**2. Results**

In order to quantify the affinity between tBid and Bax, we incubated SLB of mitochondrialike composition with purified full-length tBid (labelled with Alexa647) and purified full-length Bax (labelled with HyLite488), at concentrations low enough to achieve singleparticle detection. Separate controls were also carried out where the membrane was either incubated with tBid alone or Bax alone. Dual-color confocal image stacks were recorded for each sample, and analyzed in order to extract two-dimensional dissociation constants for different categories of proteins. In the next three sections, we explain how the proteins were detected and classified according to their mobility, how they were further classified according to their stoichiometry, and finally how interactions between tBid and Bax were identified and characterized.

#### *2.1. Different Membrane Conformations Are Detected for tBid and Bax Based on Their Mobility*

It is well established that tBid and Bax can each adopt different conformations when interacting with a lipid membrane [29]. Proteins with different conformations may have different mobilities, resulting in distinct signatures in both widefield [44] and confocal images [29,45]. We thus looked to classify particles detected in our confocal images according to their mobility.

#### 2.1.1. Signature of Stationary and Mobile Particles in Confocal Images

We performed simulations to establish the link between particles' apparent shape in confocal images and their mobility. We simulated the two-dimensional diffusion of particles with varying mobilities and molecular brightness, and the acquisition of confocal images using conditions similar to those typically used in our experiments (confocal detection volume radius *w*0 = 300 nm, pixel size *d* = 100 nm, pixel dwell time *δ* = 1 ms). Examples of simulated images for both completely stationary particles and diffusing particles ( *D* = 2 μm<sup>2</sup> s<sup>−</sup>1) can be seen in Figure 1. Events can easily be detected in both cases, but their appearance is strikingly different: diffraction limited spots for stationary particles and single line streaks along the scanning direction for diffusing particles (as previously observed for both proteins and lipids in SLB [29,46]).

The single particle detection procedure described in the Methods section was applied to multiple series of simulated images of either stationary or diffusing particles (noise images were also analyzed for comparison). For each detected event, this procedure returns the radii of the 2D-Gaussian spot that best fit the particle (Equation (4)), *wx*,*<sup>p</sup>* along the scanning direction and *wy*,*<sup>p</sup>* perpendicular to it, as well as the intensity of the particle, *Ip*. By inspecting the eccentricity maps (two-dimensional distributions of particle radii, shown in Figure 1), multiple clusters can be identified. In images containing only background photon noise (Figure 1a), only single pixel events concentrated in a small region centred around *wx*,*<sup>p</sup>* ≈ *wy*,*<sup>p</sup>* ≈ *d* = 100 nm are detected, as expected since photon noise is not spatially correlated. (There is both a horizontal gap and a vertical gap around ≈50 nm, the result of the instability of the Gaussian fitting of a signal detected in a single pixel.) Stationary particles (Figure 1b) appear as a cluster of diffraction-limited events around *wx*,*<sup>p</sup>* ≈ *wy*,*<sup>p</sup>* ≈ *w*0 = 300 nm and *Ip* ≈ *B* = 20 kHz. They are well separated, both by their dimensions and intensity, from events due to noise, also detected in this case. We thus decided to classify events as stationary particles if they were found within a distance *w*0/2 of their expected position (*<sup>w</sup>*0, *<sup>w</sup>*0) on the eccentricity map. For diffusing particles (Figure 1c), the eccentricity map shows an extended cluster of events with *wy*,*<sup>p</sup>* < *w*0/2 = 150 nm and *Ip* around or below *B* = 20 kHz. The distinction between diffusing and stationary particles, based on their shape, is therefore straightforward in this case. However, the distinction between noise and diffusing particles is not, as the distributions of these two types of events overlap, both on the eccentricity map and on the intensity map. As a compromise between false positive and false negative detection, we decided to classify events as mobile particles only if *wy*,*<sup>p</sup>* < *w*0/2 and *wx*,*<sup>p</sup>* > 1.2 *d* = 120 nm. In these conditions, noise events

only contribute a maximum of 10% of the mobile particle detection events, which was judged acceptable.

