Application limits and data correction in number of molecules and brightness analysis

Application Limits and Data Correction in Number ofMolecules and Brightness AnalysisANTONIO TRULLO,1,2 VALERIA CORTI,1,2 ELVIRA ARZA,2 VALERIA R. CAIOLFA,1,2* AND MORENO ZAMAI1,2*1Experimental Imaging Centre, San Raffaele Scientific Institute, Milan, Italy2Microscopy and Dynamic Imaging Unit, Vascular Biology and Inflammation Department, Centro Nacional de InvestigacionesCardiovasculares Carlos III, Madrid, Spain

KEY WORDS protein clusters; GPI-anchored proteins; fluorescence fluctuation microscopy

ABSTRACT Number of molecules and Brightness (N&B) has been proposed for measuringthe molecular brightness and number of fluorophores in time-sequence of images, in live cells. Ifthe fluorescently tagged-proteins are mobile in the illumination volume, the stoichiometry oftheir oligomers can be derived from the increase of the brightness of the fluorescent dyes due toclustering. We examine aspects concerning extra-fluctuation effects induced by cell shifts andphotobleaching, which yield large overestimates of the clusters size and sub-unit counts. Wedevelop an offline corrective approach consisting in frame re-alignment and boxcar filtering forrecovering precision of the analysis. Using simulations we derive general criteria for approach-ing this analysis, and assess the application limits of the corrective procedure. We tested theapproach in extreme experimental conditions (few pixels, large extra-variance perturbations), inwhich we analyzed the minimal increases of brightness as that expected between a monomericand dimeric GPI-mEGFP constructs. We show how most of the perturbing effects can be abol-ished, and obtain the correct the brightness of GPI-mEGFP monomers and dimers. Microsc. Res.Tech. 76:1135–1146, 2013. VC 2013 Wiley Periodicals, Inc.

INTRODUCTION

Over the past few years, growing importance hasbeen attached to the elucidation of the spatio-temporaldynamics of protein clustering, since several signalingcascades induced by external stimuli are initiatedthrough the assembly of membrane receptors (Alarconet al., 2006; Duke et al., 2009; Franco et al., 2003;Jones et al., 2012; Schlessinger, 2000). However,despite the importance and ubiquity of this mecha-nism, very few methods can be employed for real-timeanalysis of clustering events in live cells. Moreover,the degree of clustering is generally not quantified andis often a matter of debate (Kin et al., 2004; Morikiet al., 2001; Shi and Boettiger, 2003).

Colocalization studies do not have the lateral spatialresolution (about 300 nm) sufficient for determiningmolecular interaction and stoichiometry. Even modernsuper-resolution methods such as PALM (Betzig et al.,2006), STORM (Rust et al., 2006), and STED (Nagerlet al., 2008), which achieve spatial resolutions around20–70 nm, cannot determine the sub-unit compositionof protein clusters on a purely spatial basis. Moreover,the temporal resolution of these methods is in theorder of minutes per image. Single molecule imagingresolve the stechiometry of clusters that remain immo-bile by step-bleaching counting (Nakajo et al., 2010).

Alternatively, quantitative studies of protein clus-ters can be performed by fluorescence-correlation spec-troscopy (FCS) (Qian and Elson, 1990) and photoncounting histogram (PCH) analysis (Chen et al., 1999),and by the more recently introduced Number andBrightness (N&B) approach (Dalal et al., 2008; Dig-man et al., 2008; Moens et al., 2011; Unruh and Grat-

ton, 2008). These three methods are based on theanalysis of intensity fluctuations caused by the diffu-sion of the fluorophores in an illumination volume(Figs. 1a and 1b). They start from the notion that theamplitudes of the intensity fluctuations are uniquelydescribed by two parameters: the molecular brightnessof the fluorophore and the average number of fluoro-phores within the illumination volume (Chen et al.,1999).

FCS is complementary to N&B and PCH, and itdetermines the diffusion coefficient of the fluorophoresand the G(0) value, which is inversely related to theaverage number of molecules within the illuminationvolume (Hess and Webb, 2002). FCS is, however,rather insensitive to changes in molecular massbecause the diffusion time only scales, as first approxi-mation, with the cubic root of the mass (Muller et al.,2003). PCH uses more than two moments of the ampli-tude distribution to resolve species of different bright-ness co-existing in the same illumination volume(Caiolfa et al., 2007). The information attainable by

*Correspondence to: V.R. Caiolfa, San Raffaele University Scientific Institute,DIBIT-4A1, via Olgettina 60, I-20132 Milano. E-mail: [email protected], Microscopy and Dynamic Imaging Unit, Centro Nacional de Investiga-ciones Cardiovasculares (CNIC), Melchor Fern�andez Almagro, 3, 28029 Madrid,Spain. E-mail: [email protected]

Received 12 May 2013; accepted in revised form 24 July 2013

Contract grant sponsor: Fondazione Cariplo (Milan, Italy), and the ItalianMinistry of Health (Ricerca Corrente 2011,) Fondazione Banca del Monte diLombardia (Pavia, Italy), Spanish Ministry of Economy and Pro-CNICFoundation.Additional Supporting Information may be found in the online version of thisarticle.

