Dual-color dual-focus line-scanning FCS for quantitative analysis of receptor-ligand interactions in living specimens

Cellular communication in multi-cellular organisms is mediated to a large extent by a multitude of cell-surface receptors that bind specific ligands. An in-depth understanding of cell signaling networks requires quantitative information on ligand-receptor interactions within living systems. In principle, fluorescence correlation spectroscopy (FCS) based methods can provide such data, but live-cell applications have proven extremely challenging. Here, we have developed an integrated dual-color dual-focus line-scanning fluorescence correlation spectroscopy (2c2f lsFCS) technique that greatly facilitates live-cell and tissue experiments. Absolute ligand and receptor concentrations and their diffusion coefficients within the cell membrane can be quantified without the need to perform additional calibration experiments. We also determine the concentration of ligands diffusing in the medium outside the cell within the same experiment by using a raster image correlation spectroscopy (RICS) based analysis. We have applied this robust technique to study the interactions of two Wnt antagonists, Dickkopf1 and Dickkopf2 (Dkk1/2), to their cognate receptor, low-density-lipoprotein-receptor related protein 6 (LRP6), in the plasma membrane of living HEK293T cells. We obtained significantly lower affinities than previously reported using in vitro studies, underscoring the need to measure such data on living cells or tissues.


Text S1: Fluorescence correlation spectroscopy (FCS)
In FCS experiments 1 , intensity fluctuations due to fluorescent molecules diffusing through a static observation volume are continuously monitored over time (Fig. S1).

Text S2: Line-scanning FCS (lsFCS)
Conventional FCS experiments with a static confocal volume are not well suited for measuring diffusion of molecules in cell membranes because movements of the entire cell membrane within the volume will cause intensity fluctuations that can entirely obscure the fluctuations due to molecules diffusing within the membrane, which the FCS method aims to analyze. Moreover, the slow diffusion of fluorescent molecules in membranes increases the probability of photobleaching. Schwille and coworkers 2 have introduced line-scanning FCS to alleviate these problems. In this approach, the observation volume is repeatedly raster-scanned perpendicularly through a membrane (Fig. S2). The data can be visualized as a kymogram, in which the intensity is plotted as a function of the scanner position along the horizontal axis for each individual line scan.
Lines from individual scans are plotted sequentially, each new scan below the previous one, so that the vertical dimension represents the scan number (and thus also the overall measurement time). Due to membrane fluctuations, the intersection of the confocal volume with the membrane will generally be different for each individual scan.
Locating the maximum in each individual scan allows one to shift the data from all scans to a common time origin. A corrected intensity time trace, , results, from which the autocorrelation curve, , can be calculated with Eq. S1. For a line scan along the (lateral) x-axis, the model autocorrelation function, applies to two-dimensional diffusion within the membrane along the y-and z-directions.
Here, we again assume a Gaussian shape of the observation volume, and 〈 〉 , with concentration C and effective observation area, . The time resolution of lsFCS is given by the duration of a single scan line, i. e., the pixel dwell time times the total number of pixels.

Text S3: Dual-focus lsFCS
In standard FCS experiments, the spatial extension of the observation volume has to be precisely known to determine concentrations and diffusion coefficients. Enderlein and coworkers 3 have introduced dual-focus FCS to circumvent the need for a separate calibration experiment. In dual-focus lsFCS, two parallel lines having a well-defined displacement, d, are scanned in an alternating fashion (Fig. S3). From the intensity time traces, the autocorrelation (i = j, with i = 1, 2) and cross-correlation (i ≠ j) functions are computed, We note that the spatial displacement has to be small enough to ensure that there is an appreciable probability to collect photons from the same molecule during both scans. By scanning two lines along the x-direction with a displacement d along the y-direction, we can measure free diffusion of molecules in the yz-plane of the membrane. The model function of the two-focus pair-correlation is given by For the autocorrelation functions from both scans, G ii () and G jj (), d = 0, so that Eq. S5 becomes identical to Eq. S3, whereas the cross-correlation function (i ≠ j) contains the additional exponential term. By globally fitting the two autocorrelation and the crosscorrelation functions, the parameter  0 can be extracted from the data. We note that a dual-focus experiment with line displacement along z yields the parameter z 0 . In practice, the ratio  0 /z 0 is a well-controlled parameter and, therefore, such a measurement is typically not required. [S5]

