<figure><img src="image_39.png" /></figure>

**Strengths:**

They also nicely show that caveolin1 KO mice are more susceptible to death from infections with pathogens that create TEMs.

Overall, the paper is well-conducted and nicely written. There are however a few details that should be addressed.

**Reviewer #2 (Public Review):**

**Summary:**

The manuscript by Morel et al. aims to identify some potential mechano-regulators of transendothelial cell macro-aperture (TEM). Guided by the recognized role of caveolar invaginations in buffering the membrane tension of cells, the authors focused on caveolin-1 and associated regulator PTRF. They report a comprehensive in vitro work based on siRNA knockdown and optical imaging approach complemented with an in vivo work on mice, a biophysical assay allowing measurement of the mechanical properties of membranes, and a theoretical analysis inspired by soft matter physics.

**Strengths:**

The authors should be complimented for this multi-faceted and rigorous work. The accumulation of pieces of evidence collected from each type of approach makes the conclusion drawn by the authors very convincing, regarding the new role of cavolin-1 as an individual protein instead of the main molecular component of caveolae. On a personal note, I was very impressed by the quality of STORM images (Fig. 2) which are very illuminating and useful, in particular for validating some hypotheses of the theoretical analysis.

**Weaknesses:**

While this work pins down the key role of caveolin-, its mechanism remains to be further investigated. The hypotheses proposed by the authors in the discussions about the link between caveolin and lipids/cholesterol are very plausible though challenging. Even though we may feel slightly frustrated by the absence of data in this direction, the quality and merit of this paper remain.

- The analogy with dewetting processes drawn to derive the theoretical model is very attractive. However, although part of the model has already been published several times by the same group of authors, the definition of the effective membrane rigidity of a plasma membrane including the underlying actin cortex, was very vague and confusing. Here, for the first time, thanks to the STORM analysis, the authors show that HUVECs intoxicated by ExoC3 exhibit a loose and defective cortex with a significantly increased mesh size. This argues in favor of the validity of Helfrich formalism in this context. Nonetheless, there remains a puzzle. Experimentally, several TEMs are visible within one cell. Theoretically, the authors consider a simultaneous opening of several pores and treat them in an additive manner. However, when one pore opens, the tension relaxes and should prevent the opening of subsequent pores. Yet, experimentally, as seen from the beautiful supplementary videos, several pores open one after the other. This would suggest that the tension is not homogeneous within an intoxicated cell or that equilibration times are long. One possibility is that some undegraded actin pieces of the actin cortex may form a barrier that somehow isolates one TEM from a neighboring one. Could the authors look back at their STORM data and check whether intoxicated cells do not exhibit a bimodal population of mesh sizes and possibly provide a mapping of mesh size at the scale of a cell? In particular, it is quite striking that while bending rigidity of the lipid membrane is expected to set the maximal size of the aperture, most TEMs are well delimited with actin rings before closing. Is it because the
**Strengths:**

They also nicely show that caveolin1 KO mice are more susceptible to death from infections with pathogens that create TEMs.

Overall, the paper is well-conducted and nicely written. There are however a few details that should be addressed.

**Reviewer #2 (Public Review):**

**Summary:**

The manuscript by Morel et al. aims to identify some potential mechano-regulators of transendothelial cell macro-aperture (TEM). Guided by the recognized role of caveolar invaginations in buffering the membrane tension of cells, the authors focused on caveolin-1 and associated regulator PTRF. They report a comprehensive in vitro work based on siRNA knockdown and optical imaging approach complemented with an in vivo work on mice, a biophysical assay allowing measurement of the mechanical properties of membranes, and a theoretical analysis inspired by soft matter physics.

**Strengths:**

The authors should be complimented for this multi-faceted and rigorous work. The accumulation of pieces of evidence collected from each type of approach makes the conclusion drawn by the authors very convincing, regarding the new role of cavolin-1 as an individual protein instead of the main molecular component of caveolae. On a personal note, I was very impressed by the quality of STORM images (Fig. 2) which are very illuminating and useful, in particular for validating some hypotheses of the theoretical analysis.

