Chapter 8 - Spectral imaging and its use in the ...static.sif.it/SIF/resources/public/files/va2011/vogel_0718.pdfFo¬rster resonance energy transfer (FRET) imaging is a form of microscopy

CHAPTER 8

Spectral imaging and its use in

the measurement of Forster resonance

energy transfer in living cells

Steven S. Vogel,1 Paul S. Blank,2 Srinagesh V. Koushik,1

and Christopher Thaler1

1National Institute on Alcohol Abuse and Alcoholism,National Institutes of Health, 5625 Fishers Lane,

Rockville, Maryland 208922National Institute of Child Health and Human Development,

National Institutes of Health, 10 Center Drive Bldg. 10Bethesda, Maryland 20892

Forster resonance energy transfer (FRET) imaging is a form ofmicroscopy that allows the visualization of interaction between twofluorophores on a 1–10 nm scale. FRET imaging is based on mea-suring subtle changes in fluorescence that arises from nonradiativeenergy transfer from a ‘‘donor’’ fluorophore to an ‘‘acceptor.’’Interest in applying FRET to image molecular interactions insideliving cells has been growing, but has been hampered by technicalproblems encountered when accurate and precise measurements offluorescence is necessary. Ironically, a requirement for FRET tooccur, spectral overlap of donor emission with acceptor absorptionmakes it technically diYcult to accurately and eYciently measurethe fluorescent signals required to quantify FRET. Spectral imag-ing is a relatively new form of fluorescence light microscopy where

DOI: 10.1016/S0075-7535(08)00008-9

Laboratory Techniques in Biochemistry and Molecular Biology, Volume 33FRET and FLIM TechniquesT. W. J. Gadella (Editor)

Author's personal copyAuthor's personal copy

a fluorescent emission spectrum is recorded at each location in animage. Many of the technical problems encountered when acquir-ing FRET images can be eliminated by analyzing the data encodedin spectral images with an image analysis algorithm called linearunmixing. In this chapter, we will cover the theory of linear unmix-ing of spectral images, and describe how it can be used to acquireaccurate FRET measurements.

8.1. Introduction

Forster resonance energy transfer (FRET) is a physical phenomenain which photon energy absorbed by a fluorophore is transferred bynonradiative dipole–dipole coupling to a nearby chromophore [1].While this arcane phenomenon was first observed in the 1920s,there has been a reemergence of interest in FRET driven in partby the need for a microscope based assay for monitoring protein–protein interactions inside living cells. Commercial interest inFRET has also grown, driven by the conviction that FRET canbe used eVectively as the basis for developing new biosensors.Spectral imaging microscopy [2–4] is a relatively new form ofmultidimensional fluorescence microscopy that can potentiallyeliminate several of the obstacles one encounters in FRET imaging[5–7]. In spectral imaging, each picture element or pixel maps to aspecific Cartesian coordinate within a sample and encodes thecomplex spectrum emitted from the population of fluorophorespresent at each specific location. Compared with more convention-al forms of fluorescence microscopy in which the emission intensityis detected through a filter, spectral imaging holds the promise ofpotentially revealing information about the abundance and identityof the fluorescent species present. Vis‐a‐vis FRET, the emissionspectrum of a donor should be attenuated and the emission spec-trum of acceptors should be potentiated as energy transfer in-creases. Moreover, spectral imaging has the potential to detect

352 FRET AND FLIM TECHNIQUES

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these FRET related spectral changes in a photon eYcient manner,which is critical for eVective live‐cell imaging. One goal of thischapter is to describe how spectral imaging can be used to detectand measure FRET and to convey the strengths and weaknesses ofthe approach. FRET is not a rare event in biology as it is funda-mental to the process of photosynthesis [8]. FRET can also occur,often unintentionally, upon the introduction of fluorophores into abiological milieu, particularly into crowded environments such asin membranes [9]. Fluorophore tagged membrane proteins, that arenot commonly thought to specifically interact, often undergo non-specific FRET by virtue of their close proximity [10, 11]. Thus, itshould be clear that the apparent abundance of fluorophores dis-cerned by both conventional light microscopy through emissionfilters, as well as spectral imaging will be erroneous if energy tran-sfer is occurring [12]. We call this the FRET problem. Accordingly,a second goal of this chapter will be to convey an appreciation ofthis fundamental problem in quantitative fluorescence microscopy,and to outline how spectral imaging can be used to measure thetrue abundance of fluorophores, even when FRET is occurring.Finally, we wish to state that this chapter is not intended to be areview of the literature addressing spectral imaging or how it hasbeen used to measure FRET, rather, our goal is to convey a moreintuitive appreciation of the spectral FRET method, the strengthsand weaknesses of the approach, as well as to identify some of thecurrent technical limitations that we are hopeful will soon be over-come, perhaps by some of our readers.

8.2. Understanding spectral imaging

As mentioned above, spectral imaging microscopy is a form ofmultidimensional fluorescent microscopy where a fluorescent emis-sion spectrum is acquired at each coordinate location in the sample.Thismode of imaging has been implemented for wide field, confocal,and two‐photon laser scanning microscopy, and several excellent

Ch. 8 SPECTRAL FRET IMAGING 353


reviews on spectral imaging microscopy have been published[2, 4, 13–18]. To illustrate and contrast spectral imaging with con-ventional filter‐based imaging, we imaged three glass capillaries(Fig. 8.1). The first capillary (from top to bottom) contained Ceru-lean (10 mM) [19], a cyan spectral variant of green‐fluorescentprotein (GFP); the second contained Venus (10 mM) [20], a yellowspectral variant of GFP; and the third capillary contained a mix-ture of Cerulean and Venus at unknown concentrations. The mo-nomeric variant of Cerulean and Venus were used to avoidnonspecific interactions between these proteins [21]. Two‐photonmicroscopy with 900 nm infrared excitation light was used to ac-quire a spectral image of the three capillaries (Fig. 8.1). In panel A,we see 32 individual images of the capillaries. In the implementationof spectral imaging used to acquire these images (a Zeiss 510NLO/META), the fluorescence emitted from a sample is spectrallydispersed by a diVraction grating and projected onto a 32‐nodephotomultiplier tube array. Each of the images depicted in panel Awas acquired from a single node of this photomultiplier array andrepresents a !10–11 nm spectral slice of the emission spectrum.The center wavelength is indicated in yellow in the upper left cornerof each image. You can see that none of the three capillariescontained samples that emit below 446 or above 596 nm. Between457 and 510 nm, the top and bottom capillaries are emitting but notthe center. Between 521 and 596 nm, all three capillaries emit. Theemission wavelength and intensity information encoded in the stackof images depicted in Fig. 8.1A can be distilled down into a color‐coded ‘spectral image’ shown in panel B. This image depicts howthe sample would appear if observed by the human eye. The color ateach pixel is based on the weighted mean of the emitted photonwavelengths, and the intensity is based on the number of photonsdetected at that pixel location. In panel C, we show the emissionspectra for regions of interest (ROI) centered over the Cerulean capil-lary (blue solid line), Venus capillary (yellow solid line), the mixturecapillary (green dashed line), and from an ROI centered over aregion that did not have a capillary (background, red dotted line).



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Fig. 8.1. Spectral Imaging. Panel A shows 32 individual images that comprise aspectral imageof three capillaries containing fromtop tobottom10 mMCerulean,10 mM Venus, and a mixture of Cerulean and Venus of unknown stoichiometryacquired on a Zeiss 510 META/NLO laser scanning confocal microscope with900 nm two‐photon excitation. Each image was acquired from a single node of a32 node photomultiplier array, and represents sequential !10 nm portion of theemission spectrum that are detected on each node after being dispersed by adiVraction grating. The emission wavelength measured by each node is indicatedin yellow. Panel B shows a color‐coded representation of the images shown inpanel A. The color (wavelength) is the intensity weighted average of the 32individual emission wavelengths, and the brightness is proportional to the totalnumber of photons detected at each pixel. Each capillary is labeled as is abackground region. Size bar is 100 mm.PanelC shows emission spectra calculatedmeasured from ROI centered over the Cerulean capillary, Venus capillary,

mixture capillary or from a background region.


It is useful to monitor the background spectrum because it canindicate if there is any back‐scattered excitation light or higher‐order scattering reaching the detector [12], as well as an indicator ofthe presence of any autofluorescence in a sample. These spectrawere calculated from the mean pixel intensity of the images in panel1A for the specific ROI regions indicated, and plotted as a functionof wavelength.

