor the contemporary relevance of FRET.This chapter will cover the main aspects of what FRET is, what FRETcan be used

for (and for what it should better not be used), how a FRET experiment should bedesigned and performed, what mathematics is absolutely necessary, and how theexperimental results can be processed and interpreted. It must also be mentionedthat there is no one recipe for all FRET experiments. The main part of this chaptershould rather be understood as a guide to FRET, providing useful information that

FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.Edited by Igor Medintz and Niko Hildebrandt.� 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.

j105

must be considered for every FRET experiment in order to receive the correctanswers from the investigated systems. Combination with the theory described inChapters 3 and 4 and the specific tools and applications presented at the end of thischapter as well as the following application chapters will further enlarge the scope ofpossibilities of the powerful FRET technology. Moreover, there are several excellentmonographs and review articles available [2–20] that are related to FRETapplicationfor more specific problems that are not covered within this chapter and/or book.

5.2FRET: Let’s get started!

Before treating the concept, some inevitablemathematics, and the experimental workrelated to FRET, I would like to introduce some first ideas about what FRET can beuseful for and what kind of prethoughts should be taken into consideration. If thesefirst questions are clarified, one can continue with understanding FRET in order toperform and interpret a successful experiment. Most of the aspects mentioned in thefollowing paragraph might seem evident and even more than obvious for the FRETexpert. However, often such first simple thoughts can avoid later trouble, when theproject and/or experiment have already been planned or maybe even carried out.FRET is a strongly distance-dependent transfer of energy between two molecules.

This energy transfer will take place only at a distance range of approximately1–20 nm, and if the system to be studied (the object of interest) does not providesuch distances, FRET is not a good solution for its investigation. If the distance rangeis possibly met by the system, two molecules are required between which FRETcantake place – the so-called FRET pair. The energy donor (D) must be a luminophore[luminescent molecule or particle – it should be noted that fluorescence (singlet–singlet optical transition) is a subterm of luminescence, which is the general termfor the emission of light originating from the electronic transition between twodifferent energy states [15,17,18]]. The energy acceptor (A) must be able to absorblight in the same spectral range as the emission of D. The absorption and emissionspectra of the FRET pair should be chosen (e.g., from Chapter 14) in a suitablewavelength range, which fits to the available instrumentation (excitation source anddetection setup) and does not interfere with the object of interest (e.g., excitation oremission of some components within the investigated system). Moreover, it shouldbe taken care that the optical properties of the FRET pair are preserved within theenvironment of the object of interest (e.g., for experiments that need to beperformed in aqueous solution, D and A should be avoided that are only solublein organic solvents). Once a good FRETpair has been identified, it should be ensuredthat D and A can be attached to the object of interest (e.g., bioconjugation to aprotein) and that the properties of the object as well as of D and A are only minimallyinfluenced by this conjugation. Another aspect to be taken into consideration is ifthe object of interest will be studied on the single-molecule level or in an ensembleof many objects. A single FRET pair gives only yes or no answers (FRET wassuccessful or not) and many of these FRET pairs (or many excitations of the sameFRETpair) need to be analyzed in order to calculate FRETefficiencies. The ensemble

106j 5 How to Apply FRET: From Experimental Design to Data Analysis

measurement results in averaged luminescence intensities or lifetimes, whichmustbe analyzed to reveal FRET efficiencies. One should also keep in mind that (due tothe additional FRETenergy path) the overall luminescence quantum yield of a FRETpair (nomatter if the luminescence of D or A is measured) is in themost cases lowerthan the luminescence quantum yields of D or A alone. Therefore, the use of FRETonly makes sense in cases where it can provide specific information on two siteswithin the object of interest due to D–A proximity (ligand–receptor or antibody–antigen binding, distances of two specific positions within a biological molecule,colocalization of two molecules, ratiometric D–A sensor, reduced photobleaching ofA by excitation via D, etc.). If only one event needs to be monitored (e.g., the bindingof a specific antibody to the cell membrane), pure luminescence measurements(using excitation and emission without FRET) are usually the preferred method ofchoice and the additional step of FRET can be avoided. Scheme 5.1 illustrates themain aspects that should be taken into consideration before thinking about anapplication of FRET.

Scheme 5.1 Flowchart for prethoughts concerning the application of FRET.

5.3FRET: The Basic Concept

FRET is an energy transfer process between a luminescent donormolecule or particle(the donorD) and a light-absorbing acceptormolecule or particle (the acceptor A). Theluminescence energy (in spectroscopy and imaging usually expressed in wavelength,but wavenumber can also be found) of D must be equal to the absorption energy(wavelength)ofA,which isreferredtoas resonance condition (FRET¼ F€orsterResonanceEnergyTransfer).TheenergyistransferrednonradiativelyfromDtoAwithanefficiencythat isdependentonthedistance rbetweenDandA(gFRET�r�6).Theoriginsof this r�6

5.3 FRET: The Basic Concept j107

distance dependence were discovered long before F€orster’s contributions to FRETand a very nice historic overview by Robert Clegg describes the early findings ofenergy transfer between two molecules separated by distances beyond orbitaloverlap [21]. FRET is based on the approximation that dipole–dipole coupling canbe represented by Coulombic coupling (coupling of two charges) VCoul. In fact,VCoul should be dominant at the usually considered FRET distance range ofapproximately 1–20 nm, where orbital overlap-related mechanisms (for very shortdistances) and radiative mechanisms (for long distances) play minor roles. TheFRET rate can be represented by Fermi’s golden rule:

kFRET ¼ 2p�hjV j2r; ð5:1Þ

where �h is the reduced Planck constant, V is the electronic coupling between D andA, and r is the density of the interacting initial and final energetic states, which isrelated to the spectral overlap integral J, describing the overlap of D emission and Aabsorption (see below). In Equation 5.1, V can be replaced by the r�3 distancedependent VCoul:

VCoul ¼kj~mD k~mAj4pe0n2r3

; ð5:2Þ

where~mD and~mA are the transition dipole moments of D and A, k is the orientationfactor between them (cf. Equation 5.9), e0 is the vacuum permittivity, n is therefractive index, and r is the distance between D and A.By substituting Equation 5.2 into Equation 5.1, one arrives at the r�6 distance

dependence of the FRET rate:

kFRET ¼ 9ðln 10Þk2WD

128p5NAn4tDr6J; ð5:3Þ

where WD is the luminescence quantum yield of D, NA is Avogadro’s number, andtD is the luminescence lifetime of D (in the absence of FRET).Figure 5.1 shows the basic principle of FRET, including the Coulombic mecha-

nism, where an electronic transition from a higher to a lower energy level in D leadsto an electronic transition from a lower to a higher energy level in A (withoutelectron exchange!) if these transitions are in energetic resonance.At a distance r, where the FRET rate and all other decay rates are in equilibrium

ðkFRET ¼ kRD þ kNRD ¼ t�1D Þ, the FRETefficiency gFRET is 50%. This distance is the so-

called F€orster distance (or F€orster radius) R0, which can be calculated by replacingkFRET with t�1

D and r with R0 in Equation 5.3:

R0 ¼ 9ðln 10Þk2WD

128p5NAn4J

� �1=6

: ð5:4Þ

J is the spectral overlap integral [defined in the wavelength (l) or wavenumber (~n) scale]:

J ¼ð�IDðlÞeAðlÞl4dl ¼

ð�IDð~nÞeAð~nÞd ~n

~n4; ð5:5Þ


which is dependent on the acceptor molar absorptivity (or extinction coefficient)spectrum eA and the donor emission spectrum�ID normalized tounity (cf. Figure 5.2):ð

�IDðlÞdl ¼ð�IDð~nÞd~n ¼ 1: ð5:6Þ

Combination of Equations 5.3 and 5.4 leads to the relation between the FRETrate, the luminescence decay time of the donor, and the distances (r�6 distance

Figure 5.1 Basic FRET principle. (a) Simplifiedenergy level scheme (Jablonski diagram)representing the excitation of the donor (hn)from an electronic ground state (D) to anexcited state (D�), followed by inner relaxation(vibrational and rotational – dotted arrow) to anexcited electronic ground state, followed byradiative decay (kR), nonradiative decay (kNR),or FRET (kFRET). In order to realize the FRETprocess from D� to A�, the difference between

the respective energy levels need to be equal(resonance condition: E(D�)� E(D)¼ E(A�)� E(A)), as emphasized by the coupled transitions(horizontal lines with dots on each end). AfterFRET, the acceptor is in an excited state (A�),followed by radiative or nonradiative decay to itsground state (A). (b) Different energy pathwaysafter donor excitation (hnex) possibly leading toluminescence emission of D (hnD) or A (hnA)for FRET analysis.

Figure 5.2 The overlap (gray area) of the area-normalized emission spectrum of D (cf.Equation 5.6) and the extinction coefficient (ormolar absorptivity) spectrum of A (eA) definesthe overlap integral J (cf. Equation 5.5), which is

directly proportional to the FRET rate (cf.Equation 5.3). In this graph, a wavelength scalewas chosen (wavenumber is also possible – cf.Equations 5.5 and 5.6).


dependence of the FRET rate):

kFRET ¼ t�1D

R0

r

� �6: ð5:7Þ

The FRET efficiency is then

gFRET ¼ kFRETkFRET þ t�1

D¼ 1

1þ ðr=R0Þ6: ð5:8aÞ

As shown in Figure 5.3, the sensitivity of the FRETefficiency to the D–A distanceis most prominent in a region between about 0.5R0 and 2.0R0, with the efficiencycurve being very steep around R0 (high dynamic range).The last important variable for the basic FRET concept is the so-called

orientation factor kappa-squared (k2 in Equations 5.3 and 5.4 or k in Equa-tion 5.2), which is often forgotten to be taken into account seriously and is alsooften considered too much in detail even though a relatively easy averagingmight be applicable. In this regard, it is very important if the FRETexperiment isperformed on a single-molecule level (where only averaging over time will makesense) or the ensemble (where averaging over time and/or over the molecularensemble might be reasonable). In any case, one should seriously think aboutkappa-squared for any FRET application and then choose the most appropriateoption of treating the dipole–dipole orientation. Figure 5.4 describes the orien-tation of the donor and acceptor dipoles within the basic concept of FRET. Takingthe different angles between the transition dipole moments of D and A (~mD and~mA) and the connection vector between D and A (~r ) allows the calculation of theorientation factor:

k ¼ m̂D � m̂A � 3ðm̂D � r̂Þðm̂A � r̂Þ ¼ cos qDA � 3cos qD � cos qA; ð5:9Þ

r

η FR

ET

1.0

0.8

0.6

0.4

0.2

0.00.5R0 1.5R0 2.5R02R0R0

Figure 5.3 FRET efficiency (gFRET) as a function of D–A distance (r). The r�6 distancedependence (cf. Equation 5.8a) leads to a strong sensitivity of gFRET to r in the distance region ofabout 0.5R0–2.0R0 (gray background area).


where m̂D, m̂A, and r̂ represent the unit vectors of~mD,~mA, and~r , respectively, and theangles qDA, qD, and qA are shown in Figure 5.4.There are some reasonable averaging conditions, which can provide a good

approximation for k2 to be used for many practical FRET applications. When allD’s and A’s can take any possible orientation during the FRET time (1/kFRET),which means that the average rotation rate is much larger than the average FRETrate ðkrot � kFRETÞ, the system is in a dynamic averaging regime and k2 becomes2/3. This fast isotropic rotation of D and A is often fulfilled if they are bound topolypeptides or proteins [20]. If D and A are both luminescent, fast isotropicrotation can be verified by checking if their emissions are unpolarized. If one ofthe FRETpartners shows average orientation (isotropically degenerate: “sphere”)and the other has a fixed orientation (well-defined linear dipole: “line”), then k2

(from “sphere” to “line” or from “line” to “sphere”) can take values between 1/3and 4/3 (for which 2/3 is still not such a bad approximation). In case of FRETfrom “line” to “line” (two well-defined linear dipoles), it becomes much morecomplicated because the full orientation factor range (0 < k2 <4) needs to beconsidered (and 2/3 might be a very bad approximation). In the case where alldonors and acceptors are fixed (no rotational motion), each FRETpair is assumedto be isolated from all other pairs, and the electronic transitions of D and A aresingle dipoles, one can use a static regime approximation [11] for which k2 isdependent on the D–A distance r and the D–A distance r0, for which k2 would be2/3. In this case, k2 can take values between 0 (for r� 0.4r0) and 2/3 (forr� 1.4r0).As already mentioned, it is important to take into account the orientation of the D

and A transition dipole moments for every FRET experiment in order to justify anapproximation or the assumption of a special orientation. If the experiments allow amodification of the D–A distance (so that FRET can be measured at multipledifferent distances), one can try to evaluate the FRETefficiency results using F€orsterdistances (R0) calculated with different k2 values in order to get a better idea aboutwhich orientational approximation or assumption might lead to reasonable results.In any case, an estimated or exact k2 can be calculated and a detailed treatment of theorientation factor, including the presentation of how to access k2 values, can befound in Chapter 4.

Figure 5.4 Orientation of the donor emission transition dipole moment ~mD, the acceptorabsorption transition dipole moment ~mA, and the D–A connection vector~r for the calculation ofthe FRET dipole orientation factor k (Equation 5.9).


5.4FRET: Inevitable Mathematics

Understanding the basic concept of FRETand the r�6 distance dependence requiresthe equations from Section 5.3. For a profound knowledge of FRET theory and anexact theoretical calculation of different FRETparameters, Chapters 3 and 4 as wellas the available literature should be consulted [3,4,10,11,15,17–20,22–27]. As alreadymentioned in Section 5.1, many different research disciplines make use of FRETand especially in applied research, it is sometimes tried to avoid mathematics ifpossible. However, even the FRET experimentalist will need some mathematics forthe choice of the adequate D–Apair and for the interpretation of the results. In mostcases, only very few (and relatively) uncomplicated equations are necessary in orderto achieve very satisfactory experimental results. The most important FRET param-eters are the F€orster distance R0 and the FRET efficiency gFRET because theycombine spectroscopic data (e.g., luminescence quantum yields, intensities, andlifetimes or emission and absorption spectra) with distances and orientations.

5.4.1F€orster Distance (or F€orster Radius)

Equation 5.4 is a general equation that needs a careful choice of units for achievingthe correct value and unit for the resulting distances and/or FRET rates. For theexperimental case, one can predefine commonly used units within the overlapintegral J and merge all constants found in Equations 5.4 into one value:

9ðln 10Þ128p5NA

¼ 8:79 10�28 mol; ð5:10Þ

where Avogadro’s constant NA¼ 6.02 214 1023mol�1. Different examples offacilitating Equation 5.4 with preassuming different units can be found in Chapter 3.Probably the most common length unit used at the small distance scale of FRET isnanometer and, therefore, it makes sense to express r and R0 in nanometers. Quite

often the unit Angstr€om is also used for FRET (1A

¼ 0.1 nm). Moreover, simplifica-tion of Equation 5.4 can be achieved by using commonly used units for opticalspectroscopy in the overlap integral (Equation 5.5): the wavelength l in nanometerunits and the molar absorptivity (or extinction coefficient) eA in M�1 cm�1 (liter permol per centimeter). These predefinitions lead to the following F€orster distance (forwhich k2, WD, n

�4, and J are dimensionless):

R0 ¼ ð8:79 10�28 k2WDn�4JmolM�1 cm�1 nm4Þ1=6: ð5:11Þ

Taking into account that M�1 cm�1 nm4¼ 1017 nm6mol�1, this leads to

R0 ¼ 0:02108ðk2WDn�4JÞ1=6 nm; ð5:12Þ

which is the F€orster distance in nanometers. It is very important that Equations 5.11and 5.12 are valid only if the value for J is calculated inM�1 cm�1 nm4.Using differentunits will lead to a different prefactor on the right-hand side of Equation 5.12.


5.4.2FRET Efficiency

The FRET efficiency relates the F€orster distance (R0, which can be calculated byabsorption and emission spectroscopy of D and A as demonstrated above) and theD–A distance (r, which might be known from the system to be measured or whichmight be the unknown variable of interest) with spectroscopic data of D and A assingle entities and as a D–A FRETpair. The FRETefficiency gFRETcan be determinedby several different methods, which are explained in the following.

5.4.2.1 Determination by Donor QuenchingOne possibility of calculating the FRET efficiency is to use spectroscopic data(luminescence quantum yield W, lifetime t, and intensity I) of D in the absence(subscript D) or presence of A (subscript DA). Using Equation 5.8b,

gFRET ¼ kFRETkFRET þ t�1

D¼ kFRET

kFRET þ kRD þ kNRD¼ kFRETtDA ð5:8bÞ

and taking into account that WD ¼ tDkRD ¼ kRD=ðkRD þ kNRD Þ and WDA ¼ tDAk

RD ¼

kRD=ðkFRET þ kRD þ kNRD Þ, this leads to the following equation:

gFRET ¼ 1

1þ ðr=R0Þ6¼ R6

0

R60 þ r6

¼ 1�WDA

WD¼ 1� tDA

tD¼ 1� IDA

ID: ð5:13Þ

The last part of Equation 5.13 (using emission intensities) is valid only if theexcitation light intensity absorbed by D and all the measurement parameters areidentical for both measurements (D in the absence and in the presence of A). If theexperimental conditions for “D” and “DA” FRETmeasurements are similar, this isusually a good approximation leading to adequate results. FRETcauses quenching ofthe donor luminescence quantum yield, lifetime, and intensity and thus WDA, tDA,and IDA are smaller thanWD, tD, and ID, leading to efficiency values between 1 and 0.This technique requires the determination of WD, tD, or ID before the FRETmeasurement and gFRET is then calculated from data generated by the two differentexperiments. Once R0 has been calculated (Equation 5.12), the spectroscopic datacan be used for calculating the D–A distance r by converting Equation 5.13 to

r ¼ R0WDA

WD �WDA

� �1=6

¼ R0tDA

tD � tDA

� �1=6

¼ R0IDA

ID � IDA

� �1=6

: ð5:14Þ

5.4.2.2 Determination by Acceptor SensitizationDonor quenching is not an evidence of FRET, as this donor deactivation can also becaused by other quenching mechanisms. The only sure evidence of energy transferfrom D to A is to measure the luminescence of A after excitation of D. Obviously, aluminescent acceptor is necessary for this, so this technique cannot be performedwith dark quenchers as FRETacceptors. The FRETefficiency can then be calculatedby the ratio of acceptor luminescence intensity in the presence (IAD) and in the

5.4 FRET: Inevitable Mathematics j113

absence (IA) of D. For the calculation of gFRET by sensitized acceptor luminescence,one needs to take into account that there is (in almost all cases) direct excitation of Aat the excitation wavelength used for exciting D. Although this direct excitationmight be weak, it needs to be corrected for in order to achieve appropriate results forgFRET. This correction can be done by subtracting the direct luminescence IA fromIAD and multiplying the corrected luminescence ratio by the ratio of the absorptivi-ties (or extinction coefficients) of A and D (eA and eD) at the excitation wavelengthused for the FRET experiment. The FRET efficiency is then

gFRET ¼ 1

1þ ðr=R0Þ6¼ R6

0

R60 þ r6

¼ IAD � IAIA

� �eAeD

� �¼ IAD

IA� 1

� �eAeD

� �:

ð5:15ÞThis technique requires the knowledge of eA and eD and the measurement of IAbefore the FRET experiment. gFRET is then calculated from data generated by thetwo different measurements. Once R0 has been calculated (Equation 5.12), thespectroscopic data can be used for calculating the D–A distance r by convertingEquation 5.15 to

r ¼ R0IAeD

ðIAD � IAÞeA � 1

� �1=6

: ð5:16Þ

Cases of incomplete D–A labeling (free A inside the FRET sample) and the useof two different excitation wavelengths (for cases of weak FRET where the ratioIAD/IA is close to unity, which can cause significant errors in calculating gFRET)using this technique with further necessary corrections have been applied byClegg et al. [28–30].