**Weaknesses:**

While this work pins down the key role of caveolin-, its mechanism remains to be further investigated. The hypotheses proposed by the authors in the discussions about the link between caveolin and lipids/cholesterol are very plausible though challenging. Even though we may feel slightly frustrated by the absence of data in this direction, the quality and merit of this paper remain.

- The analogy with dewetting processes drawn to derive the theoretical model is very attractive. However, although part of the model has already been published several times by the same group of authors, the definition of the effective membrane rigidity of a plasma membrane including the underlying actin cortex, was very vague and confusing. Here, for the first time, thanks to the STORM analysis, the authors show that HUVECs intoxicated by ExoC3 exhibit a loose and defective cortex with a significantly increased mesh size. This argues in favor of the validity of Helfrich formalism in this context. Nonetheless, there remains a puzzle. Experimentally, several TEMs are visible within one cell. Theoretically, the authors consider a simultaneous opening of several pores and treat them in an additive manner. However, when one pore opens, the tension relaxes and should prevent the opening of subsequent pores. Yet, experimentally, as seen from the beautiful supplementary videos, several pores open one after the other. This would suggest that the tension is not homogeneous within an intoxicated cell or that equilibration times are long. One possibility is that some undegraded actin pieces of the actin cortex may form a barrier that somehow isolates one TEM from a neighboring one. Could the authors look back at their STORM data and check whether intoxicated cells do not exhibit a bimodal population of mesh sizes and possibly provide a mapping of mesh size at the scale of a cell? In particular, it is quite striking that while bending rigidity of the lipid membrane is expected to set the maximal size of the aperture, most TEMs are well delimited with actin rings before closing. Is it because the
surrounding loose actin is pushed back by the rim of the aperture? Could the authors better explain why they do not consider actin as a player in TEM opening?

- Instead of delegating to the discussion the possible link between caveolin and lipids as a mechanism for the enhanced bending rigidity provided by caveolin-1, it could be of interest for the readership to insert the attempted (and failed) experiments in the result section. For instance, did the authors try treatment with methyl-beta-cyclodextrin that extracts cholesterol (and disrupts caveolar and clathrin pits) but supposedly keeps the majority of the pool of individual caveolins at the membrane?

- Tether pulling experiments on Plasma membrane spheres (PMS) are real tours de force and the results are quite convincing: a clear difference in bending rigidity is observed in controlled and caveolin knock-out PMS. However, one recurrent concern in these tether-pulling experiments is to be sure that the membrane pulled in the tether has the same composition as the one in the PMS body. The presence of the highly curved neck may impede or slow down membrane proteins from reaching the tether by convective or diffusive motion. Could the authors propose an experiment to demonstrate that caveolin-1 proteins are not restricted to the body of the PMS and can access to the nanometric tether?

**Author Response**

We thank the Editors and the Reviewers for their comments on the importance of our work "showing a new role of caveolin-1 as an individual protein instead of the main molecular component of caveolae" in building membrane rigidity and also for constructive and thoughtful remarks that shall allow to improve the manuscript.

Indeed, we here establish the contributing role of caveolin-1 to membrane mechanics by a molecular mechanism that needs to be further addressed. To that respect, we thank the reviewers for suggesting avenues to improve the presentation and discussion of our hypotheses based on results of theoretical model and independent biophysical measurements in tube pulling from plasma membrane spheres, which concur to support the key role of caveolin-1 in building membrane rigidity.

To fulfill the recommendations of the reviewers we will amend the manuscript as discussed below.

**Public Reviews:**

**Reviewer #1 (Public Review):**

**Summary:**

Because of the role of membrane tension in the process, and that caveolae regulate membrane tension, the authors looked at the formation of TEMs in cells depleted of Caveolin1 and Cavin1 (PTRF): They found a higher propensity to form TEMs, spontaneously (a rare event) and after toxin treatment, in both Caveolin 1 and Cavin 1. They show that in both siRNA-Caveolin1 and siRNA-Cavin1 cells, the cytoplasm is thinner. They show that in siCaveolin1 only, the dynamics of opening are different, with notably much larger TEMs. From the dynamic model of opening, they predict that this should be due to a lower bending rigidity of the membrane. They measure the bending rigidity from Cell-generated Giant liposomes and find that the bending rigidity is reduced by approx. 50%.

