Abdou Rachid Thiam
email: thiam@ens.fr

Aymeric Chorlay

Lionel Forêt
email: lionel.foret@phys.ens.fr

Origin of gradients in lipid density and surface tension between connected lipid droplet and bilayer

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction.

Except for lipid droplets (LDs), most cellular organelles are bilayer bounded [START_REF] Thiam | The biophysics and cell biology of lipid droplets[END_REF]. LDs are made of neutral lipids, which are non-membrane lipids and often oily molecules. These neutral lipids are encapsulated in the core of the LDs, covered by a single phospholipid monolayer in which proteins are embedded. LD forms in the ER bilayer following a multiple steps process [START_REF] Walther | Lipid droplet biogenesis[END_REF][START_REF] Jackson | Lipid droplet biogenesis[END_REF]. Neutral lipids are synthesized and sheltered in the ER bilayer's hydrophobic region. The neutral lipids phase separates from the ER bilayer at a critical concentration and condenses into an LD [START_REF] Thiam | Lipid Droplet Nucleation[END_REF][START_REF] Khandelia | Triglyceride blisters in lipid bilayers: implications for lipid droplet biogenesis and the mobile lipid signal in cancer cell membranes[END_REF][START_REF] Choudhary | A conserved family of proteins facilitates nascent lipid droplet budding from the ER[END_REF]. At this stage, the LD is contiguous with the ER bilayer and can exchange proteins and lipids with its membrane [START_REF] Salo | Seipin regulates ER-lipid droplet contacts and cargo delivery[END_REF]. The nucleated LDs grow by acquiring more neutral lipids and proteins. At maturation, LDs can be physically disconnected from the ER bilayer but may reconnect with it later to exchange content [START_REF] Thiam | COPI buds 60-nm lipid droplets from reconstituted water-phospholipid-triacylglyceride interfaces, suggesting a tension clamp function[END_REF][START_REF] Wilfling | Arf1/COPI machinery acts directly on lipid droplets and enables their connection to the ER for protein targeting[END_REF].

Hence, the droplet monolayer surface is functionally connected to the ER bilayer to maintain the homeostasis of lipids and proteins of the LDs [START_REF] Jacquier | Lipid droplets are functionally connected to the endoplasmic reticulum in Saccharomyces cerevisiae[END_REF][START_REF] Markgraf | An ER protein functionally couples neutral lipid metabolism on lipid droplets to membrane lipid synthesis in the ER[END_REF][START_REF] Wilfling | Triacylglycerol synthesis enzymes mediate lipid droplet growth by relocalizing from the ER to lipid droplets[END_REF]. A crucial question is how these organelles manage to share phospholipids and proteins while keeping their respective identity. Answering this question will help understand LD biogenesis and protein targeting principles [START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF][START_REF] Kory | Targeting fat: mechanisms of protein localization to lipid droplets[END_REF][START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF][START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF]. In particular, understanding how the density of phospholipids is set between contiguous bilayer and monolayer interfaces will allow better knowing mechanisms of LD assembly and protein binding [START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF][START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF][START_REF] Thiam | Lipid droplet-membrane contact sites-from protein binding to function[END_REF].

Important parameters controlling LD biogenesis are the monolayer and bilayer surface tension and curvature [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF][START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF][START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF], which depend on the phospholipid composition of the organelles [START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Choudhary | Architecture of lipid droplets in endoplasmic reticulum is determined by phospholipid intrinsic curvature[END_REF][START_REF] Zanghellini | Phospholipid demixing and the birth of a lipid droplet[END_REF]. The phospholipid density regulates both the LD monolayer surface tension and its accessibility to proteins [START_REF] Thiam | COPI buds 60-nm lipid droplets from reconstituted water-phospholipid-triacylglyceride interfaces, suggesting a tension clamp function[END_REF][START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Caillon | Triacylglycerols sequester monotopic membrane proteins to lipid droplets[END_REF][START_REF] Prévost | Mechanism and determinants of amphipathic helix-containing protein targeting to lipid droplets[END_REF][START_REF] Kim | The Surface and Hydration Properties of Lipid Droplets[END_REF][START_REF] Kim | Stressed lipid droplets: How neutral lipids relieve surface tension and membrane expansion drives protein association[END_REF][START_REF] Kumanski | Lipid Droplets Are a Physiological Nucleoporin Reservoir[END_REF]. Firstly, while the ER bilayer can behave as an infinite phospholipid reservoir to the connected LD, reconstitution approaches, cell data, and molecular dynamics simulations suggest that the droplet monolayer is less packed with phospholipids than the ER bilayer [START_REF] Prévost | Mechanism and determinants of amphipathic helix-containing protein targeting to lipid droplets[END_REF][START_REF] Bacle | Interdigitation between triglycerides and lipids modulates surface properties of lipid droplets[END_REF][START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF][START_REF] Čopič | A giant amphipathic helix from a perilipin that is adapted for coating lipid droplets[END_REF]. Such a discrepancy partly explains the higher recruitment of peripheral or monotopic membrane proteins to LDs than bilayer membranes [START_REF] Caillon | Triacylglycerols sequester monotopic membrane proteins to lipid droplets[END_REF][START_REF] Prévost | Mechanism and determinants of amphipathic helix-containing protein targeting to lipid droplets[END_REF][START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF][START_REF] Ajjaji | Hepatitis C virus core protein uses triacylglycerols to fold onto the endoplasmic reticulum membrane[END_REF][START_REF] Ajjaji | Dual binding motifs underpin the hierarchical association of perilipins1-3 with lipid droplets[END_REF]. Secondly, while the ER bilayer is of low surface tension, circa 0.01mN/m [START_REF] Upadhyaya | Tension in tubulovesicular networks of Golgi and endoplasmic reticulum membranes[END_REF], cellular LDs, made from and contiguous with the ER, have a surface tension above 1mN/m [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF][START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF], two orders of magnitudes higher. This tension difference is crucial for the proper emergence of LDs from the ER bilayer [START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF][START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF]. Reasons for the discrepancies in phospholipid densities and surface tensions between LDs and the ER bilayer are unclear as yet.

Understanding the molecular basis of such differences between the two contiguous organelles will improve our knowledge of their biology.

