# Analysis of molecular concentration and brightness from fluorescence fluctuation data with an electron multiplied CCD camera.

**ABSTRACT** We demonstrate the calculation of particle brightness and concentration from fluorescence-fluctuation photon-counting statistics using an electron-multiplied charge-coupled device (EMCCD) camera. This technique provides a concentration-independent measure of particle brightness in dynamic systems. The high sensitivity and highly parallel detection of EMCCD cameras allow for imaging of dynamic particle brightness, providing the capability to follow aggregation reactions in real time. A critical factor of the EMCCD camera is the presence of nonlinearity at high intensities. These nonlinearities arise due to limited capacity of the CCD well and to the analog-to-digital converter maximum range. However, we show that the specific camera we used (with a 16-bit analog-to-digital converter) has sufficient dynamic range for most microscopy applications. In addition, we explore the importance of camera timing behavior as it is affected by the vertical frame transfer speed of the camera. Although the camera has microsecond exposure time for illumination of a few pixels, the exposure time increased to milliseconds for full-field illumination. Finally, we demonstrate the ability of the technique to follow concentration changes and measure single-molecule brightness in real time in living cells.

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**ABSTRACT:**The ability to measure biomolecular dynamics within cells and tissues is very important to understand fundamental physiological processes including cell adhesion, signalling, movement, division or metabolism. Usually, such information is obtained using particle tracking methods or single point fluctuation spectroscopy. We show that image mean square displacement analysis, applied to single plane illumination microscopy data, is a faster and more efficient way of unravelling rapid, three-dimensional molecular transport and interaction within living cells. From a stack of camera images recorded in seconds, the type of dynamics such as free diffusion, flow or binding can be identified and quantified without being limited by current camera frame rates. Also, light exposure levels are very low and the image mean square displacement method does not require calibration of the microscope point spread function. To demonstrate the advantages of our approach, we quantified the dynamics of several different proteins in the cyto- and nucleoplasm of living cells. For example, from a single measurement, we were able to determine the diffusion coefficient of free clathrin molecules as well as the transport velocity of clathrin-coated vesicles involved in endocytosis. Used in conjunction with dual view detection, we further show how protein-protein interactions can be quantified.Scientific Reports 11/2014; 4:7048. · 5.08 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Single plane illumination microscopy based fluorescence correlation spectroscopy (SPIM-FCS) is a new method for imaging FCS in 3D samples, providing diffusion coefficients, flow velocities and concentrations in an imaging mode. Here we extend this technique to two-color fluorescence cross-correlation spectroscopy (SPIM-FCCS), which allows to measure molecular interactions in an imaging mode. We present a theoretical framework for SPIM-FCCS fitting models, which is subsequently used to evaluate several test measurements of in-vitro (labeled microspheres, several DNAs and small unilamellar vesicles) and in-vivo samples (dimeric and monomeric dual-color fluorescent proteins, as well as membrane bound proteins). Our method yields the same quantitative results as the well-established confocal FCCS, but in addition provides unmatched statistics and true imaging capabilities.Optics Express 02/2014; 22(3):2358-75. · 3.53 Impact Factor - Biophysical Journal 07/2014; 107(1):1-2. · 3.83 Impact Factor

Page 1

Analysis of Molecular Concentration and Brightness from Fluorescence

Fluctuation Data with an Electron Multiplied CCD Camera

Jay R. Unruh and Enrico Gratton

Laboratory for Fluorescence Dynamics, Department of Biomedical Engineering, University of California, Irvine, California

ABSTRACT

countingstatisticsusinganelectron-multipliedcharge-coupleddevice(EMCCD)camera.Thistechniqueprovidesaconcentration-

independent measure of particle brightness in dynamic systems. The high sensitivity and highly parallel detection of EMCCD

cameras allow for imaging of dynamic particle brightness, providing the capability to follow aggregation reactions in real time. A

critical factor of the EMCCD camera is the presence of nonlinearity at high intensities. These nonlinearities arise due to limited

capacity of the CCD well and to the analog-to-digital converter maximum range. However, we show that the specific camera we

used (with a 16-bit analog-to-digital converter) has sufficient dynamic range for most microscopy applications. In addition, we

explore the importance of camera timing behavior as it is affectedby the vertical frame transfer speed of the camera. Although the

camera has microsecond exposure time for illumination of a few pixels, the exposure time increased to milliseconds for full-field

illumination. Finally, we demonstrate the ability of the technique to follow concentration changes and measure single-molecule

brightness in real time in living cells.

We demonstrate the calculation of particle brightness and concentration from fluorescence-fluctuation photon-

INTRODUCTION

In the past 10 years, there has been a virtual explosion in the

number of fluorescence fluctuation techniques available to

researchers for analysis of particle brightness, concentration,

and diffusion coefficient in complex samples. Perhaps the

greatest benefit of these techniques lies in their capability to

observe molecular interactions in living cells. It is important

to note that fluctuation techniques are uniquely sensitive to

weak homointeractions that play an important role in rapid

signaling events. Fo ¨rster resonance energy transfer (FRET)

measurements make it possible to look at heterogeneous

interactions, but require the successful incorporation of

multiple fluorophores into a living sample. In addition, there

is no guarantee that FRET will occur between two interacting

species due to the large size of biological chromophores.

Also, FRET has limited or no sensitivity to distinguish be-

tween aggregates with more than two partners. The need for

techniques to study molecular interactions directly inside

living cells has been highlighted recently by advances in

systems biology and modeling. These techniques rely on

characterization of biological binding partners for the de-

velopment of network models for cellular function.

In the early 1990s, Qian and Elson developed a particular

version of fluorescence fluctuation spectroscopy, moment

analysis,thatusedthestatisticsoffluorescencefluctuationsto

determine particle concentration and brightness while omit-

ting the time dependence of the signals (1). That study cal-

culated the contribution to the first three moments from

Poisson shot noise to correct for these fluctuations in the

analysis. In 1999, Chen et al. developed the photon-counting

histogram analysis (PCH), and Kask et al. developed the

fluorescence intensity distribution analysis, which accounted

forshot noise throughfittingofthe data(2).In2004, Joachim

Mueller developed an equivalent method, termed fluores-

cence cumulant analysis, which is a general extension of

moment analysis into higher-order moments with error anal-

ysis (3). This allows for the rapid calculation of molecular

concentration and brightness without the complicated com-

putation involved in other approaches. Recently, our group

appliedmomentanalysiswithcorrectionforshotnoiseineach

pixel of a photon-counting confocal image, allowing for the

mapping of particle aggregation in a spatial manner. This

technique, termed ‘‘N and B analysis’’ has proven to be an

invaluable tool for mapping out the cellular location of sig-

naling processes (4). More recently, this technique was ex-

tended for use with analog detectors, which dominate the

confocal microscopy field (5).

