SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION doi: 1.138/nchem.892 Mutual modulation Modulation between membrane-embedded Membrane Embedded receptor Receptors clustering lustering and ligand binding in lipid membranes Ligand Binding Salvador Tomas and Lilia Milanesi Supporting Information Supplementary Figure 1. lustering-binding thermodynamic cycle of membrane-embedded receptors. Derivation of the clustering isotherm We call n1, n, nd and nm the number of molecules of 1,, D, and M respectively. We define the concentration of 1 in the solvent 1 (i.e. 1 in the form) in terms of molar fraction as follows: n X = (S1) n1 While the concentration of 1 in the solvent M is : nd X D = (S2) nm + nd which, since nm >> nd we can simplify to: nature chemistry Macmillan Publishers Limited. All rights reserved.

2 supplementary information doi: 1.138/nchem.892 nd X D = (S3) nm The equilibrium constant that relates the and D forms of 1 is the partition coefficient of 1 between both solvents, D : X D = (S4) X D ombining equations (S1), (S3) and (S4) we have that D n nm = (S5) n 1 nd The relationship between the number of molecules and their concentration in the aqueous buffer is the volume of solution, e.g. n = Vol*[], thus D in terms of the bulk aqueous concentration of the species is: [ ][ M ] D = (S6) [ 1][ D] where [M] and [1] are the total concentration of M and 1 respectively. Since R L = [M]/[1], we have that [ ] R = L D [ D] (1) the variation of the apparent molar extinction coefficient, ε A, can be expressed as ε = ε x + ε x (2) A D D where x and x D are the fraction of the and D form respectively relative to the total amount of 1 and ε and ε D the molar extinction coefficients of and D. ombining equation (2) with the mass balance and equation (1) we have the following expression for the clustering isotherm: ε + ε R D D L ε A = (3) D + RL We define f as the factor of proportionality that relates the fluorescence intensity F with the concentration of the fluorofore, c, i.e., f = F/c. We can use this factor of proportionality in equation (3) to treat fluorescence data, i.e. 2 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

3 doi: 1.138/nchem.892 supplementary information f A f D D L = (3b) D + f + R L R where f A is the apparent proportionality factor (i.e, F/[1]), f is the proportionality factor for the fluorescence of the form and f D is the proportionality factor for the fluorescence of the form D. 1:1 binding isotherm The apparent binding of membrane embedded 1 to L follows a straightforward 1:1 association model: [ 1 L] A = (S7) [ 1][ L] The apparent extinction coefficient is: ε ] ε = (S8) A 1[ 1] + ε 1 L[ 1 L [ 1] Where [1] is the total concentration of 1. ombining with the mass balances (i.e. [1] = [1 L] + [] and [L] = [1 L] + [L]) we have that: ([ 1] ε = ε + ( ε ε ) A 1 1 L 1 + [ L] + 1 ) ([ 1] 2 [ 1] + [ L] + 1 ) 2 4 [ 1] [ L] (S9) Using fluorescence proportionality factors instead of extinction coefficients we have that equation (S9) is: f A + ( f = f1 1 L ([ 1] f ) 1 + [ L] + 1 ) ([ 1] 2 [ 1] + [ L] + 1 ) 2 4 [ 1] [ L] (S9b) nature chemistry Macmillan Publishers Limited. All rights reserved.

4 supplementary information doi: 1.138/nchem.892 Supplementary Figure 2. lustering of the receptor at different concentrations of 1. a) UV vis spectra of the Soret band region of 1 in absence of lipids (grey trace) and of lipid-embedded 1 at values of R L 1 (black traces). The grey arrows indicate the direction of change as R L increases and the dotted line the wavelength of the increment shown in panel c). b) Fluorescence excitation spectra (emission 62 nm) of 1 in absence of lipids (grey trace) and of lipid-embedded 1 at values of R L 1 (black traces). The grey arrow indicates the direction of change as R L increases and the dotted line the wavelength of the increment shown in panel d). c) Increase of the apparent molar extinction coefficient at 429 nm upon increase of R L and concentration of lipids. The concentration of 1 was fixed at 1 M. The grey trace represents the best fit to a clustering isotherm (equation (3), with a D = 12 ± 3 or to a 1:1 binding isotherm (equation (S9), using the concentration of lipids instead of the concentration of ligand L) with apparent binding constant 1-lipid of ± M -1. d) Increase of the apparent molar extinction coefficient at 429 nm upon increase of R L and lipids concentration. The concentration of 1 was fixed at.2 M. The grey trace represents the best fit to a clustering isotherm (equation (3b)), with a D = 12 ± 3 or to a 1:1 binding isotherm (equation (S9b), using the concentration of lipids instead of the concentration of ligand L) with apparent binding constant 1-lipid of ± M nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

