A guided tour into subcellular colocalization analysis in light microscopy

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1 Journal of Mcroscopy, Vol. 224, Pt 3 December 2006, pp Receved 13 Aprl 2006; accepted 28 June 2006 Blackwell Publshng Ltd TUTORIAL REVIEW A guded tour nto subcellular colocalzaton analyss n lght mcroscopy S. BOLTE* & F. P. CORDELIÈRES *Plateforme d Imagere et de Bologe Cellulare, IFR 87 la Plante et son Envronnement, Insttut des Scences du Végétal, Avenue de la Terrasse, Gf-sur-Yvette Cedex, France Insttut Cure, CNRS UMR 146, Plateforme d Imagere Cellulare et Tssulare, Bâtment 112, Centre Unverstare, Orsay Cedex, France Key words. Colocalzaton, confocal mcroscopy, fluorescence mcroscopy, mage analyss, wde-feld mcroscopy. Summary It s generally accepted that the functonal compartmentalzaton of eukaryotc cells s reflected by the dfferental occurrence of protens n ther compartments. The locaton and physologcal functon of a proten are closely related; local nformaton of a proten s thus crucal to understandng ts role n bologcal processes. The vsualzaton of protens resdng on ntracellular structures by fluorescence mcroscopy has become a routne approach n cell bology and s ncreasngly used to assess ther colocalzaton wth well-characterzed markers. However, mageanalyss methods for colocalzaton studes are a feld of contenton and engma. We have therefore undertaken to revew the most currently used colocalzaton analyss methods, ntroducng the basc optcal concepts mportant for mage acquston and subsequent analyss. We provde a summary of practcal tps for mage acquston and treatment that should precede proper colocalzaton analyss. Furthermore, we dscuss the applcaton and feasblty of colocalzaton tools for varous bologcal colocalzaton stuatons and dscuss ther respectve strengths and weaknesses. We have created a novel toolbox for subcellular colocalzaton analyss under ImageJ, named JACoP, that ntegrates current global statstc methods and a novel object-based approach. Introducton Colocalzaton analyss n optcal mcroscopy s an ssue that s afflcted wth ambguty and nconsstency. Cell bologsts have to choose between a rather smplstc qualtatve evaluaton of Correspondence to: S. Bolte. Tel: ; Fax: ; e-mal: Susanne.Bolte@sv.cnrs-gf.fr. F. P. Cordelères. E-mal: Fabrce.Cordeleres@cure.u-psud.fr overlappng pxels and a bulk of farly complex solutons, most of them based on global statstc analyss of pxel ntensty dstrbutons (Manders et al., 2003; Costes et al., 2004; L et al., 2004). The complexty of some of these dfferent analyss tools makes t dffcult to mplement the approprate method and reflects the fact that the majorty of colocalzaton stuatons demand customzed approaches. All-round analyss tools do not necessarly ft all crcumstances as cells contan a plethora of structures of multple morphologes, startng from lnear elements of the cytoskeleton, punctate and sotropc compartments such as vescles, endosomes or vacuoles, gong to more complex ansotropc forms such as Golg stacks and the network-lke endoplasmc retculum. The colocalzaton of two or more markers wthn these cellular structures may be defned as an overlap n the physcal dstrbuton of the molecular populatons wthn a three-dmensonal volume, where ths may be complete or partal overlap. The lmts of resoluton n optcal mcroscopy mply an uncertanty of the physcal dmensons and locaton of small objects n the two-dmensonal and even more n the threedmensonal space. The frequent queston s: are two fluorochromes located on the same physcal structure or on two dstnct structures n a three-dmensonal volume? The answer depends on the defnton of terms and lmts, bearng n mnd that the fluorochrome dstrbuton may be n the nanometre range whereas the optcal mcroscope s resoluton s closer to the mcrometre. The veracty of any statement concernng colocalzaton wll thus be lmted not only by a good understandng of the three-dmensonal organzaton of the cell and ts subcellular compartments, the qualty and relablty of the labellng technques or the fathfulness of the markers appled to hghlght and dentfy the dfferent cellular addresses. It wll be equally lmted by the dmensons defned by the optcal system and the mage-acquston procedure. The authentc Receved 13 Aprl 2006; accepted 28 June The Royal Mcroscopcal Socety No clam to orgnal US government works

2 214 S. BOLTE AND F. P. CORDELIÈRES vsualzaton of ths three-dmensonal organzaton thus depends on a good control of the optcal system used and, as a matter of fact, on the mastery of some bascs n optcs, mage processng and analyss. We therefore propose a gudelne for the acquston, qualtatve evaluaton and quantfcaton of data used for colocalzaton purposes. We gve an overvew on the state of the art of colocalzaton analyss by revewng the most mportant features avalable n standard magng software. Fnally, we ntroduce a novel tool for colocalzaton analyss, named JACoP ( Just Another Co-localzaton Plugn), that combnes these currently used colocalzaton methods and an object-based tool named three-dmensonal object counter as plugns to the publc doman ImageJ software (Rasband, ). Before gettng started Basc optcal prncples Before usng any mcroscope to collect mages, one has to be aware of ts lmtatons. One of these s closely lnked to the dual nature of lght, whch s both a wave and partcle phenomenon. The objectve lens allows the collecton of lght that s only partal and s quantfed by a parameter called numercal aperture (NA). It s lnked to the angle of collecton of lght emtted from the specmen and wll determne the ablty to dstngush between two adjacent punctate lght sources. Under crtcal llumnaton, the NA of the condenser llumnatng the sample should be the same as that of the objectve. In epfluorescence mcroscopy, the objectve acts as the condenser and so ths crtcal condton s met. Each pont of a lght wave extng a lens can then be consdered as a sngle lght source emttng a crcular wave front (Huygens prncple). Therefore, when placng a screen after a lens, a dffracton pattern can be collected, resultng from nterferences between adjacent waves. Ths pattern defnes the two-dmensonal dffracton fgure, whch conssts of concentrc rngs alternatng from lght to dark (Fg. 1A). The frst lght dsc s called the Ary dsc (Inoué, 1995). When tracng a lne through ths pattern, we obtan a curve (Fg. 1D) representng the fluorescence ntensty dstrbuton of the partcle along ths lne. The Ary dsc then corresponds to the area below the major peak of ths curve and the full wdth at half maxmum of ths fluorescence ntensty curve (Fg. 1D) s used to defne the resoluton of the optcal system. To be able to dstngush between two smlar punctate lght sources through a lens, the correspondng Ary dscs should Fg. 1. An mage of a pont s not a pont but a pattern of dffracted lght. (A C) Two-dmensonal dffracton patterns of the centres of 170-nm green fluorescent beads seen through a wde-feld mcroscope. (D) and (E) Correspondng fluorescence ntensty curves traced along a lne passng through the centre of the beads n (A) and (B), respectvely (I beng the maxmum ntensty). (F) Three-dmensonal projecton of the z-stack representng the dffracton pattern of the fluorescent bead seen from the sde. (A) and (D) Note the concentrc lght rngs around the Ary dsc of a sngle fluorescent bead. The Ary dsc s the frst lght patch n ths dffracton pattern. Two characterstc dmensons may descrbe the bell-shaped curve: 1, Ary dsc dameter, whch s the dstance between the two ponts where the frst lght rng extngushes; 2, full wdth at half maxmum (FWHM), whch s drectly related to resoluton (see below). (B) and (E) Dffracton pattern of two beads. Two objects are resolved f ther correspondng ntensty curves at I/2 are dstnct. The crtcal dstance d between the centres of the ntensty curves defnes the lateral resoluton (x, y) of the optcal system. It s equal to FWHM. (C) Three-dmensonal projecton of a z-seres of a fluorescent bead seen from the sde (x, z) representng the dffracton pattern of the same fluorescent bead. Note that the axal resoluton (z) of an optcal system s not as good as the lateral resoluton (x, y). (F) The dffracton pattern s not symmetrc around the focal plane, beng more pronounced on the upper sde proxmal to the objectve. Note that a brght 10-nm bead would produce patterns of the same dmensons as ths 170- nm bead The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