ThisworkintendstoexploretheuseoftheNandBanalysis

technique with an important subset of analog detection

systems—the electron-multiplied charge-coupled device

(EMCCD)camera.Thesedeviceshaveproventhemselvesfor

use in ultralow-light imaging conditions, becoming the stan-

dard for single-molecule imaging of surface-bound proteins

or surface reactions via the total internal reflection fluores-

cence (TIRF) imaging modality. In addition, the parallel

character of detection with these systems allows for the most

rapid large-scaleimagingofany technique andalso forms the

basis for rapid confocal techniques like spinning-disk mi-

croscopy.

These cameras have been successfully employed under

several circumstances for fluorescence correlation spectros-

copy in both the spatial correlation modality (6) and the

doi: 10.1529/biophysj.108.130310

SubmittedFebruary29,2008,andacceptedforpublicationAugust13,2008.

Address reprint requests to Enrico Gratton, University of California, Irvine,

Biomedical Engineering, Irvine, CA 92697. Tel.: 949-824-2674; E-mail:

egratton22@yahoo.com.

Editor: Taekjip Ha.

? 2008 by the Biophysical Society

0006-3495/08/12/5385/14 $2.00

Biophysical JournalVolume 95December 20085385–5398 5385

Page 2

temporal correlation modality (7–10). In the spatial correla-

tion modality, the spatial average of the molecular brightness

is measured over a minimum of several point-spread func-

tions. This limits the spatial resolution of brightness mea-

surements, but also enhances the signal/noise ratio of such a

measurement. In the temporal correlation modality, the spa-

tial extent of the acquired correlation stack is limited by the

readout speed of the camera. For example, the 512 3 512

chip cameras have a maximum full-frame rate of 30 fps,

corresponding to a time resolution of 33 ms, but with a much

smaller region of interest, this time resolution can be in-

creased to a few milliseconds. One study employed the ul-

trafast 128-pixel camera for these measurements (7). Other

studies have limited themselves to slower-moving objects or

small regions of interest. It is also important to note that

temporal correlation analysis with these systems requires a

significant investment in signal/noise due to the nonlinear

least-squares fitting requirements of correlation analysis.

This work seeks to overcome these challenges with a ‘‘fit-

free’’ moment analysis approach to the determination of

molecular brightness and concentration at each pixel in an

image with minimal required signal/noise. This approach is

limitednotbytheframerateofthecamerabutbyitsexposure

resolution, thereby maximizing the analysis size for such

measurement. In addition, we demonstrate that by changing

the exposure time of the camera it is possible to capture the

time dependence of molecular fluctuations using techniques

described previously.

Despite their advantages, EMCCD detectors present some

unique challenges. The presence of charge-well saturation

and leakage gives rise to unique statistics that must be un-

derstood to accurately calculate the particle concentration

and brightness. In addition, the exposure timing of these

cameras is complex and strongly influenced by the frame

transfer characteristics of the camera. We show that the judi-

ciouschoiceofacquisitionparametersresultsinmeasurements

thathavehighdynamicrangeandtimeresolution,maximizing

the capabilities of the camera system. Finally, we demonstrate

the ability to resolve the relative concentration and brightness

of single enhanced green fluorescent protein (EGFP) mole-

cules in living cells within a few seconds, allowing for real-

time observation of brightness and concentration dynamics.

THEORY

Following Qian and Elson, our previous work defined N and

B as follows (4):

N ¼ðÆIæ ? offsetÞ2

s2? s2

0

; B ¼

s2? s2

ÆIæ ? offset:

0

(1)

Here, offset is the intensity offset of the detection electronics

ands2

0isthereadoutnoisevarianceofthedetectionelectronics.

The above equations are based purely on signal fluctuations

in a given pixel. Therefore, shot noise is not separated from

particle number fluctuation, and these expressions do not

give the true molecular number (denoted n) and brightness

(denoted e). In the appendix, we show that the variance and

average intensity for an analog detector are given as follows

in terms of molecular brightness and number of molecules:

s2? s2

ÆIæ ? offset ¼ Gen;

0¼ SGen1G2ge2n

(2)

(3)

where G is the analog gain in digital levels (DL)/photon, S is

theslopeoftheintensityversusvarianceplotforaconstantin-

tensityattheanalogdetector,g isafactorrelatingtotheshape

of the pixel detection volume. Using these expressions, it is

straightforward to calculate B in terms of e:

B

S¼G

Sge11:

(4)

Therefore, the quantity B/S is linearly dependent on e. Exper-

imentally, e is a complex function of laser intensity and the

detection efficiency of the system. Therefore, it is only im-

portant that we determine the relative value of e for a specific

detectionmodality.Wecancalibratethis value usingaparticle

with known brightness. This allows us to simplify Eq. 4 to

B=S ¼ e911;

(5)

where e9 is proportional to e. The solution for n is more

complex, but as with e we are generally only interested in the

relative value of n, not its absolute value. One can then show

that: n9e9 ¼ (ÆIæ ? offset)/S. Note that n9 ¼ n/g, which is the

reciprocal of the G(0) term from fluorescence correlation

spectroscopy (FCS) analysis.

As was mentioned above, only the relative brightness will

be considered in this work. Nevertheless, for completeness,

we will attempt to approximate the g factor according to the

definition given by Mu ¨ller (3). For diffusion in three di-

mensionsinandoutofaTIRFfield,thepoint-spreadfunction

has been described as an exponential in z and a Gaussian in x

and y. For this point-spread function, the g factor is 0.25. It is

important to note that this is only an approximation. Several

studies have suggested that the TIRF point-spread function is

better approximated by a multiexponential function in z. In

this case, the g factor is weakly dependent on the shape of the

point-spread function, but similar to what is seen for a single-

exponential point-spread function; therefore, we will retain

0.25 as an estimate only for rough calculations. For TIRF or

brightfieldstudiesonamembrane,itisoftenassumedthatthe

membrane thickness is significantly less than the axial di-

mension of the point-spread function. This would produce a

2D Gaussian point-spread function with a g factor of 0.5.

This approximation is only as good as the approximation of a

thin membrane. If undulations in the membrane are larger

than thez-dimension ofthepoint-spread function,this will be

an overestimate. It should therefore only be used for rough

calculations, as with the TIRF approximation.

It is important to note the specific contribution of back-

ground to this signal. Background here is defined as constant

(relativetothetimescaleofthefluctuations)signalcontaining

5386Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 3

only shot noise. This contribution must be estimated a priori

from a control experiment. The variance of the background

component can be shown to be SÆIæ. Since variance is addi-

tive, this can be simply subtracted from the overall variance.

The same can be done for the average intensity. It is easy to

show that the presence of background will reduce the ap-

parent brightness and increase the apparent number of mol-

ecules. When large immobile aggregates are present in an

image, they will generally appear much brighter than small

fluctuating molecules or even small aggregates. Using our

expression for brightness, these regions of the image will

show up as high intensity with zero brightness. This can be

used as a measure of mobility (4).

Given these developments, we now have a straightforward

recipe for performing number and brightness analyses. The

offset and s2

0parameters can be determined from a dark

image or a region of the acquired image without mobile

particles. The S parameter is determined from a plot of var-

iance versus intensity for a constant source of light. It is

tempting to calculate e9 and n9 for every pixel in an image.