5 doi: 1.138/nchem.892 supplementary information Supplementary Figure 3. artoon representation of the clustering equilibrium of embedded 1 in lipid membranes. 1 molecules are represented as dark spheres and lipids as light spheres. 1 can either partitions into the lipids, adopting the dispersed D form, or partitions into 1, taking the form. The model defines any grouping of 2 or more 1 molecules as and does not distinguish between the association processes labeled i, ii or iii in the figure. Therefore any molecule of 1, regardless of it being in the or D form, is part of 1 solvent. nature chemistry Macmillan Publishers Limited. All rights reserved.

6 supplementary information doi: 1.138/nchem.892 Supplementary Figure 4. Variation of the apparent binding constant A upon increase of R L. The empty circles represent the experimental values and the grey line the best fit to equation (3). The error bars are twice the standard deviation. The fitted curve falls outside the error bars for some values of A, illustrating the low accuracy of the model due to oversimplification. 6 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

7 doi: 1.138/nchem.892 supplementary information Supplementary Table 1. Binding and clustering parameters a L b b D c D d DL e DL 15 ± ± ± ± 1 58 ± 42 2 ± ± ± ± ± ± ± ± ± 1 1 ± ± ± ± ± ± ± ± ± 2 52 ± ± ± ± ± ± ± ± ± ± ± ± 1.7 a Quoted errors are twice the standard deviation and D units are M -1 and refer to moles of 1. D and DL are a-dimensional. The titration experiments were performed at 33. For 2, 3 and 5 the solvent was carbonate buffer 1 mm, ph 1.3. b alculated with equation (5), entering D as fixed parameter calculated from the fitting of the UV-vis data. c. alculated from the fitting of the UV-vis data in absence of ligand. Variations of the D values determined from different experiments are attributed to small errors in lipid concentration inherent to the preparation of the samples (see methods section for details). d alculated using equation (6) e alculated by fitting the UV-vis data in presence of an excess of ligand. lustering-binding model In a rigorous notation, the clustering equilibrium should be expressed as 1 n n +1 (S1) where 1 n is the clustered form when n 2, and D when n = 1. As we have seen (equation (3)) the clustering constant D can be expressed as a function of, D and the ratio of lipids, R L, and, since [R L ] >> [] and [R L ] >> [D], this expression is identical to that of a 1:1 binding equilibrium, where R L is a pseudo-specie that binds to form the complex D. This form of the clustering equilibrium allows the use of the bulk concentrations of and D, rather than the in-membrane concentrations. In doing so, we reduce considerably the complexity of the model, especially when analysing the clustering in combination with other binding processes that take place in solution. Therefore, we can express all the chemical equilibria relating the clustering and binding as 1:1 association equilibria in solution: + R L D (S11) + L L (S12) D + L D L (S13) L + R L D L (S14) nature chemistry Macmillan Publishers Limited. All rights reserved.