An important control for any quantitative spectral imagingexperiment is to compare emission spectra of pure fluorophoresamples obtained on the microscope with spectra obtained usinga fluorimeter [22]. DiVerences between spectra measured with aspectral microscope and those obtained using a fluorimeter canoccur due to (1) the presence of filters or dichroic beam splittersin the emission light path, (2) the spectral throughput of the objec-tive and other optics in the light‐path, (3) wavelength aliasing dueto the limited bandwidth of the spectral detector, (4) misalignmentof the dispersed emission beam and the spectral detector, and asmentioned previously, (5) contamination by backscattered excita-tion light including higher‐order scattering. The impact of thesepotential artifacts must be considered when quantitative spectralimaging is desired. Because the emission spectra of the capillariescontaining only Cerulean or Venus shown in panel C closelymatched the emission spectra obtained for these samples asmeasured on conventional nonimaging fluorimeters, these artifactscould be eliminated from further consideration.

One of the major advantages of spectral imaging can be appre-ciated by noting that the emission spectrum of Cerulean inFig. 8.1C completely overlaps the emission spectrum of Venus. Atthe excitation wavelengths used here, conventional filter‐based im-aging can never isolate Venus emission from Cerulean emission. Toquantify the abundance of Venus in the presence of Cerulean usingfilter‐based technology requires the existence and use of excitationwavelengths that excite Venus without exciting Cerulean. As weshall see shortly, this is not a requirement for quantifying Venusand Cerulean using spectral imaging.



Next, we will explore how spectral images change as a function ofexcitation wavelength. In Fig. 8.2A, we see spectral images of thesame three capillaries depicted in Fig. 8.1 but nowobtainedwith 820,900, 920, and 940 nm two‐photon excitation. With 820 nm excita-tion Cerulean is readily excited while Venus is poorly excited. Incontrast, with 940 nm excitation, Cerulean is poorly excited whileVenus is excited well. With 900 and 920 nm excitation, intermediateexcitation behavior is observed. The Cerulean capillary emittedblue fluorescence at all excitation wavelengths. Similarly, themiddle Venus capillary appeared green at all excitation wavelengths.

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Fig. 8.2. Spectral Images can change with excitation wavelength. Spectralimages of the same three capillaries depicted in Fig. 8.1 were imaged at fourdiVerent excitation wavelengths: 820, 900, 920, and 940 nm (A). Normalizedemission spectra (at all four excitation wavelengths) from ROI’s centered overthe Cerulean capillary (B), the Venus capillary (C), and the mixture capillary(D) are co‐plotted. Note that the color and normalized emission spectra donot change for a sample containing a single fluorophore. In contrast the colorand normalized spectrum changed as a function of excitation wavelength in

the capillary containing both fluorophores.



In contrast, the color of the Cerulean–Venus mixture capillary (bot-tom) appeared blue at 820 nm, blue‐green at 900 and 920 nm, andgreen at 940 nm. The normalized emission spectra of the Cerulean(Fig. 8.2 B) and Venus (Fig. 8.2 C) capillaries did not change as afunction of excitation wavelength, yielding the expected characteris-tic spectrum of these fluorophores. In stark contrast, the normalizedemission spectra of the Cerulean–Venus mixture capillary was di-Verent at each excitation wavelength used (Fig. 8.2 D) with subtlediVerences between the emission spectra observedwith 820, 900, and920 nm excitation, and a dramatic diVerence with 940 nm excitation.These diVerences can be understood if one considers that while theshape of the emission spectrum of a fluorophore is typically not afunction of excitation wavelength, the emission intensity of a fluor-ophore is a function of excitation wavelength [23]. The emissionintensity is also a function of the fluorophore’s abundance and theintensity of the excitation light source [23]. With regard to theCerulean and Venus mixture capillary shown in Fig. 8.2, the con-centrations of the two fluorophores and their relative abundancewere obviously the same at each excitation wavelength (they areafter all the same sample). In this demonstration, however, excita-tion energy was not the same at each excitation wavelength (thoughthe excitation energy for the mixture capillary was the same for theCerulean and Venus capillaries), and it is known that Cerulean andVenus have significantly diVerent absorption spectra [19, 20] andtwo‐photon absorption cross sections [12]. At aVenus concentrationfar less than 1–3 mM, there should not be any appreciable FRETbetween Cerulean ‘‘donors’’ and Venus ‘‘acceptors’’ as a result ofmolecular crowding [23]. Thus, for the mixture capillary, the com-plex spectrum observed should be a linear sum of the Cerulean andVenus emission spectrum (a function of excitation light intensityand their absorption coeYcients at each excitation wavelength)weighted by their respective abundance. Amathematical formalism,called linear unmixing, based on this idea of the abundance‐weightedsummation of individual fluorophore spectra, can be used to



measure the concentration of individual fluorophores in a mixedpopulation, but only if energy transfer between diVerent fluoro-phores is not occurring [12, 24].

8.2.1. Linear unmixing and its limitations

As mentioned previously, the complex emission spectrum F i(l) ofsamples containing multiple fluorophores is assumed to be thelinear sum of individual component spectra F1(l), F2(l), F3(l),weighted by their abundance x1, x2, x3. Let F

i1ðlÞ and Fi

2ðlÞ be thereference emission spectra of pure samples of fluorophore (e.g.,Cerulean and Venus). The term reference emission spectra is usedbecause these spectra describe the emission at excitation wave-length liex of a defined concentration of fluorophore (e.g.,10 mM)acquired using the same excitation light intensity as was used toacquire an emission spectra of an unknown sample mixture. Underthese conditions, the shape and magnitude of the fluorophoremixture spectra will be:

FiðlÞ ¼ x1Fi1ðlÞ þ x2F

i2ðlÞ þ x3F

i3ðlÞ þ . . . ð8:1Þ

If reference emission spectra of a set of pure fluorophores areavailable, and if an emission spectrum of an unknown mixture ofany combination of these fluorophores is acquired under the sameconditions, this equation can be used to determine the abundanceof the diVerent fluorophores in the mixture. The use of this equa-tion to determine the abundance of the fluorophores present iscalled linear unmixing. To illustrate the basis of linear unmixing,we will first use this equation to analyze the emission spectra of themix capillary containing an unknown mixture of Cerulean andVenus depicted in Fig. 8.1. The unmixing approach we describewill utilize reasonable guesses for the values of x1 (representing theabundance of Cerulean) and x2 (representing the abundance of



Venus) in the linear unmixing equation, and then use these guessesto generate spectra to compare with actual data. In Fig. 8.3A, wesee a 10 mM reference emission spectrum of Cerulean and Venus, aswell as a spectrum of our unknown mixture. All three spectra wereacquired at the same excitation wavelength (900 nm) at the samelaser intensity. Thus, all of the requirements for linear unmixingoutlined above have been met. In Fig. 8.3 B, the linear unmixingequation is used to model complex emission spectra of mixturescontaining 10 mM Venus and either 14 mM Cerulean (blue dashedtrace), 10 mMCerulean (white dotted trace), or 6 mMCerulean (reddashed trace). These models can be compared with the actualemission spectra from the mixture capillary (green circles). Themodel represented by the white trace is the closest match to thedata set, particularly below 500 nm. Next, we explore models wherewe hold the Cerulean concentration at 10 mM and vary the Venusconcentration (Fig. 8.3 B). In the blue trace, Venus is held at10 mM; in the white trace, it has been reduced to 6 mM; and in thered trace, it has been reduced further to 2 mM. We can now see thatwhile all three models are reasonable matches to the data, the bluemodel overestimates emissions between 500 and 600 nm and the redmodel underestimates emissions from this same spectral region. Incontrast, the white model (10 mM Cerulean, 6 mM Venus) matchedthe experimental data well.

