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IntroDuctIonHumans have an uncanny visual capability to recognize patterns, making microscopy a powerful analysis tool. This is one of the reasons why developments in light microscopy and advances in the biological sciences have run in parallel since the first microscopes were produced at the end of the 16th century. By contrast, many time-resolved spectroscopic measurements, such as fluorescence correlation and cross-correlation spectro-scopy (FCS and FCCS), are still mainly conducted at single points, and thus they do not provide a contiguous image of a sample. Only with the recent advent of fast and sensitive electron- multiplying charge-coupled device (EMCCD) and scientific complementary metal-oxide-semiconductor (sCMOS) cameras has it become possible to record intensities on a large number of pixels in parallel at sufficient speed to do time-resolved spectro-scopic analyses. This provides images with new contrast mecha-nisms that are not based on fluorescence intensity only, but that are created by any observable parameter that can be extracted from the measurement. In this work, we focus on the imaging modalities of FCS and FCCS, which we refer to as imaging FCS for brevity. Typically measured parameters of imaging FCS include the diffusion coefficient and other parameters of molecular mobility, concentration or molecular affinities.

Imaging FCS does not require customized systems, but it can be implemented on any TIRF microscope or SPIM. Here, we provide a detailed protocol for sample preparation, setup calibration, data acquisition and evaluation, based on published methods routinely used in our laboratory1–3.

Fluorescence correlation spectroscopyFCS was developed in the early 1970s (ref. 4). It analyzes the fluo-rescence intensity fluctuations from a small observation volume within the sample in order to determine the molecular processes that cause these fluctuations (Fig. 1): typically, diffusion of par-ticles into and out of the focal region. These random fluctuations

are analyzed by calculating the correlation functions of the meas-ured intensity time trace I(t) = ⟨I⟩ + δI(t):

GI t I t

I( )

( ) ( )t d d t= ⟨ ⋅ + ⟩⟨ ⟩2

where ⟨I⟩ is the time-averaged intensity and δI(t) are the zero-mean fluctuations on top of ⟨I⟩. The FCS autocorrelation curves, as defined by equation (1), typically decay on a time scale τD (see Fig. 1a), which relates the size of the observation volume to the diffusion coefficient (here denoted as D) of the moving particles5:

t DA

DA

x y x y

x y x y=

⋅= ∫∫

∫∫eff

eff 24with

MDE( , ,0)d d

MDE ( , ,0)d d

( )

( )

2

where the function MDE(x,y,z) (molecular detection efficiency) describes the observation volume and Aeff the area of a section through the center of the MDE. The amplitude of the measured intensity fluctuations δI(t) scales with the square root of the number of particles N in the focus (Poisson process). Therefore, the amplitude of G(τ) scales with 1/N, and it is best measure-able at low particle numbers N—that is, in small observation volumes on the order of femtoliters (1 fl = 1 µm3)6. Furthermore, the measurement of G(0) allows estimation of the concentration within a sample if the observation volume is known.

Since its inception, FCS has been used to measure, amongst others, chemical reaction rates, molecular mobility (diffusion coefficients and flow velocities), particle sizes and concentra-tions, as well as molecular aggregation and interactions7–9. It is especially widely used in the biological sciences, as it gives access to affinity constants, diffusion coefficients and reaction rates even in live cells and small organisms. FCS has also been applied

(1)(1)

(2)(2)

Imaging fluorescence (cross-) correlation spectroscopy in live cells and organismsJan W Krieger1,8, Anand P Singh2–4,8, Nirmalya Bag2,3,5, Christoph S Garbe6, Timothy E Saunders4,5,7, Jörg Langowski1,9 & Thorsten Wohland2,3,5,9

1German Cancer Research Center (DKFZ), Heidelberg, Germany. 2Department of Chemistry, National University of Singapore, Singapore. 3National University of Singapore (NUS) Centre for BioImaging Sciences, National University of Singapore, Singapore. 4Mechanobiology Institute, National University of Singapore, Singapore. 5Department of Biological Sciences, National University of Singapore, Singapore. 6Interdisciplinary Center for Scientific Computing, University of Heidelberg, Heidelberg, Germany. 7Institute for Molecular and Cell Biology, A*Star, Singapore. 8These authors contributed equally to this work. 9These authors jointly directed this work. Correspondence should be addressed to T.W. (twohland@nus.edu.sg).

Published online 5 November 2015; doi:10.1038/nprot.2015.100

single-plane illumination (spIM) or total internal reflection fluorescence (tIrF) microscopes can be combined with fast and single-molecule-sensitive cameras to allow spatially resolved fluorescence (cross-) correlation spectroscopy (Fcs or Fccs, hereafter referred to Fcs/Fccs). this creates a powerful quantitative bioimaging tool that can generate spatially resolved mobility and interaction maps with hundreds to thousands of pixels per sample. these massively parallel imaging schemes also cause less photodamage than conventional single-point confocal microscopy–based Fcs/Fccs. Here we provide guidelines for imaging Fcs/Fccs measurements on commercial and custom-built microscopes (including sample preparation, setup calibration, data acquisition and evaluation), as well as anticipated results for a variety of in vitro and in vivo samples. For a skilled user of an available spIM or tIrF setup, sample preparation, microscope alignment, data acquisition and data fitting, as described in this protocol, will take ~1 d, depending on the sample and the mode of imaging.

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to high-throughput measurements on automated microscopes10–12. It has been extended to many different modalities including the use of spatial correlations in image correlation spectroscopy (ICS)13; fluorescence lifetimes in fluorescence lifetime correlation spectroscopy14; polarization for rotational diffusion measurements; and wavelengths for spectrally resolved FCS15–17.

However, most of these modalities, with the exception of ICS, use a single focal spot for their measurements. This limits the available information (and hence statistical power) for any biolog-ical sample, and it does not provide a full overview of the spatially varying sample characteristics. Although ICS provides images of the sample, it has been used primarily for studying spatial cor-relations, and it is limited in temporal resolution. Spatiotemporal ICS18,19 and raster image correlation spectroscopy20–22 have been developed to achieve higher spatial and temporal resolution. However, Spatiotemporal ICS still has limited temporal resolu-tion, as it focuses on the analysis of spatial correlations in time, whereas raster image correlation spectroscopy uses a scanning approach, which leads to anisotropic temporal resolution and limited spatial resolution as pixel averaging is often required.

Fluorescence cross-correlation spectroscopyA particularly powerful extension of FCS is FCCS (Fig. 2), which allows the quantitative measurement of molecular interactions with much greater ease than FCS23,24. Here, the fluorescence fluctuations from two spectrally (two-color FCCS (2c-FCCS)) or spatially (two-focus FCCS (2f-FCCS)) separated observa-tion volumes are recorded and analyzed through their cross- correlation function (CCF):

GI t I t

I t I tgrg r

g r( )

( ) ( )

( ) ( )t

d d t=

⟨ ⋅ + ⟩⟨ ⟩ ⋅ ⟨ ⟩

where Ig(t) and Ir(t) are the intensities from the two volumes g and r and δIg(t) and δIr(t) are their fluctuations. In 2c-FCCS, the intensities come from two-color channels (e.g., ‘green’ and ‘red’), which detect two differently colored fluorescent dyes. Co-diffusion of the differently labeled particles will result in correlated sig-nals from both channels and consequently in high amplitudes of Ggr(τ) (at most, the cross-correlation amplitude can reach

(3)(3)

the levels of the autocorrelation amplitudes). Independently moving particles, on the other hand, result in amplitudes close to 0. Theoretical considerations show that the zero-lag ampli-tude of the CCF depends especially on the number of green-red double-labeled particles Ngr (the number of green- and red-only labeled particles are denoted as Ng, Nr):

GN

N N N Ngrgr

g gr r gr( + ) ( + )( )0 ∝

⋅

Therefore, by measuring the ACFs Ggg(τ) and Grr(τ), as well as the CCF Ggr(τ), the relative dimer concentrations may be determined. If the two dyes label two reactants of a dimerization reaction, then their binding strength can be deduced. Often the relative CCF amplitude

qG

G G= gr

gg rr

( )

min( ( ), ( ))

min

min min

tt t

is used to quantify interaction. Here Ggr(τmin) represents the aver-age correlation function amplitude either at lag times that are significantly lower than the correlation time τD or τmin = 0 if the curves were fitted with a model function. Note that a variant of this expression has been derived that also corrects for different instrument artifacts, such as spectral cross talk25. Details of that expression are given in the Supplementary Discussion.

In 2f-FCCS (Fig. 2b), the two observation volumes g and r are not separated spectrally, but spatially. This approach allows directed molecular motion (such as flow processes) to be measured with respect to the separation vector between the two volumes. By combining multiple directions in the same sample, any planar direction of these flow processes may be measured.

Development of imaging FCS/FCCS Early developments in multiplexed FCS/FCCS provided measurements on too few points (4–100) in a sample to build contiguous parameter maps; see Bag and Wohland26 and Singh

(4)(4)

(5)(5)

b Basic workflow of imaging FCS

Image series and time traces

Imageseries

Time t

Lag time � [s]0.

001

2013_08_080

0.002

0.004

0.01 0.

1 1

Correction

Time t

Timetraces

Artifact correction Calculate correlation functions forevery pixel

Fit curves and build parametermaps and images and statistics

Diffusion coefficient D (µm2/s)

Steps 16–19 Steps 20 and 21 Steps 20–29 Steps 30–37

Principle of FCSaDiffusing particles

Observationvolume

Flu

ores

cenc

e in

tens

ity l(

t)

Aut

ocor

rela

tion

G(τ

)

Correlation

amplitude g(0

) ∝ 1/N

δl(t

) ∝

δN

(t)

⟨l ⟩∝⟨N ⟩

Diffusingparticles

Fluorescence fluctuations Autocorrelation analysis

Decaytime �D

Lag time TTime t

many fast particlesfew slow particles

Figure 1 | Principle of FCS and imaging FCS. (a) In FCS, particles diffusing through a small observation volume are observed via their fluorescence. The measured fluorescence fluctuations are then analyzed in terms of an autocorrelation function G(τ), which yields a decay time τD that measures the average retention time of particles in the volume. The zero-lag amplitude of g(τ) is inversely proportional to the number of particles N in the volume. (b) In imaging FCS, a series of images is acquired and then corrected for background and bleaching artifacts. Temporal auto- and cross-correlation functions are subsequently calculated and fitted with analytical models. Finally, the fit results are displayed as color-coded maps and evaluated statistically. For each step in b, the relevant PROCEDURE steps are given.

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No

Principle of 2c-FCCS

Principle of 2f-FCCS

Time t

Time t

Time t

Lag time T

Cor

rela

tion

func

tion

Green autocorrelationRed autocorrelation

Cross-correlation

GRGR

GRGR

Increasing relativeconcentration of

Flu

ores

cenc

e in

tens

ity Green intensity Ig(t )

Red intensity Ir(t )

Left autocorrelationRight autocorrelation

Cross-correlation

Particlevelocity

TF = d/v

TF = d/v Lag time T

Left intensity Ig(t )

Right intensity Ir(t )

Flu

ores

cenc

e in

tens

ity Green intensity Ig(t )

Red intensity Ir(t )

Many dimers:

a

b

No dimers:

Flu

ores

cenc

e in

tens

ity

Cor

rela

tion

func

tion

Left/right observation volume

Diffusingparticles

Green/red observation volume

Distance d = r2–r1

v

and Wohland27 and references therein. With the advent of fast and sensitive EMCCD cameras, temporal correlations at each pixel of the camera can now be recorded. Initially, this technology was used to perform single-position confocal (Fig. 3) FCS measurements28,29. Spatially resolved measurements were performed on a spinning-disk confocal microscope using EMCCDs as detectors30. However, such schemes are either limited in the number of points that can be acquired simultane-ously or, as in the case of the spinning-disk microscope, illuminate each pixel for only a fraction of the measurement time, and thus they could only be used to measure very bright samples (e.g., fluorescent beads). Full use of the spatial resolution of the EMCCD cameras was only achieved by combining them with advanced microscopy techniques that offer good z-sectioning, such as SPIM or TIRF (Fig. 3b,c). With these combinations (termed SPIM-FCS and imaging TIR-FCS or ITIR-FCS), auto-correlation and cross-correlation functions can be calculated simultaneously for many pixels within an image31–33.

Overview of the procedureImaging FCS/FCCS can be performed in two modalities, either using a TIRF microscope for thin samples close to a surface, e.g., cell membranes, or using a SPIM for larger 3D samples. It provides information on molecular dynamics, concentration and organization in complex samples. Using two-color detection and an FCCS analysis, it can also measure molecular interactions. For these purposes, the measurement system has to be calibrated (see PROCEDURE Steps 8–15) and samples have to be mounted in specific ways depending on the modality (Step 16). We describe how to mount adherent cells on coverslips, liquids in plastic sample bags, or whole organisms embedded in a gel cylinder for light-sheet microscopy.

Generally, imaging FCS/FCCS measurements are performed following the sequence in Figure 1b. After aligning and calibrat-ing the instrument (Steps 1–15), a fast image series is acquired from the sample (Steps 16–19). Next, diverse artifacts, such as a constant background or fluorophore bleaching, are corrected (Steps 20 and 21). Finally, autocorrelation functions from each pixel and cross-correlation functions between two color channels or any two pixels can be calculated (Steps 20–29). These correla-tion functions, as defined in equations(1) and (3), are typically calculated using a multiple-τ algorithm34, which is implemented on a standard computer. Theoretical model functions are then fitted to the measured correlation curves, in order to quantify the molecular mobility, concentrations, interactions and other parameters (Steps 30–35). The resulting parameters are finally presented as a map or image that shows their spatial distribu-tion (Steps 36 and 37). These data sets can be further evaluated statistically, e.g., by calculating and evaluating their histograms, or by calculating correlations between different parameters and other information (Step 37).

Advantages and applicationsThe most obvious advantage of imaging FCS is its multiplex-ing capability, which provides hundreds or thousands of FCS

measurements from a single acquisition, thus markedly improving the statistical power compared with that of confocal FCS. Equally important, though, is the fact that imaging FCS provides all possi-ble spatial cross-correlations for any pair of pixels or group of pixels. This increases

Figure 2 | Principle of FCCS. (a) The two-color variant (2c-FCCS) for a sample with many and with no dimeric molecules (labeled GR in the figure). (b) 2f-FCCS in a sample in which particles flow in the direction of the focus separation with a velocity v.

Objectivelens

Pinhole

Photon-countingdetector

Dichroicmirror

Illuminationlight

Confocalfluorescence light

Fluorophores

a

Detectionobjective

Illuminationlight

Light sheet

Sample

Cylindrical lens

Fluorescencelight

Camera

Cover slip

Objectivelens

Evanescentfield

b c

Cover slip

Direction ofdetection

fedSample

IlluminationObservationvolume

Camera

Figure 3 | Schematic diagrams of microscopes typically used for FCS. (a) A confocal microscope. (b) A camera-based TIRF. (c) A SPIM microscope. (d–f) The small cartoons illustrate the illuminated (blue) and observed (red) region within a sample for each of the three microscopy schemes (gray, in this case a single cell).

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the information content several-fold as compared with single spot measurements35, and it also permits analysis of nonlocal mobility processes36.

A further advantage over confocal FCS is that imaging FCS is much easier to calibrate by using the known pixel size of the camera as an internal ruler. In this way, TIRF-based imaging FCS is calibration free, if only 2D motions are observed (as, for example, in a cell membrane). It thus provides absolute diffusion coefficients, contrary to confocal FCS and FCCS, whose align-ment procedures are more cumbersome and have to be performed at least daily37. SPIM-FCS benefits from the same principles, but it requires the additional measurement of the light-sheet thickness, which, however, is easily accomplished as described in the PROCEDURE.

Applications of imaging FCS have been recently reviewed27. By using this methodology, maps of diffusion coefficients33,38, flow profiles39, concentrations, interactions3,40, molecular transi-tions41 and time-lapse videos of diffusion coefficient maps42 have been created and used to analyze dynamic processes in live cells and also whole organisms. As an in vivo example, imaging FCS has been proposed as a powerful tool for disentangling differ-ent proposed mechanisms for morphogen gradient formation43. In addition, the recording of multiple contiguous pixels allows the flexible application of the FCS diffusion laws44,45 in order to characterize the structure and organization of lipid bilayers and cell membranes beyond the diffraction limit1.

Limitations of the techniqueDespite its advantages, imaging FCS is still limited by the available technology, as discussed below. The two most important restric-tions are that a calibration is needed for absolute concentration measurements and currently available cameras are limited with respect to their readout speed.

Concentration measurements. At the time of writing, the con-centration measurements in camera-based imaging fluorescence fluctuation methods (e.g., imaging FCS) deviate from those in confocal FCS with photon-counting detectors. This has been

shown with EMCCDs used in number and brightness meas-urements46 and from a direct comparison of confocal FCS and imaging FCS with different camera types2. Thus, imaging FCS does not provide absolute concentration measurements, but it requires a further calibration with a concentration standard. It should be noted, however, that the response of the cameras is linearly proportional to concentration, and therefore the calibrations are simple2,3.

Readout speed. The readout speed affects the accessible time range. EMCCD cameras can be read out with different speeds, depending on the number of lines recorded and their position on the camera chip. Although a time resolution down to 10–20 µs can be achieved by reading out only a small number of pixels or lines29,47, these approaches restrict the usability of the method by confining the measurement to only a part of the camera, thus giving up either continuous readout or the imaging aspect of the technique. For continuous readout of any area of the chip (hence using the full field of view of the camera), the time resolution is more restricted. A small number of lines, approximately four, can be read out with ~0.25-ms time resolution, but a more practical region of interest with at least 20 lines, anywhere on the chip, can be read out with, at best, 0.5–2 ms at the moment, depending on the camera model. sCMOS cameras can be read out faster, with a time resolution of 40 µs. However, their photosensitivity is still too low to acquire enough photons from organic dyes or fluores-cent proteins, precluding low-noise correlation curves at read-out speeds of much less than a millisecond. Because of these restric-tions, accurate diffusion coefficients can only be determined below ~100 µm2/s (ref. 5). However, this regime includes protein diffusion in the cytoplasm and cell membranes, which are today the most common samples for imaging FCS studies. The diffusion of small labeled molecules with D > 200 µm2/s (e.g., small labeled protein substrates, drugs or nucleic acids in solution or cells) can still be measured with camera-based FCS, but the recovered dif-fusion coefficients are biased to lower values by a factor of ~2 or more3 (Table 1 and ANTICIPATED RESULTS). This limit should be overcome by next-generation imaging detectors, such as fast

table 1 | Example diffusion coefficients obtained with EMCCD camera–based SPIM-FCS.