DOI 10.1002/jemt.22277Published online 12 August 2013 in Wiley Online Library (wileyonlinelibrary.com).

VVC 2013 WILEY PERIODICALS, INC.

MICROSCOPY RESEARCH AND TECHNIQUE 76:1135–1146 (2013)

FCS and PCH analyses is robust and complete, butboth are essentially single-point (i.e., single pixels)techniques. Since they require many consecutiveobservations at each pixel, data acquisition usuallytakes seconds and data analysis is slow. Alternatively,N&B can be applied to relatively small time series ofimages on a pixel-by-pixel basis, with the specific aimof obtaining information on the stoichiometry of pro-tein complexes in live cell imaging, simply by monitor-ing intensity fluctuations.

N&B introduces a simplification whereby only thefirst (mean intensity) and the second (variance)moments of the amplitude distribution are considered(Figs. 1c and 1d). In this way, N&B reduces the effec-tive time per pixel to a few microseconds, which allowsacquisition of images on a time scale of seconds in thecase of raster scanning microscopy (e.g., confocal, 2-photon) and milliseconds in the case of camera-basedmicroscopy (e.g., TIRF).

Several reports have demonstrated the capability ofN&B to quantify the number of subunits in proteinclusters when large ROIs are imaged at the basal sideof a cells, well adhered to the extracellular matrix. InCHO-K1 cells, large Paxillin-EGFP clusters weredetected at the borders of some regions of adhesion ofthe cells, distinct from cytoplasm, where N&Breturned brightness comparable to that of monomericEGFP monomeric in solution (Digman et al., 2008).Ossato et al. measured by N&B the intracellularaggregation of the pathogenic Httex1p peptide in COS-7 cells (Ossato et al., 2010). The ligand-driven oligome-rization of the ErbB receptor in the cell membrane(Nagy et al., 2010), and the molecule distribution ofKlothob (KLB) and FGFR1c in the presence of co-receptor and FGF21-ligand were followed in HeLacells (Ming et al., 2012). Finally, by applying N&B tostacks collected with a total internal reflection fluores-cence (TIRF) microscope, Ross et al. could demonstrate

that dynamin-2 is primarily tetrameric throughout theentire cell membrane (Ross et al., 2011).

We have previously demonstrated by N&B that theATF-induced dimerization of GPI-mEGFP-uPAR, inHEK293 cells is independent of the interaction of thereceptor with vitronectin in the extracellular matrix(Hellriegel et al., 2011). For that work we had to facethe problem of analyzing optical sections of the cellmembrane taken far away from the extracellularmatrix, with the aim of distinguishing the minimalchanges of the brightness indicative of dimerizationevents.

In such a case, extra perturbations due to shifts ofthe membrane and photobleaching can heavily inter-fere, if not hamper, the measurement.

On the base of this experience, here we analyze anddiscuss the application limits of N&B, describe optimi-zation criteria, and provide a practical guide for awider utilization of the approach. We report in detailthe analysis of two GPI-anchored mEGFP constructs,and we quantify by simulations the overestimation ofbrightness due to photobleaching.

MATERIALS AND METHODSCell Lines and Transfection

HEK293 cells (ATCCVR Number: CRL-1573TM) werecultured at 37�C and 5% CO2 in DMEM High GlucoseGlutaMAX medium with phenol red (Gibco), supple-mented with 10% FBS, 1 mM Sodium Pyruvate, 0.1mM NEAA, 100 U/mL penicillin and 100 mg/mL strep-tomycin. For microscopy, cells were plated in glass-bottom 35-mm wells (MatTek Corporation) and main-tained in DMEM High Glucose GlutaMAX completemedium without phenol red, and with 25 mM HEPESbuffer. Transfections were carried out using TransIt-LT1 reagent (MirusBio LLC) according to the manu-facturer’s instructions. In particular, the following con-ditions were used: 100 ng of DNA/35-mm well, DNA-

Fig. 1. Principles of N&B. From left to right: Time stack series ofimages (a); Diffusing molecules in pixel “J” and oligomers in pixel“H”. (b) Examples of small and large amplitude fluctuations producedby many small molecules in pixels “J” and by few oligomers in pixel

“H” that, over time, yield equal mean fluorescence intensity, <k> (c),but different variance (r2), (d). [Color figure can be viewed in theonline issue, which is available at wileyonlinelibrary.com.]

1136 A. TRULLO ET AL.

Microscopy Research and Technique

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transfection reagent ratio 1:3. The vectors encodingGPI-mEGFP and tandem GPI-mEGFP-mEGFP weredescribed previously (Hellriegel et al., 2011). Cellswere imaged 24 h after transfection at 37 6 0.5�C.