Nevertheless, for most single molecules, e9 lies quite close to

zero. Therefore, the statistical error of the measurement, es-

pecially foravery few frames, willlead toinfinite ornegative

values of n9. A 2D histogram of B/S vs. (ÆIæ ? offset)/S rep-

resents a plot of e9 vs. e9n9. This plot contains all of the in-

formation necessary to characterize the system in question

without the physically unreasonable values of n9.

Although the analog solution for number and brightness is

quite simple, it would be ideal to eliminate shot noise from

theanalysis.If,forexample,twosimultaneousmeasurements

can be done on the same sample, their shot noise and readout

noise will be uncorrelated. As a result, only the molecular

fluctuations will be correlated and the covariance is repre-

sentativeonlyoftheparticlenumberfluctuations.Thiscanbe

accomplished trivially with a 50% beam splitter, as is often

done to eliminate afterpulsing from fast autocorrelation

analyses. Nevertheless, this uses up valuable camera pixels

and reduces the signal intensity by half.

For fast cameras, it is possible to sample faster than the

diffusion time of the molecule of interest. In this case,there is

a temporal redundancy present in that the molecule does not

move significantly between subsequent frames. Since the

read noise and shot noise are not correlated in time, the co-

variance of subsequent frames in time is given by the second

term in Eq. 2, and B is given by

B ¼ Gge ¼ e9:

(6)

Thus, B is directly proportional to e for this analysis. Sim-

ilarly, n9e9 ¼ ÆIæ ? offset, where n9 ¼ n/g. Therefore, this

analysisisindependentofS,andBisinunitsofthegainofthe

system, greatly simplifying the analysis. This is similar to

calculating the extrapolated G(0) point of the FCS autocor-

relation function and therefore will be referred to as G1

analysis. Of course, this is only true in the limit of fast

sampling relative to the diffusion time.

In the same way, one could use the spatial redundancy of

the system, assuming that shot noise and read noise are not

correlatedinneighboringpixels.Givenagreatenoughdegree

ofspatialoversampling,eachparticlewillbevisibleinseveral

pixels simultaneously. Here, one must be quite careful that

this analysis is done in the orthogonal direction to the readout

coordinate of the camera. This is because the analog system

will inevitably have some damping time constant that corre-

lates slightly from pixel to pixel in the horizontal direction

during the readout process. This can easily be identified by

calculating the spatial correlation of the dark noise of the

camera. The mathematical analysis is identical to the case of

temporal oversampling, except that it is the covariance of

neighboring pixels that is calculated rather than the covari-

ance of subsequent time points. This is identical to the cal-

culation of the first point of the spatial autocorrelation

functionintheydimensionandthereforewillbereferredtoas

G1y analysis throughout this article. Both of these analysis

methods sacrifice signal/noise in exchange for simplicity. In

the case of temporal oversampling, the effect is to reduce the

number of photons collected per analysis frame by a factor of

2,thus reducing thesignal/noisebya factorof 1.4.In thecase

of spatial oversampling, the penalty is instead a factor of 4,

since spatial oversampling affects both the x and y dimen-

sions.Here,thesignal/noiseispenalizedbyafactorof2.High

amounts of spatial oversampling are commonly used to

identify single molecules via image correlation analysis (11),

so it is not likely that this will be a significant limitation.

Wu and Mueller have described the exposure time de-

pendence of the molecular brightness as it applies to fluo-

rescence cumulant analysis (12). The following equation

relates the brightness to a binning function, B2(Tr):

eðTÞ

T

}B2ðTrÞ

T2 ;

(7)

where T is the exposure time and Tr¼ T/tDis the exposure

time in units of the radial diffusion time (tD¼ v2

binning function is given as follows (12):

ZTr

where G(tr) is the normalized autocorrelation function in

unitsofthediffusiontime(tr¼t/tD).Wehavechosentoplot

the ratio of brightness to exposure time because this function

closely resembles the autocorrelation function. At short

exposure times relative to the diffusion time, the function

approaches a constant, and at long exposure times, this

function approaches zero. For one-photon confocal detec-

tion, the point-spread function is approximated by the 3D

Gaussian function and the autocorrelation function has its

familiar form:

0=4D). The

B2ðTrÞ ¼ 2

0

GðtrÞðTr? trÞdtr;

(8)

GðtrÞ3DG¼

1

ð11trÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

11r2tr

p

;

(9)

Number and Brightness with EMCCD Camera5387

Biophysical Journal 95(11) 5385–5398

Page 4

whereristheratiobetweentheradialandaxialdimensionsof

the focal volume. This gives rise to the binning function

B2ðTrÞ3DG¼4ð1 ? yÞ

1 ? a

12ð11TrÞ

pffiffiffia

p

lnðy ?

ðy1

ffiffiffia

pÞð11

ffiffiffia

and a ¼ 1 ? r2for

ffiffiffia

pÞ

ffiffiffia

pÞð1 ?

pÞ

??

;

(10)

where we have introduced y ¼

brevity. For TIRF illumination, we can approximate the

point-spread function by a Gaussian in the radial direction

and an exponential with average height, d, in the axial

direction. Hassler et al. (13) showed that the autocorrelation

is then given by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

11r2Tr

GðtrÞTIRF¼ð1 ? tr=2Þexpðtr=4Þerfcð

ffiffiffiffiffiffiffiffiffi

tr=4

p

Þ1

ffiffiffiffiffiffiffiffiffiffi

tr=p

p

11tr=r2

:

(11)

Here, tris defined relative to the axial diffusion time (tr¼

t/tz), where tz¼ d2=4D. As before, r is the ratio between

radial and axial dimensions of the focal volume. There is no

simple analytical solution for the binning function here, so

it was calculated by numerical integration.

MATERIALS AND METHODS

Materials

Dioleoylphosphatidylcholine (DOPC) was obtained from Avanti Polar

Lipids (Alabaster, AL). DiO-C16 and 110 nm fluospheres were obtained

from Molecular Probes (Eugene, OR). FITC-dextran was obtained from

Sigma (St. Louis, MO). Purified monomeric EGFP (14) was obtained from

Michelle Digman (Department of Biomedical Engineering, University of

California, Irvine, CA). Chinese hamster ovary (CHO) K1 cells were

maintained in low-glucose D-MEM supplemented with penicillin/strepto-

mycin and 10% fetal bovine serum (Invitrogen, Carlsbad, CA). The cells

weretransientlytransfectedwiththegrowth-associatedprotein(GAP)-EGFP

plasmid (obtained from Alan Horwitz, Department of Cell Biology, Uni-

versity of Virginia (15)) using Lipofectamine 2000 (Invitrogen) 24 h before

imaging. Imaging was accomplished at 37?C with a Warner Instruments

stage incubator (Warner Instruments, Hamden, CT).

