The current view of biological membranes is that proteins are densely packed and often organized into functional modules that perform specific biological functions (Engelman, 2005; Nicolson, 2014). Lipids play an important role in organizing membrane proteins, and the resulting specialized membrane domains are now commonly known as lipid microdomains or lipid rafts (Karnovsky et al., 1982; Lingwood and Simons, 2010; Simons and Ikonen, 1997; Simons and Toomre, 2000; Stier and Sackmann, 1973; Vereb et al., 2003).

Lipid microdomains are enriched in cholesterol (Barenholz, 2002; Korade and Kenworthy, 2008; Simons and Ikonen, 1997) and characterized by a lipid phase that is distinct from the surrounding membrane (Ahmed et al., 1997; Schroeder et al., 1991). Cholesterol has a planar four-aromatic ring structure with a short isooctyl alkyl chain and a small 3-β-hydroxyl head group that can form a hydrogen bond with a polar group (Figure 1—figure supplement 1A). Because the aliphatic groups linked to the ring system are asymmetrically distributed, cholesterol features a smooth (or α) face and a rough (or β) face (Figure 1—figure supplement 1A). It makes up 40–90% of the lipids in eukaryotic cell membranes (Liscum and Munn, 1999; van Meer et al., 2008). Cholesterol can form non-covalent interactions with lipid acyl chains, preferentially with saturated ones (Epand and Epand, 2004; Zheng et al., 2007). As a result, the membrane can transition from a liquid-disordered to a liquid-ordered phase (de Meyer et al., 2010; Ghysels et al., 2019; Marsh, 2010; Seelig, 1977), which has been linked to the formation of lipid microdomains (Quinn and Wolf, 2009; Silvius, 2003).

Mammalian lens membranes contain a high percentage of sphingomyelin (SM) – a lipid consisting of a phosphocholine head group, a sphingosine amino alcohol, and a fatty acid (Figure 1—figure supplement 1B) – and cholesterol, lipids that are characteristic for lipid rafts (Simons and Ikonen, 1997; Zelenka, 1984). With a molar ratio of cholesterol to other phospholipids ranging from 2.02 to 2.52, the human lens core plasma membrane features the highest molar cholesterol content of all membranes found in human tissues (Fleschner and Cenedella, 1991; Zelenka, 1984). Aquaporin-0 (AQP0), a lens-specific water channel, is the most abundant membrane protein in lens membranes (over 60% of the total protein content) (Alcalá et al., 1975; Bloemendal et al., 1972), where it forms large two-dimensional (2D) arrays (Gorin et al., 1984; Kistler and Bullivant, 1980; Zampighi et al., 1982).

The propensity of AQP0 to form 2D crystals was used to determine its structure by electron crystallography (EC) of in vitro assembled 2D crystals grown with the lipid dimyristoyl phosphatidylcholine (DMPC) (Gonen et al., 2005). Later, AQP0 2D crystals were grown with a variety of different lipids (Hite et al., 2015; Hite et al., 2010). All these crystals had the same lattice constants, which were identical to those of AQP0 arrays in native lens membranes (Buzhynskyy et al., 2007). Thus, in vitro grown 2D crystals recapitulate the organization of AQP0 tetramers in 2D arrays in the native lens membrane. Interestingly, however, high-resolution EC studies, which also resolved the annular lipids (Gonen et al., 2005; Hite et al., 2010), showed that AQP0 tetramers in the 2D crystals are separated by a layer of lipids and form essentially no direct protein–protein interactions. As the crystal contacts are almost exclusively mediated by lipids, it is surprising that AQP0 2D crystals could be obtained with almost every lipid tested.

Molecular dynamics (MD) simulations further advanced our understanding of how lipids interact with AQP0. Initial simulations probing the interactions of AQP0 with lipids were carried out with pure DMPC and mixed DMPC:cholesterol membrane patches, predicting the existence of a cholesterol hotspot at the extracellular side of the AQP0 surface (O’Connor and Klauda, 2011). Later, MD simulations demonstrated that the positions of lipids around AQP0 seen in EC structures obtained from 2D crystals, in which the lipids are constrained by the protein crystal packing, are indeed representative of the localization of unconstrained lipids around individual AQP0 tetramers (Aponte-Santamaría et al., 2012). Molecular aspects, such as protein mobility and surface roughness, were identified to play key roles in defining the lipid positions (Aponte-Santamaría et al., 2012; Briones et al., 2017). Furthermore, a combination of coarse-grained and atomistic MD simulations revealed that annular lipids adopt similar positions around several members of the aquaporin family (Stansfeld et al., 2013), while mass spectrometry demonstrated the weak nature of the interaction of lipids with AQPZ (Laganowsky et al., 2014).