Text S4: Dual-color lsFCS
Dual-color FCS is a cross-correlation method to reveal if two differently labeled molecules bind to each other and thus diffuse as an entity 4 . Here, the fluorescence from the two molecules is monitored in two separate color channels. Assuming that cross-talk between the channels is absent (see below), a cross-correlation between the two channels is only observed if the two binding partners (e.g., receptor and ligand) diffuse together (Fig. S4). It is important to consider that the sizes of the observation volumes associated with the two color channels are in general different. The dual-color crosscorrelation function between the two color channels, G r,g (), with labels r for red and g for green, is given by Here,  r ( g ) and z r (z g ) are the radial and axial extensions of the red (green) observation areas, respectively. The effective detection area for dual-color cross-correlation is given by , with effective observation areas 2 ⁄ and 2 ⁄ . Artificial, false-positive cross-correlations can arise from spectral cross-talk.
This problem is avoided by using alternating excitation, so that every other line is scanned with a different color 2 . In this way, the emission from the two fluorophores can be completely separated. The autocorrelation (green and red squares) and cross-correlation functions (blue squares) of the extracted intensity traces from molecules diffusing in the membrane can be calculated and fitted with Eqs. S3 and S6. In this experiment, the cross-correlation amplitude is zero, indicating that the differently labeled DPPE molecules do not bind appreciably to each other.
Text S5: Implementation of the 2c2f lsFCS method

Principle of 2c2f lsFCS
In 2c2f lsFCS, the observation volumes are repeatedly scanned perpendicularly through a vertical membrane, using a scan sequence consisting of four consecutive scans, i.e., two parallel line scans for two spectral channels (Fig. 2a). Spectral cross-talk is completely avoided by selecting only photons from one or the other color channel to calculate the intensity trace. The key advantage of this approach is the simultaneous assessment of the observation volume sizes of both spectral channels and the measurement of the receptor and complex concentrations with high statistical accuracy and short measurement time.
After evaluating the four intensity traces, a total of 16 autocorrelation and crosscorrelation curves are calculated with Eq. S4 (Fig. 2b). The expressions for the autocorrelation functions and the dual-focus and dual-color cross-correlation functions are given by Eqs. S3, S5 and S6, respectively. In 2c2f lsFCS, we analyze the intensity pair correlations of red focus 1 with green focus 2 and red focus 2 with green focus 1 in addition. Assuming different observation volume sizes for the two color channels and a spatial distance d between the scan lines, we obtain the following model function for freely diffusing molecules in two dimensions, with one direction along the optical axis, Note that, by setting d = 0, we recover the dual-color cross-correlation function (Eq. S6).
By globally fitting the data (Fig. 2c), the receptor and complex concentrations, diffusion coefficients and sizes of the observation volumes can be determined.

Background correction
Ligands in the extracellular space diffuse freely; these movements do not give rise to correlations on the millisecond time scale of line-scanning FCS but still contribute as an uncorrelated background to the signal in the (green) ligand channel and, thereby, affect the correlation amplitudes. To remove this background, we calculate the mean pixel intensity, B g , by averaging over all pixels outside the cell. The total intensity, F total , from the membrane is determined from the pixel intensities of the line scan by fitting a Gaussian of width σ, which is calculated in terms of the number of pixels, p. The [S7] corrected intensity trace with contributions only from the membrane, F membrane , is then given by 2 . [S8] A factor of 1/2 has to be included here because the free ligand is present only in the extracellular space.

Perturbation correction
In FCS experiments on biological specimens, many perturbations exist that may render [S10] Depending on the length of the trace and the nature of the perturbation, the number of oscillations, N, has to be suitably adjusted. An excessive number of sine functions will cause the model function to suppress diffusional fluctuations and thus distort the results.
We tested this approach thoroughly in experiments with GUVs to assess its reliability. In time traces without obvious artifacts, the results of the corrected and uncorrected intensity traces were identical within the statistical error. By applying the correction to data showing clear perturbations, correlation data identical to those from unperturbed data were usually recovered. In our experiments, with typically 50,000 data points in an intensity trace, we found a sum of eight sine functions most suitable.