**Figure 1.** Confocal image simulations for (**a**) background Poisson noise (*iB* = 1.3 kHz), (**b**) stationary particles (*B* = 20 kHz) and (**c**) mobile particles (*D* = 2 μm<sup>2</sup> s<sup>−</sup>1, *B* = 20 kHz). For each condition, a single image section is shown as an example (top panel), as well as the particle size distribution (eccentricity map) generated from the analysis of a large number of such images (middle panel), and the relationship between particle width and intensity (bottom panel). In the eccentricity map in (**a**), the dashed lines indicate the position of the two peaks corresponding to spurious photon noise events. In (**b**), the dashed lines show the expected dimensions of an immobile particle (*<sup>w</sup>*0 both along and perpendicular to the scanning direction), and the circle delimitates the area in which particles are considered "spots". In (**c**), the rectangle delimitates the area in which the particles are considered "streaks". In the bottom panels in (**b**,**<sup>c</sup>**), the dashed line indicates the value of the molecular brightness, *B*.

To further characterize the mobility of the diffusing particles, we considered the length and eccentricity of the streaks, which depend on the particles' trajectory during the imaging, and therefore on their mobility [47]. Simulations (Figure 2) show that the average streak length, *wx*,*<sup>p</sup>*, decreases as *D* increases, while the average eccentricity, *wx*,*<sup>p</sup>*/*wy*,*<sup>p</sup>*, first increases from 1 to 2*w*0/*d* = 6, then decreases. For *D* > 20 μm<sup>2</sup> s<sup>−</sup>1, particle events become difficult to separate from noise events, as the lengths of the streaks shorten. The time needed to image a full line in the confocal image is *nxδ* = 0.1 s in the conditions of our experiments, thus the time necessary to capture a stationary particle is *nxδ* × *w*0/*d* = 0.3 s. The cut-off between particles appearing as "spots" and "streaks" should occur when they are able to diffuse over a distance *w*0 during that time, in other words when *D* > *Dc* = *w*20/(<sup>4</sup>*nx<sup>δ</sup>* × *w*0/*d*) = 0.08 μm<sup>2</sup> s<sup>−</sup>1. This is indeed what is observed in our simulations (Figure 2a). Thus, the classification method introduced here allows, in the conditions of our experiments, sorting events into "stationary" proteins (*D* 0.1 μm<sup>2</sup> s<sup>−</sup>1) and "mobile" proteins (*D* 0.1 − 20 μm<sup>2</sup> s<sup>−</sup>1).

**Figure 2.** Influence of particle diffusion coefficient on the appearance of events detected in simulated confocal images. Simulation parameters were otherwise the same as in Figure 1. (**a**) Distribution of *wx*,*<sup>p</sup>* and *wy*,*<sup>p</sup>* values for particles with different diffusion coefficients (red: 0 μm<sup>2</sup> s<sup>−</sup>1, blue: 0.1 μm<sup>2</sup> s<sup>−</sup>1, green: 1 μm<sup>2</sup> s<sup>−</sup>1, yellow: 2 μm<sup>2</sup> s<sup>−</sup>1, purple: 10 μm<sup>2</sup> s<sup>−</sup>1). (**b**) Average streak length and (**c**) average eccentricity of all events with *wx*,*<sup>p</sup>* > 120 nm (error bars are the standard deviation) as a function of diffusion coefficient. The dashed line and the grey area represents the values obtained for stationary particles.

