Masoud Hoore

François Yaya

Thomas Podgorski

Christian Wagner

Gerhard Gompper

Dmitry A Fedosov

Effect of spectrin network elasticity on the shapes of erythrocyte doublets †

Red blood cell (RBC) aggregates play an important role in determining blood rheology. RBCs in plasma or polymer solution interact attractively to form various shapes of RBC doublets, where the attractive interactions can be varied by changing the solution conditions. A systematic numerical study on RBC doublet formation is performed, which takes into account the shear elasticity of the RBC membrane due to the spectrin cytoskeleton, in addition to the membrane bending rigidity. RBC membranes are modeled by two-dimensional triangulated surfaces embedded into three dimensions. The phase space of RBC doublet shapes in a wide range of adhesion strengths, reduced volumes, and shear elasticities is obtained. The shear elasticity of the RBC membrane changes the doublet phases significantly. Experimental images of RBC doublets in different solutions show similar configurations. Furthermore, we show that rouleau formation is affected by the doublet structure.

Introduction

In whole blood, red blood cells (RBCs) experience a pronounced attractive interaction, which is mediated by plasma proteins such as fibrinogen 1,2 . Similar attraction between RBCs is also observed in solutions of dextran [3][4][5] or other macromolecules. Such attractive interaction leads to the formation of RBC aggregates, in particular large rouleaux, which play an essential role in the strong shear-thinning behavior of blood at low and moderate shear rates [6][7][8] . Thus, the interaction of RBCs with each other and with adhesive surfaces is of high interest to understand the rheology of blood and rouleau formation. The first step for studying RBC assemblies into rouleaux is an aggregate of two RBCs, called doublet. The formation and shape of RBC doublets is determined by the competition between bending and shear elasticity, and the † Electronic Supplementary Information (ESI) available: Supplementary Movie S1 illustrates the performance of two different discretizations (KN and GK) of the Helfrich bending energy from Eq. (1) for a fluid vesicle in equilibrium. The KN model fails to properly capture a characteristic biconcave shape in equilibrium, while the GK model leads to the biconcave resting shape. Supplementary Movie S2 demonstrates the formation of RBC doublets for different shear moduli and reduced adhesion strengths. See DOI: 10.1039/b000000x/ ‡ Correspondence should be sent to d.fedosov@fz-juelich.de.

adhesion energy.

RBC membrane has a characteristic biconcave shape, which can be well described by the Helfrich bending elasticity 9,10 similar to fluid vesicles, whose shape is determined by the bending free energy and volume and area conservation of a closed membrane 11,12 . However, in addition to bending resistance, RBC membranes possess a shear elasticity supplied by their spectrin cytoskeletal network, which differentiates them from lipid vesicles [START_REF] Fung | Biomechanics: Mechanical properties of living tissues[END_REF][START_REF] Lim | Proc. Natl. Acad. Sci[END_REF][START_REF] Gov | [END_REF] .

The first theoretical studies [16][17][18] of RBC doublets considered a flat shape for the contact surface between RBCs to simplify the analysis. Later, numerical studies have shown that two fluid vesicles with bending rigidity and constant volume form a curved contact surface [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF][START_REF] Svetina | [END_REF][21] . Different shapes of vesicle doublets as a function of their adhesion strength and bending rigidity were predicted. These shapes are also qualitatively consistent with those obtained in several two-dimensional (2D) investigations [22][23][24] . In a recent work 25 , various RBC doublet phases have been explored depending on the dextran and fibrinogen concentration, which modifies the attractive interaction between RBCs. The experimental data have been mainly supported by two-dimensional (2D) simulations 25 , and therefore, it remains unclear whether the whole phase space of the system has been explored or not and whether some other RBC doublet phases exist in practice. Furthermore, another interesting question is how the shear elasticity of RBC membrane affects different doublet phases, since previous investigations [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF][START_REF] Svetina | [END_REF] have primarily focused on bending Fig. 1 Schematic of the two discretization models for the bending energy. The KN discretization 35 in Eq. ( 2) considers the bending between each two triangles, while the GK discretization 32 in Eq. ( 3) represents the bending of each vertex with respect to all of its linked vertices.

rigidity. Similar issues are important for the complexation of vesicles with particles of similar size, such as colloidal particles or other vesicles 26 , as well as for similar complexes of RBCs with other micro-particles.

Here, we systematically study the phase space of RBC doublets using simulations of high resolution triangulated membranes with bending and shear elasticity in three dimensions (3D). Specifically, we focus on the effect of membrane shear elasticity in determining different RBC doublet phases and find that a change in RBC shear elasticity significantly modifies doublet phase space. Furthermore, we explore the influence of RBC reduced volume on doublet shapes. The various phases of RBC doublets, predicted theoretically, are also compared with experimental results.

Methods & models

Membrane model

The RBC membrane is represented by a triangular mesh, as described in detail in Refs. [27][28][29][30] . The important energies for RBC doublets are the bending energy from lipid bilayer elasticity, shear elasticity of the spectrin network, and the adhesive energy between the two RBCs. The bending energy for fluid membranes, which do not possess a preferred radius of curvature, reads 9,[31][32][33][34]

U b = 1 2 k c I A dA (c 1 + c 2 ) 2 + k g I A dAc 1 c 2 , ( 1
)
where k c , k g , c 1 , and c 2 are the bending rigidity, Gaussian bending modulus, and principal curvatures of the membrane, respectively. The energy is integrated over the whole membrane area A enclosing the volume V . The integral over the Gaussian curvature K = c 1 c 2 is constant for a fixed topology, due to the Gauss-Bonnet theorem 32,34 .

The simplest discretization of the bending energy in Eq. ( 1) has been proposed by Kantor & Nelson (KN) 35 for every pair of 28,29 adjacent triangles,

U KN = Â i, j k b 1 n i jk • n i jk 0 , ( 2
)
where k b is the bending constant, and n i jk is the unit normal vector of the triangle with vertices i, j, and k (see Fig. 1). The quantity k b is related to the bending rigidity k c as k c = k b p 3/2 for a sphere in continuum limit 28,32,36,37 . Even though such discretized bending model for RBCs has been quite successful in predicting RBC behavior, including membrane fluctuations 38 , RBC mechanical properties [27][28][29] , and flow dynamics [START_REF] Lanotte | Proc. Natl. Acad. Sci[END_REF][START_REF] Fedosov | [END_REF] , it is not accurate enough if the bending energy of the membrane dominates.

A similar conclusion has been also reached in a recent investigation 41,42 , where different discretizations of the bending energy were tested.

A more accurate discretization for the bending energy has been proposed by Gompper & Kroll (GK) 32 as

U GK = 1 2 k c  i 1 s i  j(i) s i j rij ! 2 , ( 3
)
where s i = 1 4 Â j(i) s i j r i j , s i j = r i j (cot q k + cot q k 0 ) /2, r i j is the distance from vertex i to j, rij is the unit vector pointing to vertex i from j, j(i) are the vertices connected to vertex i by bonds, and q k and q k 0 are the angles opposite to the bond between vertex i and j in triangles ik j and ik 0 j (see Fig. 1). s i and s i j are the area of each cell and the length of each bond, respectively, in the dual lattice of the triangulated lattice of the membrane 32 , as shown in Fig. 1. Different discretization models have been explained in more detail in Refs. [41][42][START_REF] Gompper | Statistical mechanics of membranes and surfaces[END_REF] .

The membrane elasticity due to the spectrin bonds is represented by a combination of the worm-like chain (WLC) and power (POW) potentials, as described in Refs. 28,29 . The network model of the membrane conserves its global surface area and volume by harmonic constraint potentials with stiffnesses k a and k v , respectively 28,29 . The local area of each triangle is also softly constrained by a harmonic potential with a stiffness k l 28,29 . The Young's and shear moduli are derived from the WLC potential and the area conservation potentials, as described in Refs. 29,50,51 .

Since our main interest is in final doublet configurations in equilibrium, which are determined by a minimum of energies involved, dynamic effects are not contributing and the effect of membrane and fluid viscosities can be neglected. In simulations, the motion of membranes is governed by Langevin dynamics [START_REF] Allen | Computer simulation of liquids[END_REF] . It Fig. 2 Vesicle shapes from the two discretization schemes of the bending energy. The elastic bond (spring) potential is turned off, so that no shear elasticity is present. The standard biconcave shape of a RBC is maintained if the discretization is based on the GK scheme. The KN scheme fails to keep the RBC biconcave shape (see Supplementary Movie S1).

is worth mentioning that our simulation approach includes thermal fluctuations, which, however, are of minor importance for doublet shapes. The membrane properties of RBCs are provided in Table 1.