5.4.2.3 Determination by Donor Quenching and Acceptor SensitizationIn order to calculate gFRET from a single measurement, the quenched donorluminescence intensity (D in the presence of A) and the sensitized acceptorluminescence intensity (A in the presence of D) can be analyzed. This techniquecan offer the advantage of high precision in calculating the FRETefficiency becausedata from simultaneously measured luminescence spectra are used. However, theacceptor luminescence caused by direct excitation of A still needs to be corrected forand thus it needs to be measured by a preexperiment. Moreover, the luminescencequantum yields of D and A need to be known. For the calculation of gFRET, theexcitations (intensity divided by quantum yield: I/W) of D and A are taken intoaccount. In this case, the FRET efficiency can be defined as the number of donorexcitations leading to acceptor excitations (FRET) divided by all donor excitations(leading to FRET and all other radiative and nonradiative deactivation pathways):

gFRET ¼ 1

1þ ðr=R0Þ6¼ R6

0

R60 þ r6

¼ ðIAD � IAÞ=WA

ðIAD � IAÞ=WA þ IDA=WD

¼ ðIAD � IAÞðIAD � IAÞ þ ðWA=WDÞIDA ¼ 1þWA

WD

IDAIAD � IA

� ��1

: ð5:17aÞ


In this equation, IAD is the luminescence intensity of A during FRET (in thepresence of D), which needs to be corrected for acceptor luminescence due to directexcitation (IA). IDA is the luminescence intensity of D during FRET (in the presenceof A) andWA andWD are the luminescence quantum yields of A and D, respectively.Once R0 has been calculated (Equation 5.12), the spectroscopic data can be used forcalculating the D–A distance r by converting Equation 5.17a to

r ¼ R0WAIDA

WDðIAD � IAÞ� �1=6

: ð5:18Þ

5.4.2.4 Determination by Donor PhotobleachingApart from measuring the luminescence quenching of donor and/or acceptor,another possibility to determine the FRET efficiency is photobleaching, which isespecially useful in imaging setups, where the necessary light sources, providingenough power for photobleaching, are often readily available. Using the photo-bleaching time constant tbl of D in the absence (subscript D) or in the presence of A(subscript DA), gFRET can be calculated [16,31]:

gFRET ¼ 1

1þ ðr=R0Þ6¼ R6

0

R60 þ r6

¼ 1� tblDtblDA

: ð5:19Þ

In contrast to the luminescence properties W, t and I in Equation 5.13, the

photobleaching time constant of D in the absence of A (tblD, no FRET) is foundin the numerator, whereas the photobleaching time constant of D in the presence of

A (tblDA, FRET) is found in the denominator on the right-hand side of Equation 5.19.

In this case, tblD is smaller than tblDA because FRET opens a new energy pathway forthe excited donor to return to the ground state and, therefore, the photobleachingtime constant of the donor is increased in the presence of the acceptor [16]. Similar

to the D or A quenching approaches, this technique requires the determination of tblDbefore the FRETmeasurement and gFRET is then calculated from data generated bythe two different experiments (no FRET and FRET). Once R0 has been calculated(Equation 5.12), the D–A distance r can be calculated by converting Equation 5.19 to

r ¼ R0tblD

tblDA � tblD

� �1=6

: ð5:20Þ

5.4.2.5 Determination by Acceptor PhotobleachingIn order to be able to determine gFRET from a single sample, one can use acceptorphotobleaching. In this approach, the initially FRET-quencheddonor luminescence (D inthe presence ofA) is recovered by photobleaching the acceptor (destroying theFRETpathtoA). TheFRETefficiency can thenbe calculated using the luminescence intensities ofDbefore (superscript pre) and after (superscript post) the photobleaching of A:

gFRET ¼ 1

1þ ðr=R0Þ6¼ R6

0

R60 þ r6

¼ 1� IpreDA

IpostDA

: ð5:21Þ


Note that donor and acceptor are still physically connected after photobleaching,but the acceptor (and the FRET path) is irreversibly “switched off.” The mainadvantage of this technique is the avoidance of measuring two different samples(such as pure D and photobleached D in the previous paragraph). This can beespecially problematic for cellular imaging, for example, due to different proteinexpression levels from cell to cell, which will cause variable donor concentrations inthe different cells. Once R0 has been calculated (Equation 5.12), the photobleachingdata can be used for calculating the D–A distance r by converting Equation 5.21 to

r ¼ R0IpreDA

IpostDA � IpreDA

!1=6

: ð5:22Þ

5.4.3FRET with Multiple Donors and/or Acceptors

Inmany FRETexperiments, the interaction betweenmultiple donors and acceptors ispossible. For example, this can be the case for random labeling of proteins, cellsurfaces, or nanoparticles, where the amount of D and A that can possibly interact ismainly defined by the density of D and A within the labeled systems. There can bedifferent or equal distances between the D’s and A’s, there can be very few D’sinteracting with A’s and vice versa, there can be D’s and A’s that do not interact at all,and there can beone-, two-, and three-dimensional distributions that canbe randomorcontain excluded spaces (so that random distribution cannot be assumed anymore).Raicu has proposed a theoretical model for multiple donor–acceptor interactions,which becomesmore complicated ifmore possibilities are included in themodel [32].Using an approximation of equal distances between all D’s and A’s and assuming thatall FRETrates are equal for anyD–AFRETpair, Raicuderived anequation for theFRET

efficiency (gmultiFRET), which is purely dependent on the number of acceptors nA (and not

on the number of donors) and the efficiency of a single D–A pair (gFRET):

gmultiFRET ¼ nAgFRET

1þ ðnA � 1ÞgFRET: ð5:23Þ

The same result was found by Clapp et al. in an experimental study for single D tomultiple A FRET, where several organic dye acceptors were placed around one quasi-spherical semiconductor quantum dot donor in order to achieve approximatelyequal distances [33]. The authors derived (and confirmed experimentally) thefollowing equation:

gmultiFRET ¼ nAkFRET

nAkFRET þ t�1D

¼ nAR60

nAR60 þ r6

; ð5:24Þ

which is equal to Equation 5.23. An increasing FRET efficiency with an increasingnumber of A’s per D can be explained by the fact that there are simply more (nAinstead of 1 for a single pair) possible de-excitation pathways available for the exciteddonor and, therefore, the probability of de-exciting D via FRET becomes higher.


The independence of the FRET efficiency from the number of donors is not soobvious, as in the case of multiple donors with one acceptor, the multiple D’s need tocompete for FRET to the single A (unless there is always only oneD or Aexcited duringthe time of excitation, energy transfer, and de-excitation). This problem has been takeninto account by Berney and Danuser (with further developments by Corry et al. fordifferent geometrical distributions) [34,35]. As the integration of the many possibleparameters for multiple D–A systems inside an analytical model can become verycomplicated, numerical approaches are an excellent alternative. The authors developedaMonteCarlo simulation (MCS) for an experimental setup inwhich they could controldonor and acceptor concentrations (and thereby the D to A ratio RDA) as well as theaverage distance between D and A using a PLL-g-PEG-biotin-coated microscopecoverslip surface and controlled amounts of streptavidin labeled with D or A. TheMCS resultswere used as a reference to compare differentmethods from the literatureto use the experimental data for FRET efficiency determination. The beauty of thenumerical approach is the stepwise calculationof theFRETefficiencyphotonbyphoton(or exciton by exciton). In the following, the MCS scheme is briefly outlined [34,35]:

Step 1: The coordinates and types of D’s and A’s are assigned, accounting for aregular arrangement and for excluded volume effects.

Step 2: The transfer probability from each donor Di to every acceptor Aj is calculated by

Pij ¼ R60=r

6ij; ð5:25Þ

where R0 is the F€orster distance and rij is the distance between the Di–Aj FRETpairs.

Step 3: The exciton flux (dependent on the photon flux and the extinction coefficientand concentration of the donors) is calculated by

f e ¼ pa2Ilh�1c�1 1� 10�½ðeDnDÞ=ð1000NApa2Þ��

; ð5:26Þ

where a is the radius of the simulated system, I is the irradiance of the excitationlight source with wavelength l, h is the Planck’s constant (6.626 10�34 Js), c isthe speed of light (3 108ms�1), eD is the molar extinction coefficient of thedonor at wavelength l, nD is the number of donor molecules, and NA is theAvogadro’s constant (6.022 1023mol�1).

Step 4: A time sequence giving the play time of each exciton within the time intervalof excitons being incident on the fluorophores is defined; for each exciton, a targetdonor is randomly assigned and the experimental clock is set to zero.

Step 5: The excitons are played (sequentially) to see if they are absorbed by the donorand, if yes, whether it is de-excited by FRET or fluorescence. First it is checked ifthe donor is already “busy” (already excited) and if yes the exciton is lost and thenext one will be played. If the donor is not “busy”, it gets excited, is then set to“busy” and a list of free acceptors (which are not already excited) around the donoris generated. The overall rate of energy release is calculated by

t�1T ¼ t�1

D 1þXafreej¼1

Pij

!; ð5:27Þ


where tD is the luminescence lifetime of D in the absence of A (unquenched). Thetime for the donor to release its energy in the simulation is calculated by

TD ¼ �tTln ðcDÞ; ð5:28Þwhere cD is a uniformly distributed random generator delivering a value between0 and 1. TD defines the time point of energy release of the excited D (the time pointat which the donor is set from “busy” back to “free”).Next it needs to be decided (using probabilities) whether Di will release its

energy as FRET or fluorescence. This is determined by creating a cumulativehistogram with the classes of all possible pathways, where the probability of theclasses FRET to Aj is (tT/tD)Pij and the probability of the class fluorescence istT/tD. Another uniform random number between 0 and 1 is picked to decide forthe de-excitation class. If the selection falls in the class of fluorescence, thevariable Fluo is incremented by 1 and the next exciton is played. If Di was selectedfor FRET to Aj, this acceptor is set to “busy” and the variable FRET is incrementedby 1. The time interval of a “busy” Aj (TA) is determined by a MCS step similar toEquation 5.28, where TA¼�tA ln (cA) with tA denoting the luminescencelifetime of A and cA is another random number between 0 and 1. The completestep 5 is repeated for all excitons.

Step 6: Finally, the simulated FRET efficiency can be calculated by comparing thenumber of donors undergoing FRET and fluorescence, respectively:

gFRET ¼ FRETFRET þ Fluo

: ð5:29Þ

5.5FRET: The Experiment

This section will cover the most important aspects of how to design, perform, andanalyze a general FRET experiment using steady-state and time-resolved opticalspectroscopy and microscopy and applying the equations from the previous section.

5.5.1The Donor–Acceptor FRET Pair

A well-designed FRET experiment can provide a lot of useful qualitative andquantitative information. As already mentioned in Section 5.2, every FRET experi-ment starts with considering how the system of interest can be most efficientlyanalyzed by FRET, which is closely related to the choice of a suitable donor–acceptorFRETpair. One of the first considerations should concern the physical parameter tobe determined, which could be the following:

1) Quantitative distance: FRET as a spectroscopic (or molecular) ruler to determinethe distance between two molecules in a range of about 1–20 nm.


2) Qualitative distance: FRET to prove a proximity (colocalization) between twomolecules or FRETas an optical switch between twomolecules in about 1–20 nmdistance.

3) Quantitative concentration: FRET to determine the amount of two (or more)bound molecules in about 1–20 nm distance.

4) Qualitative (or semiquantitative) concentration: FRET to prove the existence of two(or more) bound molecules in about 1–20 nm distance.

In all cases, a convenient FRET pair should be chosen, which combines brightluminescence of D and/or A for an efficient detection or signal generation with asufficiently large R0 for the distance between the two molecules. It is not alwaysadvisable to choose the highest possible F€orster distance. For example, if R0¼ 6 nmand the D–A distance is r¼ 2 nm, the FRET efficiency will be very close to 100%(WDA¼ IDA¼ tDA¼ 0) leading to a pure on–off luminescence signal, which couldcause problems in evaluating and/or quantifying the physical phenomenon behind(disruption of D–A binding and disappearance of D, photobleaching of D, FRETdueto very close proximity, and other quenchingmechanisms independent of FRET). Inmost cases, the FRETpair should be chosen such that the distance (or distances) ofinterest is in the 0.5R0–2.0R0 distance range (cf. Figure 5.3) because this is the mostsensitive distance range for FRET.Another important aspect is the techniquewithwhich FRETwill be analyzed (donor

quenching and/or acceptor sensitization, donor or acceptor photobleaching) (cf.Section 5.4) as well as the available equipment because this defines the photophysicalproperties (absorption and emission wavelength range, quantum yield, lifetime, etc.)of D and A.Many fluorophores are available for FRET, such as organic dyes (and darkquenchers), polymeric and dendrimeric dyes, naturally occurring fluorophores,lanthanide, and metal-based complexes, as well as nano- and microparticles. For adetailed overview of the different fluorophores, the reader is referred to Chapter 6 andto Ref. [1], in which the important topic of bioconjugation (how to attach D and A tothe system of interest) is also outlined. The most comprehensive Chapter 14concerning FRET data contains much information about F€orster distances, photo-physical properties, availability, and applications ofmanyD–AFRETpairs. It is alwaysrecommended to choose at least three fluorophores, that is, one preferred D–A FRETpair with at least one alternative D and/or A for control experiments or backupsolution in case the original FRET pair does not perform sufficiently well.

5.5.2F€orster Distance Determination

After having made the initial choice of a D–A FRETpair, the F€orster distance shouldbe determined (or verified in case an R0 value could already be found in theliterature). Assuming that sufficient donor and acceptor material is available(especially absorption measurements require higher concentrations than fluores-cence detection) and that the orientation factor can be sufficiently well estimated orcalculated, the determination of R0 is usually not a very challenging task, which

5.5 FRET: The Experiment j119

requires standard steady-state spectroscopy equipment such as absorption andfluorescence spectrometers. Both spectra (donor emission and acceptor absorption)should be measured as precisely as possible, but in a reasonable manner. Somesuggestions of acquiring such spectra are outlined below. More details can be found,for example, in Refs [15,18].

a) Molar absorptivity (or extinction coefficient) spectrum of the acceptor: As manyabsorption spectrometers (especially plate readers) provide lower spectral reso-lution (often limited to minimum 1nm) than fluorescence spectrometers(usually well below 1 nm), it is recommended to start with measuring theabsorption spectrum of A (usually the absorbance A or optical density OD ismeasured for a light path length of 1 cm). For the calculation of R0 in aspreadsheet program, it is quite convenient to use the same wavelength stepsfor emission and absorption spectra. One can save time erasing out data pointson the computer by already recording the spectra with matching wavelengths. Itdoes not make much sense to measure the emission spectrum of D (ID(l)) with a10-fold higher spectral resolution than the absorption spectrum of A becauseboth spectra are multiplied in the overlap integral (Equation 5.5). However, caremust be taken when spectra with very narrow peaks (e.g., lanthanide emissionspectra) are used, for which the spectral resolution should be high enough not toomit emission (or absorption) peaks by not measuring them because of too largewavelength steps or by erasing them in a spreadsheet when calculating theoverlap integral. Apart from the acceptor sample, the pure solvent (or buffer)should be measured and subtracted from the sample spectrum (backgroundcorrection). The OD (for 1 cm light path) of the sample should not be too lowbecause this can cause large errors after background correction. On the otherhand, too high ODs can cause saturation. In most cases, a maximum absorptionintensity between 0.1 and 3 OD should provide satisfactory results. Measuring anemission excitation spectrum (variation of the excitation wavelength whilerecording a fixed emission wavelength) of the same but highly diluted acceptorsample on a fluorescence spectrometer is a good option to qualitatively (shape ofthe spectrum) verify the absorbance spectrum. Once the background-correctedabsorbance spectrum A(l) has been determined, it can be calculated into themolar extinction coefficient spectrum e(l) using Lambert–Beer’s law:

AðlÞ ¼ eðlÞ � c � l ) eðlÞ ¼ AðlÞc � l ; ð5:30Þ

where c is the concentration of the sample and l is the light path length (e.g., 1 cmfor a standard cuvette).

b) Emission spectrum of the donor: Most emission spectra (unless they have verynarrow emission bands) can be measured quite precisely by recording anemission intensity every 0.5 or 1.0 nm (wavelength step). As already mentioned,it is recommended to use the same wavelength steps as for the absorption spectraif possible. Important aspects for recording emission spectra are to avoid highsample concentrations (which can cause inner filter effects), solvent and/orcuvette contaminations (which might contain other luminescent materials) and


light scattering (Raman peaks inside the emission spectrum), and to use anadequate quantum correction (detector sensitivity changes as a function ofwavelength) in order to obtain a correctly shaped emission spectrum. As thespectrum is area-normalized for the calculation of R0, total intensities are notimportant. However, the relative intensities must be correct.