In vitro sample D20 °c (m2/s) proteins in live cells Dfast,20 °c (m2/s) Dslow,20 °c (m2/s) slow (%)

200-nm Fluorescent beads 2 ± 0.7 eGFP (HeLa) nuc./cyt 35 ± 8 0.4 ± 0.3 15 ± 5

100-nm Fluorescent beads 3.8 ± 1 eGFP-4x (HeLa) nuc./cyt 15 ± 5 0.4 ± 0.2 20 ± 5

QDot-565 ITK 18 ± 6 Histone H2A-GFP, nuc. 7.3 ± 2.1 0.22 ± 0.05 57 ± 8

(HeLa) cyt. 18 ± 7 0.2 ± 0.1

607-bp dsDNA 8 ± 5 Fos/Jun (HeLa) nuc. 17 ± 10 0.4 ± 0.1 50 ± 10

170-bp dsDNA 22 ± 3 PMT-eGFP (CHO-K1) cyt. 27 ± 10 0.1 ± 0.1 30 ± 10

28-bp dsDNA 66 ± 10 mem. 24 ± 10 0.1 ± 0.1 45 ± 10

eGFP 69 ± 20

Alexa-488a 270 ± 50All values are renormalized to 20 °C. The in vitro samples were measured in water. For the in vivo samples, the cell line and potentially the position inside the cell (cyt: cytoplasm, nuc: nucleoplasm, mem: membrane) are given. For the in vitro sample, a one-component fit was performed, and for the in vivo sample a two-component normal diffusion fit was performed.aThese particles are so fast that the measured diffusion coefficients are not absolutely accurate (see ref. 5).

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and sensitive arrays of avalanche photodi-odes2,48,49. However, for now, these detec-tors are not yet commercially available, and they are still a topic of active research and development.

Camera-generated artifacts. The different camera techniques lead to specific artifacts in imaging FCS/FCCS measurement, such as the camera offset, a varying baseline in EMCCDs. Such artifacts are explained and their correction is detailed at the corresponding position in the PROCEDURE with TROUBLESHOOTING advice, as well as in the Supplementary Discussion and Supplementary Figures 1–17.

Limitations of TIRF and SPIM. Good z-sectioning is essential for imaging FCS; hence, TIRF microscopes and SPIMs are used, but they have specific limitations. TIRF microscopy only measures in a 100- to 200-nm-thin slice of the sample, which has to be posi-tioned directly above a coverslip. Therefore, it is most suitable for measurements in membrane systems, such as supported bilayers or cell membranes. In contrast, SPIMs can be used to observe any part of a cell and penetrate ~10–100 µm into larger organisms, such as embryos (see ANTICIPATED RESULTS) or cell spheroids. However, most SPIMs require a special sample mounting scheme. Often the samples have to be mounted vertically into the sample chamber (Fig. 4)50,51. In some variants of SPIM, the sample can also be prepared on a standard horizontal microscope slide, but some types of samples have to be elevated by special gel struc-tures38,52,53. Another drawback of currently available SPIMs is that they are typically limited to a few samples at any time, which makes them unsuitable for high-throughput experiments.

Generally, the parallelization of FCS/FCCS on SPIM and TIRF microscopes reduces the phototoxicity of such measurements, as substantially less energy is deposited in the samples while a large number of correlation curves are acquired. However, the simultane-ous illumination of large parts of the sample also leads to different effects of photobleaching on the measurements, as seen in confo-cal FCS/FCCS3,39,54. Such artifacts are also discussed in the corre-sponding PROCEDURE steps, and further details can be found in the Supplementary Discussion and the given references.

Experimental designMicroscope setups. In principle, any commercial or custom- built SPIM instrument or objective-type TIRF microscope can be used for Imaging FCS. Other microscopy variants, such as variable angle illumination or prism-type TIRF setups, can also typically be used, but these will not be discussed further in

this paper. However, we note that major parts of the protocol should be applicable to these other systems with only minor changes (e.g., fit models, alignment procedures), depending on the individual system.

For SPIMs, it is necessary to use a high-numerical-aperture detection objective (NA >0.8) and a thin light sheet to achieve a small sample volume. Typically, the thickness of the light sheet should be in the range of <2 µm (1/e2 radius), and the Rayleigh length should be 10–20 µm. This can be achieved by overfill-ing the back-focal plane of an illumination objective with an NA of 0.2–0.5 and a long working distance. The quality of the light sheet can be tested by imaging the laser beam in a dilute dye solution, or by reflecting the laser at different positions within the field of view directly onto the camera (step-by-step building protocol of SPIMs dedicated for imaging FCS/FCCS can be found in Krieger55 and Singh56). All objective-type TIRF microscopes are immediately usable for imaging FCS because of their use of high-NA objectives.

To quantify protein binding (membrane, cytosolic and nuclear proteins), FCCS measurements can usually be performed on the same setups. Such measurements require a dual-color illumina-tion with two lasers (typically 488 and 561 nm), unless single-wavelength excitation FCCS57 is used, which is not discussed further in this protocol. In both cases, the fluorescence signal has to be collected by an image splitting device that images two spectrally distinct color channels either on the same camera chip side by side or on two cameras. Both the illumination laser and detection channel overlap have to be aligned carefully, and they should be tested properly to ensure a maximum cross-correlation amplitude. Often, spectral cross talk is seen between the green and red channel. This cross talk is usually 3–12% and should be mini-mized by selecting proper filter sets for the used fluorophores. Its impact can also be minimized by tuning the laser intensity so that both color channels appear equally bright on the camera.

Furthermore, the camera-based correlation can be extended to spatial cross-correlation to measure active protein transport from one compartment to another in living cells35. For this type of analysis, a standard single-channel imaging FCS acquisition is sufficient, as any spatial correlations can be extracted from this same data set during evaluation.

Compatible cameras, data collection and data processing computers. Fast and sensitive cameras are required for imaging

Sample embedded in gel roda b c

g

j

fe

i

d

h

Detectionobjective

Adherent cells on cover slip Sample bags

TweezersSample bag Tweezers

5mm

Syringe or capillary

Gel cylinderGlass slipwith cells

Syringe/capillary

Plunger

Gel cylinder

Sample

Light sheet

0.5–1 mm

Observedregion

Figure 4 | SPIM sample mounting procedures. (a,d,e,h) Samples, such as fluorescent beads or embryos, embedded in a clear gel cylinder. (b,f,i) adherent cells on a coverslip. (c,g,j) Liquid samples inside sample bags. (a–j) The top row (a–c) shows photographs of the actual samples in front of the detection objective of a light-sheet microscope. The second row (d–g) shows 3D illustrations of the samples, and the third row (h–j) shows a top view with the observed region marked in red. Note the direction of propagation of the light sheet (blue arrow).

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FCS measurements, typically either EMCCD or sCMOS cameras. These can be read out with at least 500 frames per second (f.p.s.) for a region of interest (ROI) of at least 20 × 20 pixels, and a quantum efficiency of more than ~50%. Higher frame rates are desirable, as the time resolution limits the resolvable time scales. Higher quantum efficiencies provide a better signal-to-noise ratio of the calculated correlation curves. The cameras can be oper-ated with their own control software or with additional software, such as µManager58 (a freely available open-source program for microscope control). The key software requirement is support for fast and continuous readout of 10,000–100,000 frames of a selected ROI. The supported file formats are of minor impor-tance, as binary camera files can typically be converted to standard file formats, such as the tagged image file format (TIFF), after the acquisition. Most of the measurements described in this article were performed with an EMCCD camera (Andor iXon 860) that was operated at ≥1,000 f.p.s. for an ROI of 20 × 20–128 × 20 pixels and a quantum efficiency of >90%. The use of a compara-ble EMCCD camera is advised for imaging FCS measurements, although modern sCMOS cameras can work with appropriate pixel binning (Supplementary Fig. 1). Note that, as discussed above, the baseline of the camera can be unstable during acquisi-tion and thus the camera should allow stabilization of its baseline (Supplementary Fig. 2). If an EMCCD camera is used, it is crucial to choose a proper EM-gain setting, which substantially influ-ences the noisiness of the calculated correlation curves and thus determines the accuracy and precision of the recovered mobility parameters and concentrations. A test measurement that can be used to determine a good EM-gain setting for a given sample is described in Supplementary Method 1.

A standard desktop computer is sufficient for data recording and analysis, although a large random access memory (RAM) of >8 GB is desirable. Any of the major operating systems (i.e., Microsoft Windows, MacOS X and Linux) can be used for the data evaluation, but a 64-bit operating system is strongly recom-mended for the evaluation of large data sets, or of many measure-ments in a batch mode.

Sample mounting and compatible samples. TIRF microscopes selectively excite molecules close to the coverslip by creating a homogeneous lateral illumination profile, which decays expo-nentially in axial direction. Therefore, TIRF is the ideal method to study basal membrane dynamics and organization. Because of the limitations in the axial direction, the observations are largely independent of the cytosolic or bulk dynamics. All objective-based TIRF microscopes use standard glass-bottom dishes or chamber cover slides for supported bilayer and cell membrane study. These sample-mounting techniques are also compatible with imaging FCS measurements.

The sample preparation for SPIM imaging requires special care, and the sample mounting methods are typically very different

from conventional (upright) microscopes. In a SPIM instrument, the sample is often mounted vertically (either from top or bot-tom) in a chamber filled with buffer solution (using appropriate medium, such as ‘egg water’ for zebrafish), or it has to be elevated above the bottom of a Petri dish (e.g., using agar structures). As the objectives in a SPIM are often fixed in space, the sample needs to be mounted on a micrometer-precision stage to enable its positioning in the microscope’s field of view. Consequently, specialized sample mounting techniques have been developed for light-sheet microscopes, and we give protocols for mounting samples that are typically used in imaging FCS:

Liquid samples (e.g., beads for calibration, typical sample volume: ~20–50 µl) are mounted in a transparent (UV-visible-IR transparency 90%), heat-sealed plastic bag made from fluorinat-ed poly-ethylene-propylene films with thickness of 10–25 µm. These films have a refractive index of 1.341–1.347, which is close to that of water. Figure 4c shows a photograph of such sample bags, filled with a bead solution. The sample bags are created by cutting the film in rectangular shapes and sealing it by using a plastic bag sealer (see Supplementary Figure 3 and the starting steps of the PROCEDURE).Adherent live cells are plated onto small cleaned and autoclaved cover glass pieces (size: ~5 × 10 mm2). With these samples, care must be taken to avoid scratching the detection objective and reflecting the laser onto the camera sensor (the angle between coverslip and laser should be below 45°, see Fig. 4b). A list of cell lines that have been successfully used in imaging FCS can be found in the Supplementary Note.Large samples, e.g., Drosophila or zebrafish embryos, are mounted in a transparent agar cylinder (agar concentration: 0.5–1.0%, wt/vol). To image a specific section of an embryo, it can be helpful to mount the embryo on a cross-marked cover glass slide before placing it in the microscope (Fig. 4).For nonadherent cells or cell aggregates, the same mounting scheme as for embryos can be used, but with a gel matrix prepared with a proper culture medium and using specialized gels (e.g., MatriGel).

Further SPIM sample mounting techniques have been discussed in the literature52,59–61, but note that you might have to modify the proposed protocols to suit the geometry of your SPIM.

As imaging FCS/FCCS measurements take only 10–60 s, the stability of the sample mounting and sample translation stages is of minor importance, as long as they are stable enough during the acquisition time. In our experience, the sample translation stages of commercial TIRFs and also of most home-built SPIMs will not cause any artifacts in imaging FCS/FCCS. Typically, motion of the sample (e.g., of cells on a coverslip) is the major source of artifacts.

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Yellow-green fluorescent microspheres, 100 nm, carboxylate-modified FluoSpheres YG (Invitrogen, cat. no. F8803)Red fluorescent microspheres, 100 nm, carboxylate-modified FluoSpheres YG (Invitrogen, cat. no. F8801)

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Multicolored microspheres, 100 nm, TetraSpec (Invitrogen, cat. no. T7279)Microsphere dilution buffer (e.g., 10 mM Tris, pH 8.5) for carboxylate-modified spheres should deprotonate the –COOH groups and lower aggregation due to the increased surface charge

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For live-cell measurements: a clear, nonfluorescent and nonscattering cell culture medium, in which the cells can survive for at least 1 h (e.g., FluoroBright DMEM; Invitrogen, cat. no. A18967)Hank’s Buffered Salts Solution (HBSS)An organic fluorophore, compatible with your filter sets (e.g., Alexa Fluor 488, Alexa Fluor 594, Atto-488 or Atto-565, rhodamine dyes)Coverslip coating for cells: collagen type I (rat tail) (e.g., BD Biosciences) or poly-l-lysineDrosophila dechorionation: household bleach ! cautIon It is corrosive. Wear protective clothing during dechorionation.Low-melting agar (Sigma-Aldrich, cat. no. A9414)Deionized water (filtered with a pore-size <100 nm if used as a measure-ment buffer)Ethanol, 70% vol/vol (Sigma-Aldrich, cat. no. E7023) for various cleaning and sterilization tasks

Gels for beadscanPhytaGel (Sigma-Aldrich, cat. no. P8169)MgSO4·6 H2O, 10% (wt/wt) (Sigma-Aldrich, 00627 Fluka) solution

Lipid bilayersPrepared as described in Supplementary Method 2: 2 M Sulfuric acid, H2SO4 (Sigma-Aldrich, cat. no. 33974) ! cautIon It is corrosive.Technical ethanol (Sigma-Aldrich, cat. no. E7023)DOPC lipids (Avanti Polar Lipids, cat. no. 890704)Fluorescently labeled lipids (Avanti Polar Lipids, cat. no. 810157)

EQUIPMENT crItIcal In this section, we list the components that have been tested for application in SPIM-FCS in our laboratories. However, note that other components with comparable specification should also work. We provide alternative choices for some of the components where appropriate.Equipment for sample preparation and mounting

Fluorescent bead scan gels: 1-ml plastic syringes (~4.6 mm inner diameter (i.d.), Nipro Corporation, Japan)Embryos: glass capillary (Fisher Scientific, cat. no. 22-260943) with an i.d. larger than the diameter of the embryo (e.g., for Drosophila an i.d. of ~0.6 mm is required)Adherent cells: no. 3 coverslips (Neolab, cat. no. 16301)Foil for sample bags: 10–25 µm thin heat-sealable foil with a refractive index close to that of water (e.g., Lumox Folie 25 M, Sarstedt)Sample bag sealing: plastic bag sealer (e.g., Kingstar impulse sealer, Kingstar Packing Machine Ltd) or modified Soldering tweezers (e.g., Star Tec ST 505; Conrad Electronic, cat. no. 588754-62) modified with two copper plates (2- to 3-mm-thick and rounded at the corners); see Supplementary Figure 3cMounting of sample bags and cells: self-closing tweezers (Dumont; Ted, Pella, cat. no. 5748)Sample mounting on a TIRF microscope: standard (chambered) microscopy slides or dishes with a glass bottom (no. 1 cover slides, Fisher Scientific)Bath sonicator (for sonicating fluorescent microsphere samples and for the preparation of lipid bilayers; Fisher Scientific, cat. no. FB15051)Rotary evaporator (Rotavap R-210, Büchi, Switzerland) for lipid bilayer productionMetal syringes (Hamilton) for lipid bilayer production

Illumination (laser)Excitation of eGFP, YFP, Alexa Fluor 488, Atto-488, quantum dots and comparable ‘green’ fluorophores: Laser with 10–100 mW at 488–491 nm ! cautIon Laser light can severely harm the eye. Ensure that laser light is always shielded from the user, and wear protective glasses while working with lasers.Excitation of mRFP, mCherry, Alexa 594 and comparable red fluorophores: laser with 10–100 mW at 561–568 nmLaser clean-up filters for 488/491-nm diode-pumped solid-state (DPSS) and diode lasers, as they often emit a small amount of green lightA transmission illumination lamp (LED, halogen lamp) ! cautIon High-Power LEDs and light sources can harm the eye. Avoid looking directly into these.

For TIRF microscopyAny objective-based TIRF setup (Fig. 3a) equipped with a high-NA objective (e.g., Zeiss Plan-APOCHROMAT 100×/1.46 oil-immersion objective, Olympus PlanApo 100×/1.45, oil-immersion objective). See Figure 3a for the FCS/FCCS setup and Table 2 for camera specifications

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Fixed fluorescent beads on a cover glass for determining the lateral point spread function (PSF)

For SPIMsA SPIM with a high-NA detection lens (typically NA >0.8 at 40–60× magnification) and a light-sheet width of 1–2 µm (1/e2 half-width, typically created with, e.g., an NA 0.2–0.3 air objective). We use custom-built setups with an air objective for projection (Nikon Plan Fluor 10×/0.3 or Olympus SLMPlan 20×/0.25) and a water-dipping objective for detection (Nikon CFI Apo-W NIR 60×/1.0 or Olympus LUMPLFLN 60×/1.0 W). See Supplementary Figure 4 and refs. 2,3,48,55,56 for detailsSmall mirror mounted under 45° (e.g., silver mirror 5 × 5 × 1 mm3 on steel mount) for light-sheet calibration and alignmentEM-grid, 1,500–2,000 lines per inch for alignment of dual-channel image-splitting systems (e.g., Agar Scientific, cat. no. AGG2785C, AGG2786C)

CamerasA high-speed and high-sensitivity camera. The same cameras can be used for both microscopy techniques. Examples include Andor iXon X3 860 EMCCD camera (128 × 128 pixels, ∆tframe = 2 ms full-frame and, e.g., ∆tframe = 530 µs for 128 × 20 pixels); Photometrics Evolve 512 EMCCD camera (512 × 512 pixels, ∆tframe = 30 ms and, e.g., ∆tframe = 2.4 ms for 20 × 512 pixels); Hamamatsu ORCA-flash 4.0 V2 sCMOS camera (2,048 × 2,048 pixels, ∆tframe = 10 ms full-frame and, e.g., ∆tframe = 39 µs for 2,048 × 8 pixels)

Detection filters for single-channel measurementsNotch filters to filter direct scattering light from the laser onto the camera. crItIcal See Supplementary Figure 4 for detailed proposals on filters.Green fluorescence channel for ‘green’ dyes, such as Alexa Fluor 488, Atto-488, green fluorescent beads, multicolored beads or eGFP: a band-pass filter with a transmission range of ~500–550 nmGreen/yellow fluorescence detection for ‘green/yellow’ dyes, excited at 488 nm, such as eYFP, diverse quantum dots: a long-pass filter with a transmission range of >500 nmRed fluorescence channel for ‘red’ dyes, such as Alexa Fluor 594, mRFP, mCherry, red quantum dots, red fluorescent beads or multicolored beads: A band-pass filter with a transmission range of ~600–700 nm or a long-pass filter with a transmission range of >580 nm

Multichannel image splitting system with a filter setDualView DV2 (Photometrics, optimized for typical EMCCD sensors). All example FCCS measurements in this paper were recorded with this device. Alternatives include Optosplit II (Kairn, optimized for typical EMCCD sensors) or W-View Gemini (Hamamatsu, optimized for large field-of-view sCMOS sensors)Filters for image splitter optics, chosen according to dye combination. For the fluorophore combinations eGFP–mRFP, eGFP–mCherry, Alexa Fluor 488–Alexa Fluor 594, we use, e.g., beam-splitter: splitting at 565 nm; green channel: band-pass, transmission range: ~500–550 nm; red channel: long-pass, transmission range: >600 nm