In order to test the performance of the two discretization schemes for bending energy, we model the equilibrium shape of a fluid vesicle with a reduced volume n = 3V /4pR 3 s = 0.64, where 4pR 2 s = A. For this value of reduced volume, the vesicle must attain a biconcave shape [START_REF] Seifert | [END_REF] , which is also the equilibrium shape of RBCs [START_REF] Canham | [END_REF] . Here, A and V correspond to the membrane area and volume, respectively. Note that the shape of a vesicle is determined by the bending energy and reduced volume 11,12,[START_REF] Seifert | [END_REF] . By removing shear elasticity from the membrane model (i.e. omitting the bond potential), we find that the KN discretization from Eq. ( 2) does not preserve the initial biconcave shape of the membrane (see Fig. 2 and Supplementary Movie S1), indicating that this state does not remain the equilibrium point for the membrane. In contrast, the GK discretization from Eq. (3) successfully keeps the biconcave shape without the spectrin network elasticity, as shown in Fig. 2 and Supplementary Movie S1. The shear elasticity of the RBC membrane from spectrin network partially compensates the inaccuracy of the KN model; however, the GK model is clearly more accurate and is employed in this work.

Adhesion model

To represent aggregation between two RBCs, attractive interactions between two membranes are introduced similar to other models [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF][START_REF] Svetina | [END_REF]25,54 of interacting membranes. Note that such interactions cannot be directly associated with any underlying mechanism for RBC aggregation (e.g. depletion or bridging). Therefore, this model constitutes an effective representation of the aggregation between RBCs, which is characterized by the strength of attractive interaction and contact area.

The attractive interaction between adjacent vertices of membranes in contact is modeled by the Lennard-Jones (LJ) potential

U LJ (r) = 4e  ⇣ s r ⌘ 12 ⇣ s r ⌘ 6 , (4)
where e and s are the energy and characteristic length of the LJ interaction. The LJ potential is cut off at r cut = 2.5s . The contact interaction of two RBCs can be represented by the adhesion free energy [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF][START_REF] Svetina | [END_REF]

E adh = GA c , ( 5
)
where G is the adhesion strength and A c is the contact area. Providing that the adhesion is modeled by a pairwise interaction, such as the LJ potential in Eq. ( 4), between membrane vertices, the adhesion strength G can be related to the potential energy e. If N c vertices from one RBC interact with the vertices from another RBC, the total adhesion energy is N c ẽ, where ẽ is the effective adhesion energy of one RBC vertex with the other RBC vertices. ẽ can be calculated approximately by considering the Fig. 4 The ratio of the effective adhesion energy ẽ to the pairwise energy e. This ratio depends weakly on the configuration of the two adhered RBCs, as illustrated in Fig. 3. Simulations are conducted for the system until it reaches equilibrium. The reported data are averaged over 250 uncorrelated points in simulations from the equilibrium states. On average, ẽ/e = 4.23 ± 0.03.

closest vertices to a vertex from another membrane, as illustrated in Fig. 3. In a minimal energy state, a vertex sits on top of three vertices in a tetrahedral configuration with equal distance s to all of them. The adhesion energy of this vertex with the other closest neighbors sums up to about 5.37e. Consequently, the total adhesive energy, when N c vertices participate in the adhesion from each membrane, is equal to about 5.4N c e. However, this high symmetry situation of course does not occur for all of the vertices, resulting in a somewhat smaller adhesion energy.

As vertices of a membrane are homogeneously distributed on the membrane, N c /A c = N/A, in which N and A are the total number of vertices and total area of the RBC membrane. Thus, the adhesion strength is directly proportional to the vertex density N/A, i.e. G = N c ẽ/A c = N ẽ/A. This implies that the adhesion strength is proportional to the LJ parameter e via ẽ.

The reduced adhesion energy, g, is defined as the ratio of the total possible adhesion energy (i.e. when A c = A) to the bending energy of a sphere,

g = GA 8pk c = N ẽ 8pk c . ( 6
)
The ratio ẽ/e as a function of g and reduced volume n 4, which shows how the effective adhesion energy ẽ is related to the pairwise LJ energy e. For different e values, the equilibrium distance between the two membranes may change, leading to a different relation between e and ẽ. This is the main reason for an increase in ẽ/e with decreasing g. A very weak dependence of ẽ/e on the reduced volume n can be due to the local curvature of contact. Additionally, for large enough n, membranes in a doublet configuration are under tension, which may contribute to the dependence of the ratio ẽ/e on n. Finally, the amplitude of thermal fluctuations of a RBC membrane is known to be spatially non-uniform along the surface 55,[START_REF] Park | Proc. Natl. Acad. Sci[END_REF] , and to depend on membrane shape, local curvature, and tension [START_REF] Evans | Proc. Natl. Acad. Sci[END_REF] . Membrane thermal fluctuations are included in the model (see Supplementary Movie S2) and would effectively introduce short-range repulsion between two membranes.

(n 1 = n 2 = n) is presented in Fig.

Experiments

Blood was obtained by finger pricking from healthy donors after giving an informed consent in compliance with the ethical requirements of the Saarland University, Saarbrücken, Germany (Ärztekammer des Saarlandes, approval number 24/12). RBCs were washed twice with Phosphate Buffered Saline (PBS, 290 mOsm) following the standard procedure [START_REF] Baskurt | [END_REF] . Then, RBCs were resuspended in several solutions to obtain several doublet configurations. In order to have various adhesion energies 4 , we prepared dextran solutions with different molecular weights:

• 40 kDa at a concentration of 10 mg/ml with an adhesion energy close to 1 µJ/m 2 ;

• 70 kDa at a concentration of 20 mg/ml with an adhesion energy close to 4 µJ/m 2 ;

• 500 kDa at a concentration of 10 mg/ml with an adhesion energy close to 6 µJ/m 2 .

Fibrinogen was added with a concentration of 6 mg/ml to autologous plasma as it does not induce spontaneous aggregation on its own. A hypotonic solution of NaCl at 0.6% was also prepared to increase RBC volume. To induce aggregation, dextran 70 kDa was added with a concentration of 50 mg/ml into this solution. The hematocrit level was kept at 0.5% in every sample. Such low concentration of RBCs allows us to manipulate cells freely with holographic optical tweezers. Then, cells were held at their edge with four optical traps. RBCs were brought together to form doublets and the traps were released, so that they can spontaneously aggregate. As dextran is known to induce spontaneous aggregation 59 , we observe the formation of rouleaux over time. Finally, RBCs were let to sediment for 30 mins and micro-photographs were taken using a 60-fold objective. Morphologies of these aggregates were characterized similarly to those in the simulations.

Doublet shapes

The theoretical adhesion strength G is related to dextran and fibrinogen concentrations in experiments 59,60 . RBC doublet shapes are determined by the adhesion strength (G, or equivalently g), the reduced volumes n 1 and n 2 , and the elastic parameters such as bending rigidity k c and shear elasticity G. The adhesion strength of the RBC membranes is about 1µJ/m 2 in plasma and about 10µJ/m 2 in dextran solutions 61 , corresponding to g ⇡ 4 in plasma and g ⇡ 40 in dextran. The RBC volume is also subject to change in different solutions, and may also vary from one cell to the other.

Figure 5 shows doublet conformations, contact area, and bending energy for various n 1 = n 2 = n and g. The contact area A c is normalized by the RBC area A. The bending energy E b is calculated directly from simulations and normalized by the bending energy 8pk c of a sphere, where e b denotes the reduced bending energy.

e b = E b 8pk c , ( 7
The contact area is more sensitive to the reduced adhesion strength and bending energy is more sensitive to the reduced volume, see Fig. 5(a). Overall, as the reduced volumes decrease and the adhesion strength increases, both contact area and membrane bending energy increase.

The configurations both for the initially aligned and for offset doublets (Fig. 5(c)) are depicted in Figs. 5(e) and (f). The phases of RBC doublets for the initially aligned and offset configurations match at high adhesion strengths or high reduced volumes. However, a mismatch of doublet phases is observed for low adhesion strengths and low reduced volumes, see Figs. 5(d), (e), and(f).

This indicates the existence of several local minima in the freeenergy landscape, making the first point of contact important for RBC doublets. Multiple local minima in the free-energy should also exist for fluid vesicles, even though it has not been demonstrated so far. In comparison to vesicles, RBCs also possess an elastic spectrin network, which may have an anisotropic local prestress. This additional property likely contributes to a complex energetic landscape for RBC doublets with several metastable states or local minima.

Various phases can be distinguished, as illustrated in Figs. 5(e) and (f). All observed shapes are categorized by their contact surface and their non-adhered free surfaces, as follows: • Male-Female (M-F) phase: Both RBCs attain a cup shape and plug into each other similar to the male and female terminals of a socket. The M-F phase provides the highest contact surface at the cost of bending energy, so that the total energy is minimized.