**Strengths:**

They also nicely show that caveolin1 KO mice are more susceptible to death from infections with pathogens that create TEMs.
surrounding loose actin is pushed back by the rim of the aperture? Could the authors better explain why they do not consider actin as a player in TEM opening?

- Instead of delegating to the discussion the possible link between caveolin and lipids as a mechanism for the enhanced bending rigidity provided by caveolin-1, it could be of interest for the readership to insert the attempted (and failed) experiments in the result section. For instance, did the authors try treatment with methyl-beta-cyclodextrin that extracts cholesterol (and disrupts caveolar and clathrin pits) but supposedly keeps the majority of the pool of individual caveolins at the membrane?

- Tether pulling experiments on Plasma membrane spheres (PMS) are real tours de force and the results are quite convincing: a clear difference in bending rigidity is observed in controlled and caveolin knock-out PMS. However, one recurrent concern in these tether-pulling experiments is to be sure that the membrane pulled in the tether has the same composition as the one in the PMS body. The presence of the highly curved neck may impede or slow down membrane proteins from reaching the tether by convective or diffusive motion. Could the authors propose an experiment to demonstrate that caveolin-1 proteins are not restricted to the body of the PMS and can access to the nanometric tether?

**Author Response**

We thank the Editors and the Reviewers for their comments on the importance of our work "showing a new role of caveolin-1 as an individual protein instead of the main molecular component of caveolae" in building membrane rigidity and also for constructive and thoughtful remarks that shall allow to improve the manuscript.

Indeed, we here establish the contributing role of caveolin-1 to membrane mechanics by a molecular mechanism that needs to be further addressed. To that respect, we thank the reviewers for suggesting avenues to improve the presentation and discussion of our hypotheses based on results of theoretical model and independent biophysical measurements in tube pulling from plasma membrane spheres, which concur to support the key role of caveolin-1 in building membrane rigidity.

To fulfill the recommendations of the reviewers we will amend the manuscript as discussed below.

**Public Reviews:**

**Reviewer #1 (Public Review):**

**Summary:**

Because of the role of membrane tension in the process, and that caveolae regulate membrane tension, the authors looked at the formation of TEMs in cells depleted of Caveolin1 and Cavin1 (PTRF): They found a higher propensity to form TEMs, spontaneously (a rare event) and after toxin treatment, in both Caveolin 1 and Cavin 1. They show that in both siRNA-Caveolin1 and siRNA-Cavin1 cells, the cytoplasm is thinner. They show that in siCaveolin1 only, the dynamics of opening are different, with notably much larger TEMs. From the dynamic model of opening, they predict that this should be due to a lower bending rigidity of the membrane. They measure the bending rigidity from Cell-generated Giant liposomes and find that the bending rigidity is reduced by approx. 50%.

**Strengths:**

They also nicely show that caveolin1 KO mice are more susceptible to death from infections with pathogens that create TEMs.
Overall, the paper is well-conducted and nicely written. There are however a few details that should be addressed.

**Reviewer #2 (Public Review):**

**Summary:**

The manuscript by Morel et al. aims to identify some potential mechano-regulators of transendothelial cell macro-aperture (TEM). Guided by the recognized role of caveolar invaginations in buffering the membrane tension of cells, the authors focused on caveolin-1 and associated regulator PTRF. They report a comprehensive in vitro work based on siRNA knockdown and optical imaging approach complemented with an in vivo work on mice, a biophysical assay allowing measurement of the mechanical properties of membranes, and a theoretical analysis inspired by soft matter physics.

**Strengths:**

The authors should be complimented for this multi-faceted and rigorous work. The accumulation of pieces of evidence collected from each type of approach makes the conclusion drawn by the authors very convincing, regarding the new role of caveolin-1 as an individual protein instead of the main molecular component of caveolae. On a personal note, I was very impressed by the quality of STORM images (Fig. 2) which are very illuminating and useful, in particular for validating some hypotheses of the theoretical analysis.

**Weaknesses:**

While this work pins down the key role of caveolin-1, its mechanism remains to be further investigated. The hypotheses proposed by the authors in the discussions about the link between caveolin and lipids/cholesterol are very plausible though challenging. Even though we may feel slightly frustrated by the absence of data in this direction, the quality and merit of this paper remain.

