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Modeling of annexin A2—Membrane interactions by molecular dynamics simulations

The annexins are a family of Ca2+-regulated phospholipid binding proteins that are involved in membrane domain organization and membrane trafficking. Although they are widely studied and crystal structures are available for several soluble annexins their mode of membrane association has never been studied at the molecular level. Here we obtained molecular information on the annexin-membrane interaction that could serve as paradigm for the peripheral membrane association of cytosolic proteins by Molecular Dynamics simulations. We analyzed systems containing the monomeric annexin A2 (AnxA2), a membrane with negatively charged phosphatidylserine (POPS) lipids as well as Ca2+ ions. On the atomic level we identify the AnxA2 orientations and the respective residues which display the strongest interaction with Ca2+ ions and the membrane. The simulation results fully agree with earlier experimental findings concerning the positioning of bound Ca2+ ions. Furthermore, we identify for the first time a significant interaction between lysine residues of the protein and POPS lipids that occurs independently of Ca2+ suggesting that AnxA2-membrane interactions can also occur in a low Ca2+ environment. Finally, by varying Ca2+ concentrations and lipid composition in our simulations we observe a calcium-induced negative curvature of the membrane as well as an AnxA2-induced lipid ordering.


Introduction
Annexins are peripheral membrane-binding proteins involved in the regulation of membrane organization and membrane traffic [1,2]. More than 100 Annexins have been identified in different species and twelve proteins referred to as Annexin A1-13 (A12 gene is unassigned) have been identified in humans. Annexins reversibly associate with the cytosolic surface of cellular membranes in a Ca 2+ -dependent manner and are involved in the control of membrane organization, membrane-cytoskeleton contacts and membrane trafficking events (for reviews see [1][2][3]). Annexin A2 (AnxA2) is a member of the family that serves important functions in organizing membrane microdomains and regulating Ca 2+ -evoked exocytosis in non-neuronal cells. Moreover, the protein has been implicated in early endocytic events and the resealing of The Ca 2+ mediated AnxA2-membrane binding is interesting both in terms of membrane reorganization as well as of changes of AnxA2 binding properties. Different forms of AnxA2 (core, monomer, heterotetramer) can affect lipid segregation in membranes composed of POPC, 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), PI(4,5)P 2 , POPS, and cholesterol (CHOL) [28]. Here it was suggested that AnxA2 primarily and directly interacts with PI(4,5)P 2 in a Ca 2+ -dependent manner and clusters this lipid into larger domains. On the other hand binding of Ca 2+ to annexins in the absence of membranes induces a conformational change of the protein [24,[29][30][31][32][33]. The major difference between the membrane-free and membranebound forms of the Ca 2+ -AnxA2 complex is the Ca 2+ sensitivity [27]. Therefore, it is of major interest to study the Ca 2+ mediated AnxA2 -membrane interaction on the microscopic level which, however, is not yet possible with experimental techniques. Due to the absence of membrane structures in the protein crystals, the experimental observations of Ca 2+ -mediated AnxA2 configurations interacting with membrane remain mostly indirect.
Some computer simulation studies were conducted previously to investigate annexinmembrane interaction. For example, MD simulations limited to 7 ns were performed to study the conformation changes of the Ca 2+ -bound Annexin A1 as compared to the Ca 2+ -free protein without the presence of a membrane [34]. Another two MD studies with simulation times less than 60 ns were devoted to studying the influence of the N-terminal part of the molecule to the binding affinity of preconfigured Annexin A1 to the membrane [35,36]. In the case of annexin A5 another force field was suggested [37]. The Ca 2+ -dependent annexin A5-membrane interactions were also investigated to study interaction specificities as well as the influence of annexin A5 on the properties of the membrane, i.e. lipid order parameters, membrane bending and formation of H-bonds [38]. Moreover, MD simulations support the formation of supramolecular assemblies of annexin A5 in Ca 2+ -dependent membrane binding experiments [39]. Monte Carlo simulations based on experimental data were also performed to model annexin A5 -membrane interaction and suggested that the protein-PS interaction together with a protein-protein interaction provide a driving force for the formation of large PS-rich domains and that the presence of cholesterol may provide a further contribution to the clustering of such PS domains [40]. In the case of annexin B12, MD simulations in combination with NMR studies were employed to investigate water diffusion and retardation effects as a function of distance from annexin B12 and the membrane [41].