• Sigmoid-Concave (Yin-Yang) phase: The RBCs make a sigmoid contact area, which is different from the native sigmoid (concave) shape of a RBC membrane. This condition occurs at high adhesion strengths, since the bending free energy of the RBCs increases substantially, but is compensated by the decrease in the adhesion energy. Since the cross-sectional view of the Sigmoid-Concave shape looks similar to the Yin-Yang symbol, we also call it Yin-Yang phase.

• Sigmoid-Biconcave (S-B) phase: This phase is located between the Yin-Yang and M-F phases. The RBCs are attached to each other in such a way that the concave part of one RBC fills the convex part of the other. In other words, the contact surface is sigmoid, while the free surface remains biconcave.

• Flat-Concave (F-C) phase: If both RBCs are swollen, the M-F phase becomes unstable and both RBCs reconcile by making a flat contact surface and keeping their free surfaces near spherical. This phase appears at large reduced volumes.

• Flat-Biconcave (F-B) phase: This phase with a flat contact area and remaining concavities at the free surfaces is obtained for n 1 = n 2 ⇡ 0.3-0.4 and g . 8 when the RBCs align with no offset. Figures 5(e) and (f) show that the F-B phase shrinks to a very small region if the RBCs are initially in contact with an offset. Thus, the F-B phase is less probable to be seen under physiological conditions, where the offset contact is far more probable than the aligned contact.

Although the F-B phase is the stable doublet configuration for the aligned doublets, the bending energy at this state is not at a global minimum. It can be seen from the free energy difference between the aligned and offset configurations in Fig. 5(d). Under physiological conditions (n ⇡ 0.64), the M-F phase can be observed when the RBCs make the first contact in an aligned configuration, which is unlikely to be observed experimentally. Figure 6 illustrates various doublet shapes of two RBCs with different reduced volumes for a fixed reduced adhesion energy g = 8. Another phase, the sheath phase, appears here • Sheath phase: If the reduced volume of one RBC is large, and of the other is small, the former would swell to an elliptical shape and the latter would bend to a cup shape. Therefore, the best configuration for their adhesion occurs when the inner cup of the latter RBC matches the swollen curvature of the former RBC. This configuration corresponds to the minimal free energy condition for almost all adhesion strengths. Since most RBCs have a reduced volume in the range 0.4 to 0.8, such phase does not occur under physiological conditions.

In the case of unequal reduced volumes (see Fig. 6), the contact area is roughly proportional to the inverse of the average of the reduced volumes (A c /A µ (n 1 + n 2 ) 1 ) and varies from about 0 to 0.7. The reduced bending energy e b,1 of the first RBC decreases with increasing n 1 , but is not very sensitive to a variation in the reduced volume n 2 of the second RBC.

In order to study the effect of the spectrin network's shear elasticity on the doublet phases, the membrane shear modulus G is varied. Figure 7 shows the phase diagram together with the contact area and reduced bending energy as a function of shear modulus and adhesion strength for a constant reduced volume of healthy RBCs n ⇡ 0.64. The shear modulus of healthy RBCs lies in the range 2-12 µN/m 29,[START_REF] Waugh | [END_REF][47][48][49]62 , which corresponds to the reduced shear modulus µ = GA/8pk c of 35-215, provided that the bending rigidity is 70 k B T . The phases obtained for very low shear moduli agree well with the numerical energy-minimization study for vesicles [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF] , where the contact area is flat for low adhesion strengths and it buckles as the adhesion strength increases. The F-B phase appears in a broader range of adhesion strengths when the shear modulus is much lower than that for a healthy RBC. Also, the F-C phase, which has never been detected for normal RBC reduced volumes of n ⇡ 0.64, appears at very low shear moduli. On the other hand, at shear moduli of healthy RBCs, the M-F and S-B phases are found at low adhesion strengths. If the shear modulus is very high, the RBCs do not tend to form contact area from their center. High shear modulus is relevant for diseased RBCs, such as in malaria 63 .

The doublet phases are determined by the balance of deformation energies and adhesion energy. The shear elasticity of the membrane attributed to the spectrin network has a strong effect on the doublet phases, as shown in Fig. 7. For vesicle doublets, the effect of shear elasticity is absent since vesicles are made of fluid membrane. Accordingly, the lower region of the phase diagram (µ ! 0) in Fig. 7 corresponds to the previous works on doublets with the three phases F-C, F-B, and Sigmoid-Concave (Yin-Yang) [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF][START_REF] Svetina | [END_REF]25,54 , characterized by the contact surface only. A distinct difference between our results and those from previous studies on vesicles is that the F-B phase appears only if the shear elasticity of the RBC spectrin network is small enough, as shown in Fig. 7(c). Therefore, such phase cannot be observed for RBC doublets, because they have significant shear elasticity.

Figure 7(b) shows that by increasing the adhesion strength, the contact area exhibits two discontinuous jumps for a fixed µ. The first jump in A c at very low g . 1 occurs when the adhesion interaction overcomes membrane thermal fluctuations and cell diffusion. The second discontinuity in A c manifests a transition when one or both RBCs loose their original biconcave shape by forming suddenly a larger contact area in a doublet. For example, it happens when F-B, S-B, and M-F shapes are first attained for 1 < g < 10, such that a larger contact area is rapidly formed. Interestingly, further transitions with increasing g (e.g. to the Yin-Yang phase) are continuous, since the contact area is continuously gained with an increase in adhesion strength. Thus, buckling out of a membrane dimple and rapid formation of a larger area of contact can be considered as signatures of discontinuous transition. An increase in shear elasticity generally delays this discontinuous transition in terms of g and reduces the contact area, as can be seen in Fig. 7(b) and Supplementary Movie S2. These results are qualitatively consistent with a discontinuity in A c found for vesicle doublets [START_REF] Ziherl | Proc. Natl. Acad. Sci[END_REF] .

Since shear elasticity of membranes has a significant effect on the doublet configurations, the stress-free shape of RBC might also play an important role in determining the shape of the RBC membrane and their doublet phases. Whether the spectrin network of a RBC is stress-free in the biconcave or spherical shape or something in-between is still under debate [64][65][66][67] . So far in this work, the RBCs were stress-free at their biconcave shape. In order to study the effect of the stress-free state of RBCs on doublet phases, the stress-free biconcave shape is compared with a case where the network is stress-free at a deflated sphere shape with eccentricity 0.94. The change in the configuration of the doublets is appreciable, as shown in Fig. 8(b). The most important difference between the two cases is the change of the S-B phase to the M-F phase at small adhesion strengths. If the stress-free shape of RBCs is close to a sphere, the change to the Yin-Yang phase occurs at slightly lower adhesion strengths in comparison to the biconcave stress-free shape, as shown in Fig. 8(b). In practice, this small change cannot be detected experimentally, not only because of the lack of the imaging precision, but also because of the natural variance in the mechanical properties of RBC membranes and their reduced volumes 68,69 . As discussed above, the transition from original biconcave shape of both RBCs to a doublet shape with a large contact area (e.g. F-B, S-B, M-F shapes) is discontinuous in A c for the biconcave stress-free shape, see Figs. 7(b) and 8(a). Fig. 8(a) also demonstrates that this transition is discontinuous in A c for the stress-free shape of 0.94.

Strong changes in RBC shapes (e.g. for a Yin-Yang doublet) likely lead to appreciable local in-plane deformations of the cell membranes. At the contact area, it is intuitive to expect that RBC membranes are compressed due to adhesive interactions, while the free surfaces are presumably subject to an area expansion. These modes of deformation are mainly controlled by the areacompression modulus of a membrane. The area-compression modulus in our model is equal to 2G+k l +k a , where G is the shear modulus and the other terms correspond to local and global areaconservation constraints. Here, k l ⇡ G, while k a G such that the local area constraint leads to a rather slight enhancement of the area-compression modulus. Therefore, under strong enough deformations local area of a membrane should experience appreciable deformation.

In order to elucidate local strains, local area changes, and the role of the local area constraint, we present in Fig. 9 a comparison of local membrane deformations for a Yin-Yang doublet (g ⇡ 85 and µ = 80) using a RBC model with and without the local area constraint. Fig. 9(c) confirms that the membranes are compressed at the contact area and expanded at the free surfaces. This is also seen in the bimodal distributions of bond and localarea strains in Figs. 9(a-b). Here, the bimodality in the local area arises from the differences between adhered and free parts of the membrane. The bimodality in the bond lengths is related to the positive Poisson ratio of our elastic network model, which implies that stretching in one direction is accompanied by a compression in the orthogonal direction. The local strains remain approxi-Page 8 of 13 Soft Matter mately within the range of [ 0.3, 0.3] and their absolute values are slightly smaller for the case with the local area constraint in comparison to that without this constraint. However, in both cases Yin-Yang doublets are observed and their shapes are visually indistinguishable. Thus, for the employed strength of the local area constraint, it plays at most a secondary role in determining doublet shapes for the range of adhesion strengths studied here.