In vitro, AQP0 can be induced to form 2D crystals by choosing a very specific lipid-to-protein ratio (LPR) for reconstitution, but this in vitro approach does not explain why AQP0 tetramers form 2D arrays in native lens membranes, which contain an excess of lipids as well as other membrane proteins. Since lipids mediate the interactions in AQP0 2D arrays, it is likely that specific lipids play a role in the assembly of AQP0 2D arrays in the native lens membrane. As AQP0-containing lens membrane junctions are greatly enriched in cholesterol and sphingomyelin (Fleschner and Cenedella, 1991), lipids that play a key role in raft formation (Brown and London, 2000), these lipids were prime candidates to drive AQP0 array formation. To gain structural insights into how cholesterol and/or sphingomyelin may induce AQP0 to form 2D crystals in vivo and potentially to obtain a more general understanding of how these lipids can establish lipid microdomains, we determined structures of AQP0 in membranes formed by mixtures of sphingomyelin and cholesterol and performed extensive equilibrium and force-probe MD simulations.

In this study, we determined two EC structures of AQP0 in membranes formed by sphingomyelin and cholesterol. As these so-called raft lipids are the main constituents of lens membranes, they represent the natural environment of AQP0. The AQP0 crystals formed in sphingomyelin/cholesterol membranes have the same lattice constants as previous 2D crystals obtained with other lipids (Gonen et al., 2005; Hite et al., 2010) as well as the 2D arrays found in lens membranes (Buzhynskyy et al., 2007). The 2D crystals thus reflect the arrangement of AQP0 tetramers in native 2D arrays.

Our structure of AQP0_2SM:1Chol reveals seven sphingomyelins (Figure 3A), the same number of lipids also seen in structures of AQP0 in bilayers formed by DMPC (Gonen et al., 2005) and EPL (Hite et al., 2010), and these are also located in almost identical positions (Figure 3B and C). The interaction of sphingomyelins with AQP0 thus seems to be governed by the same principles that were found for phosphoglycerolipids, namely that the acyl chains locate to grooves in the protein surface and that the lipid head groups make few if any interactions with the protein (Hite et al., 2010). However, compared to the acyl chains in the EPL bilayer, those of the sphingomyelins appear to be straighter, which likely reflects the saturated nature of the sphingomyelin acyl chains. Despite this difference, the structure of the sphingomyelin bilayer is very similar to those of bilayers formed by phosphoglycerolipids, indicating that sphingomyelin by itself is unlikely the reason for AQP0 to form 2D arrays in lens membranes.

Cholesterol has a higher affinity for sphingomyelin than for phosphoglycerolipids (Niu and Litman, 2002), because the mostly saturated acyl chains of sphingomyelin can better accommodate the planar ring system of cholesterol (Epand and Epand, 2004; Zheng et al., 2007) and because the sphingomyelin backbone has two hydrogen-bond donor groups, an amide and a hydroxyl group, that make hydrogen bonding to cholesterol more effective (Róg and Pasenkiewicz-Gierula, 2006). Furthermore, the interaction of the sphingomyelin amide group with the hydroxyl group of cholesterol orients the smooth (α) face of the cholesterol toward sphingomyelin, leaving only the rough (β) face to interact with membrane proteins (Fantini and Barrantes, 2013). In the context of AQP0 2D arrays, however, these interactions do not appear to occur. While Chol1 does interact with sphingomyelin acyl chains in both structures, the additional cholesterols in the AQP0_1SM:2Chol structure seem to have little interactions with sphingomyelin acyl chains and instead seem to substitute for some of the sphingomyelin acyl chains seen in the AQP0_2SM:1Chol structure (Figure 4A and C). We also do not observe interactions between the hydroxyl head group of any cholesterols with an amide group of the sphingomyelins. While we cannot rule out that specific sphingomyelin–cholesterol interactions occur in the membrane area enclosed by four AQP0 tetramers (where we were unable to build models for the lipids due to the fourfold symmetry axis), our structures suggest that specific sphingomyelin–cholesterol interactions do not play a critical role in AQP0 array formation in the lens membrane.