3 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 215 Table 1. The laws of Abbe and ther effect on optcal resoluton and pxel szes n wde-feld and confocal mcroscopy. Wde-feld Confocal Lateral resoluton dx, y Axal resoluton dx, z Lateral resoluton dx, y Axal resoluton dx, z Expresson 0.61 λ em /NA 2 λ em /NA λ em /NA 1.4 λ em /NA 2 Lmt resoluton of a 63 ol 232 nm 574 nm 152 nm 402 nm mmerson objectve wth NA = 1.32 at λ em = 500 nm Mnmal justfed pxel sze for ths objectve 101 nm 250 nm 66 nm 175 nm NA, numercal aperture. be apart from each other (Fg. 1B). The mnmal dstance (d) between ther centres, whch gves an ntegral energy dstrbuton whose mnmum s I/2, s taken to defne the optcal resoluton or separatng power (Fg. 1E). Ths parameter may be calculated accordng to the laws of Abbe (Table 1). It depends on the NA of the objectve that, n turn, s dependent on the refractve ndex of the medum and on the wavelength of emtted lght. Furthermore, the optcal resoluton depends on the type of mcroscope used. A wde-feld mcroscope may separate two dots 200 nm apart from each other (63 ol mmerson objectve, NA = 1.32, emsson wavelength 510 nm). Introducng a confocal pnhole of 1 Ary wdth (.e. an aperture whose dameter corresponds to the dameter of the frst Ary dsc for the current wavelength) nto the optcal system wll result n an mprovement by approxmately 30% of ths lateral resoluton because out-of-focus lght s elmnated from the detector (Abbe, 1873, 1874; Mnksy, 1961). As a frst approxmaton, only lght comng from the frst Ary dsc s collected. Ths means that the aperture of the pnhole wll manly depend on the objectve used and on the refracton ndexes of all meda encountered by lght on ts way to and away from the sample. It should be set to 1 Ary unt to ensure confocal acquston. Bologcal samples are not two-dmensonal lmted. The use of stepper motors or pezo-electrcal devces n wde-feld or confocal laser scannng mcroscopes allows the collecton of optcal sectons representng the three-dmensonal volume of the sample by movng the objectve relatve to the object or vce versa. As a consequence, the dffracton pattern of lght should be consdered as three-dmensonal nformaton and wll defne the pont spread functon (PSF) (Castelman, 1979). The Ary dsc along the z-axs appears elongated, lke a rugby ball (Fg. 1C), and the overall dffracton pattern of lght has axal symmetry along the z-axs wth a three-dmensonal shape of the PSF that s hourglass-lke (Fg. 1F). The mnmum dstance separatng two dstngushable adjacent Ary dscs along the depth of the PSF wll defne the axal resoluton of the mcroscope (Table 1). The optcal laws ntroduced here mply that colocalzaton must be measured n the threedmensonal space. The mbalance between the lateral and axal resoluton of optcal mcroscopes leads to a dstorton of a round-shaped object along the z-axs. Bear n mnd that a brllant nanometrc object wll nevertheless yeld an mage whose wast s at least 200 nm and whose depth s about 500 nm, as defned by the Ary dsc. Therefore, any colocalzaton analyss must be carred out n the three-dmensonal space. Furthermore, t s self-evdent that three-dmensonal projectons of mage stacks must not be analysed as they shrnk volumetrc nformaton to two dmensons, leavng asde the depth component. Dgtal magng The lmts of optcal resoluton depend on the PSF and drectly nfluence magng parameters. Once an mage has been formed by the optcal system, t wll be collected by an electronc devce that wll translate a lght sgnal nto an electronc sgnal for further processng by the computer. Mcroscope mages are generally captured ether by dgtal cameras (a parallel matrx) or photomultplers (a sweep of pont measurements) that compose the fnal mage as a matrx of dscrete pcture elements (pxels). The defnton of an mage as pxels mples some precautons n mage acquston. To resolve two ponts and to avod under- or over-samplng, the pxel sze appled should be equal to the lateral lmt of resoluton between the two ponts dvded by at least 2 accordng to the Nyqust samplng theorem (Oppenhem et al., 1983). In mcroscopy t s wdely accepted that, accordng to ths theorem, to reproduce fathfully formed mages the detector should collect lght at 2.3 the frequency of the orgnal sgnal. Bascally, ths means that the projected mage of a sngle dot should appear on at least two adjacent senstve areas of the detector n a gven axs, namely on four pxels (2 2 for x, y). Therefore, the samplng frequency should be at least twce greater than the resoluton of the current dmenson (x, y or z). For twodmensonal acqustons ths means that the mnmal justfed pxel sze s calculated by dvdng the lateral resoluton by at least 2. In three-dmensonal magng, the sze of the z-step reles on the same laws,.e. the axal resoluton also has to be dvded at least by 2. The mnmal justfed pxel sze and the z-step sze depend on the NA of the objectve, e.g. a The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

4 216 S. BOLTE AND F. P. CORDELIÈRES objectve (ol mmerson, NA = 1.32) collectng emtted lght of 500 nm wth a lateral resoluton of 232 nm and an axal resoluton of 574 nm mples a mnmal justfed pxel sze of 101 nm and a z-step sze of 250 nm (see also Table 1). It s mportant to note that mage acquston for colocalzaton analyss should always be carred out on several subsequent optcal sectons,.e. n three dmensons, and near to the resoluton lmt of the optcal system,.e. wth the approprate justfed pxel sze and z-step sze. A frequent mstake n mcroscopy s oversamplng. Ths happens when a sngle subresoluton lght source s ftted on more than 2 (or 2.3) adjacent pxels on the detector,.e. usng pxel szes smaller that the mnmal justfed pxel sze defned by optcal resoluton and the Nyqust theorem. The resultng mage looks larger but the sgnal looks dmmer as the lght s spread out on more parts of the detector than requred. Even though the sample seems to be hghly magnfed, there s no gan n resoluton as the optcal resoluton lmt cannot be surmounted. It s furthermore mportant to avod saturaton of mages, as saturated pxels may not be quantfed properly because nformaton of the most ntense grey level values n a hstogram gets lost. It s dffcult to judge by eye f an mage composed of grey values, or green or red hues s saturated, as the human eye s not senstve enough. Our eye can, however, dstngush between hundreds of colours and therefore most mage-acquston software provdes colour look-up tables wth hues ndcatng saturated pxels and provdng the possblty of adjustng the dynamcs of grey values on the detector sde. Choce of the acquston technque We have learned that optmal mage acquston for colocalzaton analyss reles manly on the lmts of optcal resoluton; t s thus mportant to adapt the optcal system to the bologcal queston and to choose the approprate mcroscope. Confocal magng gves hgh resoluton, elmnatng out-of-focus lght by ntroducng a pnhole on the detector sde. Confocal magng s recommended when handlng thck or hghly dffusve samples such as plant tssue or bran tssue. It s mportant to note that mage acquston wth standard confocal mcroscopes s farly slow (1 s mage 1 ) and thus has been more suted to threedmensonal magng of colocalzaton n fxed samples rather than n lve samples. A dsadvantage of excludng out-of-focus lght from the detector by a confocal pnhole s that valuable nformaton may get lost and low sgnals mght not be detected (Fg. 2A). The Ary dsc n fact comprses only 10% of the total energy from a pont source. Wde-feld mcroscopes equpped wth rapd charge-coupled devces mght be a good alternatve f one wants to cope wth these knds of problems, as three-dmensonal acquston can be performed very rapdly (20 ms mage 1 ) and low-ntensty nformaton wll not be lost, as all nformaton wll be collected by the detector. The advantage of collectng all nformaton,.e. out-of-focus lght, s a constrant at the same tme as mages are blurred and dffcult to analyse drectly (Fg. 2B). Ths out-of focus lght nterferes wth accurate colocalzaton analyss and makes mage restoraton necessary. The mage that s formed on a detector by a sngle partcle (wth a sze below optcal resoluton) wll be defned by the PSF of the optcal system used. Optcs convolute mage nformaton. Ths means that the hourglasslke shape of the PSF s a model for the three-dmensonal spread of lght caused by the optcal system. Reassgnng the out-of-focus blurred lght to ts orgn s performed by a process called deconvoluton (Fg. 2C). Ths s a computatonal technque that ncludes methods that help to reattrbute the sgnal spread n three dmensons accordng to the PSF to ts orgn. Deconvoluton may restore the resoluton of mages n both wde-feld and confocal mcroscopy and s the subject of some excellent revews (Wallace & Swedlow, 2001; Sbarta, 2005). Deconvoluton n combnaton wth wde-feld mcroscopy s restrcted to thn objects (< 50 µm). Although gvng a more resolved mage, one of the major ptfalls of deconvoluton technques arses from the complexty of the mage. An mage must be consdered as a composton of multple PSFs because Fg. 2. Comparson of cellular magng by confocal and wde-feld mcroscopy. Medan plane of a maze root cell mmunolabelled wth AtPIN1/ Cyanne3.18 (Boutté et al., 2006). Scale bar, 10 µm. Images were acqured by confocal (A) and wde-feld (B) and wde-feld followed by deconvoluton (C) mcroscopy. All mages show polar dstrbuton of At-PIN1 on the plasma membrane and on subcellular punctform structures. Note that the raw sngle confocal mage (A) s sharp because out-of-focus lght was cut off by the pnhole. The wde-feld mage (B) s typcally blurred. (C) Deconvoluton of the wde-feld mage has reassgned the out-of-focus lght to ts orgn, wth a gan n sharpness and contrast. Deconvoluton has led to a slght gan of nformaton compared wth confocal mcroscopy; low-ntensty sgnals that were not detected by confocal mcroscopy have become vsble after deconvoluton of the wde-feld data (arrows). Proten subdomans at the plasma membrane may also be refned by deconvoluton of wde-feld mages (arrowheads) The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