Microscopy

Time stacks were acquired on a Ti-U microscopestand (Nikon Corp) equipped with a X60/1.2-NA water-immersion objective, combined with a Mai-Tai DS tun-able Ti:sapphire laser (Spectra Physics,) tuned to 890nm at 4 mW (power measured at the sample). Detec-tion and scanning unit was an ALBA-V module (ISSInc.) using APD detectors (SPCM-AQRH-14; EG&GPerkin Elmer). The microscope was controlled by Alba-Vista software (ISS Inc.). The setup was mounted onactive vibration-damped optical tables (Smart TableUT; Newport Corp). The temperature in the cell holderwas stabilized at 376 0.5�C. With this setup, weacquired sequences up to 200 frames at 0.5 frames/sand dwell time of 32 ms/pixel (3.3–6.6 min/sequence).

Number and Brightness Analysis

Molecules can be identified by their inherent fluores-cence intensity, defined as molecular brightness, e(expressed as the number of photons emitted per sec-ond and per molecule when the molecule is at the cen-ter of an illumination volume). The molecularbrightness is a property of each fluorophore. It dependson the fluorophore’s physico-chemical features but alsoon experimental parameters such as detectors andlaser power.

The essential idea is that individual fluorophoresdiffusing through an open observation volume producea burst of detected photons (fluctuation) (Fig. 1). If, forexample, the fluorophores diffuse synchronously astetramers, they will carry four identical fluorescentlabels, and their diffusion through the observation vol-ume will produce, on average, four time as many pho-tons, simply because tetramers will be four time asbright as the monomers, independently ofconcentration.

N&B obtains the number of fluorophores in theobservation volume and their brightness at each pixelof the image by determining the first and the secondmoment that characterize the distribution of the fluo-rescence intensity fluctuations. The first two momentsare the mean intensity (hki) and the variance (r2)(Figs. 1c and 1d). This notion is based on the observa-tion that the occupation number of particles in an openvolume follows a Poisson distribution. However, we donot detect the molecules directly, but the photons thatthey emit, which also exhibit a Poisson distribution.

Thus, the mean value for a measured intensity ver-sus time trace in a pixel of the image, hki, is given bythe product of the average number of particles, n, andtheir molecular brightness, e (equation 1).

hki5En (1)

Here, we distinguish between brightness (a propertyof each fluorophore in a given acquisition set up) andintensity (the sum of all contributions from allfluorophores).

We need to specify the variance that describes thespread of the individual intensity values around the

mean at each pixel of the image (Fig. 1d). N&B analy-sis is built on the assumption that variance is theresult of two contributions. The first is the variancedue to the occupation number, namely the diffusingparticles, and the second is the variance due to thedetector shot noise. While the variance due to the fluc-tuation of the number of particles depends on thesquare of the brightness (Eq. (2)), the detector variance(the shot noise for photon counting detectors) is equalto the intensity, and thus depends linearly on thebrightness (Eq. 3):

r2n5E2n (2)

r2d5hki5En (3)

In N&B the definition of molecular brightness andnumber of molecules is consistent with the definitionsgiven by Chen and Gratton, 1999 (Chen et al., 1999),but two additional parameters are defined: the appa-rent brightness in each pixel, B, and the apparentnumber of particles in each pixel, N.

The apparent brightness, B, is the ratio of the var-iance to the average intensity:

B5r2

hki (4)

and the apparent number of particles, N, is the ratio ofthe total intensity to the apparent brightness, B(defined in Eq. 4)

N5hki2

r2(5)

According to Eqs. (4) and (5), B has a straightfor-ward relationship with the brightness, e, of the par-ticles, measured in counts per molecule per dwell time,and is independent of their number, while N is directlyproportional to the number of particles, n. These rela-tionships can be better understood by substituting thetwo variance terms in Eqs. (4) and (5):

B5r2

hki5r2

n

hki1r2

d

hki5E2n

En1

En

En) B5E11 (6)

N5hki2

r2) N5

En

E11(7)

Interpreting the Formulas

Mean average intensity and variance can be easilyevaluated for any given set of intensity values at eachpixel by recording time stacks of images in amicroscope.

From Eq. (6), B will equal unity when there is nooccupancy fluctuation, meaning that the variance isequal to zero. This is the case with immobile fluoro-phores (E 5 0) in dry or fixed samples or background.

B will be larger than 1 if the number of particlesfluctuates in the illuminated volume, for example dueto diffusion. B is independent of hki, and consequentlyof the local concentration of the diffusing particles. Bincreases if clustering occurs, for example modifying a

N&B-LIMITS AND CORRECTIONS 1137


population of monomers (B 5 E 1 1) into dimers(B 5 2E 1 1) or multimers (B 5 3E 1 1, B 5 4E 1 1,etc. . .).

Simulations

The objective of our simulation was to construct amodel for simulating N&B time series characterizedby (1) a variance as a sum of two terms, r2

n and r2d;

and (2) a poissonian distribution (i.e., the varianceequal to the mean). The model assumes that in theobservation volume there are “n” static fluorophoreshaving “En” probability of emitting photons. In thismodel, the probability that a diffusing fluorophoreenters the observation volume is equal to “En”. Thus,the probability that a fluorophore will diffuse in theobservation volume and emit a photon will be equal toE2n.