However, in all the referenced MD studies the annexin had a predefined orientation relative to the membrane surface thus introducing a certain bias towards the mode of membrane interaction. Furthermore, systematic data on the interaction of plasma membrane-associated AnxA2 with the membrane on the atomistic scale are not available. This would be of significant general interest as it could represent a paradigm for reversible phospholipid interactions of peripheral membrane-binding proteins.
Therefore, we addressed this question by MD simulations of monomeric AnxA2 in Ca 2+containing membrane systems.
A large number of protein-protein and protein-ligand docking techniques and tools do exist [42][43][44]. For example in one of the recent studies around 382 billion configurations were tested for docking cytochrome c 2 and bc 1 complex using the rigid-body docking program DOT 2.0 [45]. We refrained from using this methodology for the following reasons. First, the topology of one of the constituents (membrane) is very simple so that only the protein needs to be rotated.Second, due to the complex binding properties, involving the appropriate localization of Ca 2+ ions, possible conformational changes of AnxA2 as well as reorganization of the local membrane composition, each attempt requires a long additional simulation in the range of μs. Thus, only a somewhat limited number of attempts can be used. Third, as explicitly shown in our work these simulation times are long enough so that even transitions between different initial orientations are possible. This strongly suggest, that we have indeed managed to cover the relevant initial orientations. However, the docking approaches could be rather efficient for the investigation of more complex systems such as aggregations of multiple AnxA2.
In the first simulation setup we keep the membrane and Ca 2+ composition the same and vary the orientation of AnxA2 in respect to the membrane. In these simulations AnxA2 was positioned above a POPC:DOPC:POPS:CHOL (0.38:0.19:0.24:0.19) membrane in 18 different orientations. In this way we systematically and efficiently assessed which surface residues of AnxA2 can favorably interact with the membrane. The Ca 2+ ions were positioned between AnxA2 and the membrane to, possibly, mediate AnxA2 -membrane binding. In the second setup we keep AnxA2 orientation (identified in the first setup as favorable) the same and change the composition of the membrane (by adding PI(4,5)P 2 lipids) as well as the concentration of Ca 2+ . The influence of AnxA2 and Ca 2+ ions on membrane curvature and ordering is investigated.
The aims of this MD work were to i) determine the favorable AnxA2 -membrane binding configurations, if any, ii) quantify the influence of Ca 2+ ions on AnxA2 -membrane total enthalpy, iii) compare the MD results with experimental findings, iv) investigate possible energetic differences of AnxA2 interactions with different types of lipids, and v) identify the protein residues which are responsible for phospholipid binding vi) determine the effect of AnxA2/membrane/Ca 2+ interactions on membrane bending and ordering.

Binding enthalpies
The initial structure from which the 18 orientations were generated is shown in Fig 2. A total of 18 orientations was obtained by a stepwise rotation of the folded AnxA2 around the axes shown (the snapshots of initial systems are shown in S1 Fig). First we calculate the different binding enthalpies, characterizing the interaction of AnxA2 with the membrane and the calcium ions, respectively, for the different initial orientations (Fig 3). Only those Ca 2+ ions are considered which, with respect to AnxA2 and the membrane have an interaction energy larger than -1 kcal/mol and a distance of less than 10 Å. The exact choice of these criteria, however, has only a minor influence on the final result. The total binding enthalpy for AnxA2 is the sum of AnxA2 -membrane and AnxA2 -Ca 2+ enthalpies. We exclude the membrane-Ca 2+ enthalpy because it strongly depends on the PS lipid localization and also because our primary interest is the AnxA2 -Ca 2+ /membrane interaction.
