nature methods Modular scanning FCS quantifies receptor-ligand interactions in living multicellular organisms Jonas Ries, Shuizi Rachel Yu, Markus Burkhardt, Michael Brand & Petra Schwille Supplementary figures and text: Supplementary Figure 1 Supplementary Figure 2 Supplementary Figure 3 Illustration of modular scanning FCS to measure receptor-ligand interactions in vivo. Expression patterns of fgf8, Fgf target genes and receptors in gastrulating zebrafish embryos Injection of mrna and fusion constructs Supplementary Figure 4 Residuals for FCS curve fitting in Figure 2 Supplementary Table 1 Supplementary Table 2 Supplementary Note 1 Supplementary Note 2 Supplementary Note 3 Supplementary Note 4 Primers used for RT-PCR and QPCR Antisense mrna probes used for whole-mount in situ hybridization Fluorescence correlation spectroscopy Principle of scanning FCS Two-focus scanning FCS Dual-color scanning FCS
Supplementary Figures a: Static FCS in extracellular space laser AOTF scanning Free ligand b: Two-focus scanning FCS on membrane laser c: Dual-color scanning FCS on membrane Receptor APD Confocal laser scanning microscope APD Complex Supplementary Figure 1: Illustration of modular scanning FCS to measure receptor-ligand interactions in vivo. Modular scanning FCS combines static confocal FCS with two-focus scanning FCS and dual-color scanning FCS and can be easily implemented with a laser scanning microscope. (a) Static confocal FCS measures the concentration of the free ligand in the extracellular space (ECS). (b) Two-focus scanning FCS determines the absolute diffusion coefficients of the transmembrane receptors and the size of the detection area. (c) Dual-color scanning FCS with alternating excitation measures the degree of binding between ligands and receptors in the cell membrane. APD: avalanche photo diode; AOTF: acousto optic tunable filter. 1
a fgf8 spry4 pea3 erm b fgfr1 fgfr4 Supplementary Figure 2: Expression patterns of fgf8, Fgf target genes and receptors in gastrulating zebrafish embryos. (a) Expressions of fgf8 and Fgf target genes spry4, pea3 and erm at shield stage in gastrulating zebrafish embryos. fgf8 is expressed in cells at the blastoderm margin during gastrulation. Its downstream target genes spry4, pea3 and erm are expressed in successively broader domains away from the margin towards the animal pole. (b) Expression of fgfr1 and fgfr4 at shield stage during gastrulation. fgfr1 is expressed ubiquitously in the embryo whereas fgfr4 is expressed everywhere except at the margin. 2
a fgfr1- or fgfr4-mrfp fgf8-egfp b Fgf8-eGFP Fgf8 signal peptide (1-22 amino acids) egfp Rest of Fgf8 Fgfr1-mRFP Fgfr4-mRFP Fgfr1 extracellular and transmembrane domains (1-39 amino acids) Fgfr 4 extracellular and transmembrane domains (1-57 amino acids) mrfp mrfp Supplementary Figure 3: (a) Injection of mrna. Schematic drawing of injection for measuring Fgf receptor-ligand affinity in vivo. 2 pg of fgfr1-mrfp or fgfr4-mrfp mrna was injected at 1-cell stage and.4 pg of fgf8-egfp mrna was then injected into a single cell at 32-cell stage into the embryos. During gastrulation, all of the cells in the embryos were expressing the mrfp labeled receptors and a restricted clone of cells was expressing and secreting the egfp labeled ligands. (b) Fusion constructs of Fgf8-eGFP, Fgfr1-mRFP and Fgfr4-mRFP. a -.4 c Residuals Residuals.4.1 1 1 1 2 1 3 1 4 τ (ms) b Residuals Residuals.2 -.2 d.4 1-2 1-1 1 1 1 1 τ (ms) -.1 1 1 1 2 1 3 1 4 τ (ms) -.4 1 1 1 2 1 3 1 4 τ (ms) Supplementary Figure 4: Residuals for FCS curve fitting in Figure 2. (a) Two-focus scanning FCS on Fgfr1-mRFP, panel b in Figure 2. (b) Confocal FCS in ECS, panel c in Figure 2. (c) Negative control, panel d in Figure 2. (d) Dual-color SFCS on Fgfr1 and Fgf8, panel e in Figure 2. 3