5 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 217 each fluorescent sgnal of the sample results n a dffracton pattern that s dsplayed on the detector. Moreover, PSFs are not constant n the three-dmensonal volume maged, as the PSFs are degraded n the depth of the sample and appear to be dsturbed at the nterface of two meda wth dfferent refracton ndexes. Further technques have been developed that overcome the constrants of acquston rate or out-of-focus lght. These nclude structured llumnaton and rapd confocal devces and are dscussed n detal elsewhere (Brown et al., 2006; Garn et al., 2005). In ths work, however, we wll focus on commonly avalable standard confocal and wde-feld mcroscopy. Incdence of fluorochromes, lght sources, flters and objectves It has already been mentoned that the resoluton capacty of an optcal system depends on the angular propertes of ts objectve, the composte refractve ndex of all meda crossed by lght and the emsson wavelength of the fluorochromes used (Table 1). A number of fluorochromes may be used to label dfferent protens of nterest. The ablty to dstngush between ndvdual emsson spectra s a prmary concern, renforced by selectve exctaton of only one fluorochrome at a tme. Ths am s acheved by optmzng: () the choce of fluorochromes, () the selectvty of exctaton and () the means of emsson dscrmnaton. Any fluorescent reagent can be characterzed by ts exctaton and emsson spectra, whch n turn may depend upon the fluorophore s envronment (Valeur, 2002). These classcal curves, respectvely, represent the probablty of makng an electronc transton from ground to excted state when exposed to photon energy of a partcular wavelength and to release a photon at a partcular wavelength when fulfllng the opposte transton. The frst value to be taken nto account s the Stoke s shft, whch s defned as the spectrum dstance between the most effcent exctaton (peak n the exctaton spectra) and the maxmum of emsson. The ablty to sort emsson from exctaton lght depends partly on ths value, as ncdent lght s about 10 4 more ntense than the sgnal beng recovered (Tsen & Waggoner, 1995). The wdth of exctaton and emsson curves contrbutes to the practcalty of fluorescent reagents for dstnctveness; the narrower the curves, the easer the fluorochromes wll be to separate. However, ths s only true for fluorochrome pars wth spectra far enough apart from each other. A wde range of fluorescent reagents s now avalable to cover the spectrum from vsble to near nfrared. Fluorochromes may be coupled to prmary or secondary antbodes for mmunolabellng. Other fluorescent compounds may accumulate n specfc cellular compartments, such as nucle, endoplasmc retculum, Golg apparatus, vacuoles, endosomes, mtochondra or peroxsomes. Genetcally encoded targeted fluorescent protens from jellyfsh or corals are readly avalable and are helpful n lve cell studes. Newly engneered semconductor collodal partcles (Q-Dots) are adapted for sngle molecule labellng (Dahan et al., 2003; Gao et al., 2004). When choosng fluorochrome combnatons for colocalzaton studes, ther spectra must be unambguously dstnctve. Furthermore, t has to be consdered that these spectra may be dependent on the physcal envronment (Bolte et al., 2004a, 2006). We have to ntroduce here the terms bleed-through and cross-talk of fluorochromes, as avodng these phenomena s crucal to colocalzaton analyss. Bleed-through s the passage of fluorescence emsson n an napproprate detecton channel caused by an overlap of emsson spectra (Fg. 3). Cross-talk s gven when several fluorochromes are excted wth the same wavelength at a tme because ther exctaton spectra partally overlap. Let s consder the fluorochrome couple fluorescen sothocyanate (FITC) and Cyanne3.18 (Cy3), whch s frequently used for mmunolabellng for colocalzaton analyss (Fg. 3). The exctaton spectra of these two fluorochromes seem to be well apart wth FITC peakng at 494 nm and Cy3 wth a mnor exctaton peak at 514 nm and a major exctaton peak at 554 nm. Even usng the narrow laser lne of 488 nm for FITC exctaton, one may already observe a slght cross-talk between FITC and Cy3, as Cy3 exctaton spectra have slght but sgnfcant Fg. 3. Defnton of cross-talk and bleed-through wth the fluorochrome couple fluorescen so-thocyanate/cyanne3.18 (FITC/Cy3). (A) Exctaton spectra of FITC (broken lne, max. 490 nm) and Cy3 (sold lne, max. 552 nm). The grey arrow marks the poston of the standard 488-nm laser lne of confocal mcroscopes. Note the overlap of the exctaton spectra at 488 nm (cross-talk). (B) Emsson spectra of FITC (broken lne, max. 520 nm) and Cy3 (sold lne, max. 570 nm). The grey bar marks the typcal detecton wndow of Cy3. Note the overlap of FITC and Cy3 emsson n ths detecton wndow (bleed-through) The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