Whether the physical properties of phospholipid bilayers and monolayers are identical was raised several decades ago [START_REF] Marsh | Lateral pressure profile, spontaneous curvature frustration, and the incorporation and conformation of proteins in membranes[END_REF][START_REF] Marsh | Lateral pressure in membranes[END_REF][START_REF] Nagle | Theory of lipid monolayer and bilayer phase transitions: effect of headgroup interactions[END_REF] because both are self-assembled interfaces with essential functions and applications in biology and physical science. For example, early studies focused on the kinetics and mechanics of the phospholipid monolayers of air/water or water/oil interfaces for better understanding the dynamics of lung surfactants [START_REF] Baoukina | The molecular mechanism of monolayer-bilayer transformations of lung surfactant from molecular dynamics simulations[END_REF] or emulsions' stability for digestion purposes [START_REF] Ajjaji | Hepatitis C virus core protein uses triacylglycerols to fold onto the endoplasmic reticulum membrane[END_REF][START_REF] Ajjaji | Dual binding motifs underpin the hierarchical association of perilipins1-3 with lipid droplets[END_REF], etc. In the meantime, biophysical approaches allowed studying the mechanics and dynamics of phospholipid bilayers, an important branch of membrane biology [START_REF] Needham | Elastic deformation and failure of lipid bilayer membranes containing cholesterol[END_REF][START_REF] Cooke | Coupling between lipid shape and membrane curvature[END_REF][START_REF] Lipowsky | The conformation of membranes[END_REF]. Altogether, these pioneer focuses on phospholipid interfaces led to the genesis of several theoretical frameworks describing the mechanics and thermodynamics of phospholipid-coated fluid interfaces [START_REF] Marsh | Lateral pressure profile, spontaneous curvature frustration, and the incorporation and conformation of proteins in membranes[END_REF][START_REF] Marsh | Lateral pressure in membranes[END_REF][START_REF] Marsh | Comment on Interpretation of Mechanochemical Properties of Lipid Bilayer Vesicles from the Equation of State or Pressure-Area Measurement of the Monolayer at the Air-Water or Oil-Water Interface[END_REF]. However, because LDs have gained focus relatively lately, little or no application was devoted to studying the case of the phospholipid monolayer interface covering an LD emerging from the ER bilayer. Mechanisms controlling the phospholipid density and surface tension equilibrium between a droplet monolayer jointed to a bilayer are currently unknown. We decided to capitalize on the established theoretical frameworks to uncover them. This paper aims to unveil the molecular origin of mechanisms maintaining the uneven phospholipid density between a droplet monolayer connected to a bilayer (Figure 1A). We customized macroscopic and microscopic frameworks of such a situation and established the relationship between the free parameters of the system.

Experiments validated our theoretical predictions, and this agreement allowed us to highlight molecular interactions underlying the difference in phospholipid densities and surface tensions between the droplet monolayer and bilayer. These interactions involve (a) the adhesion between the phospholipid monolayer leaflets forming the bilayer, which does not exist on a droplet monolayer, and (b) a pseudo-surface tension -resulting from the interaction between water molecules and phospholipid acyl chains of the bilayer-higher than the classical water/oil surface tensions. Keeping a phospholipid density difference is essential for the mechanical and thermodynamic equilibrium of the droplet and bilayer contiguity.

Results.

The result section is organized as follow. We first present the thermodynamic equilibrium relations, which govern the droplet morphology and the phospholipid distribution between the droplet monolayer interfaces and the bilayer. In the second part, we analyze one important and experimentally testable consequence of the equilibrium conditions: the interdependence between the surface tensions of the droplet and the bilayer, which reflects the coupling between the monolayer and bilayer phospholipid densities. The theoretical predictions made from this second part are successfully verified experimentally in the third part. In the fourth part, we present a microscopic theoretical description of the contiguous monolayers and bilayer, enabling us to derive the state equations of these interfaces.

These equations are then used to understand the molecular origin of the density difference (part five) and surface tension difference (part six) between the monolayers and the bilayer. In the last part, a quantitative comparison between theory and experiments is made to validate the theoretical approach and its underlying hypothesis.

Thermomechanical equilibrium of a lipid droplet connected to a phospholipid bilayer

We consider a droplet of fixed volume, above tens of nm in size, connected to a phospholipid (PL) bilayer (Figure 1A). At this scale, the contribution of the bending elasticity and long-range interactions of the different interfaces is negligible [START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF][START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF]. Hence, the PL bilayer and the droplet interfaces can be described as homogeneous fluid interfaces joining at the droplet edge [START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF]. A line tension arises at this contact, but its contribution to the order of tens of pN is negligible with respect to surface tension forces [START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF] (Discussion of the origin and influence of the line tension in Supplement text sections 1 and 3). The free energy of the droplet embedded in a bilayer is then,

= , + + , 1
where , , are the area of the three interfaces (bilayer and monolayers covering the LD at the "external" and "internal" side); , , , are the PL surface density in each bilayer leaflet and each monolayer (Fig. 1C); and are the free energy per surface unit of a PL bilayer and a PL monolayer at the water/oil interface. (A more thorough discussion of the assumptions leading to equation [START_REF] Thiam | The biophysics and cell biology of lipid droplets[END_REF] in Supplement text section 1). We consider that PLs freely diffuse and equilibrate between the droplet and the bilayer (Figure 1A). PL flip-flop, which takes several hours or days under passive conditions [START_REF] Pomorski | Lipid flippases and their biological functions[END_REF][START_REF] Anglin | Kinetics and thermodynamics of flip-flop in binary phospholipid membranes measured by sum-frequency vibrational spectroscopy[END_REF], is much slower than the lateral diffusion of PLs (~µm 2 /sec) [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF] and is negligible at relevant time scales (Figure 1A). Also, experimentally, PLs are insoluble in the neutral lipid oil phase, which is why they self-assemble into droplet interface bilayers [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF]; therefore, PL exchange does not occur through the droplet in the relevant time scales. Under these conditions, the PL number of each leaflet is constant,

= + = and = + = , 2
where and can be different.

At equilibrium, the morphology of the connected droplet and bilayer, as well as the distribution of PL between the droplet and the bilayer, minimize the free energy (equation ( 1)), under the constraints of equation ( 2) and of fixed droplet volume. This minimization yields the usual equilibrium conditions presented in the following.

The droplet and bilayer shapes obey the laws of three-fluid phase wetting systems [START_REF] De Gennes | Wetting: statics and dynamics[END_REF]. The interfaces must have a constant mean curvature (Laplace law). We focused on axisymmetric geometries for which the droplet interfaces are spherical caps, and the bilayer can either be flat or bear a constant curvature. The droplet morphology is fully characterized by the contact angles between the droplet interfaces and the bilayer, and (Figure 1B). These angles are fixed by the balance of the forces acting at the contact line (Figure 1B):

+ + = 0 or, cos + cos + = 0, sin = sin , 3
where , , are respectively the surface tension of the external and internal monolayers of the droplet ($%, $&), and the bilayer ('). In vitro experiments [START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF] confirmed the validity of equation ( 3) to describe the morphology of large membrane-embedded droplets. In the particular case, where the bilayer is tensionless, = 0, the angles are not unequivocally determined but must be such that + = 180°, which implies that the droplet is spherical.

The PL partitioning between the bilayer and droplet monolayers (Figure 1C) is controlled by the chemical potentials equilibrium, 4)).

*
In conclusion, for a given oil volume, number of PLs in each membrane leaflet and bilayer tension, the PL densities, , , , , and the contact angles, , , adjust in a coupled manner to fulfill the thermomechanical equilibrium conditions (equations (3), ( 4)).

Coupling between phospholipid densities and between surface tensions

The above equilibrium relations impose an interdependence between the different interfaces' PL density and, thus, the droplet and bilayer surface tensions via two distinct mechanisms.

The first coupling mechanism pertains to the chemical potential equilibriums, equation [START_REF] Thiam | Lipid Droplet Nucleation[END_REF]. Indeed, a slight variation in surface tension of one interface will modify the density of this interface. In response, PLs will redistribute between the adjacent interfaces to re-establish the equilibrium of the chemical potentials (equation ( 3)). Such an adjustment will change the respective PL densities and, hence, the surface tensions. The link between variations of surface tension and chemical potentials of an interface, due to variation of its PL density, is expressed by the Gibbs-Duhem relations, , = -,* and , = -,* -,* . 5

Combining these relations and the differentials of equation ( 4), ,* = ,* , ,* = ,* , we obtain a general link between surface tension variations,

, = , + , . 6
This first coupling due to the chemical potential equilibrium (4) is the unique coupling in two practical and biologically interesting situations: a symmetrical bilayer and an infinite bilayer reservoir. This relation indicates that the droplet interfacial tension increases with the bilayer one with a slope proportional to the ratio of their PL densities.