Supplementary Tables Primer name Sequence fgfr1 Forward 5 - gtgtctgtggactccagctcatct - 3 fgfr1 Reverse 5 - atcttgacggccactttggtgattctatt - 3 fgfr4 Forward 5 - tggcatggactacacctttgatgtgac - 3 fgfr4 Reverse 5 - cactcctcttgccaagccaaagtc - 3 Supplementary Table 1: Primers used for RT-PCR and QPCR of endogenous fgfr1 and 4 from shield stage zebrafish embryos. Name Plasmid Restriction enzyme RNA polymerase erm pbs-sk NotI T7 fgf8 pcs2+ BamHI T7 fgfr1 pcs2+ BamHI T7 fgfr4 pbs-sk HincII T7 pea3 pbs-sk NotI T7 spry4 pcs2+ ClaII T7 Supplementary Table 2: Antisense mrna probes used for whole-mount in situ hybridization. 4
Supplementary Note 1: Fluorescence correlation spectroscopy In fluorescence correlation spectroscopy (FCS), fluorescence fluctuations due to molecules moving through a tiny detection volume are analyzed statistically in terms of the auto-correlation curve G(τ): G(τ) = δf(t)δf(t + τ) F(t) 2 (1) F(t) is the fluorescence intensity detected at time t, denotes the average over time and δf(t) = F(t) F(t). The main contribution to the fluorescence fluctuations is the diffusion of the fluorescent molecules through the detection volume. Another source is the blinking of the fluorophores due to protonationdeprotonation or triplet population. The amplitude of the correlation curve G() is inversely proportional to the concentration and from the decay time τ D of the correlation curve the diffusion coefficient D can be calculated (Fig. A). To extract this information, the experimental correlation curve is fitted with a mathematical model describing the source of the fluctuations. For free diffusion through a Gaussian detection volume this function is: 1 G(τ) = Cπ 3/2 S w 3 1 + 4Dτ w 2 1 1 + 4Dτ w 2 S 2 1/2 ( 1 + T 1 T e τ/τ t C is the concentration of the fluorescent molecule, w is the radial extension and w z is the axial extension of the detection volume. The structure parameter S = w z /w is its aspect ratio. T denotes the fraction of molecules which are in the dark state on a time scale given by τ t. ) (2) G(τ) 1 N t t+t ddt F( t) F( t ) G( t ) = + 2 F τ D τ a b c Figure A: Principle of FCS. Fluorescent molecules diffusing through a small detection volume (a) produce a fluctuating intensity trace (b). This intensity trace is analyzed statistically by calculating the auto-correlation curve (c). The amplitude of the auto-correlation curve is inversely proportional to the concentration of the molecules. The decay time τ D is related to the residence time of the molecules in the detection volume and can be used to calculate their diffusion coefficient if the size of the detection volume has been calibrated. 5
Supplementary Note 2: Principle of scanning FCS The principle of scanning FCS is illustrated in Figure 1. The detection volume is repeatedly scanned perpendicularly through a vertical membrane. The intersection of the scan with the membrane defines the detection area. The individual line-scans can be arranged as a pseudo-image, where the vertical axis denotes the time. In this pseudo-image the membrane is clearly visible. Due to instabilities, the position of the membrane is not constant in time. These instabilities can be corrected for by shifting each line-scan in such a way that the membrane becomes a straight line. For each scan, membrane contributions are added up to give one point in the intensity trace F(t) which can then be used to calculate the auto-correlation curve G(τ) (equation 1). The time resolution of scanning FCS is determined by the repetition rate of the scan and is about one millisecond. This is sufficient to monitor the rather slow diffusion in membranes (diffusion time 2 ms), but does not capture free solution diffusion or photophysical dynamics (triplet or blinking). Depletion of fluorophores due to photobleaching can be corrected for 1. This is important especially if the reservoir of fluorophores is limited, as in the case of spherical model membranes or cells. Supplementary Note 3: Two-focus scanning