6 218 S. BOLTE AND F. P. CORDELIÈRES absorbance at 488 nm (Fg. 3A). Moreover, even when exctng FITC and Cy3 sequentally wth 488 and 543 nm, one may detect a bleed-through of the lower energy (yellow) part of the FITC emsson concdng wth the emsson maxmum of Cy3 n the Cy3 detecton channel (Fg. 3B). When usng bandpass-fltered exctaton lght, such as n wde-feld mcroscopy, nstead of laser lnes or monochromatc lght, the stuaton may get worse. It s thus essental to apply some smple strateges that help to avod cross-talk and bleed-through. Frstly, t s always mportant to have sngle labelled controls for each fluorochrome used. In ths way one may check for bleedthrough between fluorochromes on the detector sde. Secondly, n laser scannng mcroscopy, t s hghly recommended to perform sequental acqustons exctng one fluorochrome at a tme and swtchng between the detectors concomtantly. Another method of meetng the challenge s spectral unmxng, a qute smple mathematcal operaton that was orgnally developed for satellte magng. Spectral unmxng software packages are often ncluded n mage-acquston software of the mcroscope manufacturers. By ths technque, whch s a correcton of spectral bleed-through, t s also possble to enhance the chromatc resoluton of fluorescence mcroscopy. Two general approaches may be dstngushed. One s to perform mcrospectrofluorometry and to use the model (or measure) of separate fluorochromes to perform spectral deconvoluton of the complex raw mage (Zmmermann et al., 2003). Ths mples curve fttng and extrapolaton. A second, smpler approach s to expermentally determne the bleed-through factor for a gven optcal confguraton and to use ths to derve corrected values for each pxel. Ths s analogous to pulse compensaton n flow cytometry. To unmx the spectra of fluorochromes wth strongly overlappng emsson spectra, t s necessary to assgn the contrbuton of dfferent fluorochromes to the overall sgnal. Ths s done frst by determnng the spectral propertes of the ndvdual fluorochromes under the same magng condtons used for the multlabelled samples. We wll agan consder the two fluorochromes FITC and Cy3 seen through ther respectve flters A and B. Usng a monolabelled slde, FITC seen through A wll gve an ntensty a FITC and b FITC through B. Analogous notatons wll be used for Cy3. Then magng a dual-labelled FITC and Cy3 sample, the mage through A wll be a FITC + a Cy3 ; the mage of FITC acqured usng the approprate flter s contamnated by a contrbuton from Cy3. The same phenomenon wll occur for the mage of Cy3 collected through B (b FITC + b Cy3 ). The use of mono-labelled sldes allows the estmaton of the relatve contrbuton of FITC to the mage of Cy3 and s used to gve a more relable mage of FITC (a FITC + b FITC ) and Cy3 (a Cy3 + b Cy3 ). The rato FITC : Cy3 of the average ntenstes of sngle fluorochrome-labelled structures measured at the two exctaton wavelengths for FITC and Cy3, respectvely, gves a constant that s specfc for each fluorochrome under gven expermental condtons and fxed settngs. The ntensty s then redstrbuted n order to restore a corrected sgnal for each colour channel undsturbed by emsson from the other fluorochrome. Fluorochromes may also transfer energy to each other by Förster resonance energy transfer (for revew see Jares- Erjman & Jovn, 2003). Ths non-radatve energy transfer may occur when the emsson spectrum of the frst fluorochrome (donor) overlaps wth the exctaton spectrum of the second fluorochrome (acceptor) and f the donor and acceptor molecules are n close vcnty ( Å). Förster resonance energy transfer causes a reducton of the emsson of the donor fluorochrome and an ncrease of the emsson of the acceptor fluorochrome, therefore resultng n a msbalanced ntensty rato between the two mage channels. It s thus also crucal to select the frst fluorochrome wth an emsson spectrum as dstnct as possble from the exctaton spectrum of the second fluorochrome n order to avod Förster resonance energy transfer effects that would complcate the nterpretaton of colocalzaton data. The choce of lght sources and approprate flters s the next step for approprate dscrmnaton between fluorescence spectra. We have already learned that usng monochromatc lght from a laser source n a confocal mcroscope lowers the rsk of exctng several fluorochromes at a tme, even f t does not exclude cross-talk. In wde-feld mcroscopy mercury or xenon lamps have spectral output spannng from UV to nfrared, wth numerous peaked bands, notably n the case of mercury. They are used n combnaton wth approprate flters or as part of monochromators. As a consequence, when usng fltered lght the exctaton s not monochromatc and the rsk of exctng several fluorochromes at a tme s hgh. Ths nconvenence may be partally crcumvented by usng a monochromator to generate a sutably narrow subrange of wavelengths that may be optmzed for each stuaton. However, care has to be taken as the monochromator may generate a slght exctaton leakage on both boundares of the narrowed exctaton wndow, leadng to possble cross-talk. The choce of objectves used for colocalzaton analyss at the subcellular level s crucal to attan optmal resoluton. Objectves used should be of hgh qualty, wth a hgh NA (> 1.3) and magnfcatons adapted to the camera n wdefeld mcroscopy. In both knds of mcroscopy, the NA s crtcal, as z-resoluton mproves as a functon of (NA) 2 (see Table 1). Objectves should be corrected for chromatc and sphercal aberratons. Chromatc aberratons are due to the falure of the lens to brng lght of dfferent wavelengths to a common focus. Sphercal aberratons come from the falure of a lens system to mage the central and perpheral rays at the same focal plane. Objectves corrected for both aberratons are called plan-apochromatc and confocal mcroscopes are usually equpped wth these. For colocalzaton analyses t s recommended to use mmerson objectves to reduce aberratons due to the refracton ndex changes. Ths means ol mmerson for fxed mounted specmens and aqueous mmerson for lve cell studes The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

7 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 219 Checkng the system Before performng colocalzaton measurements, t s mportant to check the mcroscope s ntegrty. Ths may be done by measurng the PSF of the optcal system (Scalettar et al., 1996; Wallace & Swedlow, 2001), usng objects whose szes are just matchng or below the mcroscope s resoluton. Small fluorochrome-labelled polystyrene beads of nm are avalable for ths. Remember that the resoluton of the optcal system s closely lnked to the NA of the objectve used, refracton ndex of the mountng medum, mmerson medum (ol, glycerol or water), coverslp thckness and emsson wavelength of the fluorochrome. Indvdual PSFs should thus be measured on fluorescent beads of the respectve wavelengths mounted n dentcal condtons to the sample and wth the objectves that are used for colocalzaton analyss. The shape of the PSF of a fluorescent bead gves an ntutve characterzaton of the mage qualty. It can also be used to test the objectve performance and ntegrty. A drty objectve or a non-homogeneous mmerson medum wll result n a deformed PSF (Sbarta, 2005). Returnng to objectve qualty, one may be surprsed to observe that the maxma of ntensty for all fluorochromes may not be concdent n space. Ths observaton s due to an mperfecton n the lens desgn or manufacture resultng n a varable focalzaton of lght as a functon of wavelength. Even f most manufactured objectves are apochromatc, the refracton ndex of mmerson ol s dependent on both temperature and wavelength, gvng rse to ths phenomenon. Lkewse, glycerol s hygroscopc and ts refractve ndex wll n practce change wth tme. As a consequence, and especally n the case of colocalzaton studes, the chromatc aberraton may n ths case be determned and the shft between mages corrected (Manders, 1997). Pre-processng of mages As perfect as an optcal system can be, we have already seen that an mage s an mperfect representaton of the bologcal system. The llumnaton system used n wde-feld mcroscopy wll mpar the mage, especally f t s not well algned. As a consequence, the feld of vew may not be llumnated n a homogeneous fashon. When tryng to quantfy colocalzaton as a concdence of ntensty dstrbutons, one may need to correct uneven llumnaton. Ths may smply be done by correctng the mage of the sample usng a brght mage of an empty feld. Ths correcton s acheved by dvdng the former mage by the latter. Ths operaton may be carred out wth ImageJ usng the Image Calculator functon. Nose s another major problem n dgtal magng. However, before tryng to correct mages for t, we must frst address ts possble orgns. Illumnaton systems such as mercury or xenon lamps are not contnuously provdng photons and may be consdered as blnkng sources. As a consequence, even though all regons of a feld wll statstcally be ht by the same number of photons over a long perod, the number of photons exctng fluorochromes s not the same when comparng a regon wth ts neghbours on a mllsecond scale. Smlarly, the emsson of a photon by a fluorochrome s dependent on ts probablty of returnng to ground state. Ths so-called photon nose wll mprnt a salt-and-pepper-lke background on the mage. As t s a stochastc functon, t can be partally overcome by ncreasng the exposure tme on charge-coupled devce cameras or slowng the frequency (ncreasng dwell tme) of scannng on a confocal mcroscope. One may also collect successve mages and average them. Furthermore, nose orgnatng from the detecton devce (electronc nose or dark current) may be lmted by coolng the detecton devces. Intrnsc statstcal nose follows a Posson dstrbuton. To remove ths knd of nose, mages may be post-processed usng adaptve flterng. Ths may be done by changng the pxel value to an ntensty calculated on the bass of the local statstcal propertes of both the sgnal and nose of neghbourng pxels. Ths may, however, result n a loss of features such as sharp contours. Out-of-focus lght may be reassgned to ts orgn by deconvoluton as already mentoned (Wang, 1998). Fnally, magng may be mpared by background comng from ether natural fluorescence of the sample or beng generated when preparng the sample. In most cases, nothng can be done after mage acquston unless a unform background s observed. In ths specal case, ts mean ntensty s determned and ths value s subtracted across the full mage. More subtle processes exst, such as spectral unmxng, that may gve better results on specfc problems and the reader may consult approprate mage-processng handbooks (Gonzales & Woods, 1993; Pawley, 1995; Ronot & Usson, 2001). Vsualzng colocalzaton When vsualzng colocalzaton, the elementary method s to present results as a smple overlay composed of the dfferent channels, each mage beng pseudo coloured usng an approprate colour look-up table. For example, t s commonly accepted that the dual-channel look-up table for green and red wll gve rse to yellow hotspots where the two molecules of nterest are present n the same pxels. However, anyone who has been usng ths method knows ts lmts. The presence of yellow spots s hghly dependent on the relatve sgnal ntensty collected n both channels; the overlay mage wll only gve a relable representaton of colocalzaton n the precse case where both mages exhbt smlar grey level dynamcs,.e. when the hstograms of each channel are smlar. Ths s rarely the case when magng two fluorochromes wth dfferental sgnal strength. As a consequence, mage processng s requred to match the dynamcs of one mage to the other. Ths s often done by hstogram stretchng. However, hstogram stretchng may result n falsfed observatons because the resultant mage does not reflect the true stochometry of the molecules 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