For a droplet embedded in a large ( ≫ , and possibly asymmetrical membrane, the bilayer behaves as an infinite PL reservoir of fixed PL density, independent of the state of the droplet. This configuration is more relevant in cell conditions when nascent LDs form in the ER membrane. In this case, a similar relation as equation [START_REF] Salo | Seipin regulates ER-lipid droplet contacts and cargo delivery[END_REF] , with 3 = 1 -3 (derivation of equation ( 8) and definition of 3 in Supplement text, section 6.3). This equation shows that the monolayer tension should also increase linearly with the bilayer ones as for a symmetrical membrane, but with a numerical pre-factor depending on the membrane asymmetry; 3 > 1/2 if the external leaflet is less dense than the internal one and viceversa.

A second density coupling mechanism exists for small (bilayer area comparable to droplet area) and asymmetrical membranes. This coupling arises from the PL number conservation (equation ( 2)) and the mechanical equilibrium (equation ( 3)), together linking the PL distribution to the system's morphology. A change in surface tension affects the morphology (equation ( 3)), i.e., the surface area of the interfaces, which in turn impacts the densities (equation ( 2)), and hence tensions. No simple mathematical relations resembling equation ( 6) expressing this coupling can be derived.

Experimental determination of the interdependence between surface tensions

We wanted to experimentally test the theoretical findings by probing the interdependence between the droplet and bilayer surface tensions. For this purpose, we used the droplet-embedded vesicle system (DEV) (19, 48) (Figure 2A), which mimics the theoretically described situation of an oil droplet in contiguity with a bilayer. DEVs were formed by inserting triolein droplets within the bilayer of giant unilamellar vesicles made of DOPC (1,2-dioleyl-sn-3glycero-3-phosphocholine) [START_REF] Chorlay | Making Droplet-Embedded Vesicles to Model Cellular Lipid Droplets[END_REF].

The external droplet monolayer and the bilayer of the DEV were captured by two micropipettes (Figure 2B). We selected DEVs with a symmetrically positioned droplet, i.e., identical contact angles = , which, consequently, have similar tension, = (equation ( 3)). These DEVs meet the symmetric condition leading to equation [START_REF] Salo | Seipin regulates ER-lipid droplet contacts and cargo delivery[END_REF], which can be tested experimentally. To establish the tension dependency predicted by this equation, we imposed the DEV bilayer tension step by step, by fixing the aspiration pressure of the micropipette, and concomitantly measured the micropipette-aspirationapplied surface tension of the external monolayer of the droplet (Figure 2B). We found that the monolayer tension increased with the bilayer tension (Figure 2C), agreeing with the theoretical description: increasing the bilayer tension decreases the chemical potential in the bilayer leaflets; to keep the chemical potential equilibrium, the droplet must, therefore, supply PLs to the bilayer, resulting in its tension increase.

Interestingly, the tensions' dependency followed a linear trend line (Figure 2C). Based on equation [START_REF] Salo | Seipin regulates ER-lipid droplet contacts and cargo delivery[END_REF], this linear dependency suggests that the ratio of the monolayer-to-bilayer PL density did not vary, independently of the bilayer tension. The slope

The PL density is maximum, i.e., close to full packing, in a tensionless bilayer. Since the droplet monolayer PL density evolves like the bilayer one, one may speculate that it also reaches near close packing when the bilayer is tensionless. Thereupon, the monolayer tension would also be close to zero. Such assumption was not valid as, when the bilayer tension fell to almost zero (<0.01 mN/m), the monolayer tension was non-negligible, around 1.5 mN/m (Figure 2C). We initially hypothesized that the non-zero tension of the monolayer could be due to the nature of the tensionless bilayer of the DEV, which may have been unable to supply PLs to the droplet. To test this hypothesis, we changed the system and put the droplet in contact with another type of PL reservoir.

At the tip of a tensiometer apparatus, we generated a triolein oil-in-buffer droplet, over-supplied with PLs in the oil (0.5% w/w to triolein) (Figure 2D, left). In this setting, the oil phase acts as a PL reservoir to the droplet interface. As soon as the droplet was formed in the buffer solution, the surface tension dropped down, due to the spontaneous adsorption of PLs to the interface, to reach an equilibrium value of 1.15 mN/m (Figure 2D, Figure S1D); without PLs, the triolein/buffer tension is ~34 mN/m.

Thus, even with this reservoir, the monolayer tension was non-zero and close to the ~1.5 mN/m obtained with DEV (Figure 2C). Next, starting from the equilibrium tension at 1.15mN/m, we mechanically compressed the PL monolayer of the droplet by sucking off the droplet volume (Figure 2D, Figure S1E). Even under this action, surface tension decreased but was still not close to zero, ~0.6 mN/m, compared with the tensionless bilayer (<0.01 mN/m). These results indicate that, unlike a bilayer, a droplet monolayer has specific features, detailed hereafter, that prevent it from reaching a high PL density and near-zero surface tension.

Altogether, the experiments with DEVs are consistent with the theoretical prediction (equation ( 7)). For symmetrical conditions, the monolayer tension responds linearly to an increase in bilayer tension, implying that the phospholipid density ratio is constant between the bilayer and the monolayer.

However, our results revealed two essential aspects: (i) through the bilayer and the droplet are connected, the PL density is lower for the droplet monolayer than the bilayer, and (ii) the tensions of the droplet and the bilayer are largely different in general; even in contact with a bilayer of very low tension, the droplet remains at relatively high tension (above 1 mN/m). In the following sections, we delve deeper into these findings with a theoretical approach, subsequently validated by a quantitative analysis of the surface tensions curves of DEVs.

Microscopic description of the contiguous droplet-bilayer system

To pinpoint the origin of the molecular interactions responsible for the discrepancy in tension and PL density between the monolayer and bilayer, we developed a microscopic description closely following the approach and assumptions of refs. [START_REF] Marsh | Lateral pressure in membranes[END_REF][START_REF] Marsh | Comment on Interpretation of Mechanochemical Properties of Lipid Bilayer Vesicles from the Equation of State or Pressure-Area Measurement of the Monolayer at the Air-Water or Oil-Water Interface[END_REF]. The goal is to express the equations of state relating surface tensions, chemical potentials, and densities, for a monolayer and a bilayer.

The different contributions to the free energy of a monolayer and a bilayer are depicted in (Figure 3A).

The free energy per surface unit of a monolayer at a water/oil interface function of the PL density can be written as, = ;/< + =>? + @AB + CD . 9

The four terms account respectively for the bare oil/water surface tension, lateral PL -PL interactions, hydrophilic interaction of PL head groups with water, PL tails interaction with oil. The free energy density of the bilayer is,

, = =>? + @AB + F@DG + =>? + @AB + F@DG + CC , . 10
The functions =>? and @AB in equation [START_REF] Jacquier | Lipid droplets are functionally connected to the endoplasmic reticulum in Saccharomyces cerevisiae[END_REF], which account for the lateral interactions between PLs and from PL head -water in a bilayer leaflet, are identical to the ones in equation ( 9) for the monolayer.