As an example of calculating R0, I chose two imaginary D and A molecules withemission and absorption spectra showing the typical shape of organic dye spectrawith a pronounced maximum and a blueshifted (for absorption) or redshifted (foremission) “shoulder.” The spectra cover a wavelength range of about 400–600 nmand overlap in the 450–550 nm region (Figure 5.5).Once the spectra are recorded, the overlap integral and F€orster distance can be

easily calculated using a spreadsheet program (e.g., Excel or Origin), as shown inTable 5.1. The first column contains the wavelengths from 400–600 nm (in thepresented case, 0.5 nm steps are used) and the second one contains the determinedemission spectrum ID(l) (in arbitrary units – e.g., photon counts). The sum of allID(l) values is calculated (last cell of the second column) and used to calculate thethird column by dividing each ID(l) value with this sum in order to get the area-normalized emission spectrum �IDðlÞ (as a control, the sum of column 3 should beunity). The fourth column contains the extinction coefficient spectrum of A (eA(l) in

M�1 cm�1 units) and the fifth column is the product of l4 � �IDðlÞ � eAðlÞ. The sum ofthis column 5 is the overlap integral J, which can be used (together with thepredetermined values for k2,WD, and n) to calculate R0 (in nm) using Equation 5.12(as shown in the lower part of Table 5.1 with some arbitrarily chosen values for k2,WD, and n).

0.008ID(λ)

εA(λ)

0.006

0.004

0.002

0.000

wavelength (nm)

1.50x105

1.25x105

1.00x105

7.50x104

5.00x104

2.50x104

0.00

norm

aliz

ed e

mis

sion

inte

nsity

extin

ctio

n co

effi

cien

t (M

–1 c

m–1

)

400 450 500 550 600

M–1cm–1

Figure 5.5 Area-normalized (cf. Equation 5.6) donor emission spectrum (left – cf. column 3 inTable 5.1), acceptor molar extinction coefficient spectrum (right – cf. column 4 in Table 5.1), andresulting overlap function (shaded spectrum in the center – cf. column 5 in Table 5.1).


5.5.3The Main FRET Experiment

With the photophysical properties and the F€orster distance of the D–A FRETpair in thepocket, the real FRET experiment can begin. This section will focus on luminescencespectroscopy. FRET microscopy techniques have been recently treated in two

Table 5.1 Extract from a spreadsheet to calculate R0 from donor emission and acceptorabsorption spectra (cf. Figure 5.5) and predetermined values of k2,WD, and n.

l (nm) ID(l) (arb. units) I�D(l) eA(l) (M– 1 cm – 1) l4I�D(l) eA(l)

(nm4 M – 1 cm – 1)

400 0 0 109.4 0400.5 0 0 119.3 0401 0 0 130.1 0401.5 0 0 141.8 0402 0 0 154.4 0402.5 0 0 168.1 0403 0 0 182.8 0... ..

. ... ..

. ...

478.5 3.10Eþ 05 9.52E� 03 5.35Eþ 04 2.67Eþ 13479 3.12Eþ 05 9.56E� 03 5.36Eþ 04 2.70Eþ 13479.5 3.13Eþ 05 9.60E� 03 5.38Eþ 04 2.73Eþ 13480 3.14Eþ 05 9.62E� 03 5.40Eþ 04 2.76Eþ 13480.5 3.14Eþ 05 9.64E� 03 5.42Eþ 04 2.79Eþ 13481 3.14Eþ 05 9.64E� 03 5.45Eþ 04 2.81Eþ 13481.5 3.14Eþ 05 9.64E� 03 5.48Eþ 04 2.84Eþ 13... ..

. ... ..

. ...

513.5 1.20Eþ 05 3.67E� 03 1.54Eþ 05 3.93Eþ 13514 1.19Eþ 05 3.64E� 03 1.54Eþ 05 3.91Eþ 13514.5 1.18Eþ 05 3.61E� 03 1.54Eþ 05 3.90Eþ 13515 1.17Eþ 05 3.58E� 03 1.54Eþ 05 3.88Eþ 13515.5 1.16Eþ 05 3.55E� 03 1.54Eþ 05 3.85Eþ 13516 1.15Eþ 05 3.52E� 03 1.53Eþ 05 3.83Eþ 13516.5 1.14Eþ 05 3.50E� 03 1.53Eþ 05 3.80Eþ 13... ..

. ... ..

. ...

597.0 0 0 0 0597.5 0 0 0 0598.0 0 0 0 0598.5 0 0 0 0599.0 0 0 0 0599.5 0 0 0 0600.0 0 0 0 0Sum 3.3Eþ 07 1.0 1.6Eþ 07 4.6Eþ 15

J (nm4 M – 1 cm – 1) k2 WD n R0 (nm)

4.6Eþ 15 0.67 0.55 1.40 5.8


comprehensive books [4,16]. Photobleaching FRET is mainly used for imaging and hasbeen covered in Ref. [36], so it will not be treated again in this section.The main FRET experiment will always include luminescence, because the

emission changes of D or A or both must be measured in order to determineFRET efficiencies and/or distances. Luminescence quenching can occur due tomany different reasons and therefore it is always recommended tomeasure acceptorsensitization in combination with donor quenching. As the sensitization of A mustoccur from energy transfer (assuming that direct excitation of A has been taken intoaccount and properly subtracted), the acceptor detection channel can be coined asthe “FRET-proof channel.” The best solution is to compare D-quenching and A-sensitization and if the FRET efficiencies can be calculated as equal for bothpartners, the involved mechanism is most probably FRET (or another energy orcharge transfer process – cf. Section 5.6). Luminescence can be measured usingsteady-state and/or time-resolved techniques. The latter can be divided into time-domain and frequency-domain techniques. Details about the different experimentalapproaches (steady-state and time-resolved) can be found in Refs [15,18], and only ashort technical overview will be presented here. In order to draw the correctconclusions from the experimental data, it is important to combine as manyexperiments as possible (D-quenching, A-sensitization, steady-state and time-resolved measurements, and all the necessary control experiments). The aim shouldbe the same as it used to be for Theodor F€orster: to search for the most appropriatesolution of a scientific problem, or in his favorite term “The correct interpretation ofan observation” (Die richtige Deutung einer Beobachtung) (cf. Chapter 1).

5.5.3.1 Steady-State FRET MeasurementsSteady-state luminescence spectroscopy measures emission spectra, that is, theemission intensity of the luminophores as a function of wavelength (or wavenumber)over their complete time period of emission (no temporal resolution). This is usuallyachieved by exciting the luminophores at afixedwavelength,while scanning (e.g., withamonochromator) over thewavelength of their emission, which is then detected [e.g.,by using a photomultiplier tube (PMT)] in selected wavelength intervals. Measuringthe full emission spectra offers the advantage that both D and A can be measuredsimultaneously within the same sample. The values of ID, IDA, IA, and IAD can then beextracted from themeasured overall spectrumof the sample (containing bothD andAemissions) and usedwith Equations 5.13–5.18 for the calculation of FRETparametersand distances. A correct treatment of the overall spectrum requires a deconvolution ofthe two spectra followed by integration over each single spectrum in order to obtaincorrect values for ID, IDA, IA, and IAD (cf. Figure 5.6). Depending on how spectrallyclose the two emission spectra are, the spectral cross talk between themwill be weaker(for well-separated spectra) or stronger (for close spectra). In case of well-separatedemission spectra, it might be sufficient to simply take the peak intensity values of Dand A to obtain ID, IDA, IA, or IAD.Due to the almost endless choice of possible FRET pairs (which strongly depend

on the application), a generic example of steady-state FRETresults with an imaginaryFRETpair (the same as already chosen in Figure 5.5 for the calculation of the F€orster


distance R0) is presented in Figure 5.6. The principle of this theoretical example canbe transferred to any practical experiment using real FRET pairs. Many practicalexamples using different FRETpairs can be found in Chapters 6–14 and in the FRETliterature.Figure 5.6 presents the spectroscopic data obtained from the main FRET experi-

ment. Part (a) shows the emission (and absorption) spectra of pure D and pure A,which need to be measured before the FRET experiment, but under the sameexperimental conditions (i.e., concentration, solvent, excitation and emission con-ditions, etc.). Part (b) presents the luminescence spectra obtained from 11 different

(a)

(c) (d)

(b)

Figure 5.6 Absorption and emission spectraresulting from a representative steady-stateFRET experiment with luminescent D and A (cf.Figure 5.5 for calculation of R0). (a) Peak-normalized absorption (dotted) and emissionspectra of D in the absence of A (black) and A inthe absence of D (gray). (b) Emission spectra ofdifferent mixtures of D and A excited at 420 nm.FRET causes quenching of donor luminescenceand sensitization of acceptor luminescence.Therefore, the spectra are composed ofdifferent ratios of the emission spectra of D andA [from part (a)]. (c and d) Deconvolution of theD–A spectra leads to the emission spectra of D

in the presence of A [part (c)] and of A in thepresence of D [part (d)]. The black curves inboth graphs represent the emission spectra ofD and A in the absence of A and D, respectively(donor emission without FRET quenching andacceptor emission due to direct excitation at420 nm without FRET sensitization). Integratingover these emission spectra results in theintensity values ID and IA. The gray curvesrepresent the quenched donor and sensitizedacceptor emission, respectively. Integratingover these emission spectra results in theintensity values IDA and (IADþ IA) (cf.Equations 5.13–5.18).


FRETmeasurements (11 different samples or 1 sample with changing spectra overtime), for which donor quenching and concomitant acceptor sensitization becomequite obvious. In the case where no third luminescent components (e.g., sampleautofluorescence) are present within these spectra, they are composed of differentratios of the single emission spectra from part (a). Thus, they can be deconvoluted tosingle FRETspectra of D and A, as shown in parts (c) and (d). Integration over thesespectra results in the intensities ID, IDA, IA, and IAD, which are necessary to performthe FRET calculations using Equations 5.13–5.18.With the obtained intensity values, different interpretations concerning FRET

are possible. We will begin with the analysis of the donor spectra and evaluateafterward, which advantages the acceptor spectra provide for the interpretation ofthe FRET system.

1) One can analyze the results in Figure 5.6c using donor quenching (Section 5.4.2.1).As summarized in Table 5.2, the normalized donor emission intensity IDA/IDdecreases from 1 to 0 (in steps of 0.1), which can be caused by several reasons:a) Distance: Assuming that each D is connected with one A (complete labeling),

the FRET efficiencies gFRET of each spectrum can be calculated by Equa-tion 5.13 (Table 5.2, column 4). Using the precalculated R0 of 5.8 nm(Figure 5.5 and Table 5.1), the D–A distances r can be calculated by Equa-tion 5.14 (Table 5.2, column 5). This leads to the conclusion that all different

Table 5.2 Data resulting from different interpretations of D-quenching (Figure 5.6c) and A-sensitization(Figure 5.6d) using steady-state FRET measurements.

0 1 2 3 4a) 5b) 6c) 7d) 8e)

Experimental data Distance Concentration quenching Multiple A’s

Measurement IDA/ID IAD/IA (IAD – IA)/ID gFRET r (nm) KSV�[Q] [DA]/[D]0 or [DA]/[DA]max nA with r¼ 6.7 nm

1 1 1.00 0.000 0 >13.0 0.00 0 02 0.9 2.43 0.054 0.1 8.4 0.11 0.1 Not measured3 0.8 3.86 0.108 0.2 7.3 0.25 0.2 Not measured4 0.7 5.29 0.162 0.3 6.7 0.43 0.3 1.05 0.6 6.71 0.216 0.4 6.2 0.67 0.4 1.66 0.5 8.14 0.270 0.5 5.8 1.00 0.5 2.37 0.4 9.57 0.324 0.6 5.4 1.50 0.6 3.58 0.3 11.00 0.378 0.7 5.0 2.33 0.7 5.49 0.2 12.43 0.432 0.8 4.6 4.00 0.8 9.310 0.1 13.86 0.486 0.9 4.0 9.00 0.9 21.011 0 15.29 0.540 1 0.0 1 1 Not measured

The different results are visualized in Figure 5.7.a) gFRET calculated with Equation 5.13 for donor quenching, Equation 5.15 for acceptor sensitization using eA/

eD¼ 0.07, and Equation 5.17a for combined donor quenching and acceptor sensitization usingWA/WD¼ 0.54.b) r calculated with Equation 5.14 for donor quenching, Equation 5.16 for acceptor sensitization using eD/eA¼ 1/

0.07, and Equation 5.18 for combined donor quenching and acceptor sensitization using WA/WD¼ 0.54.c) Cannot be analyzed by acceptor sensitization.d) [DA]/[D]0¼ 1� (IDA/ID) for D-quenching and [DA]/[DA]max¼ (IAD/IA)� 1)/(IAD/IA)max� 1) for A-sensitiza-

tion analysis.e) nA calculated with Equation 5.24.


samples contain the same concentration of completely labeled single D–Apairs with different D–A distances (e.g., change of structural confirmationover time or due to changes in the environment, such as temperature or pH),which decrease from measurement 1 to 11, as depicted in Figure 5.7a.

b) Concentration quenching: The D-quenching could be caused by anydeactivation process (including FRET), which can be described by theStern–Volmer equation:

IDIDA

¼ 1þ KSV Q½ �; ð5:31Þ

where KSV is the Stern–Volmer constant, which is

KSV ¼ KS ¼ ½DQ�½D� � ½Q � ð5:32Þ

in the case of static quenching and

KSV ¼ KD ¼ kqtD ð5:33Þ

SV

r = 6.7 nm = constant

(a) (b)

(c) (d)

Figure 5.7 Different interpretations of one andthe same experiment resulting from the analysisof the donor-quenching emission spectra inFigure 5.6c taken from the calculated data fromTable 5.2. (a) Different FRET efficiencies due to

different D–A distances. (b) Static or dynamicquenching with increasing quencherconcentration. (c) Increasing amount of D–AFRET pairs at fixed D–A distance. (d) Increasingamount of A’s per D at fixed D–A distance.


in the case of dynamic quenching. In these equations, [Q ], [D], and [DQ ] arethe respective concentrations of the quencher, the donor, and the donor–quencher complex, kq is the dynamic (or bimolecular) quenching constant,and tD is the luminescence lifetime of D (in the absence of Q). Static ordynamic quenching will lead to a linear quenching behavior (which is not thecase for combined static and dynamic quenching) as found for the experi-ment from Figure 5.6 (and shown in Figure 5.7b and Table 5.2, column 6). Inthe case of FRETquenching, a possible scenario for which the Stern–Volmerequation can be applied would be a FRETassay, for which increasing amountsof an analyte (e.g., a biomarker) are titrated to a constant concentration of D-and A-labeled specific binding molecules (e.g., antibodies against the bio-marker). This case will cause static quenching (because the D–A distance r isfixed) due to addition of the analyte with concentration [Q ]. As D and A are inexcess, each addition of an analyte will lead to the formation of a D–A pairwith the concentration [DA]¼ [DQ ]¼ [Q ] (assuming 100% binding effi-ciency). With [D]¼ [D]0� [DA], where [D]0 is the initial concentration ofD, Equation 5.32 will become KSV¼KS¼ ([D]0� [DA])�1 and Equation 5.31will become [DA]/[D]0¼ 1� (IDA/ID), which is presented in Figure 5.7c andTable 5.2, column 7.

c) Multiple acceptors: In the case of experimental results without the spectra frommeasurements 2, 3, and 11, another possible interpretation from Figure 5.6cwould be an increasing amount of A’s per D (nA from Equation 5.24) with afixed distance r (Figure 5.7d and Table 5.2, column 8). In the case for which r isunknown, Equation 5.24 can be used with r as a free fit parameter (R0 andgFRET are known from the measurements of Figure 5.5 and 5.6c) in order todetermine the D–A distance.

d) Environmental quenching: Cases (b) and (c) assume stable environmental condi-tions. If this is not the case and the environment (e.g., temperature, solvent, andpH) changes during the experiment (over time or from sample to sample),luminescencequenching[includingFRETduetodistancechangesasmentionedin case (a)]might alsobe causedby these factors.Often such changes also lead todeviations in the luminescence and/or absorption spectra (bathochromic orredshift, hypsochromic or blueshift, or intensity changes of different lumines-cence bands from the same luminescent species). Thus, it is wise to also have acareful look at the spectral features of the different measurements.

2) In addition to donor quenching, one can analyze the results in Figure 5.6d usingacceptor sensitization (Section 5.4.2.2). Analyzing the acceptor spectra has theadvantage that they can provide compelling evidence for FRET (or at least energytransfer) because they show that A was excited via D, whereas donor quenchingcould have other reasons than deactivation via the acceptor. As summarized inTable 5.2, IAD/IA increases from 1 to 15.29, which can be explained by the samereasons as for donor quenching and leads to the same results using differentequations for their calculation (cf. footnotes in Table 5.2). However, one shouldkeep in mind that the present example is an idealized theoretical FRET experi-ment and for most “real-world” experiments, a verification of the donor


quenching results by acceptor sensitization is necessary to draw reliable conclu-sions about FRET. In the case where D-quenching and A-sensitization providesimilar results using the FRET equations, other quenching effects can beexcluded. This is highly important for justifying results that are based onFRET, for example, if distances are reported or analyte concentrations arecalculated by assuming that all donor quenching is caused by FRET. In ourexample, the distances calculated for donor quenching can be confirmed byfinding similar results from acceptor sensitization analysis (Table 5.2, column 5).Also, concentration quenching (Table 5.2, column 7) can be confirmed by findingsimilar results from A-sensitization analysis using the D–A concentration([DA]max) found for the maximum acceptor-sensitized emission intensity insteadof the initial donor concentration [D]0. Assuming a fixed distance r, the multipleacceptors can also be confirmed by acceptor sensitization.