Soft Matter Accepted Manuscript

Comparison with experiments

The experimental images of the different phases are compared to the simulation results in Fig. 10. The F-B phase is not observed in experiments and not predicted by simulations for the physiological reduced volumes of RBCs. Both in simulations and experiments, the M-F doublets form when the adhesion strength is intermediate and the reduced volume is small. The Yin-Yang phase appears when the adhesion strength is high. The S-B phase is seen as a transition state between these two phases. The F-B phase has not been observed in experiments. The F-C phase occurs when both RBCs are swollen and the Sheath phase happens when there is a significant difference in the reduced volumes of the two RBCs. To see the F-C phase in experiments, the osmolality of the solution has to increase about two-fold. For increasing reduced volume of RBCs in experiments, they were immersed in hypotonic solution of NaCl. At low shear rates, RBCs aggregate in stacks known as rouleaux 1,2 . The rouleaux increase substantially the viscosity of blood at low shear rates [6][7][8] . The nucleation of rouleaux starts from RBC doublets. While some doublet structures allow for large rouleaux formation, others prevent the formation of large rouleaux. Among all the doublet phases, the M-F and S-B phases let the RBCs to form large rouleaux with a straight (linear) structure. However, the Yin-Yang phase prevents long straight structures to appear. Thus, the size of rouleaux in a solution of RBCs depends on their adhesion strength which is determined by the concentration of different adhesive factors in the solution (e.g. dextran, fibrinogen). Figure 11 shows several experimental and simulated results of different rouleau structures. The shapes of rouleaux for high adhesive strengths are very different, depending on the reduced volumes of the RBCs and the number of RBCs in the rouleau. In contrast, the M-F and S-B phases should allow the size of straight rouleau structures to increase with no limit. Note that at high enough adhesive strengths, more complex RBC aggregate structures, other than straight rouleaux, may appear 70 .

The limit for the rouleau nucleation can be explained by the free energy of the whole system. Doublet formation changes the free energy of the system by 2E def GA c . E def is the deformation energy of a RBC, mostly due to bending rigidity and shear elasticity. In principle, it is always positive since any deviation from the equilibrium biconcave shape of a RBC must have a higher energy. Therefore, the adhesion energy GA c must be larger than 2E def for doublet formation to be favorable. Addition of one more RBC to the doublet to make a triplet aggregate of RBCs increases the total free energy by

DE + = E def GA c + E o def
, where E o def is the additional deformation energy of the original aggregate, E def is the deformation energy of the newly added RBC to the original aggregate and GA c is the adhesion energy due to it. Assuming that the other RBCs in the aggregate do not deform substantially leads to E o def ⇡ 0; otherwise, the deformation and adhesion energy of all RBCs must be considered in the rearranged configuration. This rearranged configuration has definitely a higher energy for the RBCs already in the aggregate, since they get away from their equilibrium configuration. For S-B and M-F phases, addition of an RBC to the aggregate adds a constant negative DE + to the free energy so that the growth of the rouleau is energetically favorable. DE + is nearly constant since the contact area and curvature of the newly added RBC is similar to the other RBCs in the aggregate. On the contrary, DE + grows as a new RBC is added to a Yin-Yang doublet, because the contact area for the new RBC is less than the contact area of a doublet, and the new RBC deforms much more in order to fit to the concave shape of a rouleau. As a result, DE + becomes positive at some point preventing more RBCs to adhere to the aggregate. This limiting point occurs for larger cluster sizes as the adhesion strength G increases.

Conclusion

A systematic study of RBC doublet formation has been performed. The model employs a triangulated membrane with a polymerized mesh as representation of the spectrin network. The simulation results demonstrate various doublet phases, namely, the Male-Female, Sigmoid-Biconcave, Yin-Yang, Sheath, Flat-Concave, and Flat-Biconcave phases, with their stability determined by the ad-hesion strength between two membranes and the reduced volume of each RBC. The Male-Female phase implies a curved contact area of two RBCs similar to a female-male socket connection. The Sigmoid-Biconcave phase refers to the condition that two RBCs make a sigmoid S-shape contact while they keep their biconcave curvature. The Yin-Yang phase, then, refers to the same condition, but when the free surfaces of RBCs swell or bend to a concave form. The section view of the doublets in this phase looks like Yin-Yang symbol. The Sheath phase occurs when one RBC is swollen so that the other RBC makes a sheath by contacting it. The Flat-Concave phase is referred to the flat contact area case and occurs mostly when both RBCs are swollen. The predicted phases are compared with the experimental images obtained from optical imaging of RBCs in different solutions.

The RBC doublet phases are mainly defined by the interplay of bending energy and adhesion energy, and are closely related to the reduced volume of RBCs, which is a dimensionless ratio between the volume and area of RBCs. However, the shear elasticity of the RBC membranes, due to the spectrin network beneath their lipid bilayers, affects their doublet phases. At very low shear moduli, the Flat-Biconcave shape appears at low adhesion strengths, while this phase is never stable for healthy RBCs with normal shear moduli. The very peculiar Flat-Concave phase at the normal reduced volumes of RBCs is also reported for very low shear moduli. This shows that the spectrin network's shear elasticity is a key player in defining the RBC doublet phases, differentiating them from previously studied fluid vesicle doublets.

Rouleau nucleation depends on how RBCs make doublets first. Aggregation of RBCs always brings a rise in the bending free energy and a decrease in the adhesive energy. Depending on the doublet shape, this pair of energy-changes determines whether rouleau formation is allowed or not. As a result, at high adhesion strengths, the doublets tend to prevent large stacks, since the Yin-Yang phase makes the positive change of the bending energy so large that it cannot be compensated by the adhesion energy related to the contact area of the membranes. At low and moderate adhesion strengths, the Sigmoid-Biconcave and Male-Female phases allow the growth of the rouleaux, since the addition of a RBC to the aggregate does not change the shapes of the other RBCs, which have been already adhered to the aggregate. These results can be used for determining the adhesion strength and membrane properties of healthy and diseased RBCs.

a

  Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany. b Experimental Physics, Saarland University, 66123 Saarbrücken, Germany. c Laboratoire Interdisciplinaire de Physique, CNRS and Université Grenoble Alpes, 140 rue de la Physique, 38402 Saint-Martin d'Hères, France.

d

  Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg.

Fig. 3

 3 Fig. 3 Analysis of the contact area and the approximation of adhesion energy. The minimum adhesion energy for a vertex is obtained when it is located at the head of an equilateral tetrahedron, one of whose faces is the triangle of the other membrane vertices. The four closest neighbors to this vertex are shown by different symbols with assigned numbers 1-4. The closest neighbors are 3 vertices with distance s , the second closest neighbors are again 3 vertices with approximately p 2s away from this vertex. Also 6 neighbors with p 3s and 6 other with p 5s distance are the farthest neighbors, which affect the adhesion energy. Even further neighbors have a negligible effect on the energy and are ignored. Thus, the effective adhesion energy ẽ of one interacting vertex is equal to about 5.37e. In another configuration, where a vertex sits close to only one vertex from the other membrane, the effective adhesion energy would be approximately 4.1e.

)Fig. 5

 5 Fig. 5 RBC doublet configurations as a function of n 1 = n 2 = n and g with aligned and offset first point of contact. (a) Contour plots for the contact area and the reduced bending energy for the aligned RBCs. (b) Contour plot for the difference between the free energy of the doublet and the free RBCs (deformation energy). The change in free energy is normalized by the bending energy of a vesicle with bending modulus k c , 8pk c , and the colorbar has a logarithmic scale. The black dots (•) in contour plots represent the values for which simulations have been conducted. (c) The configuration of a doublet depends on the way the RBCs make their first contact. RBCs can make the first contact while they are in aligned or offset configurations. (d)The difference between the free energy of the doublets in the aligned and offset cases. If E alig E off is positive, it means that the offset doublet has a smaller free energy, so that it is a more favorable configuration. The phase diagrams of the (e) aligned and (f) offset cases are different in the region, where E alig E off is positive. Various phases are distinguished by their cross-sectional views. The black dots (•) in the phase diagrams represent performed simulations. Note that the phase boundaries are drawn schematically to guide the eye.