#### 2.1.2. tBid and Bax Mobility in the Mitochondria-Like SLB

We applied the single particle detection and classification method outlined in the previous section to a set of 258 dual-color confocal images of SLB incubated successively with 0.2 nM tBid-Alexa647 and Bax-HyLite488 at concentrations ranging from 0.1 to 2 nM (see Methods for experimental details). An example of a pair of such images (green and red detection channels) can be seen in Figure 3a, where detected events are marked with a box (a number of detection events are rejected, either because they are too close to the border or to another already detected event, because they cannot be correctly fitted by a Gaussian, or because they have an intensity below the set threshold intensity). In these images, both spots and streaks are observed, indicative of the presence of both stationary and mobile proteins. Accordingly, the corresponding eccentricity maps show particles both in the mobile and stationary particle regions (Figure 3b). The number of particles detected per frame varied only slightly across conditions, and was roughly the same for both proteins (SI Figure S2). In each channel, we detected on average 5 to 10 mobile particles per frame, significantly more than stationary particles, found at a rate of 1 to 3 particles per frame. Even including poorly defined particles rejected from the final analysis, the total number of detected particles remained on average below 30 per frame and per channel, i.e., below a concentration of 0.3 particles/μm2. For both Bax and tBid, our data thus indicates the presence of at least two different types of membrane conformation—an abundant highly mobile form and a rarer stationary form. When the same experiment was repeated with tBid alone, both mobile and stationary particles were also observed in the membrane, as we already reported in Ref. [29]. In contrast, when the experiment was repeated with Bax alone, no particles could be detected at the membrane (even at the highest 2 nM Bax concentration used for incubation, see SI Figure S3), highlighting the important role played by tBid in retaining Bax at the membrane in this reconstituted system.

**Figure 3.** Event detection for confocal images of SLB incubated with tBid-Alexa647 and Bax-HyLite488. (**a**) Representative example of a section of a pair of confocal images (left: green detection channel, right: red detection channel) acquired for a SLB incubated successively with 0.2 nM tBid-Alexa647 and 1.0 nM Bax-HyLite488. Black boxes highlight all the events detected in these images. (**b**) Eccentricity maps and (**c**) intensity maps obtained for the entire set of 258 images acquired (regardless of Bax concentration). Solid lines delimitate the regions used to classify the particles as stationary or mobile, considering *w*0 = 280 nm (green channel) or *w*0 = 320 nm (red channel). The distributions of observed *wx*,*<sup>p</sup>* and *wy*,*<sup>p</sup>* values are given in (**d**) for stationary particles and in (**e**) for mobile particles (green lines and bars: Bax, red lines and bars: tBid).

Stationary Bax-HiLyte488 have an average apparent radius *wx*,*<sup>p</sup>* = (280 ± 60) nm (mean ± stdv), 10 to 20% smaller than that of stationary tBid-Alexa647 ( *wx*,*<sup>p</sup>* = (360 ± 50) nm), as expected given the difference in excitation and detection wavelengths between the green and red channels, and in each case close to the radius of the confocal observation volume measured by FCS. Of note, the distributions of values for *wx*,*<sup>p</sup>* and *wy*,*<sup>p</sup>* obtained for stationary Bax and tBid (Figure 3d), while clearly belonging to a well-defined population, are more spread out than that obtained in simulations (Figure 1b), and the average eccentricity of these particles is slightly above 1 ( *wx*,*<sup>p</sup>*/*wy*,*<sup>p</sup>* = 1.1 for Bax and 1.2

for tBid). Thus, "stationary" tBid and Bax particles might include particles with a small mobility, on the order of 0 to 0.1 μm<sup>2</sup> s<sup>−</sup><sup>1</sup> (other effects, such as photobleaching, could also explain this slight eccentricity).

For mobile particles, the distribution of detected shapes, as seen in the eccentricity maps (Figure 3b), and the distributions of *wx*,*<sup>p</sup>* and *wy*,*<sup>p</sup>* values (Figure 3e), are also as expected from the simulations. From the average length of these streaks ( *wx*,*<sup>p</sup>* = 250 nm for Bax and 280 nm for tBid) and their average eccentricity ( *wx*,*<sup>p</sup>*/*wy*,*<sup>p</sup>* = 4.4 for Bax and 4.9 for tBid), which can be compared to that obtained for simulated particles with different mobilities (Figure 2), we conclude that the mobile membrane fractions of both tBid and Bax have diffusion coefficients on the order of 10 to 20 μm<sup>2</sup> s<sup>−</sup>1, corresponding to protein configurations only loosely associated with the membrane (since they are faster than lipids, which in SLB have diffusion coefficients in the 1 to 5 μm<sup>2</sup> s<sup>−</sup><sup>1</sup> range [48–50]).