One of the immediate observations in Fig 3 is the rather strong enthalpic interaction of AnxA2 and the membrane-Ca 2+ complex for orientation O5. Although the AnxA2 -membrane enthalpy in O5 is one of the strongest (-350 kcal/mol), the largest difference as compared to other orientations results from the AnxA2 -Ca 2+ interactions (additional -550 kcal/mol). It should be noted that the number of Ca 2+ ions presented in Fig 3 is time averaged and limited by the threshold of -1 kcal/mol. While the number of Ca 2+ in Fig 3 for O5 is close to 5 a closer inspection of AnxA2-Ca 2+ interaction energies (data not shown) reveals six, strongly interacting and membrane-exposed, Ca 2+ ions. The discrepancy is due to a very weak interaction of one of those six Ca 2+ ions (bound to Glu156 residue) with the membrane. We consider this as The initial system. The side view and the view from top of the initial system are shown. This system corresponds to the O2 configuration. The four AnxA2 repeats are shown in different colors: repeats 1 (Ala35 -Lys104), 2 (Ala107 -Lys176), 3 (Asp187 -Ile263) and 4 (Lys266 -Cys335) are colored in orange, mauve, green and blue, respectively. The red spheres located between AnxA2 and the membrane are calcium ions. The membrane lipids are shown in gray.
https://doi.org/10.1371/journal.pone.0185440.g002 a transient effect related to the absence of nearby negatively charged POPS lipids and, therefore, in further discussion of O5 configuration we consider all six Ca 2+ ions.
Next, we extracted from our simulations the inverse minimal distance of AnxA2 to either the membrane or the Ca 2+ ions for 17 of the 18 orientations (Fig 4). For comparison, the corresponding values for the AnxA2-Ca 2+ pairs in the experimentally determined crystal structure are also shown [25].
Remarkably, only O5 (and to a lesser extent O6) showed very good agreement with the crystal structure data with respect to the protein-Ca 2+ interactions. This is the same orientation that showed the strongest interaction with the membrane-Ca 2+ complex in the enthalpy calculations (Fig 3). In total, six binding sites of Ca 2+ are identified in O5. These include the following residues: Glu53 and Asp326 (repeat 1 and 4), Glu82 (repeat 1), Asp154 and Glu156 (repeat 2), Asp162 (repeat 2), Asp166 (repeat 2), Asp285 (repeat 4). This shows that the repeat 2membrane binding should play a major role in stabilizing the Ca 2+ -mediated membrane interaction in the favorable O5 configuration. The additional Ca 2+ binding site found in the crystal structure around the residue Asp200 is positioned in the configuration O5 rather distant from the membrane and should not be considered a AnxA2 -membrane binding site. Rather this site could be involved in stabilizing a dimeric AnxA2 complex [25]. Interestingly, for O6, which closely resembles O5, another binding site is identified which is missing in O5 (i.e. Glu125 and Asp251 which involve repeats 2 and 3) and was found when inspecting the vicinity during the MD simulations. Most likely, longer simulations allowing more thermal fluctuations of the Ca 2+ positions would have revealed this binding site in O5 as well. In summary, our numerical observations show excellent agreement of the binding sites in the O5 orientation with the crystal structure data for Ca 2+ bound AnxA2 in solution. This suggests that orientation O5 in which the convex side of the protein faces the membrane represents the most-favored membrane-bound configuration and that Ca 2+ binding is similar for soluble and membrane bound AnxA2.
Other pairs of orientations (e.g. O5 and O6 or O3 and O9) display similar binding patterns (Fig 4) and, at the same time, have similar binding enthalpies of the AnxA2-membrane interaction (Fig 3). Interestingly, within both pairs the number of relevant Ca 2+ ions is very different (Fig 3). This suggests that the direct AnxA2 -membrane enthalpy reflects the general binding pattern whereas additional modifications of, e.g., the distance to the membrane via AnxA2-Ca 2+ interaction are less relevant.