ComputersData acquisition: 2–4 cores, ≥8 GB RAM, optionally a fast hard disk or solid-state disk,Win7 (32/64-bit) or LinuxData processing and evaluation: 1–8 cores (more cores allow for faster, parallelized evaluation), ≥8 GB RAM, Win7 (64-bit), Linux or MacOS X

SoftwareCamera and microscope control (any of the following, as appropriate for your microscope): software provided with camera, µManager51,62 for custom-built setups or, e.g., an openSPIM51 or home-written software for custom microscopesimFCS software (Box 1): e.g., the self-contained software package, QuickFit3 or a plug-in for the widely used ImageJ open-source software

REAGENT SETUPPreparation of fluorescent microspheres in gel for SPIM calibration Prepare an aqueous stock solution of 10% (wt/wt) MgSO4·6H2O. Dissolve 200 mg of PhytaGel in 40 ml of deionized water and add 400 µl of the 10% stock solution of MgSO4. Heat the mixture in the microwave until the PhytaGel has dissolved. Every few seconds, take the flask out of the oven and shake it, so that the components mix well. Leave it to cool down to ~40 °C and mix it with beads (e.g., 5–15 µl of 100-nm-diameter TetaSpec Microsphere stock with 1 ml of gel) by quickly vortexing the gel in an Eppendorf tube, before it has solidified. When imaging this gel later, there should be 5–15 beads in an area of ~50 × 50 µm2. Cut the tip off a

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standard 1-ml syringe (i.d. 4.6 mm). Push the plunger to the front of the syringe and draw up ~400 µl of the fluid gel. Ensure that no air is trapped between the gel and the plunger. Let the gel solidify in the refrigerator for 5 min. The gels inside the syringe can be stored at 4 °C in a closed reaction tube that contains 1–2 ml of water, optionally supplemented with a few 100 µl of ethanol. The shelf life is typically 1–3 months. Check regularly for sample quality and sterility, as mold can sometimes form in the gels. During their shelf life, they can be reused multiple times (timing: 30 min).Preparation of fluorescent microspheres in the sample bag for SPIM calibration Cut a 5 × 3 cm2 piece of LumoxFolie25 (see a1 in Supplementary Fig. 3a). Clean the foil with 70% (vol/vol) ethanol and deionized water on both sides. If your foil has a hydrophobic and a hydrophilic side (e.g., LumoxFolie 25), also observe on which side the surface wets; this identifies the hydrophilic surface that should end up inside the sample bag. Form an ~5-cm-long sleeve with the hydrophilic side inside by bending a rectangular sheet around a 3-mm steel rod and heat-seal the long overlapping edge (see a2 and a3 in Supplementary Fig. 3a). Wash the sleeves thoroughly with 70% (vol/vol) ethanol and deionized water (use a syringe to pump liquid through the sleeve). Heat-seal the sleeve at both ends and in the center, forming two independent air-filled pockets that are each 2- to 3-cm long (see a4 in Supplementary Fig. 3a). Test the pocket seal by gently pressing down on them. If the air vents from the inside, they are not airtight. If so, try to seal them or make a new sleeve. If the pocket proves to be airtight, cut it into four equal pieces of ~ 5 × 10 × 2 mm3 in size, which are closed on three sides and open on the fourth (see a4 and a5 in Supplementary Fig. 3a). The prepared sleeves can be stored indefinitely at room temperature (21–25 °C) in a closed container. For measurements fill 30–50 µl of the liquid sample in one of the pockets and heat-seal the last side carefully (do not heat or evaporate the sample; see a5 and a6 in Supplementary Fig. 3a). If they are properly prepared, these sample bags may be stored at 4 °C and reused, typically for a

few months or until their contents have evaporated. If required, clean them with alcohol or deionized water before use. crItIcal Sonicate liquid samples containing quantum dots and microspheres for 30 min in a bath sonicator (put the sample into an Eppendorf tube, which resides in a swimmer), before filling them into the sample bags. This helps disperse them properly and reduces the number and size of aggregates (timing: 30 min). ! cautIon Wear gloves (e.g., Latex) during this process to prevent contamination of the sample by fats and dirt from the hands.Preparation of coverslips for mounting adherent cells for SPIM Cut no. 3 glass coverslips (thickness 0.28–0.32 mm) into small pieces (size: ~5 × 10 mm2) with a steel glass cutter. Thoroughly wash the glass pieces in 70% (vol/vol) ethanol or acetone to remove any remaining dirt. Remove the ethanol/acetone by a second washing step in deionized water. Leave the glass pieces to dry on low-lint cleaning paper. Sterilize the glass pieces by autoclaving. Before seeding the adherent cells, put a few (2–6) of the sterile and coated coverslips into the cell culture dishes. Seed the cells on these and let them grow for 24–28 h before taking measurements. crItIcal Cut and cleaned coverslips can be stored indefinitely in a closed container under sterile conditions for months, but they should be resterilized before use. To improve cell adhesion, coat the glass pieces with, e.g., collagen or poly-l-lysine (PLL) before use (timing: 60 min to overnight).Preparation of collagen-coated coverslips Dissolve 120 µl of collagen in 10 ml of 0.02 M acetic acid. Put the coverslips in a small dish and cover them with collagen solution. Incubate the coverslips at 37 °C for at least 30 min, and then wash them twice with PBS. Place the cells on the coated coverslip; attachment is generally complete within 30 min. crItIcal Coated coverslips should be freshly prepared before use.Preparation of PLL-coated coverslips A more detailed protocol has been published elsewhere63. Briefly, prepare 0.1% (wt/vol) of PLL solution in deionized water. Sterilize a cover glass with 70% (vol/vol) ethanol and air-dry.

table 2 | Typical camera settings for imaging FCS2 and FCCS3 with different sensor types.

eMccD scMos cMos

Quantum efficiency @ 525 nm (%) 95 70–75 35–55

Effective pixel size (µm) 12–24 6.5 6.5

Data acquisition camera pixel bin 1 1 1

Postprocessing pixel binning

Bright samples (fluorescent beads in buffer) 1 1–2 2–4

Organic dyes in buffer and fluorescent proteins 1–2 2–4 4–8

EM-gain77,78 Yes

Bright fluorescent beads in buffer 10–50 — —

Organic dyes in buffer and fluorescent proteins 250–300

Camera exposure time2 (µs)

Organic dyes in buffer 200–300 38–100 —

Fluorescent beads in buffer 500–1,000 38–1,000 500–1,000

Fluorescent proteins 500–2,000 500–2,000 500–2,000

Number of frames required5

Organic dyes in buffer 100,000–150,000 400,000–500,000 —

Fluorescent beads in buffer 50,000–100,000 50,000–100,000 50,000–100,000

Fluorescent proteins 50,000–100,000 50,000–500,000 50,000–500,000Numbers are given for an exemplary setup with a 60×/NA 1.0 detection objective and may vary for other magnifications or NAs.

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Deposit 200 µl of PLL on the cover glass and incubate it at 37 °C overnight. Rinse the coverslip with deionized water and air-dry it. Resuspend the cells in serum-free medium. Place the cells on the coated cover glass; attachment is generally complete within 30 min. crItIcal Coated coverslips should be freshly prepared before use.Mounting Drosophila embryos for SPIM Note that a more detailed version of this protocol can be found, for example, on the webpage http://openspim.org/Drosophila_embryo_sample_preparation. Select Drosophila embryos of

the desired age and dechorionate them. Put the embryos in 1% (wt/vol) agar solution (temperature should not be more than 37 °C) and suck them into 0.6-mm-i.d. capillaries. Keep the capillary at room temperature for 10 min and let the agar solidify (make sure that the agar cylinder does not dry out). Mount the capillary on the capillary holder into the SPIM sample chamber (filled with water at room temperature). Next, push the agar cylinder out of the capillary. See Figure 4e for an illustration. crItIcal Samples should be prepared directly before measurement (timing: 30 min).

Box 1 | Choices for imaging FCS/FCCS software At the moment there exist two dedicated, freely available open-source software packages for Imaging FCS:

• the self-contained software package, QuickFit 3.0• ImFCS plug-in for the widely used ImageJ/Fiji open-source software.

Both programs have similar capabilities and can read multi-page TIFF images, perform all necessary corrections, and calculate correlations, calibrations and fits. They both provide the fit results as parameter maps for further analysis, as shown in this work. A comparison of the currently available features of the two programs is given in the table below. Both programs are under active development and new versions (with new features) are published regularly on these websites:

• QuickFit 3.0: http://www.dkfz.de/Macromol/quickfit/ and https://github.com/jkriege2/QuickFit3• ImageJ plug-in: http://staff.science.nus.edu.sg/~chmwt/resources/imfcs_image_j_plugin.html

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proceDurebasic microscope alignment ● tIMInG 10–30 min1| If you are using TIRF, align the microscope as described in option A. If using SPIM, perform alignment according to option B. Other light-sheet alignment procedures can be used depending on the light-sheet system used63.(a) tIrF alignment (i) Turn on the microscope and control software: turn on the laser unit, temperature control unit and camera

control software. (ii) Let the camera cool and place the sample on the microscope sample stage. (iii) Perform an alignment of the TIRF mode, as appropriate for your microscope. In TIRF mode, the excitation beam

is totally reflected by the interface between the coverslip and the sample. Usually, the microscope’s software will provide an option to go to this mode of operation.

(iv) If you are performing 2c-FCCS, continue from Step 2. Otherwise, proceed directly to Step 8 for PSF determination and calibration.

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(b) spIM alignment (i) Perform the standard switch-on procedure for the

light-sheet microscope. For a dual-color illumination microscope (required for imaging FCCS measurements), ensure that the light sheets overlap perfectly, as described below in Step 1B(ii–iv). crItIcal step If the light sheets do not overlay properly, the cross-correlation amplitude will be reduced significantly later.

(ii) Mount a small mirror at an angle of 45° to the light sheet and use it to directly observe the light sheet with the camera (Fig. 5). To ensure a proper align-ment of the mirror, use an LED or a lamp to illuminate it from the side and find a little bit of dirt, on which you can focus, on the mirror’s surface. Make sure that the focused line is centered in the field of view. crItIcal step Take care not to scratch the front lens of the observation objective with the mirror.

(iii) Move the light sheet (e.g., using a gimbal mounted mirror; GMM in supplementary Fig. 4) to the sharp line on the mirror (Fig. 5a–d).

(iv) Acquire an image stack while moving the mirror in the direction of propagation of the light sheet to ensure a good overlap in that direction. You can use the QuickFit 3.0 plug-in ‘Light Sheet Analysis’ to analyze such stacks. It fits a Gaussian function to each column/row, cutting through the light sheet (Fig. 5e,f), and then it creates plots of width versus stack position and beam displacement versus stack position. Typically, the displacement between the two laser beams should be less than 100 nm.

(v) Optimize the overlap of the detection volume and the light sheet (Step 1B(v–ix)). This overlap has a profound effect on the diffusion coefficient D and on the particle number N for FCS/FCCS measurements (where illumination and detection objectives can be moved). Here we describe the recommended approach: alignment by moving both objectives. However, alignment can also be performed by visual inspection (box 2) or by using the alignment protocol published by Krzic et al.64, which should be applicable to most SPIM instruments. Begin by mounting the sample bag (filled with Atto-488 organic dye), and set up the camera for acquisition of the correlation functions of this type of sample (refer to table 2 for proper camera settings; e.g., for an Andor iXon X3 860 EMCCD camera, select a region

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Figure 5 | Visualization of a light sheet, using a 45° mirror. (a) Principle of focusing of the small mirror using wide-field illumination. (b) Camera image of a well-focused mirror. Some dirt on the mirror is focused in the center of the image (inset image shows a photograph of the mirror). (c) Direct imaging of the light sheet with the aligned mirror. (d) Image of the light sheet and in e its profile (blue line at the central region of the field of view and a Gaussian fit to the profile red dashed line). (f) Spatial overlap of two laser lines (488 and 561 nm) and their intensity profiles (image widths: 51.2 µm). Norm., normalized. Scale bars, 20 µm.

Box 2 | Alternative alignment of the light sheet and field of view overlap in a SPIM by visual inspection This approach can be used instead of PROCEDURE Step 1B(v–ix). It is less exact, but quicker, and with enough practice it can achieve comparable results.1. Mount a sample bag with dilute beads solution or a gel with embedded beads, make sure to image at the border and near the front of the sample bag or gel (Fig. 4).2. Move the light sheet along the optical axis of the detection objective until you get an image that is as sharp and bright as possible (Fig. 6). This can often be done with a gimbal mounted mirror in the SPIM optics (GMM in supplementary Fig. 4), which changes the angle under which light is incident on the projection objective.Note that we have to assume that the light sheet is already positioned properly along its axis of propagation (Step 1B), so we can only optimize the overlap of the light sheet with the field of view.

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of 4 × 128 pixels, set the EM-gain to 300 and the frame repetition time to 210–270 µs). The laser power should be in the range of ~100 W/cm2 for most cameras.

(vi) Acquire time image series with ~80,000–100,000 frames (or as appropriate for your camera), fit the result and obtain D and N values (Steps 16–35).

(vii) Repeat Step 1B(vi), for several positions of the illumination objective (move it in 5-µm steps, so that the thinnest part of the light sheet moves through the complete field of view; see Figure 6 for an illustration; fit results are shown as blue circles). When the illumination objective stack is complete, move the illumination objective back to its initial position and repeat Step 1B(vi), again for several positions of the detection objective (move it in 1-µm steps, so that the observation plane moves through the plane of the light sheet; fit results are shown as green circles in Fig. 6a).

(viii) Plot the obtained D and N values (from Step 1B(vi–vii)) with respect to the relative position of either objective (Fig. 6a). The optimal alignment will be in the region with the lowest particle number (shown by empty circles in Fig. 6a) and the highest diffusion coefficient (shown by filled circles in Fig. 6a)—i.e., the smallest (and the best) detection volume.

(ix) If you are performing 2c-FCCS, continue from Step 2 for alignment of the image-splitting system. Otherwise, proceed directly to Step 8 for PSF determination and calibration.

alignment of the dual-channel image-splitting system and determination of cross-talk coefficient (for 2c-Fccs only) ● tIMInG 10–30 min crItIcal Image-splitter alignment (Steps 2 and 3) has to be performed and checked very carefully to ensure a good overlap of the observation volumes from the two-color channels and to achieve a high cross-correlation amplitude. In addition, see the extended discussion in the TIMING section.2| Alignment of the dual-channel image splitting system for two-color FCCS (Steps 2 and 3). Switch the image splitter system (see supplementary Fig. 4, in which it is labeled ‘DualView’) to the color-splitting mode and mount an electron microscopy grid (or a comparable small grid sample) in the microscope. Use transmission illumination to image this sample. Focus the grid by moving and rotating the mounted grid until a sharp image of the grid is obtained in the center of the field of view, where later the imaging FCS/FCCS measurements will be acquired (Fig. 6a). Ideally, use a mode of the imaging software that shows the two-color channels as an overlay or difference image (green image − red image, see Fig. 7). For example, the ‘SplitView’ plug-in (available from https://micro-manager.org/wiki/SplitView) of µManager can be used.

3| Now move one (or both) half-image of the image-splitter system, so that it overlays as well as possible in the center of the image, again where the measurement will be done (Fig. 7). If the two half-images are shown as the green and red color channels of an RGB image, or as a difference image (e.g., using the microscope control plug-ins of QuickFit 3.0), there should not be any colored borders at the edges of the grid (compare Fig. 7b, left). To check the quality of the overlap, either calculate the colocalization between the two half-images (using either an ImageJ plugin65 or the ‘Colocalization Analysis’ plugin in QuickFit 3.0, see Fig. 7d) or calculate the image cross-correlation coefficient

ICL R

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Figure 6 | The volume overlap optimization of the observation plane and the light sheet in a SPIM. (a) Diffusion coefficient D and particle number N of Atto-488, measured at different displacements of the two objectives from the ideal position, determined with our alignment procedure. (b) The images show a sample of TetraSpec fluorescent beads, diluted in water (inside a sample bag) at different relative positions of the light sheet and the observation plane along the optical axis of the observation objective (schematic below the images: image width, 51.2 µm; scale bars, 10 µm; the color scale was adapted for each sub-image to have maximum contrast).

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4| Determination of the cross-talk coefficient for 2c-FCCS (Steps 4–7). Mount a sample that contains only the dye that is observed in the first color channel (e.g., cells expressing eGFP only or a solution of the green chemical dye, used for labeling). crItIcal step Steps 4–7 only need to be performed for 2c-FCCS. They do not have to be performed daily, as the cross-talk coefficient only depends on the dyes and the filters used. Therefore, it is very stable over long periods of time (months or years, see supplementary Fig. 5). However, these steps should be performed separately for every dye and filter combination that you use.

5| Switch on the laser and acquire a single long-exposure frame with good contrast and low noise (e.g., for an Andor iXon X3 860 EMCCD camera use: exposure time = 100 ms, EM-gain = 0–50, laser intensity = 50–100 W/cm2). Next, estimate the fluorescence intensities Ig and Ir in the green and red channel, by averaging over a large homogeneous region in the image, using, e.g., ImageJ.

6| Next, estimate the background intensities Bg and Br, by acquiring another image, as in Step 5, but with the laser turned off. The background should be measured in the same regions as in the bright image in Step 5.

7| Calculate the cross-talk coefficient as follows:

KI BI Bg

grr r

g= −

−

psF determination and calibration ● tIMInG 30–60 min crItIcal The results (PSF parameters) of this step will be used to evaluate all further measurements, and they will ensure comparability of the results between different days and setups. Therefore, it is crucial to ensure that calibration measurements are of high quality and that they do not contain any artifacts, such as aggregates. In addition, these parameters can also hint at the state of the microscope and optics (e.g., a change of the PSF can hint at problems with the microscope objective). Therefore, keeping track of the alignment results can help maintain the microscope in good condition. For further discussion, see the TIMING section.8| To measure the calibration sample and to determine the PSF parameters for TIRF, follow option A. For SPIM, follow option B.(a) tIrF calibration and psF determination (i) Prepare a dilute solution (~500 pM concentration) of 100-nm fluorescent beads, or a labeled lipid bilayer sample, as

explained in supplementary Method 2. (ii) Prepare the microscope for TIRF imaging (temperature control unit, laser, filters and correct objectives for TIRF imaging). (iii) Mount 40–100 µl of the dilute fluorescent bead solution in a chambered cover slide (e.g., a MatTek chamber) on the

sample stage. (iv) Turn on the microscope and camera control software and let the camera sensor cool. The actual temperature is camera-

dependent, so please refer to the manual of your camera. For an Andor iXon 860, we typically cool the sensor to −80 °C to ensure a low background noise level.