Accordingly, we have used the following Poissoniannested algorithm implemented in a custom-builtMatLabVR software routine:

ph tð Þ5Poiss En1Poiss E2n� ��

(8)

where:ph(t) is the simulated random photon counts per

time step; Poiss is a function that generates pseudo-random numbers according to a Poisson distributionhaving the argument of the function as the mean; E isthe theoretical brightness; n is the number of fluoro-phores in the observation volume.

The above algorithm runs with arbitrary input of Eand n, and it fulfills the variance condition because itrepresents a stochastic nested process for which the var-iance, r2, is given by the sum of the variances of the indi-vidual stochastic processes (Van Kampen, 2007). Foreach (E, n) input we collected 200 time steps (E, n) of inte-ger random numbers that simulate a single data series.

In the simplest case, namely absence of diffusing flu-orophores, the algorithm returns B 5 1, regardless the

input values of “n” and “E”, because this is a purelyPoissonian process:

ph tð Þ5Poiss En10½ � 8t 2 1; . . . ;200f g (9)

When we add diffusing fluorophores in the observa-tion volume, the process becomes sub-Poissonian (Eq.(8)), the variance increases and the algorithm returnsan apparent brightness B> 1.

Photobleaching is the monotonic decrease of the flu-orescence intensity over time represented by equation:

f tð Þ5e2at (10)

where the exponential coefficient, a, indicates theextent of photobleaching (Fig. 2a).

The photobleaching of the immobile particles isexpressed as:

ph tð Þ5Poiss Enf tð Þ1Poiss E2n� ��

8t 2 1; . . . ;200f g(11)

Notice that we simulated a stochastic process, whichresulted in the generation of a temporal series of 200time steps (Eq. (11)). The process was repeated 3,600times to obtain a stable mean for each (E, n) inputdata.

RESULTS

The applicability of N&B is mainly hampered by theperturbations arising from long-term dynamics, thepresence of auto-fluorescent species, photobleachingand modest signal-to-noise ratios.

Overestimate of B occurs if the system is perturbedby long-term extra variance introduced often by diffu-sion of vesicles, oscillations, or shifts of the cell. Sourceof perturbation is also the presence of unsynchronizedframes due to mechanical jitter (if the stage is per-turbed), or errors in synchronization during acquisi-tion. Because N&B does not require a contiguous stackof images, frames can be removed at any point of the

Fig. 2. Effect of photobleaching on N&B analysis. (a) Simulationsillustrating the decrease of a theoretical mean intensity of time stacksdue to photobleaching. Photobleaching was simulated at increasingphotobleaching coefficients (a); (b) Effect of a on the retried value of Bat four simulated values: B1 51.043, slope 5 0.0078 6 0.0010;

B2 5 1.090, slope 5 0.0127 6 0.0006; B3 5 1.126,slope 5 0.0191 6 0.0006; and B4 5 1.178, slope 5 0.0245 6 0.0014. Thebrightness in counts per molecule per dwell time is derived from Eq.(6) as e 5 B-1. [Color figure can be viewed in the online issue, which isavailable at wileyonlinelibrary.com.]




sequence, provided that the remaining stack is largeenough for N&B statistics. Thus as routine, we identi-fied and removed the unsynchronized frames simplyplaying back the image stack before analysis. A similarcorrection procedure was described before (Nagy et al.,2010).

We have conducted a series of simulations in theattempt of quantifying the effect of photobleaching(Fig. 2a) on the estimated brightness (Fig. 2b).

Figure 2b illustrates the results of a series of simula-tions in which we have assigned increasing photo-bleaching coefficients to time stacks of 200 images ofspecies having theoretical brightness of 0.043, 0.089,0.126, and 0.178 counts per molecule per dwell time.We have derived these brightness values from experi-mental observations on mEGFP-tagged proteinsimaged at medium-low laser power, at 32 ms dwelltimes, and using our microscope set up equipped withphoton counting detectors. As from Figure 2b, for expo-nential coefficients comprised between 0.003 and0.005, the molecular brightness can be overestimatedas much as 50–60%.

The simulations also indicated that errors increaseas the theoretical brightness of the fluorophoresincreases.

This study revealed the limits of N&B and allowedto derive a practical guideline for analysis, as in gen-eral a time stack of about 100 images that photo-bleaches more than 20% cannot be analyzed.

To recover data that would otherwise be discardedand obtain a more precise estimate of B, we have intro-duced a simple form of short-pass data-filtering algo-rithm, the boxcar filtering that is commonly used inanalog signal filtering (Hellriegel et al., 2011; Linde-mann et al., 1969).

Boxcar filtering analyzes the stack of images on asegment-by-segment basis (Fig. 3a). The sliding boxcaris a small segment of data of user-defined length (threeor more frames), which is shifted in a frame-by-framefashion. The B-values in each step, and then averagedto obtain short-pass-filtered B distribution of thestack.

We studied the boxcar size as a function of the photo-bleaching coefficient, a. Figures 3b–3e show the resultsof simulations in which time stacks of 200 images offluorophores with four different theoretical brightnessvalues were analyzed at increasing boxcar sizes.