Supported planar bilayer

Supportedplanarbilayers(SPBs)weregeneratedaccordingtotheprotocolof

Burns and co-workers with minor modifications (16). Briefly, 1.25 mg of

DOPC in chloroform was mixed with the appropriate amount of DiOC16,

also in chloroform. The chloroform was evaporated under a stream of dry

nitrogen. The sample was further dried for 1 h in a lyophilizer. After re-

suspension in 500 mL of buffer (100 mM NaCl and 40 mM sodium phos-

phate, pH 7.4) by vortexing, the sample was subjected to three freeze-thaw

cycles. The sample was then extruded through two stacked 100-nm poly-

carbonate filters using the Avestin extruder. Vesicle size was confirmed by

FCS of the labeled vesicles.

Glass coverslips (Corning, Corning, NY) were cleaned in a piranha so-

lution created by mixing seven parts x-grade H2SO4with 3 parts x-grade

hydrogen peroxide. Coverslips were immersed in this solution for 1 h and

rinsed copiously with ultrapure water. Before SPB deposition, coverslips

were dried under a stream of nitrogen. Vesicles were pipetted onto the slide

and then diluted 1:5 with imaging buffer (150 mM NaCl, 50 mM sodium

phosphate, and 1.5 mM sodium azide, pH 7.4). After 15 min of incubation,

the SPB was washed vigorously with imaging buffer.

Fluorescence microscopy

Images were acquired at the image plane of an Olympus IX81 (Olympus

America, Center Valley, PA) microscope with a Cascade 512B EMCCD

camera equipped with a Dual View image splitter (Photometrics (a division

of Roper Scientific), Tucson, AZ). Electron multiplication was used at the

maximum level for all experiments shown here. Confocal mode experiments

were done with the laser collimated to overfill the back aperture of the ob-

jective to form a diffraction-limited spot within the sample. These experi-

ments were done with a 603 1.2 NA water objective (Olympus, Melville,

NY) and the 488 line of an argon ion laser (Melles Griot (a division of CVI

Laser), Carlsbad, CA) with a power at the sample of ;10 kW/cm2. A single

16 3 16-mm pixel of the camera was used as a pinhole for the measurement.

This corresponds to ;0.5 airy diameter units (dairy¼ 1.22lM/NA). Bright-

field mode was accomplished by focusing a laser beam at the center of the

back aperture of a 603 1.45 NA oil objective (Olympus) with a 20-cm lens,

so that a collimated beam was emitted from the front aperture of the objec-

tive.Here,thelaserintensityattheimageplanewas;50W/cm2.TIRFmode

imaging was accomplished by translating the focused brightfield beam to the

edge of the objective aperture.

Camera exposure calibration

Cameraexposuretimeandfrequencyweremeasuredusingheterodyningwith

a 471-nm frequency-modulated diode laser from ISS (Champaign, IL)

modulatedwithapulsegenerator(PM5786B,Fluke,Everett,WA).Thelaser

was collimated overfilling the back aperture of the objective so that a dif-

fraction-limited spot was formed within the focal plane. A concentrated so-

lution of fluorescein was used as a fluorescent reporter of the laser intensity.

The laser pulse was set to 100 ms for all experiments. For each camera ac-

quisition frequency, the laser frequency was set slightly lower so that the

camera exposure behavior could be observed on the timescale of many ac-

quisition frames.

Simulations

Simulations were calculated using a program written in-house. The program

updates the positions of particles randomly distributed in two dimensions

with a Gaussian random number generator with standard deviation

where T is the period of the simulation and D is the diffusion coefficient. For

each frame, a Gaussian intensity distribution was superimposed on the po-

sition of each particle with amplitude corresponding to the average intensity/

frame. A Poisson random number generator was then used to calculate the

photon counts corresponding to each intensity. For analog simulations, a

multiexponential random number was calculated for each photon in a pixel

according to the desired single-photon response. These were then added

togethertogettheanalogdistribution.Finally,aGaussianrandomnumberand

anoffsetwereaddedtoeachpixeltosimulatetheanalogoffsetandreadnoise.

ffiffiffiffiffiffiffiffiffi

2DT

p

;

Data analysis

Data analysis was performed as described in the Theory section, using either

software written in-house or SimFCS (Laboratory for Fluorescence Dy-

namics, Irvine, CA). For all 2D histogram analyses, the average andvariance

images were smoothed before calculation of the 2D histogram. The

smoothing was a 3 3 3-pixel spatial moving average, with the center pixel

weighted twice as much as the surrounding pixels.

RESULTS

Simulations

Fig. 1 A shows simulations for 2D diffusion of a particle with

a diffusion coefficient of 2 mm2/s. There are ;1.6 particles

5388Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 5

per diffraction-limited area. Fig. 1 B shows this same plot for

data with the same single-photon pulse height distribution as

the Cascade 512B (see Appendix). Fig. 1 also shows the B

versus (ÆIæ ? offset)/S plot for G1 and G1y analyses of the

analog simulated data. We also performed simulations at the

lowest brightness point with no read noise and achieved

essentially the same result (data not shown). Finally, we

performed simulations with the lowest brightness and con-

centration increases to produce intensities equivalent to the

brightest data point. Here, the error in the measured bright-

ness has decreased dramatically and is approximately the

same as for the photon-counting measurement. The error in

the photon-counting measurement at the same brightness and

concentration does not differ from the error at low concen-

tration (data not shown).

Pixel uniformity

The ease of statistical calculations is strongly related to the

uniformity among camera pixels. Since our calculations in-

volve the relationship between detector variance and overall

intensity, we tested the pixel uniformity by calculating the

slope of this relationship for all pixels at intermediate inten-

sity (1/10 of output range). Variances and intensities were

calculated using an image stack size of 1024 frames. The

microscope transmission lamp was used as a constant and

uniform source of light. The contribution from long-term

lamp-intensity fluctuations was assessed by subtracting a

moving average with a period of three images (shot noise is

instantaneous and therefore is not affected by the subtrac-

tion). The results were not changed significantly, indicating

that lamp fluctuations do not contribute to the variance. The

plot of the variance versus intensity slope at each pixel is

shown in Fig. 2 A. The standard deviation among pixels is 7,

with an average slope of 114.

The range of variance versus intensity slope values could

be due to either a random distribution of static pixel char-

acteristics, or to random error in measuring the slope. To test

this, we split the image series in half and calculated the slope

from each image set. Fig. 2 B shows the 2D scatter histogram

of the slopes from the two experiments. The distribution is

nicely round, indicating that the two experiments were in-

dependentofoneanother.ThePearsoncorrelationcoefficient

is 0.006, reinforcing this conclusion. This indicates that the

variation in slope from the pixels is not a result of static

variation in pixel character but rather of random error in

measuring the slope.