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Figure 7 | Illustration of the dual-channel image splitter alignment process used to optimize the overlap between the two image halves for imaging FCCS measurements. (a) The typical image obtained from trans-illuminating a TEM grid. (b) The alignment process by images, where the two color channels are overlaid (top row, as green and red channel of an RGB image) or subtracted from each other (bottom row). The parameter IC at the top of the subfigure denotes the image cross-correlation coefficient between the two image halves. (c) A sketch of the EM-grid and a possible mount for such an EM-grid to be used in a SPIM. (d) The start and end of the alignment process as scatter plots of the green and red intensity of each pixel. Such plots typically result from a colocalization analysis, as described in the protocol. Scale bars, 10 µm. ADU, analog-to-digital converter units of the camera.

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(v) Focus the sample in transmitted mode and turn on the camera (set camera gain and laser power). (vi) First visualize floating beads in wide-field mode and then turn to TIRF mode (set the angle for a given laser wavelength). (vii) Move the z-stage to see adherent beads on the cover glass, and move the stage up so that you do not see any

adherent beads. (viii) Select the region of interest on the camera (e.g., a central region on the camera of 20 × 20 pixels), set the frame rate

(e.g., 500–1,000 f.p.s., depends on the camera and the ROI; table 2) and finally define the total number of frames (e.g., ~40,000–60,000 frames for an EMCCD camera). See Step 18 and table 2 for a detailed discussion of how to choose the correct camera settings.

(ix) Acquire the data and save the raw data as a multipage TIFF file (16 bit). Acquire a background image series, by repeating Step 8B(ix) using the same settings as in Step 8B(viii), but with the laser turned off and acquiring ~500–2,000 frames only.

(b) spIM calibration and psF determination (i) Calibration measurement to determine lateral PSF size (Step 8B(i–vi)). Turn on the microscope and camera control

software. Let the camera sensor cool to its operating temperature. The actual temperature is camera-dependent, so please refer to the manual of your camera. For an Andor iXon 860, we typically cool the sensor to −80 °C to ensure a low background noise level.

(ii) Mount the sample bag with a dilute solution of fluorescent beads, making sure to image at the border and near the front of the sample bag (Fig. 4).

(iii) Set the laser power so that the intensity is I ≈ 50–100 W/cm2 at the thinnest part of the light sheet (the given value is appropriate for most cameras and microscopes).

(iv) Acquire an image series for imaging FCS of the sample (e.g., for an Andor iXon X3 860 EMCCD: 128 × 20 pixels, ~100,000 frames, frame time ~500 µs, EM-gain: 100 for beads). See Step 18 and table 2 for a detailed discussion of how to choose the correct camera settings.

(v) Switch off the laser and acquire a background image series (~500–2,000 frames) with the same camera settings as Step 8B(iv), but with the laser turned off.

(vi) Repeat the acquisition (Step 8B(iv,v)) two or three times to ensure that a measurement without larger aggregates is obtained (supplementary Fig. 6a,b for an illustration of such artifacts).

(vii) Bead stack to determine longitudinal PSF size (Step 8B(vii–x)). Mount the gel with fluorescent TetraSpec beads (see Reagent Setup) and move it so that imaging takes place at the surface with a minimal light path of the light sheet inside the sample.

(viii) Perform a z-stack with this sample (laser intensity: 50–100 W/cm2, camera settings for iXon X3 860 EMCCD: exposure time: 10 ms, EM-gain: 10–50). You should acquire ~1,000 frames at a step size of ~200 nm. Save the result as a multi-frame TIFF file.

(ix) Use the QuickFit 3.0 ‘PSF Analysis’ plug-in or any other appropriate tool to determine the parameters of the PSFs from the beadscan (available, e.g., from http://www.dkfz.de/Macromol/quickfit/beadscan.html, https://github.com/jkriege2/B040_BeadScanEvaluation, http://www.knoplab.de/psfj/ or detailed, e.g., in Cole et al.66). The tool should automatically locate the beads in the 3D image stack and fit a 3D Gaussian function to each bead. Finally, the statistics (median, average, s.d.) of the PSF parameters for each bead should be calculated. From this evaluation, you will need the median (or average) of the longitudinal size of the beads. Depending on the parameterization of the 3D Gaussian model, also simply the longest width might be a good choice. (In the QuickFit 3.0, this parameter is called ‘PSF 3D: width 3’ or ‘wlarge’.)

(x) For a setup with a dual-channel image splitting system, check whether the displacement of the beads in the two-color channels is below 200 nm in each direction, which indicates that the alignment of the dual-channel image splitting system in Steps 2 and 3 was good. If the displacement is larger, return to Step 2. ? troublesHootInG

9| Check the measurements from Step 8 for aggregates. To do so, load the stack into ImageJ and fast-forward through the time series. You will see aggregates moving as bright spots in the video. Discard all measurements that had large aggregates moving through the field of view (see supplementary Fig. 6a for an example). Optionally, sonicate the sample again and repeat the measurement.

10| Evaluate the calibration measurement to yield the PSF parameters (Steps 10–15). Correlate the measurement from Steps 8 and 9 with a series of increasing pixel binning settings. This can be done with any of the proposed imFCS software packages listed in Materials and in box 1 (bleach correction is not required for fluorescent microspheres). The pixel binning should start at no binning and end at a value that is significantly larger than the expected PSF diameter (e.g., 400 × 400 nm2 to 2,000 × 2,000 nm2 for an NA 1.0 objective and a 24 × 24 µm2 camera, which results in 400 × 400 nm2 pixels in the

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image plane). For a dual-channel image splitting system setup (required for 2c-FCCS only), perform this evaluation initially for the first color channel (e.g., green, when splitting into a green and a red channel) only. crItIcal step QuickFit and the imFCS ImageJ plug-in provide wizards that simplify Steps 10–15. Please refer to the manuals and/or online help for these programs for detailed instructions on how to use them.

11| Choose an appropriate fitting model for the microscope and fit each of the correlation results. Ensure that the binned pixel size abinned is preset properly. Select only the diffusion coefficient D and the particle number N as free-fitting parameters. Perform several fits, in which different sizes of the lateral PSF size wxy are assumed (e.g., wxy = 300, 500, 700 nm if you expect wxy= 500 nm). For SPIM, set the longitudinal focus size wz to the value obtained in Step 8B(ix).

12| From each of the fits in the Step 11, obtain the average and s.d. diffusion coefficient D(abinned, wxy). Obtain a reliable estimate of the diffusion coefficient Dfinal at the largest pixel size abinned (Fig. 8a).

13| Perform a final fit to the correlation result without pixel binning. This time, fix the diffusion coefficient to Dfinal and use N and wxy as free-fit parameters. The average and s.d. of wxy from this fit is the final estimate for the PSF size, and it will be used for all further fits of the measurement day (Fig. 8b).

14| For a dual-channel image splitting system setup (required for 2c-FCCS only), repeat Steps 10–13 for the second color channel separately. If TetraSpec beads were used as a sample, the diffusion coefficients Dfinal obtained for the two-color channels should be the same (within their error), because the same beads are observed in both channels.

15| For a dual-channel image splitting system setup (for 2c-FCCS only), check the instrument alignment, using a sample with an expected high cross-correlation amplitude (e.g., multicolored fluorescent beads give usually ≥100% relative cross-correlation amplitude, and double-labeled DNAs yield ~50–70%). See supplementary Figure 7 for example calibration measurements for different samples (TetraSpec beads, double-labeled DNA and eGFP-mRFP expressed as monomers or dimers in living cells) from a SPIM-FCCS setup.? troublesHootInG

Data acquisition ● tIMInG 1–5 min per sample16| Sample mounting. To mount samples for TIRF, follow option A. To mount sample bags for SPIM, follow option B. To mount cells on coverslips for SPIM, follow option C. To mount organisms or embryos in gel cylinders (e.g., Drosophila embryo, see Reagent Setup), follow option D.(a) Mounting samples for tIrF (i) Turn on the TIRF microscope, laser unit, temperature control unit and camera control software. Let the camera cool

and place the sample on the microscope sample stage. (ii) Focus the cell in transmitted mode, and select the filter and laser settings according to fluorophore.(b) Mounting sample bags for spIM (i) Mount a sample bag in the SPIM: either glue it to a glass capillary, which is mounted in the sample chamber,

or hold it with self-closing tweezers (Fig. 4c,g,j). (ii) Move the sample bag, so that the camera field of view is as close as possible to the front and the side, where the

laser enters (Fig. 4j). (iii) Set the laser intensity to 50–100 W/cm2.

Binned super-pixel size abinned (nm)

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Figure 8 | Results of an imaging FCS calibration with increasing pixel size. (a) Plot of the diffusion coefficient D obtained for different virtual pixel sizes abinned (the width of the un-binned camera pixels was acam = 400 nm) and for several test values for the lateral PSF width wxy. (b) Plot of the fit results wxy for different pixel size abinned, where Dref = 3.9 µm2/s was fixed. Data points in both graphs show the average and s.d. over the whole imaging FCS measurement. Sample: TetraSpec multi-fluorescent microspheres (diameter = 100 nm), camera: Andor iXon X3, EMCCD, acam = 400 nm, wz = (1250 ± 100) nm.

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(c) Mounting cells on coverslips for spIM (i) Mount the coverslips using self-closing tweezers (Fig. 4b,f,i). (ii) Position the coverslip at an angle shallower than 45° to the light sheet. (iii) Set the laser intensity to 50–100 W/cm2.(D) Mounting organisms or embryos (e.g., Drosophila embryo, see reagent setup) embedded in a gel cylinder for spIM (i) Mount the capillary with the embedded organisms or embryo in the microscope and extrude the organisms from the

capillary (Fig. 4a,d,e,h). (ii) Move the measurement region inside the organisms or embryo into the field of view, and focus as required. Note that

measurements deep inside the tissue might contain artifacts because of absorption and scattering in the tissue. (iii) Set the laser intensity to 50–100 W/cm2.

17| Acquisition (Steps 17–19). Optionally, acquire a transmission illumination and fluorescence image to document the sample. Especially for measurements in cells and organisms, this can help evaluate and document the health of the sample, and it allows the determination of the position of the field of view within the sample.

18| Acquire the image stack (see table 2 for acquisition settings for different camera sensors). The camera parameters should be set as follows: Choose the size of the ROI, so that the frame time is as fast as possible, while still acquiring a reasonable section of the cell. For an Andor iXon X3 860 and live cells, we often use a range of 128 × 20 pixels. Choose a frame rate kframe, which is as high as possible, while also keeping the exposure time as high as possible. In Sankaran et al.5, it was proposed to set the frame rate at least to kframe ≥ 10/tD, where τD is the diffusion time of the fastest process you want to observe. For example, for a 128 × 20 ROI, an Andor iXon X3 860 can achieve a frame rate of 1,886 f.p.s. Set the number of frames, so that enough data are acquired to get unbiased measurements. As discussed in Sankaran et al.5, at least 10,000 frames should be acquired or at least 100 times longer than the diffusion time of the slowest process to be observed. We often use 50,000–100,000 frames for the observation of protein diffusion in live cells, the given ROI and frame rate on an Andor iXon X3 860. For EMCCD cameras, set the EM-gain, so that the signal is significantly above the background (e.g., background: 100, signal: >150, see supplementary Method 1 for a detailed protocol on how to determine a proper EM-gain setting for a given sample). For live cells, a setting of EM-gain = 100–300 is often used on an Andor iXon X3 860. See supplementary Figure 8 for an example of how the acquired data typically look. Finally, check the acquired image stack for obvious artifacts, such as sample motion.? troublesHootInG

19| Switch off the lasers and acquire a background image stack of ~500–2,000 frames, using the same camera settings as for the image stack in Step 18.

Data processing ● tIMInG 1–20 min per measurement (1–10 min: correlation + 1–10 min: data fitting)20| Setup of data processing software for the correlation of the measured image series (Steps 20–26). Use one of the different evaluation software options (see box 1 for different options of data processing software) to correlate the acquired data. Be sure to set the camera properties (frame time, pixel size) properly and supply the acquired background image stack, so that the camera offset and any stray light contribution is corrected for.

21| Choose a bleach correction method. For liquid samples with organic dyes, a simple exponential model is often a good choice. For cell samples, more complex models, such as an exponential model with a polynomial as argument (‘exp(poly4)’ in QuickFit, or a double-exponential decay is advised (see supplementary Discussion, especially supplementary Fig. 9 and refs. 3,54,55 for details on the bleach correction models and methods).

22| If it is available in your imaging FCS software, choose an option to estimate errors for the correlation curves that can be used to weight the fit and thus increase the accuracy of its results. A simple option is to cut the complete measure-ment into 3–10 segments. Each segment should not be shorter than 10–100× the maximal anticipated correlation time5. (We often use 3–5 segments on a measurement of 60 s, which allows resolving time scales up to ~1 s). A more accurate option is calculating the errors from the ‘blocking curve’ method described elsewhere67. This method can also estimate the full highly correlated variance-covariance matrix of the correlation data.

23| Set up the correlation algorithm (we typically use a variant of the multiple-τ algorithm34, but ACFs and CCFs can also be calculated, based on the Wiener-Khinchin theorem and a Fourier transform11), so that the maximum lag time is comparable to the segment length. Ensure that the correlator calculates the fluctuation correlation, as defined in equation (1) (see INTRODUCTION), which decays to 0. Some correlation algorithms work on the full signal, and the calculated correlation

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functions then decay to 1, which might cause problems with some evaluation methods, and which has to be taken into account in all fit functions with an additional offset parameter, sometimes called G. For the sake of this protocol, we assume that equation (1) is used (e.g., in QuickFit, use ‘Direct Correlation with Averaging’, averaging factor m = 2, lags per correla-tor P = 8 or 16 and set the number of linear correlators S so that τmax is larger than the segment duration. In the ImageJ plug-in, set P = 16 and choose Q, as described above for S).

24| Choose the correlation functions to be computed:

analysis Function

FCS analysis Calculate the autocorrelation function for every pixel

2c-FCCS Calculate the green and red autocorrelation and the cross-correlation function between those two channels for every pixel

Two-pixel FCCS Calculate the cross-correlation between the desired pixels (e.g., to the four direct neighbors of every pixel) and optionally the autocorrelation function for every pixel

25| Choose the appropriate pixel binning (table 2). For EMCCD cameras, 1 × 1 binning is reasonable in most cases, but 2 × 2 pixel binning may improve the results for fast diffusing or dim samples (i.e., when the correlation curves are very noisy). For sCMOS cameras, choose a pixel binning so that the signal-to-noise ratio of the correlation function is reasonable (supplementary Fig. 1 shows ACFs acquired with an sCMOS camera, where the curves in b and c can be seen as ‘reasonable’ in terms of noise, but the curve in a is too noisy for a reliable fit) and the pixel size is 1–2× the diameter of the PSF (typically 4–8× binning at a single-pixel size of 110 nm in the object plane, which corresponds to a pixel size of 6.5 µm at 60× magnification; see supplementary Fig. 1).

26| Start the correlation process.

27| Review of correlation results and preparation for data fitting (Steps 27–29). After the correlation has been completed, review the results. The resulting curves should have good quality and low noise. Compare your curves with the different example curves given in Figures 9–11, which are all of ‘good quality’. Generally, the curves decay from a significant ampli-tude at low lag times τ to 0 for large lag times. Sometimes, a second decay is visible at long lag times (supplementary Fig. 6c). This is typically caused by a variation of the fluorescence signal on long time scales (100 ms–10 s). Different rea-sons (and solutions) for this problem are listed in the TROUBLESHOOTING table. Also check the curves for other artifacts that cause deformations of the curves, as shown in supplementary Figures 6a,b,d and 10. These are caused by different effects,

c

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Figure 9 | Examples of typical SPIM-FCS measurements. (a) Normalized (norm.) single-pixel SPIM-FCS autocorrelation functions acquired with an Andor iXon X3 EMCCD camera for different samples and 2 × 2 binning. Data is the average and s.d. over 5 consecutive segments of ~10 s length each. The inset shows histograms of the diffusion coefficients from the measurements. Samples were 100-nm fluorescent microspheres (red), a 170-bp double-stranded DNA (green), an eGFP dimer (eGFP-2x, blue), and the chemical dye Alexa Fluor 488 (magenta). (b) Results from a SPIM-FCS measurement of eGFP-labeled histones H2A in HeLa cells, with an intensity image, a map of the concentration and of the fraction of the slow diffusing component (from a two-component normal diffusion fit), as well as two single-pixel CFs. (c) Histone (His2Av-mRFP1) protein diffusion in live Drosophila embryo. The overview image (left most) was acquired on a Zeiss light sheet Z1. The middle and right images show the fluorescence intensity and a map of the diffusion coefficient form a one-component fit (during cycle 13 or 14), acquired on a home-built SPIM setup. The bottom row shows an example single-pixel ACF with a fit (dashed) and a histogram of the data in the diffusion coefficient map. Scale bar lengths differ between panels and are indicated on the figure.

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such as a disturbance of the light sheet during the acquisition (e.g., by air bubbles or dirt in the sample chamber), or oscillations of the setup and/or the camera. The curves for most samples are noisy (as shown in the figures), but the amplitude of the noise should generally be smaller than the amplitude of the correlation curves (see supplementary Fig. 1 for curves with large noise in a, and a tolerable noise level in b and c). If such artifacts do not affect all pixels, simply exclude the affected pixels before performing the next evaluation Steps 28–37. crItIcal step The quality of the correlation curves heavily influences the results of any further evaluation. Uncorrected or unfiltered artifacts in particular may significantly bias the results.? troublesHootInG

28| (Optional) If the software supports it, mask all pixels that should be ignored for the evaluation (e.g., pixels outside of cells, or affected by artifacts as suggested in the last Step 27). This can, e.g., be done by hand or by a threshold on the pixel intensity.

29| (Optional) Estimate the background intensity as the average intensity over a set of background pixels or pixels outside a sample such as a cell. This improves the result of concentration measurements, which are very sensitive to any uncorrected background light contribution, as illustrated in supplementary Figure 11.? troublesHootInG

30| Data fitting (Steps 30–35). Choose a fitting method and model. Models that work for many typical samples are listed in supplementary table 1 and table 3, but any other model that is suitable for the microscope and sample can be chosen. For most liquid samples, a one-component normal diffusion model is sufficient, but two or more components might be appropriate for mixture samples and in vivo. Options for 2c-FCCS are detailed in box 3. crItIcal step For all these models, fitting gets more difficult for more complicated models (especially for global 2c-FCCS models) and the fit algorithms may not find a solution at all, or the solution may no longer be unique, if (too) many model parameters are used. Therefore, you should select the simplest model that describes your data well—i.e., follow the principle of parsimony. This can be achieved in a statistically unbiased way, by using model selection methods, such as Akaike’s or Bayes information criterion10,68,69 or the Bayesian FCS method67,70,71, or by applying, e.g., the maximum entropy method72,73. However, these more complex methods are beyond the scope of this protocol, and they are discussed in the given references. See box 1 for a detailed list of software packages that support (at least some of) the highlighted evaluation methods. In any case, detailed tutorials on how to use the software to perform these evaluations are given in the respective documentation and online-help systems.