FCS For quantitative analysis of FCS correlation curves, the size of the detection area w needs to be known. It cannot be inferred from fitting auto-correlation curves since it is always coupled to the diffusion coefficient in form of the diffusion time τ D = w 2 /4D (equation 2). Usually, it is determined by a calibration measurement using free dye in solution with a known diffusion coefficient. Optical artifacts, saturation or mispositioning of the laser focus with respect to the membrane lead to a change in the size of the detection area, rendering quantitative measurements challenging. This problem can be overcome by two-focus FCS which employs two spatial detection areas with a well defined and known distance 2. In two-focus scanning FCS, two parallel lines, spatially offset by a distance d, are scanned through the membrane in an alternating fashion. The intersections with the membrane give rise to two intensity traces F 1 (t) and F 2 (t), from which the auto-correlation curves G 1 (τ) and G 2 (τ) (equation 1) and also the spatial cross-correlation curves G 12 (τ) and G 21 (τ) can be calculated: G 12 (τ) = δf 1(t)δF 2 (t + τ) F 1 (t) F 2 (t) (3) The model function for the experimental cross-correlation curves in case of free diffusion is 3 : 1 G 12 (τ) = G 21 (τ) = CπS w 2 1 + 4Dτ 1/2 w 2 1 + 4Dτ 1/2 w 2 S 2 exp d 2 w 2 + 4Dτ (4) The structure parameter S = w z /w describes the aspect ratio of the elliptical Gaussian detection area. Once the distance d is known, the diffusion coefficient D, the concentration C and the waist of the laser focus w can be determined directly by fitting the data with equation 4 without any additional calibration measurement 2. The auto-correlation function follows from equation 4 for d =. The photons in the two foci are not collected within the same time window, but with a delay t d, which is usually given by the scan period. Therefore the cross-correlation curves are shifted with respect to the auto-correlation curves by this delay time and this needs to be taken into account during the data analysis 3. 6
Two-focus scanning FCS not only permits accurate diffusion measurements, but also provides a calibration of the detection area which can be used for quantitative evaluation of the dual-color scanning FCS measurements. Supplementary Note 4: Dual-color scanning FCS To measure binding between two distinctly labeled molecules, dual-color fluorescence cross-correlation spectroscopy (FCCS) 4 can be employed. Here two spectral channels are used to calculate the autocorrelation curves and also the spectral cross-correlation curve. Only if the two binding partners diffuse as an entity, they give rise to a significant cross-correlation amplitude which can then be used to study the degree of binding. However, spectral cross-talk, usually from the green fluorophore into the red channel, introduces additional similarities between the fluorescence fluctuations in the two channels and can therefore result in a false-positive cross-correlation. In membranes, binding can be measured with dual-color scanning FCS using two spectral channels. By scanning every other line with a different color and detecting the photons only in the corresponding channel, contributions from the two different fluorophores can be separated completely and spectral cross-talk is avoided 3,5,6. From the two intensity traces, the red and the green auto-correlation curves and the cross-correlation curve can be calculated. By fitting the correlation curves with equation 4 with d =, their amplitudes can be obtained. From these amplitudes we can then calculate the degree of binding. Here we derive equations which relate the correlation amplitudes to the concentrations and dissociation constants of the receptors and the ligands using an elementary binary binding model. We start by introducing the simplest case, in which a red-labeled