Annexins induce curvature on free-edge membranes displaying distinct morphologies

Annexins are a family of proteins characterized by their ability to bind anionic membranes in response to Ca2+-activation. They are involved in a multitude of cellular functions including vesiculation and membrane repair. Here, we investigate the effect of nine annexins (ANXA1-ANXA7, ANXA11, ANXA13) on negatively charged double supported membrane patches with free edges. We find that annexin members can be classified according to the membrane morphology they induce and matching a dendrogam of the annexin family based on full amino acid sequences. ANXA1 and ANXA2 induce membrane folding and blebbing initiated from membrane structural defects inside patches while ANXA6 induces membrane folding originating both from defects and from the membrane edges. ANXA4 and ANXA5 induce cooperative roll-up of the membrane starting from free edges, producing large rolls. In contrast, ANXA3 and ANXA13 roll the membrane in a fragmented manner producing multiple thin rolls. In addition to rolling, ANXA7 and ANXA11 are characterized by their ability to form fluid lenses localized between the membrane leaflets. A shared feature necessary for generating these morphologies is the ability to induce membrane curvature on free edged anionic membranes. Consequently, induction of membrane curvature may be a significant property of the annexin protein family that is important for their function.

1 Model for membrane rolling on a support with adhesion 1.1 Condition for stability of a supported membrane λ d Figure S1: Stability of a supported membrane patch of radius d. The free membrane edge has a line tension λ.
We consider a membrane placed on top of a primary supported membrane. The top membrane is mechanically stable if its attractive interaction energy with the primary supported membrane is larger than the line tension energy of the membrane edges. The adhesion energy is proportional to the membrane area while the line tension is proportional to its total perimeter. Considering initially a disk-shaped membrane, there is a critical radius d 0 = 2λ/w ad below which the bilayer is unstable and will transform to a vesicle. Here λ is the line tension of the free membrane edge and w ad is the adhesion energy per area. For d > d 0 , the membrane can be stable and remain flat. However, upon binding of curvature inducing proteins (e.g. annexins) there is an curvature energy penalty in the flat configuration due to a spontaneous curvature (c 0 ) induced by the proteins bound to the membrane. If this energy penalty is sufficiently large, the top membrane may start to curve, even for large areas where d d 0 . We consider the rolling of a planar membrane on a support surface consisting of a primary membrane and a solid material underneath. In the initial state, the membrane is flat and is terminated by a linear free edge.

Initiation of membrane rolling
Upon binding of a protein (e.g. annexins) to the membrane surface the effect of the protein is modeled as the induction of a spontaneous curvature (c 0 ) of the combined membrane/protein sheet. We will determine the energy difference between the initial flat configuration and a final state where the membrane is rolled. The energy of the initial (flat) state is: The energy in the final (rolled) state is: where k c is the mean curvature elastic modulus [1]. In the case of a linear roll, the mean curvature c = 1 R1 + 1

R2
reduces to c = 1 R(s) where R(s) is the local radius of curvature in the roll at arc length s. The energy change for a roll of width W from the flat to the rolled state is: From equation (3) it can be concluded that ∆E is minimal when 1 R(s) = c 0 . Rolling is energetically favored when ∆E < 0 or when: Equation (4) provides a condition for the initiation of rolling.

Rolling
Once the barrier in equation (4) has been overcome, the membrane can roll and separate from the bilayer continuously. However, during rolling the curvature radius R(s) increases and eventually the adhesion energy will overcome the gain in curvature elastic energy and rolling stops. Experimentally we find that rolling proceeds to distances of at least 100 µm. Below we investigate the energetics of the rolling process and determine the rolled distance L in terms of the system parameters k c , c 0 and w ad .
First we note that equation (3) simplifies to: To model the rolling process, we assume that the roll is shaped as an archimedean spiral defined by: r(θ) = a+bθ.
Here r(θ) is the radius of the spiral at the rolling angle θ, a is the radius of the inner roll and 2πb is the repeat distance between roll layers. In the following, the parameter a will be determined by energy minimization while b is estimated from experiments. A significant simplification is obtained if the curvature radius is approximated by the radius of the spiral: R ≈ r. We discuss the validity of this approximation in the subsequent section. We also note that ds ≈ rdθ = r b dr. With these simplifications, equation (5) becomes: After integration, equation (6) becomes: The variables θ and a are determined by minimization of the energy change ∆E: Here θ m is the maximal rolling angle corresponding to the angle when rolling stops. Corresponding to this is the maximum (final) radius of the roll: r m = a + bθ m . By inserting ∆E from equation (7) we arrive at the following expressions for the parameters in the final state of the roll: Maximum roll radius r m : The maximal rolling angle θ m : Rolled distance L: The slope b of the archimedean spiral can be found as: From which the layer spacing 2πb is easily found from experimentally measured values of L and r m .

Rolling model without approximated curvature radius
We now investigate the rolling model in the case where the curvature radius R is described exactly and not approximated by r. Given the expression r(θ) = a + bθ for the spiral, the radius of curvature is given exactly as: where r θ = dr dθ and r θθ = d 2 r dθ 2 . The arc length s is given as: Inserting equation (14) and (15) into equation (5) we obtain: Next we need to find the minimum of ∆E according to equations (8). Here we take advantage of Leibnitz rule: Minimization of ∆E in equation (16) leads to the following polynomium: with the roots x 1 and x 2 given as: Equation (18) is solved numerically and the value of a and θ m found from equations (19). The rolled distance L is determined by integration of ds:

Results
Next we evaluate the rolled distance and compare the results of the two models described above. We estimate values for the parameters: k c , c 0 , w ad and b. Precise values corresponding to our experimental system (POPC,  [4].
w ad will cover a range of relevant values. Literature values for neutral SOPC bilayers in 0.1 M PBS report a value of w ad 1.0·10 −5 J/m 2 [6].
A comparison of the rolled distance L versus w ad /k c for the two models described above is shown in Figure S3.
Values of the system parameters are indicated above. The two models are indistinguishable on a doublelogarithmic scale and therefore the approximate model gives a reasonable estimation of the rolled length L. Below is a series of extended data for the annexins interacting with membrane patches. The membrane composition is in all cases: POPC,POPS (90%:10%). DiD-C 18 Figure S5: Negative control experiments for membrane patches exposed to annexins in the absence of Ca 2+ .

Negative controls: Absence of Ca
Frames (a-f) show the membrane patches immediately before addition of annexin while frames (g-l) show the same patches 10 min after exposure to 13 nM annexin with the type indicated above frames. There is no response of the membrane patches to annexin except for a weak physical relaxation of the membrane shape in some cases (e.g. c to i) which is also observed without annexin. For comparison, the time point 10 min shows a strong response to all tested annexin types in the presence of 2 mM Ca 2+ . Control experiment with ANXA4-Ca3mut (m-p), a mutation of ANXA4 where 3 out of 4 Ca 2+ -binding sites are passivated. Binding does not induce rolling, but instead leads to a slow vesiculation from the patch within 10-15 min. Control experiment with the PS-binding domain Lact-C2-GFP from lactadherin (q-y) [7]. In this case binding is observed in the GFP channel and does not produce rolling. However, small holes in the membrane patch are generated by Lact-C2-GFP and these are partly closed again after 10 min. Concentrations: ANXA4-Ca3mut: 43 nM, Lact-C2-GFP: 81 nM.