Figure 11 | Example results for an in vivo, two-color SPIM-FCCS measurement of the AT-1 transcription factor system (c-Fos-GFP + c-Jun-mRFP). (a) The auto- and cross-correlation curves are single-pixel data for the Fos/Jun wild type expressed in HeLa cells. (b,c) The histograms give the distribution of the relative dimer concentration CGR/Call (b) and the fraction of the slowly diffusing component ρslow, green in the green channel (c). Measurements are shown on a double-deletion mutant without the DNA- and dimer-binding domains for comparison. (d) The distribution of the histogrammed parameters in an example cell nucleus for the wild-type protein. The dotted curves (in all correlation function plots) are global parameter fits with appropriate models. Data was acquired on an Andor EMCCD camera with EM-gain 300 and 128 × 20 pixels. The dark blue dashed line gives the level of cross-correlation, which can be explained by cross talk. Scale bars, 10 µm.

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table 3 | Scheme for fit model selection.

Microscopy sample Mode

Model in supplementary table 1G: usable with global fit Ncomp Model in QuickFit 3.0

Model in ImagingFcs plugin for

ImageJ/Fiji

TIRF Calibration FCS 1 1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

FCS (wz ≥ 106, rx = ry = 0)

Microspheres and other in vitro samples

FCS 1 1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

FCS (wz ≥ 106, rx = ry = 0)

2c-FCCS 1 1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

DC-FCCS (wz ≥ 106)

3 + 5G 1 TIR-FCCS: normal diffusion, species A+B+AB, c/D per species

DC-FCCS (wz ≥ 106)

2f-FCCS 7G 1 TIR-FCCS: diffusion+flow, ACF + 4 neighbors

FCS (wz ≥ 106)

Supported bilayers FCS 1 ≥1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

FCS (wz ≥ 106, rx = ry = 0)

2c-FCCS 1 ≥1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

DC-FCCS (wz ≥ 106)

3/4+5G ≥1 TIR-FCCS: normal diffusion, species A+B+AB, c/D per species OR: TIR-FCCS: 2-comp. 2D diffusion (xy), species A+B+AB, c per species, D1/D2 per channel

DC-FCCS (wz ≥ 106)

2f-FCCS 7G ≥1 TIR-FCCS: diffusion+flow, ACF + 4 neighbors

FCS (wz ≥ 106)

Membrane-bound proteins in live cells

FCS 1 ≥1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

FCS (wz ≥ 106, rx = ry = 0)

2c-FCCS 1 ≥1 TIR-FCS: 2D diffusion (rect. pixel, 1/e2 radii)

DC-FCCS (wz ≥ 106)

3/4+5G ≥1 TIR-FCCS: 2-comp. 2D diffusion (xy), species A+B+AB, c per species, D1/D2 per channel

DC-FCCS (wz ≥ 106)

2f-FCCS 7G ≥1 TIR-FCCS: diffusion+flow, ACF + 4 neighbors

FCS (wz ≥ 106)

SPIM Calibration FCS 1 1 SPIM-FCS: 3D diffusion (rect. pixel, 1/e2 radii, new Veff)

FCS + SPIM (rx = ry = 0)

Microspheres and other in vitro samples

FCS 2 1 SPIM-FCS: 3D diffusion (rect. pixel, 1/e2 radii, new Veff)

FCS + SPIM (rx = ry = 0)

2c-FCCS 2 1 SPIM-FCS: 3D diffusion (rect. pixel, 1/e2 radii, new Veff)

DC-FCCS

3+6G 1 SPIM-FCCS: normal diffusion, species A+B+AB, c/D per species

DC-FCCS

2f-FCCS 8G 1 SPIM-FCCS: diffusion+flow, ACF + 4 neighbors

FCS + SPIM

Fluorescent proteins in cells

FCS 2 ≥1 SPIM-FCS: 3D diffusion (rect. pixel, 1/e2 radii, new Veff)

FCS + SPIM (rx = ry = 0)

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31| If the software provides the option, choose an appropriate fit method, e.g., a simple or weighted least-squares fit, a global least-squares fit or a generalized least-squares fit, GLS67,70) and optionally an algorithm (typically a Levenberg- Marquardt least-squares fit74 works well for global or local fits). The choice of the method influences the statistical accuracy of your results and the speed of the evaluation. A simple (weighted) least-squares fit gives good results in many cases, but a GLS can make full use of the correlated noise in a multi-τ correlation function, but at the cost of much longer processing times. If your fit method (e.g., GLS) does not do that implicitly, you should choose a data weighting method to improve accuracy and precision of the fit results. Often a weighting by the errors of the correlation function (see Step 22) is used.

32| Perform the fit for each sample separately (Steps 32–35). First, set all known parameters in the model—(e.g., pixel size (camera pixel size/magnification), PSF parameters (Steps 8–15) and cross-talk coefficient κgr (Steps 4–7).

33| (Optional) If the software supports or requires it, set the parameter ranges to reasonable values. Typical choices that work for many samples in imaging FCS/FCCS are summarized in table 4. crItIcal step This step ensures that the model parameters do not run out of reasonable bounds during the fit. For example, if you try to fit a two-component FCS model to a sample, which requires only one component, the fit algorithm might try to use very high diffusion coefficients for the second component to get rid of it, instead of setting its fraction to 0. Using parameter bounds, you can also introduce prior knowledge about your sample into the fit.

table 3 | Scheme for fit model selection (continued).

Microscopy sample Mode

Model in supplementary table 1G: usable with global fit Ncomp Model in QuickFit 3.0

Model in ImagingFcs plugin for

ImageJ/Fiji

2c-FCCS 2 ≥1 SPIM-FCS: 3D diffusion (rect. pixel, 1/e2 radii, new Veff)

DC-FCCS

3/4+6G ≥1 SPIM-FCCS: normal diffusion, species A+B+AB, c/D per species OR: SPIM-FCCS: 2-comp. 3D diffusion, species A+B+AB, c per species, D1/D2 per channel

DC-FCCS

2f-FCCS 8G ≥1 SPIM-FCCS: diffusion+flow, ACF + 4 neighbors

FCS + SPIM

The column Ncomp encodes the number of diffusing components in the model. This value is only a recommendation for simple cases. In more complex situations, more components might be necessary. The models marked with a superscript G (G) in the model column may benefit from a global fit, in which some parameters (especially concentrations and velocities) may be linked over the autocorrelation and cross-correlation curves, as they appear in all the models. 2f-FCCS = two-focus FCCS (FCCS between spatially separated observation volumes); rect., rectangular.

Box 3 | Different evaluation options for two-color imaging FCCS data sets (Step 30)Several options exist to evaluate two-color imaging FCCS data sets. These are listed below in order of increasing complexity. In some cases, the simplest option may already give reliable results.1. You can omit the fit and simply calculate the relative CCF amplitude q in equation (5), or the cross talk–corrected variant derived in ref. 25. However, keep in mind that this measure can become unreliable if the diffusion coefficients are large and thus the plateau of the correlation functions (at low lag-times τ) is not sampled because of, for example, the slow cameras3.2. You can perform a simple FCS fit to each of the three curves (ACF1, ACF2 and CCF) separately and evaluate the amplitudes of these fit models, e.g., calculating again the relative CCF amplitude q in equation (5), but now evaluating the fit models at τ = 0. This is typically more reliable than option 1. In addition, more involved analyses on the amplitudes of the fit parameters can be done, as proposed in Liu et al.79.3. You can perform a global FCCS fit. Fit functions for such a fit typically incorporate a detailed model for the interaction that takes place in the sample (e.g., a dimerization reaction G R GR+ of two differently labeled species G and R) and can therefore extract the concentration of all species simultaneously. Refs. 3,79,80 contain a detailed discussion of several variants of such models that could be used here. These fit models can also be extended to more complex cases, in which, for example, homo-dimers can also exist.

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34| Set reasonable initial parameters by fitting the average correlation function over a larger region of pixels or by using a global optimization algorithm (e.g., SimAnneal in QuickFit, or the algorithm proposed in Rao et al.75).

35| Fit all pixels. To improve convergence, it can help to repeat the fit once or twice.? troublesHootInG

36| Post-processing the fit results (Steps 36 and 37). First exclude all pixels with outliers and nonconverged fits, and exclude regions of the samples that contain artifacts or stripes (see supplementary Figs. 6 and 12 for examples of artifacts). If the correlation functions are distorted, check for movement of the cell in the raw data (the bleach-corrected data sometimes occludes this), and possibly exclude segments that were affected or recorrelate only parts of the complete image series, and then repeat the evaluation.

37| Evaluate fit results (maps, histograms, correlations, see table 1 for typical values for diffusion coefficients), as described in box 4.? troublesHootInG

? troublesHootInGTroubleshooting advice can be found in table 5.

Box 4 | Post-processing options for the results obtained from an imaging FCS/FCCS measurement (Step 37) The protocol describes the acquisition, correlation and model fitting steps of the evaluation. The results of these steps are typically maps or images of the parameters that have to be further evaluated to yield the desired conclusions about the system. Several often-used options exist for this step:1. Prepare histograms of the fit results in each cell.2. To summarize the results of many cells, it is advisable to calculate the median of the parameter distribution in each cell and then give average and s.d. of these medians. The median has the advantage to be an outlier-robust statistical measure for the center of the distribution. Comparably robust estimators for the width of a distribution are also available (e.g., the median absolute deviation about the median, MAD). This helps, because often the fits for some pixels do not converge (→ outliers).3. To reconstruct the FCS diffusion law44,45, repeat the evaluation for different pixel binnings (pixel size abinned) and plot the obtained averaged diffusion time τD(abinned) versus the size of the effective focus area Aeff(abinned). Both software options (QuickFit 3 and the ImageJ plug-in) provide tools to easily plot these curves.4. From imFCCS measurements on binding proteins, compute a measure of the relative dimer concentration as a measure of binding, e.g., the relative CCF amplitude from equation (5), or if your fit models provide the concentrations of different species (e.g., cG, cR for monomeric species and cGR and cGR for the dimer in a dimerization reaction as proposed before) you can calculate relative concentrations, such as cGR/(cG + cR + cGR), which is the relative dimer concentration amongst all particles, or 2cGR/(cG + cR + 2cGR), which is the concentration of dimerized proteins among all proteins. In some cases, this is automatically done by the imaging FCC software.

table 4 | Reasonable choices for fit parameter ranges in typical imaging FCS/FCCS measurements.

parameter sample parameter range

Diffusion coefficient Small molecules/dyes in solution 0.001–400 µm2/s

Proteins in cells, one-component fit 0.001–100 µm2/s

Proteins in cells, two-component fit 0.001–5 µm2/s (slow component) 1–100 µm2/s (fast component)

Concentrations Any 10−10–106 nM (The lower concentration bound of 10−10 nM prevents division by zero in some models, but this is effectively zero for all practical purposes)

Fraction of a diffusing component Any 0–1

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table 5 | Troubleshooting table.

step problem possible reason solution

8B(x) Large separation between green and red PSF (more than 100–200 nm)

Poor alignment of image splitter Realign image splitter

15 Low relative cross- correlation amplitude

Poor calibration sample Check the sample, e.g., using confocal FCCS, or use a different sample, such as multicolored fluorescent beads

Poor alignment of image splitter Realign the image splitter

18 Cells move Freshly mounted sample Wait for 5–10 min. Cells often move less when they have had 5–10 min to adjust to the measurement conditions

Laser intensity too high Reduce the laser intensity, as cells often tend to move when illuminated with lasers that are too strong

Cells die Unsuitable measurement buffer or medium

Use different buffer, but keep in mind that the buffer should be clear and not contain scattering (e.g., FBS) or colored/fluorescent agents (e.g., phenol red). Tested buffers are proposed in the MATERIALS section

Unsuitable temperature or CO2 level Heat the sample chamber (e.g., to 37 °C for human cell lines) and/or use a perfusion chamber, which can maintain a proper CO2 level If this is not possible, limit measurement time on the sample to ~30 min and exchange it for a fresh sample and fresh measurement buffer after that time

Flow inside the SPIM sample bags

Sample bag not properly sealed Reseal the sample bag, or better prepare a new one

Temperature gradient over the sample bag (e.g., from the sample chamber heater, which only heats the lower part of a SPIM sample chamber)

Sometimes the flow (convection between a colder and warmer part of the bag) settles after some time. If not, measure at room temperature, or change the heater configuration, so that there is no temperature gradient inside the sample chamber (use a heater at the base and at the top of the sample chamber)

27 Oscillations in correlation curves (supplementary Fig. 6d)

Unstable laser Check with a photodiode and oscilloscope; use better stabilized laser Some lasers are more stable at higher set powers. You can then use neutral density filters to reduce the laser power

Vibrations of optical table Use antivibration optical table (on air bumpers)

Camera fan Switch off the camera fan and possibly use water cooling for the camera (supplementary Figs. 6d and 10)

Air-conditioning airflow Control the airflow or cover the microscope body

No correlation curves Check light-sheet thickness (SPIM) Light-sheet thickness should be 1–2 µm (Fig. 5)

Check overlap of light sheet and observation plane (SPIM)

You should get a sharp and bright image of the sample (Fig. 6b and Step 1B(v))

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table 5 | Troubleshooting table (continued).

step problem possible reason solution

Improper instrument alignment and sample focusing

Properly focus the sample. You should get a sharp image of the sample. For cells, the cell boundary should be very well defined

Sample too dim To exclude problems with the setup: Test the setup with a brighter sample, e.g., fluorescence beads (~500 pM). If instrument problems are excluded, increase the laser power, increase the EM-gain of the camera or use a brighter dye (if possible)

Camera gain too low (supplementary Fig. 15)

If using an EMCCD camera, increase the EM-gain. If using another camera, increasing the analog gain usually does not help, as it also amplifies the readout noise. In those cases, use pixel-binning, higher laser power or longer exposure times

Very noisy correlations Too few photons per molecule Increase the laser power (but keep bleaching below 50%) Prolong exposure time (frame repetition time) Use EMCCD camera and higher EM-gain settings for this camera (supplementary Fig. 15) Use pixel binning (supplementary Fig. 1)

Too high concentration (low amplitude of ACFs)

Cells: alter the transfection protocol (lower DNA concentration) to achieve a lower expression level; select dim cells Liquid samples: reduce the concentration (best results were obtained at SPIM 1–100 nM, and TIRF 30–50 nM)

Slow-decaying component or a global offset on the correlationurve, distorted correlation curve

Single dips/peaks in intensity trace due to air bubbles/particles in the measurement buffer (supplementary Fig. 6b)

Exchange the imaging buffer with fresh and clean buffer Remove the affected segments of the image time series from data evaluation

Nonstationary count rate traces because of suboptimal bleach correction

Use higher-order fit function for the bleach correction

Slow-decaying component because of motion of the sample, especially near intensity steps (supplementary Fig. 6c)

Exclude affected pixels (if few) or try to correlate only a nonaffected part of the time series. If both do not help, discard the whole measurement

Aggregates or speckles in the sample (especially in samples of fluorescent microspheres; see supplementary Fig. 6a)

Exclude affected pixels (if few) or try to correlate only a nonaffected part of the time series. If both do not help, discard the whole measurement

Nonstable baseline signal of an EMCCD camera (supplementary Fig. 2)

Switch on the baseline-stabilization method provided by your camera (for example, called ‘Baseline Clamp’ in Andor EMCCD cameras)

Low FCCS relative cross- correlation curve amplitude

Too few dimers in the sample Check the sample and the instrument with a highly cross-correlating sample (for example, double-labeled DNA should yield 50–70% rel. cross-correlation ampli-tude and multicolored fluorescent beads usually show ≥100% relative cross-correlation amplitude)

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table 5 | Troubleshooting table (continued).

step problem possible reason solution

Poor overlap of green and red focal volumes

Check the focus volume overlap with a PSF bead scan (Step 8B(vii–x)) and with a FCCS positive control sample (e.g., multicolored fluorescent beads). Finally, realign the image splitting optics and recalibrate the microscope

Strong photobleaching Reduce the laser intensity and balance by, for example, increased integration time, pixel-binning or EM-gain of the camera

One of the two fluorophores bleaches faster than the other

Reduce the laser intensity of the laser for the stringer bleaching fluorophore

Most of the FCCS relative cross-correlation amplitude is explained by cross talk

Poor choice of filters Choose a better filter set (supplementary Fig. 4 for tested filter sets)

Red fluorophore much dimmer than the green fluorophore

Reduce the blue laser intensity relative to the green one (but take care to keep good quality of the curves), or choose another fluorophore

29 High background intensity Scattering or fluorescence by buffer Do not add FBS to the buffer Choose imaging media diluted in 1× PBS Filter the buffer before use

Ambient light Shield ambient light

Direct scattering from sample or glass surface

Choose better filters or add notch filter in detection beam path

Blue laser emits a tiny bit of green light Add cleanup filter to the excitation laser

Laser reflection from sample cover glass (SPIM)

Change the sample cover glass angle with respect to light-sheet illumination (Fig. 4f,i)

35 Fits do not converge Poor initial parameter estimates Estimate better initial parameters, either by hand, or, e.g., by using a stochastic fitting routine (e.g., ‘SimAnneal’ in QuickFit 3.0)

Parameters (especially diffusion coefficients) have unrealistically high or low values

Refine the parameter ranges for the fit parameters and use information that you have on the system for that (highest measureable D for a given camera, lowest measureable D for a given maximum lag-time and so on)

35 Model does not fit the data well (S-shaped residuals …)

Too few diffusing components Use a multicomponent model and increase the number of components. Possibly use a model selection method (Bayes-FCS67,70,71 or Akaike’s information criterion10,68,69) to prevent overfitting

Model does not incorporate all effects in the sample (for example, flow)

Use a fit model, which incorporates the effects (for example, diffusion+flow). Possibly use a model selection method (Bayes-FCS or Akaike’s information criterion) to prevent overfitting

37 Particle number not correlated with intensity (at large intensity differ-ences in overview image)

Suboptimal background correction Use better estimate of background intensity and repeat fit (see supplementary Fig. 16 for an example of the impact of a good background correction)

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table 5 | Troubleshooting table (continued).

step problem possible reason solution

Particle number or concentration too high

EM-gain is too low (supplementary Fig. 11)

Increase EM-gain

Measurements with analog cameras often have to be calibrated with a linear factor to yield correct concentrations

Perform a calibration measurement to get the factor between the measured concentration and the true concentration. For this task, use a dilution series of a bright sample in water (for example, fluorescent beads, quantum dots of DNA, labeled with chemical fluorophores) and determine the concentration of the sample independently (for example, by absorption spectroscopy or confocal FCS)

● tIMInGStep 1, basic microscope alignment: 10–30 min (once per day or less)Steps 2–7, optional alignment of dual-channel image-splitting system for 2c-FCCS measurements: 10–30 min (once per day)Steps 8–15, calibration: 30–60 min (once per day or less)Steps 16–19, data acquisition: 1–5 min per sampleSteps 20–37, data processing: 1–20 min per measurementCorrelation (depends on the chosen bleach correction, data size, and so on): 1–10 minFit (depends on the chosen fit model, type of fit, software, computer, and so on): 0.5–10 min A note on how often to perform the calibrations: Depending on the microscope, the calibration is rather stable and does not have to be performed every day. TIRF microscopes are especially stable in our experience (supplementary Fig. 5), and the PSF properties only have to be determined or checked once every few months. If a SPIM is used for one-color FCS only, the PSF is also very stable, but the objective alignment still should be done every day (depending on the stability of the respective microscope). Typical image splitters for two-color detection are not very stable in our experience, especially when the filter cubes are exchanged or the device is switched to a nonsplitting mode. In addition, the overlap of the two-color channels is a crucial parameter in 2c-FCCS measurements, and typically it has to be done to a precision of better than 200 nm (Krieger et al.3). Therefore, these devices have to be aligned every day. As such an alignment can also affect the PSF, the PSF calibration should then be done on a daily basis.

antIcIpateD resultsCompletion of the protocol in this paper will yield fully evaluated imaging FCS/FCCS measurement for the sample of your choice. This includes the fluorescence intensity image stack and any autocorrelation and cross-correlation functions extracted from it (for every pixel). Also you will have performed FCS/FCCS model fits to the data that yield maps of the fit parameters and their statistics (e.g., average, median, variance, histograms and correlation plots). Careful alignment calibration of the microscope is very important for reliable imaging FCS/FCCS measurements; a typical result of an imaging FCS calibration is shown in Figure 8. We and others have published several papers demonstrating imaging FCS and FCCS under different conditions (see ‘Advantages and applications’ in the INTRODUCTION); specific examples are discussed in this section.