3) Instead of analyzing donor quenching and acceptor sensitization separately, theycan also be combined within Equations 5.17a and 5.18 for calculating FRETparameters and distances (donor quenching and acceptor sensitization – Section5.4.2.3). In this case, it is not necessary to know the emission intensity of the puredonor (ID), but the intensity arising from direct excitation of A (IA) must besubtracted from IAD and the luminescence quantum yields of D and A need tobe known (cf. Equation 5.17a). As summarized in Table 5.2, IDA decreases, while(IAD� IA) increases (columns 1 and 3, both normalized to ID), as alreadydiscussed above for donor quenching and acceptor sensitization analysis.Figure 5.8a shows the deconvoluted (from Figure 5.6b) emission intensityspectra of simultaneous donor quenching and acceptor sensitization. Again,the same results are found using different equations for their calculation(cf. footnotes in Table 5.2). Changing Equation 5.17a can be used to calculateluminescence quantum yields of D and A.

wavelength (nm)

(a)(b)

emis

sion

inte

nsity

(co

unts

)

norm

aliz

ed e

mis

sion

inte

nsity

IDA/ID = 1-ηFRET

-slope = ΦA/ΦD

IDA

(IA

D-I

A)

/ ID

(IAD-IA)

Figure 5.8 (a) FRET quenching of D(decreasing IDA) and FRET sensitization of A(increasing IAD–IA, spectra without emissionfrom direct acceptor excitation) deconvolutedfrom the spectra of Figure 5.6b (D in theabsence of A: black curve). (b) The negative

slope of FRET-sensitized acceptor emissionintensity as a function of FRET-quenched donoremission intensity (both intensities normalizedto ID) gives the luminescence quantum yieldratio of A and D.


gFRET¼IAD�IA

ðIAD�IAÞþðWA=WDÞIDA)gFRETWA

WDIDA¼ðIAD�IAÞð1�gFRETÞ

)gFRETWA

WDIDA¼ðIAD�IAÞIDAID )gFRET

WA

WD¼ IAD�IA

ID)WA

WD�WA

WD

IDAID

¼ IAD�IAID

:

ð5:17bÞ

The negative slope or the intersection with the ordinate of (IAD� IA)/IDas a function of IDA/ID (Figure 5.8b) is the luminescence quantum yieldratio of acceptor and donor (WA/WD), and therefore the calculation ofunknown D or A quantum yields becomes possible, in case one of them isknown.Although all these different possibilities of FRET data analysis exist, many

studies use only donor intensity quenching in order to relate the experimentaldata to FRET. This is often not correct, as many other processes (cf. Section 5.6)can be the cause of donor quenching. The choice of donor quenching, acceptorsensitization, or the combination of both strongly depends on the experimentalconditions and the required experimental accuracy. In general, it is moreprecise to use all the different possibilities and to carefully deconvolve thedifferent emission spectra in order to avoid spectral overlap problems. How-ever, for well-separated spectra, high emission intensities, and many datapoints supporting the experimental interpretation, it can be sufficient to useonly donor quenching. Moreover, highly sensitive luminescence detectionapplications make use of optical bandpass filters for spectral separation, whichmeans that the full spectral information is not available. In such cases, oneshould ensure that D and A bandpass filters with minimal spectral overlap to Aand D are used or that the emission spectra are measured before the filter-based FRET measurement, such that this information can be combined withthe filter transmission spectra to achieve an adequate spectral correction.Measuring emission spectra without an adequate quantum correction (cor-recting the wavelength-dependent detection efficiency of photodetectors suchas PMTs), autofluorescence from the sample medium, sample scattering andreabsorption (inner filter effects), and low signal-to-noise ratios are commonsources of error that should be taken into account for FRET measurements.Please keep in mind that the theoretical generic example presented here waschosen to demonstrate the different possibilities of interpreting a FRETexperiment. Therefore, donor quenching, acceptor sensitization, and theircombination deliver exactly the same results for FRETcalculations. As reality isusually not so kind to adapt all energy transfer or luminescence quenchingsystems to FRET theory, the different approaches leading to different resultswill usually be quite helpful to find reasonable explanations for the experimentaldata. As the large variety of different energetic excitation and relaxation processesinvolved in FRETexperiments can lead tomany paths of energy flow and thereforemany paths of interpretation, one should always consider a reasonable amountof control experiments adapted to each individual FRET system of interest.


5.5.3.2 Time-Resolved FRET MeasurementsTime-resolved luminescence spectroscopy can be divided into two technologies formeasuring luminescence decay times, namely, time-domain and frequency-domainmeasurements [15,18]. Time-domain methods measure the time-dependent lumines-cence intensity of a sample following a short excitation pulse of light (usually in thenanosecond range for lasers and up to somemicroseconds for flash lamps – preferably,the excitation pulse is much shorter than the decay time of the sample). Frequency-domain methods use intensity-modulated (usually sinusoidal modulation) excitationlight (e.g., I¼ Iav(ex)þ Ip(ex) cos vt). The modulation frequency ( f¼v/2p) is typicallyin the same range as the reciprocal of the luminescence decay time of the sample (e.g.,100MHz¼ 1/(10ns)). The emitted light will follow thismodulation frequency, but witha time delay (e.g., I¼ Iav(em)þ Ip(em) cos (vt�w)), which is usually called phase shiftor phase angle (w). Moreover, the peak intensity (Ip(ex) and Ip(em) for excitation andemission, respectively)will be lower and the average intensity (Iav(ex) and Iav(em)) can bedifferent. This is usually expressed in themodulation ratioM¼ [Ip(em)/Iav(em)]/[Ip(ex)/Iav(ex)]. Bothmethods (time-domain and frequency-domain) (cf. Figure 5.9) can be usedto determine single or multiple luminescence decay times (ti).The mathematical description of a time-dependent luminescence decay (with i

decay times) is the luminescence intensity (I) as a function of time:

I ¼Xi

Ai exp � tti

� �¼ A

Xi

ai exp � tti

� �: ð5:34Þ

For the frequency domain, the phase shift (w) or the modulation ratio (M) can beused for the determination of single or multiple decay times. The mathematicalrelation between phase shift and decay times is

w ¼ arctan

Piðaivt

2i Þ=ð1þ v2t2i ÞP

iðaitiÞ=ð1þ v2t2i Þ� �

: ð5:35Þ

1.00(a) (b) 1.0

0.8

0.6

0.4

0.2

0.00 10 20 30 40 50

inte

nsity

inte

nsity

0.75

0.50

0.25

0.000 2 4 6 8

time t (ns) time t (ns)

Ip(ex)

Iav(ex) Iav(em)

Ip(em)

φ

10 12

Figure 5.9 Examples of time-domain (a) andfrequency-domain (b) measurements for thedetermination of luminescence decay times.Excitation is displayed in black [(a): usuallymany pulses, for example, with 80MHzrepetition rate or one pulse every 12.5 ns, are

necessary to record a full decay curve; (b):modulated intensity with 80MHz modulationfrequency). Emission with a decay time of 2 nsis displayed in gray [(a): intensity decay; (b):modulated intensity with 80MHz).


The mathematical relation between modulation ratio and decay times is

M ¼P

iðaivt2i Þ=ð1þ v2t2i Þ

� 2 þ PiðaitiÞ=ð1þ v2t2i Þ

� 2Piaiti

� 2" #1=2

: ð5:36Þ

Equations 5.34–5.36 can be used within a least-square analysis, for which theparameters ai and ti are varied until a best fit between the experimental data and themathematical fit values is achieved. Figure 5.10 shows typical curves for time-domain and frequency-domain data, which were generated for a double-exponentialluminescence decay using Equations 5.34–5.36.No matter how the luminescence decay times for a FRET system are measured,

they can be used to determine FRET efficiencies and distances (in case R0 wasdetermined before). In most cases, donor quenching (Equations 5.13 and 5.14) isused for decay time FRET analysis (for decay time analysis using photobleaching,refer to Ref. [36]). FRET analysis of sensitized acceptor luminescence decays isusually complicated because both the donor and the acceptor excited states areinvolved in FRET. Therefore, the acceptor decay will be a combination of the FRET-quenched donor excited-state lifetime (tDA) and the acceptor excited-state lifetime(tA) [37]. The concentration of an excited acceptor ([A�]) after excitation of the donorcan be expressed as a differential equation:

d½A� �dt

¼ kFRET D� �� ðkRA þ kNRA Þ A

� �; ð5:37Þ

where [D�] is the excited donor concentration and kRA and kNRA are the radiative and

nonradiative decay rates of the acceptor. In this equation, kFRET½D� � describesthe increase in the A excited-state population due to FRET from excited D and

ðkRA þ kNRA Þ½A� � represents radiative and nonradiative deactivation of excited A.Solving Equation 5.37 and assuming the donor decay as single-exponential lead

time t (ns)

(a) (b)lu

min

esce

nce

inte

nsity

I1

0.1

100

80

60

phas

e sh

ift φ

(º)

or m

odul

atio

n ra

tio M

(%

)

40

20

00.1 1 10 100 1000 10 0000 5 10 15 20 25

frequency f (MHz)

Figure 5.10 (a) Luminescence intensity decaycurve resulting from a time-domainmeasurement. (b) Phase shift (gray) andmodulation ratio (black) curves resulting fromfrequency-domain measurement. For both

results, the decay times are t1¼ 2 ns (witha1¼ 0.7) and t2¼ 14 ns (with a2¼ 0.3). Thesingle lifetime components are shown in thedash-dotted (2 ns) and dotted (14 ns) curves.


to an excited-state acceptor concentration as a function of time (luminescence decayfunction of excited-state acceptors) [18]:

A� � ¼ ½D� �0kFRET

t�1DA � t�1

A

þ ½A� �0� �

exp � ttA

� �� ½D� �0kFRET

t�1DA � t�1

A

� �exp � t

tDA

� �ð5:38aÞ

or

A� � ¼ ½D� �0gFRET

1� ðtDA=tAÞ þ ½A� �0� �

exp � ttA

� �� ½D� �0gFRET

1� ðtDA=tAÞ� �

exp � ttDA

� �;

ð5:38bÞwhere [D�]0 and [A�]0 are the initial (at t¼ 0) concentrations of excited D and A,respectively, and tA is the luminescence decay timeofA in the absence ofD.As alreadymentioned, these acceptor excited-state decay functions (representing thedecayofA inthepresence ofDwith decay time tAD) are composed of the “pure” acceptordecay (firstterm in Equation 5.38a or 5.38b) and the FRET-quenched donor decay (increase of theacceptor luminescence with the time-component tDA represented by the negativeterm in Equation 5.38a or 5.38b). Figure 5.11 shows the excited-state decay curves(with decay time tAD) of FRET-sensitized A (in the presence of D) for different tAvalues in comparison to decay curves of FRET-quenched D (in the presence of A withdecay time tDA) andpureD (in the absence ofAwith decay time tD). These curveswerecalculated from Equation 5.38b for gFRET values of 50 and 95%, respectively, andassuming no direct acceptor excitation ([A�]0¼ 0).Figure 5.11 shows that the decay times tAD (or the slopes of the black curves) and

tDA (or the slope of the gray curves) are equal for tA� tD (gray dotted curves for tD).The higher the FRETefficiency, the larger the required difference between tA and tD(for the case of 95% efficiency, Figure 5.11b, a value of tA¼ 0.1tD already shows

(a) (b)

Figure 5.11 Excited-state decay curves of Awith tA values of 0.001, 0.01, 0.1, 0.5, 1, 2, and 5times tD, respectively – black curves frombottom to top calculated with Equation 5.38bfor FRET efficiencies of gFRET¼ 50% (a) and

gFRET¼ 95% (b). Pure donor decays with decaytime tD (dotted gray curves) and FRET-quenched donor decays with decay times tDA(gray curves) are shown for comparison.


clear differences in tAD and tDA). Figure 5.11 also visualizes that the FRET decaycurves for similar tA and tD values can become complicated as they show a rise timeat the beginning of the acceptor decay curves and significantly longer decays than fortDA. The use of donors with long decay times (e.g., lanthanide complexes as treatedin Section 5.6) and acceptors with short decay times (e.g., organic dyes) allows thereplacement of tDA by tAD in Equations 5.13 and 5.14 and, therefore, a time-resolvedFRET analysis of quenched donor emission and sensitized acceptor emission. Onebig advantage of the analysis within the “FRET-proof” acceptor channel is theabsence of pure donor emission (D in the absence of A) and therefore a lowerbackground signal (non-FRET signal).

5.5.3.3 Interpretation of Time-Resolved FRET DataIn this section, we will only treat donor quenching (acceptor-sensitized time-resolved analysis will be treated in the next section) and only decay time resultsfrom time-domainmeasurements will be shown (frequency-domain measurementswill result in the same luminescence decay times and therefore lead to the sameFRETresults). In the example of Figure 5.6, the luminescence intensity of the donoris quenched from 100 to 0% of the initial (D in the absence of A) donor intensity (insteps of 10%). Assuming a monoexponential luminescence decay function (I¼Aexp(�t/t) with an arbitrary chosen luminescence decay time of t¼ 5 ns) of theunquenched donor (D in the absence of A), there are several possible scenarios oftime-dependant donor (D in the presence of A) luminescence intensity decays,which can lead to the steady-state spectra presented in Figure 5.6. The amplitudes(AD and ADA) and decay times (tD and tDA) of the luminescence decays canprovide useful information about the investigated FRET system concerning static(concentration-dependent) and dynamic (distance-dependent) quenching or a mix-ture of both. This information cannot be found by analyzing only the steady-statespectra. A comparison of steady-state and time-resolved quenching in the so-calledStern–Volmer plots (Figure 5.12) can give good evidence of the quenching situation.In the case where the ratio of initial to quenched steady-state intensity (I0/I) and theratio of initial to quenched decay time (t0/t) increase equally over quencher

[Q]

1 1 1

τ0/τ = I0/I

τ 0/τ

or

I 0/I

τ 0/τ

or

I 0/I

τ 0/τ

or

I 0/II0/I

I0/I

τ0/ττ0/τ

[Q] [Q]

highertempe-rature

highertempe-rature

(a) (b) (c)

Figure 5.12 Stern–Vomler plots of dynamic (a), static (b), and combined dynamic and static (c)quenching. The influence of temperature on dynamic and static quenching is also indicated withinthe graphs.


concentration [Q ], the quenching is purely dynamic. If the intensity ratio increasesover quencher concentration and the decay time ratio is unaffected, the quenching ispurely static. If both the intensity ratio and the decay time ratio increase overquencher concentration but the intensity ratio increases stronger, the quenching is amixture of dynamic and static deactivation.Different from the steady-state results, where one set of spectra (experimental data

in Table 5.2) was used to provide different possible interpretations, we will discusshere different sets of possible decay curves, which can confirm or disprove thedifferent possible interpretations from the steady-state measurements. Thus, thedifferent time-resolved scenarios (Figures 5.13–5.16 and Tables 5.3–5.5) will bediscussed in relation to the steady-state experimental data (spectra from Figure 5.6).

1) Distance (dynamic quenching)As already mentioned in Section 5.5.3.1, increased quenching of D can be

explained by decreased D–Adistances. If themeasured samples lead to the spectra

(a) (b)

(c) (d)

measurement

norm

alized l

um

inescence i

ntensity

Figure 5.13 (a and b) [part (b) intensitynormalized with logarithmic intensity scale]Dynamic luminescence quenching representedby decay curves (D in the presence of A – gray)with constant amplitudes and decreasing decaytimes compared to the unquenched D curve(black). (c) Unchanged amplitudes (circles) and

decreasing decay times (squares) as a functionof intensity quenching. (d) The purely dynamicquenching behavior is confirmed by a Stern–Volmer plot, for which both the intensity ratio(triangles) and the decay time ratio (squares)increase equally from measurement tomeasurement.


in Figure 5.6c (steady-state measurements) in combination with the decay curvesfrom Figure 5.13, the FRET quenching was most probably caused by decreasingD–A distances (e.g., change of structural confirmation over time or due to changesin the environment, such as temperature or pH), as depicted in Figure 5.7a.Withinthe decay time functions (Equation 5.34), the amplitudesADA (amplitudes for D inthe presence of A) stay at a constant value (ADA/AD¼ 1), whereas the decay timestDA decrease (tDA/tD decreases from 1 to 0 in steps of 0.1), which is well illustratedby the decreasing slopes in the logarithmic plot. The Stern–Volmer plot (for whichthe quencher concentration was replaced by the measurement number – in caseconcentrations are known, they can be used instead) shows an equal increase ofintensity and decay time ratio, which confirms the purely dynamic quenchingbehavior. The FRET efficiencies gFRET (Equation 5.13) and D–A distances (Equa-tion 5.14) calculated by using luminescence intensities (Table 5.2, columns4 and5)are confirmed by the values calculated by using luminescence decay times(Table 5.3, columns 4 and 5).

measurement

(a) (b)

(c) (d)

no

rm

alized

lu

min

escen

ce i

nten

sity

Figure 5.14 (a and b) [part (b) intensitynormalized with logarithmic intensity scale]Static luminescence quenching represented bydecay curves (D in the presence of A – gray)with constant decay times and decreasingamplitudes compared to the unquenched Dcurve (black). (c) Decreasing amplitudes

(circles) and unchanged decay times (squares)as a function of intensity quenching. (d) Thepurely static quenching behavior is confirmedby a Stern–Volmer plot, for which the intensityratio (triangles) increases, whereas the decaytime ratio (squares) is unchanged.


2) Concentration or environmental conditions (static quenching)If the steady-state spectra from Figure 5.6c are accompanied by the decay

curves from Figure 5.14, the FRET quenching was most probably caused byincreasing concentrations of D–Apairs described by Equation 5.32 (with A beingthe quencher Q) or a change in environmental conditions (e.g., temperature,solvent, and pH). Within the decay curves, the amplitudes ADA decrease (ADA/AD

decreases from 1 to 0 in steps of 0.1), whereas the decay times tDA stay at aconstant value (tDA/tD¼ 1), which becomes quite obvious in the logarithmic plotwith all decay curves showing the same slope. The Stern–Volmer plot shows anincrease of intensity ratio in combination with a constant decay time ratio, whichconfirms the purely static quenching behavior. In the case of FRETquenching, apossible scenario would be a FRET assay, for which increasing amounts of ananalyte (e.g., a biomarker) are titrated to a constant concentration of D- and A-labeled specific binding molecules (e.g., antibodies against the biomarker).Although FRET is a dynamic quenching process, this case will cause static

measurement

(a) (b)

(c) (d)

norm

alized l

um

inescence i

ntensity

Figure 5.15 (a and b) [part (b) intensitynormalized with logarithmic intensity scale]Combined dynamic and static luminescencequenching represented by decay curves (D in thepresence of A – gray) with changing decay timesand amplitudes compared to the unquenched Dcurve (black). (c) Changing (overall decreasing

tendency) amplitudes (circles) and changing(overall decreasing tendency) decay times(squares) as a function of intensity quenching.(d) The combined dynamic and static quenchingbehavior is confirmed by a Stern–Volmer plot,for which the intensity ratio (triangles) increasesstronger than the decay time ratio (squares).


Table 5.4 Data resulting from a combination of dynamic and static D-quenching (Figure 5.15).