In this example of linear unmixing, the value x2 was first heldconstant while the value of x1 was varied. Next, the value of x1 washeld constant and the value of x2 was varied. This illustration wasused to provide an intuitive example of how linear unmixing findsvalues for the abundance of each fluorophore that are consistentwith a given complex emission spectrum. In practice, linear unmix-ing software utilizes curve fitting algorithms [25] to rapidly findvalues of x1, x2,. . . which can generate spectra that best match theexperimental data. These calculations are repeated for every pixelin an image. Ultimately, separate images are created representingthe abundance of each fluorophore present. An example set ofimages generated by linear unmixing of the data set presented in



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Fig. 8.1 is shown in Fig. 8.4. In panel A, we show the Ceruleanchannel image (left) generated by linear unmixing, the Venus chan-nel image (middle), and an overlay image of these two channels(right). In the Cerulean channel image, it is clear that the top andbottom capillaries each contain Cerulean at the same concentra-tion. The Venus channel image revealed that the middle and lowercapillaries each contain Venus, but the concentration of Venus inthe middle capillary was higher than in the lower capillary. A morequantitative view of this data can be seen by plotting the intensities(calibrated to concentration) of a line scan across these images(Fig. 8.4 B). The dashed red line in panel A depicts the positionof the line scan across all three capillaries. Because known concen-trations of Cerulean and Venus were used in the top and middlecapillaries (10 mM), the intensities measured for these capillaries(blue for the Cerulean channel, yellow for the Venus channel) couldbe calibrated to that concentration of fluorophore (dotted blackline in Fig. 8.4 B). In essence, the Cerulean and Venus capillariescan be considered as calibration controls for interpreting the signalsobtained by linear unmixing of the mixture capillary. In the line

Fig. 8.3. The basis of linear unmixing. Unnormalized emission spectra of thethree capillaries are shown in panel A. The linear unmixing algorithm is basedon the hypothesis that a complex emission spectrum (an emission spectrum ofa sample containing 2 or more fluorophores) can be modeled as a weightedsum of the emission spectra of the individual fluorophores present. Thus, theMix spectrum should be the sum of the Cerulean and Venus spectra after eachis multiplied by an abundance factor. In panel B the abundance factor forVenus is held at a value of 1, while the value of the Cerulean abundance factoris varied from 0.6 to 1.4. Because the Cerulean and Venus capillaries eachcontained 10 mM of fluorophore, an abundance range of 0.6–1.4 correspondsto a concentration range of 6–14 mM. In panel C the Cerulean abundancefactor is held at a value of 1 (10 mM) while the abundance factor for Venuswas altered from 0.2 to 1 (2–10 mM). Note that when the Cerulean spectrumwas multiplied by 1 (corresponding to 10 mM) and added to the Venusspectrum multiplied by 0.6 (corresponding to 6 mM), the linear unmixing

model matched the complex spectrum measured for the mix capillary.



scan trace corresponding to the position of the mixture capillary(the far right), we see a Cerulean signal (blue trace) of 10 mM(dotted line), and a Venus signal (yellow trace) of 6 mM (dashedline). These values are consistent with the values generated byspectral analysis in Fig. 8.3.

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Fig. 8.4. Linear unmixing with curve fitting algorithms. Linear unmixing imageprocessing software utilize least‐square curve fitting routines to fit a spectrafrom each pixel of a spectral image to the linear unmixing equation and predictvalues for the abundance factors for each fluorophore. These abundance factorsfor Cerulean and Venus are then multiplied by the concentration of theindividual reference spectrum samples (10 mM) to produce a Cerulean Channelimage (blue), a Venus Channel image (yellow), and an overlay image (panel A).Now it can be seen that the top and bottom capillaries have the sameconcentration of Cerulean. Themiddle and bottom capillaries both have Venus,but at diVerent concentrations. The dashed red line indicates the location of aline scan across the two image channels. Line scan plots for each channel areuseful for measuring the actual concentration of fluorophores observed in a

sample, and are plotted in panel B.



Before describing how spectral imaging in conjunction withlinear unmixing can be used to measure FRET, we should firstconsider what limitations exist for successful quantitative linearunmixing of spectral images. First and foremost, linear mixingwill fail if the emission spectra of the fluorophores present in asample are nearly indistinguishable. As a rule of thumb, if twofluorophores have emission maxima separated by at least 10 nm,conditions can be found where the emissions of those fluorophorescan be separated by linear unmixing [2]. However, even if thefluorophores emission spectra are clearly diVerent, quantitativelinear unmixing can still fail if the emission from one fluorophoreis significantly brighter than that from the others [24]. An obviousquestion is ‘‘At what point will quantitative linear unmixing faildue to diVerences in fluorophore intensity?’’ This question wasaddressed in a study using mixtures of purified CFP and YFP atdiVerent defined molar ratios (1:9, 1:1, and 9:1) and at diVerentemission intensity ratios [24]. Spectral images of these mixtureswere acquired and used to determine how well the CFP:YFPratio predicted by linear unmixing matched the specific samples.It was found that linear unmixing could accurately predict thecorrect CFP:YFP ratio for all three mixtures. Linear unmixingyielded the correct molar ratios even under conditions where onefluorophore was 90 times brighter than the other. It must bepointed out, however, that the variance in the fluorophore ratiomeasurement observed under these extreme diVerences in intensitywas quite large. Because of signal‐to‐noise limitations in spectralmicroscopes in conjunction with limitations in the dynamic rangeof data acquisition instrumentation (typically 12 bits), it is diYcultto use linear unmixing to accurately separate signals whose inten-sities are greater than an order of magnitude apart. Essentially, ifthe dynamic range of a spectral detector is set to capture the peakemission of the brightest fluorophore (without clipping the signal),that dynamic range will be poorly matched to accurately measurethe emission of a much dimmer fluorophore. Under these condi-tions, linear unmixing will yield accurate measurements for the



abundance of the bright fluorophore, but the accuracy of the dimfluorophores abundance may be compromised. This problem iscompounded by the fact that it is often diYcult to control theabundance of fluorophores in a biological experiment, and evenmore diYcult to control their relative abundance in living cells. Therelative brightness of the light emitted from the fluorophores pres-ent in a mixed sample is a function of their absorption spectra (andthus the excitation wavelength), their quantum yields, as well astheir relative abundance. Thus, one solution to this problem is toempirically select an excitation wavelength for a given sample thatyields a complex emission spectrum whose shape is significantlydiVerent from the emission spectrum of the individual fluorophoresalone. To illustrate this approach, linear unmixing was applied tothe four spectral images depicted in Fig. 8.2. The same set ofcapillaries was imaged at four diVerent excitation wavelengths. At820 nm, Cerulean was excited well but Venus was barely excited. At900 and 920 nm, both were excited well, and at 940 nm Venus wasexcited more eYciently than Cerulean. In Fig. 8.5A, we replot theemission spectra of the Cerulean capillary (blue) and the Mixcapillary (red) at each excitation wavelength, but here each spec-trum is normalized to the intensity of its Cerulean emission peak at478 nm. Because the Cerulean spectrum is overlaying the Mixspectrum in these graphs, the visible part of the Mix spectrum(red) represents the portion of the Mix spectrum resulting fromVenus emission. With 820 nm excitation, the Mix emission spec-trum is almost identical to the Cerulean spectrum (note the tokenred signal between 500 and 600 nm). In contrast, the Mix spectraresulting from 900, 920, and 940 nm excitation were all significantlydiVerent than the Cerulean alone spectrum (blue), as well as from aVenus alone spectrum (data not shown). Furthermore, at thesethree excitation wavelengths the fractional contribution of Cerule-an and Venus to the Mix spectra emissions was all within an orderof magnitude of each other. Thus, we would predict that the 900,920, and 940 spectral images (but not the 820 nm spectral image)will yield accurate estimates of the abundance of Cerulean and



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Fig. 8.5. The eVects of excitation wavelength on linear unmixing. In panel Awe see the Cerulean normalized emission spectra of the mixture capillary (red)overlaid with the normalized emission spectrum of Cerulean alone (blue) atthe four diVerent two‐photon excitation wavelengths used in Fig. 8.2. Notethat with 820 nm excitation the mix spectrum was not significantly diVerentthan the Cerulean spectrum, while with 900, 920, and 940 nm excitation theywere diVerent. When the four spectral images depicted in Fig. 8.2 wereprocessed by linear unmixing they produced the four unmixing channel‐setsdepicted in panel B. The unmixed images with 900, 920, and 940 nm excitationwere all identical, while with 820 nm excitation erroneous results wereobtained. In panel C the results of linear unmixing of a spectral image of thesame samples, obtained with one‐photon excitation at 458 nm is shown. Theseimages looked identical to the images obtained with 900, 920, and 940 nmtwo‐photon excitation, and a line scan across the one‐photon image confirmed

this conclusion (compare panel D with Fig. 8.4B).