Cholesterol increases the order of lipid acyl chains (de Meyer and Smit, 2009; Lafleur et al., 1990), and the resulting phase transition is thought to contribute to the segregation of cholesterol-enriched membrane areas (Pandit et al., 2007). A potential mechanism by which cholesterol could induce AQP0 array formation could thus be that cholesterol bound to AQP0 would order the surrounding lipids, leading to a phase transition that leads to an initial segregation and crystallization of the AQP0/cholesterol/sphingomyelin units in the membrane.

In an attempt to assess this possibility, we looked at the B-factors of the acyl chains, which are affected, among other factors, by the mobility of the atoms. Comparison of corresponding acyl chains showed that the B-factors of the acyl chains in the AQP0_1SM:2Chol structure tend to be slightly lower than those of the acyl chains in the AQP0_2SM:1Chol structure (Figure 4—figure supplement 2), suggesting that the cholesterols could have an ordering effect on the sphingomyelin acyl chains. However, the B-factors of the acyl chains in the AQP0_EPL structure, which contain double bonds and are not constrained by cholesterol and should thus be much less ordered, are similar to those of the acyl chains in the AQP0_2SM:1Chol structure. A likely explanation is that acyl chains, including unsaturated ones, preferentially fill in grooves in the protein surface (Hite et al., 2010), which should already substantially constrain their mobility. Therefore, cholesterol bound to the protein surface may not add much additional constraints to their already restricted mobility. Cholesterol-induced phase separation thus does not seem to be a likely cause for AQP0 array formation.

The hydrophobic thickness is an important characteristic of a lipid bilayer, which depends on the length and saturation of the acyl chains of the lipids forming the bilayer. Mismatch of the hydrophobic thickness between a membrane protein and the lipid bilayer is thought to be one mechanism by which membrane proteins can cluster in a membrane (Hanulová and Weiss, 2012; Schmidt et al., 2008). One factor that affects the hydrophobic thickness of a membrane is its cholesterol content, which is related to the ordering effect of cholesterol on the lipid acyl chains (de Meyer and Smit, 2009; Lafleur et al., 1990). Change in cholesterol-induced hydrophobic thickness may thus be another potential force that drives the formation of AQP0 arrays in the lens membrane. Our measurements of the average distance between the phosphorus atoms of the phosphodiester groups and the nitrogen atoms of the amide groups of the sphingomyelins in the two leaflets (Figure 4A and B) show that both distances are larger for the bilayer with the higher cholesterol content, by ~3 Å for the phosphodiester groups and ~4 Å for the amide groups, suggesting that a higher cholesterol content indeed increases the hydrophobic thickness of the bilayer formed by the annular sphingomyelins.

In cells, sphingomyelin is predominantly found in the extracellular leaflet of the plasma membrane (Devaux, 1991), so that sphingomyelins seen in the extracellular leaflet in our two structures likely represent true positions of sphingomyelin in native AQP0 2D arrays. The two sphingomyelins in the extracellular leaflet that are seen in both sphingomyelin/cholesterol membranes are in exactly the same position (Figure 4C), establishing that the extracellular leaflet does not change its position relative to AQP0 upon thickening of the membrane with increasing cholesterol content. Sphingomyelin SM3 may be responsible for the fixed position of the extracellular leaflet. In all structures of AQP0 in different lipid bilayers, the lipid at the position equivalent to that of SM3 always has the best-defined density and the lowest B-factors (including for the acyl chains; Figure 4—figure supplement 2). The lipid at this position is always the only one whose head group makes interactions with AQP0. It is thus possible that the lipid at this position defines and locks in the position of the extracellular leaflet with respect to AQP0. As a result, the extracellular leaflet does not play a role in defining the thickness of the membrane.

The increase in hydrophobic thickness with higher cholesterol content is the result of the three sphingomyelins in the cytoplasmic leaflet moving further out from the bilayer center, which they do even though this leaflet contains only a single cholesterol (Figure 4C). The notion that an increase in hydrophobic thickness is predominantly due to movements of lipids in the cytoplasmic leaflet is consistent with the observation that these lipids are usually more mobile, i.e., have higher B-factors in crystal structure than lipids in the extracellular leaflet (Belrhali et al., 1999). Comparison of the lipid arrangement in the cytoplasmic leaflet shows that Chol4 in the AQP0_1SM:2Chol structure assumes the position of SM6 in the AQP0_2SM:1Chol structure (Figure 4A–C). The new position of the displaced SM6 in the AQP0_1SM:2Chol structure is further out from the bilayer center and potentially is the cause for similar outward movements of lipids SM5 and SM7, thus defining the new position of the cytoplasmic leaflet and increasing the hydrophobic thickness of the annular lipid bilayer. Hence, a higher cholesterol concentration of the membrane does increase the hydrophobic thickness of the lipid bilayer formed by the annular lipids surrounding AQP0 tetramers, thus creating a hydrophobic mismatch with the remaining lipid bilayer, which, in turn, would provide a driving force for AQP0 tetramers to cluster in the native lens membrane.