At high intensities (three-fourths of the output range) and

lowamplifier gain,significantsaturation isobserved from the

system (see below). Therefore, it is of interest to characterize

the uniformity in saturation intensity across pixels. The slope

of intensity versus variance is also a good measure of this

characteristic. As aresult,werepeatedthe aboveexperiments

FIGURE 1

(A) and simulations with the same analog noise as the Cascade camera

(B–D). (C and D) G1 and G1y analyses, respectively, of the simulation. All

simulations used 2D diffusion with 1250 molecules in a 3.5 3 3.5-mm box,

except for the high-intensity, low-brightness point in B, which used 25,000

molecules in the same box size. The diffusion coefficient was 2 mm2/s, with a

framerateof200frames/s.Eachsimulationwasrunfor100frameswithaframe

resolution of 128 3 128 pixels. Brightness values were 0.5, 2, 5, and 10 cpfm.

B/S versus ÆIæ ? offset/S plots for photon-counting simulations

FIGURE 2

for the Cascade camera. Image size is 68 mm. (B) Two-

dimensional correlation scatter plot for two measurements

of the variance versus intensity image.

(A) Image of variance versus intensity slope

Number and Brightness with EMCCD Camera5389

Biophysical Journal 95(11) 5385–5398

Page 6

at higher intensity. The resulting slope was ?67, indicating

that we have indeed reached saturation, with a standard de-

viation of 33. Again we performed correlation between two

identical experiments. Here, the Pearson coefficient was

0.06, indicating that there is a small amount of correlation.

Nevertheless, the 2D scatter histogram remains relatively

round,indicatingthatthecorrelationissmall(datanotshown).

Detection linearity and saturation

As was mentioned before, the determination of particle

number and brightness is dependent on the linearity between

intensity and variance. This linearity is strongly affected by

saturation of components in the system, the most obvious

being the analog-to-digital converter. Given the high degree

of uniformity among pixels, this linearity can easily be

measured by illuminating the camera with a gradient of in-

tensity. A plot of variance versus intensity should be linear.

Such a plot is shown in Fig. 3 A. It is obvious from this figure

that significant nonlinearities exist for the EMCCD camera.

The deviation from linearity starts at ,20,000 DL and is

complex. If the highest amplifier gain is used, the read noise

increases as well, but the only saturating component is the

saturationoftheanalog-to-digitalconverterat65,535DL(Fig.

3 B). This allows for the use of the system up to ;40,000 DL.

Camera stability

Fig. 4 shows the value of the offset, S parameter, and readout

noise variance as a function of time on the timescale of

seconds and minutes. The data were collected starting when

the camera had reached its equilibrium temperature as de-

termined by the camera utility software. The S parameter

quickly reaches an equilibrium value and remains relatively

constant over 1 h. The read-noise variance shows a bit of a

short-term trend, but this is at least two orders of magnitude

smaller than the photon contributions to variance, and

therefore does not contribute significantly. We have also

observed that these parameters do not change significantly

throughout the course of a day and are relatively constant

from day to day (data not shown), though there is long-term

drift associated with camera aging. Thus, these parameters

can be calibrated at the beginning of a day and used

throughout the day without change. Conversely, the offset

parameter shows an exponential change at the beginning of

each exposure sequence and must be corrected for in each

measurement. This correction can be made using a region of

the camera that is not illuminated during capture. In our sit-

uation, this is accomplished by blocking one ofthe dual-view

channels. Alternatively,onecan omitthedatacollected inthe

first 30 s of each exposure.

Dynamic range

Totestthedynamicrangeofthecamerasystem,weused110-

nm fluorescent beads diffusing freely in and out of a TIRF il-

lumination field. Fig. 5 A shows the B/S versus (ÆIæ ? offset)/

S plot for a 64 3 64-pixel region as a function of maximum

average intensity. The image stacks were 1000 frames for

this measurement. The plot is linear over B/S values from

1.08 to 9, corresponding to brightness values from 0.08 to 8,

giving a dynamic range of 100 for the measurement. At high

intensities, saturation becomes an issue and the plot deviates

from linearity. Fig. 5 B shows the recovered n9, which is also

recovered accurately over the linear region of the system.

G1 analysis

As was mentioned in the Theory section, it is possible to

avoid use of the S calibration factor if there is spatial or

temporal redundancy in the acquisition. Fig. 6 A shows the

temporalautocorrelationfunctionfor110-nmbeadsdiffusing

into and out of a TIRF field. Fig. 6 B shows the spatial

autocorrelation function in the y dimension for this same

sample. The amplitude of the first point of the spatial auto-

correlationishigherthantheamplitudeofthefirstpointofthe

FIGURE 3

nation on the Cascade camera with maximum electron multiplication and

minimum analog-to-digital conversion gain. (B) Same plot as in A, but with

maximum analog-to-digital conversion gain. Lines portray the slope of the

initial part of the data.

(A) Plot of variance versus intensity for a gradient of illumi-

5390Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 7

temporal autocorrelation method, indicating that we are

oversampling in space more than in time. Fig. 6 C shows a

plot of B/S versus (ÆIæ ? offset)/S acquired using both the G1

and G1y analysis methods. The brightness is higher for the

spatial autocorrelation method, as suggested by the ampli-

tudes of the spatial and temporal autocorrelation curves.

Camera exposure timing calibration

The Cascade 512B camera operates in two basic modes,

overlap and nonoverlap. In the overlap mode, the camera is

continuously exposed and the frame is transferred to the read-

outregionofthecameraeachtimeareadout eventisfinished.

In this way, the exposure time is defined by the readout time.

In nonoverlap mode, the camera is cleared, exposed for the

specified time, and finally transferred for reading. The only

difference is the clearing step.

To elucidate more carefully the timing of the exposure

sequence, we illuminated the camera with a diffraction-lim-

ited pulsed laser spot. The frequency of the laser was set

slightly lower than the camera frame rate so that the laser

pulse provides a reduced-frequency time-lapse series of the

camera response. The laser pulse was a 100-ms square-wave

and therefore willadda total of100 ms tothe observedcamera

exposure width. The exposure can be easily defined in terms

of percentage of the camera period and then transformed into

real time based on the known camera frame rate. Fig. 7 A

shows a time series for a 375-ms exposure in nonoverlap

mode. At time zero, the camera is cleared by shifting in new

rowsfrom thetopofthecamera,resultinginasmearedimage

on the upper half of the device. Throughout the exposure, the

laser spot is seen in the center of the image. At the end of the

exposure, the frame is transferred for readout, resulting in a

smearedimageonthelowerhalfofthedevice.Fig.7Bshows

the measured exposure times, which agree very well with the

exposure times set via software. A linear fit gives a slope of

0.99 with an intercept at 97 ms, as expected for this experi-

ment. The exposure time for overlap mode is ;1 ms shorter

than the total frame time, indicating that the shift process

takes ;1 ms (data not shown). Photometrics lists the vertical

shift rate for this camera at 2 ms/row, giving a total shift time

of ;1 ms for the camera, in agreement with the observed

behavior.

Given the high fidelity of the camera exposures, it should

be possible to perform brightness analysis as a function of

exposure time for confocal illumination of fast moving par-

ticles. Fig. 8 A shows brightness/exposure time as a function

of exposure time for monomeric EGFP at 40 nM in buffer.

The data fit well with Eq. 7 using the binning function in Eq.