8 220 S. BOLTE AND F. P. CORDELIÈRES maged. An alternatve to hstogram stretchng s the use of specfcally desgned look-up tables that wll enhance the vsual effect of concdental locatons (Demandolx & Davoust, 1997). These authors proposed a new pseudo-colourzaton method n the form of a look-up table enablng vsualzaton of the frst fluorophore alone n cyan and the second alone n magenta. As the colocalzaton event s generally dffcult to vsualze and as the rato of fluorophores may vary locally, they used green and red to hghlght regons where one fluorophore s more ntense than the other and yellow n the case where both ntenstes are the same. Ths method mproved the dscrmnaton of fluorescence ratos between FITC and Texas Red. Measurng colocalzaton Overlay methods help to generate vsual estmates of colocalzaton events n two-dmensonal mages; however, they nether reflect the three-dmensonal nature of the bologcal probe nor the restraned resoluton along the z-axs. Furthermore, these overlay methods are not approprate for quantfcaton purposes because they may result n msnterpretaton of relatve proportons of molecules. To overcome these problems mage analyss s crucal. There are two basc ways to evaluate colocalzaton events, a global statstc approach that performs ntensty correlaton coeffcent-based (ICCB) analyses and an object-based approach. The theory behnd some of these tools s rather complex and sometmes dffcult to comple and the results obtaned have been dffcult to compare untl now. Here, we ntroduce a publc doman tool named JACoP ( plugns/track/jacop.html) that groups the most mportant ICCB tools and allows the researcher to compare the varous methods wth one mouse-clck. Furthermore, an objectbased tool called three-dmensonal object counter ( rsb.nfo.nh.gov/j/plugns/track/objects.html) s also avalable that may be used for object-based colocalzaton analyss. These tools process mage stacks and allow an automated colocalzaton analyss n the three-dmensonal space. To ntroduce these tools and ther utlty n colocalzaton analyss we wll gve a general overvew on the roots of ICCB and object-based methods. For ths purpose, we have compared four dfferent possble subcellular colocalzaton stuatons (Fg. 4). A complete Fg. 4. Reference mages for colocalzaton analyss. Images for colocalzaton analyss were acqured from fxed maze root cells wth Golg stanng (A) (Boutté et al., 2006) or endoplasmc retculum stanng (B) (Kluge et al., 2004) and on fxed mammalan HeLa cells wth mcrotubule plus-end trackng protens EB1 and CLIP-170 stanng (C) (Cordelères, 2003), and nuclear and mtochondral stanng (D). Scale bars, 10 µm. These mages llustrate the four commonly encountered stuatons n colocalzaton analyss. (A) Complete colocalzaton. (B) Complete colocalzaton wth dfferent ntenstes. (C) Partal colocalzaton. (D) Excluson. Grey level mages of the green and red mage pars (A D) were used for subsequent treatments wth ImageJ. A zoomed vew of the nsets s shown on each sde of the colour panels The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

9 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 221 colocalzaton stuaton has been modelled by duplcatng a raw mage of a Golg stanng n a plant cell (as n Boutté et al., 2006) and assgnng t to two dfferent colour channels (Fg. 4A, Raw and Duplcated). Another stuaton, complete colocalzaton wth dfferent ntenstes, s gven by the colabellng of the endoplasmc retculum wth two endoplasmc retculum-specfc antbodes (as n Kluge et al., 2004; Fg. 4B). A partal colocalzaton stuaton s shown by the colabellng of mammalan cells wth dfferent mcrotubule plus-end trackng protens (Cordelères, 2003; for revews, see Schuyler & Pellman, 2001; Galjart, 2005) (Fg. 4C). Excluson of fluorescent sgnals has been acheved by stanng mtochondra and the nucleus n mammalan cells (Fg. 4D). To nvestgate the nfluence of fluorescence background or photonc nose on colocalzaton analyss wth JACoP, we added dfferent levels of random nose to the complete colocalzaton mage par (mage data not shown). The sgnal-to-nose ratos n these mages were calculated and vared from to 3.52 db. Correlaton analyss based on Pearson s coeffcent The ICCB tools manly use statstcs to assess the relatonshp between fluorescence ntenstes. A wealth of colocalzaton analyss software now avalable as part of basc mage-analyss tools or more specalzed magng-analyss software s based on ICCB analyss. Ths s manly due to the relatve ease of mplementng the software. In ths case, statstcal analyss of the correlaton of the ntensty values of green and red pxels n a dual-channel mage s performed. Ths s mostly done usng correlaton coeffcents that measure the strength of the lnear relatonshp between two varables,.e. the grey values of fluorescence ntensty pxels of green and red mage pars. Pearson s coeffcent. A smple way of measurng the dependency of pxels n dual-channel mages s to plot the pxel grey values of two mages aganst each other. Results are then dsplayed n a pxel dstrbuton dagram called a scatter plot (Fg. 5) or fluorogram. The ntensty of a gven pxel n the green mage s used as the x-coordnate of the scatter plot and the ntensty of the correspondng pxel n the red mage as the y-coordnate. In some software the ntensty of each pxel represents the frequency of pxels that dsplay those partcular red and green values n the fluorogram mage. Leavng asde nose and low background, we wll frstly examne the scatter plot to see f there are numerous pxels wth only one sgnfcant sgnal (Fg. 5E). Secondly, where both sgnals are present, we shall descrbe ther relatonshp as a strong, lower, weak or non-exstent correlaton that may be postve or negatve. If we consder that the labellng of both fluorochromes s proportonal to the other and the detecton of both has been carred out n a lnear range, the resultng fluorogram pattern should be a lne. The slope would reflect the relatve stochometry of both fluorochromes, modulated by ther relatve detecton effcences. In practce n a complete colocalzaton stuaton, dots on the dagram appear as a cloud centred on a lne (see Fg. 5A). The spread of ths dstrbuton wth respect to the ftted lne may be estmated by calculatng the correlaton coeffcent, also called Pearson s coeffcent (PC). As most ICCB tools are based on the PC or ts dervatves, we wll ntroduce t here n detal. The lnear equaton descrbng the relatonshp between the ntenstes n two mages s calculated by lnear regresson. The slope of ths lnear approxmaton provdes the rate of assocaton of two fluorochromes. In contrast, the PC provdes an estmate of the goodness of ths approxmaton. Its value can range from 1 to 1, wth 1 standng for complete postve correlaton and 1 for a negatve correlaton, wth zero standng for no correlaton. Ths method has been appled to measure the temporal and spatal behavour of DNA replcaton n nterphase nucle (Manders et al., 1992). We used the JACoP tool to analyse the Pearson s correlaton coeffcents and to vsualze the correspondng scatter plots of the four dfferent colocalzaton stuatons descrbed n Fg. 4. Fgure 5(A) shows the scatter plot wth the dots on the dagram appearng as a cloud centred on a lne n the case of complete colocalzaton. The PC approaches 1 n ths case. A dfference n the ntenstes of the green mage wth stll completely colocalzed structures results n a rotaton of the dotted cloud towards the red axs (Fg. 5B). As a consequence, the ftted lne changes ts slope and comes closer to the axs of the most ntense channel. We can state that colocalzaton s observed whenever both sgnals are sgnfcant but that a subpopulaton of purely red pxels has appeared because of poor senstvty n the green channel. In the partal colocalzaton stuaton the dots of the scatter plot form a rather unform cloud wth a PC of 0.69 (Fg. 5C). Mutual excluson of the fluorescent sgnals shows scattered dstrbutons of the pxels close to both axes (Fg. 5D) and a negatve PC. Scatter plots and PCs pont to colocalzaton especally where t s complete (Fg. 5A and B); however, they rarely dscrmnate dfferences between partal colocalzaton or excluson, especally f mages contan nose. The nfluence of nose and bleed-through on the scatter plots and PCs s shown n Fg. 5(A*) and (F) (black bars). Random nose has been added to the mage pars of Fg. 4(A) and s recognzable by the shapeless cloud of dots near the orgn (Fg. 5A*). As a consequence, the PC wll decrease and fnally tend to zero as more nose s added (Fg. 5F, black bars). Ths demonstrates the senstvty of PC to background nose and hence to thresholdng. These results show that an evaluaton of colocalzaton events usng PCs alone may be ambguous, as values are hghly dependent on nose, varatons n fluorescence ntenstes or heterogeneous colocalzaton relatonshps throughout the sample (Fg. 5A C). Nose and background must be removed. Moreover, the coeffcent wll soon be domnated, not by the central phenomenon, but by the permeter gven to the analyss (the near-threshold events). Values other than those close to 1 and especally md-range coeffcents ( 0.5 to 0.5) do not allow conclusons to be drawn The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