#### *2.2. tBid and Bax form Oligomers at the Membrane*

Because of photon noise, and because of eventual motions during imaging, the intensity of an event may not be equal to the particle molecular brightness (see Figure 1b,c, bottom panels). Simulations of stationary particles for different values of the brightness *B* (and at a concentration of 20 particles per image, comparable to those encountered in our experiments), do show that the distribution of intensities for detected particles is usually quite narrowly peaked around *B* (Figure 4a). For low intensity particles, for which the fixed detection threshold becomes on the order of *B*, the intensity distribution becomes broader and is centred slightly above *B* (Figure 4a, left panel). However, as the mobility of the particles increases, the centre of the distribution shifts from *B* towards lower values (Figure 4a, right panel). In stark contrast, the distribution of intensities for recorded images of tBid and Bax is very broad, in some cases with visible peaks at intensities that are much larger than *B* (Figures 3c and 4b), as was previously observed for both proteins separately [29,30]. These extended distributions are consistent with the presence of oligomers, with intensities representative of the number of monomers it contains (barring issues with incomplete labelling or photobleaching). When comparing the size distribution of the tBid oligomers observed in the presence of Bax (Figure 4b, lower panels) with that observed in the absence of Bax (as reported in Ref. [29]), the only visible difference is a slight shift of the distribution towards smaller size oligomers in the presence of Bax.

We first concentrate on the distribution of intensities for stationary tBid and Bax (Figure 4b, left panels, in which the results of all our experiments are congregated regardless of Bax concentration). Detected event intensities have been normalized by the known intensity of the monomer, which was separately measured before each experiment using fluorescence correlation spectroscopy (FCS), and found to be on average *B* = 13 kHz for cBid-Alexa647 and *B* = 7.6 kHz for Bax-HyLite488. For both tBid and Bax, we see a peak around a normalized intensity of 1 (corresponding to particles with brightness *B*) followed by a series of harder to distinguish peaks going up to a normalized intensity of about 10. Intensity bins of width 1 and centred on integer values (corresponding to *B* = 1, 2, etc.) were used to sort the data into putative monomers, dimers, etc. Although this classification is not very precise (because of day-to-day variation in the value of *B*, incomplete labelling and photobleaching), it allows us to conclude that, for both proteins, there is a broad distribution of stationary oligomers up to the tetramers, with rarer oligomers as large as decamers.

The distribution of intensities for mobile particles is noticeably different than that of stationary particles, with a shorter tail at higher intensities (Figure 4b, right panels). Since these particles have a diffusion coefficient around 10 to 20 μm<sup>2</sup> s<sup>−</sup>1, our simulations show that an oligomer with brightness *nB* should have an intensity around 0.7 nB (Figure 4a, right panel). The abundance of different mobile oligomers was therefore estimated by binning the distributions of normalized intensities into bins of width 0.7 centred around multiples of 0.7. For both tBid and Bax, the proportion of low stoichiometry detections is higher for mobile particles than for stationary particles. This is true even if, for mobile

particles, the intensity threshold (*B*/2) is close to the centre of the monomer bin, meaning that a significant number of mobile monomers must go undetected. This suggests that oligomer immobilization in the SLB, which is probably due to deeper insertion into the lipid bilayer, tends to be associated with larger stoichiometries (in agreemen<sup>t</sup> with previous observations for tBid [29]).