In the current study, we did not find the technical conditions allowing us to properly address the role of cholesterol in the dynamics of TEM due to adverse effects of cholesterol depletion with methyl-beta-cyclodextrin on the morphology of HUVEC. To answer the Reviewer remark, we will mention our attempts to address a role of cholesterol in the dynamics of TEM in the results section. Moreover, we will thoroughly discuss in the section related to data of tube pulling experiments from PMS that caveolin-1 by controlling membrane lipid composition, may indirectly affect membrane rigidity (see comments below about the presence or absence of caveolin-1 in the tubes pulled from PMS and our hypotheses about a direct or indirect role of caveolin-1 in the control of membrane rigidity).

The analogy with dewetting processes drawn to derive the theoretical model is very attractive. However, although part of the model has already been published several times by the same group of authors, the definition of the effective membrane rigidity of a plasma membrane including the underlying actin cortex, was very vague and confusing.

In the revised manuscript, we will clearly define the membrane bending rigidity parameter, which was missing in the current version. The membrane bending rigidity is defined as the energy required to locally bend the membrane surface. In a liposome, a rigorous derivation leads to a relationship between the membrane tension relation and the variation of the projected area, which are related by the bending rigidity: this relationship is known as the Helfrich law. This statistical physics approach is only rigorously valid for a liposome, whereas its application to a cell is questionable due to the presence of cytoskeletal forces acting on the membrane. Nevertheless, application of the Helfrich law to cell membranes may be granted
Overall, the paper is well-conducted and nicely written. There are however a few details that should be addressed.

**Reviewer #2 (Public Review):**

**Summary:**

The manuscript by Morel et al. aims to identify some potential mechano-regulators of transendothelial cell macro-aperture (TEM). Guided by the recognized role of caveolar invaginations in buffering the membrane tension of cells, the authors focused on caveolin-1 and associated regulator PTRF. They report a comprehensive in vitro work based on siRNA knockdown and optical imaging approach complemented with an in vivo work on mice, a biophysical assay allowing measurement of the mechanical properties of membranes, and a theoretical analysis inspired by soft matter physics.

**Strengths:**

The authors should be complimented for this multi-faceted and rigorous work. The accumulation of pieces of evidence collected from each type of approach makes the conclusion drawn by the authors very convincing, regarding the new role of caveolin-1 as an individual protein instead of the main molecular component of caveolae. On a personal note, I was very impressed by the quality of STORM images (Fig. 2) which are very illuminating and useful, in particular for validating some hypotheses of the theoretical analysis.

**Weaknesses:**

While this work pins down the key role of caveolin-1, its mechanism remains to be further investigated. The hypotheses proposed by the authors in the discussions about the link between caveolin and lipids/cholesterol are very plausible though challenging. Even though we may feel slightly frustrated by the absence of data in this direction, the quality and merit of this paper remain.

In the current study, we did not find the technical conditions allowing us to properly address the role of cholesterol in the dynamics of TEM due to adverse effects of cholesterol depletion with methyl-beta-cyclodextrin on the morphology of HUVEC. To answer the Reviewer remark, we will mention our attempts to address a role of cholesterol in the dynamics of TEM in the results section. Moreover, we will thoroughly discuss in the section related to data of tube pulling experiments from PMS that caveolin-1 by controlling membrane lipid composition, may indirectly affect membrane rigidity (see comments below about the presence or absence of caveolin-1 in the tubes pulled from PMS and our hypotheses about a direct or indirect role of caveolin-1 in the control of membrane rigidity).

The analogy with dewetting processes drawn to derive the theoretical model is very attractive. However, although part of the model has already been published several times by the same group of authors, the definition of the effective membrane rigidity of a plasma membrane including the underlying actin cortex, was very vague and confusing.