More details on O5 and O6, including the minimal distances of AnxA2 from certain types of lipids and Ca 2+ ions as well as the different binding enthalpies, are given in Fig 6. Evidently, AnxA2 predominantly interacts with Ca 2+ ions and the POPS lipids. For the given concentrations the interaction enthalpies for O5 average to 0, -51, -102, -220 and -550 kcal/mol for CHOL, DOPC, POPC, POPS and Ca 2+ , respectively.
A closer comparison of AnxA2 residues that were bound to Ca 2+ ions in O5/O6 and those identified as Ca 2+ coordination sites experimentally [25] reveal some differences. Table 1 provides a list of the Ca 2+ binding residues for O5/O6 and those seen experimentally: The list of binding residues found in O5/O6 is larger than it was reported experimentally. Visual inspection of experimentally identified Ca 2+ binding sites suggests that some of those sites are unlikely to be preserved with the presence of a membrane. For example 2 Ca 2+ are bound, on the one hand, to Asp162 and Asp322 residues and, on the other hand, to AB loops of repeats 2 and 4, respectively. However, our observations show that such AB loops gets frequently buried at some extent into the interior of membrane (data not shown) and, therefore, it appears less likely that they could support Ca 2+ binding in the presence of the membrane as strongly as they do in the membrane free structure.  Table 1. Ca 2+ binding residues in O5/O6 and in experiment [25].
The initial configurations of O14 and O5 differ by a maximum change in the orientation around the x-axis (180˚difference). Both configurations show very different properties. Whereas the N-terminal tail in O5 is found at the top and repeats 1 and 2 are facing to the membrane, in O14 the N-terminal tail is located at the bottom of AnxA2 and the repeats 1 and 2 are facing to the direction opposite of the membrane (S1 Fig). More generally, the members of the corresponding group (O2, O14, O15, O16, O18) differ significantly from O5 in terms of the RMSD but also display strong total interaction energies as well as significant values of the AnxA2 -membrane interaction. Binding residues close to the membrane within this group are Glu189, Asp192, Asp230, Asp239, Asp322, Asp338 and Asp339. Bringing together the significant total interaction enthalpies of orientations of this group and the roughly inverted configuration as compared to O5 one may speculate that a dimer of that group with O5 may be a good candidate for the "up-side-down" configuration (see Fig 1).

AnxA2 and PS interaction
To address the possibility of a direct interaction between AnxA2 and POPS we focused on configuration O6. The O6 is interesting in two aspects: i) it demonstrates large rotation of AnxA2 toward the favorable configuration O5 under the condition of only a single bound calcium and ii) it serves as a good example of how direct interaction of specific lysine residues with the POPS lipids further changes the O6 configuration towards O5. In Fig 8, snapshots of the initial, intermediate and the final states of membrane-bound AnxA2 are shown for O6. Six lysine residues shown in the second row are of particular interest. At the initial times, AnxA2 interacts with the membrane without the help of Ca 2+ ions as the only Ca 2+ bound to Glu125 and Asp251 is positioned too far from the membrane. After about 150 ns the AnxA2-bound Ca 2+ start to interact with the POPS lipids, giving rise to a rotation of AnxA2 as shown in the side view. At the end of the simulation, AnxA2 appears even more tilted and rotated. At this time, repeat 1 (orange, front view) is pulled toward the membrane because of three lysine residues, Lys49, Lys81 and Lys88 that interact with POPS lipids. Repeat 3 (green) is rotated by almost 90˚after 400 ns as compared to the 10 ns configuration (side view). Repeat 4 (blue) is pulled down to the membrane with help of Lys281 and Lys286 and POPS interactions.
It should be noted that the interaction of the six lysine residues with lipids other than POPS or with cholesterol was close to zero for all times (data not shown). The temporal interaction of the lysine residues with lipids can be seen at the bottom of Fig 8. Initiation of the tilt toward the membrane by Lys49/81/88 residues is followed by a rather strong interaction of also Lys281 with POPS lipids (the enthalpy values of the latter is about the half of the sum of the enthalpies of Lys49/81/88).