Venus with linear unmixing analysis. To test this prediction, thelinear unmixing algorithm was applied to these data sets(Fig. 8.5 B). As expected, the Cerulean and Venus unmixing chan-nels generated by linear unmixing of the 900, 920, and 940 nmexcitation spectral images (as well as the overlay channel) werevirtually identical. In contrast, the unmixing of the 820 nm spectralimage dramatically underestimated the abundance of Venus in theMix capillary. Clearly, judicious selection of excitation wavelengthis important for quantitative linear unmixing of spectral images,and the guidelines mentioned earlier can help in the selection ofthose wavelengths.

8.2.2. Single‐ versus multiphoton spectral imaging

Can conventional one‐photon excitation be used to acquire spectralimages for quantitative linear unmixing, and if so, are there anyadvantages or disadvantages of two‐photon excitation over one‐photon? Fig. 8.5C depicts the Cerulean, Venus, and overlay chan-nels generated by linear unmixing of a spectral image of our threecapillaries acquired with one‐photon excitation using the 458 nmlaser line of an argon laser. These images were nearly identical tothe linear unmixing images generated for the same sample excitedwith 900, 920, and 940 nm two‐photon excitation (Fig. 8.5B). Simi-larly, a line scan across this unmixed one‐photon image (red dottedline in Fig. 8.5C) was equivalent to a line scan across a linearunmixed two‐photon image (compare Fig. 8.5D with Fig. 8.4B).Thus, we conclude that quantitative linear unmixing can work wellwith spectral images acquired with either one‐photon or two‐photon excitation. There are diVerences between two‐photon andone‐photon microscopy that may impact on their suitability forquantitative spectral imaging microscopy. First, the spectral bandinvolved in two‐photon excitation (typically from 700 to 1000 nm)is well separated from the spectral region where most commonlyused fluorophores emit (400–600 nm). Thus, with two‐photon



excitation, the whole emission spectrum of a sample can be easilycollected. In contrast, because the wavelength for one‐photon exci-tation often overlaps with a samples emission spectrum a portion ofthe emission spectrum typically is lost. Even when one‐photonexcitation is left shifted from emission, the emission filters anddichroic beam splitters involved in preventing one‐photon excita-tion from reaching the spectral detector can attenuate the emissionsignal over a portion of the emission spectrum. The ability tocollect a full emission spectrum potentially translates into a morephoton‐eYcient microscope, and this is key for successful live cellimaging. Second, because the lasers used in most two‐photon mi-croscopes are tunable, it is relatively easy and straightforward toselect an excitation wavelength that is optimized for the specificfluorophores present in a sample as well as to their stoichiometry inthe sample. In contrast, one‐photon laser scanning confocal micro-scopes typically use lasers with a limited number of fixed laser linesand are thus poorly suited for optimizing the excitation wavelengthfor spectral imaging. Recently, however, new white light lasersources have become available which can support one‐photon exci-tation over a broad range of wavelengths. Wide‐field conventionalfluorescence microscopes typically use broad wavelength lightsources in conjunction with excitation filters. Although the excita-tion wavelength can be optimized for a particular sample, thiswould require having a large set of diVerent excitation filters onhand that can be rapidly changed to optimize excitation. This istypically not available. One alternative is to replace excitationfilters with a tunable programmable excitation filter. This couldpotentially allow easy and convenient matching of one‐photonexcitation to a particular sample. Third, the depletion of fluoro-phores by bleaching with two‐photon excitation is typically muchslower than with one‐photon excitation because with two‐photonexcitation there is no fluorophore excitation occurring above andbelow the image plane [26]. If diVerent fluorophores are bleachedat diVerent rates in a sample, emission spectra will change asa function of acquisition time. This will greatly complicate the



quantitative analysis of spectral images. Alternatively, for somefluorophores, multiphoton excitation can have diVerent selectionrules than one‐photon excitation. Thus, it may be possible withtwo‐photon excitation to directly populate a fluorophores tripletstate. If this happens, the bleach rate, at least in the image plane,can be much faster [27]. Finally, two‐photon absorption cross‐sections are in general broader than that of one‐photon absorptionspectra. Thus, with two‐photon excitation it is relatively easy tofind wavelengths that excite multiple fluorophores simultaneously.

8.2.3. Baseline correction and emission wavelength selection

We have demonstrated how the selection of the excitation wave-length for acquiring spectral images can influence how accuratelinear unmixing can be in predicting the abundance of fluorophorespresent in a mixed sample. For this reason, there is a great advan-tage in having a spectral microscope with a large, preferably con-tinuous selection of excitation wavelengths so that the relativeintensities of the fluorophores present can be modulated to opti-mize the signal to noise ratio obtainable for all fluorophores pres-ent. Two‐photon microscopy is well suited for this task. We willnow address two other factors that can influence how quantitativethe results of linear unmixing can be: (1) baseline corrections ofreference spectra, and (2) the wavelength range and resolution ofthe spectral detector used. The Cerulean, Venus, and Mix capillaryspectra shown in Fig. 8.3A all have baseline intensities of zero (seenbelow 425 and above 625 nm). In practice, the baseline of spectraobtained using a spectral microscope will have a positive oVsetfrom zero as a result of dark noise and instrumentation noise thatis added to the true signal. If these oVsets are not corrected beforeapplying the linear unmixing algorithm, significant errors can beintroduced [24]. Baseline correction can be implemented in hardwareby properly configuring the gain and oVset of the spectral detector.Alternatively, Baseline corrections can also be implemented with



postprocessing by measuring the oVset for the spectra and subtract-ing it from the signals. A third approach for Baseline correction isonly partially eVective. In this approach, in addition to usingreference spectra for each fluorophore present in a sample, thespectrum of the background signal (e.g., see red trace in Fig. 8.1 C)can also be used by the linear unmixing algorithm. This will produce,in addition to image channels for each fluorophore, an additionalimage channel of the background which will not be used in anysubsequent overlay images. While this approach can eVectively re-move the oVset from the sample image, it does not remove oVsetfrom the individual fluorophore unit reference spectra. These oVsetsmust be corrected before the linear unmixing algorithm is applied.For the best photon eYciency, the wavelength range of a spectraldetector used for linear unmixing should cover the full range of asamples complex emission spectrum. For the sample depicted inFig. 8.1, this range would be from 450 to 600 nm. To eVectivelyimplement the Baseline corrections described earlier, however, thisrange should be extended a bit (i.e., from 400 to 650 nm), so that thetrue baseline can be defined. In the example depicted in Fig. 8.1, thespectral detector used captured a spectral image comprised of 32separate images (Fig. 8.1 A). Theoretically, linear unmixing of asample containing n fluorophores will require a spectral image com-posed of at least n spectral points (or subimages) [28], and thoseimages must cover the portions of the spectrumwhere the individualfluorophores emission spectra diVer. Thus, theoretically, Ceruleanand Venus emissions from the mixture capillary could be accuratelyseparated using the linear unmixing algorithm if applied to aspectral image composed of only two spectral points; one recordingfrom 450 to 500 nm, and the other covering 500–600 nm. Althoughthe theory describing the influence of detector wavelength range,and resolution on linear unmixing has been described [28],experimental confirmation would be a welcome addition to theliterature.



8.3. What is the spectral signature of FRET?

Finally, an underlying assumption of quantitative linear unmixingis the absence of mechanisms that can selectively alter the emissionspectra of the individual fluorophores present in a sample. BecauseFRET shifts energy from donor to acceptor fluorophores, FRETactivity will decrease the magnitude of a donors emission spectrumand increase the magnitude of the acceptors emission spectrum. Inpractice, this means that quantitative linear unmixing of a samplewith a FRET eYciency greater than zero will fail to yield accurateestimates of the abundance of donors and acceptors present. Thishas been confirmed experimentally [12]. This is both good and badnews. The bad news is that studies that have used quantitativelinear unmixing of spectral images without regard to the possibi-lities that the fluorophores present in their sample might be trans-ferring energy by FRETmay be based on erroneous unmixing data.The good news is that because linear unmixing will yield diVerentresults in the presence or absence of FRET, this behavior can beused to measure FRET from spectral data sets.