10 222 S. BOLTE AND F. P. CORDELIÈRES Fg. 5. Colocalzaton analyss wth JACoP; Pearson and Manders, scatter plots and correlaton coeffcents. Scatter plots (A D) correspond to the colocalzaton events as shown n Fg. 4. (E) Model scatter plot explanng the effects of nose and bleed-through. (F) Pearson s and Manders coeffcents n the dfferent colocalzaton stuatons. A complete colocalzaton results n a pxel dstrbuton along a straght lne whose slope wll depend on the fluorescence rato between the two channels and whose spread s quantfed by the Pearson s coeffcent (PC), whch s close to 1 as red and green channel ntensty dstrbutons are lnked (F, a n0, black bar). (B) A dfference n fluorescence ntenstes leads to the deflecton of the pxel dstrbuton towards the red axs. Note that the PC dmnshes even f complete colocalzaton of subcellular structures s stll gven (F, b, black bar). (C) In a partal colocalzaton event the pxel dstrbuton s off the axes and the PC s less than 1 (F, c, black bar). (D) In exclusve stanng, the pxel ntenstes are dstrbuted along the axes of the scatter plot and the PC becomes negatve (F, d, black bar). Ths s a good ndcator for a real excluson of the sgnals. (E) The effect of nose and bleed-through on the scatter plot s shown n the general scheme. (F) The nfluence of nose on the PC was studed by addng dfferent levels of random nose (n1 n4)* to the complete colocalzaton event (A = n0, no nose). (F) Note that the PC (black bar) tends to 0 when random nose s added to complete colocalzng structures. The nset (A*) n (A) shows the scatter plot for the n2 nose level. Note that all of the mentoned colocalzaton events (A D) may only be detected fathfully once mages are devod of nose. (F) Manders coeffcents were calculated for (A D). The thresholded Mander s tm 1 (cross-hatched bars) and tm 2 (dagonal hatched bars) are shown. Compare complete colocalzaton (a n0 ), complete colocalzaton wth random nose added (a n1 a n4 ), and complete colocalzaton wth dfferent ntenstes (b), partal colocalzaton (c) and excluson (d). Note that the orgnal Manders coeffcents are not adapted to dstngush between these events, as they stay close to 1 for all stuatons (not shown). *Sgnal-to-nose ratos are: n1 = db, n2 = 6.26 db, n3 = 4.15 db and n4 = 3.52 db. Ths also apples when lookng at mages corrupted by bleedthrough. A thn cloud of correlated pxels wll appear on the scatter plot, close to one or both axes (data not shown). As a consequence, PC wll tend to 1 or 1 although not representng a bologcal correlaton. Although provded n most standard mage-analyss software packages, scatter plots n combnaton wth the PC only gve a frst estmate of colocalzaton. They are especally useful for ntal dentfcaton of dverse relatonshps (correlatons, bleed-through, exceptonal coexpresson of sgnals) and for examnaton of complex overlays through the wndows (regons of nterest) so defned. However, they are not suffcent to evaluate colocalzaton events rgorously. The PC defnes the qualty of the lnear relatonshp between two sgnals but what f the sample contans two or more dfferent stochometres of assocaton? The lnear regresson wll try to ft the segregated dot clouds as one, resultng n a dramatc decrease of the PC. The best alternatve would be to ft dot clouds by ntervals, resultng n several PCs for a sngle par of mages. Manders coeffcent. Manders overlap coeffcent s based on the Pearson s correlaton coeffcent wth average ntensty values beng taken out of the mathematcal expresson (Manders et al., 1992). Ths new coeffcent wll vary from 0 to 1, the former correspondng to non-overlappng mages and the latter reflectng 100% colocalzaton between both 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

11 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 223 mages. M 1 s defned as the rato of the summed ntenstes of pxels from the green mage for whch the ntensty n the red channel s above zero to the total ntensty n the green channel and M 2 s defned conversely for red. Therefore, M 1 (or M 2 ) s a good ndcator of the proporton of the green sgnal concdent wth a sgnal n the red channel over ts total ntensty, whch may even apply f the ntenstes n both channels are really dfferent from one another. Ths defnton could reveal both coeffcents to be perfect for colocalzaton studes. Unfortunately, ths s only true f the background s set to zero. Furthermore, t s not possble to dstngush between complete and partal colocalzaton stuatons wth the M 1 and M 2 coeffcent. The Manders coeffcent s very senstve to nose. To crcumvent ths lmt, M 1 and M 2 may be calculated settng the threshold to the estmated value of background nstead of zero (Fg. 5F, cross-hatched and dagonal hatched bars). When nose or cross-talk are present, the automatcally retreved threshold may be too hgh, leadng to the loss of valuable nformaton. In ths case, nose and cross-talk must be corrected before calculatng the coeffcents. Costes approach. Recently, a statstcal sgnfcance algorthm based on the PC has been ntroduced (Costes et al., 2004). The Costes approach s performed n two subsequent steps. Frstly, the correlaton n dfferent regons of the two-dmensonal hstogram s taken nto account to estmate an automatc threshold and the PC of ths thresholded mage par s calculated. To calculate ths automatc threshold, lmt values for each channel are ntalzed to the maxmum ntensty of each channel and progressvely decremented. The PC s concomtantly calculated for each ncrement. The fnal thresholds are then set to values that mnmze the contrbuton of nose (.e. PC under the threshold beng null or negatve). As a second step, Costes et al. (2004) ntroduced a new statstcal analyss based on mage randomzaton and evaluaton of PC. The authors ponted out that a sngle mage reflects a partcle dstrbuton wth szes above optcal resoluton. These partcles appear as a collecton of adjacent pxels wth ntenstes correlated to ther neghbours. The ntensty dstrbuton depends on the PSF of the acquston system and the approxmate partcle sze may be calculated usng the full wdth at half maxmum of the fluorescence ntensty curve. The full wdth at half maxmum defnes the area over whch a sgnal belongng to a sngle partcle s spread out, gven the fact that the partcle sze s convolved by the PSF of the optcal system. The authors created a randomzed mage by shufflng pxel blocks wth the dmensons defned by the full wdth at half maxmum for the mage of the green channel. Ths process s done 200 tmes for a sngle mage and the PC s calculated each tme between the random mages of the green channel and the orgnal mage of the red channel. The PC for the orgnal non-randomzed mages s then compared wth the PCs of the randomzed mages and the sgnfcance (p-value) s calculated. The p-value, expressed as a percentage, s nversely correlated to the probablty of obtanng the specfed PC by chance (.e. on randomzed mage pars). Ths value s calculated as the ntegrated area under the PC dstrbuton curve, from the mnmum PC value obtaned from randomzaton to the PC obtaned from orgnal mages (see Fg. 6). Ths method ntroduces for the frst tme a statstcal comparson that may exclude colocalzaton of pxels due to chance. We performed ths two-step analyss wth JACoP for the four colocalzaton events mentoned earler. However, for clarty we only show the scatter plot and mage pars analysed for the partal colocalzaton event (Fg. 6). We obtaned a scatter plot that s dvded nto four dfferentally coloured zones by horzontal and vertcal lnes that represent the borders of the automatc thresholds for the red and green channel, respectvely (Fg. 6A). The PC s Subsequently, we created a set of 200 randomzed mages (see Fg. 6B, randomzed green mage) from the green mage and calculated the colocalzaton map and the p-value (Fg. 6B). An overlay of green and red channels wth the mask of the colocalzng pxels n whte (Fg. 6B, colocalzaton map) gves a topologcal map of colocalzaton dstrbuton. The PC calculated earler has a p-value of 100%, suggestng that colocalzaton n the regons masked n whte s hghly probable. Fgure 6(C) and (D) show the confdence nterval,.e. the range of PC varaton obtaned from randomzed mages (C, curve; D, grey bars), n comparson to the PCs obtaned for the ntal set of mages (red lnes and bars). Surprsngly, the orgnal PC s above the upper boundary of the confdence nterval n the complete colocalzaton stuaton, n complete colocalzaton wth dfferent ntenstes and n partal colocalzaton (Fg. 6D, a n0 to c). Ths means that all of those stuatons may be consdered as true colocalzaton cases. As expected n the case of excluson, the PC s below the lower boundary of the nterval and the p-value s equal to 0% (Fg. 6D, d). It seems that ths method ponts out true colocalzaton even when mages are corrupted by hgh levels of nose (Fg. 6D, a n1 a n4 ). However, the Costes approach may reach ts lmts when ncreasng the statstcal parameters of nose and especally the SD of nose. The confdence nterval may encompass the orgnal PC, whch may mpar a prognostc of a true colocalzaton, as the p-value s dependent on the dstance between the lower boundary of the nterval and the orgnal PC value. In that partcular stuaton, the colocalzaton dagnostc may not gve rse to a vald concluson. Although provdng a frst statstcal estmate of colocalzaton, Costes approach s also hghly dependent on the way n whch the test s set up. The authors ntally proposed 200 randomzaton rounds to obtan a sgnfcant statstcal dstrbuton wth more randomzaton leadng to more relable elmnaton of false postves. Van Steensel s approach. Another development based on PC has been proposed for colocalzaton analyss usng, as an example, glucocortcod and mneralocortcod receptors n 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