After 400 ns, residues Lys49/81/88 as well as Lys281 and, partially, Lys286 are in full contact with the POPS lipids. Lys279 and Lys281 were suggested to directly interact with PI(4,5)P 2 lipids in membrane-bound AnxA2 [28]. Here we observe that Lys279 is not capable to directly interact with POPS lipids. Its preference for PI(4,5)P 2 is very likely due to the larger headgroup of PI(4,5)P 2 , which, however, is not present in the lipid mixture used to simulate the 18 orientations. The observed interaction of Lys281 with POPS suggests that in case of different lipid mixtures, a significant Lys281 -PI(4,5)P 2 interaction could occur, in agreement with the experimental data.
Except of the discussed six lysine residues there are other lysines that are in direct contact with the membrane (i.e. POPS) in the final O6 configuration. However, presumably, due to either not so favorable localization of POPS or the positioning of the side-chains of those lysine residues their interactions with the membrane were significantly weaker during the simulated period.

Membranes containing PI(4,5)P 2
The results shown so far were obtained for membranes containing only POPS as a negatively charged lipid. We additionally simulated AnxA2-membrane-Ca 2+ systems where different concentrations of PI(4,5)P 2 lipids were included into membranes. In all of these systems containing PI(4,5)P 2 AnxA2 was oriented in its favorable O5 configuration with respect to the membrane. Table 2 shows the characteristic concentrations of POPS, PI(4,5)P 2 and Ca 2+ of those systems: Due to a large negative charge of PI(4,5)P 2 (-4) the direct interaction of AnxA2 with the membrane strongly increases. This is particularly relevant in system B where 12% of PI(4,5)P 2 is present. System C contains a much larger number of Ca 2+ which corresponds to a 250 μM concentration of Ca 2+ in experiments (i.e. 1 Ca 2+ ion per lipid, see S1 Text in Supplementary Material). The interaction energies of AnxA2 with membrane components and Ca 2+ in those systems are shown in Fig 9. The 200 ns simulation period is not enough for the systems to reach full equilibration, so that at later times the effects, reported in this work, should be even stronger. Nevertheless, for system A with 3% PI(4,5)P 2 AnxA2 could interact with only one PI(4,5)P 2 (six PI(4,5)P 2 were distributed randomly per bilayer leaflet for this system).while simultaneously interacting with 3-4 Ca 2+ ions. The total AnxA2-membrane and AnxA2-Ca 2+ interactions are about the same. On the other hand, in system B the total AnxA2-PI(4,5)P 2 interaction is significantly stronger Annexin A2-Membrane interaction while, on the contrary, the AnxA2-Ca 2+ is weaker than in system A. In case of system C with high concentration of Ca 2+ the AnxA2-membrane (including PI(4,5)P 2 ) interaction is very small. These observations suggest that, at high Ca 2+ concentrations, the AnxA2-Ca 2+ interaction dominates over the AnxA2-membrane interaction. In intact cells, however, where the Ca 2+ concentration is way below 1 μM (similar to system A) the PI(4,5)P 2 and Ca 2+ interactions both will support AnxA2-membrane binding.
In system B the AnxA2-membrane interaction through PI(4,5)P 2 lipids is the strongest but can still be compared with the membrane-Ca 2+ interactions. Fig 10 shows the membrane curvature as reflected by the z coordinates of the lipids' phosphor atoms P relative to the average z value of all P atoms in the corresponding leaflet as well as the interaction energies of membrane-AnxA2 and membrane-Ca 2+ pairs, respectively.