Figure 9 shows a collection of several imaging FCS measurements. Figure 9a depicts the autocorrelation curves that can be expected from an EMCCD camera for different samples: yellow-green fluorescent microspheres with a diameter of 100 nm (red) give very low-noise ACFs (the image shows the average ACF and its s.d. from five consecutive segments of ~10-s length each). The other curves are Alexa Fluor 488–labeled dsDNA (170 bp long, green), an eGFP dimer (blue) and free Alexa Fluor 488 (magenta), all in aqueous solution. These dyes are all dimmer than the microspheres, and consequently the curves are noisier. An important feature of all curves is that they decay to 0 for large lag times τ. For the slow samples, the plateau of the ACF at low lag times is visible, whereas it is outside the accessible lag time range for the fast samples (e.g., Alexa Fluor 488). This missing plateau leads to an underestimation of the diffusion coefficient and an overestimation of the particle number, as discussed in the introduction and elsewhere2,3. The inset in Figure 9a shows histograms of the diffusion coeffi-cients extracted from one measurement of each of these samples using a 1-component normal diffusion fit.

Figure 9b contains measurements of the nucleus of a HeLa cell expressing eGFP-labeled histone H2A. The data were fitted with a two-component normal diffusion model. The image of the fraction ρslow of the slow diffusing component from this fit shows a spatial pattern, in which motion seems to be slower toward the border of the nucleus (also compare the blue and

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red correlation curve from a pixel with a low fraction and a pixel with a high fraction of the slow component). This can be interpreted as regions of denser and slower moving hetero-chromatin within the nucleus38. The graph on the right hand side shows example correlation curves from this sample at different locations with significantly different ρslow. The ACFs again decay to 0 for large lag times, which shows that there were no long-time correlated motions and the two-component fits (dashed lines) described the data well.

Finally, Figure 9c depicts an imaging FCS measurement inside a living Drosophila melanogaster embryo expressing histone His2Av. This measurement demonstrates the applicability of imaging FCS not only to in vitro samples and single cells but also to cells embedded in a living organism. As can be seen from the resulting correlation curves and diffusion coefficient histo-gram, the measurement results are comparable to measurements of labeled histones in single cells (see the last paragraph).

supplementary Figures 13 and 14 show that SPIM-FCS is even applicable to measurements in a membrane (here: giant unilamellar vesicles and non-basal cell membranes), although TIRF-based FCS is usually the better choice, if the membrane can be brought near to the coverslip in the microscope (e.g., for the basal membrane of cells or supported bilayers). Figure 10 shows results from a supported bilayer, which exhibits a phase separation. This is especially visible in the ‘islands’ of slower diffusion within the diffusion coefficient map. This measurement was acquired in a TIRF setup with an EMCCD camera. More details can be found, for example, in refs. 1,71,76. In addition, supplementary Figures 15 and 16 show results from TIRF-based imaging FCS measurements with an EMCCD camera. In all cases, the sample was a DOPC bilayer. Head group–labeled rhodamine dye 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) ammonium salt) (RhoPE) was used as the fluorophore in those measurements.

Finally, Figure 11 shows typical results of two-color SPIM-FCCS measurements on the AP1 transcription factor system (proteins c-Fos-eGFP and c-Jun-mRFP). A DualView DV2 (Photometrics) image splitter was used in front of the EMCCD camera in order to simultaneously acquire green and red color channels. The ACFs show two diffusing components, whereas the significant CCF only has a single slow component. This can be interpreted as c-Fos and c-Jun dimerizing (positive cross-correlation). In addition, because of the missing fast component in the CCF, the dimers have to be associated with a slowly moving structure inside the cell. Interestingly, the diffusion coefficient of the CCF (and the slow components of the ACFs) is comparable to the diffusion coefficient of the histone in Figure 9b. Therefore, a possible explanation is that the ‘slowly moving structure’ is in fact chromatin. The evaluation of these SPIM-FCCS measurements was performed with a global least-squares fit to the two ACFs and the CCF, choosing a model in which the diffusion coefficients were specific to each channel (i.e., models 4+6 in supplementary table 1). Also see supplementary Figure 7 for additional examples of typical SPIM-FCCS control samples (multicolored beads, double-labeled DNA, as well as eGFP and mRFP monomers and dual-colored dimers expressed in living cells).

An example of a 2f-FCCS measurement on fluorescent microspheres, which show diffusion and a convective flow, is shown in supplementary Figure 17. Here the ACF and the CCFs to the four direct neighbor pixels were calculated. Finally, a global least-squares fit to these five curves was performed.

Finally, supplementary Figure 6 summarizes some typical artifacts that often occur in imaging FCS measurements. Most of these artifacts are related to imperfect bleach correction, motion of the sample, oscillations of the setup and so on. These often leave behind fluorescence intensity changes on large time scales of 100 ms–10 s in the intensity traces that manifest as distortion of the correlation curves, or very often additional components on long time scales (supplementary Fig. 6a,c). Such artifacts and their correction or exclusion (if possible at all) are discussed in detail in the troubleshooting section (table 5).

Note: Any Supplementary Information and Source Data files are available in the online version of the paper.

acknowleDGMents The project was supported by a NUS-BW (National University of Singapore/Baden-Württemberg BW2010-2) joint grant to T.W. and J.L., a doctoral and postdoc fellowship of the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences to J.W.K., a doctoral scholarship by the National University of Singapore to A.P.S., a Singapore National Research Foundation funding for T.E.S. and A.P.S. and a doctoral scholarship of the National University of Singapore and a post-doctoral fellowship by a grant from the Singapore Ministry of Education (MOE2012-T3-1-008) to N.B. The authors thank G. Müller for preparing many of the cells that were measured for this paper. We also thank M. Suresh Sawant for providing the protocol for collagen coating. We thank P. Ingham for providing access to his light-sheet microscope.

autHor contrIbutIons T.W., J.L. and C.S.G. conceived the project; J.W.K., A.P.S. and N.B. performed the experiments and worked out major parts of the protocol; C.S.G. helped with the necessary image processing algorithms; T.E.S. and A.P.S. were responsible for the Drosophila measurements;

J.W.K. and T.W. developed the software for data evaluation; all authors contributed to the writing of the paper.

coMpetInG FInancIal Interests The authors declare no competing financial interests.

Reprints and permissions information is available online at http://www.nature.com/reprints/index.html.

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Supplementary Figure 1

Effect of pixel size on the measured autocorrelation functions.

(a-c) Autocorrelation curves from a HeLa cell, expressing eGFP-4x, acquired on a pco.edge

sCMOS camera. (d-f) Intensity images of the same cell at different binning stages. The plots show

different pixel binning settings. 2×2-binning was done during acquisition and additional binning was

imposed during the correlation step. Minimum lag time and frame repetition time were τmin = 761.5

μs, exposure time was Δtexp = 500 μs, the pixel size (a) is given above the plots.

Nature Protocols: doi:10.1038/nprot.2015.100

Supplementary Figure 2

Baseline clamping in Andor EMCCD cameras.

The upper two plots show the background intensity over time with (a) and without (b) the baseline clamp function activated. Subfigures (c) and (d) show typical ACFs calculated from data with and without the baseline clamping applied. For the latter case, there is a significant decay of the ACF on long timescales. As can be seen, this function significantly improves the stability of the signal. The camera was an Andor iXon 860, operated at 1 ms frame time and an EM-gain setting of 300.

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Supplementary Figure 3

Preparation of sample bags for SPIM.

(a) Shows the actual process from a sheet of LumoxFolie, which is heat-sealed to form a sheath. Then small sample bags are formed which may be filled and held by a self-closing tweezer. (b) Shows the controller built to control the temperature of a modified soldering tweezer, as shown in (c).

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Supplementary Figure 4

Schematic of a dual-color SPIM with a multichannel imaging systems (DualView DV2).

The upper part of the image shows a top view of the instrument. The lower, shaded part shows a side-view of the illumination beam path. Optical components are labeled with abbreviations that are explained in the legend. Red lines are signal connection to the control computer. The table lists the parts we use in this SPIM.

Nature Protocols: doi:10.1038/nprot.2015.100

Supplementary Figure 5

Stability over several years of the PSF-parameters determined with an imaging FCS focal volume calibration on a TIRF microscope and SPIM microscopes.

(a, b) Independent measurements on different RhoPE labelled DOPC bilayer preparations were performed across several years. The experimental conditions were kept identical. The measurements were taken at 1000 fps and an EM-gain of 300 (scale 6-300) with an Andor iXon 860 camera. The variation of (a) diffusion coefficient and (b) point spread function, which were determined following the protocol described in the main text, are shown. The solid blue line is the average and the dotted lines are the standard deviations of all the measurements. (c) Mean and standard deviation of the largest and (d) of the smallest width determined in a 3-dimensional Gaussian fit. The violet bands and numbers in the graphs are average and standard deviation over all mean values. All PSF-widths are given as 1/e² half-widths. For the TIRF with an NA of 1.45 this is significantly smaller than for the SPIM with a detection objective NA of only 1.0.

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Supplementary Figure 6

Examples of the most often occurring artifacts in SPIM-FCS measurements.

(a) The effect of aggregates in a microspheres solution (as often used for calibration) on the autocorrelation curves (green: no aggregates, red: aggregates) and the maps of diffusion coefficient and particle number. (b) Typical distortions of autocorrelation curves by air bubbles and dirt in the buffer inside the sample chamber. If these swim through the light sheet, small dips in the count rate trace occur (see grey marked regions in the non-bleach corrected count rate curves on the right), that lead to long-term components and distortions of the correlation curves. The measurements were taken on HeLa cells expressing a fluorescent protein. (c) Distortions of the autocorrelation curves (EGFP-4x in HeLa cells) at moving intensity steps (green) and in unperturbed regions (red) inside a sample. The inset shows the bleach-corrected intensity traces for the two pixels. (d) Artifacts in a measurement of a membrane-bound protein in living cells, due to oscillations of the microscope setup (bad vibrational isolation of the optical table). All measurements were acquired on a home-built SPIM-FCS setup, using an EMCCD camera.

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Supplementary Figure 7

Example results of SPIM-FCCS calibration measurements.

(a) Typical calibration measurements with 100 nm TetraSpec beads. The first graph shows auto- (green/red) and cross-correlation curves (blue) from a single pixel. The histograms (with parameter images as insets) show the distribution of three important fit results in a single measurement (128x20 pixels). (b) Shows single-pixel auto-and cross-correlation curves of a sample of 170bp dsDNA that is labeled on opposing ends with the dyes Alexa-488 and Alexa-594. (c) Shows example measurement of an eGFP-P30-mRFP dimer and separate eGFP and mRFP monomers, transfected into HeLa cells. For each sample, typical single-pixel auto- and cross-correlation curves are given. The images show the fluorescence intensity and a map of the relative dimer concentration CAB/Call. The histogram shows the distribution of CAB/Call in the images. All data was acquired on an Andor EMCCD camera with EM-Gain 300 (except beads: 100) and 128x20 pixels (except 170bp DNA: 128x6 pixels). The dark blue dashed line gives the level of cross-correlation, which can be explained by crosstalk. Scale bar lengths differ between subfigures and are indicated in the figure.

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Supplementary Figure 8

Example raw data from a SPIM-FCS measurement.

(a,b) Single transmitted and fluorescence image of a cell to select the region-of-interest (shown in blue color), (c) Time image series of a region-of-interest (~60,000 frames of 20x64 pixels at ~2,000 frames per second, here just shown three representative images), (d) Background time image series for background correction, (e) ACF and/or CCF parameter fits and statistical analysis; in this example measurement, the pixelated image on left shows the diffusion coefficient of membrane protein and the right side is the cytosolic protein diffusion coefficient.

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Supplementary Figure 9

Bleach correction in FCS.

This figure demonstrates the effect of fluorophore reservoir depletion on the fluorescence intensity signal (a) and on the ACFs calculated from it (b) in the first row. (c,d) The second row shows the result of the bleach correction, described in the main text both on the count rate and the ACF curves. Note, how also the intensity signal variance (height of the intensity fluctuations) is recovered by the proposed transformation, which can be seen especially well for the light blue curve. As can be seen in (d), the bleach correction cannot recover the correct ACF amplitude, if too much bleaching occurs (typically >50%), but this effect usually only influence the particle number

(i.e. amplitude of G()) and with little effect on the diffusion coefficient (decay time of G()).

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Supplementary Figure 10

FCS autocorrelation curves with vibrations present in the microscope.

Typical correlation plots in presence and absence of vibration present due to either laser instability, cooling fan vibration (laser and camera), drift in the sample bag/mount or drift in sample stages.

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Supplementary Figure 11

Effect of the background correction on fit results.

(a-c) Autocorrelation curves from a HeLa cell, expressing eGFP-4x, acquired on a pco.edge sCMOS camera. (d-f) Intensity images of the same cell at different binning stages. The plots show different pixel binning settings. 2 × 2-binning was done during acquisition and additional binning was imposed during the correlation step. Minimum lag time and frame repetition time were τmin = 761.5 μs, exposure time was Δtexp = 500 μs, the pixel size a is given above the plots.

Nature Protocols: doi:10.1038/nprot.2015.100

Supplementary Figure 12

Typical stripe artifacts in SPIM-FCS measurements.

(a,b) Fluorescence intensity images with dark stripes due to dirt on the sample bag. (c) Map of the diffusion coefficient D. (d) Map of the concentration c. (e) Plot of D vs. x-coordinate. (f) Plot of c vs. x-coordinate. The color bars for (b,d) are placed on the right of (c,e). (g) Fluorescence intensity image of the cell. (h) Map of the diffusion coefficient D in the cell. (i) Map of the concentration c in the cell. A 1-component normal diffusion fit was used for all samples.

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Supplementary Figure 13

Example result of SPIM-FCS experiment on a giant unilamellar vesicle.

(a) The figure shows the cross-section fluorescence image of a giant unilamellar vesicle embedded in agar (GUVs, POPC 89%, POPG 10% and PI(4,5)P2 1% and TopFluor PI(4,5)P2), (b) the ACF and (c-d) diffusion and concentration maps.

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Supplementary Figure 14

Example results of SPIM-FCS experiments on a membrane-bound protein

The figure shows the results of a SPIM-FCS measurement (using an EMCCD camera) of eGFP fluorescent proteins, which carry a plasma membrane targeting sequence (PMT) expressed in a CHO cell. (a) Shows the autocorrelation functions for a pixel in the cytosol (red) and a pixel in the membrane (blue). (b) Shows a fluorescence intensity image, which shows that the fusion protein is enriched in the cell membrane. (c,d) Show maps of the fast diffusion coefficient and of the fraction of the slow diffusing component from a 2-component normal diffusion fit. The fraction of the slow component is significantly increased for the membrane pixels.

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Supplementary Figure 15

Fluorescence fluctuations and ACFs extracted from the same lipid bilayer sample at different EM-gain settings of the used EM-CCD camera.

This figure shows the improvement of the quality of ACF as the EM gain is raised. The first column shows the single-pixel intensity signal (red) and non-illuminated/background signal (black) of a labeled supported bilayer acquired on a TIRF microscope at different EM-gain settings. The second column shows the ACFs of the background signal (no illumination) and the third column the ACFs of the illuminated sample. The sample was a DOPC bilayer labeled with 30 nM Rho-PE. Measurements were performed on a TIRF microscope. The camera was an Andor iXon 860, operated at 1ms frame time.

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Supplementary Figure 16

Dependence of the diffusion coefficient D and particle number N in dependence of the EM gain setting of the EM-CCD camera, used for the measurements.

This figure shows how the evaluated D and N of a sample changes with EM-gain. In the inset the change of the coefficient of variation (SD/mean) of the two parameters is shown. The sample was a DOPC bilayer labeled with 30 nM Rho-PE. Measurements were performed on a TIRF microscope. The camera was an Andor iXon 860, operated at 1 ms frame time.

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Supplementary Figure 17

Example results of a 2-pixel imaging FCCS measurement with a directed flow.

The figure shows the results of a 2-pixel SPIM-FCCS measurement of a sample of fluorescent microspheres (100

nm), which show a directed flowing motion. (a) Shows the auto- G(;0,0) and cross-correlation functions

G(;Δx,Δy) to the direct neighbor pixels of a single pixel (pixel size: a). The lines are the results of a global imaging FCCS fit. (b) Shows a map of retrieved 2D flow vectors and (c) the histogram of the two flow velocity vector components. (d) Shows a long-exposure overview image (100 ms) of the sample. The white stripes are tracks of larger aggregates.