In the revised manuscript, we will clearly define the membrane bending rigidity parameter, which was missing in the current version. The membrane bending rigidity is defined as the energy required to locally bend the membrane surface. In a liposome, a rigorous derivation leads to a relationship between the membrane tension relation and the variation of the projected area, which are related by the bending rigidity: this relationship is known as the Helfrich law. This statistical physics approach is only rigorously valid for a liposome, whereas its application to a cell is questionable due to the presence of cytoskeletal forces acting on the membrane. Nevertheless, application of the Helfrich law to cell membranes may be granted
on short time scales, before active cell tension regulation takes place (Sens P and Plastino J, 2015 J Phys Condens Matter), especially in cases where cytoskeletal forces play a modest role, such as red blood cells (Helfrich W 1973 Z Naturforsch C). The fact that the cytoskeletal structure and actomyosin contraction are significantly disrupted upon cell intoxication-driven inhibition of the small GTPase RhoA supports the applicability of Helfrich law to describe TEM opening. Because of the presence of proteins, carbohydrates, and the adhesion of the remaining actin meshwork after toxin treatment, we expect the Helfrich relationship to somewhat differ from the case of a pure lipidic membrane. We account for these effects via an “effective bending rigidity”, a term used in the detailed discussion of the model hypotheses, which corresponds to an effective value describing the relationship between membrane tension and projected area variation in our cells. These considerations will be included in the revised manuscript.

> Here, for the first time, thanks to the STORM analysis, the authors show that HUVECs intoxicated by ExoC3 exhibit a loose and defective cortex with a significantly increased mesh size. This argues in favor of the validity of Helfrich formalism in this context. Nonetheless, there remains a puzzle. Experimentally, several TEMs are visible within one cell. Theoretically, the authors consider a simultaneous opening of several pores and treat them in an additive manner. However, when one pore opens, the tension relaxes and should prevent the opening of subsequent pores. Yet, experimentally, as seen from the beautiful supplementary videos, several pores open one after the other. This would suggest that the tension is not homogeneous within an intoxicated cell or that equilibration times are long. One possibility is that some undegraded actin pieces of the actin cortex may form a barrier that somehow isolates one TEM from a neighboring one.

As pointed by the Reviewer, we expect that membrane tension is neither a purely global nor a purely local parameter. Opening of a TEM will relax membrane tension over a certain distance, not over the whole cell. Moreover, once the TEM closes back, membrane tension will increase again. This spatial and temporal localization of membrane tension relaxation explains that the opening of a first TEM does not preclude the opening of a second one. On the other hand, membrane tension is not a purely local property. Indeed, we observe that when two TEMs enlarge next to each other, their shape becomes anisotropic, as their enlargement is mutually hampered in the region separating them. We account for this interaction by treating TEM membrane relaxation in an additive fashion. We emphasize that this simplified description is used to predict maximum TEM size, corresponding to the time at which TEM interaction is strongest. As the reviewer points out, it would be more questionable to use this additive treatment to predict the likelihood of nucleation of a new TEM, which is not done here.

> Could the authors look back at their STORM data and check whether intoxicated cells do not exhibit a bimodal population of mesh sizes and possibly provide a mapping of mesh size at the scale of a cell?

To address the question raised by the Reviewer we decided to plot the whole distribution of mesh sizes in addition to the average value per cell. We did not observe a bimodal distribution but rather a very heterogeneous distribution of mesh size going up to a few microns square in all conditions of siRNA treatments. Moreover, we did not observe a specific pattern in the distribution of mesh size at the scale of the cell, with very large mesh sizes being surrounded by small ones. We also did not observe any specific pattern for the localization of TEM opening, as described in the paper, making the correlation between mesh size and TEM opening difficult.

> In particular, it is quite striking that while bending rigidity of the lipid membrane is expected to set the maximal size of the aperture, most TEMs are well delimited with actin
on short time scales, before active cell tension regulation takes place (Sens P and Plastino J, 2015 J Phys Condens Matter), especially in cases where cytoskeletal forces play a modest role, such as red blood cells (Helfrich W 1973 Z Naturforsch C). The fact that the cytoskeletal structure and actomyosin contraction are significantly disrupted upon cell intoxication-driven inhibition of the small GTPase RhoA supports the applicability of Helfrich law to describe TEM opening. Because of the presence of proteins, carbohydrates, and the adhesion of the remaining actin meshwork after toxin treatment, we expect the Helfrich relationship to somewhat differ from the case of a pure lipidic membrane. We account for these effects via an “effective bending rigidity”, a term used in the detailed discussion of the model hypotheses, which corresponds to an effective value describing the relationship between membrane tension and projected area variation in our cells. These considerations will be included in the revised manuscript.