The term CC accounts for the trans interaction between the two leaflets, i.e., the interaction between the tails of PLs belonging to different leaflets. Lastly, F@DG accounts for the hydrophobic interaction of PL tails with water, responsible for the cohesion of bilayer in water. Following ref. [START_REF] Nagle | Theory of lipid monolayer and bilayer phase transitions: effect of headgroup interactions[END_REF], this contribution is supposed to be negligible for monolayer (and is thus absent in equation ( 9)) and nearly constant F@DG = F@DG for bilayer, with the parameter F@DG of the order 34 to 39 mN/m for DOPC. The contributions CD and CC are assumed to be linear in PL densities [START_REF] Nagle | Theory of lipid monolayer and bilayer phase transitions: effect of headgroup interactions[END_REF] The surface tension and the chemical potential of a monolayer, functions of the PL density, can be deduced from the free energy equation ( 9) and equation (MM1) (material and method):

= ;/< -I 11 and * = J I K , + H CD , 12
where the prime denotes the derivative of the function. The quantity I , named the lateral pressure, is defined as I = L =>? ′ + @AB ′ N -=>? -@AB : it arises from lateral PL -PL interactions and hydrophilic PL head interactions. This lateral pressure can be measured and well described theoretically by classical equations of state of two-dimensional fluids, such as the van der Waals equation of state [START_REF] Nagle | Theory of lipid monolayer and bilayer phase transitions: effect of headgroup interactions[END_REF], see below. . The parameter characterizes the excluded area due to steric repulsion and T the strength of the lateral interactions between PL molecules (Materials and Methods, Figure S2B). The determination of I enabled us to determine (up to a constant) * ( using equation [START_REF] Wilfling | Triacylglycerol synthesis enzymes mediate lipid droplet growth by relocalizing from the ER to lipid droplets[END_REF] (Figure 3C). Note that the exact profile of I depends on the PL type, yet the global features of the curves in Fig. 3B and C should be generic.

Combining the state equations (11 -14) with the equilibrium conditions (4), we discuss in the following two sections the origin of the density difference between the connected monolayers and bilayer, and then the basis of their surface tension difference. Additionally, these equations of state allow performing a complete quantitative analysis of the surface tension curves obtained for DEVs, in particular in the case of asymmetric DEVs (last section).

Droplet-bilayer phospholipid equilibration following the microscopic description

PL partitioning is governed by the equilibrium condition (4): the PL densities in adjacent monolayer and bilayer leaflet, and , are such that * = * . The chemical potentials of the monolayer and bilayer leaflet, * and * , functions of the PL density, as given by the state equations ( 12) and ( 14), are shown in Figure 3C. The two curves have the same profiles, but are shifted by

H CC -H CD .
Then, for the chemical potentials to be equal, the densities of contiguous monolayer and bilayer must be different in general, ≠ , as long as H CC ≠ H CD . Thereupon, the microscopic description (equation ( 14)) pinpoints the parameter H CC -H CD as the primary lever imposing the phospholipid density difference between the monolayer and bilayer. We remind that this parameter quantifies the difference in interactions of PL tails with their underneath environments which are: the tails of PLs in the opposite leaflet for the bilayer, and the NL oil phase for the droplet monolayer (Figure 3A). Depending on the sign of H CC -H CD , the monolayer lipid density is always larger or smaller than the bilayer leaflet density.

However, according to the surface tension measurements (Figure 2C) and equation ( 5), the PL density is expected to be lower at the droplet interface V , meaning that H CC -H CD V 0.

Consequently, trans-interactions between PL tails in the bilayer are energetically more favorable than the interactions of PL tails with oil molecules in the droplet.

Assuming a slight relative difference of PL density between the droplet monolayer and bilayer leaflet, and expanding the equilibrium relation * = * to the linear order (Supplement text, section 8), one obtains

- ≃ H CD -H CC I K 15
This equation shows that the relative density difference between the bilayer and droplet monolayer is modulated by H CC -H CD (Figure 3A). A bilayer is stable only in a narrow range of PL density, near close packing, and can be stretched by only about 5% [START_REF] Santinho | Fat Inclusions Strongly Alter Membrane Mechanics[END_REF][START_REF] Kwok | Thermoelasticity of large lecithin bilayer vesicles[END_REF]. Consequently, I K should be very large and, according to equation ( 15), the relative difference in density between a bilayer leaflet and its contiguous droplet monolayer should be relatively small. This interpretation agrees with the density ratio obtained from the slope of Figure 2C using equation ( 7) and our recent experimental finding in DEVs [START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF], suggesting that for 100 PLs on a bilayer leaflet, droplet monolayer in contiguity with this leaflet has ~90 PLs.

Surface tensions comparison following the microscopic description

Combining the previous results on the PL distribution with the state equations [START_REF] Markgraf | An ER protein functionally couples neutral lipid metabolism on lipid droplets to membrane lipid synthesis in the ER[END_REF][START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF] allows understanding how the droplet tension compares with the bilayer one. In particular, we wanted to understand why the droplet remains with a non-zero tension while being in contact with a tensionless bilayer (Figure 2C).

According to equation [START_REF] Markgraf | An ER protein functionally couples neutral lipid metabolism on lipid droplets to membrane lipid synthesis in the ER[END_REF], the droplet surface tension is maximal in the absence of PLs, equal to ;/< , and decreases when the PL density or the lateral pressure increases. The bilayer tension has a similar dependency on the PL density (equation 13), with F@DG being reminiscent of ;/< , though they have different molecular origins (Figure 3A). As found above, the bilayer PL density should always be slightly higher than the droplet monolayer one. Consequently, the monolayer should be of lower lateral pressure than the bilayer leaflet, i.e., I > I .

At zero bilayer tension, the mechanical equilibrium condition (3) imposes the same tension and thus the same PL densities between the two droplet monolayers. It follows from equation ( 4) that the two bilayer leaflets also have the same density, X . Under this condition, the lateral pressure in the bilayer balances exactly the hydrophobic contribution in equation [START_REF] Markgraf | An ER protein functionally couples neutral lipid metabolism on lipid droplets to membrane lipid synthesis in the ER[END_REF], F@DG = I X . On the droplet monolayer side, the lateral pressure is lower, i.e., I X < I X , and too small to completely cancel the tension of the droplet interface (equation ( 10)), X = ;/< -I X ≠ 0. Assuming a slight relative difference in PL density between a monolayer and a bilayer leaflet [START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF], the tension of a droplet embedded in a tensionless bilayer can be approximately expressed by (Supplement text, section 8), This equation shows that ;/< -F@DG and H CD -H CC , which controls the monolayer-bilayer density mismatch, are the two key parameters keeping the droplet monolayer tension to a non-zero value when the bilayer is tension-free.

The parameters ;/< and H CD , are a function of the oil type. Thus, changing the oil type should vary the tension of the droplet when the bilayer is tensionless (equation ( 11)). To test this prediction, we established the monolayer-bilayer tension diagram of DEVs made with different oils. Namely, we used a triolein-sterol ester mixture or squalene (Figure 3D-E). Independently of the oil type, a linear trend was observed for symmetric DEVs, as expected from equation [START_REF] Salo | Seipin regulates ER-lipid droplet contacts and cargo delivery[END_REF]. The slopes were also conserved, confirming that these oils' monolayer-bilayer densities were similar [START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF]. However, the droplet tension at zero bilayer tension was significantly different (Figure 3E), agreeing with our prediction from the theoretical analysis (equation ( 16)). At very low bilayer tension (<0.1mN/m), the squalene droplet had a lower tension than the triolein one (Figure 3E). Since ;/< was respectively 23.7 mN/m and 34 mN/m for squalene and triolein, the term I ;/< -F@DG I would be lower for squalene, which, following equation ( 16), would partly explain the lower droplet monolayer tension value for squalene.