0 1 2 3a) 4 5b)

Measurement Dynamic and static quenching

tDA/tD gFRET r (nm) ADA/AD [DA]/[D]0

1 1.0 0.0 >13.0 1.0 0.0002 0.989 0.011 12 0.910 0.0903 0.952 0.048 9.6 0.840 0.1604 0.921 0.079 8.7 0.760 0.2405 0.968 0.032 10 0.620 0.3806 0.685 0.315 6.6 0.730 0.2707 0.784 0.216 7.2 0.510 0.4908 0.476 0.524 5.7 0.630 0.3709 0.357 0.643 5.3 0.560 0.44010 0.256 0.744 4.9 0.390 0.61011 0 1.0 0 0 1.000

a) r calculated with Equation 5.14.b) [DA]/[D]0¼ 1� (ADA/AD).

Table 5.3 Data resulting from purely dynamic or purely static D-quenching (Figures 5.13 and 5.14).

0 1 2 3 4a) 5b) 6 7 8c)

Measurement Overall quenching Distance (dynamic quenching) Concentration (staticquenching)

IDA/ID tDA/tD ADA/AD gFRET r (nm) tDA/tD ADA/AD [DA]/[D]0

1 1.0 1.0 1.0 0.0 >13.0 1.0 1.0 02 0.9 0.9 1.0 0.1 8.4 1.0 0.9 0.13 0.8 0.8 1.0 0.2 7.3 1.0 0.8 0.24 0.7 0.7 1.0 0.3 6.7 1.0 0.7 0.35 0.6 0.6 1.0 0.4 6.2 1.0 0.6 0.46 0.5 0.5 1.0 0.5 5.8 1.0 0.5 0.57 0.4 0.4 1.0 0.6 5.4 1.0 0.4 0.68 0.3 0.3 1.0 0.7 5.0 1.0 0.3 0.79 0.2 0.2 1.0 0.8 4.6 1.0 0.2 0.810 0.1 0.1 1.0 0.9 4.0 1.0 0.1 0.911 0 0 1.0 1.0 0.0 1.0 0.0 1

a) gFRET calculated with Equation 5.13.b) r calculated with Equation 5.14.c) [DA]/[D]0¼ 1� (IDA/ID)¼ 1� (ADAtDA/ADtD)¼ 1� (ADA/AD) because tDA/tD¼ 1 for all

measurements.


quenching (because the D–A distance r is fixed). The D–A pair concentration([DA]/[D0]) increases in steps of 10% (Table 5.3, column 8).

3) Multiple acceptors (dynamic quenching)The steady-state spectra from Figure 5.6c and the decay times from Figure 5.13

(in case measurements 2, 3, and 11 are not taken into account) can also be causedby an increasing amount of A’s per D (nA from Equation 5.24) with a fixeddistance r (Figure 5.7d and Table 5.2, column 8). Although the distance betweenD and the multiple A’s is fixed, this configuration leads to dynamic quenchingbecause the FRET efficiency increases with an increasing number of A’s per D.This is not the case for static quenching of an increasing number of single D–Apairs (same FRETefficiency), as discussed in the previous paragraph. In the casefor which r is unknown, Equation 5.24 can be used with r as a free fit parameter(R0 and gFRETare known from the measurements of Figure 5.5 and 5.6c) in orderto determine the D–A distance. A very nice study of multiple dye acceptors persemiconductor quantum dots was performed by Clapp et al.. The authors usedsteady-state donor quenching, steady-state acceptor sensitization, and time-resolved donor quenching to find the correct interpretation of their FRETsystem [33].

4) Distance and concentration (dynamic and static quenching)If the steady-state and time-resolved measurements lead to the spectra from

Figure 5.6c and the decay curves from Figure 5.15, the luminescence deactivationwas caused by a combination of dynamic (e.g., decreasing D–A distances) andstatic quenching (e.g., increasing concentrations of D–A pairs or a change inenvironmental conditions). Within the decay curves, the amplitudes ADA as wellas the decay times tDA change. This change usually has a decreasing tendency forboth ADA and tDA (luminescence is quenched), but as amplitude and decay timecan compensate for each other, an interpretation of the different decay curves,amplitudes, and decay times might not be as facile as for the pure dynamic orstatic quenching cases. The Stern–Volmer plot shows a stronger increase ofintensity ratio compared to the decay time ratio, which confirms the combinationof dynamic and static quenching. In the case of FRETquenching, one of themostimportant aspects of the time-resolved measurements is the possibility ofcalculating distances (using the decay times and Equation 5.14). This wouldnot be possible for steady-statemeasurements because the dynamic (decay times)and the static (amplitudes) quenching parts cannot be distinguished.

5) Multiexponential donor decays and multiple distancesFRET systems can be much more complicated than within the simulated

examples mentioned above. The first complication can already be the puredonor (D in the absence of A) luminescence decay because it must notnecessarily be monoexponential. In an ensemble measurement, the multipledonor molecules can take different conformations (e.g., structural or chemicalconfigurations), which might lead to different decay times for each species andthus an overall multiexponential luminescence decay function. This meansthat each of these multiple decay times (tDi) or an average decay time (ktDi)must be taken as the pure donor decay time. Averaging is performed using


amplitude-averaged decay times, because FRET is a dynamic quenchingprocess and a detected signal at a particular time interval is proportional tothe excited-state population (and not to the integrated intensity, for which theintensity-averaged decay time would be used) [13,38]. Taking the multiexpo-nential luminescence decay function from Equation 5.34 leads to the followingamplitude-averaged decay time:

hti ¼P

AitiPAi

¼X

aiti: ð5:39Þ

Another aspect making FRET analysis more complicated is the possibility ofhaving multiple D–A distances within a D–A pair ensemble. This means that(apart from the multiexponential tD values) the quenched donor decay times(tDAi) will be multiexponential and depending on the number of differentdistances (and thus decay times), the time-resolved analysis can become com-plicated and high signal-to-noise ratios are necessary to recover the differentamplitudes and decay times.As if these two difficulties were not enough, complicated FRET systems can

also be composed of dynamic and static quenching processes, which means thata careful distinction of amplitudes and decay times (which can compensate foreach other within a least-square fit) is necessary for a correct interpretation of theexperimental data. In Section 5.6, we will discuss such a FRET system withmultiexponential donor decay, multiple distances, and mixed dynamic and staticquenching. Moreover, this system uses semiconductor quantum dots as accept-ors, which poses another problem, because these nanoparticles are excited at anywavelength below their emission wavelength. Steady-state measurements withsuch acceptors are useless in most cases because the acceptor will be excited veryefficiently (more efficiently than the donor) and the interpretation of quenchingand sensitization becomes very difficult. However, the use of lanthanide-baseddonors with very long excited-state lifetimes (up to several milliseconds) allowsthe time-resolved analysis of acceptor sensitization due to the large difference indonor and acceptor excited-state lifetimes (cf. Figure 5.11).

5.6FRET beyond F€orster

In more than six decades that have passed since F€orster’s paper “Energiewanderungund Fluoreszenz” [22] from 1946, the FRET toolbox has been filled up with manynew possible donor and acceptor fluorophores, including a multiplicity of organicdyes, metal-based chelates, fluorescent proteins, and nanoparticles (cf. Chapters 6and 14). Within all the FRET applications that have been developed, one can findmany “nonclassical” approaches, such as FRET from lanthanide donors withmultiplet–multiplet transitions (quintet–septet in the case of Eu and Tb) andmultiple transition dipole moments, FRET with quantum dot nanoparticles (withdiameters of up to 10 nm), which do not present an ideal point-dipole system, and

5.6 FRET beyond F€orster j139

FRET without the use of donor excitation by light [bioluminescence resonanceenergy transfer (BRET) and chemiluminescence resonance energy transfer (CRET)]or energy transfer to metal nanoparticles, which has been related to FRET, nano-surface energy transfer (NSET), dipole to metal particle energy transfer (DMPET), ornanoparticle-induced lifetime modification (NPILM). Moreover, there are otherenergy transfer mechanisms, such as plasmonic coupling, charge transfer, or singletoxygen transfer, which can enlarge the distance range of two interacting speciesfrom about 1 to 200 nm. In this section we will discuss such systems, which gobeyond the classical treatment of Theodor F€orster.

5.6.1Time-Resolved FRET with Lanthanide-Based Donors

The many advantages of lanthanide-based donors have been known for more thantwo decades, and especially Paul Selvin should be mentioned here for a lot ofpioneering work in this area [9,39–45]. Probably the most important property oflanthanide-based donors for FRET is their long luminescence decay time reachingup to several milliseconds for some supramolecular lanthanide complexes (e.g.,chelates or cryptates) [46–52]. This means that the excited-state lifetimes of mostlanthanide-based donors are several orders of magnitude larger than those of anyother acceptor. Thus, the same decay time analysis can be applied for D-quenchingand A-sensitization (cf. Figure 5.11). Moreover, the sensitized acceptor emission canbe measured against a very low background. This can be achieved by using anacceptor that emits at a wavelength region void of lanthanide emission (cf.Figure 5.16 for Tb as donor) for minimizing the background of the donor. Manydifferent acceptors (e.g., fluorescent proteins, organic dyes, and quantum dots) areavailable for the best choice of emission wavelength [1,53,54]. In order to suppressthe acceptor background (directly excited acceptor emission), which is usually in thenanosecond time range, one can use pulsed excitation and gate the detector off for a

Figure 5.16 Typical emission spectrum of a Tb chelate. The arrows indicate wavelength areas inwhich an acceptor can be measured without Tb background emission.


short period of time (i.e., several microseconds). This will lead to a pure FRETsignalafter the detector has been gated on again because almost any photon that will bedetected then must arise from an excitation via the donor – the acceptor detectionchannel becomes a “FRET-proof” channel. This also means that the sensitizedacceptor signal is insensitive to concentration effects and incomplete labeling andbinding because only those species containing both D and A can contribute to theFRET signal (pure D and pure A signals are completely suppressed).Another advantage is the possibility of large overlap integrals with different

acceptors due to the multiple emission bands of lanthanides over a wide spectralrange. F€orster distances of 9 nm for an Eu chelate donor and an APC acceptor [55]and up to 11 nm for a Tb chelate donor and quantum dot acceptors [53] have beendemonstrated. Such large R0 values can significantly increase the FRET distancerange up to about 20 nm (or larger in case of very sensitive detection).One very comfortable aspect of Eu- and Tb-based (most often used lanthanides for

FRET applications) donors is their unpolarized emission. Due to their multipletransition dipole moments, they act as randomized donors (even in the absence offast isotropic rotation) and the orientation factor k2 is limited to values between 1/3and 4/3 even if the acceptor has a fixed orientation (cf. averaging conditions for k2 inSection 5.3). The following example (lanthanide to quantum dot FRET) will illustrateall the different aspects (including donor quenching, acceptor sensitization, anddynamic and static quenching) of a sophisticated time-resolved FRETanalysis usinglanthanide-based donors.

5.6.1.1 Terbium to Quantum Dot FRET Using Time-Resolved Donor Quenching andAcceptor Sensitization AnalysisIn a recent example, we performed a time-resolved analysis of one Tb chelate donorand different quantum dot acceptors in a FRET system, for which Tb and QD arebrought in proximity via biotin–streptavidin binding [56]. In this configuration,several Tb donors can attach to the surface of QDs (consisting of the centralsemiconductor QD and a polymer-based coating for biocompatibility). The lumi-nescence decay of the Tb donor is double-exponential with an amplitude-averageddecay time of ktDi¼ 2.3ms and a luminescence quantum yield of 67%. The QD (wewill only discuss one QD here) has an emission wavelength maximum of 655 nm, amultiexponential decay in the nanosecond time range (about 30 ns average decaytime), and a luminescence quantum yield of 7%. Due to the random labeling of theTb donor to the streptavidin protein and the ellipsoidal shape of the QD, the FRETsystem consists of a D–A distance distribution. The different samples contain aconstant concentration of Tb donors (0.2 nM) and increasing concentrations of QDacceptors (0� 0.6 nM). Due to the varying ratios of Tb/QD in the different samples,different concentrations of pure Tb donors and QD acceptors are present in theFRET systems. The pure Tb donors (at different concentrations) result in varyingintensities (amplitudes) of Tb background emission at a fixed decay time (ktDi),which leads to different static contributions with significant intensities in the donordetection channel (optical bandpass filter: 494 20 nm) and minor intensities in theacceptor detection channel (optical bandpass filter: 660 13 nm). In summary, wehave investigated a FRETsystem with a multiexponentially decaying donor, multiple


D–A distances, and dynamic (distances) as well as static (free Tb concentration)quenching contributions using time-resolved detection of donor quenching andacceptor sensitization.The increasing QD acceptor concentration leads to Tb D-quenching and QD A-

sensitization, as shown in Figure 5.17 in the intensity decay curves as well as in thetime-gated intensities. No background correction was performed for these graphs.The Tb emission cross talk to the QD acceptor detection channel can be seen in thelowest decay curve in Figure 5.17c and the time-gated intensity offset inFigure 5.17d. Due to the relatively low luminescence quantum yield of the QDs,the sensitized QD emission is relatively weak, but distinguishes significantly fromthe Tb background signal. The appearance of new short decay times due to FRETbecomes clearly visible within both the Tb donor and the QD acceptor decay curves.

(a) (c)

(b) (d)

0.1–0.9 ms 0.1–0.9 ms

Figure 5.17 Time-resolved Tb donorquenching (a and b) and QD acceptorsensitization (c and d). (a) Luminescence decaycurves detected within the Tb donor channel forincreasing QD acceptor concentrations: 0 nM(gray), 0.06, 0.1, and 0.15 nM (black from top tobottom). The white lines within the curves arethe fitted curves. (b) Time-gated (0.1–0.9ms)luminescence intensities detected withinthe Tb donor channel for increasing QDconcentrations. (c) Luminescence decay

curves detected within the QD acceptorchannel for increasing QD acceptorconcentrations: 0 nM (gray), 0.06, 0.1, and0.15 nM (black from bottom to top). Thewhite lines within the curves are the fittedcurves. (d) Time-gated (0.1–0.9ms)luminescence intensities detected within theQD acceptor channel for increasing QDconcentrations. (Adapted with permissionfrom Ref. [56]. Copyright 2013, AmericanChemical Society.)


The FRET-quenched donor curves can be conveniently fitted with triple-expo-nential decay functions (pure D was fitted with a double-exponential), whereas theFRET-sensitized acceptor curves require a quadruple-exponential fit function. Dueto strong background fluorescence in the very short time range (strong saturatedsignals in the first 10–50 ms mainly due to sample autofluorescence and direct QDexcitation) and the very low signal intensities for the acceptor channel in the verylong time range (weak signal due to the Tb cross talk within the QD acceptorchannel), the time ranges for the fits were chosen differently for D (0.02–8ms) and A(0.05–4ms). In most software tools for least-square fitting of exponential lumines-cence decays, such fits are called “tail fits,” which means that the fit starts at adifferent time t0 for D (t0¼ 0.02ms) and A (t0¼ 0.05ms). However, the completeluminescence decays of A and D start immediately after the excitation at 0ms (the t0values for the fits were chosen differently to improve the fit quality). Although suchtail fits do not change the different single decay times, the single amplitudes (Ai-FIT)must be corrected (from the t0 fit values to the correct start of the luminescencedecay at 0ms) to yield the correct amplitudes (Ai) of the complete decay function:

I ¼ Ai�FIT � exp � t� t0t

� �¼ Ai � exp � t

t

� �) Ai ¼ Ai�FIT � exp t0

t

� �: ð5:40Þ

This is especially important when the amplitudes are necessary for the interpre-tation of the results (e.g., calculation of amplitude-averaged decay times or molecu-lar fractions). For all fits of FRET-quenched and FRET-sensitized decay curves, theTb donor decay time was a fixed value. The fitted curves are presented in Figure 5.17and all fit results are presented in Table 5.5 for the Tb donor detection channel and inTable 5.6 for the QD acceptor detection channel.The triple-exponential FRET-quenched Tb donor decay curves were fitted for the

amplitude fractions aDA�1, aDA�2, and aDA�0 and the decay times tDA1, tDA2, andtDA0, for which the third decay time component was fixed to tDA0¼ tD2 [the pure Tbdonor has two decay times of tD1¼ (0.56 0.06)ms and tD2¼ (2.56 0.5)msleading to an amplitude-averaged decay time of ktDi¼ (2.27 0.5)ms] (cf. Tables 5.5and 5.6) in order to take into account the emission of unquenched donors. For thecalculation of the average donor decay time in the presence of the acceptor htDAi,only the first two amplitudes and decay times were used (as the third componentrepresents unquenched donors). Therefore, the amplitude fractions must beredefined for these two decay times tDA1 and tDA2:

aDA1 ¼ aDA�1

aDA�1 þ aDA�2and aDA2 ¼ aDA�2

aDA�1 þ aDA�2: ð5:41Þ

As the unquenched donor possesses two decay time components (tD1 and tD2),htDAi must be corrected for the shorter time component (tD1). As the value of tD1falls within the time range of the FRET-quenched decay times, the use of anadditional exponential (with fixed tD1) for the fit procedure leads to inconsistent fitresults. Therefore, a correction factor zD (the fraction of unquenched donors in theshort time components) can be applied. zD is determined by comparing the


amplitude fractions of tD2 and tDA0 (tDA0¼ tD2) multiplied by the amplitudefraction aD1:

zD ¼ aD1ðaDA�0=aD2Þ: ð5:42Þ

The average FRET-quenched decay time is then (with aDA1þaDA2¼ 1)

htDAi ¼ aDA1tDA1 þ aDA2tDA2 � zDðaDA1 þ aDA2ÞtD1aDA1 þ aDA2 � zDðaDA1 þ aDA2Þ ¼ aDA1tDA1 þ aDA2tDA2 � zDtD1

1� zDð5:43Þ

and the average FRET efficiency hgFRETi is calculated by Equation 5.13 using theaverage decay times htDAi and htDi.The quadruple-exponential FRET-sensitized QD acceptor decay curves were

fitted for the amplitude fractions aAD�1, aAD�2, aAD�3, and aAD�0 and the decaytimes tAD1, tAD2, tAD3, and tAD0, for which the fourth decay time component wasfixed to tAD0¼ tD2 in order to take into account the emission of unquencheddonors, which is much less intense compared to the donor channel, but stillpresent due to spectral cross talk of the Tb emission in the QD acceptor detectionchannel. The correction factor zA (the fraction of unquenched donors in the shorttime components) is almost negligible, but is still taken into account for a correcttreatment:

zA ¼ aD1ðaAD�0=aD2Þ: ð5:44Þ

In order to calculate the average FRETdecay time htADi, only the amplitudes andlifetimes with i¼ 1–3 are taken into account (i¼ 0 represents the unquenched donoremission). Moreover, the amplitudes aAD�i must be corrected by the FRET rates

kFRETi ¼ t�1ADi � htDi�1 (combination of Equations 5.8b and 5.13) to take into account

the FRET efficiency-dependent excitation of the acceptors. The corrected amplitudefractions are (for i¼ 1–3)

aADi ¼ ðaAD�i=kFRETiÞðaAD�1=kFRET1Þ þ ðaAD�2=kFRET2Þ þ ðaAD�3=kFRET3Þ : ð5:45Þ

The average FRET decay time is then calculated by

htADi ¼ aAD1tAD1 þ aAD2tAD2 þ aAD3tAD3 � zAtD11� zA

ð5:46Þ

and the average FRET efficiency hgFRETi is calculated by Equation 5.13 using theaverage decay times htADi (instead of tDA) and htDi.For each FRET decay time (from the donor and the acceptor fits), a specific D–A

distance r can be calculated using Equation 5.14. The fractions of FRETpairs foundat the different distances corresponding to tDAi and tADi are given by the amplitudefractions of these decay times.