Obviously, the bending of the leaflet represented in the upper row is a result of the bending of the leaflet in the bottom row where the membrane and most of Ca 2+ are localized. Interestingly, the membrane regions with negative curvature correlate with membrane-Ca 2+ interactions much better than with membrane-AnxA2 interactions. Similar behaviors can be observed for systems A and C shown in S2 Fig. Table 3 shows the correlation coefficients of curvature and the interaction of lipids with either AnxA2 or Ca 2+ . It can be noted that for systems A and B the correlation coefficient of the membrane leaflet with AnxA2 is 0.4-0.5 for membrane-Ca 2+ interaction while the influence of membrane-AnxA2 on the curvature is close to zero. In most of in-vitro experiments as well as in MD simulations a high Ca 2+ concentration was used. As a Table 2  Annexin A2-Membrane interaction result, the large number of Ca 2+ ions mask the direct membrane-AnxA2 interaction. Our results suggest that the membrane bending occurs due to membrane-Ca 2+ interactions and is not driven by the interactions with the convex face of AnxA2. We also analyzed the correlation of the order parameter (S CD ) of membrane lipids with the interaction strength with either AnxA2 or Ca 2+ ions. Fig 11 shows the dependence of the average order parameter on the respective interaction energy for system B. Those lipids which significantly interacted with both AnxA2 and Ca 2+ ions are shown separately with yellow circles. Such lipids were predominantly PI(4,5)P 2 lipids.

Systems POPS (%) PI(4,5)P 2 (%) CA 2+ (N)
Interestingly, a stronger interaction of the membrane with AnxA2 gives rise to an increase of the order parameter of the corresponding interacting lipids while, on the contrary, a stronger interaction with Ca 2+ results in the opposite effect. Somewhat weaker but similar effects can be observed for system A in S3 Fig. For system C the bilayer seems to be saturated by Ca 2+ (membrane-AnxA2 interaction is negligible) and the order parameter does not show a particular dependence on the interaction with Ca 2+ (S3 Fig). In recent work Chen and co-workers have found that the lipid order was decreased upon interaction with annexin A5 [38]. This apparent discrepancy may be a result of structural differences between AnxA2 and annexin A5. Another reason can be the fact that Chen et al. used a high Ca 2+ concentration which played a primary role in annexin A5 and membrane interaction even when annexin A5 was positioned very close to the membrane. Thus, the interaction with the annexin A5 could be dominated by the presence of Ca 2+ . This would be fully compatible with the present results where we could individually analyze both contributions. The upper and lower rows represent the membrane leaflets which are non-interacting and interacting with AnxA2, respectively. The first column represents the difference in the Z direction of the phosphor P atoms in all lipids relative to the average Z value in Å. The second column displays the total interaction energy of membrane-AnxA2 pairs while the last column represents the total interaction energy of the membrane-Ca 2+ pairs. The energies in the second and third columns are in units kcal/mol. The points in the X and Y planes reflect the coordinates of the P atoms of the lipids.
https://doi.org/10.1371/journal.pone.0185440.g010 Table 3. Correlation coefficients of membrane bending and interaction energies in systems A, B and C. Two additional results are helpful for our systematic analysis of the membrane-AnxA2 interaction. (1) When simulating AnxA2 and 12 Ca 2+ ions together with a neutral membrane i.e. with only DOPC and POPC lipids, no binding of AnxA2 was observed. The protein was detached from the membrane surface together with most of the calcium ions (data not shown). Thus, charged lipids are indeed essential for the membrane-AnxA2 binding. (2) When placing the full length AnxA2 with reconstructed first 20 residues of its N-terminal tail toward the membrane (with composition DOPC 19% :POPC 38% :POPS 19% :PI(4,5)P 2 5% :CHOL 19% ) we also observed fast detachment within the first 50 ns (data not shown). Thus, a potential interaction of the membrane with the N-terminal tail of AnxA2 is by far too weak. This agrees with the suggestion that AnxA2 core is solely responsible for membrane binding and lipid segregation [28].