10, giving a diffusion time of 120 6 40 ms. The axial/radial

ratio was fixed at 1:3,as expectedfor confocal detection (17).

Given the diffusion coefficient of mEGFP (90 mm2/s (18)),

this corresponds to a radial beam waist of 200 6 40 nm,

which is close to the expected diffraction-limited focal size

for this microscope.

For acquisitions of areas larger than a few pixels, one

expects the exposure time resolution to be a function of

camera vertical shift rate. Fig. 8 B shows the brightness of

110-nm beads in a TIRF field as a function of exposure time

using aperture illumination over ;64 pixels, as well as full-

FIGURE 4

ance, and S parameter for the cascade

cameraasa functionof timeover (A) 60s

after 1 h warm-up time, and (B) 60 min

starting at the end of camera cool-down.

Plots of offset, read vari-

Number and Brightness with EMCCD Camera5391

Biophysical Journal 95(11) 5385–5398

Page 8

frame illumination. The tzand r values were determined

fromtheautocorrelationfunctionusingEq.11(Fig.8C).The

two plots are significantly different, indicating that illumi-

nated area has a significant influence on exposure due to the

shifting time of the camera. The lines show the expected

brightnesses assuming that the brightness with 5300 ms ex-

posure is unaffected by the vertical pixel shifts. The aperture

illumination is much closer to the expected value than the

full-field illumination, as expected due to the influence of the

vertical shift rate.

Concentration independence of

brightness measurement

Fig. 9 A shows a plot of recovered n9 value for a serial di-

lutionofEGFPinphosphate-bufferedsolution.Theexposure

time was set at 100 ms for this measurement. In addition, the

laser was focused to a diffraction-limited spot within the

sample. The plot is nicely linear, indicating that we are, in

fact, recovering concentration independent of brightness.

Fig. 9 B shows the recovered brightness, which is constant

and independent of concentration.

Dynamic N and B measurements

Given the highly parallel nature of brightfield detection, it

seems possible that Nand Bmeasurements could be analyzed

asafunctionoftimeforasampleinwhicheitherbrightnessor

concentration is changing. To demonstrate this, we measured

DiOC16 in DOPC supported bilayers. DOPC forms a highly

uniform bilayer with no liquid ordered domains at room

temperature.Thus,itshouldprovideauniformbrightnessand

concentration.Inaddition,attheintensitiesusedinthisstudy,

the concentration of DiO bleaches out within 1 min. There-

fore, if our technique works, we should see a decrease in

concentration over time with no change in brightness.

Fig. 10 shows a time series of brightness versus intensity

images for a hexagonally illuminated region of the bilayer. In

FIGURE 6

autocorrelation in the y dimension (B) for 110-nm beads diffusing in a TIRF

field. (C) Brightness as a function of intensity from the G1 (circles) and G1y

(squares) analysis methods. Data were the same as in Fig. 5. For C, the lines

are the best fit to the data.

(A and B) Temporal autocorrelation function (A) and spatial

FIGURE 5

intensity for 110-nm beads diffusing in a TIRF field. The brightness was

changed by changing the laser power. For A, the lines are best fit to the linear

region of the data. For B, the line represents the average over the linear

region of the data.

Plot of brightness (A) and particle number (B) as a function of

5392Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 9

addition,abackgroundcomponentof1500DLperframewas

subtracted as described in materials and methods. There ap-

pears to be an exponential decrease in overall intensity as

a function of time for the system, whereas the brightness

doesn’t change significantly. Therefore, the intensity de-

creasesarearesultofconcentrationchangesduetobleaching.

Due to the diffusion of the molecules, there should be a

spatial concentration gradient with the fewest number of

molecules in the center of the illuminated volume. Fig. 11

shows selected high- and low-intensity regions of the histo-

gram and the corresponding regions of the image. High-in-

tensity histogram points correspond to the outer region of the

illuminated volume and low-intensity points correspond to

the inner region, as predicted. In addition, a small ring at the

edge of the illuminated volume is selected at low intensity.

This is a result of the clipping of the point-spread function in

this region, resulting in a reduced focal volume and thus a

decrease in apparent particle number.

N and B analysis in living cells

Fig. 12 B shows the B/S versus (ÆIæ ? offset)/S histogram for

two CHO K1 cells transfected with a GAP-EGFP construct.

The histogram shows two distinct regions with equal

brightness. Selection of the image pixels that correspond to

these regions of the histogram shows that these spots corre-

spond to two cells in the image with different transfection

efficiencies of the GAP-EGFP. The average relative bright-

nesses of the high-intensity and low-intensity cell were 0.33

and 0.28 and the corresponding n9 values were 150 and 39. If

we assume a g factor of 0.5, there are 74 particles/point-

spread function in the bright cell and 20 particles/point-

spread function in the dim cell. Fig. 12 C shows the 2D

histogram for the cell after illumination for 50 s. The con-

centration has decreased significantly, especially for the

brightest cell, but the brightness has not changed.

DISCUSSION

Camera characteristics

The N and B analysis method relies on the determination of

variance and intensity from an image. It is important to

scrupulously test the camera for stability and linearity. We

havedemonstratedthatintermsofgainandreadoutnoise,the

FIGURE 7

750-ms exposure as determined by pulsed laser illumination at a slightly

lower frequency than the frame rate. (B) Plot of measured exposure time

versus exposure time set via software. The line is the best fit to the data.

(A) Time-lapse images at the beginning, middle, and end of a

FIGURE 8

exposure time for (A) EGFP in solution with confocal excitation and (B)

110-nmbeadsin a TIRFfieldwithfull-field(circles) andapertured(squares)

illumination. (C) Temporal autocorrelation function for the apertured data in

B. For A and C, the solid line is the fit to the data to Eqs. 7 and 9. For B, the

solid line is the expected brightness according to Eq. 7 extrapolated from the

brightness at 5.3 ms exposure time, with the diffusion time determined from

the autocorrelation function in C.

(A andB) Brightnessdivided by exposuretime as a function of

Number and Brightness with EMCCD Camera5393

Biophysical Journal 95(11) 5385–5398

Page 10

camera shows negligible drift over the timescale of a typical

experiment (1 h). Also, we proved that there is a high degree

of pixel uniformity. This uniformity is critical for producing

accurate maps of particle number and brightness.

The offset of the camera shows drifts on timescales from

seconds to minutes. In this study, we have corrected for this

by using a nonilluminated region of the camera. Several

camera manufacturers produce cameras with dynamic offset

correction mechanisms. These cameras may provide a solu-

tion to this problem. A disappointing feature of the camera

under study was the high degree of nonlinearity. A large

portionofthecamera’sdynamicrangeisunusablebecause of

this effect. Given these effects, it is crucial that any study

using these methods test each camera for its stability and

linearity.