8 supplementary information doi: 1.138/nchem.892 with association constants 1/ D,, and 1/ DL respectively. Note that (S14) (and the corresponding association constant 1/ DL ) are a combination of the other equilibria (and binding constants, see equation (6)). The three independent binding constants 1/ D, and D can be simultaneously determined from the changes in observed absorbance (A o ) by solving the system of equations defined by the mass balances and binding constants: 1 [ D] = (S15) [ ] D R L D [ L] = (S16) [ ][ L] [ D L] = (S17) [ D][ L] [ L ] = [ L] + [ L] + [ D L] (S18) [ 1 ] = [ ] + [ D] + [ L] + [ D L] (S19) A o = D L ε D L ε [ ] + ε [ D] + ε [ L] + [ D L] (S2) The fitting parameters are the binding constants (1/ D, and ) and the extinction coefficient of the each specie (ε, ε D, ε L and ε D L ) at the observed wavelength. This system of equations can not be resolved analytically. Instead, a minimization routine is needed to find the fitting parameters. We use the program Specfit 3. (see ref 34) for this purpose (Table 1, Fig. 3c, Supplementary Fig. 5; see Equipment and Settings section for details), which is capable of fitting a large set of data, including multiple wavelengths, simultaneously and quickly. The program returns a value of extinction coefficient for each of the wavelengths entered, allowing to reproduce the UV-vis spectra of the pure species (Fig. 3d and Supplementary Fig. 6). The program also allows determining the full speciation profile (e.g. the percentage of a certain specie; for example in our case the percentage of clustered specie) of a system subjected to clustering and binding processes (Fig. 4c-e). 8 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

9 doi: 1.138/nchem.892 supplementary information Supplementary Figure 5. Fitting to the clustering-binding model. hanges in absorbance around the maximum of 1 s Soret band (427 to 43 nm, where changes in absorbance are more pronounced, see Supplementary Table 2), upon increasing R L and the concentration of ligand (dark spheres). The white surface is the best fit to the clustering-binding model (using Specfit 3.), and represents the changes in absorbance with R L and [L] as defined by the clustering and binding constants and the values of the extinction coefficient of the pure species. nature chemistry Macmillan Publishers Limited. All rights reserved.

10 supplementary information doi: 1.138/nchem.892 Supplementary Table 2. hanges in absorbance in Fig. 3c and Supplementary Fig 5. Fig. [1] (µm) a λ (nm) b Min. Abs c Max. Abs d - A Fig. 3c Sup. Fig. 5a Sup. Fig. 5b Sup. Fig. 5c Sup. Fig. 5d Sup. Fig. 5e Sup. Fig. 5f a Bulk concentration of 1 used in the experiment. b Wavelength used in the figure c Value of absorbance in the farthest corner of the figure, i.e., at lowest R L and highest L. d Value of absorbance in the closest corner of the figure, i.e. at highest R L and L=. e Total change in absorbance observed in the experiment at the specified wavelength. 1 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

11 doi: 1.138/nchem.892 supplementary information Supplementary Figure 6. Soret band region of the UV-vis spectra for the pure species derived from the global fitting procedure, using Specfit 3.. For 8 the spectra of the L specie returns some negative values. For this ligand the percentage of L formed at any moment during the titrations is very low, and the determination of the corresponding spectrum is subject to a large uncertainty. nature chemistry Macmillan Publishers Limited. All rights reserved.

12 supplementary information doi: 1.138/nchem.892 Full Methods General. hemicals and solvents were obtained from commercial sources and used without further purification. UV-vis absorbance spectra were recorded with a Thermoelectron orporation UV1 Thermospectronic UV-vis spectrometer. Fluorescence spectra were recorded with a F7 Hitachi spectrophotometer. Size exclusion LPL experiments where performed on a self-packed glass column (Pharmacia), using sepharose 4B as stationary phase. The column was attached to a Gilson 3 series HPL setup and run at low pressure. Liposome preparation. A stock solution of lipids was prepared by dissolving synthetic dimyristoylphosphatidylcholine (DMP) and cholesterol in a 8:2 molar ratio DMP/holesterol in ethanol, with a concentration of 2 mmol/l. A stock solution 1 in ethanol with a concentration 1 mm was also prepared. To prepare the liposomes, lipid and 1 stocks were mixed in the appropriate proportions. The bulk of the solvent was removed under a nitrogen steam and traces of solvent removed under vacuum for a minimum of 1 hours. The solid was then re-suspended in the appropriate buffer by vortexing during 2 minutes. Excess of air and foam in the suspension were removed by sonicating the vortexed sample for 2 seconds in an ultrasound bath. The suspension was then extruded (Avanti Mini-Extruder) through 2 nm pore-size polycarbonate filters a minimum of 31 times. The resulting vesicle suspension was used within 24 hours of preparation (for buffers at ph 7.2) or within 6 hours of preparation (for buffers at a ph 7.2), to minimize distortions due to the presence of lyso-phospholipids from hydrolysis of the DMP. Receptor clustering experiments. In a typical experiment, 15 samples of 1 doped liposomes were prepared separately, each using 4 µl of 1 stock and the appropriate amount of lipid stock to yield liposomes with R L values covering the range from 1 to 5. The samples were prepared following the procedure described in the liposome preparation section, adding 2 ml of the appropriate buffer to yield the vesicular suspensions. Before extrusion, the concentration of 1 in the suspensions was 2 µm and the concentration of lipids ranged from 2 µm up to 1 mm. Upon extrusion the polycarbonate filter was stained by 1, indicative of the lost of a small part of 1 during the extrusion process. The concentration of 1 was therefore re-measured by UV after extrusion, by diluting 5 ml of each sample with 5 ml of a solution of Triton X-1 5%, which yields samples of 1 of known extinction coefficient (39 cm -1 mol -1 ). The potential loss of lipid during the extrusion process was monitored by comparing the intensity of the scattering band at 3 nm in the fluorimeter against samples of known lipid concentration. No loss was detected using this method. Small loses however can not be completely discarded, and to this non-quantified factor is attributed the variability in the clustering constant from experiment to experiment (see table 2, main text). To 12 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