12 224 S. BOLTE AND F. P. CORDELIÈRES Fg. 6. Colocalzaton analyss wth JACoP; Costes. (A) Scatter plot of a partal colocalzaton stuaton (such as Fgs 4C and 5C). We dstngush four regons of nterest (red, yellow, green and blue overlay); the yellow regon represents all pxels above the dual automatc thresholds; the red regon represents all pxels wth red channel ntenstes over the automatc threshold and the green channel represents ntenstes below the automatc threshold. The green regon represents pxels wth green pxels over and red pxels below threshold and the blue regon desgnates pxels under the threshold n both channels. (B) A green and red mage par (Green and Red channel) was used for mage randomzaton, creaton of a colocalzaton map and subsequent p-value calculaton. A set of 200 randomzed mages was created from the green channel mage (randomzed green mage s one example out of 200). Co-localzng pxels are shown as a whte overlay on the green and red channel merge (Colocalzaton map). (C) Plot of the dstrbuton of the Pearson s coeffcents (PCs) of randomzed mages (curve) and of the green channel mage (red lne). The red lne ndcates the PC and the curve shows the probablty dstrbuton of the PCs of the randomzed mages. Note that the p-value for ths analyss was 100% ndcatng a hgh probablty of colocalzaton. (D) Range of PCs obtaned from randomzed mages (grey bars, mean value ± SD) compared wth the PC obtaned for the ntal set of mages (red lnes) n cases of complete colocalzaton events (a) wth dfferent levels of nose added (a n0 a n4 ), dfferent ntenstes (b), partal colocalzaton (c) and excluson (d). The P-values were 100% for (a c) and 0% for (d). the nucle of rat hppocampus neurones (Van Steensel et al., 1996). These receptors are concentrated n punctate clusters wthn the nucleus that partally colocalze. The authors appled a cross-correlaton analyss by shftng the green mage n the x-drecton pxel per pxel relatve to the red mage and calculatng the respectve PC. The PC s then plotted as the functon of δx (pxel shft) and the authors thus obtaned a cross-correlaton functon. We performed the analyss on the four dfferent colocalzaton stuatons wth the followng results. Completely colocalzng structures peak at δx = 0 and show a bell-shaped curve (Fg. 7A). A dfference n fluorescence ntensty leads to a reducton of the heght of the bell-shaped curve, 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

13 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 225 whereas the peak s stll at δx = 0 (Fg. 7B). Partally overlappng structures show a peak asde of δx = 0 (Fg. 7C). Structures that are mutually excluded from each other show a dp at δx = 0 (Fg. 7D). The cross-correlaton functon allows ready dscrmnaton between the dfferent colocalzaton events. However, t has the major drawback that t s only valuable for small and sotropc partcles, as t may vary dependng on ther orentaton relatve to the selected shft axs. The cross-correlaton functon calculaton allows an estmaton of the dmensons of the partcles, as the wdth of the bell-shaped curve at half maxmum reflects the approxmate partcle sze convolved by the PSF of the optcal system. L s approach. The work of L et al. (2004) s of partcular nterest n the search for an nterpretable representaton of colocalzaton to dscrmnate concdental events n a heterogeneous stuaton. They frst assumed that the overall dfference of pxel ntenstes from the mean ntensty of a sngle channel s equal to zero, n pxels( A a) = 0 and n pxels( B b) = 0 wth the upper-case character beng the current pxel s ntensty and the lower-case character beng the current channel s mean ntensty. As a consequence, the product of the two equaltes should tend to zero. Now f we consder colocalzng pxels ths product should be postve as each dfference from the mean s of the same sgn. The dfferences of ntenstes between both channels are scaled down by fttng the hstogram of both mages to a 0 1 scale. The ntensty correlaton analyss results are then presented as a set of two graphs, each showng the normalzed ntenstes (from 0 to 1) as a functon of the product (A a)(b b) for each channel (Fg. 8). In ths representaton the x-axs reflects the covarance of the current channel and the y- axs reflects the ntensty dstrbuton of the current channel. As prevously stated, n the case of colocalzaton the product (A a)(b b) s postve and therefore the dot cloud s mostly concentrated on the rght sde of the x = 0 lne, although adoptng a C shape (Fg. 8A, A* and E). Its spread s dependent on the ntensty dstrbuton of the current channel as a functon of Fg. 7. Colocalzaton analyss wth JACoP; Van Steensel. (A D) Crosscorrelaton functons (CCFs) were calculated (wth a pxel shft of δ = ±20) for complete colocalzaton (A), complete colocalzaton wth dfferent ntenstes (B), partal colocalzaton (C) and excluson (D). Completely colocalzng structures peak at δ = 0 (A), even f dfferent ntenstes of the two fluorescent channels are present (B). Partally colocalzng structures show a shft away from 0 n the maxmum of the CCF (C). When the regon of nterest s qute crowded, shftng one mage wth respect to another may enhance the probablty of obtanng colocalzaton, therefore slghtly ncreasng the Pearson s coeffcent (arrowheads). Excluson of structures leads to an nverson of the CCF, whch shows a dp around δ = 0 (D). (E) Effect of random nose (n1 n4) on the CCF n comparson to A = n0. Random nose results n a decrease of the maxmum whle full wdth at half maxmum ncreases; t s stll possble to dentfy the colocalzaton event The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