Determination of equilibrium dissociation coefficients of LRP6-Dkk binding
Here we have studied HEK293T cells expressing mCherry labeled and unlabeled LRP6 receptors in their plasma membranes; their concentrations are denoted by C R and C r , respectively, in the ligand-free form. They can bind Dkk-GFP ligands, with concentration C L in the external medium, to yield receptor-ligand complexes (C RL , C rL ). For such a bimolecular binding reaction, assuming that there is no association of the free ligand to the membrane, we can globally fit our FCS data by using the following equations for the correlation curves involving the red, green and both color channels, [S13] Here, G r () (G g ()) is the autocorrelation or dual-focus cross-correlation function of the red (green) channel; for the autocorrelation, d = 0. G x () is the dual-color or dual-color dual-focus cross-correlation function; for the former, d = 0. D R and D RL are the diffusion coefficients of the receptor without and with bound ligand, respectively. A r and A g are the confocal observation areas of the red and green channels, respectively, and A eff is the effective area in the dual-color experiment, i.e., the quadratic average.
The concentrations of labeled and unlabeled receptor (C R , C r ) as well as receptor-ligand complexes (C RL , C rL ) are obtained from a global fit of Eqs. S11 -S13 to the 2c2f lsFCS data. In the following, we show that the equilibrium dissociation coefficient, K d , can be calculated with these data plus additional information of the free ligand concentration, C L .
Although EGFP matures to close to 100%, 7 we may assume here for reasons of generality that there is a fraction of Dkk-GFP ligands with functional fluorophore, C L , and another one that is nonfluorescent, C l . Thus, . [S14] We assume that the mCherry protein fused to the receptor does not perturb its ligand binding affinity, so that With equation S15, we eliminate (C rL + C rl ) from Eq. S14, . [S16] Eq. S16 can be further simplified to read . [S17] Furthermore, we assume that the GFP protein fused to the ligand does not perturb its receptor binding affinity, Upon solving Eq. S18 for C Rl and plugging this expression into Eq. S17, we obtain , [S19] . [S15] . [S18] which can be simplified to yield the standard law of mass action expression, . [S20] In conclusion, as long as ligand-receptor binding is not affected by the presence of fluorescent protein domains, the equilibrium dissociation coefficient, K d , can be calculated on the basis of the concentrations of the fluorescent species, and does not hinge on knowing the fraction of fusion proteins that carry a functional fluorescent protein. However, we stress that we still require ligand labeling efficiencies close to one in the 2c2f lsFCS experiment. Otherwise, we have no means to distinguish between a ligand-free receptor and one with a bound, unlabeled ligand.

Analysis of the control experiment for examining ROR2-Dkk1 binding
The control experiment was designed to reveal lack of binding for a ligand-receptor pair that is known not to interact. To this end, we performed 2c2f lsFCS measurements on HEK293T cells expressing mCherry labeled and unlabeled ROR2 receptors and, in addition, non-fluorescent LRP6 receptors with concentrations C R , C r and C r2 , respectively.
Free Dkk-GFP ligands with concentration C L in the extracellular space can associate with these receptors in the membrane and form three different receptor-ligand complexes (C RL , C rL and C r2L ). The global model (Eqs. S11 -S13) has to be modified slightly to analyze the 2c2f lsFCS data taken on these cells. Equation S11 is not affected because there are no changes for the red channel; just ROR2 is fluorescently labeled instead of LRP6. In Eq. S12, which describes correlations in the green channel due to ligands bound to receptors, we model the three ligand-receptor species with their respective concentrations and the diffusion coefficients of ROR2-Dkk1, D RL , and LRP6-Dkk1, D r2L , The expression for the cross-correlation, Eq. S13, also needs a modification to account for the presence of three ligand-receptor species with a green-labeled ligand, Thus, the global fit returns two more parameters than the one using Eqs. S11 -13, characterizing the second receptor, C r2 and D r2L .

Text S6: Free ligand diffusion analysis from a RICS-like analysis of lsFCS data
In FCS studies of ligand binding to cell surface receptors, the concentration and the diffusivity of the free ligand are usually measured with a conventional FCS experiment in the volume outside the cell. Here we show that we can obtain these quantities also from our lsFCS data directly; therefore, an extra FCS experiment is not required.
In raster image correlation spectroscopy (RICS 8 ), a method conceptually closely related to FCS, raster-scanned images are acquired by moving the observation volume across the sample with a well-defined timing protocol defined by the pixel and line dwell times.
Because the spatial relation between any two pixels can be recast into a time interval, dynamic information can be obtained from a two-dimensional spatial correlation function, which is calculated between pixels along the two scan directions, Here, , is the pixel intensity at position x, y; , is the fluorescence intensity at a position shifted pixels along the x and lines along the y axis, similar to the time shift τ in FCS experiments. This analysis can be applied to kymograms measured in line-scanning FCS experiments (Fig. S5). The computed correlation function can be fitted with Here, N is the average number of fluorophores within the observation volume. The term , accounts for free, three-dimensional diffusion, ⁄ . [S23]

〈 〉 〈 〉 〈 〉 〈 〉 〈 〉
[S13A] The pixel and line dwell times are denoted by τ p and τ l , respectively. In line-scanning FCS experiments, the displacement along the y axis, , denotes only a temporal but not a spatial shift. Therefore, the scanning part, , , of the correlation function is modified from the one given in Ref. 8      An exponential fit (red line) yields a characteristic time of (45 ± 1) s. was detected by an antibody recognizing residue Ser1490, when phosphorylated (Sp1490), and represents an activated form of the receptor. β-catenin accumulation itself was revealed by using a specific antibody.  Our home-built confocal laser scanning microscope setup is also capable of STED super-resolution microscopy 9 ; this feature (shaded part) is not used here. A detailed description of the components is given in Materials and Methods.