It has been shown that the linear unmixing equation used toestimate the abundance of fluorophores in a sample will fail ifFRET is occurring between the fluorophores in a sample. Devisinga strategy for using spectral imaging to measure FRET requires aquantitative understanding of how the shape and magnitude of acomplex emission spectrum changes with FRET. A FRET adjusted

spectral equation which accurately describes the shape and magni-tude of the complex emission spectrum (F i(l)) from a populationcontaining two fluorophores that might be transferring energy byFRET is:

FiðlÞ ¼ dð1& EDÞFiD;refðlÞ þ aFi

A;refðlÞ þ dEDQA

QDkiFi

A;refðlÞ

ð8:2Þ



where d and a represents the donor and acceptor fluorophoresconcentrations, Fi

D;refðlÞ and FiA;refðlÞ are the reference emission

spectra of the donor and acceptor at the same concentration asmeasured on the spectral microscope being used. It is important tonote that these spectra are a function of the excitation wavelength,liex. ED is the apparent FRET eYciency of the sample, that is thefraction of donor excitation events that results in energy transfer toan acceptor for all of the donors present at a specific pixel in animage. QD and QA are the quantum eYciency of the donor oracceptor, and ki is a transfer factor (see the Appendix) [12]. Thisequation can be understood intuitively by realizing that the com-plex emission spectrum of a population of donor and acceptorfluorophores (that may be transferring energy by FRET) is com-prised of the sum of three parts. The first part describes the fluores-cent emission from directly excited donor fluorophores in a sample:

dð1& EDÞFiD;refðlÞ ð8:3Þ

It is the reference emission spectrum of the donor, multiplied by itsabundance, but attenuated by the fraction of donors that are nottransferring energy by FRET. The second part of the equationdescribes emission from directly excited acceptors:

aFiA;refðlÞ ð8:4Þ

It is simply the reference emission spectrum of the acceptor, multi-plied by the abundance of acceptor. Finally, the last part of theequation represents the energy transferred from directly exciteddonors to acceptors by FRET, and then emitted as acceptor fluo-rescence:

dEDQA

QDkiF i

A;refðlÞ ð8:5Þ

It is the emission spectrum of the acceptor multiplied by the abun-dance of the donor (attenuated by the fraction of donoremissions that actually result in FRET), then multiplied by a factor



QA/QD ' ki that equates how the emission intensity increase of theacceptor corresponds to the attenuation of the donors emission.This factor is equal to the extinction coeYcient ratio of the donorand acceptor at the used excitation wavelength, liex, see appendix. IfFRET is not occurring in a sample (i.e., ED ¼ 0), the wholeequation reduces to:

FiðlÞ ¼ dFiD;refðlÞ þ aFi

A;refðlÞ ð8:6Þ

This is the same equation as the standard linear unmixing equationfor two fluorophores.

Standard linear unmixing of a spectral image of a sample com-posed of two fluorophores yields a measure of the concentration ofeach fluorophore present for each pixel. If FRET is occurring,linear unmixing will produce an apparent donor concentration(dapparent) that underestimates the true donor concentration (d ) bya factor of 1‐ED:

dapparent ¼ dð1& EDÞ ð8:7Þ

Linear unmixing will also produce an apparent acceptor con-centration (aapparent) that will over‐estimate the true abundance ofthe acceptor (a):

aapparent ¼ aþ dEDQA

QDkiF i

A;refðlÞ ð8:8Þ

A prediction based on these two equations is that the value ofdapparent will remain constant for spectral images taken at diVerentexcitation wavelengths, while values for aapparent can change withdiVerent excitation wavelength (because aapparent is a function ofexcitation wavelength) but only when FRET is occurring. Thisprediction has been experimentally verified [12], and is in essencethe spectral signature of FRET. This behavior can also be used as asimple test to determine if FRET is or is not occurring in a sample.Spectral images are taken at two excitation wavelengths that yieldgood signal to noise ratios for both donors and acceptors.



Linear unmixing is applied to each spectral image to produce

four measurements at each pixel, d1apparent and a1apparent at l1ex; and

d2apparent and a2apparent at l2ex. If the ratio of ðd1apparent þ a1apparentÞ=ðd2apparent þ a2apparentÞ equals 1 then FRET is not occurring.

8.3.1. Strategies for measuring FRET using spectral imaging

Strategies for using spectral imaging to measure FRET begin withthe realization that the FRET adjusted spectral equation describedabove has three independent variables, d the abundance of donor, athe abundance of acceptor, and ED the FRET eYciency. In con-trast, at a single excitation wavelength, quantitative linear unmix-ing produces only two observables, dapparent, the apparent donorconcentration in a sample and aapparent, the apparent acceptorconcentration. Thus, with three unknown variables and two obser-vables there can and will be multiple combinations of values for d,a, and ED that can produce the same complex emission spectrumobserved in a sample [7, 12]. Strategies for using spectral imaging tomeasure d, a, and ED therefore must either reduce the number ofindependent variables in the FRET adjusted spectral equation, orproduce at least one additional observable to supplement the twovalues measured by spectral unmixing.

One way to reduce the number of independent variables in theFRET‐adjusted spectral equation is to use samples with a fixeddonor‐to‐acceptor ratio. Under these conditions, the values of d

and a are no longer independent, but rather the concentration of dis now a function of a and vice‐versa. This approach is typical forthe situation of FRET‐based biosensor constructs. These sensorsnormally are designed to have a donor fluorophore attached to anacceptor by a domain whose structure is altered either as a result ofa biological activity (such as proteolysis or phosphorylation), or byits interaction with a specific ligand with which it has high aYnity.In general, FRET based biosensors have a stoichiometry of one



donor to one acceptor. FRET activity for biosensors is typicallyreported as a ‘‘FRET‐ratio’’ index value rather than as a FRETeYciency. This is unfortunate because FRET indices are oftennonlinear [11, 29]. For this example, where a single donor is linkedto a single acceptor, the FRET‐adjusted spectral equation will haveonly two variables, x, the concentration of the donor and acceptor(x ¼ d ¼ a), and ED, the FRET eYciency. Linear unmixing willyield:

dapparent ¼ xð1& EDÞ ð8:9aÞ

aapparent ¼ x 1þ EDQA

QDki

! "ð8:9bÞ

In this situation because these equations have only two variablesED and x, and two observables dapparent and aapparent this problem isdetermined, and these two simultaneous equations can be solvedfor ED and x:

ED ¼ aapparent & dapparent

aapparent þ dapparentQA

QDki

ð10aÞ

x ¼aapparent þ dapparent

QA

QDki

1þ QA

QDki

ð10bÞ

Using these equations, the values of ED and x can be calculatedfrom the measured values of dapparent and aapparent. The advantageof this approach is that it is simple and only requires a microscopecapable of producing spectral images, as well as software that canperform quantitative linear unmixing to produce dapparent andaapparent images, and then process those images according to theequations listed earlier to yield x and ED images. The main limita-tion of this approach is that it will only work for samples with fixeddonor‐to‐acceptor stoichiometry such as FRET‐based biosensors.



In many biological applications of FRET, the donor to acceptorratio of a specimen is not fixed, and unknown. Even with samplesthat do have a fixed donor to acceptor ratio such as in a biosensor,it is possible that cellular activities such as proteolysis might alterthis ratio in unknown ways. Under these circumstances, an occultchange in donor to acceptor ratio might be misinterpreted as achange in the biological activity that the biosensor was designedto monitor. Obviously, knowing the real donor to acceptor ratio ina sample as well as the actual concentrations of these fluorophorescan be very useful for avoiding these types of errors, as well as forinterpreting the meaning of FRET. For example, if the donorconcentration in a FRET experiment is known to be much greaterthan the acceptor concentration, a low FRET eYciency would beexpected (because most donors will not have even a single acceptorto interact with) even if the molecule that the donor fluorophore isattached to does have a high aYnity for the acceptor tagged com-ponent. In contrast, a low FRET eYciency when the donor con-centration is known to be much lower than the acceptorconcentration might indicate that the molecule with an attacheddonor does not interact with the acceptor tagged molecule (thoughother reasons for having a low FRET eYciency must also beconsidered). Donor and acceptor stoichiometry and concentrationscan be obtained by acquiring a spectral image in conjunction withFRET eYciency measurements obtained by another imaging meth-od. Typically, FRET eYciency can be measured by monitoring thesensitized emission before and after acceptor bleaching [30–34], orby monitoring the fluorescence lifetime of the donor in the presenceor absence of acceptors [34–38]. Regardless of the auxiliary meth-ods used to measure the FRET eYciency hybrid approaches reducethe number of independent variables in the FRET adjusted spectralequation from three (d, a, and ED) to two (d and a), by indepen-dently finding the value of the FRET eYciency (ED) at each loca-tion in an image. The benefit of this approach is that under thesecircumstances, the true donor (d) and acceptor (a) concentrationscan be calculated at each pixel in a spectral image using the



independently measured FRET eYciency (ED), in conjunction withthe dapparent and aapparent values produced by linear unmixing usingthe following equations:

d ¼dapparent1& ED

ð8:11aÞ

a ¼ aapparent &dapparent1& ED

EDQA

QDki ð8:11bÞ

One criticism of this approach, however, is that in addition torequiring the specialized hardware for obtaining spectral images,additional instrumentation is often required to measure the FRETeYciency. Furthermore, the limitations specific to the FRET meth-od used in conjunction with spectral imaging will also apply to thishybrid approach.