> Here, for the first time, thanks to the STORM analysis, the authors show that HUVECs intoxicated by ExoC3 exhibit a loose and defective cortex with a significantly increased mesh size. This argues in favor of the validity of Helfrich formalism in this context. Nonetheless, there remains a puzzle. Experimentally, several TEMs are visible within one cell. Theoretically, the authors consider a simultaneous opening of several pores and treat them in an additive manner. However, when one pore opens, the tension relaxes and should prevent the opening of subsequent pores. Yet, experimentally, as seen from the beautiful supplementary videos, several pores open one after the other. This would suggest that the tension is not homogeneous within an intoxicated cell or that equilibration times are long. One possibility is that some undegraded actin pieces of the actin cortex may form a barrier that somehow isolates one TEM from a neighboring one.

As pointed by the Reviewer, we expect that membrane tension is neither a purely global nor a purely local parameter. Opening of a TEM will relax membrane tension over a certain distance, not over the whole cell. Moreover, once the TEM closes back, membrane tension will increase again. This spatial and temporal localization of membrane tension relaxation explains that the opening of a first TEM does not preclude the opening of a second one. On the other hand, membrane tension is not a purely local property. Indeed, we observe that when two TEMs enlarge next to each other, their shape becomes anisotropic, as their enlargement is mutually hampered in the region separating them. We account for this interaction by treating TEM membrane relaxation in an additive fashion. We emphasize that this simplified description is used to predict maximum TEM size, corresponding to the time at which TEM interaction is strongest. As the reviewer points out, it would be more questionable to use this additive treatment to predict the likelihood of nucleation of a new TEM, which is not done here.

> Could the authors look back at their STORM data and check whether intoxicated cells do not exhibit a bimodal population of mesh sizes and possibly provide a mapping of mesh size at the scale of a cell?

To address the question raised by the Reviewer we decided to plot the whole distribution of mesh sizes in addition to the average value per cell. We did not observe a bimodal distribution but rather a very heterogeneous distribution of mesh size going up to a few microns square in all conditions of siRNA treatments. Moreover, we did not observe a specific pattern in the distribution of mesh size at the scale of the cell, with very large mesh sizes being surrounded by small ones. We also did not observe any specific pattern for the localization of TEM opening, as described in the paper, making the correlation between mesh size and TEM opening difficult.

> In particular, it is quite striking that while bending rigidity of the lipid membrane is expected to set the maximal size of the aperture, most TEMs are well delimited with actin
rings before closing. Is it because the surrounding loose actin is pushed back by the rim of the aperture? Could the authors better explain why they do not consider actin as a player in TEM opening?

Actin ring assembly and stiffening is indeed a player in TEM opening, and it is included in our differential equation describing TEM opening dynamics (second term on the left-hand side of Eq. 3). In some cases, actin ring assembly is the dominant player, such as in TEM opening after laser ablation (ex novo TEM opening), as we previously reported (Stefani et al. 2017 Nat comm). In contrast, here we investigate de novo TEM opening, for which we expect that bending rigidity can be estimated without accounting for actin assembly, as we previously reported (Gonzalez-Rodriguez et al. 2012 Phys Rev Lett). Such a bending rigidity estimate (Eq. 5) is obtained by considering two different time scales: the time scale of membrane tension relaxation, governed by bending rigidity, and the time scale of cable assembly, governed by actin dynamics. We expect the first-time scale to be shorter, and thus the maximum size of de novo TEMs to be mainly constrained by membrane tension relaxation. The discussion of these two different time scales will be added to the revised manuscript.

Instead of delegating to the discussion the possible link between caveolin and lipids as a mechanism for the enhanced bending rigidity provided by caveolin-1, it could be of interest for the readership to insert the attempted (and failed) experiments in the result section. For instance, did the authors try treatment with methyl-beta-cyclodextrin that extracts cholesterol (and disrupts caveolar and clathrin pits) but supposedly keeps the majority of the pool of individual caveolins at the membrane?

We will state in the results section that we could not find appropriate experimental conditions allowing us to deplete cholesterol with methyl-beta cyclodextrin without interfering with the shape of HUVECs, thereby preventing the proper analysis of TEM dynamics.