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Title:

SUPPLEMENTARY INFORMATION:

Imaging Fluorescence (Cross-) Correlation Spectroscopy in Live Cells and

Organisms

AUTHORS:

J.W. Krieger*,1, A.P. Singh*,2,3,4, N. Bag2,3,5, C.S. Garbe6, T. E. Saunders4,5,7, J. Langowski#,1, T. Wohland#,2,3,5

* Equally contributing first authors

# Equally contributing senior authors

1 German Cancer Research Center (DKFZ), Im Neuenheimer Feld 580, D-69120 Heidelberg, Germany

2 Department of Chemistry, National University of Singapore, 3 Science Drive 1, Singapore 117543

3 NUS Centre for BioImaging Sciences, National University of Singapore, 14 Science Drive 4, Singapore

117557

4 Mechanobiology Institute, National University of Singapore, Singapore

5 Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543

6 Interdisciplinary Center for Scientific Computing, University of Heidelberg, Speyerer Straße 6, D-69115

Heidelberg, Germany

7 Institute for Molecular and Cell Biology, A*Star, Proteos, Singapore

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SUPPLEMENTARY DISCUSSION: DETAILED IMAGING FCS/FCCS THEORY

This supplementary section gives a more detailed introduction to the FCS theory used to derive the fit models

shown and applied in the main text. A mathematically detailed introduction to FCS and especially FCCS theory

is also given in Refs.1,2.

FLUORESCENCE CORRELATION SPECTROSCOPY (FCS)

In a fluorescence correlation spectroscopy (FCS) measurement, a microscope illuminates a small volume (~1

µm³) inside a sample of the fluorescently labeled molecules of interest (cf. main text Figure 1a). The

fluorescence emitted within this volume is collected and quantified as an intensity time series I(t) on a fast and

sensitive detector, usually an avalanche photodiode (SPAD), a scientific CMOS camera or an electron-

multiplying charge coupled device camera (EMCCD camera). To extract the concentration and mobility

parameters of the labeled particles, the fluctuating intensity signal I(t) is analyzed by calculating its temporal

autocorrelation function (ACF)

𝐺(𝜏) =⟨𝛿𝐼(𝑡) ∙ δ𝐼(𝑡 + 𝜏)⟩

⟨𝐼(𝑡)⟩2=⟨𝐼(𝑡) ∙ 𝐼(𝑡 + 𝜏)⟩

⟨𝐼(𝑡)⟩2− 1, (1)

where ⟨∙⟩ is a temporal average over the variable t. For a dilute, homogeneous sample of small rigid particles,

these functions decay on a timescale τD given by the smallest (lateral) diameter of the illuminated volume wxy

within the sample and the diffusion coefficient D of the particles:

𝜏D =𝑤xy2

4 ∙ 𝐷. (2)

In addition, the amplitude of G() is inversely proportional to the average number of particles ⟨𝑁⟩ within the

observed volume Veff and therefore also to the average particle concentration ⟨𝐶⟩ = ⟨𝑁⟩/𝑉eff. To extract the

concentration and diffusion coefficient from the measured quantities particle number and diffusion time τD the

size of the observation volume (i.e. wxy and Veff) must be known. In single-point FCS, the observation volume is

typically calibrated with a fluorescent dye of known diffusion coefficient, and the measurements are always

relative with respect to a given reference sample.

Theoretical model functions for FCS correlation data in different microscopy modalities have been derived, such

as confocal, total internal reflection fluorescence (TIRF) or selective plane illumination microscopes (SPIM).

See main text, Figure 2 for an illustration of these microscope types. The major properties that make

microscopes usable in FCS are small observation volume, i.e. high numerical apertures (NA) of the objectives,

and a good out-of-focus light suppression, which corresponds to good z-sectioning capabilities. Both of these

conditions are met by all three microscopy schemes: they all use high-NA objectives for detection, which

guarantees a small observation volume. In addition, all three methods have good z-sectioning capabilities. The

confocal microscope, which is often used in single-point FCS, uses a pinhole to exclude out-of-focus light and

to limit the z-extent of the PSF and MDE. Typical confocal microscopes have observation volumes on the order

of Veff0.2-0.5 µm³ (wxy0.2-0.4 µm). The TIRF microscope illuminates the sample with an evanescent wave,

created above a glass coverslip. This exponentially decaying light field penetrates the sample only a few 100 nm

deep (wxy0.3-0.8 µm). Therefore, fluorescence is only excited in this small region. Finally, a SPIM uses a light

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sheet to illuminate only the observed slice in the sample. SPIMs typically used for FCS in cells or small

organisms have light sheets with a thickness of 1-2 µm (1/e² half width). The corresponding observation

volumes are Veff0.5-1.5 µm³ (wxy0.5-0.8 µm), depending on the NA of the detection objective.

THE IMAGING-FCS METHOD

In imaging FCS, the concept of FCS is extended to wide field observation with a fast imaging detector (e.g. an

EMCCD camera or an array of SPADs). Now an ACF gxy() can be calculated for the time series Ixy(t) acquired

on every pixel xy of the camera simultaneously (cf. main text Figure 1b). Then a fit to each of these ACFs

results in maps or images of the mobility parameters within the samples, thus the name of the technique.

When developing fit models for imaging FCS, the geometry of the detectors has to be taken into account. Most

sensitive cameras contain square pixels, which modulate the shape of the observation volume. A set of fit

functions for different types of motion (2-/3-dimensional diffusion, anomalous diffusion, directed flows …),

measured with square pixel detectors has been developed.3-5 These models typically assume that the point

spread function (PSF) of the microscope optics (without the detector) can be modeled by a 2-dimensional

Gaussian function

PSF(𝑥, 𝑦, 𝑧) = const ∙ exp [−2 ∙𝑥2 + 𝑦2

𝑤xy2

− 2 ∙𝑧2

𝑤z2], (3)

where wxy and wz are the lateral and longitudinal 1/e² half-widths of the volume. The observation volume,

described by the molecular detection efficiency (MDE) of the microscope including a square detector of pixel

width a in the object plane, is then given by the convolution of the pixel with the PSF:

𝑀𝐷𝐸Pixel(𝑥, 𝑦, 𝑧) = ∫ ∫ PSF(

𝑎/2

−𝑎/2

𝑎/2

−𝑎/2

𝑥 − 𝜉, 𝑦 − 𝜇, 𝑧) d𝜉 d𝜇. (4)

Main text Table 1 summarizes the most important models for imaging FCS on TIRF and SPIM microscopes.

Both these models were derived with the scheme described above and will be used for data fitting throughout

this protocol. These models are usually written in terms of the diffusion coefficient D, instead of the diffusion

time τD, because the observation volume now does not only depend on wxy. A reasonable generalization for the

definition of τD in equation (2) is given by6

𝜏D =𝐴eff4 ∙ 𝐷

with 𝐴eff ≔(∬MDE(𝑥, 𝑦, 0)𝑑𝑥 𝑑𝑦)2

∬MDE2(𝑥, 𝑦, 0) d𝑥 d𝑦. (5)

Again, this expression enables diffusion coefficient measurements if the observation volume geometry (i.e. the

MDE) is known. To measure also concentrations, equation (5) can be further generalized to yield the effective

observation volume Veff:

𝑉eff ≔(∭MDE(𝑥, 𝑦, 𝑧)𝑑𝑥 𝑑𝑦 d𝑧)2

∭𝑀𝐷𝐸2(𝑥, 𝑦, 𝑧) 𝑑𝑥 𝑑𝑦 𝑑𝑧 and from this 𝐶 =

𝑁

𝑉eff=

1

𝐺(0) ∙ 𝑉eff. (6)

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The known pixel size a of the image detectors also introduces a known length scale into the experiments that

can be used for calibration instead of a sample of known diffusion coefficient, as described for the focal volume

calibration of single-point FCS measurements3,7; hence, any arbitrary sample can be measured within an

imaging FCS setup. Then the measurement is evaluated several times, binning together more pixels in each

instance (11, 22, 33 … pixels) before calculating the ACF in equation (1). While the pixel size a increases,

the parameters of the PSF (i.e. wxy and wz) do not change and the MDE is less and less effected by the PSF

parameters. The MDE is then mostly given by the known pixel size and the diffusion coefficient Dref can be

determined accurately at large a without exact knowledge of wxy and wz. This diffusion coefficient Dref can

finally be used for a calibration of wxy. On a TIRF, where mostly 2-dimensional diffusion within the plane of

observation (xy-plane) is recorded, this scheme is sufficient to calibrate the setup for FCS measurements. In

contrast, when 3-dimensional diffusion is observed using a SPIM, the size of wz also has to be determined,

which is easily possible using a simple bead scan that can be automatically evaluated.

The idea of the described calibration can also be used to identify the type of diffusion within a membrane by

plotting so called FCS diffusion laws, i.e. τD=Aeff/D vs. Aeff.8 The resulting graphs are usually linear functions. It

has been shown that their extrapolated ordinate intercept at τD=0 classifies the type of motion in the membrane:

free diffusion; diffusion hindered by a meshwork of barriers; or diffusion hindered by micro-domains. This

technique was first described by Wawrezinieck et.al.8,9 and later used in imaging FCS on a TIRF microscope10.

THE IMAGING-FCCS METHOD

Fluorescence cross-correlation spectroscopy extends simple FCS by comparing two different fluorescence

fluctuations by means of a cross-correlation function (CCF) analysis. The different fluctuation traces typically

originate either from two spectrally11-13 or two spatially distinct observation volumes. The first case, 2-color

FCCS (2c-FCCS), allows particle concentration measurements of both fluorophores that can then be used to

observe binding reaction equilibriums of differently labeled particles (e.g. the reaction of single labeled particles

G and R to a dimer GR: G + R ⇌ GR). The second case, 2-focus FCCS (2f-FCCS), enables direction and

velocity measurements of planar directed motion within the sample; this is not possible in single-focus FCS due

to the symmetry of the focal volume.

In 2-color FCCS (see main text Figure 3 a), the fluorescence intensity from an observation volume is split e.g.

by a dichroic mirror into two color channels, e.g. one for a green fluorescent protein (Ig(t)) and one for its red

counterpart (Ir(t)). Then the CCF between these channels is defined as:

𝐺gr(𝜏) =⟨𝛿𝐼g(𝑡) ∙ 𝛿𝐼r(𝑡 + 𝜏)⟩

⟨𝐼g(𝑡)⟩ ∙ ⟨𝐼r(𝑡)⟩. (7)

Main text Table 1 again summarizes the most important models for FCCS on TIRF and SPIM microscopes that

can be derived from equation (8). It can be shown that the zero-lag amplitude of Ggr() depends on the

concentration Cgr of double-labeled molecules, as well as the concentrations Cg and Cr of the single-labeled

molecules (under the assumption of zero crosstalk between the channels, a more realistic dependence is given in

Main text Table 1):

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𝐺gr(0) ∝𝐶gr

(𝐶g + 𝐶gr) ∙ (𝐶r + 𝐶gr). (8)

This allows extracting the dimer concentration, as well as the monomer concentrations, if the single-channel

ACFs are also calculated from the measured fluorescence traces, because their amplitudes scale as

𝐺gg(0) ∝1

(𝐶g + 𝐶gr) and 𝐺rr(0) ∝

1

(𝐶r + 𝐶gr). (9)

Finally, these particle concentrations can be used to calculate relative concentrations

𝑝GR =𝐶GR

𝐶G+𝐶G+𝐶GR or 𝑝GR

′ =2 𝐶GR

𝐶G+𝐶G+2 𝐶GR, (10)

which quantify the amount of molecular interaction if a dimerization equilibrium is assumed. As explained in

the main text, often the simpler relative cross-correlation amplitude is calculated instead of performing a full fit

with a model that has to specifically assume a certain reaction scheme:

𝑞 =𝐺gr(𝜏min)

min (𝐺gg(𝜏min), 𝐺rr(𝜏min)). (11)

Here the correlation function terms 𝐺gr(𝜏min), … are either an average over the measured correlation function at

the first few lag-time (e.g. 𝜏min…5 ∙ 𝜏min ), or they can be estimated by evaluating the best fit models at 𝜏min =

0. If the first option is used, or the fit models do not contain an implicit correction for the spectral cross-talk gr,

then a corrected version of equation (11) has to be used, which was derived in Ref.14:

𝐺ggc (𝜏) = 𝐺gg(𝜏), (12)

𝐺rrc (𝜏) =

𝜅gr2 ∙ 𝐼g

2 ∙ 𝐺gg(𝜏) + 𝐼r2 ∙ 𝐺rr(𝜏) − 2 ∙ 𝜅gr

∙ 𝐼g ∙ 𝐼r

∙ 𝐺gr(𝜏)

(𝐼r − 𝜅gr

∙ 𝐼g )2 , (13)

𝐺grc (𝜏) =

𝐼r ∙ 𝐺gr(𝜏) − 𝜅gr

∙ 𝐼g ∙ 𝐺gg(𝜏)

𝐼r − 𝜅gr

∙ 𝐼g

. (14)

In these equations, the correlation functions with an upper index c are the cross-talk corrected functions,

whereas the ones without an index are the un-corrected or measured correlation functions.

In 2-focus FCCS4,15-17 (see Main text Figure 3b), the CCF is defined as in equation (7), but the two intensities

Ig(t) and Ir(t) are taken from two spatially separated focal volumes (at 𝑟1 and at 𝑟2), e.g. from two camera pixels.

In this case, the CCF will contain information on the mobility of the particles, in particular in the direction of

𝑟2 − 𝑟1. Therefore, by calculating the cross-correlation between 𝑟1 and different locations of 𝑟2 (e.g. all four

direct neighbors of a camera pixel) one may extract the non-isotropic components in the mobility, as e.g. a

directed flow velocity. In addition, the known distance |𝑟2 − 𝑟1| between two focal volumes can – as already

shown for the pixel size a – also be used as an external ruler to determine absolute diffusion coefficients.17

As shown above, 2c- and 2f-FCCS measurements result in several ACFs and CCFs, which are all taken at the

same location and register the same particles and motions. Therefore, the parameters (e.g. the diffusion

coefficients measured in the green and red channel of a double-labeled dimer in 2c-FCCS, or the flow velocity

in 2f-FCCS) are linked. These linked parameters can be accounted for by a global fit that finds the optimum set

of parameters not only for one of the measured curves, but for all of them simultaneously.

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Recently, we have introduced imaging variants of FCCS.1,2 Here, the analysis described above is not only

performed for the single observation volume of a confocal microscope, but for the volume defined by each pixel

of a high-sensitivity camera. Therefore, imaging FCCS allows flow velocity maps or maps of molecular

interaction to be measured.

CORRECTION OF DIVERSE MEASUREMENT ARTIFACTS

The last three sections described FCS/FCCS theory in an ideal case. In real measurements, these techniques

suffer from several artifacts that have to be corrected for to achieve reliable results. The simplest of these

artifacts is a constant background intensity, as it is e.g. caused by the thermal dark-counts of an avalanche

photodiode or the constant offset of a camera. In both cases, the constant background intensity ��g/r on top of the

(ideal) fluorescence signal 𝐼g/r(𝑡) leads to a reduction of the original ACF and CCF amplitudes 𝐺gr(𝜏):

𝐺gr+back(𝜏) =

⟨[��g + 𝐼g(𝑡)] ∙ [��r + 𝐼r(𝑡 + 𝜏)]⟩

⟨��g + 𝐼g(𝑡)⟩ ∙ ⟨��r + 𝐼r(𝑡)⟩− 1 =

⟨𝐼g(𝑡)⟩ ∙ ⟨𝐼r(𝑡)⟩

⟨��g + 𝐼g(𝑡)⟩ ∙ ⟨��r + 𝐼r(𝑡)⟩⏟ <1

∙ 𝐺gr (𝜏).

(15)

By estimating the average fluorescence intensities ⟨𝐼g(𝑡)⟩, ⟨𝐼r(𝑡)⟩ and the average background intensities ��g, ��r

during the measurement, the fit models can be corrected for this background contribution. Alternatively, the

measured correlation curves can be corrected before the parameter estimation process.

A second important effect is photo-bleaching, which happens in most chemical dyes and all fluorescent proteins

at the illumination intensities typically required for FCS. Photo-bleaching causes two artifacts. If particles

bleach while they move through the observation volume, this leads to a reduced apparent diffusion time D since

the particles seem to need less time to cross the observation volume. This then induces an overestimation of the

diffusion coefficient D. Unfortunately such errors cannot be corrected for in the models due to the non-

stationarity of the bleaching process. The best solution is to choose a laser-intensity that balances the photo-

bleaching against the quality of the correlation curves. The latter is limited by the photons that are detected per

particle and therefore depends on the laser intensity. The second artifact, which is induced by photo-bleaching,

is a depletion of the reservoir of fluorophores. This manifests itself by a slow decay of the fluorescence intensity

during the measurement (see Supplementary Figure 5 for examples) and a long-term decay on the timescale of

seconds that offsets the correlation curve. Such artifacts are especially prominent in SPIM- and TIRF-based

imaging FCS, where fluorophores in a whole plane of the sample are slowly bleached and therefore the

possibilities to “refill” the observation volume are reduced, as compared to confocal microscopy with its single

and small laser focus. Fluorophore depletion can be corrected before correlating the data by fitting a model

function f(t) to the decaying intensity trace in each pixel and then applying a transformation that restores the flat

intensity trace, while also boosting the variance of the fluctuations:2,18

𝐼g/rcorrected(𝑡) =

𝐼g/r (𝑡)

√𝑓(𝑡)/𝑓(0)+ 𝑓(0) ∙ (1 − √𝑓(𝑡)/𝑓(0)). (16)

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The bleach model function can be a mono- or bi-exponential decay, or an exponential with a polynomial

argument, which is reliable to fit and was successfully used for many SPIM-FCS/FCCS measurements in our

labs:

𝑓(𝑡) = 𝑓(0) ∙ exp [−𝑡+𝑓2∙𝑡

2+𝑓3∙𝑡3+⋯

𝜏B]. (17)

Here, fi are the coefficients of the polynomial, f(0) is the amplitude of the decay and B is a decay constant.

Artifacts that are often detected in confocal FCS, such as detector afterpulsing19 or a triplet blinking20 of the

fluorophore are typically not observed in camera-based imaging FCS. The analog cameras do not show

afterpulsing and are too slow to detect the triplet blinking. On the other hand, the cameras typically used in

imaging FCS induce new artifacts, such as a varying baseline (often seen in EMCCD cameras), or a fixed-

pattern noise due to different amplification and detection efficiencies in different pixels (often seen in sCMOS

cameras). The fixed pattern noise usually influences the results only minimally, but the varying baseline largely

deteriorates the measured intensity trace (see Supplementary Figure 2 for an example) and correlation curves.

Most commercial EMCCD cameras provide an option that corrects for this changing baseline and which is

sometimes called “baseline clamp” or baseline stabilization. This function should be used for all imaging FCS

measurements.

Finally, due to the large number of curves acquired in imaging FCS, other artifacts - such as sample motion,

moving aggregates or bright speckles within the sample are often detected. The Supplementary Figure 6 gives

an overview of these artifacts. Most of them can only be corrected by excluding the affected time-segments of

the measurements or by improving the stability of the whole microscopy setup.