As mentioned previously, strategies for using spectral imagingto measure FRET (as well as the concentrations of donors andacceptors) must either reduce the number of variables in the FRETadjusted spectral equation, or increase the observables measuredusing linear unmixing. All of the methods mentioned so far work byreducing the number of variables in the spectral equation. Next, amethod will be described whose approach is to measure an addi-tional observable by acquiring two spectral images that will each beanalyzed by linear unmixing. At each excitation wavelength: (l1exand l2ex), a spectral image of the sample is acquired. Referencespectra of samples containing known concentrations of donorand acceptor are also acquired at the same excitation wavelengthsand excitation intensities. Quantitative linear unmixing of the firstspectral image obtained at l1ex using the references spectra alsoacquired at l1ex will yield two observables:

d1apparent ¼ dð1& EDÞ ð8:12aÞ

a1apparent ¼ aþ dEDQA

QDk1 ð8:12bÞ



Linear unmixing of the spectral image acquired at l2ex will also yieldtwo observables:

d2apparent ¼ dð1& EDÞ ð8:13aÞ

a2apparent ¼ aþ dEDQA

QDk2 ð8:13bÞ

Note that because the value of dapparent is not a function of excitationwavelength, the same values for dapparent should be observed at bothexcitation wavelengths (l1ex and l2ex). In contrast, the valuesmeasured for a1apparent and a2apparent will be diVerent if k

1 6¼ k2. Thus,acquiring spectral images of a sample at two diVerent excitationwavelengths can allow three observables to be observed with linearunmixing; dapparent, a1apparent, and a

2apparent. Because the FRET adjust-

ed spectral equation has three unknowns (d, a, and ED) and spectralimaging at two excitation wavelengths produces three observablesthis problem is determined, and the three simultaneous equationsdescribing these observables can be solved for ED, d, and a:

Ed ¼ DaDaþ dapparentODk

ð8:14aÞ

d ¼Daþ dapparentODk

ODkð8:14bÞ

a ¼k2a1apparent & k1a2apparent

Dkð8:14cÞ

Where the following substitutions have been made:

Da ¼ a2apparent & a1apparent ð8:14dÞ

O ¼ QA

QDð8:14eÞ

Dk ¼ k2 & k1 ð8:14fÞ



Using these equations the values of ED, d, and a can be calculatedfrom the measured values of dapparent, a1apparent, and a2apparent. Theadvantage of this approach is that it only requires a microscopecapable of producing spectral images as well as software forperforming quantitative linear unmixing. Furthermore, not onlydoes it not require knowledge of the donor–acceptor stoichiometryof a sample, it will actually yield this information. Another advan-tage of this approach is that the FRET measurements are based onchanges in both the donors’ fluorescence signal as well as the accep-tors’. Most other FRET methods are based on monitoring changesin either the donors’ fluorescence or the acceptors’ and are thussusceptible to artifacts caused by nonspecific quenching or de-quenching. The major limitation of this approach is that it requiresacquiring two spectral images at two diVerent excitation wave-lengths. Thus, a light source with a choice of several excitationwavelengths is required. Furthermore, if cell components movebetween the acquisition of the first and second spectral images,motion artifacts will introduce errors in the calculations. This istrue for any analysis whose calculations involve more than oneimage. Finally, any variance in the tuning, bandwidth, or power ofthe light source used in this approach will also necessitate obtainingreference spectra at the exact same settings. This typically meansmeasuring reference spectra before tuning to the second wavelength.

8.3.2. Measuring FRET from spectral images: sRET

Many of the strategies for measuring FRET from spectral imagesthat were mentioned above have been implemented to study FRET.We will now cover sRET [12], a specific implementation thatuses the last approach where FRET is measured from a pair ofspectral images collected at diVerent excitation wavelengths.Recently, the sRET approach has been extended to explicitly con-sider paired and unpaired fluorophores, the impact of incompletelabeling (or for fluorescent proteins fractional maturation), and the



implementation of a calibration procedure that does not requirepurified fluorophores [39]. While it is important to realize that all ofthe approaches mentioned in the previous section are valid andmay have specific advantages for particular biological problems, wehave chosen to highlight the sRET approach because: (1) it canmeasure FRET eYciencies from samples with unknown donor toacceptor stoichiometry, (2) in addition to measuring the FRETeYciency it also measures the abundance of donors and acceptors,(3) it does not require the destruction of the sample (i.e., withsensitized emission by acceptor bleaching), (4) It measures FRETsolely based on spectral images of the donor and acceptor, and (5)sRET has been shown to yield the same FRET eYciencies asobtained by fluorescence lifetime imaging (FLIM–FRET) and bya variant of the three‐cube method (E‐FRET) [40].

Spectral images of cells transfected with DNA encoding either afluorescent protein construct that has a low FRET eYciency (CTV)or a high FRET eYciency (C5V) [12] were acquired with twophoton excitation at 890 and 940 nm. Spectral images of capillariescontaining either 7.8 mM Cerulean or Venus were also acquired atthese excitation wavelengths to serve as reference spectra for linearunmixing of these spectral images, as well as to measure k1 atl1ex ¼ 890nm and k2 at l2ex ¼ 940nm for the Cerulean–Venus pair.Values measured for ki will be specific for a particular fluorophorepair, and for the microscope used to measure spectra. It can alsochange as a function of the intensity, wavelength, and bandwidth ofthe light source used, and is therefore best measured along with thesample. These values, as well as the quantum eYciencies of Cerule-an (QD ¼ 0.62) and Venus QA ¼ 0.57) will be needed to convert thelinear unmixed images of our transfected cells into a FRET‐eYciency image, a Cerulean‐concentration image, and a Venus‐concentration image.

Linear unmixing of each pair of spectral images for a givensample will produce an apparent Cerulean‐image at l1ex ¼ 890 nmðd1apparentÞ, an apparent Venus Image at l1ex ¼ 890 nmða1apparentÞ,an apparent Cerulean‐image at l2ex ¼ 940 nm ðd2apparentÞ, and an



apparent Venus‐image at l2ex ¼ 940 nm ða2apparentÞ. As mentioned

above, d1apparent and d2apparent should be indistinguishable, and there-fore an average of these two images are used for further processing(dapparent). A significant diVerence between these two images is indica-tive of quenching and/or bleaching in the sample. Additionally, sam-ple motion during the period between acquiring the two spectralimages can also be responsible for this type of artifact. Regardless, ifa ratio of the pixel intensities of these two donor images are signifi-cantly diVerent than 1 they should not be used for further processing.In contrast, a1apparent and a2apparent should be diVerent if the FRETeYciency of the sample is greater than zero.Next, these three apparentimages that were produced by linear unmixing are processed (for eachpixel) using Eq. (8.14) explained above.

