α-catenin switches between a slip and an asymmetric catch bond with F-actin to cooperatively regulate cell junction fluidity

α-catenin is a crucial protein at cell junctions that provides connection between the actin cytoskeleton and the cell membrane. At adherens junctions (AJs), α-catenin forms heterodimers with β-catenin that are believed to resist force on F-actin. Outside AJs, α-catenin forms homodimers that regulates F-actin organization and directly connect the cell membrane to the actin cytoskeleton, but their mechanosensitive properties are inherently unknown. By using ultra-fast laser tweezers we found that a single α-β-catenin heterodimer does not resist force but instead slips along F-actin in the direction of force. Conversely, the action of 5 to 10 α-β-catenin heterodimers together with force applied toward F-actin pointed end engaged a molecular switch in α-catenin, which unfolded and strongly bound F-actin as a cooperative catch bond. Similarly, an α-catenin homodimer formed an asymmetric catch bond with F-actin triggered by protein unfolding under force. Our data suggest that α-catenin clustering together with intracellular tension engage a fluid-to-solid phase transition at the membrane-cytoskeleton interface.


Supplementary
rates at zero load. a, Parameters of the force-dependent rates obtained from fitting the twostate model to the lifetime of a single a-catenin homodimer interaction (Fig. 1c).

α-catenin-actin pull-down assay
A pull-down assay was used to confirm the predicted interaction between the His(6x) tagged α-E-catenin and F-actin and measure the affinity of the complex in vitro. With such a method, proteins are mixed in solution and binding is evaluated in the absence of any external applied force (F=0). Each reaction contained increasing concentrations of α-catenin incubated with a fixed concentration of F-actin. Following binding and pelleting of the α-E-catenin-actin complexes through centrifugation, the proteins recovered from individual pull-downs were analyzed on an SDS-PAGE by densitometry ( Supplementary Fig. 11a,c). Reactions and conditions are described in Methods. The intensities of the bands corresponding to the fraction of α-catenin bound to F-actin were quantified for each concentration and normalized to the intensity of the corresponding actin band to correct for the variability in the amount of pellet collection 1 . The SDS-PAGE gel of the corresponding supernatant is shown in Fig. 11b as control. Control experiments in which α-catenin and actin were spun by themselves show that the fraction of α-catenin that pellet independently of actin is negligible ( Supplementary Fig.  11d,e; in particular, compare lanes of α-catenin at 10 μM between panels a and d). Data were fitted by a Michaelis-Menten equation = , giving a dissociation constant Kd = 1.5 ± 0.3 μM ( Supplementary Fig. 11c) , in good agreement with previous reports 2,3 .

α-catenin-β-catenin pull-down assay
A pull-down assay was also used to confirm the predicted interaction between the His(6x) tagged α-E-catenin and the GST tagged β-catenin and measure the affinity of the complex in vitro 4 . GST-tagged β-catenin was covalently bound to carboxylated polystyrene beads at the protein N-terminus. Each reaction contained increasing concentrations of α-catenin incubated with a fixed concentration of 21.7 nM β-catenin. Following binding and pelleting of the α-Ecatenin-β-catenin complexes through centrifugation, the proteins recovered from individual pulldowns were analyzed on an SDS-PAGE by densitometry ( Supplementary Fig. 12a,c). Reactions and conditions are described in Methods. The intensities of the bands corresponding to the fraction of α-catenin bound to β-catenin were quantified for each concentration. The SDS-PAGE gel of the corresponding supernatant is shown in Fig. 12a,d for reference. Note that αcatenin concentration in the 400 μl of supernatant is less than 1/10 of α-catenin concentration in the 30 μl in which is resuspended the pellet (see Methods), which is probably why residual α-catenin is not visible in the supernatant of β-catenin beads. Pellet intensity data were well fitted by a Michaelis-Menten equation, giving a dissociation constant Kd = 35 ± 13 nM. This is in good agreement with previous measurements of Kd between untagged αE-catenin and untagged β-catenin by Pokutta et al. (23.4 ± 3.7 nM) 5 , indicating that the His(6x) and GST tags are not affecting significantly the interaction between α-catenin and β-catenin. BSA control beads were used to test the influence of non-specific interactions between α-catenin and beads as in Lapetina et al. 4 . Analysis of pellet in control BSA beads shows that there is no correlation between the quantity of α-catenin that is pulled down together with β-catenin beads and αcatenin that is pulled down together with control beads. Therefore, non-specific interactions between α-catenin and beads and the fraction of α-catenin that is pulled down in the absence of β-catenin can be neglected 4 .