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Fig. 6

 6 Fig. 6 RBC doublet configurations as a function of n 1 and n 2 at a constant adhesion strength g = 8. (a) Contour plots show the contact area and the reduced bending energy of the first RBC as a function of n 1 and n 2 . The black dots (•) represent the values for which simulations have been performed. (b) The side and section views of some configurations are shown in the phase diagram, omitting some shapes for more clarity. The different phases are separated by different colors. The S-B phase occurs in a narrow region between Yin-Yang and M-F phases. The membrane is assumed to be stress-free in its biconcave shape with n = 0.64. The phase boundaries are drawn schematically to guide the eye.

Fig. 7

 7 Fig. 7 RBC doublet configurations as a function of spectrin network's reduced shear modulus µ = GA/8pk c and reduced adhesion strength g at a constant reduced volume n = 0.64. (a) Contour plots show the contact area and the reduced bending energy. The black dots (•) represent the values for which simulations have been performed. (b) Dependence of the contact area on adhesion strength for different µ values. Discontinuity in the contact area is observed when one or both RBCs loose their original biconcave shape. (c) Phase diagram of RBC doublets as a function of g and µ, where different phases are separated by various colors. The phase boundaries are drawn schematically to guide the eye. The side and section views of some configurations are shown, omitting some shapes for more clarity. The low shear moduli approximate vesicle doublets. The membrane is assumed to be stress-free in its biconcave shape with n = 0.64.

Fig. 8

 8 Fig. 8 Effect of stress-free shape of RBCs on doublet phases for n 1 = n 2 = 0.64. (a) Contact area as a function of g for biconcave and near spherical (with eccentricity 0.94) stress-free shapes. (b) The shapes of RBC doublets for µ = 81, showing appreciable differences for the two stress-free shapes. The boundaries between different shapes are drawn schematically to guide the eye.

Fig. 9

 9 Fig. 9 Effect of the local area constraint in the membrane model on a Yin-Yang doublet for g ⇡ 85, µ = 80, and n 1 = n 2 = 0.64. (a) Bond strain distributions from simulations with and without local area constraint. The bond strain is defined as l/l 0 1, where l is the length of a deformed bond and l 0 is its corresponding equilibrium length. (b) Distributions of local triangular area strains. The area strain is defined as A/A 0 1, where A is the area of a deformed triangle in the spring network and A 0 is its imposed area at biconcave equilibrium shape. (c) Distribution of local area strains on RBCs within a Yin-Yang doublet. The RBC membranes show a compressive deformation (or negative area strains) at the contact area and are stretched primarily at the free surfaces characterized by positive area strains.

Fig. 10

 10 Fig. 10 Comparison of experimental and simulated RBC doublet shapes determined by the adhesion strength, bending modulus, and the reduced volume of RBCs. For simulations, the side and section views are presented for each case. The phases (a) Sigmoid-Biconcave, (b) Male-Female, (c) Sigmoid-Concave (Yin-Yang), (d) Sheath, (e) Flat-Concave, and (f) Flat-Biconcave are shown. The Sheath, F-C, and F-B phases are not probable for RBC doublets under physiological conditions.

Fig. 11

 11 Fig. 11 Various rouleau phases in experiments and simulations. The doublet S-B and M-F phases impose no limit on the size of the rouleau. However, the F-C rouleaux are strongly dependent on the number of interacting RBCs and their reduced volumes. The nucleation point of a F-C rouleau is a Yin-Yang doublet.

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Table 1

 1 Membrane properties used in simulations and related references.

	Property (units)			Value (variability)
	number of vertices, N			3000
	surface area, A (µm 2 )			134 28,29,44,45
	volume, V (µm 3 ) effective diameter, Deff =	p	A/p (µm)	94 28,29,44,45 6.5
	bending rigidity, kc/kBT			70 28,29
	shear modulus, G (µN/m)		4.6 (2-12) 29,46-49
	global area rigidity, kaD 2 eff /kc local area rigidity, klD 2 eff /kc global volume rigidity, kvD 3 eff /kc	29,600 28,29 603 28,29 19,620

Soft Matter Accepted ManuscriptPublished on 06 July 2018. Downloaded by Universite Grenoble Alpes INP on 7/9/2018 10:42:57 AM. View Article Online DOI: 10.1039/C8SM00634B

Published on 06 July 2018. Downloaded by Universite Grenoble Alpes INP on 7/9/2018 10:42:57 AM. View Article Online DOI: 10.1039/C8SM00634B

Acknowledgments

A CPU time grant by the Jülich Supercomputing center is gratefully acknowledged. D.A.F. acknowledges funding by the Alexander von Humboldt Foundation. M.H., G. G., and D.A.F. thank the DFG Research Unit FOR 1543 "SHENC -Shear Flow Regulation in Hemostasis" for support. F.Y. and C.W. acknowledge funding from the French German University (DFH / UFA). F.Y. and T.P. acknowledge support from CNES and LabEx Tec21.

Notes and references


Thinhinane Hocine

Sebastien Blaise

Cathy Hachet

Alexandre Guillot

Herve Sartelet

Pascal Maurice

Amar Bennasroune

Laurent Martiny

Laurent Duca

Beatrice Romier-Crouzet

Hassan El Btaouri
email: hassan.elbtaouri@univ-reims.fr

Hassan El

Lactosyl-Ceramide induced by Elastin Derived Peptides, decrease adipocyte differentiation

Keywords: Elastin derived peptides, PPAR, adipocyte, Lactosyl-ceramide, Differentiation, ERK

Elastin, major protein of extracellular matrix, is specially found in cardiovascular tissues and contributing to 30-50% of the dry weight of blood vessels. Elastin regulates cell signalling pathways involved in morphogenesis, injury response, and inflammation. The function of elastin is frequently compromised in damaged or aged elastic tissues. Indeed, elastin degradation, observed during ageing, and the resulting production of elastin derived peptides (EDP), have crucial impacts on cardiovascular disease (atherosclerosis, thrombosis) or on metabolism disease progressions (type 2 diabetes or non-alcoholic steatohepatitis).

In the present study, we analysed the EDP effects on 3T3 pre-adipocyte cell differentiation. In a first part, we treated 3T3-L1 cells with EDP and visualized the lipid droplet accumulation by the oil red-O staining and measured the expression of various transcription factors and adipocyte-specific mRNAs by real-time RT-PCR. We demonstrated that elastin receptor complex, ERC, is activated by EDPs and decreased adipocyte differentiation by a modulation of crucial adipogenesis transcriptional factor particularly PPARγ. In a second part, we identified the signalling pathway implicated in EDP-reduced cell differentiation. The flow cytometry and immunocytochemistry approaches showed that ERC activated by EDP, produced a second messenger, lactosylceramide (Lac-Cer). Moreover, this Lac-Cer production favoured the phosphorylation of ERK1-2 (p-ERK1-2), to decrease adipocyte differentiation by a modulation of adipogenesis transcriptional factor PPARγ.

To conclude, the EDP/Lac-Cer/p-ERK1-2 signalling pathway may be studied further as a critical target for treating complications associated with adipocyte dedifferentiation such as obesity and diabetes insulin resistance.

KEY POINTS

Elastin Derived Peptides (EDP) decreased PPAR expression.

EDP reduced adipocytes differentiation.

Adipocytes differentiation is reduced by Lac-cer production and ERK1/2 activation.

INTRODUCTION

Although obesity is a huge challenge to global health, clinicians have had little success in fighting this disease.

Over the past decade, several defective genes have been associated with obesity in humans such as genes involved in appetite control [START_REF] Farooqi | Monogenic human obesity syndromes[END_REF]. However, such genetic mutations do not always explain the high rate of obese people. Indeed, age, environment and eating habits are the main factor leading to obesity. Research on this disease has focused on strategies for treating complications associated with obesity instead of focusing on the major risk factors that affect this pathology. In the progression of this disease, the extracellular matrix (EMC) play a key role in adipose tissue remodeling. Thus the several studies demonstrated that proteases released by adipocytes, macrophages such as Cathepsin S, MMP-11, MMP-2, MMP-12,… or the cleavage, folding alteration of collagen VI and the production of endotrophin, might influence adipogenesis [20; 28]. Among the proteases mentioned, Cathepsin S, MMP12 or MMP2 belong to the family of elastases, and involved to elastin degradation. Elastin is crucial for normal development and is a major protein in adult cardiovascular tissues, contributing 30-50% of the dry weight of blood vessels [START_REF] Bashur | Tissue engineering and regenerative strategies to replicate biocomplexity of vascular elastic matrix assembly[END_REF].