**Figure 4.** Intensity distribution and stoichiometry of detected events. (**a**) Intensity distributions for events detected in simulated confocal images for either stationary particles with different brightness (left panel) or particles with brightness *B* = 20 kHz and different diffusion coefficients. (**b**) Intensity distributions for events detected in confocal images of SLB incubated with tBid-Alexa647 and Bax-HyLite488, classified for each protein into stationary and mobile particles (regardless of Bax concentration). All intensities have been normalized by the known particle brightness of the monomer. The experimental distributions are binned in two different ways, with a small bin width of *B*/4 for visualization (orange bars) and with a larger bin width of *B* or 0.7*B* for stationary and mobile particles, respectively, representing the expected apparent brightness of a monomer for these two types of particles (blue bars). The coarse binning thus provides an estimate of the relative abundance of different protein stoichiometry. In (**<sup>a</sup>**,**b**), the dashed vertical bars indicate the threshold intensity used for particle detection. (**c**) Oligomer frequency versus Bax-HyLite488 concentration (for a constant 0.2 nM tBid-Alexa647 concentration).

Looking at relative oligomer abundance as a function of the concentration of Bax incubated with the SLB (Figure 4c), and focussing on the mobile particles which are more abundant and for which we have better statistics, shows that in all the explored experimental conditions, Bax was active enough and concentrated enough to form oligomers with a size (tetramer) generally considered large enough to constitute a pore [51]. A slight decrease in the concentration of low stoichiometry Bax oligomers (monomers and dimers), at the profit of larger size oligomers, can be seen when Bax concentration is increased (no discernible change in oligomer composition can be detected for tBid).

#### *2.3. Quantification of the Interaction between tBid and Bax*

Two-channel confocal images hold information about potential molecular interactions via the colocalization of events detected in both channels. A difficulty in positively identifying interactions is that particles might coincidentally be located within the same pixel. To avoid this issue, we have previously proposed the use of a quantity called the

particle cross-correlation coefficient, *χ*, calculated as the spatial cross-correlation between the fluorescence intensity fluctuations recorded in both channels over a small region around the particle (see the Methods section for details) [33]. For perfectly co-localized particles, we expect *χ* = 1, while for distant particles *χ* = 0. Here we explore the sensitivity of *χ* on the distance between particles through simulations, before using it to detect interactions between tBid and Bax particles.

#### 2.3.1. The Particle Cross-Correlation Coefficient Decreases with the Distance between Particles

Particle tracks and dual-channel confocal images were simulated for pairs of particles (one in the green detection channel, with *<sup>w</sup>*0,*g* = 320 nm, and one in the red detection channel, with *<sup>w</sup>*0,*r* = 370 nm). The position of the two particles was either completely independent or offset by a fixed value Δ*<sup>r</sup>*, and the particles were either mobile or stationary. For each condition, 100 pairs of confocal images (each containing 14 to 20 particles) were generated. Images were analyzed as described above, and for each detection event in the first channel, *χ* was calculated (Equation (5)). For exactly co-localized particles (Δ*r* = 0), the obtained values of *χ* are peaked around 1, but when Δ*r* is increased, the average value of *χ* decreases continuously, down to *χ*¯ 0 as Δ*r* reaches *w*0 0.35 μm, and below 0 to a minimum of *χ*¯ −0.2 for Δ*r* 2*w*0 (Figure 5a). For larger separations *χ*¯ goes back to 0. In addition, the distribution of values for *χ* broadens when Δ*r* increases. A decrease in molecular brightness (corresponding to an increase in photon noise), also results in a broadening of the peak, but not in a shift of the peak position, as expected since the systematic effect of photon noise is corrected for when calculating *χ* (data not shown). Thus, the average value of *χ* reflects the distance between the particles when it is below the diffraction limit. Similar conclusions are obtained from the simulation of mobile particles (data not shown).

**Figure 5.** Distribution of particle cross-correlation coefficients obtained for simulated two-channel confocal images. (**a**) Particle cross-correlation distribution for particles separated by a fixed distance Δ*<sup>r</sup>*. (**b**,**<sup>c</sup>**) Effect of increasing the particle concentration in the second channel for randomly placed particles, either stationary (**b**) or mobile (**c**). The lower panels in (**b**,**<sup>c</sup>**) give the frequency of accidentally correlated (*χ* > 0.3 and *χ* > 0.5) and anti-correlated (*χ* < −0.3 and *χ* < −0.5) events. All distributions show the cross-correlation of the particles detected in the green channel. Grey vertical lines in (**b**,**<sup>c</sup>**) lower panels indicate the experimental conditions.