Discussion
Our MD simulations of different AnxA2 orientations on a membrane consisting of DOPC, POPC, POPS and cholesterol have yielded for the first time atomistic information concerning the structure, enthalpy, orientation, and lipid headgroup binding characterizing the AnxA2-membrane interaction. Several open questions in the field can now be addressed in light of our observations. First, crystal structures of AnxA2 and other annexins in solution have revealed that the proteins fold into compact discs with one side, the convex side, harboring annexin-type Ca 2+ binding sites. It has been speculated but never shown that this side faces the membrane in membrane-bound annexins. Our simulations indicate that this is indeed the case as orientation O5 resembling the configuration with annexin-type Ca 2+ binding sites facing the membrane is the most favorable orientation of the protein on membranes in terms of the enthalpic interaction.
Second, while the formation of AnxA2 dimers in an "up-side-down"configuration has been discussed but never proven [25], we now present evidence that such dimeric interaction between two AnxA2 monomers in the "up-side-down"configuration could exist when Ca 2+ ions are present. Our simulations end in two main AnxA2 -membrane configurations. The first one is the most favorable configuration represented by O5 and the closely resembling O6 orientation (also covering orientation groups such as O8 and O9) and the second is represented by O14 and its group that together with O5 could form an "up-side-down"dimer. Of course, the present simulations cannot elucidate the properties of the direct AnxA2-An-xA2-interaction in the "up-side-down" configuration.
Third, we demonstrate that AnxA2 can interact with the POPS lipids present in our mixture without the need to involve Ca 2+ ions. This direct interaction was observed in the induced rotation of AnxA2 from the O6 to the O5 configuration in a Ca 2+ depleted environment (only a single AnxA2-Ca 2+ pair). Such Ca 2+ independent interactions were not observed in many experimental lipid binding studies [28,46], but possible AnxA2-membrane interactions that could occur in the absence of Ca 2+ -ions had been discussed before [47]. This discrepancy is, possibly, related to the rather unstable interaction between AnxA2 and POPS lipids due to diffusion effects of POPS lipids and the high mobility of the lysine side-chains which render the experimental observation of binding effects more difficult.
Fourth, we emphasize the role of Glu125/Asp251 as a binding site for Ca 2+ at low Ca 2+ concentration. Binding of Glu125 and Asp251 to a single Ca 2+ ion on one hand and binding of that Ca 2+ to POPS or PI(4,5)P 2 lipids on the other hand strongly stabilizes AnxA2 in the favorable O5 configuration (Fig 8) and shows significant interactions in the O6 configuration (Fig 3). In contrast to Glu125/Asp251 the other Ca 2+ binding sites revealed in O5 are localized more on periphery of the molecule which seems to require several Ca 2+ to be bound at the same time for effective membrane interaction in O5 configuration (see S1 Fig, configuration O2 where only one of the binding sites were interacting with Ca 2+ which resulted in tilting of AnxA2).
Fifth, the negative curvature of the membrane, which is observed in the AnxA2/ Ca 2+ /membrane simulations, seems to be primarily related to the membrane-Ca 2+ interaction rather than the convex membrane-binding surface of AnxA2. Clearly, once AnxA2 binds to Ca 2+ ions, the convex face of the former plays a positive and likely important role in membrane bending. However, AnxA2 seems to serve more as a platform for fixation of the negative curvature of the membrane induced by Ca 2+ ions. This agrees with a recent study of influence of Ca 2+ on negatively charged bilayers containing POPS and PI(4,5)P 2 lipids [19]. Sixth, the direct interaction of AnxA2 with the membrane induces an ordering of interacting lipids while the membrane-Ca 2+ interaction distorts the lipid order. This was observed in our MD systems only at low Ca 2+ concentrations. At high Ca 2+ concentrations the direct AnxA2-membrane interaction is minimal as it is almost completely masked by much stronger membrane-Ca 2+ interactions. To the best of our knowledge, the AnxA2-induced ordering effect of lipids is reported here for the first time, possibly, because most of the previous annexin studies used high Ca 2+ concentration.