Flow cell assay
Binding activity of α-catenin to F-actin was then evaluated through a flow cell assay to test whether a-catenin homodimers and a-b-catenin heterodimers could bind to actin under force. As in all experiments, we used His(6x) tagged α-E-catenin and GST tagged β-catenin. In this assay, α-catenin was first attached to the coverslip surface either on top of nitrocellulose or over a b-catenin bed. Next, fluorescently labelled F-actin was flowed and incubated into the chamber and then washed with an imaging buffer to remove floating F-actin and observe whether F-actin on the coverslip surface remained bound to a-catenin under the drag force applied by the buffer flow. The force applied to an actin filament by the buffer flow can be calculated as 6 : where is the length of the actin filament, ∥ is the drag coefficient per unit length along the actin filament axis, is the flow velocity (~2 mm/s), is the coefficient of viscosity of the buffer (~10 -3 N×s/m), ℎ is the distance between the coverslip surface and the center of the actin filament (~10 nm), and is the filament radius (~3 nm) 6 ( Supplementary Fig. 13). From this formula we estimate a force per unit length of about 7 pN/µm. Given filament lengths in the range 1 -10 µm, the flow cell assay allowed us to observe if multiple a-catenin molecules could bear forces of few tens of piconewton on actin.
Supplementary Fig. 14a and 14b show a field of view of a flow cell experiment in which acatenin homodimers were bound onto a nitrocellulose smeared coverslip at concentration of 1 µM and 0.4 µM, respectively. Actin filaments bound on the surface were visible after the washing step in both conditions, with a significantly higher number of filaments for the higher a-catenin concentration. Supplementary Fig. 14c show a field of view of a flow cell experiment in which a-catenin at 1 µM concentration was bound onto a bed of b-catenin, attached to a nitrocellulose smeared coverslip. Also under these conditions, actin filaments bound on the surface were visible after the washing step. A control reaction in the absence of α-catenin was also performed showing no detectable F-actin filaments on the surface ( Supplementary  Fig. 14d). Reactions and conditions are described in detail in Methods.

Supplementary discussion
Step Size Distribution In our experiments, a single α-catenin homodimer might bind to the actin filament with a single monomer or with both. Binding of both monomers to actin would lead to the possibility that the position steps observed at force > 5pN are the consequence of the unbinding of one of the two monomers. In fact, monomer unbinding would result in the displacement of the actin filament under force as a consequence of the change in the bond stiffness. Similarly, a step might result from the unbinding of one monomer in the experiments with multiple α-β-catenin heterodimers. However, we believe that such events cannot be the primary cause of the main peak observed in the step distributions, for the following reasoning. Assume that the stiffness of a single monomer bound to F-actin is km and the stiffness of the dimer bound to F-actin is kd = 2km. Under a constant force F, the dimer would be strained by , whereas the monomer by 2 = 2 ⁄ . Therefore, the step that we should observe when a monomer detaches from actin and the other stays bound is . Under this hypothesis, the d ~ 12 nm step measured at F ~ 5 pN force would imply that the stiffness of the monomer is about km = 5 pN/(2*12 nm) = 0.21 pN/nm. At 11 pN force, the unbinding of one monomer would produce a step = 2 2 ⁄ = 11 pN / (0.42 pN/nm) = 26 nm, whereas we observe a main peak in the step distribution of similar size. Therefore, in our opinion the most plausible explanation is that the step is due to a conformational change of the protein (unfolding) that does not modify substantially the protein stiffness. Under this hypothesis, since the applied force is constant and the protein is already strained by the force before the unfolding occurs (force application is much faster than the step dynamics 7 ), the unfolding step would be independent of the applied force, as we observe. It still remains the possibility that unbinding of one of the two monomers contributes to the larger steps that we see at larger forces. For example, at 11 pN force we observe a second peak around 35 nm, which might fit the sum of the unfolding step (12 nm) and monomer unbinding (26 nm).

Cooperative binding
It's well established that that the interaction between α-β-catenin heterodimers and actin is much weaker than between α-catenin homodimers and actin 8 . Different explanations have been proposed previously (i) the N-and C-terminal domains of α-catenin are allosterically coupled and binding to β-catenin on the N-terminal domain might alter the C-terminal domain ability to bind to actin 8 . (ii) Structural studies 9 indicate that β-catenin might sterically hinder Factin binding by the α-catenin binding domain, which could be at the basis of the different Factin binding between the homodimer and heterodimer. (iii) α-catenin ABD binding to actin is accompanied by a conformational change in the actin protomer that affects the filament structure. This alteration of the filament structure can be at the base of a cooperative binding mechanism that reinforces the link between an α-catenin homodimer and actin compared to an α-catenin monomer 3 . Our results indicate that a cooperative mechanism is at the basis of the bond reinforcement and the analysis of the α-catenin stiffness during the interaction with actin in the different experiments reinforces this interpretation (see discussion in the main text).
However, the identification of the structural features that are at the basis of the different kinetics of α-catenin homodimers and heterodimers is out of the scope of our article, and further studies would be required to clearly assess this point.