5.6.2BRET and CRET

The discovery of bioluminescence (of bacteria) [57–59] and chemiluminescence (oforganic compounds) [60,61] dates back to the nineteenth century. For both phe-nomena, luminescence is created by a chemical reaction (as excitation source) inside(bioluminescence) or outside (chemiluminescence) a living organism. If the chemi-cally excited molecules are used as energy donors in combination with a suitableacceptor inside a FRET system, the energy transfer is called bioluminescence reso-nance energy transfer and chemiluminescence resonance energy transfer, respec-tively. As only the donor excitation is different from FRET and the energy transfermechanism is the same, the FRET theory (r�6 distance dependence, etc.) can beapplied for BRETand CRET. The first investigations of BRETand CRETdate back toapproximately half a century ago [62–64], but BRET and CRET applications haveexperienced a recent renaissance, especially due to novel FRET acceptors such asfluorescent proteins and nanoparticles [65–67]. Most BRET applications use lucifer-ases (e.g., Renilla luciferase “Rluc” or Firefly luciferase “Fluc”), which catalyze theoxidation of their substrates (e.g., coelenterazine for Rluc or luciferin for Fluc), toproduce emission in the blue to green spectral range (emission peaks of about 480nmfor coelenterazine and 570nm for luciferin) for acting as BRET donors. In CRET,mainly luminol derivatives are used as donors. Luminol oxidation is a nonenzymaticreaction with much lower efficiency than the bioluminescence reactions [68]. BothBRETandCRETcan be usedwith different acceptors such as organic dyes,fluorescentproteins, or quantumdots. Figure 5.18 shows two recent examples of BRETandCRET.TheBRETsystempresents hybridmolecules consisting of afirefly luciferin donor anddifferent organic dye acceptors [69]. This approach allowed the development ofluciferins emitting in the near-infrared, which is an important wavelength rangebecause of deeper tissue penetration compared to UVor visible light. Moreover, thesenovel NIR luciferins did not require any ex vivo luciferasemanipulation. Although thebrightness of the BRET luminescence was very low, the authors could show NIRluminescence in live cells and livingmice using luciferase-expressing cells. TheCRETsystem is embedded in a DNA machine [70], for which a nucleic acid scaffold (1) ishybridized with three DNA footholds. The first foothold is labeled with a FAM dye (2)or a semiconductor quantum dot (3). The second foothold (4) is initially free and thethird foothold (5) is hybridized to a nucleic acid strand (6) that acts as DNAwalker andcontains a hemin/G-quadruplex DNAzyme sequence (caged in the duplex structurewith the third foothold).Additionof a fuel strand (7) leads to stranddisplacement of thewalker (6) by the formation of a more stable 7/5 duplex and the hybridization of 6overhang to the second foothold (4). In this configuration, 6 can form a hemin/G-quadruplex DNAzyme, which catalyzes the generation of chemiluminescence in thepresence of luminol andH2O2. The activated luminol is acting as aCRETdonor for theFAMdye (2) or quantumdot (3), which then produces its own luminescence. Notably,this process is completely reversible by the addition of an antifuel strand (8), leading toa strand replacement of 7 to form a stable 7/8 duplex and the reverse walking step of 6to 5, which switches the chemiluminescence (and the CRET) back to “off.”


5.6.3Energy Transfer to Metal Nanoparticles (FRET, NSET, DMPET, NPILM, etc.)

The good news about distance-dependent energy transfer tometal (mainly Au and insome cases Ag is used) nanoparticles or nanoclusters is that it works very efficiently.However, different mechanisms have been proposed to be responsible for the

Figure 5.18 Recent examples of BRET (top)and CRET (bottom) systems. (a) Emissionspectra of the pure donor aminoluciferin (AL)and the acceptor–donor complexes Cy5-AL,SiR700-AL, and Cy7-AL, which give access to theNIR wavelength range. (b) Detection of BRETfrom AL to Cy7 in luciferase-expressing cellsinjected to mice. In contrast to the BRETemission of Cy7-AL (bottom), the pure ALsample (top) does not show any Cy7luminescence. (c) Creation of CRET fromactivated luminol to a FAM dye or a quantumdot (on 2 and 3, respectively) by switchablehemin/G-quadruplex formation. The DNAmachine is switched “ON” by 7, which leads toa walkover of 6 to 4 and the generation of CRETfollowed by light emission of FAM or QD.Addition of 8 switches the machine back to

“OFF” because of a stable formation of a 7/8duplex and the reverse walk of 6 to 5, causingthe extinction of CRET. (d) Luminolchemiluminescence (large peak around420 nm) and CRET-sensitized FAMluminescence (small peak around 518 nm). Theinset shows the switchable CRET signals of theDNA walker system. (e) Luminolchemiluminescence (peak around 420 nm) andCRET-sensitized QD luminescence (peakaround 615 nm). The inset shows theswitchable CRET signals of the DNA walkersystem. (Parts (a) and (b) reprinted withpermission from Ref. [69]. Copyright 2013,Wiley-VCH Verlag GmbH. Parts (c–e) reprintedwith permission from Ref. [70]. Copyright 2012,American Chemical Society.)


distance dependence, which has been investigated in theory [71–76] and in practicefor different energy donors such as organic dyes [77–84], semiconductor quantumdots [85–90], or fluorescent proteins [91]. Among all these different systems,different mechanisms have been proposed to be responsible for the energy transferand a general model for energy transfer to metal nanoparticles does not exist. Thetwo most important aspects for influencing the distance dependence are the donor–acceptor distance and the nanoparticle size. At small distances (separation betweendonor and acceptor is smaller than the size of the donor and/or the acceptor),nonradiative energy transfer is proposed to be the main cause of quenching;whereas at larger distances, radiative energy transfer will play a major role. Oneof the main ideas for short distances is that the point dipole approximation is notvalid anymore leading to a deviation in the FRET distance dependence by over-estimating the FRET rate. One can start from a generalization of Equation 5.7 forresonance energy transfer (RET):

kRET ¼ t�1D

D0

d

� �n

; ð5:47Þ

where D0 is the donor–acceptor distance for 50% energy transfer efficiency (R0 inFRET) and d is the donor–acceptor separation distance (r in FRET). The maindifference between the RET theories can be found in the exponent n, which is n¼ 6for FRET. Agreement of the FRET theory with experimental data was shown for Aunanoparticles with diameters of 1.4 nm [85], 5 nm [89], and 15 and 80 nm [87], allusing quantum dots as donors.The DMPET model of Carminati et al. [72] takes into account the distance

dependence of radiative (mainly n¼ 3 with a n¼ 6 contribution at plasmon reso-nance) and nonradiative (n¼ 6) decay rates, which leads to some additionalcorrection terms compared to FRET [88]. Moreover, nonradiative decay is stronglyenhanced, when the donor radiates at the plasmon resonance wavelength of thenanoparticle [72]. Moroz reanalyzed Carminati’s DMPETmodel of a 10 nm diameterAg nanoparticle and pointed out that there is a significant contribution (between 50and 101% of the total value) of higher order multipoles to nonradiative rates even at5 nm donor–acceptor distance [75]. This theoretical model provided very goodagreement with luminescence decay time quenching of quantum dots by Aunanoparticles of 10, 15, and 20 nm diameter positioned at distances of about 17,15, and 13 nm from the quantum dots using DNA origami [86].The NSET model proposed by Strouse and coworkers [79,80,82–84] uses a d�4

distance dependence (n¼ 4), which significantly increases (about twofold) thedistance range of FRET. They proposed the following NSET transfer rate:

kNSET ¼ 0:225c3

v2DvFkFd

4

WD

tD; ð5:48Þ

where c is the speed of light, WD is the donor quantum yield, vD is the angularfrequency (v¼ 2pcl�1) for thedonor,vF is the angular frequency for bulk gold, and kFis theFermi vector for bulk gold.NSEThasmainly been found tobe ingoodagreementwith experimental data (using organic dyes and quantum dots as donors) if the


nanoparticles are of small size (below about 3 nm diameter) and thus do not have anyplasmon bands [79,80,82,84,87,88]. Nevertheless, also larger Au nanoparticles of up to18nm diameters showed experimental NSET behavior [77,78,90,91].Bhowmick et al. proposed a theoretical model with a n¼ 6 distance dependence of

energy transfer to surface plasmonic modes at large separation between a dye and ananoparticle and a 3< n< 4 distance dependence of energy transfer for shortseparation (similar to the nanoparticle size) between dye and nanoparticle [71].As already mentioned, for large distances the energy transfer is mainly governed

by the radiative rate with a d�3 distance dependence (n¼ 3), leading to a large energytransfer distance range compared to FRET. Indeed, such energy transfer betweendyes and Au nanoparticles over distances of more than 40 nm was found by steady-state experiments [78] and decay time measurements [81]. In the latter publication,the acronymNPILMwas introduced. Figure 5.19 shows experimental data of energytransfer over distances of up to 50 nm for different nanoparticle sizes.

5.6.4Other Transfer Mechanisms

Apart from the FRET-like energy transfer mechanisms mentioned so far, thereare several other energy or charge transfer mechanisms that can enlarge thedistance range of FRET in both the short and the long directions. On the shortend, there are electron exchange (Dexter) or electron transfer (Marcus) mecha-nisms related to orbital overlap, with exponentially decaying distance depen-dence. On the long end, there are mechanisms such as plasmon coupling (up toabout 80 nm donor–acceptor distance) or singlet oxygen diffusion (up to about200 nm). Although all of these mechanisms are not based on nonradiative

Figure 5.19 (a) Distance dependence of thequenching efficiency for different sizes of Aunanoparticles. The 8 nm Au nanoparticle was ingood agreement with NSET theory, whereas theother two were attributed to radiative energytransfer and could not be fitted with FRET,

NSET, or DMPET. (b) Increase of the 50%energy transfer efficiency value (R0) with thesize of gold nanoparticle. (Reprinted withpermission from Ref. [78]. Copyright 2009,Wiley-VCH Verlag GmbH.)


energy transfer due to dipole–dipole interactions and are thus not directlyrelated to FRET, they will be briefly described here (the interested reader isreferred to further literature within the following sections) in order to give abroader picture of distance-dependent energy/charge transfer mechanisms. Thedifferent mechanisms, their distance dependence, and their approximate dis-tance range are shown in Table 5.7.

5.6.4.1 Electron Exchange Energy Transfer (Dexter Transfer)In the case of overlapping orbitals of donor and acceptor molecules, which requireshort D–A distances, electron exchange between D and A can occur. This mecha-nism is different from the Coulombic interaction in FRETor the electron tunnelingin charge transfer (Figure 5.20). The electron exchange rate is related to the orbitaloverlap, which is expected to fall off exponentially with increasing D–A distance.Electron exchange requires energetic resonance of D and A and therefore theexchange rate will also be dependent on the spectral overlap of D and A. A theory forelectron exchange-mediated energy transfer was developed by Dexter in 1953 [92].The rate constant of electron exchange energy transfer [or Dexter transfer (DT)] isgiven by

kDT ¼ KJDTexp�2rL

� �; ð5:49Þ

where K is a constant related to specific orbital interactions and JDT is the spectraloverlap integral. This spectral overlap is similar to the J in FRET (cf. Equation 5.9)with the important difference that both the fluorescence and the absorption

Table 5.7 Overview of different distance-dependent energy/charge transfer mechanisms.

Transfermechanism

Distance rangea) Distance dependence Comments

Dexter transfer Below about 1 nm �exp(-r)(Equation 5.49)

Energy transfer by electronexchange

Charge transfer Below about 2 nm �exp(-r)(Equation 5.50)

Electron or hole transfer(Marcus theory)

FRET/BRET/CRET/DMPET

About 1–20 nm �1/r6 (Equation 5.7) Energy transfer withoutelectron exchange

NSET About 1–40 nm �1/r4 (Equation 5.48) FRET from a donor to ametal surface

Plasmoncoupling

About 5–80 nm (up to300nm in theory)

�exp(-r)(Equation 5.52)

Size, shape, material, andmedium-dependentwavelength shift

Singlet oxygentransfer

About 10–100nm (up to250nm in theory)

�exp(-r)(Equation 5.53)

Not used for distancemeasurements

a) All values refer to single-step transfer (one donor–acceptor pair). Energy migration or electron/holehopping can lead to larger overall transfer distances.


spectrum are normalized. This means that (in contrast to FRET) the spectral overlapintegral is not dependent on the molar absorptivity (extinction coefficient). r is theedge-to-edge separation between D and A and L is the sum of their van der Waalsradii. As the transfer rate of Dexter transfer decreases exponentially with r, kDTbecomes negligibly small for D–A distances of more than one or two moleculardiameters (about 0.5–1 nm). In contrast to charge transfer (next section), the solventplays a minor role (apart from establishing the collision of D and A via diffusion) forthe transfer. As the constant K cannot be easily related to experimentally determin-able quantities, it is difficult to perform a quantitative experimental characterizationof Dexter transfer. More details about the Dexter theory can be found in photo-chemistry and spectroscopy textbooks [17,18].

5.6.4.2 Charge Transfer (Marcus Theory)Similar to Dexter transfer, charge transfer requires orbital overlap and has thereforeexponential distance dependence. The main difference from the Dexter electronexchange lies in the transfer mechanism, as illustrated in Figure 5.20. Electronexchange is a concerted two-electron transfer, whereas electron transfer (or chargeseparation) requires an electron (or hole) donor and acceptor. Although chargetransfer can occur between molecules in the energetic ground state, an excitedmolecule is both a better reducing agent (or reductant) and a better oxidizing agent(or oxidant) due to a lower ionization potential and a larger electron affinity,respectively [17]. The tunneling of electrons is dependent on the reactants andthe solvent requiring a reorganization of both, which can be divided into innersphere and outer sphere reorganization. The theory of this distance-dependentcharge transfer was developed byMarcus in 1956 [93–95]. The rate of charge transfer(CT) can be written as

Figure 5.20 Different mechanisms forgenerating a ground-state donor and an excitedacceptor (DþA� as shown in the center) byFRET (top left: Coulombic coupling of D� and

A), Dexter transfer (DT, bottom left: electronexchange between D� and A� and A and D) orcharge transfer (top right, CT�: D as electrondonor; bottom right, CTþ: D as hole donor).


kCT ¼ 2p�hJ20exp ½�bðr � r0Þ�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

4plðrÞkBTp � exp �ðDGðrÞ þ lðrÞÞ2

4lðrÞkBT ; ð5:50Þ

where r is the center-to-center distance between D and A, r0 is the distance for whichD and A are in contact, b characterizes the distance dependence of the coupling, J0 isthe contact value of the donor–acceptor electronic coupling matrix element, l(r) isthe distance-dependent reorganization energy, DG(r) is the distance-dependent freeenergy change, and �h and kB are the reduced Planck’s constant and the Boltzmannconstant, respectively [96]. Equation 5.50 contains many distance-dependent param-eters, which shows that a correct treatment of distance dependence can becomplicated and simple exponential models have been applied to fit experimentaldata (e.g., for the distance dependence of electron transfer in DNA):

kCT ¼ AET exp ð�bETðr � r0ÞÞ; ð5:51Þwhere AET is a preexponential factor and bET characterizes the distance dependenceof the transfer. This short section can only give a first glance into the charge transfermechanism. The most important aspects in relation to FRET (the main topic of thisbook) are the short distance range (which can take higher values than Dexter transferdue to the different mechanism of charge transfer) of up to about 2 nm or evenhigher values (in the case of electron hopping, over several redox centers) [97,98] andthe exponential distance dependence. Electron (or charge) transfer has beenintensively studied for chemical and biological systems and details can be foundin textbooks and review articles [17,99–115]. Although the D–A distance is limited,charge transfer has the advantage that it does not require any spectral overlap (incontrary to FRET or Dexter transfer) and therefore one suitable electron donor (oracceptor) can be used to quench several different luminescent molecules formultiplexing purposes. Different biological and chemical sensing concepts usingluminescence quenching of quantum dots by different charge transfer agents havebeen recently developed [116–123]. Such charge transfer sensors allowed theanalysis of simultaneous quenching of eight different semiconductor quantumdots [124].

5.6.4.3 Plasmon CouplingUpon interaction with light, noble metal nanoparticles (most often Au and Ag areused) can display localized surface plasmon resonance (LSPR) leading to broad andstrong absorption or scattering bands in the UV-Vis wavelength region. Theseunique optical properties can be used for many different biosensing applications[125,126]. The resonant frequency (or wavelength) of metal nanoparticles dependson their material, size, shape, and surrounding medium. When two such LSPRnanoparticles are brought into proximity, their plasmon resonances can couple,which results in redshifted absorption or scattering bands of the two coupledparticles. This wavelength shift is dependent on the particle separation and cantherefore be used as spectroscopic or plasmonic ruler [127–133]. The distance-dependent wavelength shift decays approximately exponentially and covers a large


distance range. Interparticle distances of up to about 75 nm have been measured[130] and theoretical calculations predicted wavelength shifts for separations of upto about 300 nm [132]. Jain et al. derived an empirical plasmon ruler equation forthe distance dependence of the wavelength shift, which is applicable for differentparticle sizes [128]:

Dl

l0� A exp � d=D

t

� �; ð5:52Þ

where Dl/l0 is the fractional wavelength shift, A is the magnitude of the fractionalshift, d is the interparticle edge-to-edge separation, D is the particle diameter, andt is the decay constant of the exponential decay. The authors found that t is similarfor different particle materials, sizes, shapes, and medium electric constant (theseparameters change the amplitude A) and takes a value close to t¼ 0.23.Although the distance range of plasmon rulers is significantly larger than for

FRET and there is no dependence on the relative orientation of D and A, there areseveral limitations of this technique for absolute distancemeasurementsmainly dueto size and shape inheterogeneity of the nanoparticles, the relatively large size of thenanoparticles in order to achieve a strong and sensitive scattering signal, and thedependence of plasmon resonance on the refractive index of the medium [130,131].This means (although an empirical plasmon ruler equation exists) that eachplasmon ruler must be carefully calibrated before its application for the determina-tion of distances in unknown systems. Moreover, plasmon rulers cannot provide theinherent ratiometric behavior of FRET (D-quenching and A-sensitization) and arelimited in multiplexed detection.