Elastin endow tissues with elastic recoil and resilience [START_REF] Nakamura | Fibulin-5/DANCE is essential for elastogenesis in vivo[END_REF], acting as an important adhesion template for cells, and regulating cell signaling pathways involved in morphogenesis, injury response, and inflammation Kielty [START_REF] Kielty | Elastic fibres in health and disease[END_REF]. Mutations in major structural components of elastic fibers, especially elastin, fibrillins and fibulin-5, cause severe, often life-threatening diseases such as Marfan syndrome, supravalvular aortic stenosis and cutis laxa [START_REF] Kielty | Elastic fibres in health and disease[END_REF]. The function of elastic fibers is also frequently compromised in damaged or aged elastic tissues [START_REF] Maurice | Elastin fragmentation and atherosclerosis progression: the elastokine concept[END_REF]. Indeed, fragmentation of elastin into elastin derived peptides, (EDP) during ageing has crucial impacts on cardiovascular diseases such atherosclerosis, thrombosis and metabolism diseases [5; 11; 14; 24]. Recently, our team and others have shown that elastases (i.e. neutrophil elastase) are involved on elastin fragmentation and EDP induced by elastases increased obesity, insulin resistance and type 2 diabetes [17; 24; 29; 32]. During the last decade, our team has deciphered the signaling pathways triggered by the elastin receptor complex (ERC) upon its binding to the canonical human sequence VGVAPG. This receptor has a very singular composition that comprises three subunits: a peripheral 67 kDa subunit named Elastin Binding Protein (EBP) or S-Gal (spliced-galactosidase) and two membrane associated proteins, a 55 kDa protective protein/cathepsin A (PPCA) and a 61 kDa neuraminidase (Neuraminidase-1, Neu1). Although the role is still unknown, the PPCA subunit may contribute to the structural integrity of the ERC. The precise role of Neu1, the only receptor subunit with a cytosolic C-terminal tail, is still under investigation [START_REF] Wahart | Role of elastin peptides and elastin receptor complex in metabolic and cardiovascular diseases[END_REF]. So far, the role of Neu1 within the receptor complex was unknown and results from our group showed that, the catalytic activity of Neu-1 is essential for signal transduction by the ERC [START_REF] Duca | The elastin receptor complex transduces signals through the catalytic activity of its Neu-1 subunit[END_REF]. Neu-1 could directly cleave sialic acids either of N-glycosylation chain of receptor such as insulin receptor (IR) [START_REF] Blaise | Elastin-derived peptides are new regulators of insulin resistance development in mice[END_REF] or of the ceramide such as GM3 ganglioside to product lactosylceramide (Lac-Cer), which is now regarded as the second messenger of the ERC [START_REF] Rusciani | Elastin peptides signaling relies on neuraminidase-1-dependent lactosylceramide generation[END_REF]. Binding of EDP to the ERC results in a host of signaling events that depend on cell types and therefore on the triggering of specific signaling cascades such as MEK1/2 activation, PI3K pathway [9; 11]. Because ceramides are described as a major markers of obesity, we suspected that Lac-Cer produced by ERC activated might an important role in obesity and adipose homeostasis. Therefore, in this study, we analyzed the bioactive elastin-derived peptides (EDP) effect on 3T3-L1 fibroblast cell differentiation. We showed that EDP/ERC interaction converted the GM3 ganglioside to Lac-Cer. Lac-Cer acted such as second messenger to activate ERK1-2 pathway, to inhibit the expression of PPAR and adipogenesis-specific factors and to decrease 3T3-L1 cell differentiation. The EDP/Lac-Cer/ERK1-2 signaling pathway may be studied further as a critical target for treating complications associated with adipocyte dedifferentiation such as obesity and diabetes insulin resistance.

MATERIALS AND METHODS

3T3-L1 fibroblast cells were purchased from ATCC (Manassa, USA). EDPs was obtained by KOH hydrolysis as described previously [START_REF] Romier | Production of Elastin-Derived Peptides Contributes to the Development of Nonalcoholic Steatohepatitis[END_REF]. The synthetic elastin (VGVAPG) and scramble (VVGPGA) peptides were purchased from GeneCust (Dudelange, Luxembourg).

Cell line and culture conditions

3T3-L1 fibroblast cells were cultured and growing to confluence in Dulbecco's modified eagle medium (DMEM) supplemented with 10% (v/v) fetal bovine serum (FBS), 100 U/mL penicillin and 100 μg/mL streptomycin (Invitrogen). Two days postconfluence, the cells were cultured for 48h in adipogenesisinducing medium (DMI) containing 0.25 μM dexamethasone, 0.5 mM 3-isobutyl-1-methylxanthine, and 1.5 μM insulin, supplemented with 10% FBS and 100 U/mL penicillin and 100 μg/mL streptomycin in presence or absence of different agonists. This point was considered as zero of differentiation day (D0). Then, 3T3-L1 cells were incubated at different times in DMEM medium supplemented with 10% FBS, 100 U/mL penicillin and 100 μg/mL streptomycin and 1.5 μM insulin in presence or absence of different agonists.

Cell viability assay

Cells were plated in microwell plates at 10 4 cells/mL and incubated for D0 to D9 with or without EDP (50 µg/ml) UptiBlue 10% (v/v) was added in cultured medium. Plates were incubated for an additional 3 h and reduction was then measured spectrofluometrically (λex: 530-560 nm; λem: 590 nm). Results were calculated as percent of controls as follows: (Experimental absorbance / untreated control absorbance)×100.

Oil Red O Staining

Accumulation of triglycerides was visualized by staining with Oil red O (Sigma-Aldrich), essentially as described previously [START_REF] Yun | Inhibition of PPAR gamma 2 gene expression by the HIF-1-regulated gene DEC1/Stra13: a mechanism for regulation of adipogenesis by hypoxia[END_REF]. Briefly, we prepared a stock solution of 0.5% (w/v) Oil red O in isopropanol. To achieve a working concentration, 6 mL of stock solution was mixed with 4 mL of water. RNA were isolated as described previously [START_REF] Blaise | In vivo evidence that TRAF4 is required for central nervous system myelin homeostasis[END_REF] and converted to cDNA using SuperScript II RT (Invitrogen Life Technologies) and oligo dT24 primers. Quantitative RT-PCR was performed using the SYBR Green JumpStart PCR kit (Sigma-Aldrich, St. Louis, MO) according to the supplier's protocol. 36B4 and 18S RNAs were used as internal controls.

Measurement of lactosyl-ceramide

Flow cytometry: After stimulation, 3T3-L1 cells were washed with ice-cold PBS containing 50 mM Na3VO4 and harvested using PBS EDTA 10 mM at 4°C. Cells were centrifuged (400 g, 10 min, 4°C), washed with PBS, for 20 min at room temperature in darkness. Cells were then washed, centrifuged and fixed with 500 ml of 1% formaldehyde before being analysed with a FACS Calibur cytometer.

Immunofluorescence: Cells (25 × 10 4 ) were plated on glass-slides and incubated according to differentiation protocol with or without different agonists. The fixation of the samples was made using 4% (v/v) paraformaldehyde. The slides were washed with PBS, incubated with BSA 3% (w/v) for 30 min and overnight with an anti-CD 17 antibody (anti-lactosylceramide). Then cells were washed with PBS and incubated for 45 min with an anti-rabbit Alexafluor-568 ( TM ). Slides were incubated with mounting medium containing DAPI.

Immunofluorescence-labelled cell preparations were analysed using a Zeiss LSM 710 confocal laser scanning microscope.

Western blotting

After stimulation, 3T3-L1 cells were washed with ice-cold PBS, lysed in ice cold buffer containing 10 mM Tris pH 7.4, 150 mM NaCl, 5 mM EDTA, 1 mM Na3VO4, 1 mM dithiothreitol, 10 μg/mL leupeptin, 10 μg/mL aprotinin, 10% (vol/vol.) glycerol, 1% Brij (vol./vol.), placed on ice for 20 min and then centrifuged (14000g, 15 min, 4 °C to prepare whole cell extracts). The amount of proteins was determined using the BCA protein quantification kit (Interchim, Montluçon, France). Equal amounts of proteins (whole cell extracts) were resolved by 10% SDS-PAGE gels and transferred to nitrocellulose sheets and probed with the appropriate antibodies (polyclonal anti-Phospho ERK1-2, polyclonal anti-ERK1-2). Horseradish peroxidase-conjugated goat anti-rabbit was used as secondary antibodies and proteins were detected using an enhanced chemiluminescence (ECL) kit.

Statistics

Each experiment was performed at least in triplicate on three separate sets of culture. Data were expressed as mean±SEM. The statistical significance of differences was calculated using Student's test.

p values referring to corresponding control are ** and  p<0.01, *** and  p<0.001.

RESULTS

EDP impaired adipocyte differentiation.