At the lowest brightness and high photobleaching (a> 0.003), (Fig. 3b), a boxcar size between 18–27 frameswas necessary for recovering the correct B-value.Larger box sizes did not correct sufficiently for theoverestimation of B, whereas smaller sizes yielded tounderestimate the brightness. At lower photobleach-ing coefficients, larger boxcar sizes (27–38 frames)were necessary to correct the data and avoid underes-timation. Below a 5 0.001 the boxcar filter was not effi-cacious, on the contrary it returned brightness valuesthat were consistently underestimated.

The simulations at higher brightness showed a simi-lar behavior (Figs. 3c–3e). However, as the brightnessincreased, smaller boxes were necessary for correctingthe errors on the recovered B-value. These results indi-cated that small boxcar sizes can yield an underesti-mate of B, whereas over-large filters are insufficientfor abolishing extra fluctuations, and that the errors

on N&B analysis are proportional to the brightness ofthe fluorophore.

We have recently proposed GPI-mEGFP and GPI-mEGFP-mEGFP as general reference constructs formeasuring the brightness of monomeric and dimericmEGFP-tagged proteins in the cell membrane (Hellrie-gel et al., 2011). To test the results of the simulationswe examined two time-stacks acquired on the mono-meric and dimeric mEGFP proteins that were imagedon thin membrane segments of HEK293 cells, and farfrom the basal side of the cells (Fig. 4 and Supportinginformation videos 1,2).

Figure 5 illustrates the uncorrected N&B analysisfor the GPI-mEGFP-mEGFP/HEK293 stack. Theresults are displayed in two-dimensional histograms,B-plot and N-plot, showing the average intensity ver-sus B-values and N-values calculated at each pixel andrecovered from the entire time sequence. The colorscale represents the occurrence at each pair value.

As described before, (Digman et al., 2008), we use B-plots to derive E, and eventually to distinguish thepresence of spatially segregated oligomers. A subpopu-lation of pixels or region of interest (ROI) can beselected on the image (black-masked pixels) and theassociated B-values are identified in the B-plot. Con-versely, a sub-distribution of B-values can be selectedin the B-plot (rectangular cursor) and automaticallymarked on the image (black-masked pixels).

In Figure 5, the cumulative B-plots are largely dis-persed. We could recognize a dimmer peripheral areaat borders of the membrane segment (Fig. 5a) and amore intense central region (Fig. 5b). In both ROIs theB-values were highly and largely distributed. Fromthis analysis one could infer the existence of at leasttwo populations of molecules, both with high bright-ness. Additionally, the mean intensity image showedthe presence of two small regions in which the concen-tration (i.e., the intensity) was higher than in the restof the membrane (Fig. 5c). The analysis of B in thisthird ROI returned an average brightness equallyhigh. The corresponding N-plots showed an increase ofconcentration from the border to the interior of themembrane, likely due to out-of-focus effects, but didnot reveal relevant differences in the number of mole-cules detected in the localized domains.

Finally, the majority of dimmest pixels was localizedin the background of the image, and distributedaround a mean B-value equal to 1, as expected forimmobile components and background (Fig. 5d).

A closer inspection of the time stack however,revealed a shift of the membrane during acquisition(supporting video 1). Moreover, using the mean frameintensity, we could also determine a photobleachingcoefficient of 0.0017. Thus, we proceeded applying thecorrective analysis protocol (Fig. 6).

After realignment we obtained less distributed B-plots and a mean brightness of 1–2 counts per moleculeper dwell time (Figs. 6a–6c). The opposite effect wasobserved on the N-plots. In agreement with theobserved difference in fluorescence intensity, afterframe re-alignment, we obtained higher N-values inthe central membrane and in the two domains.

Boxcar filtering further corrected the dispersion of Band N-values (Figs. 6d–6f). The border of the mem-brane segment, which is expected to be more sensitive



to extra fluctuations and out-of-focus effects, was atthe lowest intensity. The mean brightness of this ROIwas as low as 0.046 6 0.002 counts per molecule perdwell time (Table 1). In the central membrane regionwe measured a largely variable concentration (N-plot),yet the distribution of the brightness was sharp andwith a mean value of 0.143 6 0.002 counts per mole-cule per dwell time (Table 1).

The two intense regions did not disappear after cor-rection of the raw data (Fig. 6f). Moreover, the correc-tion helped in detecting differences between this ROIs

and the surrounding pixels. In these two regions, weobtained the largest number of molecules (about 15)and also the highest brightness of the image (Table 1).In the area surrounding the two regions, the local con-centration of the molecule was variable (N-plot) butthe brightness was constant. In this area of 6.23 mm2,the average density of the molecules varied from 0.6 to1.6 molecules/mm2. In contrast, in the two regions(0.584 mm2) the highest local concentration, due to ahigher number of molecules (N-plot), was linked tohigher brightness. The average density of the

Fig. 3. Boxcar filter. Boxcar filtering principle: Example of a 20-frame box sliding on the time series (a). Effect of boxcar filter size atincreasing photobleaching coefficients on fluorophores having thetheoretical brightness of B1 51.043 (b); B2 5 1.090 (c); B3 5 1.126 (d)

and B4 5 1.178 (e) counts per molecule per dwell time. Simulationswere carried out on 200 frame stacks. [Color figure can be viewed inthe online issue, which is available at wileyonlinelibrary.com.]