The noise on the autocorrelation curves is mostly given by the number of photons that are detected per molecule

(brightness) and by how well the photons from the molecule can be separated from the detection noise of the

detectors (signal to noise ratio, SNR, of the detectors). Therefore, a detector with a better SNR will also yield

better correlation curves. In EMCCD cameras, the SNR can be easily influenced by the electron-multiplication

gain factor, which is usually set in arbitrary (but often linear) units in the camera control software.

Supplementary Figure 11 and Supplementary Figure 13 show this for exemplary ITIR-FCS measurements on a

labeled lipid bilayer. When the EM-gain of the camera is increased gradually, the curves get less noisy and the

fluorescence signal (red) can be better separated from the noisy background signal (black) of the detector.

Supplementary Figure 13 shows the evaluation results of a simple FCS-fit from these measurements. As can be

seen, the influence on the diffusion coefficient is only minor, but the particle number is influenced strongly.

This is due to the low amplitude of the fluorescence signal, compared to the background, which influences the

ACFs in the same way as a constant background signal (see discussion above). In addition, the inset shows that

also the coefficient of variation of both parameters decreases, which results from the lower noise on the

correlation curves and therefore more reliable fits.

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SUPLEMENTARY NOTE: CELL LINES TESTED WITH SPIM-FCS

Cells on cover slips, tested cell lines:

AT-1: rat prostate adenocarcinoma cell

BHK: baby hamster kidney cell

CHO-K1: Chinese hamster ovary cell

COS-7: transformed African green monkey kidney Fibroblast cell

HaCat B 10: humane keratinocyte cell

HEK-293: human embryonic kidney cell

HeLa: human cervical carcinoma cell

MDA-MB231: human breast carcinoma cell

SK8/18: adrenal cortex carcinoma-derived SW13 cell

MAF: mouse adult fibroblast cell

MEF: mouse embryonic fibroblast cell

RBL: rat basophilic leukaemia cell

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SUPPLEMENTARY METHODS

SUPPLEMENTARY METHOD 1: Determination of the correct EM-Gain setting

As discussed in the introduction and Supporting Information, it is crucial to choose a proper value for the EM-

Gain, if an EMCCD camera is used for the imaging FCS measurements. This optional protocol describes a

measurement that can be performed (for each sample separately) to determine such a “good” EM-gain setting:

1) Mount the sample of interest or a sample with similar properties and the same fluorophore into the

microscope and prepare the setup for a data acquisition, as described in the protocol until step 37).

2) Set the EM-gain of your EMCCD camera to a low value (e.g. EM-gain = 10 for an Andor iXon X3 860)

3) Perform a SPIM-FCS measurement (see Supplementary Figure 11 for an example).

4) Evaluate the measurement and determine the average diffusion coefficient D and the particle number N

from your measurement, as well as their standard deviations. For this: Average over a homogenous part of

the sample and exclude any pixels with artifacts and outliers before.

5) Repeat steps 2) and 3) for different EM-gain settings that span the whole available range (e.g. EM-gain =

10, 50, 100, 200, 300 for an Andor iXon X3 860).

Plot D and N, as well as their standard deviations as a function of the EM-gain (see Supplementary Figure 12 for

an example). From this graph you can select a “good” EM-gain setting for your sample, by finding the EM-gain,

where the fit results have reached a plateau and the standard deviation does not decrease any more. Instead of

the standard deviation, you can also plot the coefficient of variation, which is /µ where µ is the measured

average parameter value.

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SUPPLEMENTARY METHOD 2: Preparation of supported bilayers for TIRF calibration

measurements

The preparation of supported lipid bilayer (SLB) is discussed in detailed elsewhere21. Vesicle fusion is one of

the majorly used methods for SLB preparation. Vesicles can be prepared from a stock lipid solution by several

methods such as sonication, extrusion and freeze-thawing of the lipid suspension.

Cleaning of cover glasses and a round bottomed flask for the further steps of the protocol

Timing: 90-120 min

1) Sonicate with detergent for 30 min.

2) Rinse with de-ionized water.

3) Sonicate with 2M H2SO4 for 30 min.

4) Rinse with de-ionized water.

5) Sonicate with de-ionized water for 30 min.

6) Rinse with technical ethanol and dry before use.

Preparation of vesicles

Timing: 4-5 h

7) Prepare stock solutions of DOPC lipid and fluorescent lipid in chloroform. (Other lipids can also be

used provided their transition temperature is well below room temperature.)

8) Using a clean metal syringe, transfer appropriate amounts of the DOPC and fluorescent lipid to a clean

round bottomed flask. (Typically for ITIR-FCS experiments, the dye concentration is about 0.006-

0.01% of the lipid concentration)

9) Shake the mixture briefly.

10) Remove the chloroform in the lipid and dye mixture by evaporating it in vacuum using a rotavap for at

least 3 hours. Ensure that there is no solvent left in the round bottom flask. A thin film of lipid will be

left in the flask.

11) Add PBS buffer (or, deionized water) to resuspend the lipid film such that the final lipid concentration

is 500 M.

12) Pipette up and down thoroughly until the thin film of lipid is completely dissolved to yield a milky

suspension.

13) Sonicate the suspension until it turns clear confirming the formation of unilamellar veislces. The

vesicle solution can be stored at 4 °C for a week.

Preparation of the lipid bilayer

Timing: 45 min

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14) Deposit the vesicles on a clean cover glass and incubate at 65 °C for 20 minutes followed by cooling at

room temperature for 20 minutes to create glass supported lipid bilayer.

Remove the unfused vesicles by washing with PBS buffer (or, deionized water) thoroughly.

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SUPPLEMENTARY TABLE

Supplementary Table 1 Imaging FCS and FCCS fitting models. Note: You can find additional information on imaging FCS/FCCS model derivations in the given references

and on http://staff.science.nus.edu.sg/~chmwt/resources/cdf22_derivation_fitting_model.html.

Fitting model Ref

1 ITIR-FCS

𝐺2D(𝜏) = 𝐺∞ +𝐴eff

√𝜋 ⋅ 𝑎2⟨𝑁⟩∙ ∑ 𝜌𝑘 ∙ [

√4𝐷𝑘𝜏 + 𝑤𝑥𝑦2

√𝜋. 𝑎. {𝑒

(−𝑎2

4𝐷𝑘𝜏+𝑤𝑥𝑦2 )

− 1} + erf (𝑎

√4𝐷𝑘𝜏 + 𝑤𝑥𝑦2)]

2𝑁Components

𝑘=1

With: ∑ 𝜌𝑘𝑘 = 1, 𝐴eff =𝑎2

[

𝑒𝑟𝑓(𝑎

𝑤𝑥𝑦)+𝑤𝑥𝑦

√𝜋∙𝑎∙[𝑒−(

𝑎𝑤𝑥𝑦

)

2

−1]

] 2 and ⟨𝐶⟩ = ⟨𝑁⟩/𝐴𝑒𝑓𝑓

7,22

2 SPIM-FCS

𝐺3D(𝜏) = 𝐺∞ +𝑉eff

√𝜋 ⋅ 𝑤𝑧 𝑎2⟨𝑁⟩

∙ ∑ 𝜌𝑘 ∙ (1 +4𝐷𝑘𝜏

𝑤𝑧2)

−12⁄

∙ [√4𝐷𝑘𝜏 + 𝑤𝑥𝑦

2

√𝜋. 𝑎. {𝑒

(−𝑎2

4𝐷𝑘𝜏+𝑤𝑥𝑦2 )

− 1} + erf (𝑎

√4𝐷𝑘𝜏 + 𝑤𝑥𝑦2)]

2𝑁Components

𝑘=1

With: ∑ 𝜌𝑘𝑘 = 1, 𝑉eff =√𝜋∙𝑎2∙𝑤𝑧

[

𝑒𝑟𝑓(𝑎

𝑤𝑥𝑦)+𝑤𝑥𝑦

√𝜋∙𝑎∙[𝑒

−(𝑎

𝑤𝑥𝑦)

2

−1]

] 2 and ⟨𝐶⟩ = ⟨𝑁⟩/𝑉𝑒𝑓𝑓

3

3 ITIR/SPIM-FCCS,

full model 𝐺𝑔𝑔(𝜏) =

𝜂𝑔2 ∙ [𝑔𝑔𝑔

𝐺 (𝜏) + 𝑔𝑔𝑔𝐺𝑅(𝜏)]

𝜂𝑔2[⟨𝐶𝐺⟩ + ⟨𝐶𝐺𝑅⟩]

2

𝐺𝑔𝑔(𝜏) =𝜂𝑟2 ∙ [𝑔𝑟𝑟

𝑅 (𝜏) + 𝑔𝑟𝑟𝐺𝑅(𝜏)] + 𝜅𝑔𝑟

2 𝜂𝑔2 ∙ [𝑔𝑔𝑔

𝐺 (𝜏) + 𝑔𝑔𝑔𝐺𝑅(𝜏)] + 2𝜅𝑔𝑟𝜂𝑔𝜂𝑟𝑔𝑔𝑟

𝐺𝑅(𝜏)

[𝜅𝑔𝑟𝜂𝑔⟨𝐶𝐺⟩ + (𝜂𝑟 + 𝜅𝑔𝑟𝜂𝑔) ∙ ⟨𝐶𝐺𝑅⟩ + 𝜂𝑟⟨𝐶𝑅⟩]2

𝐺𝑔𝑟(𝜏) = 𝐺𝑟𝑔(𝜏) =𝜂𝑔𝜂𝑟𝑔𝑟𝑟

𝐺𝑅(𝜏) + 𝜅𝑔𝑟𝜂𝑔𝜂𝑟𝑔𝑔𝑟𝐺 (𝜏) + 𝜅𝑔𝑟𝜂𝑔

2𝑔𝑔𝑔𝐺𝑅(𝜏)

[𝜂𝑔⟨𝐶𝐺⟩ + 𝜂𝑔⟨𝐶𝐺𝑅⟩] ∙ [𝜅𝑔𝑟𝜂𝑔⟨𝐶𝐺⟩ + (𝜂𝑟 + 𝜅𝑔𝑟𝜂𝑔) ∙ ⟨𝐶𝐺𝑅⟩ + 𝜂𝑟⟨𝐶𝑅⟩]

1,2

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𝜂𝑔 =⟨𝐹𝑔⟩

⟨𝐶𝐺⟩ + ⟨𝐶𝐺𝑅⟩, 𝜂𝑟 =

⟨𝐹𝑟⟩

⟨𝐶𝑅⟩ + ⟨𝐶𝐺𝑅⟩

4 ITIR/SPIM-FCCS,

simplified 2-

component model

𝐺𝑔𝑔(𝜏) =1

⟨𝐶𝐺⟩ + ⟨𝐶𝐺𝑅⟩∙ 𝑔𝑔𝑔(𝜏)

𝐺𝑔𝑔(𝜏) =𝜂𝑟2 ∙ [⟨𝐶𝑅⟩ + ⟨𝐶𝐺𝑅⟩] + 𝜅𝑔𝑟

2 𝜂𝑔2 ∙ [⟨𝐶𝐺⟩ + ⟨𝐶𝐺𝑅⟩] + 2𝜅𝑔𝑟𝜂𝑔𝜂𝑟⟨𝐶𝐺𝑅⟩

[𝜅𝑔𝑟𝜂𝑔⟨𝐶𝐺⟩ + (𝜂𝑟 + 𝜅𝑔𝑟𝜂𝑔) ∙ ⟨𝐶𝐺𝑅⟩ + 𝜂𝑟⟨𝐶𝑅⟩]2 ∙ 𝑔𝑟𝑟(𝜏)

𝐺𝑔𝑟(𝜏) = 𝐺𝑟𝑔(𝜏) =𝜂𝑔𝜂𝑟⟨𝐶𝐺𝑅⟩ + 𝜅𝑔𝑟𝜂𝑔𝜂𝑟⟨𝐶𝐺⟩ + 𝜅𝑔𝑟𝜂𝑔

2⟨𝐶𝐺𝑅⟩

[𝜂𝑔⟨𝐶𝐺⟩ + 𝜂𝑔⟨𝐶𝐺𝑅⟩] ∙ [𝜅𝑔𝑟𝜂𝑔⟨𝐶𝐺⟩ + (𝜂𝑟 + 𝜅𝑔𝑟𝜂𝑔) ∙ ⟨𝐶𝐺𝑅⟩ + 𝜂𝑟⟨𝐶𝑅⟩]∙ 𝑔𝑔𝑟(𝜏)

𝜂𝑔 =⟨𝐹𝑔⟩

⟨𝐶𝐺⟩ + ⟨𝐶𝐺𝑅⟩, 𝜂𝑟 =

⟨𝐹𝑟⟩

⟨𝐶𝑅⟩ + ⟨𝐶𝐺𝑅⟩

with: 𝑔𝑔𝑟(𝜏) = [1 − 𝜌slow,𝑔𝑟] ∙𝑔𝑔𝑟fast,𝑔𝑟

(𝜏)

⟨𝐶fast,𝑔𝑟⟩+ 𝜌slow,𝑔𝑟 ∙

𝑔𝑔𝑟slow,𝑔𝑟

(𝜏)

⟨𝐶slow,𝑔𝑟⟩

1,2

5 ITIR-FCCS 𝑔𝑔𝑟𝜒(𝜏) = (

2

𝜋) 𝜂𝑔𝜂𝑟⟨𝐶𝜒⟩

∙ (1

2a2) ∏ {[(𝑎 + 𝑑𝑖)

𝑖∈{𝑥,𝑦}

∙ erf (√2(𝑎 + 𝑑𝑖)

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) + 2𝑑𝑖 ∙ erf (

−√2𝑑𝑖

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)

+ (𝑎 − 𝑑𝑖)∙erf (√2(𝑎 − 𝑑𝑖)

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)] +

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2

√2𝜋

∙ [exp (2(𝑎 + 𝑑𝑖)

2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) − 2 exp (

2𝑑𝑖2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) + exp (

2(𝑎 − 𝑑𝑖)2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)]}

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6 SPIM-FCCS

𝑔𝑔𝑟𝜒(𝜏) = (

2

𝜋)

32𝜂𝑔𝜂𝑟⟨𝐶𝜒⟩ ∙

{

exp (−

2𝑑𝑧2

√8𝐷𝜒𝜏 + 𝑤𝑧,𝑔2 + 𝑤𝑧,𝑟

2)

√8𝐷𝜒𝜏 + 𝑤𝑧,𝑔2 + 𝑤𝑧,𝑟

2

}

∙ (1

2a2) ∏ {[(𝑎 + 𝑑𝑖)

𝑖∈{𝑥,𝑦}

∙ erf (√2(𝑎 + 𝑑𝑖)

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) + 2𝑑𝑖 ∙ erf (

−√2𝑑𝑖

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)

+ (𝑎 − 𝑑𝑖)∙erf (√2(𝑎 − 𝑑𝑖)

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)] +

√8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2

√2𝜋

∙ [exp (2(𝑎 + 𝑑𝑖)

2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) − 2 exp (

2𝑑𝑖2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2) + exp (

2(𝑎 − 𝑑𝑖)2

8𝐷𝜒𝜏 + 𝑤𝑥𝑦,𝑔2 + 𝑤𝑥𝑦,𝑟

2)]}

1,2

7 2-pixel ITIR-FCCS

with flow

𝐺(𝜏) =𝐴eff⟨𝑁⟩

1

2𝑎2∙ ∏

1

𝑎𝑖∈{x,y}

∙ {[(𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏) ∙ erf (𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏

√4𝐷𝜏 + 𝑤𝑥𝑦2) + 2(𝑑𝑖 − 𝑣𝑖𝜏) ∙ erf (

𝑣𝑖𝜏 − 𝑑𝑖

√4𝐷𝜏 + 𝑤𝑥𝑦2) + (𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏)∙erf (

𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏

√4𝐷𝜏 + 𝑤𝑥𝑦2)]

+√4𝐷𝜏 + 𝑤𝑥𝑦

2

√𝜋∙ [exp (−

(𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏)2

4𝐷𝜏 + 𝑤𝑥𝑦2

) − 2 exp (−(𝑑𝑖 − 𝑣𝑖𝜏)

2

4𝐷𝜏 + 𝑤𝑥𝑦2) + exp (−

(𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏)2

4𝐷𝜏 + 𝑤𝑥𝑦2

)]}

See equation 1 for the definition of Aeff

1,4

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8 2-pixel SPIM-FCCS

with flow 𝐺(𝜏) =𝑉eff⟨𝑁⟩

∙1

2𝑎2 ∙ 𝑤𝑧 ∙ √𝜋∙exp (−

(𝑣𝑧𝜏 − 𝑑𝑧)2

4𝐷𝜏 + 𝑤𝑧2 )

√1 + 4𝐷𝜏 𝑤𝑧2⁄

∙ ∏1

𝑎𝑖∈{x,y}

∙ {[(𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏) ∙ erf (𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏

√4𝐷𝜏 + 𝑤𝑥𝑦2) + 2(𝑑𝑖 − 𝑣𝑖𝜏) ∙ erf (

𝑣𝑖𝜏 − 𝑑𝑖

√4𝐷𝜏 + 𝑤𝑥𝑦2) + (𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏)∙erf (

𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏

√4𝐷𝜏 + 𝑤𝑥𝑦2)]

+√4𝐷𝜏 + 𝑤𝑥𝑦

2

√𝜋∙ [exp (−

(𝑎 + 𝑑𝑖 − 𝑣𝑖𝜏)2

4𝐷𝜏 + 𝑤𝑥𝑦2

) − 2 exp (−(𝑑𝑖 − 𝑣𝑖𝜏)

2

4𝐷𝜏 + 𝑤𝑥𝑦2) + exp (−

(𝑎 − 𝑑𝑖 + 𝑣𝑖𝜏)2

4𝐷𝜏 + 𝑤𝑥𝑦2

)]}

See equation 2 for the definition of Veff

1,4

D, Dχ: diffusion coefficient (of species χ)

⟨𝐶⟩, ⟨𝐶𝜒⟩: concentration (of species χ)

⟨𝑁⟩ particle number in effective focal volume/area Veff / Aeff

𝑤𝑥𝑦 , 𝑤𝑥𝑦,𝑔, 𝑤𝑥𝑦,𝑟: lateral half-width (1/e²) of the PSF (in color channel g/r)

𝑤𝑧, 𝑤𝑧,𝑔, 𝑤𝑧,𝑟: longitudinal half-width (1/e²) of the PSF (in color channel g/r)

dx, dy, dz: shift of the detection volumes between channel g/r in x/y/z-direction

vx, vy, vz: flow velocity in x/y/z-direction

a: pixel size of the camera (in the sample plane)

ρχ: fraction of diffusing component χ

G∞: offset of the correlation function (usually 0 or 1)

⟨𝐹𝑔⟩, ⟨𝐹𝑟⟩: averaged and background-corrected fluorescence intensity in color channel g/r

NComponents: number of diffusing components in the sample

Veff /Aeff: effective volume/area (3D/2D mobility) of observation volume (see 1,2) for a definition

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16

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