5.6.4.4 Singlet Oxygen DiffusionAnother possibility to transfer energy over larger distances is to use singlet oxygendiffusion. This technique was developed by Ullman et al. and commercialized underthe brand name LOCI1 (Luminescent Oxygen Channeling Immunoassay, BehringDiagnostics Inc.) [134,135]. The energy transfer is based on the following principle: Ananoparticle chargedwith a photosensitizer (phthalocyanine) produces singlet oxygenupon light excitation around 680nm. The singlet oxygen can diffuse to a nearbysecond nanoparticle that is charged with dioxene (or thioxene) that produces chemi-luminescence upon reaction with singlet oxygen. As the quantum yield of thischemiluminescence is very low, an additional fluorophore [9,10-bisphenylethynylan-thracene (BPEA) or Eu(TTA)3Phen] is added, which results in a much higher overallquantum yield. A homogeneous assay format, for example, two LOCI-nanoparticle-labeled antibodies binding to a specific biomarker, can fix both nanoparticles at adistance, for which singlet oxygen can diffuse from particle one to particle two. Theproduced chemiluminescence intensity is then proportional to the biomarker con-centration. The same principle is used today in the commercial biosensing platformAlphaLISA1 by Perkin Elmer [136] and the detection of different biomarkers usingthis technology canbe found in the literature [137–141].As the concentrationof singletoxygen, which can generate chemiluminescence within the second nanoparticle, is


dependent on diffusion, the distance dependence of the energy transfer (or the singleoxygen concentration) can be calculated by Fick’s first law and is given by [134]

cSO ¼ s

4prDð1þ a=ffiffiffiffiffiffiffiffiffiffiffiD=kD

p Þ exp � r � affiffiffiffiffiffiffiffiffiffiffiD=kD

p" #

; ð5:53Þ

where cSO is the concentration of singlet oxygen at a distance r from the center of thefirst nanoparticle, S is the rate of singlet oxygen formation by the particle, a is theparticle radius, kD is the singlet oxygen decay constant in water, andD is the diffusioncoefficient in water.Due to the relatively large nanoparticles (�150 nm diameter), which need to

contain high amounts of sensitizers and chemiluminescence compounds for thegeneration of intense luminescence signals, this technology is not suited fordistance measurements (or at least – to my knowledge – it has not yet been triedout). Similar to plasmon coupling, LOCI is not inherently ratiometric and needs tobe carefully calibrated.

5.7Summary and Outlook

In summary, FRET is a very powerful technique for the measurement of distancesand concentrations with very high precision and sensitivity on a length scale ofabout 1–20 nm. F€orster’s theory for the relation between spectroscopic data andthe FRETdistance dependence dates back to 1946 and therefore FRET is probablyone of the first optical superresolution techniques. Thanks to the development ofmany types of fuorophores over the last decades, there are numerous possibilitiesof choosing an adequate donor–acceptor pair (cf. Chapters 6 and 14) for thenanometric system of interest (cf. Chapters 6–13). Before planning a FRETexperiment, one should also carefully think about the expected distances andthe (biological) recognition mechanism in which donor and acceptor will beinvolved. FRETcan be characterized by different technologies using luminescencequantum yields, intensities, and lifetimes and both the donor (quenching orphotobleaching) and the acceptor (sensitization or photobleaching) can be ana-lyzed in order to achieve accurate results. When planning the experiments as wellas when analyzing the results, one should always have in mind that there are otherenergy or charge transfer mechanisms that can be responsible for the quenchingof a donor and/or the sensitization of an acceptor, and that there are complemen-tary techniques to enlarge the distance range of FRET. The design of novel energytransfer concepts and probes by efficient combination using the large variety offluorophores and technologies will make FRET (and the other energy/chargetransfer technologies) an equally or even more important and powerful technologyin the future. FRET on, FRET jocks!

5.7 Summary and Outlook j155

Acknowledgment

I would like to thank Dr. Daniel Geißler for his comments on and review of thischapter.

References

1 H€otzer, B., Medintz, I.L., andHildebrandt, N. (2012) Fluorescence innanobiotechnology: sophisticatedfluorophores for novel applications. Small,8 (15), 2297–2326.

2 Clegg, R.M. (1996) Fluorescenceresonance energy transfer, in FluorescenceImaging Spectroscopy and Microscopy (edsX.F. Wang and B. Herman), John Wiley &Sons, Inc., New York, pp. 179–251.

3 Clegg, R.M. (2009) F€orster resonanceenergy transfer: FRETwhat is it, why do it,and how it’s done, in LaboratoryTechniques in Biochemistry and MolecularBiology (ed. T.W.J. Gadella), AcademicPress, Burlington, pp. 1–57.

4 Gadella, T.W.J. (2009) FRETand FLIMTechniques, Elsevier, Amsterdam.

5 Jares-Erijman, E.A. and Jovin, T.M. (2003)FRET imaging. Nature Biotechnology,21 (11), 1387–1395.

6 Jares-Erijman, E.A. and Jovin, T.M. (2006)Imaging molecular interactions in livingcells by FRETmicroscopy. CurrentOpinion in Chemical Biology, 10 (5),409–416.

7 Morrison, L.E. (1988) Time-resolveddetection of energy-transfer: theory andapplication to immunoassays. AnalyticalBiochemistry, 174 (1), 101–120.

8 Sekar, R.B. and Periasamy, A. (2003)Fluorescence resonance energy transfer(FRET) microscopy imaging of live cellprotein localizations. Journal of CellBiology, 160 (5), 629–633.

9 Selvin, P.R. (2000) The renaissance offluorescence resonance energytransfer. Nature Structural Biology, 7 (9),730–734.

10 Stryer, L. (1978) Fluorescence energytransfer as a spectroscopic ruler. AnnualReview of Biochemistry, 47, 819–846.

11 Van der Meer, B.W., Coker, G., and Chen,S.Y.S. (1994) Resonance Energy Transfer:

Theory and Data, John Wiley & Sons, Inc.,New York.

12 Vogel, S.S., Thaler, C., and Koushik, S.V.(2006) Fanciful FRET. Science’s STKE:Signal Transduction KnowledgeEnvironment, 2006 (331), re2.

13 Wu, P.G. and Brand, L. (1994) Resonanceenergy-transfer methods and applications.Analytical Biochemistry, 218 (1), 1–13.

14 Sapsford, K.E., Berti, L., and Medintz, I.L.(2006) Materials for fluorescenceresonance energy transfer analysis:beyond traditional donor–acceptorcombinations. Angewandte Chemie,International Edition, 45 (28), 4562–4588.

15 Lakowicz, J.R. (2006) Principles ofFluorescence Spectroscopy;, 3rd edn,Springer, New York, NY.

16 Periasamy, A. and Day, R.N. (2005)Molecular Imaging: FRET Microscopy andSpectroscopy;, Oxford University Press,New York.

17 Turro, N.J., Ramamurthy, V., and Scaiano,J.C. (2010)Modern MolecularPhotochemistry of Organic Molecules;,University Science Books, Sausalito, Calif.

18 Valeur, B. (2002)Molecular Fluorescence:Principles and Applications;, Wiley-VCHVerlag GmbH, Weinheim.

19 Andrews, D.L. and Demidov, A.A. (1999)Resonance Energy Transfer, John Wiley &Sons, Ltd, Chichester.

20 Braslavsky, S.E., Fron, E., Rodriguez,H.B., Roman, E.S., Scholes, G.D.,Schweitzer, G., Valeur, B., and Wirz, J.(2008) Pitfalls and limitations in thepractical use of Forster’s theory ofresonance energy transfer. Photochemical& Photobiological Sciences, 7 (12),1444–1448.

21 Clegg, R.M. (2006) The history of FRET:from conception through the labors ofbirth, in Reviews in Fluorescence 2006,vol. 3 (eds C.D. Geddes and J.R.


Lakowicz), Springer, New York, p. 1(online resource).

22 F€orster, T. (1946) Energiewanderung undfluoreszenz. Naturwissenschaften, 33 (6),166–175.

23 F€orster, T. (1948) Zwischenmolekulareenergiewanderung und fluoreszenz.Annalen der Physik, 2 (1–2), 55–75.

24 F€orster, T. (1949) Experimentelle undtheoretische untersuchung deszwischenmolekularen €ubergangs vonelektronenanregungsenergie. Zeitschriftf€ur Naturforschung Section A: Journal ofPhysical Sciences, 4 (5), 321–327.

25 F€orster, T. (1951) Fluoreszenz organischerVerbindungen;, Vandenhoeck & Ruprecht,Gottingen.

26 F€orster, T. (1959) 10th Spiers MemorialLecture: transfer mechanisms ofelectronic excitation. Discussions of theFaraday Society, 27, 7–17.

27 F€orster, T. (1965) Delocalized excitationand excitation transfer, inModernQuantum Chemistry, Istanbul Lectures: PartIII: Action of Light and Organic Crystals(ed. O. Sinanoglu), Academic Press,New York, pp. 93–137.

28 Clegg, R.M. (1992) Fluorescenceresonance energy-transfer and nucleic-acids.Methods in Enzymology, 211,353–388.

29 Clegg, R.M., Murchie, A.I.H., Zechel, A.,Carlberg, C., Diekmann, S., and Lilley,D.M.J. (1992) Fluorescence resonanceenergy-transfer analysis of the structureof the 4-way DNA junction. Biochemistry,31 (20), 4846–4856.

30 Clegg, R.M., Murchie, A.I.H., Zechel, A.,and Lilley, D.M.J. (1993) Observing thehelical geometry of double-stranded DNAin solution by fluorescence resonanceenergy-transfer. Proceedings of the NationalAcademy of Sciences of the United States ofAmerica, 90 (7), 2994–2998.

31 Jovin, T.M. and Arndtjovin, D.J. (1989)Luminescence digital imagingmicroscopy. Annual Review ofBiophysics and Biophysical Chemistry, 18,271–308.

32 Raicu, V. (2007) Efficiency of resonanceenergy transfer in homo-oligomericcomplexes of proteins. Journal of BiologicalPhysics, 33 (2), 109–127.

33 Clapp, A.R., Medintz, I.L., Mauro, J.M.,Fisher, B.R., Bawendi, M.G., andMattoussi, H. (2004) Fluorescenceresonance energy transfer betweenquantum dot donors and dye-labeledprotein acceptors. Journal of the AmericanChemical Society, 126 (1), 301–310.

34 Berney, C. and Danuser, G. (2003) FRETor no FRET: a quantitative comparison.Biophysical Journal, 84 (6), 3992–4010.

35 Corry, B., Jayatilaka, D., and Rigby, P.(2005) A flexible approach to thecalculation of resonance energytransfer efficiency between multipledonors and acceptors in complexgeometries. Biophysical Journal, 89 (6),3822–3836.

36 Kenworthy, A.K. (2005) PhotobleachingFRETmicroscopy, inMolecular Imaging:FRET Microscopy and Spectroscopy (eds A.Periasamy and R.N. Day), OxfordUniversity Press, New York, pp. 146–164.

37 Charbonniere, L.J. and Hildebrandt, N.(2008) Lanthanide complexes andquantum dots: a bright wedding forresonance energy transfer. EuropeanJournal of Inorganic Chemistry, 2008 (21),3241–3251.

38 Sillen, A. and Engelborghs, Y. (1998) Thecorrect use of “average” fluorescenceparameters. Photochemistry andPhotobiology, 67 (5), 475–486.

39 Selvin, P.R. (1995) Fluorescenceresonance energy-transfer.Methods inEnzymology, 246, 300–334.

40 Selvin, P.R. (1996) Lanthanide-basedresonance energy transfer. IEEE Journal ofSelected Topics in Quantum Electronics,2 (4), 1077–1087.

41 Selvin, P.R. (2002) Principles andbiophysical applications of lanthanide-based probes. Annual Review of Biophysicsand Biomolecular Structure, 31, 275–302.

42 Selvin, P.R. and Hearst, J.E. (1994)Luminescence energy transfer using aterbium chelate: improvements onfluorescence energy transfer. Proceedingsof the National Academy of Sciences ofthe United States of America, 91 (21),10024–10028.

43 Selvin, P.R., Rana, T., Klein, M.P., andHearst, J.E. (1993) Dark-backgroundfluorescence energy-transfer using

References j157

lanthanide chelates. Biophysical Journal,64 (2), A243–A243.

44 Selvin, P.R., Rana, T.M., and Hearst, J.E.(1994) Luminescence resonance energy-transfer. Journal of the American ChemicalSociety, 116 (13), 6029–6030.

45 Xiao, M. and Selvin, P.R. (2001) Quantumyields of luminescent lanthanide chelatesand far-red dyes measured by resonanceenergy transfer. Journal of the AmericanChemical Society, 123 (29), 7067–7073.

46 B€unzli, J.-C.G. (1989) Luminescentprobes, in Lanthanide Probes in Life,Chemical, and Earth Sciences: Theory andPractice (eds J.-C.G. B€unzli and G.R.Choppin), Elsevier, Amsterdam.

47 B€unzli, J-.C.G. (2004) Luminescentlanthanide probes as diagnostic andtherapeutic tools, inMetal Ions inBiological Systems, Vol 42: Metal Complexesin Tumor Diagnosis and as AnticancerAgents, vol. 42 (eds A. Sigel and H. Sigel),Marcel Dekker Inc., New York, pp. 39–75.

48 B€unzli, J.C.G. (2010) Lanthanideluminescence for biomedical analysesand imaging. Chemical Reviews, 110 (5),2729–2755.

49 B€unzli, J.C.G., Chauvin, A.S., Kim, H.K.,Deiters, E., and Eliseeva, S.V. (2010)Lanthanide luminescence efficiency ineight- and nine-coordinate complexes:role of the radiative lifetime.Coordination Chemistry Reviews, 254(21–22), 2623–2633.

50 Eliseeva, S.V. and B€unzli, J.C.G. (2010)Lanthanide luminescence for functionalmaterials and biosciences. ChemicalSociety Reviews, 39 (1), 189–227.

51 Geißler, D. and Hildebrandt, N. (2011)Lanthanide complexes in FRETapplications. Current Inorganic Chemistry,1, 17–35.

52 Richardson, F.S. (1982) Terbium(III) andEuropium(III) ions as luminescent probesand stains for biomolecular systems.Chemical Reviews, 82 (5), 541–552.

53 Geißler, D., Charbonni�ere, L.J., Ziessel,R.F., Butlin, N.G., L€ohmannsr€oben, H.G.,and Hildebrandt, N. (2010) Quantum dotbiosensors for ultrasensitive multiplexeddiagnostics. Angewandte Chemie,International Edition, 49 (8),1396–1401.

54 Geißler, D., Stufler, S., L€ohmannsr€oben,H.G., and Hildebrandt, N. (2013) Six-colortime-resolved F€orster resonance energytransfer for ultrasensitive multiplexedbiosensing. Journal of the AmericanChemical Society, 135 (3), 1102–1109.

55 Mathis, G. (1993) Rare-earth cryptates andhomogeneous fluoroimmunoassays withhuman sera. Clinical Chemistry, 39 (9),1953–1959.

56 Wegner, K.D., Lanh, P.T., Jennings, T.,Oh, E., Vaibhav, J., Fairclough, S.M.,Smith, J.M., Giovanelli, E., Lequeux, N.,Pons, T., and Hildebrandt, N. (2013)Influence of luminescence quantumyield, surface coating, andfunctionalization of quantum dots on thesensitivity of time-resolved FRETbioassays. ACS Applied Materials andInterfaces, 5 (8), 2881–2892. doi: dx.doi.org/10.1021/am3030728

57 Beyerinck, M.W. (1889) Lephotobacterium luminosum, bact�erielumineuse de la mer du nord. ArchivesN�eederlandaises des Sciences ExactesNaturelles, 13, 401–415.

58 Giard, A. (1889) Sur l’infectionphosphorescente des talitres et autrescrustac�es. Comptes rendus hebdomadairesdes s�eances de l’Acad�emie des Sciences, 7,503–506.

59 Nealson, K.H. and Hastings, J.W. (1979)Bacterial bioluminescence: its control andecological significance.MicrobiologicalReviews, 43 (4), 496–518.

60 Radziszewski, B. (1877) Untersuchungen€uber hydrobenzamid, amarin und lophin.Berichte der Deutschen ChemischenGesellschaft zu Berlin, 10, 70–75.

61 Trautz, M. (1908) Chemilumineszenz.Zeitschrift f€ur Elektrochemie undAngewandte Physikalische Chemie, 14 (33),453–460.

62 Johnson, F.H., Shimomura, O., Saiga, Y.,Gershman, L.C., Reynolds, G.T., andWaters, J.R. (1962) Quantum efficiency ofcypridina luminescence, with a note onthat of aequorea. Journal of Cellular andComparative Physiology, 60 (1), 85–103.

63 Morin, J.G. and Hastings, J.W. (1971)Energy transfer in a bioluminescentsystem. Journal of Cellular Physiology,77 (3), 313–318.


64 White, E.H. and Roswell, D.F. (1967)Intramolecular energy transfer inchemiluminescence. Journal of theAmerican Chemical Society, 89 (15),3944–3945.

65 Huang, X.Y. and Ren, J.C. (2012)Nanomaterial-based chemiluminescenceresonance energy transfer: a strategy todevelop new analytical methods. Trends inAnalytical Chemistry, 40, 77–89.

66 Pfleger, K.D.G. and Eidne, K.A. (2006)Illuminating insights into protein–proteininteractions using bioluminescenceresonance energy transfer (BRET). NatureMethods, 3 (3), 165.

67 Xia, Z.Y. and Rao, J.H. (2009) Biosensingand imaging based on bioluminescenceresonance energy transfer. CurrentOpinion in Biotechnology, 20 (1), 37–44.