receptor in a membrane binds to a green-labeled ligand in solution. c tot R = c R + c RL is the total area concentration of the receptors in the membrane, whereas c RL is the area concentration of receptor-ligand complexes and c R is the area concentration of the unbound receptor. c L is the concentration of the free ligand in solution. We can then express the amplitudes of the auto- and cross-correlation curves in terms of these concentrations: G g = (Ac RL ) 1, G rg = G r = (A(c R + c RL )) 1, G f = (V conf c L ) 1 (5) A = πs w 2 is the scanning FCS detection area, V conf = π 3/2 S w 3 is the confocal FCS detection volume, G g is the green and G r is the red auto-correlation amplitude and G rg is the cross-correlation amplitude, all measured with scanning FCS. The amplitude G f of the auto-correlation curve of the free ligand is measured with static-volume confocal FCS. Note that G rg = G r since there is no free ligand on the membrane. The dissociation constant is defined here as: Background correction K d = c Rc L c RL (6) Equation 5 is only valid in the limit of vanishing free ligand concentrations, otherwise the free ligand affects the green auto-correlation curve and the cross-correlation curve. Since scanning FCS does not resolve the fast diffusion of the free ligand, these contributions can be treated as an uncorrelated background and amplitudes can be corrected accordingly. In the general case, a background B r and B g in the red and green channel respectively reduces the amplitude of the cross-correlation curve: G meas rg = G true rg F r F r + B r 7 F g F g + B g (7)
F r and F g are the fluorescence intensities excluding the background. The expressions for the autocorrelation curves can be obtained by setting g = r. With equation 7 we corrected for an autofluorescent background and detector dark counts. To correct for contributions from the free ligand in the extracellular space (ECS), we have to relate F g and B g to quantities measured during the experiment. The free ligand does not contribute to the signal in the red channel, therefore B r =. From the average number of photons Fg SFCS, detected during the integration time t = s/v in the integration window s around the membrane (scanning speed v), we can calculate the total countrate in the green channel: F g + B g = F SFCS g / t (8) The background countrate can be inferred directly from the static confocal FCS measurement in the extracellular space: B g = F ECS /2. The factor 1/2 is due to the fact, that the free ligand is mainly found in the extracellular space, not inside the cells and therefore only in half of the detection volume. Determination of dissociation constants and unlabeled receptor concentrations In actual measurements in complex biological systems there are unlabeled and competing ligands, as well as unlabeled and competing receptors which complicate the data analysis. Further oligomerization of receptor-ligand complexes will not be considered in the following. The presence of an unlabeled Fgf8 or other competing Fgf ligands of concentration c c and dissociation constant Kd c results in an increase in the value of the dissociation constant 7. The measured (effective) dissociation constant is then: ( Kd eff = K d 1 + c ) c Kd c (9) In the system examined in this work there are two known receptors Fgfr1 and Fgfr4 which can interact with the ligand Fgf8. In our experiments with the labeled Fgfr1 (concentration c R1 ) and the labeled ligand (c L ), there are also unlabeled Fgfr1 (c r1 ) and unlabeled Fgfr4 (c r4 ) present in the system. We can express the auto- and cross-correlation amplitudes and the dissociation constants Kd 1 and K4 d of the Fgfr1 and Fgfr4 in terms of the concentrations in a similar way as in equation 5: The fractional occupancy G g = (A(c LR1 + c Lr1 + c Lr4 )) 1, G r = (A(c R1 + c LR1 )) 1 G rg = c LR1 (A(c LR1 + c Lr1 + c Lr4 )(c