Fig. 5. Uncorrected N&B analysis of the GPI-mEGFP-mEGFP/HEK293 membrane segment. From left to right: mean intensityimage, B-plot, B-histogram, N-plot, and N-histogram. Rectangularcursors were used in the B and N plots to select a subpopulation ofpixels or region of interest (ROI) in the intensity image. A frequencyhistogram (binned on 100 channels) was then obtained for determin-ing the distribution of B and N-values in each ROI. ROIs are black-

masked in the mean intensity image: (a) the dim border of the mem-brane; (b) the central region of the membrane; (c) two segregateddomains at high intensity, and (d) the background. In the case ofbackground N-plot was not considered in the analysis. [Color figurecan be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Fig. 4. Snap shots of GPI-mEGFP and GPI-mEGFP-mEGFP in the cell membrane of HEK293 cellsGalleries were taken from videos 1 and 2 (Supporting Information) illustrating the time stacks thatwere submitted to N&B. The images show frame shifts and photobleaching. [Color figure can be viewedin the online issue, which is available at wileyonlinelibrary.com.]




molecules was as high as 29 molecules/mm2 but thebrightness was only 1.6-fold that of the surroundingmembrane.

In summary, the effect of photobleaching is todecrease the average intensity and increase the var-iance. Because of that and according to Eqs. (4) and

Fig. 6. Corrected N&B analysis of the GPI-mEGFP-mEGFP/HEK293 membrane segment. The time stack shown in Figure 5 wasrealigned (panels a, b, and c) and then filtered (panels d, e, and f). Band N plots were recalculated after each correction steps. The resultsare shown as in Figure 5. Realignment of the membrane segment was

implemented using a custom-built Matlab routine (Mathworks, Inc.).A boxcar of 16 frames was used for filtering. [Color figure can beviewed in the online issue, which is available atwileyonlinelibrary.com.]




(5), the B value is overestimated while the N value isunderestimated. The example in Figure 6, shows howwe can correct for the extra variance and approach amore precise assessment of B and N values.

As control and comparison, we analyzed the bright-ness of a similar time stack acquired on monomericGPI-mEGFP in the HEK293 membrane under thesame experimental conditions (Fig. 7 and supportingVideo 2).

In this case we did not find any cluster and we lim-ited the analysis to the external border and internalmembrane regions.

The effect of the extra fluctuations due to the motionof the cell was again evident in the average intensityimage and B-plot obtained from the uncorrected data(Figs. 7a and 7b).

As before, realignment abolished most of the extravariance (Figs. 7d and 7e), reducing the slope of the B-plots and the average brightness. Boxcar filtering wasalso necessary because the time stack showed a photo-bleaching coefficient of 0.0023. After filtering, the anal-ysis of the central region (4.830 mm2) of the membranesegment returned an averaged brightness equal to0.07410.002 counts/molecule 3 dwell time (Table 1,Fig. 7g). This value was half that of GPI-mEGFP-mEGFP, and it was independent on the local concen-tration of the proteins (N-plot, Fig. 7g). The averagedensity of the molecules in this region was from 0.82 to1.5 molecules/mm2. This density was similar to thatobtained observed for the dimer GPI-mEGFP-mEGFPconstruct, indicating that the reduced brightness couldnot be related to any local concentration effect.

The average brightness and number of moleculesrecovered at the membrane borders were lower thanthose measured in the central areas for both mono-meric and dimeric proteins (Table 1). These observa-tions suggest that the peripheral regions, which alsosuffer from slight out-of-focus effects, could not beproperly corrected.

DISCUSSION

N&B is a promising approach for determining thestoichiometry of homo-clusters in live cells by meas-uring the molecule brightness of fluorescently taggedproteins.

We have previously applied N&B to determine theminimal increase of brightness associated to the ligandinduced monomer to dimer transition of uPAR-mEGFP-GPI molecules exposed at the cell membrane.Although several reports have successfully appliedN&B for following clustering of cell membrane andintracellular proteins, only three studies have

addressed dimerization events (Hellriegel et al., 2011;Ming et al., 2012; Nagy et al., 2010), two of which werelimited the analysis to the average brightness in largeROIs taken at the cell basal (Ming et al., 2012; Nagyet al., 2011). In fact, N&B works well when large ROIscan be selected in the cell (Nagy et al., 2010; Rosset al., 2011) where proteins are confined (Digmanet al., 2008) or form large oligomers, and fast acquisi-tion can be applied to prevent photobleaching (Rosset al., 2011). When the experimental conditions aresub-optimal (few pixels, large extra fluctuations), theprecision of N&B is questionable, and clustering couldbe easily overestimated if extra variance due to long-term fluctuations cannot be avoided or corrected.