Validation of the microscopic model by the quantitative analysis of the DEV system

We wished to compare quantitatively experimental data obtained with the DEV system and theory output to go beyond the qualitative agreement between theoretical predictions and experimental observations. A quantitative agreement would eventually validate our theoretical approach and the underlying hypothesis.

We built a complete theoretical description of the DEV system based on the thermodynamic approach developed in the preceding sections (Supplementary text, section 7). The model allows us to compute all the characteristics of a DEV, in particular the surface tension of the different interfaces, which are experimentally measurable and tunable observables. The parameters of the model are of two origins: geometrical and physicochemical. The geometrical parameters (oil volume, vesicle inner volume and leaflet asymmetry in PL number) are specific to each DEV and are experimentally obtained by image analysis. The physicochemical (or microscopic) parameters are the ones in the state equations [START_REF] Markgraf | An ER protein functionally couples neutral lipid metabolism on lipid droplets to membrane lipid synthesis in the ER[END_REF][START_REF] Wilfling | Triacylglycerol synthesis enzymes mediate lipid droplet growth by relocalizing from the ER to lipid droplets[END_REF][START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF][START_REF] Kory | Targeting fat: mechanisms of protein localization to lipid droplets[END_REF] and only depend on the PL and oil types composing the DEV. The physicochemical parameters ;/< and the lateral pressure were determined by the drop tensiometer method (Figure S2B). The only unknown physicochemical parameters of the model are hence F@DG and H CD -H CC (Figure 3A). We adjusted these two parameters to fit the model to the surface tensions data of Figure 2C, obtained with a symmetric DEV. We found that F@DG = 38.6 mN/m, close to reported values for DOPC [START_REF] Marsh | Lateral pressure in membranes[END_REF], and 4B). The value of H CC -H CD , looks rather low but sufficient enough to proffer a higher PL packing to the bilayer than the monolayer (equation ( 14)). This means that the small differences between the PL tail -NL interactions on the droplet and the tail-tail interactions between PLs on opposite leaflets of the bilayer are sufficient to induce a PL density gradient between the bilayer and the monolayer. For each DEV (Figure S3 A-D), including the one in Figure 2C, we measured the tension of the external droplet monolayer against the bilayer one (Figure 4A, data points); we also determined by image analysis the DEV geometrical parameters (size and droplet position asymmetry). Then, using the microscopic parameters' values (Table Figure 4B), we computed as a function of for each DEV imposing specific geometrical constraints (Figure 4A, model, solid lines). Strikingly, the computed curves were perfectly superposed to each of the experimental data they modeled, without any adjustment of the microscopic parameters (Figure 4A). Given the number of experimental data points, the perfect match with the model, with the pre-adjustment of only two microscopic parameters, i.e., F@DG and H CD -H CC , supports the validity of the theoretical approach.

H CC -H CD = -4.4 pN.nm = 1.1 Y Z [ (Table Figure
Two additional features also support the validity of our model. First, at zero bilayer tension, the tensions of the droplet interfaces are the same for all the DEVs (Figure 4A), which had different geometries. This observation agrees with equation ( 14), which predicts in this regime that the tensions of the LD interfaces should exclusively depend on the microscopic parameters and be independent of DEV size and morphology. Second, the slope of ( curve depends on the droplet position at zero bilayer tension (Figure 4A). The more the droplet budded inward, the steepest was the slope , /

, . The exact expression of the slope , /, at = 0 predicted by the theory is provided in supplement text, section 6.4 and, indeed, confirms that the larger at zero tension, the larger , /, .

In conclusion, the comparison of the DEV experimental data to the theory output showed a quantitative agreement, which supports the validity of our theoretical approach and its underlying hypothesis.

Discussion.

Lipid droplets have multiple biological functions that rely on the targeted proteins to their surface and their surface tension. The phospholipid monolayer of lipid droplets represents a barrier for proteins to access to lipid droplets and determine their tension [START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF][START_REF] Kory | Targeting fat: mechanisms of protein localization to lipid droplets[END_REF][START_REF] Thiam | Lipid droplet-membrane contact sites-from protein binding to function[END_REF][START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF][START_REF] Kory | Protein crowding is a determinant of lipid droplet protein composition[END_REF]. Since lipid droplets share a hemimembrane with the endoplasmic reticulum bilayer, at least during the steps of lipid droplet assembly [START_REF] Henne | The assembly of lipid droplets and their roles in challenged cells[END_REF], understanding how phospholipids partition between the bilayer and the droplet monolayer is crucial.

We developed macroscopic and microscopic models to establish the relationship between the system's free parameters composed of an oil droplet embedded in a phospholipid bilayer. We subsequently set up experiments based on droplet-embedded vesicles to test the theoretical outputs and found strong agreements. Such achievement led us to pinpoint molecular parameters or interactions responsible for the unequal phospholipid density and surface tensions between the droplet and the bilayer.

The phospholipid density discrepancy between the droplet monolayer and the bilayer in contiguity essentially pertains to the different environments underneath a PL layer in the bilayer and the droplet monolayer. For the bilayer, the PL-tails of a leaflet interact with the PL-tails of the counterpart leaflet (the interaction energy per molecule is H CC ) while in the monolayer, the PL-tails interact with the NL oil phase beneath the monolayer (the interaction energy per molecule is H CD ) (Figure 3A,C). At a constant bilayer tension, increasing H CC -H CD , for example by increasing the affinity between oil molecules and phospholipid acyl chains, will result in a phospholipid flux from the bilayer to the droplet, thereby increasing the droplet phospholipid density (Figure 4C, ). Such an improvement in phospholipid cover will induce a decrease in the droplet tension and, consequently, the spreading of the droplet, according to equation [START_REF] Jackson | Lipid droplet biogenesis[END_REF]. Quantitatively, a 2 pN.nm variation of H CC -H CD , at fixed bilayer tension, will result in a variation in density of the order of a few percent (Figure 4D).

Should the bilayer present an asymmetry of phospholipid composition between its two leaflets, the droplet's inner and outer phospholipid monolayers may experience different interactions with oil molecules and therefore have different densities. Such an asymmetric monolayer phospholipid distribution will promote the droplet emergence to the better-covered monolayer [START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF].

The bilayer tension also impacts the phospholipid densities (Figure 4E). If the bilayer tension is increased, the densities of the bilayer and monolayer will decrease simultaneously. However, the relative difference between the droplet density and the bilayer density remains almost constant.

Phospholipid packing voids occur more often when triacylglycerols are infused in a bilayer [START_REF] Prévost | Mechanism and determinants of amphipathic helix-containing protein targeting to lipid droplets[END_REF][START_REF] Kim | Stressed lipid droplets: How neutral lipids relieve surface tension and membrane expansion drives protein association[END_REF][START_REF] Bacle | Interdigitation between triglycerides and lipids modulates surface properties of lipid droplets[END_REF][START_REF] Ajjaji | Hepatitis C virus core protein uses triacylglycerols to fold onto the endoplasmic reticulum membrane[END_REF][START_REF] Santinho | Fat Inclusions Strongly Alter Membrane Mechanics[END_REF]. Such observations already suggested, at least qualitatively, that a lipid droplet connected to a bilayer would be less packed with phospholipids. This is confirmed by fluorescence measurement showing that a droplet monolayer connected to a bilayer is ~13% less packed with phospholipids than the bilayer. Our approach in this paper provided an alternative measurement of the relative phospholipid densities but, most importantly, it points to the origin of such phospholipid density gradient.