68 Grayeski, M.L. (1987)Chemiluminescence analysis. AnalyticalChemistry, 59 (21), A1243.

69 Kojima, R., Takakura, H., Ozawa, T., Tada,Y., Nagano, T., and Urano, Y. (2013)Rational design and development of near-infrared-emitting firefly luciferinsavailable in vivo. Angewandte Chemie,International Edition, 52 (4), 1175–1179.

70 Liu, X.Q., Niazov-Elkan, A., Wang, F.A.,and Willner, I. (2013) Switching photonicand electrochemical functions of aDNAzyme by DNA machines. NanoLetters, 13 (1), 219–225.

71 Bhowmick, S., Saini, S., Shenoy, V.B., andBagchi, B. (2006) Resonance energytransfer from a fluorescent dye to a metalnanoparticle. Journal of Chemical Physics,125 (18), 181102.

72 Carminati, R., Greffet, J.J., Henkel, C.,and Vigoureux, J.M. (2006) Radiative andnon-radiative decay of a single moleculeclose to a metallic nanoparticle. OpticsCommunications, 261 (2), 368–375.

73 Klimov, V.V., Ducloy, M., and Letokhov,V.S. (1996) Radiative frequency shift andlinewidth of an atom dipole in the vicinityof a dielectric microsphere. Journal ofModern Optics, 43 (11), 2251–2267.

74 Klimov, V.V., Ducloy, M., and Letokhov,V.S. (2001) Spontaneous emissionof an atom in the presence ofnanobodies. Quantum Electronics, 31 (7),569–586.

75 Moroz, A. (2010) Non-radiative decay of adipole emitter close to a metallicnanoparticle: importance of higher-ordermultipole contributions. OpticsCommunications, 283 (10), 2277–2287.

76 Persson, B.N.J. and Lang, N.D. (1982)Electron–hole-pair quenching of excitedstates near a metal. Physical Review B,26 (10), 5409–5415.

77 Chen, Y., O’Donoghue, M.B., Huang,Y.-F., Kang, H., Phillips, J.A., Chen, X.,Estevez, M.C., Yang, C.J., and Tan, W.(2010) A surface energy transfernanoruler for measuring binding sitedistances on live cell surfaces. Journal ofthe American Chemical Society, 132 (46),16559–16570.

78 Griffin, J., Singh, A.K., Senapati, D.,Rhodes, P., Mitchell, K., Robinson, B.,Yu, E., and Ray, P.C. (2009) Size- anddistance-dependent nanoparticle surface-energy transfer (NSET) method forselective sensing of hepatitis C virus RNA.Chemistry: A European Journal, 15 (2),342–351.

79 Jennings, T.L., Schlatterer, J.C., Singh,M.P., Greenbaum, N.L., and Strouse, G.F.(2006) NSETmolecular beacon analysis ofhammerhead RNA substrate binding andcatalysis. Nano Letters, 6 (7), 1318–1324.

80 Jennings, T.L., Singh, M.P., and Strouse,G.F. (2006) Fluorescent lifetimequenching near d ¼ 1.5 nm goldnanoparticles: probing NSET validity.Journal of the American Chemical Society,128 (16), 5462–5467.

81 Seelig, J., Leslie, K., Renn, A., Kuhn, S.,Jacobsen, V., van de Corput, M., Wyman,C., and Sandoghdar, V. (2007)Nanoparticle-induced fluorescencelifetime modification as nanoscopic ruler:demonstration at the single moleculelevel. Nano Letters, 7 (3), 685–689.

82 Singh, M.P., Jennings, T.L., and Strouse,G.F. (2009) Tracking spatial disorder in anoptical ruler by time-resolved NSET.Journal of Physical Chemistry B, 113 (2),552–558.

83 Singh, M.P. and Strouse, G.F. (2010)Involvement of the LSPR spectral overlapfor energy transfer between a dye and Aunanoparticle. Journal of the AmericanChemical Society, 132 (27), 9383–9391.

References j159

84 Yun, C.S., Javier, A., Jennings, T., Fisher,M., Hira, S., Peterson, S., Hopkins, B.,Reich, N.O., and Strouse, G.F. (2005)Nanometal surface energy transfer inoptical rulers, breaking the FRET barrier.Journal of the American Chemical Society,127 (9), 3115–3119.

85 Gueroui, Z. and Libchaber, A. (2004)Single-molecule measurements of gold-quenched quantum dots. Physical ReviewLetters, 93 (16), 166108.

86 Ko, S.H., Du, K., and Liddle, J.A. (2013)Quantum-dot fluorescence lifetimeengineering with DNA origamiconstructs. Angewandte Chemie,International Edition, 52 (4), 1193–1197.

87 Li, M., Cushing, S.K., Wang, Q., Shi, X.,Hornak, L.A., Hong, Z., and Wu, N.(2011) Size-dependent energy transferbetween CdSe/ZnS quantum dots andgold nanoparticles. Journal of PhysicalChemistry Letters, 2 (17), 2125–2129.

88 Pons, T., Medintz, I.L., Sapsford, K.E.,Higashiya, S., Grimes, A.F., English, D.S.,and Mattoussi, H. (2007) On thequenching of semiconductor quantumdot photoluminescence by proximalgold nanoparticles. Nano Letters, 7 (10),3157–3164.

89 Zhang, J., Badugu, R., and Lakowicz, J.R.(2008) Fluorescence quenching of CdTenanocrystals by bound gold nanoparticlesin aqueous solution. Plasmonics, 3 (1),3–11.

90 Zhang, X., Marocico, C.A., Lunz, M.,Gerard, V.A., Gun’ko, Y.K., Lesnyak, V.,Gaponik, N., Susha, A.S., Rogach, A.L.,and Bradley, A.L. (2012) Wavelength,concentration, and distance dependenceof nonradiative energy transfer to a planeof gold nanoparticles. ACS Nano, 6 (10),9283–9290.

91 Saraswat, S., Desireddy, A., Zheng, D.,Guo, L., Lu, H.P., Bigioni, T.P., andIsailovic, D. (2011) Energy transfer fromfluorescent proteins to metalnanoparticles. Journal of PhysicalChemistry C, 115 (35), 17587–17593.

92 Dexter, D.L. (1953) A theory of sensitizedluminescence in solids. Journal ofChemical Physics, 21 (5), 836–850.

93 Marcus, R.A. (1956) On the theory ofoxidation–reduction reactions involving

electron transfer: I. The Journal ofChemical Physics, 24 (5), 966–978.

94 Marcus, R.A. (1956) Electrostatic freeenergy and other properties of stateshaving nonequilibrium polarization: I.The Journal of Chemical Physics, 24 (5),979–989.

95 Marcus, R.A. (1964) Chemical andelectrochemical electron-transfer theory.Annual Review of Physical Chemistry, 15,155–196.

96 Tavernier, H.L. and Fayer, M.D. (2000)Distance dependence of electron transferin DNA: the role of the reorganizationenergy and free energy. Journal ofPhysical Chemistry B, 104 (48),11541–11550.

97 Gray, H.B. and Winkler, J.R. (2005) Long-range electron transfer. Proceedings of theNational Academy of Sciences of the UnitedStates of America, 102 (10), 3534–3539.

98 Boxer, S.G. (1990) Mechanisms of long-distance electron-transfer in proteins:lessons from photosynthetic reactioncenters. Annual Review of Biophysics andBiophysical Chemistry, 19, 267–299.

99 Barbara, P.F., Meyer, T.J., and Ratner,M.A. (1996) Contemporary issues inelectron transfer research. Journal ofPhysical Chemistry, 100 (31), 13148–13168.

100 Benniston, A.C. and Harriman, A. (2006)Charge on the move: how electron-transfer dynamics depend on molecularconformation. Chemical Society Reviews,35 (2), 169–179.

101 Burshtein, A.I. (2000) Unified theoryof photochemical charge separation.Advances in Chemical Physics, 114,419–587.

102 Farver, O. and Pecht, I. (2011) Electrontransfer in blue copper proteins.Coordination Chemistry Reviews, 255 (7–8),757–773.

103 Fukuzumi, S., Honda, T., and Kojima, T.(2012) Structures and photoinducedelectron transfer of protonated complexesof porphyrins andmetallophthalocyanines. CoordinationChemistry Reviews, 256 (21–22),2488–2502.

104 Heckmann, A. and Lambert, C. (2012)Organic mixed-valence compounds: aplayground for electrons and holes.


Angewandte Chemie, International Edition,51 (2), 326–392.

105 Jeuken, L.J.C. (2003) Conformationalreorganisation in interfacial proteinelectron transfer. Biochimica et BiophysicaActa, 1604 (2), 67–76.

106 Marcus, R.A. (2006) Enzymatic catalysisand transfers in solution: I. Theory andcomputations, a unified view. Journal ofChemical Physics, 125 (19), 194504.

107 Marcus, R.A. and Sutin, N. (1985)Electron transfers in chemistry andbiology. Biochimica et Biophysica Acta,811 (3), 265–322.

108 Mayer, J.M., Rhile, I.J., Larsen, F.B.,Mader, E.A., Markle, T.F., and DiPasquale,A.G. (2006) Models for proton-coupledelectron transfer in photosystem II.Photosynthesis Research, 87 (1), 3–20.

109 Moser, C.C., Anderson, J.L.R., andDutton, P.L. (2010) Guidelines fortunneling in enzymes. Biochimica etBiophysica Acta, 1797 (8), 1573–1586.

110 Adams, D.M., Brus, L., Chidsey, C.E.D.,Creager, S., Creutz, C., Kagan, C.R.,Kamat, P.V., Lieberman, M., Lindsay, S.,Marcus, R.A., Metzger, R.M., Michel-Beyerle, M.E., Miller, J.R., Newton, M.D.,Rolison, D.R., Sankey, O., Schanze, K.S.,Yardley, J., and Zhu, X.Y. (2003) Chargetransfer on the nanoscale: current status.Journal of Physical Chemistry B, 107 (28),6668–6697.

111 Bagchi, B. (1989) Dynamics of solvationand charge-transfer reactions in dipolarliquids. Annual Review of PhysicalChemistry, 40, 115–141.

112 Bredas, J.L., Beljonne, D., Coropceanu, V.,and Cornil, J. (2004) Charge-transfer andenergy-transfer processes in pi-conjugated oligomers and polymers: amolecular picture. Chemical Reviews,104 (11), 4971–5003.

113 Grabowski, Z.R., Rotkiewicz, K., andRettig, W. (2003) Structural changesaccompanying intramolecular electrontransfer: focus on twisted intramolecularcharge-transfer states and structures.Chemical Reviews, 103 (10), 3899–4031.

114 Kurreck, H. and Huber, M. (1995) Modelreactions for photosynthesis-photoinduced charge and energy-transferbetween covalently-linked porphyrin and

quinone units. Angewandte Chemie,International Edition in English, 34 (8),849–866.

115 Schuster, G.B. (2000) Long-range chargetransfer in DNA: transient structuraldistortions control the distancedependence. Accounts of ChemicalResearch, 33 (4), 253–260.

116 Algar, W.R. and Krull, U.J. (2010) Newopportunities in multiplexed opticalbioanalyses using quantum dots anddonor–acceptor interactions. Analyticaland Bioanalytical Chemistry, 398 (6),2439–2449.

117 Algar, W.R., Tavares, A.J., and Krull, U.J.(2010) Beyond labels: a review of theapplication of quantum dots as integratedcomponents of assays, bioprobes, andbiosensors utilizing optical transduction.Analytica Chimica Acta, 673 (1), 1–25.

118 Callan, J.F., Mulrooney, R.C., Kamila, S.,and McCaughan, B. (2008) Anion sensingwith luminescent quantum dots: amodular approach based on thephotoinduced electron transfer (PET)mechanism. Journal of Fluorescence, 18 (2),527–532.

119 Fan, C.H., Plaxco, K.W., and Heeger, A.J.(2005) Biosensors based on binding-modulated donor–acceptor distances.Trends in Biotechnology, 23 (4), 186–192.

120 Sandros, M.G., Gao, D., and Benson,D.E. (2005) A modular nanoparticle-based system for reagentless smallmolecule biosensing. Journal of theAmerican Chemical Society, 127 (35),12198–12199.

121 Stewart, M.H., Huston, A.L., Scott, A.M.,Efros, A.L., Melinger, J.S., Gemmill, K.B.,Trammell, S.A., Blanco-Canosa, J.B.,Dawson, P.E., and Medintz, I.L. (2012)Complex Forster energy transferinteractions between semiconductorquantum dots and a redox-active osmiumassembly. ACS Nano, 6 (6), 5330–5347.

122 Yildiz, I., Tomasulo, M., and Raymo, F.M.(2006) A mechanism to signal receptor–substrate interactions with luminescentquantum dots. Proceedings of the NationalAcademy of Sciences of the United States ofAmerica, 103 (31), 11457–11460.

123 Yildiz, I., Tomasulo, M., and Raymo, F.M.(2008) Electron and energy transfer

References j161

mechanisms to switch the luminescenceof semiconductor quantum dots.Journal of Materials Chemistry, 18 (46),5577–5584.

124 Med i n t z , I . L . , Fa r r e l l , D ., Sus u mu , K . ,Tr amme ll, S.A ., D escha mps, J.R.,Brunel, F .M ., Da ws on, P.E., andMat tou ssi , H. (2009) Multipl ex charge-transfer interactions between quantumd ot s and peptide-bridged rut h eniumc o mp l e xe s . Analytical Chemistr y, 81 (12),4831– 48 39.

125 Aslan, K., Lakowicz, J.R., and Geddes,C.D. (2005) Plasmon light scattering inbiology and medicine: new sensingapproaches, visions and perspectives.Current Opinion in Chemical Biology, 9 (5),538–544.

126 Special Issue on Plasmonics (2004).Journal of Fluorescence, 14 (4).

127 Jain, P.K. and El-Sayed, M.A. (2008)Surface plasmon coupling and itsuniversal size scaling in metalnanostructures of complex geometry:elongated particle pairs and nanospheretrimers. Journal of Physical Chemistry C ,112 (13), 4954– 4960.

128 Jain, P.K., Huang, W.Y., and El-Sayed,M.A. (2007) On the universal scalingbehavior of the distance decay of plasmoncoupling in metal nanoparticle pairs: aplasmon ruler equation. Nano Letters,7 (7), 2080–2088.

129 Quinten, M. (1998) Optical response ofaggregates of clusters with differentdielectric functions. Applied Physics B:Lasers and Optics, 67 (1), 101–106.

130 Reinhard, B.M., Siu, M., Agarwal, H.,Alivisatos, A.P., and Liphardt, J. (2005)Calibration of dynamic molecular rulebased on plasmon coupling between goldnanoparticles. Nano Letters, 5 (11),2246–2252.

131 S €onnichsen, C., Reinhard, B.M., Liphardt,J., and Alivisatos, A.P. (2005) A molecularruler based on plasmon coupling of singlegold and silver nanoparticles. NatureBiotechnology, 23 (6), 741–745.

132 Su, K.H., Wei, Q.H., Zhang, X., Mock,J.J., Smith, D.R., and Schultz, S. (2003)Interparticle coupling effects on plasmonresonances of nanogold particles. NanoLetters, 3 (8), 1087–1090.

133 Tabor, C., Murali, R., Mahmoud, M., andEl-Sayed, M.A. (2009) On the use ofplasmonic nanoparticle pairs as aplasmon ruler: the dependence of thenear-fi eld dipole plasmon coupling onnanoparticle size and shape. Journal ofPhysical Chemistry A, 113 (10), 1946–1953.

134 Ullman, E.F., Kirakossian, H., Singh, S.,Wu, Z.P., Irvin, B.R., Pease, J.S.,Switchenko, A.C., Irvine, J.D., Dafforn,A., Skold, C.N., and Wagner, D.B. (1994)Luminescent oxygen channelingimmunoassay: measurement of particlebinding-kinetics by chemiluminescence.Proceedings of the National Academy ofSciences of the United States of America,91 (12), 5426–5430.

135 Ullman, E.F., Kirakossian, H.,Switchenko, A.C., Ishkanian, J., Ericson,M., Wartchow, C.A., Pirio, M., Pease, J.,Irvin, B.R., Singh, S., Singh, R., Patel, R.,Dafforn, A., Davalian, D., Skold, C., Kurn,N., and Wagner, D.B. (1996) Luminescentoxygen channeling assay (LOCI(TM)):sensitive, broadly applicablehomogeneous immunoassay method.Clinical Chemistry, 42 (9), 1518–1526.

136 Elmer, P. (2013) http://www.perkinelmer.com/FR/Catalog/Category/ID/AlphaTech,March 2013.

137 Eglen, R.M., Reisine, T., Roby, P.,Rouleau, N., Illy, C., Bosse, R., andBielefeld, M. (2008) The use ofAlphaScreen technology in HTS: currentstatus. Current Chemical Genomics, 1,2–10.

138 Leister, K.P., Huang, R., Goodwin, B.L.,Chen, A., Austin, C.P., and Xia, M. (2011)Two high throughput screen assays formeasurement of TNF-alpha in THP-1cells. Current Chemical Genomics, 5,21–29.

139 Mechaly, A., Cohen, N., Weiss, S., andZahavy, E. (2013) A novel homogeneousimmunoassay for anthrax detection basedon the AlphaLISA method: detection of B.anthracis spores and protective antigen(PA) in complex samples. Analytical andBioanalytical Chemistry, 405 (12), 3965–3972.

140 Waller, H., Chatterji, U., Gallay, P.,Parkinson, T., and Targett-Adams, P.(2010) The use of AlphaLISA technology


http://www.perkinelmer.com/FR/Catalog/Category/ID/AlphaTech

http://www.perkinelmer.com/FR/Catalog/Category/ID/AlphaTech

to detect interaction between hepatitis Cvirus-encoded NS5A and cyclophilin A.Journal of Virological Methods, 165 (2),202–210.

141 Zhang, Y., Huang, B., Zhang, J., Wang, K.,and Jin, J. (2012) Development of a

homogeneous immunoassay based on theAlphaLISA method for the detection ofchloramphenicol in milk, honey and eggs.Journal of the Science of Food andAgriculture, 92 (9), 1944–1947.

References j163

Date post:	23-Dec-2016
Category:	Documents
Upload:	niko
View:	231 times
Download:	4 times

FRET - Förster Resonance Energy Transfer || How to Apply FRET: From Experimental Design to Data...

Documents