Image processing with these equations produces a donor‐image(d), an acceptor‐image (a), and a FRET eYciency image (ED).Examples of images produced by this process can be observed forcells transfected with either CTV, a construct that has a low FRETeYciency (Fig. 8.6), or for cells transfected with C5V, a constructthat has a high FRET eYciency (Figure 8.7). In both the figures,panel A shows the donor abundance (Cerulean concentration).Panel B shows the acceptor abundance (Venus concentration),and panel D shows the color‐coded FRET‐eYciency image wherepink to red indicates increasing amounts of FRET and whiteindicates low FRET eYciencies. Panel C shows a color‐codedratio image formed by dividing the image in panel B by the imagein panel A. This ratio image is useful for confirming that theproteins expressed and imaged have the same donor:acceptor stoi-chiometry as encoded in the construct and transfected into the cell.It is also important to realize that in live cell experiments, particu-larly when a FRET pair is composed of spectral variants of GFP,that diVerential expression, maturation, folding, as well as post-translation modifications (such as proteolysis) can all modify theobserved acceptor/donor ratio of an expressed construct. Boththe CTV and C5V constructs encode a single Cerulean molecule



14

A B

C

D

12

10

8

6

4

2

0

Cer

ulea

n (m

M)

12

10

8

6

4

2

14

0

Ven

us (mM

)

1000

500

1500

0

400

200Fre

quen

cy

600

0

1 10Venus/cerulean

2 3 4 5 678 2 3 4 5 6780.1

−0.5 0.0FRET efficiency

0.5−1.0 1.0

1002 3 4 5 678

Fre

quen

cy

1.5

1.0

0.5

2.0

0.0

Ven

us /

ceru

lean

0.5

0.0

−0.5

1.0

−1.0

FR

ET

effi

cien

cy

Fig. 8.6. sRET analysis of CTV, a Cerulean‐Venus construct with a low FRETeYciency. sRET analysis is based on linear unmixing of two spectral imagesobtained at two diVerent excitation wavelengths. Spectral images of cellsexpressing the CTV construct were acquired with 890 and 940 nm excitation.These spectral images, and theirmatching reference spectrawereprocessedusingthe sRETalgorithm toproduce (A) aCerulean concentration image, (B) aVenusconcentration Image, (C) a Venus/Cerulean ratio image, and (D) a FRET‐eYciency image. The graphs in panelsCandDshow frequencyhistogramsof thepixel values for the corresponding images. The red trace in panel C is a log‐normal fit to the Venus/Cerulean histogram, while the black trace in panel D is a

Gaussian fit to the FRET‐eYciency histogram.



concatenated to a single Venus molecule. Thus, they should have aVenus/Cerulean ratio of 1 in these images (red). To the right ofpanels C and D in Figs. 8.6 and 8.7 are frequency histograms of the

8

A

B

C

D

1.5

1.0

0.5

2.0

200

100Freq

uenc

y

300

0

150

100

Freq

uenc

y

50

200

0−0.5 0.0

FRET efficiency0.5−1.0 1.0

1 100.1 1002 3 4 5 6 78 2 3 4 5 6 78 2 3 4 5 6 780.0

0.5

0.0

FR

ET

effi

cien

cy

−0.5

1.0

−1.0

Venu

s/ce

rule

an

Venus/cerulean

6

4

2

8

0

6

4

2

0

Cer

ulea

n (m

M)

Venu

s (m

M)

Fig. 8.7. sRET analysis of C5V, a Cerulean‐Venus construct with a highFRET eYciency. Spectral images of cells expressing C5V, and their matchingreference spectra were processed using the sRET algorithm to produce (A) aCerulean concentration image, (B) a Venus concentration Image, (C) a Venus/Cerulean ratio image, and (D) a FRET‐eYciency image. The graphs inpanels C and D show frequency histograms of the pixel values for the

corresponding images.



pixel values measured for the Venus/Cerulean ratio image (panel C)or for the FRET‐eYciency images (panel D). The Venus/Ceruleanratio‐image histograms (in panels C of Figs. 8.6 and 8.7) are plottedon a log‐scale (grey bars) and are fit to a log‐normal distribution(red trace). We can see that for both CTV and C5V, these distribu-tions peak near a value of 1 confirming that on average eachCerulean expressed in these cells is attached to a single Venusmolecule and vice‐versa. The FRET‐eYciency histograms (in pa-nels D of Figs. 8.6 and 8.7) are plotted on a linear‐scale (red bars)and are fit to a Gaussian distribution (black trace). The peak of theFRET‐eYciency distribution for the CTV image (Fig. 8.6 D) wasnear 0 indicating little if any FRET. In contrast, the peak of thedistribution for the C5V construct was between 0.4 and 0.5 indicat-ing an average FRET eYciency of approximately 45%.

8.3.3. Testing and validating methods for measuring FRET

What are the relative merits of diVerent methods of measuringFRET, and is the spectral approach to FRET measurement appro-priate for a specific project? First and foremost, a method formeasuring FRET must produce accurate results. Only then shouldother factors, such as the precision of the measurements, equipmentcosts, photon eYciency, and speed of data acquisition be consid-ered when selecting a FRET method. Surprisingly, FRET referencestandards (i.e., compounds with known FRET eYciencies) haveonly become available over the past year [40]. Without referencestandards it was diYcult to compare one type of FRET measure-ment with another or even to determine if a specific implementationof FRET was in fact accurate [11]. To correct this problem, ourlaboratory produced three genetically encoded FRET standardswith the following ‘known’ FRET eYciencies: C5V (E ¼ 43 (2%), C17V (E ¼ 38 ( 3%), and C32V (31 ( 2%). These geneticconstructs are based on two spectral variants of green fluorescentprotein, Cerulean and Venus. The Forster radius (R0) for energy



transfer from Cerulean to Venus is 5.4 nm [41]. In these constructs,the donor was separated from the acceptor by amino acid linkers ofdiVerent lengths so that they would have diVerent FRET eYciencies.To date, we have provided these DNA encoding FRET standards toover 75 diVerent labs. All of the constructs mentioned above haveone donor and one acceptor. We have also produced other relatedconstructs that have two donors and one acceptor (CVC) and onedonor and two acceptors (VCV) [12]. These are particularly usefulfor evaluating how well spectral FRET methods can measure therelative abundance of donors and acceptors. Finally, we have alsoproduced a construct (CTV) that has a very low FRET eYciency.The CTV construct encodes a single Cerulean donor attached to asingle Venus acceptor. When this construct is expressed it assemblesinto trimers composed of three donors (in close proximity) and threeacceptors (also in close proximity). The donors, however, arethought to be separated from the acceptors by at least 8 nm, andtherefore this construct has a very low FRET eYciency. The CTVconstruct is useful as a negative FRET control, and can also be usedto evaluate if diVerent FRET methods are susceptible to errorscaused by homo‐FRET occurring between donors and/or acceptors.In Table 8.1 the FRET‐eYciency values measured for these con-structs by a spectral FRET method (sRET), as well as by fluores-cence lifetime imaging (FLIM–FRET) [43, 44], and by a variant ofthe three‐cubemethod (E‐FRET) [42, 45] are shown. As can be seen,the spectral method produced FRET eYciencies that were similar tothe other two methods. Furthermore, the sRET method also suc-cessfully determined the C5V, CVC, and VCV acceptor donor stoi-chiometries, demonstrating that the spectral FRET method cansuccessfully and accurately measure FRET eYciency over a rangeof 3–69% with varying donor to acceptor ratios.

Another important lesson from Table 8.1 is that all three of themethods tested yielded virtually the same FRET eYciencies for thesame samples. The sRET method as implemented used two‐photonexcitation on a Zeiss 510 META/NLO microscope, as did theFLIM–FRET method, but FLIM–FRET used auxiliary time



correlated single photon counting hardware, detectors, and soft-ware [46]. In contrast, the E‐FRET method used one photon exci-tation on a standard automated fluorescence microscope, using aCCD detector and custom written software. For reasons that we donot fully understand, the standard deviations observed with thesRET measurements were at least two times greater than thoseobserved with FLIM–FRET or with E‐FRET. We suspect thatthis is not intrinsic to the spectral approach, but arises from someaspect of the sRET hardware/software implementation. Eventhough the standard deviations observed for FLIM–FRET andE‐FRET were lower than that of sRET, all three methods werecapable of diVerentiating a 5% change in FRET eYciency [40].

TABLE 8.1FRET efficiencies and acceptor to donor ratios of FRET standards. TheFRET efficiencies of six genetic constructs expressed in cell culture were

evaluated by three different methods: sRET, FLIM‐FRET, and E‐FRET. Theacceptor to donor ratio (V/C) was also measured for each construct by

the sRET method. Key: C5V, Cerulean‐5 amino acid linker‐Venus; C17V,Cerulean‐17 amino acid linker‐Venus; C32V, Cerulean‐32 amino acid linker‐Venus; CVC, Venus flanked on each side by a Cerulean; VCV, Cerulean

flanked on each side by a Venus; CTV, Cerulean‐Traf2 protein domain‐Venus

FRET efficiency by MethodV/C of

constructs

V/Cmeasured

by sRETConstruct sRET FLIM–FRET E‐FRET

C5V 41 ( 9, n ¼ 62a 44 ( 2, n ¼ 10a 45 ( 4, n ¼ 10a 1 1.0 ( 0.3,

n ¼ 12b

C17V 35 ( 9, n ¼ 91a 39 ( 2, n ¼ 10a 40 ( 4, n ¼ 18a 1 n.d.