The cholesterols in our structures do not interact with AQP0 through consensus cholesterol-binding sites known as the Cholesterol Recognition/interaction Amino acid Consensus sequence (CRAC domain; -L/V-(X)_1-5-Y-(X)_1-5-R/K-) (Li and Papadopoulos, 1998) or the inverted CRAC domain, CARC (Baier et al., 2011). Cholesterol can also bind to membrane proteins in a fashion that does not involve a CRAC or CARC domain, as seen for example for the influenza M2 protein (Elkins et al., 2018; Elkins et al., 2017) and α-synuclein (Fantini et al., 2011). Emerging cryo-EM structures of G-protein-coupled receptors (GPCRs) also do not show a consensus motif for their interaction with cholesterol (Sarkar and Chattopadhyay, 2020; Taghon et al., 2021). Furthermore, the cholesterols interact with AQP0 through their smooth α face (Figure 4—figure supplement 1), which is not engaged in interactions with sphingomyelin as previously thought (Fantini and Barrantes, 2013), thus differing from the predominant interaction of cholesterols with GPCRs, the G-protein-gated inwardly rectifying potassium-2 (GIRK2) channel, and the Na⁺, K⁺-ATPase, which occur predominantly through the rough β face of cholesterol (Gimpl, 2016; Mathiharan et al., 2021; Shinoda et al., 2009). However, there are other cases in which cholesterol interacts with membrane proteins through its α face, such as seen for the Niemann–Pick C1-like 1 protein (Huang et al., 2020). Likely the residues on the protein surface determine whether a protein interacts with cholesterol through its α or β face. The smooth α face interacts with aromatic side chains through π-stacking (Nishio et al., 1995), whereas the β face appears to interact with hydrophobic side chains, such as leucine, valine, or isoleucine (Fantini et al., 2011).

Chol3 is the most unusual lipid in our structures, because it is located in the middle of the lipid bilayer and because it is sandwiched between two neighboring AQP tetramers. Binding sites for cholesterol in the middle of the membrane have also been described for GPCRs, and these sites have been named ‘deep binding sites’ (Genheden et al., 2017). A docking investigation with known membrane protein structures for cholesterol-binding sites revealed deep binding sites not only in GPCRs but also in ion channels and transporters (Lee, 2018). Unlike any other cholesterol in our structures, Chol3 interacts directly with two AQP0 subunits that are part of different tetramers. This interaction is different from the cholesterol-induced dimerization of GPCRs as these are mediated by interactions between two or more cholesterol molecules rather than one cholesterol directly interacting with two GPCRs (Gimpl, 2016; Hanson et al., 2008). The two adjacent AQP0 tetramers form a pocket that is ~8.5 Å wide at the position of the ring system and ~2.5 Å at the position of the acyl chain (Figure 4E). The interaction surface on the AQP0 subunit interacting with the smooth face of Chol3 encompasses 373 Ų and is formed by residues Ser106, Val103, Ala102, Ala99, and Leu21, which line the ring system, and three phenylalanine residues, Phe17, Phe18, and Phe14, which surround the acyl chain. The interaction surface on the AQP0 subunit interacting with the rough face of Chol3 is 344 Ų and is predominantly formed by residues Ile132, Ile135, Phe136, Ile210, Leu214, and Leu217 (Figure 4E). Leucine and isoleucine residues have also been found to mediate the interaction of many GPCRs with the rough β face of cholesterol (Gimpl, 2016). The hydroxyl head group of Chol3 interacts with a water molecule that may be stabilized through an interaction with Ser126 (Figure 4E). Because of its intricate interactions with two AQP0 subunits, Chol3 can likely function as a glue that can keep two tetramers together. This structural characteristic may be the reason why AQP0 can form 2D arrays in pure cholesterol membranes (Figure 1E and F).