Previous experimental and theoretical studies illustrated the relevance of the surface tension difference between a lipid droplet and its host membrane [START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Deslandes | Lipid Droplets Can Spontaneously Bud Off from a Symmetric Bilayer[END_REF][START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF][START_REF] Wang | Bulging and budding of lipid droplets from symmetric and asymmetric membranes: competition between membrane elastic energy and interfacial energy[END_REF]. This tension gap controls to a large extent the morphology of droplet, its stability and budding capacity. While the tension of organelles such as the ER is very low [START_REF] Upadhyaya | Tension in tubulovesicular networks of Golgi and endoplasmic reticulum membranes[END_REF], the surface tension of LD forming in their membrane is much larger [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF]. This could seem surprising since the monolayers at the LD interfaces and the host membrane leaflets are connected. The present work shows how the surface tensions of the forming LD and host membrane are coupled in general and reveals the microscopic origin of the different tensions. Our results explains how a lipid droplet connected to a nearly tensionless membrane can keep a relatively high surface tension.

Finally, our theoretical approach may present two limitations. First, our model does not explicitly consider the partitioning of oil molecules from the droplet to the bilayer hydrophobic region, as seen in DEVs, which alter the membrane's biophysical properties [START_REF] Santinho | Fat Inclusions Strongly Alter Membrane Mechanics[END_REF]. From a theoretical standpoint, it will be interesting to include the presence of these oil molecules to gain accuracy in the microscopic description. Nonetheless, the match between our theoretical predictions and experimental data, including fluorescent density measurements with DEVs [START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF], suggests that the oil-free description captured the dominant mechanisms controlling the phospholipid densities, as well as the interdependence between surface tensions. Secondly, in the biologically relevant tensions, below 0.1 mN/m (34), the bilayer tension mostly affects the excess area stored in the thermal undulations [START_REF] Helfrich | Undulations, steric interaction and cohesion of fluid membranes[END_REF][START_REF] Rawicz | Effect of chain length and unsaturation on elasticity of lipid bilayers[END_REF] rather than the intermolecular distance between phospholipids in the bilayer. In other words, tension impacts the effective density, i.e. the inverse of the projected area per molecule, rather than the real surface density. This effect of thermal undulations is not included in our theoretical description, in particular in the equation of state [START_REF] Dhiman | Mechanisms of protein targeting to lipid droplets: A unified cell biological and biophysical perspective[END_REF] for the bilayer tension. Our model might thus be unable to precisely reproduce curves (Figure 4A) for very low bilayer tension, provided such curves could be obtained experimentally in this range. However, the most important effect expected is that in the low-tension regime, the real surface density of the bilayer is always very close to the zero-tension density X and then the monolayer tension close to X (equation 16). Then, the conclusions drawn for the zero-bilayer tension case should hold more generally in all the low bilayer tension regime.

In conclusion, our present study highlights critical parameters that may modulate the phospholipid density at the surface of lipid droplets connected to the endoplasmic reticulum. More generally, our approach may be upgraded to study how phospholipid mixtures, and even protein mixtures, redistribute or partition between the bilayer and the droplet, a crucial question in lipid droplet biology. A) Microscopic contributions to the free energy density of a monolayer and of a bilayer. For the monolayer: the surface tension of the bare water/oil interface ( ;/< ), the interaction of the phospholipid tails with the oil phase CD = H CD , the lateral interaction between phospholipids ( =>? ), and the interaction of the phospholipid headgroups with water ( @AB ). For the bilayer: the unfavorable interactions of the PL tails with water ( F@DG = F@DG ), the trans-interaction between phospholipid tails

( CC = H CC +
) of the apposed leaflet, the lateral interaction between phospholipids ( =>? ), and the interaction of the phospholipid headgroups with water ( @AB ).

B)

Lateral pressure as a function of phospholipid density at the triolein-water interface deduced from a compression isotherm obtained from a pending droplet experiment (see supplementary Figure S2A,B). All micrographs of DEV were made on a Carl ZEISS LSM 800 with X10 air objective, and observed samples were held by Glass coverslips (Menzel Glaser (24x36mm #0)).

Micromanipulation & surface tension measurements by microaspiration.

Micro-pipettes were made from capillaries drawn out with a Sutter Instruments pipette-puller. They were used to manipulate the DEVs in order to get a side view of the system. Pipettes were treated with an mPEG-Silane solution following the protocol described below.

Additionally, surface tensions were measured and modulated using the same pipettes. As shown in (Figure 2B), the micromanipulation of the external LD monolayer (or the DEV's bilayer) enables the measurement of the external monolayer surface tension (or the bilayer surface tension). Using

Laplace's law and the measurement of the diameter, droplet (or bilayer) diameter, and suction pressure, the surface tension of the interface can be determined:

= ∆Psuc 2 L 1 ij - 1 i, N
where ΔPsuc, Rp, and Rd are the suction pressure, the pipette radius, and the droplet external radius.

The suction was carried out using a syringe. The resulting pressure was measured with a pressure transducer (DP103 provided by Validyne Eng. Corp, USA), the output voltage of which was monitored with a digital voltmeter. The pressure transducer (range 55 kPa) was calibrated prior to the experiments.

External monolayer and bilayer tension of DEV were measured simultaneously while increasing the bilayer surface tension to obtain the monolayer tension-bilayer tension graph shown in (Figure 2C).

Tension measurements of triolein-buffer interface covered with phospholipids

A pendant droplet tensiometer designed by Teclis Instruments was used to measure the interfacial tension of oil/water interfaces. All experiments were conducted at room temperature. DOPC phospholipids stored in chloroform were dried under argon and mixed with triolein oil. This mix was then sonicated and store at room temperature for 2h. To generate a phospholipid monolayer at the oilbuffer interface, phospholipid-in-triolein droplets (from 5 to 16.0 μl) were formed at the tip of a J-needle submerged in 5 ml of HKM buffer. The surface tension of the interface was automatically measured by the tensiometer.

Tension of an interface at equilibrium with a large reservoir of PLs dissolved in the oil phase.

Triolein was supplemented with 0.5% (w/w) DOPC to get above the critical micellar concentration. This mix was used in the pendent droplet tensiometer to form a DOPC monolayer at the oil-water interface.

As the phospholipids exceeded the critical micellar concentration, the oil phase acted as a phospholipid reservoir in supplying phospholipids to the monolayer. Surface tension was measured until a plateau was reached (supplementary figure S1D). This plateau of tension is the tension designated as the tension of a monolayer connected to a phospholipids reservoir.

The tension of a mechanically compressed phospholipid monolayer.

Triolein was supplemented with 0.05% (w/w) DOPC. This mix was used in the pendent droplet tensiometer to form a DOPC monolayer at the oil-water interface. The phospholipids relocated at the oil-buffer interface resulting in a decrease of surface tension. After tension stabilization, we started to record tension while gradually sucking up the oil back in the needle. This resulted in the compression of the phospholipid monolayer at the interface, increasing of the phospholipid density and decreasing surface tension. At some compression level, a tension plateau was reached (supplementary figure S1E). This plateau of tension is the tension designated as the tension of a monolayer mechanically compressed at its maximal PLs density.