Tether pulling experiments on Plasma membrane spheres (PMS) are real tours de force and the results are quite convincing: a clear difference in bending rigidity is observed in controlled and caveolin knock-out PMS. However, one recurrent concern in these tether-pulling experiments is to be sure that the membrane pulled in the tether has the same composition as the one in the PMS body. The presence of the highly curved neck may impede or slow down membrane proteins from reaching the tether by convective or diffusive motion. Could the authors propose an experiment to demonstrate that caveolin-1 proteins are not restricted to the body of the PMS and can access to the nanometric tether?

As pointed out by the reviewer, a concern with tube pulling experiments is related to the dynamics of equilibration of membrane composition between the nanotube and the rest of the membrane. In our experiments, we have waited about 30 seconds after tube pulling and after changing membrane tension. We have checked that after this time, the force remained constant, implying that we have performed experiments of tube pulling from PMS in technical conditions of equilibrium that ensure that lipids and membrane proteins had enough time to reach the tether by convective or diffusive motion. We will add a representative example of force vs time plot in our revision. In principle, this could be further checked using cells expressing GFP-caveolin-1 to generate PMS as done in Sinha et al., 2011: a steady protein signal in the tube will further confirm the equilibration, provided that caveolin is recruited in the nanotube due to mechanical reasons. Indeed, since caveolin-1 is inserted in the cytosolic leaflet of the plasma membrane, when a nanotube is pulled towards the exterior of the cell as in our experiments, we can expect 2 situations depending on the ability of caveolin-1 to deform membranes, which is not clear, in particular after the paper of Porta et al, Sci. Adv., 2022. i) If caveolin-1 (Cav1) does not bend membranes, it could be
rings before closing. Is it because the surrounding loose actin is pushed back by the rim of the aperture? Could the authors better explain why they do not consider actin as a player in TEM opening?

Actin ring assembly and stiffening is indeed a player in TEM opening, and it is included in our differential equation describing TEM opening dynamics (second term on the left-hand side of Eq. 3). In some cases, actin ring assembly is the dominant player, such as in TEM opening after laser ablation (ex novo TEM opening), as we previously reported (Stefani et al. 2017 Nat comm). In contrast, here we investigate de novo TEM opening, for which we expect that bending rigidity can be estimated without accounting for actin assembly, as we previously reported (Gonzalez-Rodriguez et al. 2012 Phys Rev Lett). Such a bending rigidity estimate (Eq. 5) is obtained by considering two different time scales: the time scale of membrane tension relaxation, governed by bending rigidity, and the time scale of cable assembly, governed by actin dynamics. We expect the first-time scale to be shorter, and thus the maximum size of de novo TEMs to be mainly constrained by membrane tension relaxation. The discussion of these two different time scales will be added to the revised manuscript.

Instead of delegating to the discussion the possible link between caveolin and lipids as a mechanism for the enhanced bending rigidity provided by caveolin-1, it could be of interest for the readership to insert the attempted (and failed) experiments in the result section. For instance, did the authors try treatment with methyl-beta-cyclodextrin that extracts cholesterol (and disrupts caveolar and clathrin pits) but supposedly keeps the majority of the pool of individual caveolins at the membrane?

We will state in the results section that we could not find appropriate experimental conditions allowing us to deplete cholesterol with methyl-beta cyclodextrin without interfering with the shape of HUVECs, thereby preventing the proper analysis of TEM dynamics.

Tether pulling experiments on Plasma membrane spheres (PMS) are real tours de force and the results are quite convincing: a clear difference in bending rigidity is observed in controlled and caveolin knock-out PMS. However, one recurrent concern in these tether-pulling experiments is to be sure that the membrane pulled in the tether has the same composition as the one in the PMS body. The presence of the highly curved neck may impede or slow down membrane proteins from reaching the tether by convective or diffusive motion. Could the authors propose an experiment to demonstrate that caveolin-1 proteins are not restricted to the body of the PMS and can access to the nanometric tether?