Non-specific interactions
We made many control experiments to rule out non-specific interactions, which are one of the well-known issues in this kind of single molecule experiments. In experiments on α-β-catenin heterodimers, α-catenin was attached on the coverslip surface on top of a nitrocellulose-coated surface saturated with GST-β-catenin, followed by BSA (see methods). We made several control slides in which the coverslip surface was coated as described above but in the absence of α-catenin and looked for non-specific interactions on several tens of beads in each slide. We could very rarely (less than one bead per slide) find non-specific interactions with this control surface. Moreover, non-specific interactions were very different from the interactions observed in the presence of α-catenin, showing few short interactions when the dumbbell was close to the coverslip surface and the actin filament was pushing on the bead (as detected from the change in the position signal) and disappeared when the dumbbell was moved slightly farther from the coverslip surface. On the other hand, in the presence of α-catenin at single molecule concentration, we observed interactions in one every 4 beads on average, the interactions were much longer at low forces (tens of milliseconds) and the number of interactions increased with force. A single molecule was able to produce as much as several tens of thousands interactions. The interactions were observed also when the actin filament was not pushing on the bead. This behavior was never observed in the absence of α-catenin.

Dimeric vs monomeric α-catenin
Before our experiments, we separated dimeric from monomeric α-catenin by using size exclusion chromatography. This procedure assures that less than 1% of the catenin was in a dimeric form in the experiments with α-β-catenin heterodimers (see supplementary Fig. 9). The concentration of the monomeric catenin that we used in the experiments at single molecule concentration was about 1 μg/ml (10 nM); in the ones at "high" concentration, catenin concentration was 10 μg/ml (100 nM). Since the dissociation constant of the α-catenin homodimer is 25 μM, at equilibrium about 0.04% and 0.4% would be dimeric at the singlemolecule and high concentrations, respectively. Moreover, Pokutta et al. showed that the αcatenin homodimer does not bind to β-catenin even after overnight incubation 5 . Therefore, the few % contamination of dimeric catenin was most likely washed away after few minutes of incubation in the sample chamber (see methods).

Possible effect of the GST tag in β-catenin
In the experiments reported in this work, we used GST-tagged β-catenin. The presence of the GST tag might in principle influence the interaction of β-catenin with α-catenin and actin. Although previous studies indicate that the GST tag does not introduce non-specific interactions with actin 2 , we directly tested whether the GST tag might introduce non-specific interactions with actin, α-catenin, or both. We checked non-specific interactions between the GST-tagged β-catenin and actin using a flow cell assay and single molecule experiments. Using the flow cell assay, we did not observe binding of actin filaments on the coverslip surface coated with GST-tagged β-catenin (see Supplementary Methods, section "flow cell assay" and Supplementary Fig. 14d). In single molecule experiments, we made several control coverslips coated with the GST-tagged βcatenin and very rarely observed non-specific interactions with an actin filament, similarly to what is observed in the absence of the GST-tagged beta-catenin (see methods, section "Optical trapping experiments" and supplementary discussion, section "non-specific interactions"). We also performed experiments to evaluate whether the presence of the GST tag would affect the interaction between β-catenin and α-catenin. To this end, we made pull-down experiments in which we bound GST-β-catenin to microbeads and made them react with α-catenin at growing concentrations. From these experiments, we measured a dissociation constant between α-catenin and β-catenin of Kd = 35 ± 13 nM (see methods, section "Pull down and flow-cell assay", and supplementary materials, section "α-catenin-β-catenin pull-down assay"). Previous work by Koslov et al. (1997) determined kd of 100nM between untagged full-length alpha-E-catenin and untagged full-length beta-catenin, but no experimental error was reported on this value 10 . Later, Pokutta et al. (2014) determined kd = 23.4 ± 3.7 on the same constructs, which is in good agreement with our measurement 5 . This result indicates that the interaction between α-catenin and β-catenin is not affected significantly by the presence of the GST tag. Another aspect that should be taken into account is that the GST tag can form dimers, which might in principle influence the single molecule or cooperative action of α-β-catenin heterodimers. However, in our experiments we used β-catenin to coat the coverslip surface at saturating concentration and we bound α-catenin on top of this β-catenin carpet at lower concentration. Under this condition, we expect to find β-catenin molecules tightly packed on the coverslip surface regardless of their dimeric or monomeric state and α-catenin distribution on the surface dictated mostly by α-catenin concentration, not by β-catenin dimeric or monomeric state. In support to this argument, we have strong experimental evidence that in the experiments at low α-catenin concentration we observe interactions with single α-β-catenin heterodimers. In fact, the 5.5 nm periodicity that we observe in our position data (Fig. 2d-f) can be observed only if one α-catenin molecule is interacting with actin, whereas α-catenin dimers or multiple molecules positioned randomly on the surface would average out this precise distribution. Therefore, it is very unlikely that single molecule experiments are affected by the presence of GST dimers. At higher α-catenin concentration, we expect to have multiple α-catenin molecules interacting with actin. It remains possible that two adjacent α-catenin molecules might be bound to two βcatenin dimerized through the GST tag, which might possibly be arranged differently from two adjacent α-β-catenin heterodimers that are not dimerized through the GST tag. However, the present experimental arrangement does not allow us to control how α-β-catenin heterodimers are distributed on the coverslip surface and if and how particular arrangements of the molecules might affect their cooperative behavior. Understanding the details of this aspect is out of the scope of the present work and further studies would be needed to assess it.