Phospholipids monolayer characterization (DOPC).

A DOPC monolayer was formed at the triolein buffer interface using the pendent droplet tensiometer using the same condition as described in the above paragraph. After tension stabilization, the droplet area was decreased while recording surface tension (supplementary figure S2A,B). This surface tension -droplet area isotherm is then fitted by equation ( 11 Determination of the contact angles between the droplet and the bilayer.

DEVs were imaged at their equatorial plane (side view). Two osculating circles are adjusted to delimit the droplet and bilayer of the DEV. θe, the contact angle formed by the two tangents originating from the intersection point of the two circles (see supplementary figure S3 A-D), can be determined geometrically using the following equation derived from the law of cosines: cos = , : -i k : -i l :

2 i k i l

Where (i l ) is the radius of the droplet auscultating circle, (i k ) is the radius of the bilayer auscultating circle, and (,) is the distance between the two centers of the two osculating circles.

QUANTIFICATION AND STATISTICAL ANALYSIS

Statistical analysis

Unless mentioned, all values shown in the text and figures are mean ± S.D.

EQUIPMENT AND REAGENTS

Equipment: All micrographs were made on a Carl ZEISS LSM 800. Glass coverslips: Menzel Glaser (24x36mm #0). Micro-pipettes made from capillaries (1.0ODx0.

14 (

 14 The surface tension of a bilayer function and the chemical potential of one of its leaflets, functions of the leaflet densities, are deduced from equation[START_REF] Jacquier | Lipid droplets are functionally connected to the endoplasmic reticulum in Saccharomyces cerevisiae[END_REF] and equations (MM2-MM3) (Materials and Method), and read, The chemical potential of a leaflet is independent of the density of the other leaflet under our assumptions.)A central parameter in these state equations(11 -14) is the lateral pressure I . By using the pending drop experiment, described Fig.2Cand ref.[START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF], we obtained I for a DOPC monolayer at the water -TO interface (Figure3B, FigureS2A); it was well described by a van der Waals state equation,

  By definition, the above values of the different physicochemical (or microscopic) parameters should only be set by molecular interactions, exclusively depending on the PL and oil type and not on DEV geometry. Therefore, the values of these parameters should allow fitting the model for any DEV geometry. To test this prediction, we considered DEVs, made of DOPC vesicles and triolein droplets of different sizes, and different asymmetries in DOPC number between their internal and external leaflets. PL asymmetry is obvious at low bilayer tension, as the droplets are spherical[START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF] and differently positioned in the bilayer[START_REF] Chorlay | Membrane asymmetry imposes directionality on lipid droplet emergence from the ER[END_REF][START_REF] Chorlay | An asymmetry in monolayer tension regulates lipid droplet budding direction[END_REF]: the droplets are either centered, = I/2, or emerged outward, V I/2, or inward, > I/2, (Figure4A, FigureS3A-D). We took advantage of this variability in DEV geometry, i.e., in size and asymmetry, to test whether the microscopic parameters' values (Table Figure4B) allow us to predict the correct DEVs tensions for all DEV geometry.

Figure 1 :

 1 Figure 1: Equilibrium conditions of a lipid droplet connected to a phospholipid bilayer A) Schematic view of a lipid droplet embedded in a bilayer. The two phospholipid monolayers covering the oil droplet are in continuity with the leaflets of the bilayer allowing phospholipid exchanges. B) The mechanical equilibrium, resulting from the balance of the surface tension forces acting on the contact line, imposes the shape of the droplet reported by the two contact angles and . The bilayer tension, the external monolayer tension and the internal monolayer tension are respectively ( ), ( ) and ( ). C) Chemical equilibrium between phospholipids in the bilayer leaflet and in the monolayer. The equilibrium distribution between phospholipids in contiguous bilayer leaflet and LD monolayer is determined by the balance of their chemical potentials * and * . Phospholipids of a given membrane leaflet are free to exchange by lateral diffusion between the contiguous LD monolayer and the bilayer leaflet but phospholipid flip-flop is considered irrelevent. and are the phospholipid density in the external and internal monolayer, and are the density in the external and internal leaflet of the bilayer.

Figure 2 :

 2 Figure 2: Experimental determination of the interdependence between surface tensions A) Formation of the droplet-embedded vesicle (DEV) system: Giant unilamellar vesicles (GUVs) are mixed with nano emulsion droplet that are incorporated into the intermonolayer space of the GUVs to form DEVs. B) Left, Schematic view of micropipette measurement of the monolayer surface tension of a DEV while simultaneously measuring and increasing its bilayer surface tension with a second micropipette. Right, representative confocal micrograph showing a brignthfield image of a triolein-DOPC DEV merge with the fluorescence image of the phopholipids reported by rhodamine DOPE. Scale bar is 10 μm. C) Monolayer-bilayer surface tension diagram of a triolein-DOPC DEV. This DEV was selected with a droplet symmetrically positioned with respect to the bilayer, i.e. identical contact angles and . See supplementary figure S1A for confocal images of the experiment. See supplementary figure S1B,C for monolayer-bilayer tension diagram of DEVs with asymetric droplet position and of DEVs with other phospholipidic compositions. A trend line is drawn to highlight the linear dependence the tensions. D) (left) Scheme of the droplet tensiometer method: an oil-in-water droplet is generated at the tip of a tube, with phospholipids added in excess in the oil phase. Compression is achieved by decreasing the droplet volume through withdrawing the oil phase. (right) Quantification of the surface tension of DOPC monolayer at triolein-buffer interface, respectively for a monolayer in continuity with a lipid bilayer with tension<0.01mN/m (DEV), a monolayer in contact with a large phospholipid reservoir disolved in the oil phase and a monolayer mechanically compressed. Data are represented as mean ±SD. Related to supplementary figures S1 D,E.

Figure 3 :

 3 Figure 3: Microscopic description of the contiguous droplet-bilayer system

C)

  Chemical potential of a bilayer and a monolayer as a function of phospholipid density. The two chemical potentials vary identically but are shifted by the amount H CC -H CD . At equilibrium a monolayer in contact with a bilayer have the same chemical potential (* = * ) and therefore have different phopholipid densities, whose values are directily impacted by the H CC -H CD gap. D) Molecular structure of the different oils used to probe the effect of oil composition on monolayerbilayer surface tension diagram. E) Monolayer-bilayer surface tension diagram of DOPC DEVs made with different oil composition: sterol ester-triolein (1:3) (red circles), triolein (black circles) and squalene (blue circles). DEVs were selected with a droplet symmetrically positioned with respect to the bilayer. Black dot represent the average monolayer tension of osmotically deflated triolein DEVs (bilayer tension < 0.03mN/m ; n=17). Blue dot represent the average monolayer tension of osmotically deflated squalene DEVs (bilayer tension < 0.09mN/m ; n=9). See supplementary Figure S2C for monolayer-bilayer tension diagram of squalene and sterol ester-triolein (1:3) DEVs with asymmetric positions of the droplet.