As pointed out by the reviewer, a concern with tube pulling experiments is related to the dynamics of equilibration of membrane composition between the nanotube and the rest of the membrane. In our experiments, we have waited about 30 seconds after tube pulling and after changing membrane tension. We have checked that after this time, the force remained constant, implying that we have performed experiments of tube pulling from PMS in technical conditions of equilibrium that ensure that lipids and membrane proteins had enough time to reach the tether by convective or diffusive motion. We will add a representative example of force vs time plot in our revision. In principle, this could be further checked using cells expressing GFP-caveolin-1 to generate PMS as done in Sinha et al., 2011: a steady protein signal in the tube will further confirm the equilibration, provided that caveolin is recruited in the nanotube due to mechanical reasons. Indeed, since caveolin-1 is inserted in the cytosolic leaflet of the plasma membrane, when a nanotube is pulled towards the exterior of the cell as in our experiments, we can expect 2 situations depending on the ability of caveolin-1 to deform membranes, which is not clear, in particular after the paper of Porta et al, Sci. Adv., 2022. i) If caveolin-1 (Cav1) does not bend membranes, it could be
<figure><img src="image_40.png" /></figure>

recruited in the nanotubes, at a density similar to the PMS body. The tube force measurement
in this case would reflect the bending rigidity of the PMS membrane. Then, Cav1 could stiffen
membrane either as a stiff inclusion at high density or/and by affecting lipid composition, as
suggested in our text. ii) If Cav1 bends the membrane (i.e. it has a non-zero spontaneous
curvature), it should create a positive curvature considering the geometry of the caveolae,
opposite to the curvature of the nanotubes that we pull, and thus be excluded of the
nanotubes. In this case, the force would reflect the bending rigidity of the membrane
depleted of Cav1 and should be the same in both types of experiments (WT and Cav1 depleted
conditions) if the lipid composition remains unchanged upon Cav1 depletion. Our
measurements suggest again that Cav1 depletion affects the plasma membrane composition,
probably by reducing the quantity of sphingomyelin and cholesterol. Note that the presence
of a very reduced concentration of Cav1 as compared to the plasma membrane has been
reported in tunneling nanotubes (TNT) connecting two neighboring cells (A. Li et al., Front.
Cell Dev. Biol., 2022). These TNTs have typical diameters of similar scale than diameters of
tubes pulled from PMS. Some of us have addressed these specific questions related to Cav-1
spontaneous curvature and its effect on the lipid composition of the plasma membrane in
two separate manuscripts (in preparation). They represent comprehensive studies by
themselves that clarify these points. We propose to add this discussion in the manuscript,
with perspectives on future studies, but stressing the point that the presence of Cav1 stiffens
plasma membranes, and that the exact origin of this effect must be further investigated.
<figure><img src="image_37.png" /></figure>

recruited in the nanotubes, at a density similar to the PMS body. The tube force measurement
in this case would reflect the bending rigidity of the PMS membrane. Then, Cav1 could stiffen
membrane either as a stiff inclusion at high density or/and by affecting lipid composition, as
suggested in our text. ii) If Cav1 bends the membrane (i.e. it has a non-zero spontaneous
curvature), it should create a positive curvature considering the geometry of the caveolae,
opposite to the curvature of the nanotubes that we pull, and thus be excluded of the
nanotubes. In this case, the force would reflect the bending rigidity of the membrane
depleted of Cav1 and should be the same in both types of experiments (WT and Cav1 depleted
conditions) if the lipid composition remains unchanged upon Cav1 depletion. Our
measurements suggest again that Cav1 depletion affects the plasma membrane composition,
probably by reducing the quantity of sphingomyelin and cholesterol. Note that the presence
of a very reduced concentration of Cav1 as compared to the plasma membrane has been
reported in tunneling nanotubes (TNT) connecting two neighboring cells (A. Li et al., Front.
Cell Dev. Biol., 2022). These TNTs have typical diameters of similar scale than diameters of
tubes pulled from PMS. Some of us have addressed these specific questions related to Cav-1
spontaneous curvature and its effect on the lipid composition of the plasma membrane in
two separate manuscripts (in preparation). They represent comprehensive studies by
themselves that clarify these points. We propose to add this discussion in the manuscript,
with perspectives on future studies, but stressing the point that the presence of Cav1 stiffens
plasma membranes, and that the exact origin of this effect must be further investigated.