14 226 S. BOLTE AND F. P. CORDELIÈRES Fg. 8. Colocalzaton analyss wth JACoP; L. (A D) Intensty correlaton analyss (ICA) was performed for complete colocalzaton (A and A*), complete colocalzaton wth dfferent ntenstes (B), partal colocalzaton (C) and excluson (D). (A D) ICA of the green channel; (A*) and nsets of (B D) ICA of the red channel. The x-value s dependent on covarance of both channels and the y-value reflects the ntensty dstrbuton of the current channel. Pxels wth values stuated left of the x = 0 lne do not colocalze or have nversely correlated ntenstes, whereas pxels stuated on the rght sde colocalze (see E for detals). The horzontal lne ndcates the poston of the mean ntensty of the current channel allowng the vsual estmate of the spread of ntensty dstrbuton wth respect to the mean value. (A and A*) Complete colocalzaton results n a C-shaped curve on the rght sde of both graphs. The addton of random nose leads to the expanson of the C-shaped curve (A and A*, nsets, grey dots). (B) In the case of complete colocalzaton wth dfferent ntenstes the pxel cloud s shfted up or down the ordnate axs, wth most pxels stuated on the postve sde of the graph. (C) Partal colocalzaton results n a loss of valuable nformaton as the mnorty of colocalzed pxels fal to form a strong dentfable dense cloud. (D) Excluson of the fluorescent sgnals results n a pxel dstrbuton wth most of the pxels found on the left sde of the plot. Pxels wth low ntenstes that are found on the rght sde are due to nose. (E and F) Intensty correlaton quotent (ICQ) values, whch are dependent on the proporton of pxels on the left sde of the x = 0 lne to the total number of pxels, are plotted for compete colocalzaton events (a) wth dfferent levels of nose added (a n0 a n4 ), dfferent ntenstes (b), partal colocalzaton (c) and excluson (d) The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

15 GUIDED TOUR INTO SUBCELLULAR COLOCALIZATION ANALYSIS IN LIGHT MICROSCOPY 227 the covarance of both channels ntenstes. Ths becomes clearer when addng random nose to the completely colocalzng mages. Compare the C-shaped curve of complete colocalzaton (Fg. 8A and A*) wth the expanded curve when nose s added (Fg. 8A and A*, nsets). Note that the addton of nose may also result n the spread of dots to the left sde of the graph. In the case of complete colocalzaton wth dfferent ntenstes, the pxel cloud n the red channel s shfted up the ordnate axs (Fg. 8B). Non-colocalzng pxels are found on the left sde of the plot. Partal colocalzaton spreads the pxel cloud wthn the rght sde of the plot (Fg. 8C). Mutual excluson of the fluorescent sgnals results n a pxel dstrbuton wth most of the pxels found on the left sde of the plot (Fg. 8D). Pxels wth low ntenstes that are found on the rght sde are due to nose randomly concdent between the two channels. For random dstrbuton of fluorescent sgnals, badly deconvolved mages or, n the case of hgh contamnaton by nose, a rather symmetrcal hourglass-shaped dstrbuton of dots s observed (Fg. 8E). In these cases, the result s qute dffcult to nterpret and therefore the ntensty correlaton quotent mght be calculated. Ths s defned as the rato of postve (A a)(b b) products dvded by the overall products subtracted by 0.5. As a consequence, the ntensty correlaton quotent vares from 0.5 (colocalzaton) to 0.5 (excluson), whereas random stanng and mages mpeded by nose wll gve a value close to zero (Fg. 8E and F). The development of ths graphcal method nterpretng mage sets based on ther respectve ntenstes s a step forward compared wth the prevously descrbed scatter plots as t allows a drect dentfcaton of colocalzaton and excluson. However, t s stll a global method that does not allow conclusons n ntermedate cases. Object-based analyss The man dsadvantage of the ICCB tools ntroduced so far s that no spatal exploraton of the colocalzed sgnal s possble. All methods prevously descrbed rely on ndvdual pxel concdence analyss, consderng that each pxel s part of the mage and not part of a unque structure. Although gvng a global estmaton of colocalzaton, ther numercal ndcators suffer from the composte nature of the mages, whch s a patchwork of both structures and, even though mnmzed, background. There are several possbltes for measurng and evaluatng subcellular structures by object-based approaches. The methods depend on the nature of the colocalzaton event but also on the sze, form and ntensty dstrbuton of the fluorescent sgnal. Concernng the nature of colocalzaton stuatons, we have to dstngush between those wth two markers occupyng the same space on all subcellular structures (complete colocalzaton, such as Fg. 4A) or on some subcellular structures (partal volumetrc colocalzaton, such as Fg. 4C) and between ncomplete colocalzaton stuatons wth two markers overlappng partally on all or some subcellular structures (partal topologcal colocalzaton, such as n Bolte et al., 2004b). It s recalled that any entty below optcal resoluton wll occupy at least 2 2 = 4 pxels (or even 3 3 = 9 pxels n the case of samplng at 2.3 pxels per resoluton unt) n the two-dmensonal space so no dscrmnaton can be expected between subresoluton objects. However, respectng the Nyqust samplng crteron, an object may be postoned wth an error of 70 nm (Webb & Dorey, 1995). Bologcal structures are three-dmensonal and t has already been mentoned that the dscrepancy between lateral and axal resoluton of optcal mcroscopes leads to a dstorton of the object along the z-axs. Therefore, object-based analyss needs to be carred out n the three-dmensonal space by takng account of the degree of dstorton by the optcal devce. A method of choce to measure colocalzaton on structures wth a sze close to or larger than the resoluton lmt and especally n the case of partal volumetrc colocalzaton reles on a manual dentfcaton of structures and a subsequent measurement of ther fluorescence ntensty curves. Ths s done by drawng a vector through these structures and plottng the fluorescence ntenstes for the green and red channel aganst the length of the vector. Ths can be done n any mage software and s bascally a lne scan through a twodmensonal mage of a fluorescent object, representng the fluorescence ntenstes along a vector traced across the object. Colocalzaton s present when the true overlap dstance of the fluorescence ntensty curves at md-heght s larger than the resoluton of the objectve used for mage acquston (Fg. 9B). Fluorescence ntensty profles of overlappng subcellular structures should gve smlar overlap results n those successve sngle sectons from an mage stack representng the two structures and matchng the z-resoluton of the optcal system used. Ths method has been appled to show the partal colocalzaton of plant Golg stacks and prevacuolar compartments (Bolte et al., 2004b). Although powerful on colocalzaton estmaton, ths method s tme consumng and wll only be applcable to a lmted number of structures as postonng of the vector s nteractve. Furthermore, mspostonng of the vector may lead to underestmaton of colocalzaton events. Moreover, ths method s lkely to work only on sotropc, sold structures such as doughnut-shaped or elongated structures. One step forward n colocalzaton quantfcaton reles therefore on ts local estmaton based on object dentfcaton and delneaton. Ths challengng area of mage processng s known as mage segmentaton. Although many technques exst, we wll only descrbe segmentaton procedures that have already been used for colocalzaton analyss. Lookng for objects: basc mage segmentaton. In an optmal stuaton, pxels dervng from nose should have lower ntenstes than pxels dervng from structures. A frst step to dentfyng these structural pxels as objects may be acheved by applyng a 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works

16 228 S. BOLTE AND F. P. CORDELIÈRES Fg. 9. Object-based colocalzaton analyss by fluorescence ntensty profles and connexty analyss. The analyss was performed on grey level mages of partally colocalzng fluorescent structures (as shown n Fg. 4C). (A) Raw mages showng partal colocalzaton of fluorescent subcellular structures wth green (left panel) and red (rght panel) channels. (B) Inset of overlay of raw mages as shown n (A) and ntensty curves measured along a vector across two fluorescent structures (whte arrow). (C) Magnfed vew of the nset shown n (B). The segmentaton process by connexty analyss results n partcle (D) and centrod (E) detecton. (F) Nearest-neghbour dstance approach by mergng green and red channel centrods. Colocalzaton s present when centrods have dstances below optcal resoluton (yellow arrowheads). (G) Merged vew of centrods of the green mage (E) and partcles of the red mage (D) llustrates the overlap. Note that the overlap method doubles apparent colocalzaton events. threshold to the mage; all pxels wth ntenstes above a lmt value (threshold) wll be consdered to be part of an object. In most cases, ths threshold value may be defned manually followng vsual nspecton (Fg. 9C and D). It s also possble to apply an automatc threshold as we have already seen (Costes et al., 2004). Nose s not fully elmnated as t remans wthn structures but at least two man areas are now defned on the mage, regons where structures (and nose) are present and regons where only nose s present. Although thresholdng enables one to dstngush between background and objects, one more step s requred to delneate each structure. As a frst approxmaton, the lmt of an object 2006 The Royal Mcroscopcal Socety, Journal of Mcroscopy, 224, No clam to orgnal US government works