R1 + c LR1 )) 1 (1) K 1 d := (c R1 + c r1 )c L c LR1 + c Lr1, K 4 d := c r4c L c Lr4 c RL = G rg() c R + c RL G g () follows directly from the amplitudes of the auto- and cross-correlation curves. From equations 1 the effective dissociation constant Kd 1 can be calculated from the scanning FCS correlation amplitudes (background corrected) and the concentration of the free ligand c L, determined with confocal FCS in the extracellular space: (11) K 1 d = G g G rg G rg c L (12) Here we assumed equal dissociation constants for labeled and unlabeled receptors which leads to c Lr1 /c LR1 = c r1 /c R1. Note that the presence of unlabeled receptors does not change the value of 8
Kd 1 (equation 12). K4 d can be determined with a second set of measurements with labeled Fgfr4 but without labeled Fgfr1. Then the indices 1 and 4 have to be exchanged in equations 1 and 12. We can express the correlation amplitudes in terms of the primary physical parameters Kd 1, K4 d, c L, c tot R1 = c R1 + c LR1, c tot r1 = c r1 + c Lr1 and c tot r4 = c r4 + c Lr4 = r 41 c tot r1 : G f = G r = 1 1, G g = 1 (Kd 1 + c L)(Kd 4 + c L) c L V conf Ac L (Kd 4 + c L)(c tot R1 + ctot r1 ) + (K1 d + c L)r 41 c tot r1 Kd 4 + c L Ac tot R1, G rg = 1 A (Kd 4 + c L)(c tot R1 + ctot r1 ) + (K1 d + c L)r 41 c tot r1 r 41 is the ratio between the concentrations of the endogenous receptors Fgfr4 and Fgfr1. We assumed that the protein levels of endogenous Fgfr1 and Fgfr4 are proportional to the corresponding mrna levels. Therefore we could estimate the ratio between the endogenous receptors using QPCR as described in the Online Methods section. For experiments with labeled Fgfr4, indices 1 and 4 have to be exchanged. We can use equation 13 to globally fit the experimental correlation amplitudes (background corrected) from all experiments by treating the dissociation constants and concentrations as free fitting parameters. In this way we can determine the dissociation constants Kd 1 and K4 d and the concentrations of the labeled receptors c tot R1 or ctot R4 with a high accuracy. In addition, this global analysis allows one to estimate the concentrations of the unlabeled, endogenous receptors c tot r1 and ctot r4. Note that c tot R1, ctot R4 and c L vary from measurement to measurement, whereas Kd 1, K4 d, ctot r1 and ctot r4 are here assumed to be constant (Fig. B) and are therefore described by one value each. (13) Ladder fgfr1 fgfr4 1 2 3 1 2 3 3bp 2bp Figure B: RT-PCR of endogenous fgfr1 and 4 at shield stage using RNA extracted from 1) wild type embryos 2) embryos overall injected with 2 pg fgfr1-mrfp mrna at 1-cell stage 3) embryos overall injected with 2 pg fgfr4-mrfp mrna at 1-cell stage. Injection of the fgfr1-mrfp or fgfr4- mrfp mrnas does not alter the level of endogenous fgfr1 and 4 mrnas significantly, hence the endogenous concentrations c tot r1 and ctot r4 are assumed to be constant in our experiments. References [1] Ries, J., Chiantia, S. & Schwille, P. Accurate determination of membrane dynamics with line-scan fcs. Biophys J 96, 1999 28 (29). [2] Dertinger, T. et al. Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements. ChemPhysChem 8, 433 443 (27). [3] Ries, J. & Schwille, P. Studying slow membrane dynamics with continuous wave scanning fluorescence correlation spectroscopy. Biophys J 91, 1915 1924 (26). 9
[4] Schwille, P., Meyer-Almes, F. & Rigler, R. Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution. Biophys J 72, 1878 1886 (1997). [5] Muller, B., Zaychikov, E., Brauchle, C. & Lamb, D. Pulsed interleaved excitation. Biophys J 89, 358 3522 (25). [6] Thews, E. et al. Cross talk free fluorescence cross correlation spectroscopy in live cells. Biophys J 89, 269 276 (25). [7] Maeder, C. I. et al. Spatial regulation of Fus3 MAP kinase activity through a reaction-diffusion mechanism in yeast pheromone signalling. Nat Cell Biol 9, 1319 1326 (27). 1