EDP were described to induce insulin resistance or Nonalcoholic steatohepatitis involved in metabolism syndrome. In this study, we wanted to know if EDP impact the adipocyte differentiation. Therefore, 3T3-L1 cells were treated with DMI (Dexamethasone, IBMX, Insulin) to induce adipocyte differentiation with or without Elastin-derived peptides (EDP) (50 μg/ml) according to Blaise et al. [START_REF] Blaise | Elastin-derived peptides are new regulators of insulin resistance development in mice[END_REF], and the lipid accumulation was visualized by the oil red-O staining on days 0, 3, 6 and 9 (Fig. 1A). The lipid droplet accumulation in the cells appeared on day 3 and increased with the culture duration confirming the induction of differentiation.

Whereas the stained area for Oil-red O in the EDP-treated cells was significantly decreased by approximately 90% after 9 days of treatment. Under these same conditions, the cell viability was not affected by the different treatments as showed in Fig 1B.

Various transcription factors such as C/EBP-α, C/EBP-β, PPAR-γ and aP2 and adipocyte-specific proteins (ACC, ACDC, Ob) are known to be expressed throughout the progression of adipogenesis [START_REF] Ntambi | Adipocyte differentiation and gene expression[END_REF]. So, we examined the influence of EDP on the expression of these adipogenesis-specific markers and factors by real-time RT-PCR. As showed in Fig. 2A, from 6 th day of differentiation, we observed that expression of mature adipose markers such as ACC, ACDC and Ob was significantly increased upon exposure to adipogenic stimuli Elastin degradation by elastases generates elastin-derived peptides. Among them, peptides harbouring a GxxPG consensus motif (where x represents any amino acid) are bioactive because this sequence motif [3; 5; 8; 11; 19; 25; 26]. Here, we analyzed the VGVAPG peptide on 3T3-L1 differentiation (Fig 4). We showed that VGVAPG peptide reduced PPAR and adiponectin expression and reduced 3T3-L1 cell differentiation compared to scramble peptide. Those results give a direct evidence for the involvement of ERC in the EDPreduced adipocyte differentiation.

Lactosyl ceramide is involved to adipocyte differentiation.

Previously, we demonstrated that ERC is responsive to the GM3 conversion into lactosyl ceramide (Lac-Cer) [START_REF] Rusciani | Elastin peptides signaling relies on neuraminidase-1-dependent lactosylceramide generation[END_REF]. Therefore, we measured by Flow cytometry and immunocytochemistry the Lac-Cer accumulation after 6, 12 and 24h of EDP adipocyte treatment with or without DANA (200 μM) or CS (200 μg/ml). Fig. 5 and6 showed that EDP induced an increase of Lac-Cer level. This effect was amplified up to 12h. However, Lac-Cer

level

ERK1-2 pathway and adipocyte differentiation

In our previous studies [START_REF] Rusciani | Elastin peptides signaling relies on neuraminidase-1-dependent lactosylceramide generation[END_REF], we characterized Lac-Cer as a second messenger able to activate intracellular

DISCUSSION

Our data provide important point regarding the relative contribution of ceramides, in particularly Lac-Cer in the obesity. In our study, we demonstrated for the first time that Lac-Cer reduced the adipocyte differentiation. Circulating ceramides were described to be a strong markers of metabolic dysfunction, such as type 2 diabetes, lipid accumulation in liver or in adipose tissue. Thus, GM3 is particularly abundant in those organs, wherein it comprises between 80% and 90% of total ganglioside content, respectively. It plays a major role in modulating insulin sensitivity and energy homeostasis [START_REF] Prokazova | Ganglioside GM3 and its biological functions[END_REF]. In accord with this, 3T3-L1 adipocytes incubated with exogenous GM3, presented a decrease of phosphorylation of insulin receptor phosphorylation and that of IRS-1, concomitant with impaired insulin-stimulated glucose uptake [START_REF] Chavez | Ceramides and glucosylceramides are independent antagonists of insulin signaling[END_REF]. In parallel GM3 is involved in lipid accumulation, inducing then an hypertrophy of adipocytes. GM3 acts as a metabolic precursor for the formation of more complex gangliosides. Indeed, gangliosides can be degraded through hydrolytic cleavage of sialic acid chains by the action of sialidase enzymes (such as Neuraminidase-1 ou -3) localized in lysosome or in cell membranes. Neu-1 can be found at the plasma membrane coupled to either PPCA (protective protein cathesine A) or PPCA and EBP (elastin binding protein), thus called ERC, elastin receptor complex [START_REF] Bennasroune | Elastic fibers and elastin receptor complex: Neuraminidase-1 takes the center stage[END_REF]. ERC is activated by elastin-derived peptides (EDP) and induce several signaling events beginning by sialic acid cleavage of GM3 into Lactosyl-Ceramide (Lac-Cer). Lac-Cer as an intermediate in the synthesis of complex sphingolipids. Nevertheless, recent works demonstrated this Lac-Cer is also a bioactive sphingolipid which regulates various cell signaling pathways and can be considered as a second messenger. Thus the conversion of ganglioside GM3 into Lac-Cer by the Neuraminidase-1 activated by EDP favored the MAPK pathway in cells, the proliferation or the migration of cells. In pre-adipocyte, we demonstrated that Lac-Cer could be produced by the elastin receptor complex activation on the one hand and on the other hand, induced the phosphorylation of ERK ½. Additionally, we showed here that 3T3-L1 cells incubated with Lac-Cer or produced by EDP stimulations cause reduction in the protein levels of the crucial adipogenesis marker PPARγ, which is both necessary and sufficient for adipocyte differentiation [START_REF] Lodhi | Peroxisomes: a nexus for lipid metabolism and cellular signaling[END_REF].

Thereby suggesting that the Lac-Cer production might be detrimental for optimal adipogenic differentiation.

Using a specific ERK inhibitor which reversed the reduction in PPARγ [START_REF] Tanabe | Inhibition of adipocyte differentiation by mechanical stretching through ERK-mediated downregulation of PPARgamma2[END_REF], suggested that EDP -Lac-Cer -ERK1-2 pathway was involved in PPARγ activity or transcription. Indeed, PPARγ presents an activation function called (AF)-1 domain corresponding a consensus mitogen-activated protein kinase (MAPK) site. The phosphorylation by extracellular signal-regulated kinase (ERK)-1/2) leads to inhibition of PPARγ transactivation [1; 6] and to degradation of PPARγ by the ubiquitin-proteasome system [START_REF] Hauser | Degradation of the peroxisome proliferator-activated receptor gamma is linked to ligand-dependent activation[END_REF]. Adipocyte effects [START_REF] Hu | ERK1 and ERK2 activate CCAAAT/enhancer-binding protein-beta-dependent gene transcription in response to interferon-gamma[END_REF]. Therefore, our study suggested that EDP -Lac-Cer -ERK pathway decrease adipocyte differentiation by a modulation of transcriptional factor cascade in particularly C/EBP- -PPARγ transition.

Interestingly, in previous studies, we showed, that exogenous EDP injections increase the fat pad of young adult mice, fed with non-energetic diet. The size of perigonadal adipocytes presented a large lipid droplet suggesting that EDP and ERC activation are responsive to adipocyte hypertrophy and to overweight of mice.

From 3T3-L1 mature adipocytes EDP induced an oil-Red-O accumulation and an increase of mRNA levels of PPAR and C/EBP, confirming that EDP induces in vitro lipogenesis in mature adipocytes [START_REF] Blaise | Elastin-derived peptides are new regulators of insulin resistance development in mice[END_REF]. Here, our study showed that EDP inhibited the expression of transcription factors involved in differentiation of preadipocytes. With those two studies, we can suppose that EDP and ERC present a dual effect to exacerbate lipid storage in mature adipocyte but limit the formation of new adipocyte from preadipocytes. This point is crucial in the obesity development. Indeed, recent studies showed in obese animal models or patients, that matrix remodeling is major: Large areas of fibrosis, a high expression of proteases and curiously an elastin expression [18; 27]. In physiological condition, elastin biosynthesis starts during the fetal stage and reaches a peak just before birth, in 3 main tissues (skin, lungs, and large arteries). The process of elastogenesis, which consists in formation of elastic fibers, decreases during early life to disappear at puberty. Finally, elastin production is low or inexistent during adulthood. During obesity, the expression of elastases such as cathepsin S or MMP2, MMP9 or MMP12, in adipose tissue, can degrade newly synthesized elastin to form EDP. Thus those EDP might be considered as a protective factor to limiting the adipocyte differentiation.

In conclusion, we demonstrated in this studies that EDP produced by elastin degradation during ageing or obesity, is responsible to a decrease of adipocyte differentiation. Molecular mechanism involved the formation of Lac-Cer and ERK ½ pathway activation which might explain a PPAR decrease.