As the issue of accidental co-localization becomes more preponderant at high surface concentration of particles, we also performed simulations where the concentration of the particles in the second channel was increased up to 200 particles per image (2 particles per μm2). When particles in both channels are stationary (Figure 5b), the fraction of particles for which *χ* > 0.3 increases up to 14%, as more particles in the second channel accidentally co-localize with detected particles in the first channel. Interestingly, this is accompanied by a comparable increase in the fraction of particles with *χ* < −0.3, as some of the particles in the second channel happen to be within a distance *w*0 to 2 *w*0 of the detected particles. Similar results are obtained when the particles in the second channel are mobile, except that the frequency of accidental co-localizations is slightly lower (SI Figure S4). Thus, accidental co-localizations, when the detected particles are immobile (and regardless of whether the particles in the second channel are mobile or immobile), have a characteristic signature which is different from that of true colocalization events (which never result in *χ* < −0.3).

The situation is different when the detected particles are mobile (Figure 5c), since in that case accidental co-localizations (i.e., events with high *χ*) are much less likely to occur, even at high surface concentration of particles in the second channel. This is both because events have a smaller footprint and because each mobile particle has a unique trajectory and therefore a unique shape in the confocal image, which is unlikely to be accidentally matched by that of another particle. Calculating the particle cross-correlation coefficient is therefore especially interesting in this case. In our experimental conditions (mobile particle concentration of 0.15 particles/μm2), we expect accidental co-localizations to occur for only 4% of events (if choosing *χ* = 0.3 as the detection threshold) or 1.7% of events (if choosing *χ* = 0.5 as the detection threshold).

#### 2.3.2. Co-Localization of tBid and Bax

The result of the particle cross-correlation analysis applied to the set of confocal images acquired for SLB incubated with tBid-Alexa647 and Bax-HiLyte488 is shown in Figure 6, where the distributions shown are aggregated data for all the Bax concentrations studied. All these distributions (whether the particles are detected in the tBid or the Bax channel, and whether particles are stationary or mobile) show a dominant narrow peak exactly centred at *χ* = 0 (corresponding to a large population of non-interacting particles), a second smaller peak centred at *χ* = 0.3–0.5 (corresponding to a population of particles with significant cross-correlation with a particle in the other channel), and a few rare events with *χ* > 0.5 (corresponding to particles positively bound to a particle in the other channel). Almost no events with clear anti-correlation ( *χ* < −0.3) are detected.

Concentrating first on stationary particles (Figure 6, two left panels), we see that the number of positively correlated events is above the expected maximum number of false positives (lower panels), both when considering all events together, and when separating them into different stoichiometries. In addition, since these positively correlated events are not accompanied by any negatively correlated events, they do not fit the pattern expected for accidental co-localizations. We therefore considered all stationary events with *χ* > 0.3 as corresponding to tBid-Bax complexes.

In the case of mobile tBid oligomers, the frequency of positively correlated events (whether they are defined as *χ* > 0.3 or *χ* > 0.5) is significantly larger than what would be expected for accidental co-localizations (Figure 6, right panels), and becomes very substantial for larger oligomers. The case is not as clear cut for mobile Bax oligomers, as the levels of detected positively correlated events are very close to the maximum expected level for accidental co-localizations, except for larger Bax oligomers where an above-background positive correlation is clearly seen. We note that when separating the data according to the Bax concentration used for incubation, no obvious trend was observed (SI Figure S5). For mobile particles, we conservatively estimated the number of tBid-Bax complexes by subtracting the maximum number of accidental co-localizations from the number of mobile events with *χ* > 0.3.