In this work we have systematically reviewed theapplication of N&B for improving the precision of themeasurement at limiting conditions, as those we haveexperienced when low brightness fluorophores such asfluorescent proteins are expressed at low levels incells, and form small clusters. Therefore, our simula-tion model was tested in the range of B 5 1.05–1.15,with a number of molecules up to 20. In more favorableconditions, such as proteins tagged with brighterchemical fluorophores or undergoing large clustering,N&B analysis would not require so much caution,unless photobleaching is massive.

We have reported the case study of two standardconstructs that were designed for exposing mEGFP atthe cell membrane by a GPI anchor. The two con-structs expressed in HEK293 cells were used before forcalibrating the B-plots for the brightness of the mono-meric and dimeric mEGFP (Hellriegel et al., 2011).The mutated monomeric variant of EGFP (Campbellet al., 2002) inserted in these constructs derives fromour previous studies of a uPAR-mEGFP-GPI fused pro-tein that was also expressed in the HEK293 cell line(Caiolfa et al., 2007). In that system, extensive photoncounting histogram (PCH) analysis revealed that thebrightness of the mutated mEGFP in the cell mem-brane was equal to that of the protein in solution overa large range of concentrations, confirming the evi-dence that we produced a GPI-mEGFP protein thatdoes not self-aggregate, at least under the experimen-tal condition we apply in our systems.

Since the brightness depends on the chosen dye andalso on the specific experimental conditions (i.e., laserpower, pixel dwell time), any N&B measurementrequires the use of control constructs with well-defineddye stoichiometry. Therefore, in this work we haveaddressed three points: (i) provide a better characteri-zation of the two reference constructs, (ii) test theapplicability conditions and limits of N&B analysis,

TABLE 1. Brightness and number of molecules measured after boxcar filtering of realigned time stacks

Membrane border Membrane interior Segregated spots

hei 6 sem hNi6 sem hEi6 sem hNi6 sem hEi6 sem hNi 6sem

GPI-mEGFP-mEGFP 0.04660.002 1.43760.008 0.14360.002 4–12a 0.23660.008 15.660.1GPI-mEGFP 0.01360.002 0.5-2 0.07460.002 4–7b n.f.Backgroundc 0.00660.002 n.d.

aLarge distribution.bBimodal distribution fitting: 7 6 3 (amplitude 25%); 4 6 1 (amplitude 75%).cMeasured before realignment. Sem5 standard error on the mean; n.d., not determined; n.f., not found. hEi and hNi were computing as it follows: after fitting the his-togram with a Gaussian curve, the values comprised in the interval [m22*r, m1 2*r] were selected, where m and r are the mean and the standard deviation of theGaussian fitting. This area includes 95% of the total histogram area.



Fig. 7. N&B analysis of the GPI-mEGFP/HEK293 membrane seg-ment. The figure illustrates the analysis of the uncorrected time stack(a, b, and c); the stack after realignment (d, e) and after filtering (f,g). From left to right mean intensity image, B-plot, B-histogram, N-plot and N histogram are shown. As in Figures 5 and 6, rectangularcursors were used to select a subpopulation of pixels or region of

interest (ROI) in the intensity image, for which frequency histogramswere obtained. The blackmasked ROIs identify: the dim border of themembrane (a, d, f); the central region of the membrane (b, e, g); andthe background (c). Realignment and filtering was as in Figure 6.[Color figure can be viewed in the online issue, which is available atwileyonlinelibrary.com.]




and (iii) verify the performance and the limits of theboxcar filtering for achieving a more precise determi-nation of the brightness.

We have demonstrated that time stacks of imagesthat are deteriorated by shifts of the structure andphotobleaching cannot be analyzed as such. Thebrightness would be largely overestimated by an addedextra variance independently on the diffusion of themolecules. As a consequence the number of proteinsubunits in cluster would result erroneously higher.Both effects can be hardly avoided during data acquisi-tion, and as a consequence, data should be discarded.If frames shift over time in the X,Y plane, the sequencecannot be properly analyzed by N&B. This is becauseN&B is a pixel-based analysis, in which the imagestack can be seen as groups of time series of photoncounts, one for each pixel; if a region of interest (ROI)selected in frame #1 shifts over time in the X,Y plane,its position will change in the following frames and thepixel-to-pixels relationship will be lost (an analysis ofthe errors due to frame shifts is reported in the appen-dix of the supporting information).

In this work we have shown that simple frame re-alignment can be performed if the frame shift is rigid.However, simple alignment routines cannot correct forlarge deformation of the cell structure, and in thesecases, still we had to discard the data.

Using simulations, we have examined the overesti-mation of the brightness due to photobleaching. Wehave shown that a boxcar filter can minimize the extravariance introduced by the photobleaching, and wehave been able to derive general criteria for choosingthe size of the boxcar filter as a function of the photo-bleaching coefficient. In the range of applicability ofour simulations (1.05�B� 1.15; n� 20) we show thatthe box size is critical for obtaining a more preciseassessment of the brightness, and we have used simu-lation for guiding the optimization of the filter in theexperimental cases. A boxcar size of 16 frames workedout well for correcting both, GPI-mEGFP and GPI-mEGFP-mEGFP time stacks. Simulations properlypredicted the filter size, although an empirical esti-mate of the experimental brightness was necessary atthe beginning of the analysis. We have found theapplicability limits of our corrective approach. The fil-ter can be applied to time stacks with a values com-prises between 0.001 and 0.005; time stack serieshaving a >0.005 cannot be corrected, whereas ata< 0.001 box-car filtering is unnecessary. Our analysisprocedure allows an unbiased selection of subpopula-tions of pixels in the mean intensity images. In otherwords, we could discriminate different ROIs on thebasis of pixel intensity rather following an empiricalselection of B-values.