ACKNOWLEDGMENTS

We thank Stephane Betoulle for her technical support with Flow cytometry. This work was supported by the University of Reims Champagne Ardennes and the Centre National de la Recherche Scientifique (CNRS).

COMPLIANCE WITH ETHICAL STANDARDS

We confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

This work does not involve humans or animals.

  FITC-anti-CD 17 antibody (anti-lactosylceramide) or FITC-anti-IgM control (1/25 dilution)

  according lipid droplet staining with Oil Red O. Treatment with EDP during differentiation significantly reduced the expression of these mature adipose markers. We also analyzed the expression of PPAR, cEBP and SREBP-1c, an adipogenesis-specific transcription factors. As showed in Fig 2B, the mature adipocytes expressed high levels of PPAR, cEBP and SREBP-1c. However, only PPAR expression was abolished by EDP treatment cell. These results indicated that EDP significantly inhibited the differentiation of preadipocytes to mature adipocytes by down-regulating the expression of PPAR transcription factors involved in lipid metabolism.ERC induced by EDP is associated to the decrease of adipocyte differentiation.The biological effects of EDP are mainly induced by Elastin receptor complex composed by 3 subunits, "elastin binding protein", protective protein cathepsin A and neuraminidase 1. EBP and Neu-1 functions are inhibited by chondroitin sulfate (CS) and 2, 3-didehydro-2-deoxy-N-acetylneuraminic acid (DANA), respectively, according to Wahart et al.[START_REF] Wahart | Role of elastin peptides and elastin receptor complex in metabolic and cardiovascular diseases[END_REF]. To confirm the involvement of ERC in EDP-inhibited 3T3-L1 differentiation, we treated at the same time 3T3-L1 cells by DMI with or without EDP (50 μg/ml) in presence or absence of DANA (200 μM) or CS (200 μg/ml) 6 and 9 days. In the condition of DANA or CS, the oil red O staining increased as compared to EDP condition, suggesting that inhibitors of ERC favored lipid accumulation in 3T3-L1 during differentiation progression (Fig3A). We demonstrated also that DANA and CS inhibited the effects of EDP on adiponectin and PPAR expressions (Fig3B). Those results suggested that ERC is involved in the EDP-reduced adipocyte differentiation and implicated neuraminidase 1.

  was slightly affected in presence of DANA or CS. These results suggested the implication of ERC in EDPinduced Lac-Cer production. To confirm that Lac-Cer was responsible for EDP-inhibited 3T3-L1 differentiation, we treated 3T3-L1 cells by DMI with or without exogenous Lac-Cer (2 and 10 μM) for 6 and 9 days. The lipid accumulation analyzed by the oil red-O staining is reduced and is dependent to the Lac-Cer concentrations (Fig 7). As expected, Lac-Cer mimicked the EDP effect such as reduction of adiponectin and PPAR expression confirming the decrease of 3T3-L1 cell differentiation (Fig 7).

  signals, in particularly ERK1-2 pathway. So, we analyzed the phosphorylation of ERK1-2 following EDP treatment cells. We treated 3T3-L1 cells by DMI with or without EDP (50 μg/ml) or Lac-Cer (2 μM) in presence or absence of DANA (200 μM) for 0.5, 1 and 2h. We analyzed the ERK1-2 phosphorylation by western blot. As shown in Fig. 8, EDP treatment cells induced ERK1-2 phosphorylation. This effect was significant up to 60 min and implicated ERC signaling pathway. DANA treatment cells inhibited EDP-induced ERK1-2 activation. Similarly, addition of exogenous Lac-Cer in cell medium reproduced the same EDP effects such as the ERK1-2 phosphorylation in same time. In order to determine the role of ERK1-2 phosphorylation in EDP-inhibited 3T3-L1 cell differentiation, we treated 3T3-L1 cells by DMI with or without EDP (50 μg/ml) or exogenous Lac-Cer (2 μM) in presence or absence of MEK-1,2 Inhibitor (U0126) at 10 μM for 6 and 9 days and analyzed the degree of differentiation by the oil red-O staining and adiponectin and PPAR expression by qPCR. As expected, EDP and Lac-Cer inhibited adiponectin and PPAR expression and reduced the 3T3-L1 cell differentiation (Fig 9). Moreover, the presence of U0126 abolished the EDP and Lac-Cer effects and restored the 3T3-L1 cell differentiation. This result confirmed the implication of ERK1-2 pathway in EDP-reduced 3T3-L1 cell differentiation and implicated Lac-Cer such as second messenger.

  differentiation needs the activation of two cascades of transcription factors. The first is transiently induced by adipogenic stimuli and involves CCAAT/enhancer-binding protein-β and - (C/EBP-β and C/EBP-, respectively). In turn, those factors directly induce expression of the second wave, consisting of PPARγ and C/EBPα. Transactivation domain (RD2) of C/EBP-β contains a threonine (T235), essential for gene expression. The phosphorylation by ERK1-2 of this threonine regulate C/EBP- -dependent gene stimulatory

Figure 1 :

 1 Figure1: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ) for 3, 6 and 9 days. Lipid droplet accumulation was visualized the by the oil red-O staining and assessed microscopically with inverted microscope (A). Cell viability was measured using UptiBlue assay. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments (B).

Figure 2 :

 2 Figure2: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ) for 3, 6 and 9 days. The expression of adipogenesis-specific markers (A) and adipogenesis-specific transcription factors (B) was analysed by Quantitative RT-PCR using the SYBR Green JumpStart PCR kit. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments.

Figure 3 :

 3 Figure 3: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ), DANA (400 µM) and CS (200 µg.mL -1 ) for 6 and 9 days. Lipid droplet accumulation was visualized the by the oil red-O staining and assessed microscopically with inverted microscope (A). The expression of ACDC and PPAR was analysed by Quantitative RT-PCR. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments (B).

Figure 4 :

 4 Figure 4: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with VGVAPG peptide or scramble peptide (50µg.mL -1 ) for 9 days. Lipid droplet accumulation was visualized the by the oil red-O staining and assessed microscopically with inverted microscope. The expression of ACDC and PPAR was analysed by Quantitative RT-PCR. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments.

Figure 5 :

 5 Figure5: 3T3-L1 fibroblast cells were incubated on glass-slides at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ), DANA (400 µM) and CS (200 µg.mL -1 ) for 6, 12 and 24 hours. Lactosyl-ceramide was visualised by immunofluorescence using an anti-CD 17 antibody (anti-lactosyl-ceramide) and an antirabbit Alexafluor-568 (TM). Immunofluorescence-labelled cell preparations were analysed using a Zeiss LSM 710 confocal laser scanning microscope.

Figure 6 :

 6 Figure6: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ), DANA (400 µM) and CS (200 µg.mL -1 ) for 6, 12 and 24 hours. Lactosyl-ceramide was quantified by flow cytometry using FITC-anti-CD 17 antibody (anti-lactosylceramide). Immunofluorescence-labelled cell preparations were analysed with a FACS Calibur cytometer.

Figure 7 :

 7 Figure 7: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with Lactosyl-ceramide (2 and 10 µM) for 6 and 9 days. Lipid droplet accumulation was visualized the by the oil red-O staining and assessed microscopically with inverted microscope. The expression of ACDC and PPAR was analysed by Quantitative RT-PCR. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments.

Figure 8 :

 8 Figure 8: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ), DANA (400 µM) or Lactosyl-Ceramide (10 µM) for 30, 60 and 120 min. Detection of p-ERK and ERK were evaluated by Western-blot.

Figure 9 :Fig1Fig2Fig3Fig4Fig5Fig6Fig7

 9 Figure 9: 3T3-L1 fibroblast cells were incubated at zero of differentiation day (D0) with or without EDP (50 µg. mL -1 ) or Lactosyl-Ceramide (10 µM) in presence or absence of U0126 (10 µM) for 6 and 9 days. Lipid droplet accumulation was visualized the by the oil red-O staining and assessed microscopically with inverted microscope. The expression of ACDC and PPAR was analysed by Quantitative RT-PCR. Results were calculated as percent of control and represent mean ± standard deviation (S.D.) of at least three independent experiments.

Fig8Fig9

  Fig8Click here to access/download;Colour Figure;Fig8.pptx

RNA preparation and quantitative RT-PCR.

	The cells were directly
	fixed in situ with 10% buffered formaldehyde at 40°C for 1 hour, washed with phosphate-buffered saline
	(PBS), stained with Oil red O working solution for 15 minutes, and finally washed with water. The triglyceride
	accumulation was assessed microscopically with inverted microscope