**Figure 6.** Particle cross-correlation coefficients measured for stationary and mobile tBid and Bax oligomers. (**a**) Crosscorrelation coefficient distributions for all oligomers. The light grey areas correspond to slight cross- or anti-correlation (0.3 < *χ* < 0.5 or −0.5 < *χ* < −0.3) and the dark grey area highlights strong cross-correlation (*χ* > 0.5). (**b**) Fraction of correlated particles (*χ* > 0.3, upper panels, triangles and dashed lines) and strongly correlated particles (*χ* > 0.5, lower panels, squares and continuous lines) in each oligomer class. The highlighted areas show the absolute maximum amount of accidental positive correlations to be expected given a particle concentration similar to that observed in experiments (0.05 particles/μm<sup>2</sup> for stationary particles and 0.15 particles/μm<sup>2</sup> for mobile particles), as obtained from the simulations shown in Figure 5b,c. In each panel, the fraction of detected anti-correlated particles (*χ* < −0.3 or *χ* < −0.5) are also shown (X symbols and dotted lines). (**c**) Representative examples of detected particle pairs with either slight or strong correlation. The shown particle cross-correlation coefficient is the one calculated for the green particle.

#### 2.3.3. Dissociation Constant of tBid-Bax Complexes

The two-dimensional dissociation constant for tBid and Bax (2*D* − *KD*), was obtained using either the tBid or the Bax channel to detect complexes, and for particles with different mobilities or stoichiometries. The 2*D* − *KD* was calculated from the observed surface concentrations of non-interacting particles (*<sup>c</sup>*Bax and *c*tBid with *χ* < *χ*tresh) and of interacting complexes (*<sup>c</sup>*Bax-tBid, calculated from the number of events with *χ* > 0.3 in the considered channel, and in the case of mobile tBid subtracting the maximum number of accidental co-localizations predicted from simulations), using Equation (7). Dissociation constants have the dimension of a concentration, thus the 2 *D* − *KD* has the dimension of a surface concentration. When considering all membrane species of tBid and Bax (mobile and stationary, regardless of stoichiometry and initial Bax concentration), we find an apparent dissociation constant 2 *D* − *KD* = 1.1 μm<sup>−</sup>2. However, separating the data into mobile particles (using the tBid channel to detect complexes) and stationary particles (using either the tBid or the Bax channel to detect complexes) show that the nature of that equilibrium changes significantly when the proteins change conformation: the complex is much more stable for stationary (membrane-inserted) proteins (2 *D* − *KD*,stationary = 0.1 μm<sup>−</sup>2) than for mobile (loosely-bound) proteins (2 *D* − *KD*,mobile = 1.6 μm<sup>−</sup>2).

In contrast, we see no significant change in the dissociation constant when considering samples incubated with different Bax concentrations, or populations of either tBid or Bax with different apparent stoichiometries. This is illustrated in Figure 7, which shows the concentration of protein complexes, *c*Bax-tBid, as a function of the product *c*Bax *c*tBid, for all these different populations. Populations with the same 2 *D* − *KD* should lay on the same line of slope 1. All subpopulations of mobile particles (regardless of the initial Bax concentration or particle stoichiometry) more or less fall on a line corresponding to 2*D* − *KD*,<sup>m</sup> 1.6 μm<sup>−</sup>2, while all subpopulations of stationary particles fall on a 2 *D* − *KD*,<sup>s</sup> 0.1 μm<sup>−</sup><sup>2</sup> line. Thus, the main determinant of the 2 *D* − *KD* is the conformation of the protein and its degree of insertion in the membrane.

**Figure 7.** Surface concentration of the tBid-Bax complexes (defined as particles with *χ*thresh > 0.3) detected either in the Bax channel (green symbols) or the tBid channel red symbols) as a function of the product of the reactants. Data are shown both for stationary particles (dark red and dark green symbols) or mobile particles (light red and light green symbols). Each circle represents the aggregated data for a specific Bax concentration used for incubation (indicated on the figure, in nM), while each triangle represent the aggregated data for a specific oligomer size (also indicated on the figure). Squares represent the value obtained for the whole data set. The solid lines are fit of the data with Equation (7) for stationary proteins on the one hand and mobile proteins on the other hand, assuming a constant 2 *D* − *KD* (on this log-log plot the slope of these lines is 1 and their vertical offset, log[2*D* − *K*−<sup>1</sup> *D* ] is linked to the inverse of the dissociation constant).