13 doi: 1.138/nchem.892 supplementary information carry out the clustering experiment, each extruded sample was diluted with the appropriate buffer to a concentration 1 µm in 1, incubated for a minimum of 1 hour at 3 o and the UV spectrum in the Soret band region at 3 o was recorded. Alternatively, the samples were diluted down to.2 µm 1, incubated for a minimum of 1 hour at 3 o and the fluorescence excitation spectra in the Soret band region at 3 o (emission 62 nm) was recorded. Titration experiments. Samples of liposomes doped with 1 were prepared following the procedure described in the liposome preparation section. In a typical titration experiment 6 µl of 1 stock together with the appropriate amount of lipid stock were evaporated. The sample was suspended in 2 ml of the appropriate buffer and extruded, yielding a vesicular suspension 15 µm in 1 approx. (the precise concentration of 1 was determined using the method described above).this sample was used as a secondary stock to prepare 15 samples 1 µm in 1 with increasing concentrations of ligand. These samples were incubated at 3 o for a minimum of 1 hour and then the UV spectrum at 3 o was recorded. Titration experiments were performed over liposomes with a composition ranging from R L = 1 up to R L = 5 for every ligand. For internal consistency, the clustering constant used for the global fitting of each ligand was the clustering constant calculated from fitting the initial point ([L] = ) of each titration to the clustering isotherm (see table 2). Gel permeation chromatography (GP) experiments. Samples were prepared as described for the clustering experiments, with R L ranging from to 5. We used a self-packed glass column (Pharmacia), loaded with Sepharose 4B as stationary phase (1 1 cm bed size). 1mL of each sample was injected and eluted with buffer phosphate 1 mm, ph 7.2 and the chromatogram recorded using a UV detector at 43 nm. After recording the chromatogram (3 minutes) the column was washed with a mixture buffer/ethanol 8:2 for 1 minutes and then pure buffer for a further 1 minutes, before another sample was injected. ryo-tem experiments. Samples containing liposomes ( R L = 1 and R L = 1) were prepared as described above, using the appropriate amounts of 1 and lipid stocks. The final concentrations were 2 µm of lipids in both samples and 2 µm of 1 for R L = 1 and 2 µm of 1 for R L = 1, both in buffer phosphate 1 mm, ph 7.2. The sample containing only 1 (R L = ) was prepared by evaporating the appropriate amount of 1 stock and suspending it in buffer phosphate 1 mm, ph 7.2 (vortex mixer, 2 minutes) to a concentration of 1 2 µm. Samples (3.5 µl) were loaded on freshly discharged (6 s) holey carbon Lacey grids (S166-3; Agar Scientific). The grids were blotted and plunged into liquid nitrogen cooled liquid ethane to embed the samples in vitreous ice. Low dose images were recorded on a 4,96 x 4,96 charge coupled device (D) Gatan camera at a nature chemistry Macmillan Publishers Limited. All rights reserved.