C32V 30 ( 8, n ¼ 81a 33 ( 4, n ¼ 10a 31 ( 2, n ¼ 16a 1 n.d.CVC 41 ( 5, n ¼ 6b 41 ( 3, n ¼ 20b 40 ( 1, n ¼ 28c 0.5 0.5 ( 0.3,

n ¼ 6b

VCV 70 ( 6, n ¼ 6b 65 ( 3, n ¼ 20b 69 ( 1, n ¼ 21c 2 2.1 ( 1.0,n ¼ 6b

CTV 2 ( 7, n ¼ 12b 6 ( 3, n ¼ 30b 3 ( 1, n ¼ 13c 1 0.9 ( 0.4,

n ¼ 12b

aFrom Ref. [40].bFrom Ref. [12].cFrom Ref. [42].



Another diVerence in these FRET methods is the cost of themicroscopes. The two‐photon microscope and its mode‐lockedlaser used for sRET and FLIM–FRET cost approximately anorder of magnitude more than the E‐FRET system. Clearly, ifcost is a limiting factor then the E‐FRET approach is superior.

Theoretically, spectral imaging should be among the most pho-ton eYcient methods for measuring FRET because every photonemitted by either the donor or acceptor (if detected) can be used inthe FRET calculation. With FLIM–FRET only emissions from thedonor are typically used, and any part of the donors emissionspectrum that overlaps with the acceptors emission spectrum isalso not typically used. Clearly, FLIM–FRET, as implemented, isnot very photon eYcient. E‐FRET is typically more photon‐eYcient than FLIM–FRET because emissions from both donorsand acceptors are used. However, the use of emission filters toisolate donor emissions from acceptor emissions prevents manyphotons from being detected. Complicating this analysis ofphoton‐eYciency is the fact that three separate excitation periodsmust occur to acquire the images required for E‐FRET analysis.FLIM–FRET requires only one excitation period but it can lasttens of minutes, and sRET requires two excitation periods, one foreach excitation wavelength. Finally, not all photon detectors havethe same quantum eYciency. Photomultipliers used for FLIM–FRET (and in confocal microscopes) typically have quantum eY-ciencies for detecting photons in the range of 10–40% [46]. A recentstudy compared the eYciencies of the spectral detector used in aZeiss META confocal with nonspectral detectors and concludedthat the spectral detectors were fivefold less eYcient in detectingphotons [47]. State of the art CCD cameras that can be used forE‐FRET imaging, can have quantum eYciencies as high as 90%.Because of all of these diVerent factors, it is often diYcult to predictthe photon eYciency of diVerent FRET methods. Nonetheless, anempirical estimate of their relative photon eYciencies can bederived from the time each method requires to acquire a FRET‐eYciency image. A single FRET image acquired on a time‐domain



FLIM–FRET system (Becker and Hickl SPC 830 with a Hama-matsu R3809 detector mounted on a Zeiss 510 META/NLO) cantake between 5 to 20 min to acquire. On a sRET system (Zeiss 510META/NLO) a single FRET image (i.e., two spectral images) takesapproximately 100 s to acquire, but tuning the laser (CoherentChameleon) to the second excitation wavelength adds an additionalminute or two. Acquiring a FRET‐eYciency image on an E‐FRETsystem typically requires only a few seconds. Thus, even thoughE‐FRET does not produce thin optical sections as does sRET andFLIM–FRET (with a two‐photon pulsed laser), E‐FRET’s low costand rapid acquisition time aVords it a great advantage, particularlyfor time‐lapse studies. It is also important to realize that empiricalcomparisons like these only contrast specific implementations ofthese FRET methods. For example, a comparison of FRET meth-ods similar to our own reached noticeably diVerent conclusions [48].With future improvements in the quantum eYciencies of spectraldetectors, improvements in their signal to noise ratio, as well astechnology to rapidly and reproducibly tune lasers [49], we predictthat spectral imaging will ultimately become the most photon eY-cient, and rapid method for accurately measuring FRET whilesimultaneously measuring the abundance of donors and acceptors.

Acknowledgments

This work was supported by the intramural program of the National Institutesof Health, National Institute on Alcohol Abuse and Alcoholism, Bethesda,MD 20892.

Appendix

The detected fluorescence emission spectrum F i(l) at excitationwavelength liex is composed of three components. These threecomponents are (analogous to the notation in Chapter 7) the



spectrum originating from (partly) quenched donors I iD&SðlÞ(corresponding to IDA in the general notation, referring to residualdonor fluorescence in the presence of the acceptor), the spectrumoriginating from sensitized emission (I iSðlÞ) and the spectrum dueto direct acceptor excitation I iAðlÞ.

FiðlÞ ¼ I iD&SðlÞ þ I iSðlÞ þ I iAðlÞ ð8:A1Þ

The spectra are a product of the number of molecules (N ), the laserintensity ‘i (at liex), the (excitation wavelength dependent) extinc-tion coeYcient ei, the quantum yield Q, the corrected emissionspectra F(l), and the instrument response or gain g(l) that istypically wavelength dependent. If we have Ns molecules thatshow FRET with an eYciency E, and ND (total) donor moleculesand NA (total) acceptor molecules, Eq. (8.A1) can be rewritten:

FiðlÞ ¼ ‘igðlÞ ðND &NSÞeiDQDFDðlÞ þNS½eiDQDð1& EÞFDðlÞ#

þ eiDEQAFAðlÞ* þNAeiAQAFAðlÞgð8:A2Þ

If we define ED + NS

NDE ¼ fDE where fD is the fraction of Donor

molecules involved in FRET ( 8.A2) can be rewritten as:

FiðlÞ ¼ ‘igðlÞ fNDð1& EDÞeiDQDFDðlÞ

þ NA þNDeiDeiA

! "eiAQAFAðlÞg

ð8:A3Þ

If we consider two reference samples of pure donor and acceptorwith a known concentration, two reference spectra can be recordedaccording to Eq. (8.A4):

FiD;refðlÞ ¼ ‘igðlÞeiDQDFDðlÞND;ref

FiA;refðlÞ ¼ ‘igðlÞeiAQAFAðlÞNA;ref

ð8:A4Þ



Then we can perform the following integration:Ðl

FiD;refðlÞFDðlÞ

¼ ‘ieiDQDND;ref

ÐlgðlÞ

Ðl

FiA;refðlÞFAðlÞ

¼ ‘ieiAQANA;ref

ÐlgðlÞ

ð8:A5Þ

From which it is apparent that:

eiDeiA

¼ kiNA;ref

ND;ref

QA

QDwith ki ¼

ð

l

FiD;refðlÞFDðlÞ

=ð

l

FiA;refðlÞFAðlÞ

ð8:A6Þ

Note that for the calculation of ki, two reference samples of knownconcentrations are required in addition to calibrated unit areaspectra of donor and acceptor fluorophores. In case the instrumentresponse curve is not wavelength dependent (g(l)¼ g) then unitreference spectra are not required because in this case:

ki ¼ð

l

FiD;refðlÞ=

ð

l

FiA;refðlÞ ð8:A6bÞ

With Eqs. (8.A4–8.A6), (8.A4) can be reformulated accordingto:

FiðlÞ ¼ ND

ND;refð1& EDÞFi

D;refðlÞ

þ NA

NA;refFiA;refðlÞ þ

ND

ND;refED

QA

QDkiFi

A;refðlÞð8:A7Þ

If we define the relative donor and acceptor concentration as:

d ¼ ND

ND;refand a ¼ NA

NA;refð8:A8Þ



Then Eq. (8.A8) rewrites as:


A;refðlÞ þ dEDQA

QDkiFi

A;refðlÞ

ð8:A9Þ

which is identical to Eq. (8.2).Note that if from a separate experiment the molar extinction

coeYcients of the donor and acceptor at both excitationwavelengths are known, the determination of ki is not requiredsince Eq. (8.A9) rewrites in:


A;refðlÞ þ dEDeiDeiA

ND;ref

NA;refFiA;refðlÞ

ð8:A9aÞ

¼ dð1& EDÞFiD;refðlÞ þ a 1þ eiD

eiAEA

! "FiA;refðlÞwith

EA + NS

NAE ¼ fAE

ð8:A9bÞ

However, in case of multiphoton excitation, the determinationof

eiD

eiA

will be diYcult.

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Chapter 8 - Spectral imaging and its use in the ...static.sif.it/SIF/resources/public/files/va2011/vogel_0718.pdfFo¬rster resonance energy transfer (FRET) imaging is a form of microscopy