To assess the relationship between the measurements

made by the camera system and a photon-counting system

with equivalent quantum efficiency, we performed simula-

tions. The simulations demonstrate that the analog mea-

surement of intensity and molecular brightness is reasonably

equivalent to the photon-counting measurement in terms of

signal/noise. The major differences in brightness error lie at

low intensities. We have also shown that this is not a result of

read-noise contribution, as simulations with no read noise do

not have this problem (data not shown). We have also shown

thatforhigherconcentrationsatthesamebrightness,theerror

becomes comparable to the photon-counting situation. Note

that the high concentration data point has ;28 molecules in

the focal volume. This is well within the range of physio-

logical conditions as calculated from GAP-EGFP in the Re-

sults section.

Dynamic range

Previous studies have shown that an analog confocal system

with a 12-bit analog-to-digital converter had a dynamic

brightness range of ;20 (5). Here, we demonstrate that the

camera-based system has a linear dynamic range of at least

100. The camera has a 16-bit analog-to-digital converter

which accounts for the increase in dynamic range of almost

an order of magnitude. The key limitation of the dynamic

range for the system is the nonlinearity of the camera, which

forced us to use the highest digital gain and therefore the

lowest dynamic range. Nevertheless, simultaneously mea-

FIGURE 9

for EGFP in solution with confocal excitation. For A, the line is the best fit to

the data, and for B, the line represents the average of the data.

Number (A) and brightness (B) as a function of concentration

FIGURE 10

for DiOC16 in a DOPC planar sup-

ported bilayer at different time points

after the start of illumination. The image

size is 17 mm. (Lower) Brightness ver-

sus intensity histograms corresponding

to the images in A.

(Upper)Intensityimages

5394 Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 11

suring particles with brightness ratios of .100 is unlikely.

Therefore, this dynamic range ismore than adequate for most

biological aggregation measurements.

G1 analysis

Although accounting for the analog noise of the camera

system is a straightforward process, it requires additional

measurements and precautions that are not ideal for routine

measurements. Shot noise has no time correlation and

therefore could be removed by measuring the covariance of a

pixel with itself at subsequent time points when the molecule

has not moved significantly. This is equivalent to measuring

the first point of the autocorrelation rather than the zeroth

point, and therefore is referred to as G1 analysis. In the same

way, one can use the spatial redundancy of oversampled

acquisition and calculate the covariance of a pixel with

neighboring pixels that show the same molecular informa-

tion. This is equivalent to measuring the first point of the

spatial autocorrelation function and is referred to as G1y

analysis. Both of these cases are shown in Fig. 6 for 110-nm

beads diffusing in and out of a TIRF field. The spatial auto-

correlation is oversampled to a greater extent than the tem-

poralautocorrelation,andtherefore,theG1yanalysisrecovers

a higher brightness than the G1 analysis. The relative accur-

acy of such methods will depend on the experimental setup,

namely on resolution, magnification, and time resolution.

Camera timing

One distinct advantage of N and B analysis over traditional

autocorrelation methods is the dependence on exposure time

as opposed to overall acquisition rate. To accurately assess

thenumberandbrightnessofamoleculethatdiffusesthrough

the focal volume in 100 ms, one must have an exposure time

on the order of 100 ms, but the acquisition rate couldbe much

slower, perhaps 30frames/s.Thissame concept appliestothe

G1y analysis (but not the G1 analysis, as it relies on temporal

redundancy).Itisalsoimportanttonotethatthetimebetween

frames need not be conserved, as it is only the shape of the

intensity that is important, not its time dependence. This

should allow similar measurements to be done on spinning-

disk confocal systems where the pixels are not sampled in a

linear fashion.

To assess the exposure time of the EMCCD, we used a

heterodyning approach with a pulsed diode laser. Although

the exposure time is conserved quite accurately down to

,100 ms, there is obvious vertical pixel shifting at the be-

ginning and end of each exposure (Fig. 7). Therefore, it is

possible to accurately measure the brightness of EGFP,

which has a diffusion coefficient of 90 mm2/s (18) and a

diffusiontimethroughthefocalvolumeof;100ms,butonly

with confocal excitation illuminating a few pixels of the

camera (Fig. 8 A). Under these circumstances, the vertical

shift has negligible effect on the exposure time, because the

vast majority of the camera pixels experience no light

FIGURE 11

illumination. Red regions correspond to selected pixels from the B/S versus

(ÆIæ ? offset)/S histogram.

Images of the supported bilayer from Fig. 8 after 20 s of

FIGURE 12

EGFP. (B) Red regions in A correspond to selected pixels from the B/S

versus (ÆIæ ? offset)/S histograms. (C) B/S versus (ÆIæ ? offset)/S histograms

after 50 s of illumination.

(A and B) Images of CHO K1 cells transfected with GAP-

Number and Brightness with EMCCD Camera5395

Biophysical Journal 95(11) 5385–5398

Page 12

throughout the exposure. As the exposure time becomes

significantly shorter than the diffusion time, one expects

relativelylittlechangeine9/T.ThesolidlineinFig.8Bshows

how this behavior is borne out in the theory of the depen-

dence of brightness on exposure time (Eq. 7). From the black

squares in Fig. 8 B, we can see that illumination of the entire

camera for TIRF excitation of fluorescent beads leads to a

significant underestimation of the brightness below a few

milliseconds. This is likely due to spatial shifting of the

camera. The overall shift time of the camera is 1 ms, which is

consistent with our observations. Fortunately, one can illu-

minate a somewhat smaller (64-pixel) vertical portion of the

camera and resolve the brightness much more accurately

down to fractions of a millisecond, as observed for apertured

illumination (Fig. 8 B, circles). With our microscope setup,

this apertured region is ;17 mm in size. A typical cell is ;10

mm in diameter and should be amenable to such analyses.

Concentration independence of brightness

In Fig. 9, we performed a serial dilution of EGFP in buffer.

The number of particles tracks linearly with the known

concentration while the brightness remains constant, con-

firming the efficacy of our technique for such measurements.

The resolved concentrations are on the order of 100 nM. This

is similar to native expression levels for many cellular pro-

teins. Therefore this technique should be well suited to such

measurements.

Supported bilayer experiments

Asamodelsystemformembranediffusion,wechoseaDOPC

supported planar bilayer doped with DiOC16. The DiOC16

molecular brightness is easily resolved above background

(B/S¼1)inonly3.25s ofacquisition (500frames) ona643

64 pixel region. The supported bilayer provides another op-

portunity to verify the concentration independence of the

brightness measurement. Due to the slow diffusion of the

membrane-confined molecules, photobleaching occurs rap-

idly, so that after 1 min of acquisition, the fluorophore is

completely depleted from the center of the illuminated vol-

ume. The ability to resolve the brightness within a few sec-

onds allows for tracking of this process. The intensity

decreases exponentially with the decrease in number of

particles, whereas the brightness remains constant through-

out the process. It is important to note that a nonbleached

background will become predominant as bleaching occurs

and therefore must be subtracted from the average and vari-

ance before calculating the brightness. In our case, the

background corresponds to 1500 DL, .10% of the overall

intensity at time zero. Nevertheless, simple subtraction re-

moves this background contribution from the measurement.