14 supplementary information doi: 1.138/nchem.892 magnification of 1, and between 1 and 3 µm underfocus with a Tecnai F2 FEG electron microscope operated at 2 kv and equipped with a Gatan cold stage. Equipment and settings. In addition of the equipment and settings mentioned in the full methods section, the following procedures were followed in generating the display figures used in this work. GP traces and deconvolution (figure 2a): Raw chromatograms (ASII format) were loaded onto the program PeakFit v4.12. The chromatogram was then deconvoluted to a minimum number of peaks (i.e. with r 2.99) using a half-gaussian modified Gaussian function, allowing for peak tailing. ryo-tem images (figure 2b): Sections of the micrograph containing the relevant feature (i.e. a liposome) were cut and edited with the program Gimp The contrast of the image was then increased in order to make the features visible when using a small sized picture. UV spectra (figures 3a and 3b): The spectra of all the samples between 36 and 54 nm was recorded. In all the cases, the absorbance of the Soret band is located between 385 and 465 nm. In the rest of the acquired range 1 does not absorb. Therefore the data between and was used to re-construct the baseline due to the light scattering of the liposomes, fitting a third polynomial function, and this baseline was subtracted from the relevant spectra. The corrected spectra were used for display purposes (figures 3a and 3b) and also for the determination of the binding and clustering parameters. For these calculations, the corrected spectra from 37 to 48 nm was entered in the program Specfit 3.. lustering-binding data fitting (Figs 3c and 3d, Supplementary Figs 5 and 6): all the corrected spectra for a given ligand at different values of R L and [L] were entered in the program Specfit 3.. Specfit uses a Newton-Raphson method to determine the speciation and the stability constants for systems with up to 4 titrable components. The extinction coefficients of the pure species are also determined from the fitting of the data. We use a model with three titrable species, X, Y and Z, and define the appropriate complexes as combinations of these three species. The relationship of these species with the species used in this work is: X = Y = L (S21) (S22) and 14 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.

15 doi: 1.138/nchem.892 supplementary information Z = R L. (S23) and the complexes are: X Y = L X Z = D (S24) (S25) and X Z Y = D L (S26) Thus, the stability constants directly determined by Specfit are: X [ X Y ] Y = (S27) [ X ][ Y ] X [ X Z] Z = (S28) [ X ][ Z] and X [ X Z Y ] Z Y = (S29) [ X ][ Z][ Y ] The desired clustering and binding constants displayed in Table 1 were calculated from these constants as follows: = (S3) X Y D = 1 X Z (S31) D X Z Y = (S32) X Z and DL as combination of the other constants as follows: D D DL = (6) nature chemistry Macmillan Publishers Limited. All rights reserved.

16 supplementary information doi: 1.138/nchem.892 X Z (and therefore D, see equation (S31)) was determined from the spectra of membrane embedded 1 in absence of L. This value was used as a fixed parameter during the global fitting procedure. The fitted parameters were therefore the extinction coefficient of all the species at each wavelength and the constants X Y and X Z Y. The parameters where not constrained. We judged a fitting acceptable if the program was able to find a global minima during the fitting procedure and if the standard deviation of logarithmic form of the constant was lower than.6, i.e., less 15% of the stability constant. In order to construct Supplementary Fig. 5 and Fig. 3c, we selected the experimental values of absorbance at the wavelength of maximum variation during the experiment (between 427 to 43 nm, depending on the ligand used) and the theoretical values of absorbance calculated using the parameters determined in the fitting procedure. The experimental data were represented in the figure as dark spheres; the calculated data were used to define the white semitransparent surface. The figure was constructed using the program PovRay v3.6. The fitting of the data in Specfit returns the extrapolated spectra of the pure species between 37 and 48 nm, and these were used in Fig. 3d and Supplementary Fig. 6. lustering landscape modulation (Figs 4c-e): The program Specfit 3. was use to calculate the percentage of clustered species ( and L) upon variation of [L] and R L for a known set of clustering and binding parameters. The data were entered in the program PovRay v3.6, and the figure constructed, using the percentage of clustered receptor to define a surface. 16 nature chemistry 21 Macmillan Publishers Limited. All rights reserved.