To gain further insights into the role cholesterol plays in the stability of AQP0 arrays, we used MD simulations to investigate the interplay between cholesterol and AQP0. The first set of simulations investigated the localization of cholesterol around a single AQP0 tetramer. Cholesterol positioned at well-defined positions, i.e., hotspots, that were in notable agreement with both the predicted positions from a previous computational study (O’Connor and Klauda, 2011) and the positions in the EC structures (Figure 5). Therefore, as it has been previously demonstrated to be the case for phospholipids (Aponte-Santamaría et al., 2012), the crystal packing in the crystallographic structures does not greatly affect the positioning of cholesterol around AQP0. In consequence, crystallographic cholesterol positions recapitulate the behavior of unconstrained cholesterol molecules around a single AQP0 tetramer. This is the case for all cholesterols except for one, the deep cholesterol, which will be discussed in detail below. Cholesterol localization around membrane proteins has been extensively studied, especially in the context of the regulation and activity of GPCRs, exchangers, and ion channels, but also aquaporins (for a comprehensive review, see Corradi et al., 2019). Interestingly, in coarse-grained MD simulations, when AQP1 was embedded in a lipid bilayer resembling the plasma membrane, cholesterol was enriched at two positions that qualitatively correspond to the lateral projections of Chol3 and Chol4 positions observed here for AQP0 (compare Figure 5 with Figure 2 of Corradi et al., 2018). This suggests that individual AQP0 and AQP1 tetramers share similarities in their cholesterol-binding fingerprints, as was already shown for phospholipids in this protein family (Stansfeld et al., 2013). Nevertheless, cholesterol was rather depleted from the Chol1 position in AQP1. The shape of the protein surface has been shown to critically define the positions where lipids non-specifically associate with AQP0 (Aponte-Santamaría et al., 2012; Briones et al., 2017) and also other proteins (e.g. ion channels [Niemelä et al., 2010] and GPCRs [Kurth et al., 2020], among many others reviewed in Corradi et al., 2019). This principle presumably applies here, too, i.e., the different surface of AQP0 at the Chol1 position, compared to that of AQP1, may result in a greater association of cholesterol over sphingolipids in this position (Figure 8—figure supplements 1 and 3).

In a second set of simulations, we attempted to understand the molecular reasons for the unusual position of deep-binding Chol3 (Figure 6). We demonstrate that neither a single AQP0 tetramer (Figure 6C and D) nor a specific bulk cholesterol concentration (Figure 6B) is sufficient to maintain annular cholesterol molecules at such a deeply inserted position. Instead, the constraint imposed by two adjacent AQP0 tetramers and the coordination of two water molecules were required (Figures 6E and 8A and Figure 8—figure supplement 1). Our data are thus consistent with the existence of deep cholesterol positions but only in a highly constrained setup that involves two AQP0 tetramers. The immediate questions raised by the existence of deep cholesterols are whether these affect the formation and/or stability of 2D AQP0 arrays.

Our simulations provide strong evidence for a direct influence of deep cholesterol molecules on the mechanical stability of the association between two adjacent AQP0 tetramers. We demonstrate that two adjacent tetramers can withstand larger lateral detachment forces when their interface contains deep cholesterol molecules (Figure 7C–F). Crystal structures of several membrane proteins already revealed that cholesterol can mediate crystal packing interactions (Crnjar and Molteni, 2021; Khunweeraphong et al., 2020; Wu et al., 2014). Moreover, the presence of cholesterol has been reported to influence membrane–protein oligomerization, a feature mainly explored for GPCRs (Corradi et al., 2019; Gahbauer and Böckmann, 2016). We expand on these data, by providing evidence of cholesterol—directly—engaging in the stronger attachment of two membrane proteins. We attribute this to cholesterol facilitating the formation of transient protein–protein contacts (Figure 8A–D) together with providing higher surface complementarity when sandwiched between two AQP0 tetramers (Figure 8E and F). Cardiolipin is a phospholipid that has been implicated in stabilizing transient α-helical membrane protein oligomers (Gupta et al., 2017). More specifically, cardiolipin has been described to serve as a ‘glue’ for the cytochrome components of the respiratory chain in mitochondrial membranes (Arnarez et al., 2013; Zhang et al., 2002). Interestingly, cardiolipin also impacts the resistance of AQPZ, the bacterial homolog of AQP0, to unfolding (Laganowsky et al., 2014). In addition, lipids have been recently shown to mediate protein assembly in the outer membrane of bacteria (Webby et al., 2022). Analogous to these systems and based on our EC structures and MD simulations, we propose that deep cholesterol increases the mechanical stability of associated AQP0 tetramers. Although we provide solid evidence here that deep cholesterol imparts mechanical stabilization, free energy calculations would be required to obtain the full picture of thermodynamic stabilization. However, such free energy calculations are challenging for lipids, due to the chemical complexity and poor convergence involved (Wang et al., 2021), and are thus beyond the scope of the current work.