Although the average number of molecules/diffraction-

limited volume is 14 at the 20-s time point, it is straightfor-

ward to see from the average image that the intensity is not

uniform over the field of view. Therefore, we should be able

to resolve spatialdifferences in particle number. Alook atthe

brightness versus intensity histogram for this time point

shows that the distribution is broader over the intensity axis

than the brightness axis. The pixels that correspond to high

intensity in the histogram also correspond to the edges of the

illuminated area, which are expected to have higher con-

centration.

Live-cell experiments

Although supported membranes are excellent model systems

for the study of single-molecule diffusion, they bear a limited

resemblance to live cells, where diffusion is quite likely

anomalous and concentrations are heterogeneous. Therefore,

weundertookmeasurementsonliveCHOK1cellsexpressing

GAP-EGFP. This protein is monomeric in the basal mem-

brane (15). Fig. 12 A shows two cells expressing vastly

different amounts of the construct. Nevertheless, their bright-

nesses are identical and easily resolved from the background,

demonstrating the appropriateness of this technique for mea-

suring single-molecule brightnesses independent of concen-

trationforlivingcells.Theobservedconcentrationsarewithin

the range shown to demonstrate the best signal/noise ac-

cording to our simulations. The standard deviation in the

brightness distribution for both cells was 0.09. Given an av-

erage brightness of 0.3 for both cells, this is well within the

necessaryrangeforobservationofoligomerization.Giventhe

strong dependence of the TIRF illumination on distance from

the surface, one might expect spatial deviations in brightness

due to membrane undulations. This is not observed, sug-

gesting that either these undulations are uniform and below

the resolution of the measurement or the undulations are of

insignificant amplitude to influence the measurement. In ei-

ther case, they cause a small enough perturbation that mea-

surements of oligomerization would not be affected. In

addition, extended bleaching of the cells shows significant

changes in intensity but not in brightness (Fig. 12 C). If the

GAP-EGFPweremultimericinthecellmembrane,onewould

expect to see the brightness change with photobleaching as

EGFPtags on themultimericspeciesare bleached oneby one

until the multimer appears monomeric, containing only one

fluorescent EGFP.

CONCLUSION

Given the highly parallel nature of camera data acquisition

and the single-molecule sensitivity of EMCCD cameras, it is

desirable to characterize them for molecular brightness mea-

surement. We have shown that these devices present signifi-

cant challenges in terms of drift and nonlinearity. The drift

issue can be easily overcome through real-time subtraction

methods.Thenonlinearityissuepersists,anditseverelylimits

the dynamic range of acquisition. Nevertheless, we show that

evenwiththislimitation,thedynamicrangeisalmostanorder

5396Unruh and Gratton

Biophysical Journal 95(11) 5385–5398

Page 13

of magnitude greater than that seen previously for analog

detectors used in confocal microscopy. The timing of the

camera exposures has also proven to be complex, with a

significant spatial dependence. Nevertheless, with an illumi-

nation aperture larger than that of a typical living cell, the

timing is maintained to submillisecond exposures, which is

fast enough for observation of most cellular processes. The

parallel acquisition of the EMCCD compared with confocal

measurements has proven to be quite fruitful, allowing for

accuratedeterminationofbrightnessasafunctionoftimeand

space in the presence of significant concentration heteroge-

neity.Thisallowsforreal-timemonitoringofparticlenumber

and brightness in living cells. This technique holds great

promiseforelucidatingdynamicandcomplexprotein-protein

interactions that form the basis for important cellular pro-

cesses.

APPENDIX

In an analog detection system, it is not photon counts that are detected, but

rather pulses of photocurrent. For most analog detectors, the photon pulse

height distribution is quasiexponential. This is a result of the probabilistic

nature of photon multiplication, where several electron impact events have a

similar probability of generating secondary electrons. In addition, the

amplifier and analog-to-digital converter in the system contribute a readout

noise that is Gaussian. Fig. 13 shows the pulse height distribution for the

512B camera in the dark at full gain. A fit of the distribution to a Gaussian

plus that Gaussian convoluted with a multiexponential function is shown in

red. The read noise standard deviation is 26 DL with an average single-

photon intensity (gain) of 130 DL.

The addition of independent random variables (convolution) results in an

average and variance that are the sums of the average and variance of such

variables. As a result, the offset and read noise variance can simply be

subtracted from the average and variance, leaving only the gain-dependent

single-photon pulse height distribution. This distribution is the photon

probability-weighted sum of the k photon probability distributions as

follows:

PðIÞ ¼ +

N

k¼0

PCHðkÞPkðIÞ:

(12)

Here PCH(k) is the photon-counting histogram as described previously (2).

Its specific form is not important for this derivation. In turn, the individual k

photon probability distributions are generated from the single-photon analog

probability distribution through multiple convolutions:

PkðIÞ ¼ P1ðIÞ5Pk?1ðIÞ:

(13)

As mentioned previously, the variance of convoluted functions is the sum of

the individual variances. As a result, the k photon variance is simply k 3 Va

where Vais the analog single-photon variance.

When distributions are added (as in Eq. 12), the variance is only additive

when the distribution averages are equal. This is not the case with the k

photonanalogdistributions.Asaresult,Eq.12mustbesolvedintermsofthe

average intensity squared (raw moment as opposed to central moment),

whichisadditiveforshifteddistributions.Onecaneasilyshowthatthisvalue

is given as

ÆI2æ ¼ VaÆIæ1G2ÆI2æ;

(14)

where G is the analog gain, which is given by the average intensity of the

single-photon pulse-height distribution (ÆIæ ¼ ÆkæG). Using the standard

definition of variance, we obtain the final equation for the analog variance in

terms of the average photon counts and PCH variance:

s2¼ VaÆkæ1G2VarðPCHÞ:

(15)

For a single species, the average photon counts are given by the brightness

times the occupation number (en) and the variance is given by VarðPCHÞ ¼

ge2n1en; where g is a point-spread function shape factor given by the

normalized integral over the point-spread function squared (3). The analog

variance can then be written in terms of number and brightness as

s2¼ ðVa1G2Þen1G2ge2n:

(16)

It is not trivial to measure the single-photon variance; therefore, we define a

parameterSthatisgivenbytheslopeofanintensityversusvarianceplotfora

light source with constant intensity (no temporal fluctuations). Such a light

source would give a Poisson photon counting signal and it is easy to derive

the value of S from Eq. 4:

S ¼Va

G1G:

(17)

Incorporating the read variance and offset, the analog variance and intensity

are then given by

s2? s2

0¼ SGen1G2ge2n

(18)

and

ÆIæ ¼ Gen:

(19)

We thank Michelle Digman for providing the soluble EGFP and Alan

Horwitz for providing the GAP-EGFP plasmid.

We also acknowledge National Institutes of Health grants P41 RR03155

and RO1 DK066029, which provided funding for this work.

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FIGURE 13

a maximum electron multiplication gain and maximum analog-to-digital

gain, along with a fit (red line) to the model described in the Appendix.

Histogram of dark intensities for Cascade 512B camera with

Number and Brightness with EMCCD Camera5397

Biophysical Journal 95(11) 5385–5398

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