Other authors have applied a moving average proce-dure to correct the large variance (large brightness)caused by collective macroscopic motion of the cell andfor a (not quantified) photobleaching of the time stack(Digman et al., 2009). The moving average producesthe opposite effect, rendering long-pass-filtered datasets, which are then subtracted from the raw data toyield a de-trended intensity versus time trace. How-ever, we are not aware of any report discussing termsand limits of applicability of the moving average cor-rection for the N&B analysis.

N&B can return quantitative information at themolecule level within the optical resolution limit ofconventional fluorescence microscopes and on livecells, by applying a cautious analysis such as that wehave described. N&B has the advantage of not requir-ing the occurrence of any kind of energy transfer, as inFRET approach, and it is not limited to specific dyes,but the temporal resolution of the detector must matchthe time scale of the fluctuation (otherwise the fluctua-tion vanishes due to averaging). Unlike FRET, N&Bdoes not strictly demonstrate molecule proximity, how-ever, it does not impose any restriction on the distancebetween molecules. Any condition that causes mole-cules to diffuse together will increase the brightnesscompared with that due to the components individu-ally. For example, receptor molecules forming a signal-ing assembly that diffuses as a unit in the cellmembrane would generate a brightness higher thanthat of the individual receptors. In such a circum-stance the increased brightness cannot be interpretedin terms of “direct interaction” in the absence of addi-tional information on the biological system underinvestigation.

In particular, we have captured some brightnessheterogeneity in GPI-mEGFP-mEFGP/HEK293 mem-branes, and we have shown it as an example of theanalytical process. In these discrete areas the bright-ness was about 3-fold that of monomeric GPI-mEGFP,and the average number of molecules was significantlyhigher than in the rest of the membrane (Table 1). Wedo not make any attempt of comparing our observa-tions with previously reported works in which GPI-GFP proteins have been used to probe microdomainsin the cell membrane (Brameshuber et al., 2010; Gos-wami et al., 2008; Sharma et al., 2004). Our experi-mental system and our constructs are not directlycomparable, although we have never observed hereand before (Hellriegel et al., 2011) 3–4 molecule clus-ters of our GPI-mEGFP protein. We do not have anybiological evidence for speculating on the nature of theimaged structures. The statistical significance of ourobservation in terms of reproducibility of these struc-tures goes beyond the scope of our report. The meanbrightness detected in these regions might indicate thepresence of a mixture of species that cannot beresolved by N&B. In fact, when different species coex-ist in the same pixel, the measured B-values is a coa-lescence of the two or more sub-populations, andquantification requires further calibrations and someassumptions, as we have previously discussed (Hellrie-gel et al., 2011). Nevertheless, combining the informa-tion of mean brightness, mean number of moleculesand ROI size, we tend to conclude that we have cap-tured vesicles containing partially aggregated GPI-mEGFP-mEGFP molecules.

In our previous work we showed that the brightnessmeasured for GPI-mEGFP and GPI-mEGFP-mEGFPwas reproducible within a standard deviation of about10% (Hellriegel et al., 2011). Here we further improvethe precision of N&B analysis, which can be well tunedto detect minor changes in protein assembly even inextreme conditions (few pixels, large extra-varianceperturbations). Data that would be discarded can berecovered and minor changes in brightness canemerge. We have found practical criteria for



determining the appropriate filtering conditions andthe limits of the corrective approach for time stacksthat would be otherwise discarded. We show how thenumber of molecules and brightness analysis can high-light local protein segregation, combining subunitcounting and local density analysis. Under these anal-ysis conditions, the two GPI-mEGFP constructsemerge as suitable control proteins to be used in stud-ies addressed to determine functional oligomerizationof mEGFP-tagged membrane receptors and proteins inlive cells.

ACKNOWLEDGMENT

The authors acknowledge Fondazione Cariplo (Milan,Italy), and the Italian Ministry of Health(Ricerca Cor-rente 2011,) for the financial support to this work. Wethank Enrico Gratton for his suggestions and discus-sion of our work. A-T is grateful to Fondazione Bancadel Monte di Lombardia (Pavia, Italy) for funding hispost-doctoral training within the “Educational PathProgetto Professionalit�a Ivano Becchi, 2011”, and toValerio Vercesi for his tutorship. CNIC is funded bythe Spanish Ministry of Economy and Pro-CNIC Foun-dation. Microscopy was carried out at the Microscopy& Dynamic Imaging Unit at the CNIC.

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Application limits and data correction in number of molecules and brightness analysis