Our structures of AQP0 arrays in sphingomyelin bilayers with low and high cholesterol content and the results from the MD simulations allow us to propose a model for cholesterol-induced array formation (Figure 9). In a lipid bilayer with a low cholesterol concentration, cholesterol may interact with AQP0 predominantly through the most specific cholesterol-binding site, the one occupied by Chol1, but this interaction would be transient and would not have a meaningful effect on the organization of the surrounding lipid molecules (sphingomyelin in our AQP0_2SM:1Chol structure) (Figure 9A). An increase in cholesterol concentration will cause more cholesterols in the extracellular leaflet to bind to AQP0. In addition, cholesterol will also enrich in the cytoplasmic leaflet and associate with AQP0. This interaction will shift the annular lipids in this leaflet further away from the membrane center and create a hydrophobic mismatch between the shell of annular lipids and the surrounding lipid bilayer (Figure 9B). Driven by the force to minimize membrane tension induced by hydrophobic mismatch, AQP0 tetramers will cluster. Cholesterols in between the tetramers can diffuse deeper into the membrane and associate with deep binding sites on AQP0, thus stabilizing the interaction between adjacent tetramers (Figure 9C). Alternatively, it may also be possible that cholesterol first interacts with a deep binding site on one AQP0 but is only stabilized as the second AQP0 traps it in position. As each AQP0 tetramer has four deep cholesterol-binding sites, the avidity effect would result in the formation and stabilization of large 2D arrays as those seen in native lens membranes (Figure 9D).

Figure 9

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This model is specific for the formation of AQP0 arrays in lens membranes, but we speculate that similar principles may underlie the organization of lipid rafts. AQP0 may be special in that it forms tetramers and thus has four deep cholesterol-binding sites, so that the avidity effect allows it to form much larger domains than seen for typical lipid rafts (Simons and Ikonen, 1997; Zelenka, 1984). In addition, it is presumably not common that the same protein has surfaces that can interact with both the smooth α and the rough β face of cholesterol. However, cholesterol would have the potential to mediate the association of any protein with an α face-interacting surface with any other protein that features a β face-interacting surface. Thus, while hydrophobic mismatch and phase separation may be driving forces that bring proteins into close proximity, cholesterol may be the actual glue that increases the time they remain associated.

Electron diffraction data have been deposited in PDB under the accession codes 8SJY and 8SJX.Molecular dynamics simulations data have been deposited on GitHub (copy archived at Chiu et al., 2024).

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Author details

1. Po-Lin Chiu

   Department of Cell Biology, Harvard Medical School, Boston, United States

   Present address

   School of Molecular Sciences, Biodesign Center for Applied Structural Discovery, Arizona State University, Tempe, United States

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing – original draft, Writing – review and editing

   Contributed equally with

   Juan D Orjuela

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8608-7650

2. Juan D Orjuela

   1. Max Planck Tandem Group in Computational Biophysics, Universidad de los Andes, Bogotá, Colombia
   2. Biomedical Engineering Department, Universidad de los Andes, Bogotá, Colombia

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing – original draft, Writing – review and editing

   Contributed equally with

   Po-Lin Chiu

   Competing interests

   No competing interests declared

3. Bert L de Groot

   Computational Biomolecular Dynamics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany

   Contribution

   Supervision, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3570-3534

4. Camilo Aponte Santamaría

   1. Max Planck Tandem Group in Computational Biophysics, Universidad de los Andes, Bogotá, Colombia
   2. Molecular Biomechanics Group, Heidelberg Institute for Theoretical Studies, Heidelberg, Germany

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing – original draft, Writing – review and editing

   For correspondence

   camilo.aponte@h-its.org

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8427-6965

5. Thomas Walz

   Department of Cell Biology, Harvard Medical School, Boston, United States

   Present address

   Laboratory of Molecular Electron Microscopy, The Rockefeller University, New York, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing – original draft, Writing – review and editing

   For correspondence

   twalz@rockefeller.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2606-2835

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