In more general terms, the AnxA2 -membrane binding is an interesting example where different cooperative effects are important. First, as seen for the time evolution of the initial O6 configuration, the simultaneous rotation and the clustering of the negatively charged lipids gives rise to an increased stability, rendering the O6 configuration more O5-type. Second, the presence of negatively charged lipids will increase the attraction of Ca 2+ ending up in the stable O5 configuration, including the large number of calcium ions. Molecular Dynamics simulations can help to elucidate the details of these mechanisms.

Initial structure preparation
The system consisting of a membrane of the composition POPC:DOPC:POPS:CHOL at relative concentrations of 0. 38 [25] was prepared using the CHARMM-GUI Web-based graphical interface [48,49] and CHARMM36 force field [50,51]. This structure generated by CHARMM-GUI is further manipulated with the CHARMM package [52]. First the water molecules were removed from the unit cell and the AnxA2 was centered on the membrane surface such that its first and second principle axes were parallel to X and Y directions, respectively, i.e. AnxA2 was lying in a very flat position over the membrane. Then AnxA2 was moved away in Z direction to a large enough distance (100 nm). The resulting initial structure served as a basis for generation of all the relative orientations of AnxA2 in respect to membrane.

Generation of the 18 AnxA2 orientations
To generate the different initial orientations of AnxA2 in a systematic way, the initial structure of AnxA2 was rotated around its center of mass, first around the X axis and subsequently around the Y axis. After rotation of AnxA2 in each of the 18 orientations AnxA2 was dragged in Z direction back to the membrane such that the minimal distance between the membrane and AnxA2 became about 6 Å. The respective angles of rotations are shown in Table 4.
All the 18 systems were solvated with the TIP3P type water molecules. 12 water molecules were randomly selected within the region between membrane and AnxA2 and replaced by Ca 2+ ions. The final system sizes of each 18 systems on average was 135 x 135 x 150 Å. With the presence of negatively charged lipids such as POPS the membrane-Ca 2+ binding takes place at sub-nanosecond times. Because of this fast kinetics, the AnxA2-membrane interaction studied in our MD simulations can be considered as starting at a condition where Ca 2+ is bound to the membrane. To finalize the preparations of the 18 systems the required amount of chloride and sodium ions were added to each system to obtain~150 mM salt concentration and to guarantee neutral charge. Each of the 18 systems on average contained 190000 atoms.
Additionally, three systems A, B and C were prepared with PI(4,5)P 2 lipids added to membranes. The first two systems A and B contained 3% and 12% of PI(4,5)P 2 lipids (84 POPS and 12 PI(4,5)P 2 lipids for system A and 48 POPS and 48 PI(4,5)P 2 for system B) and 16 Ca 2+ ions (i.e. the concentrations of POPS lipids in these systems were decreased to 21% and 12%, respectively). The third system C with 5% PI(4,5)P 2 and 19% POPS (76 POPS and 20 PI(4,5)P 2 lipids) included much higher Ca 2+ concentrations with a total number of 150 Ca 2+ ions. In all system A, B and C AnxA2 was placed above the membrane at the predefined orientation O5 and at a 2 Å minimal distance from the membrane. Here the minimal distance from the membrane was chosen smaller to account for the larger head groups of PI(4,5)P 2 lipids to keep the direct interaction of AnxA2 with the membrane strong enough.

Simulation settings
The MD simulations were performed with the Gromacs package [53][54][55] and analyzed by the CHARMM program. The electrostatic and van der Waals interactions were calculated through Annexin A2-Membrane interaction the particle mesh Ewald [56] and cutoff schemes, respectively, with cutoff distance of 1.2 nm. The NPT ensemble, semiisotropic pressure tensor of 1 bar, Parrinello-Rahman pressure coupling [57] and Nosé-Hoover temperature coupling [58,59] methods were used together with the time step of 2 fs. Each of the 18 systems were simulated at 293 K temperature for 400 ns. The three systems A, B and C with PI(4,5)P 2 were simulated at 310 K for 200 ns.