Figure 4 :

 4 Figure 4: Validation of the microscopic model by the DEV experimental system A) Monolayer-bilayer surface tension diagram of a triolein-DOPC DEVs having droplets with different positions relatively to the bilayer: centered droplet (θ ] = π/2, black dots), droplet budding outward of the bilayer (θ ] V π/2, blue dots), or droplet budding inward of the bilayer (θ ] > π/2, red dots). See supplementary figure S3 A-D and material and methods for angle determination. Theoretical model was used to fit the centered experimental data (black line) and enabled to extract the microscopic parameters. Using the same parameters and only adjusting the droplet's size and position parameters, the model perfectly fit the data of the other DEVs with asymmetric droplet positions (blue and red lines). B) Main microscopic parameters obtained by fitting the model to the centered experimental data.C) Schematic illustration of the effect of the variation of (ε CC -ε CD ) on phopholipid density at the surface of a droplet in contiguity with a bilayer. If the bilayer tension is kept constant, the increase ε CC -ε CD leads to a higher density of phopholipids on the surface of the droplet and therefore a lower surface tension of the droplets which causes the droplet to spread. This can be achieved by increasing the affinity of the phospholipid tails for the oil, or decreasing the strength of the trans-interactions between phospholipid tails in the bilayer. D) Theoretical prediction of the effect of the variation of (ε CC -ε CD ) on the difference between the density of phospholipids in a bilayer sheet and that at the droplet surface. The bilayer surface tension (γ G )) was kept at 0.5mN/m. E) Theoretical prediction of the variation of the surface tension of the bilayer ( ) on the phospholipid density in the bilayer and in the monolayer of droplets. H -H ; was kept contant at -4.4 pN.m.

  and is the number of PL on the droplet interface. It allows deducing the values of the parameters ;/< , , T (and ).

  58IDx150Lmm 30-0017 GC100-15b Harvard Apparatus) with a micropipette puller (Sutter instrument model P-2000). Micromanipulation (Eppendorf TransferMan® 4r). Pressure measurement unit (DP103 provided by Validyne eng. corp, USA). Plasma cleaner was purchased from Harrick Plasma (PDC-32G-2 (230V) and used at 0,8 mbar of air pressure. dioleyl-sn-3glycero-3-phosphocholine), DOPA (1,2-dioleoyl-sn-glycero-3-phosphate, Pufa (18:0-20:4) (1-stearoyl-2-arach-idonoyl-sn-glycero-3-phosphocholine), Rhodamine-DOPE (1,2dioleyl-sn-glycero-3-phosphoethanolamine-N-lissamine rhodamine B sulfonyl) were from Avanti Polar Lipids (Alabaster, AL). triolein (Glyceryl trioleate T7140), Squalene (S3626), sterol-ester (C9253 1G),Hepes (54457-250-F), K acetate (P1190), MgCl2 (M8266-100G), BSA 98% (A7906-100G), and sucrose 99.5% (59378-500G) and mPEG5K-Silane (JKA3037) were from Sigma-Aldrich.

5:4 7 of 0.45±0.02, indicates that the bilayer PL density is slightly higher than the monolayer one, agreeing with our previous fluorescence and droplet tensiometer measurements where this value was of 0.435[START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF].

Acknowledgments.

We are thankful to our group members for their valuable comments and critical discussions about the manuscript. This work was supported the ANR-MOBIL and ANR-21-CE11-LIPRODYN to ART.

Declaration of Interest.

The authors declare no competing interests.

Author Contributions.

AC, LF and ART designed, performed research, analyzed data and wrote the paper.

Material and methods: theory.

Definition of the intensive thermodynamic quantities

The surface tension and chemical potential of a PL monolayer are defined by (supplement text, section 2),

where the prime denotes the derivative of the function. For each monolayer, Materials and Methods experimental.

Preparation of GUVs.

All experiments were performed in the following HKM buffer: 50 mM Hepes, 120 mM Kacetate, and 1 mM MgCl2 (in Milli-Q water) at pH 7.4 and 275±15 mOsm.

GUVs were prepared by electro-formation. Phospholipids and mixtures thereof in chloroform at 0.5 µM were dried on an indium tin oxide (ITO) coated glass plate. The lipid film was desiccated for 1 h. The chamber was sealed with another ITO-coated glass plate. The lipids were then rehydrated with a sucrose solution (275+-15 mOsm). Electro-formation is performed using 100 Hz AC voltage at 1.0 to 1.4 Vpp and maintained for at least 1 h. This low voltage was used to avoid hydrolysis of water and dissolution of the titanium ions on the glass plate. GUVs were either stored in the chamber at 4 °C overnight or directly collected with a Pasteur pipette.

GUVs composition:

DOPC GUVs: 99 % DOPC (1,2-dioleyl-sn-3glycero-3-phosphocholine) stained with 1% Rhodamine-DOPE (1,2-dioleyl-sn-glycero-3-phosphoethanolamine-N-lissamine rhodamine B sulfonyl).

DOPA-DOPC GUVs: 30% DOPA (1,2-dioleoyl-sn-glycero-3-phosphate), 69 % DOPC, and 1%

Rhodamine-DOPE.

Pufa-DOPC GUVs: 30% Pufa (18:0-20:4) (1-stearoyl-2-arach-idonoyl-sn-glycero-3-phosphocholine), 69 % DOPC, and 1% Rhodamine-DOPE.

Preparation of DEV (GUVs + oil droplet)

To prepare the oil droplets, 5 µL of the oil (triolein or squalene) was added to 45 µL of HKM buffer.

The mixture was sonicated. The diameter of the resulting droplets is on the order of a few hundred nanometers. To make DEV, GUVs were then incubated with the LDs for 5 min. The GUV-LD mixture was then placed on a glass coverslip (pretreated with 10 % (w/w) BSA and washed three times with buffer).

Confocal microscope images.


MD, PhD Marc-Olivier Fischer
email: fischer-mo@chu-caen.fr.

MD, PhD Pierre-Grégoire Guinot

Stéphane Debroczi

MD Pierre Huette

MD Christophe Beyls

MD, PhD Gérard Babatasi

Kevin Bafi

MD Mathieu Guilbart

MD, PhD Thierry Caus

MD Emmanuel Lorne

MD, PhD Hervé Dupont

MD ; Jean-Luc Hanouz

PhD Momar Diouf

MD Osama Abou-Arab

Marc-Olivier Pr

M.D Fischer

PhD, Pôle Réanimations Anesthésie

Individualised or liberal red blood cell transfusion after cardiac surgery: a randomised controlled trial

Keywords: cardiac surgery, red blood cell transfusion, outcomes, haemoglobin, central venous oxygen saturation

Background: Current practice guidelines for red blood cell (RBC) transfusion in intensive care units are based on the haemoglobin threshold, without consideration of oxygen delivery or consumption. We aimed to evaluate an individual physiological threshold guided by central venous oxygen saturation (ScVO2).

Methods:

In a randomised bicentric study in two French academic hospitals, 164 patients who were admitted in an intensive care unit following cardiac surgery with postoperative haemoglobin < 9 g dl -1 were assigned to receive a transfusion with one unit of RBCs (haemoglobin group) or only if the ScVO2 was < 70% (individualised group). The primary outcome was the number of patients receiving at least one unit of RBCs. The secondary composite outcome was acute kidney injury, stroke, myocardial infarction, acute heart failure, mesenteric ischemia, or in-hospital mortality. One-and six-month mortality were evaluated during the follow-up.

Results

The primary outcome was observed for 80 of 80 patients (100%) in the haemoglobin group and in 61 of 77 patients (79%) in the individualised group (absolute risk -21% [-32.0; -14.0] P < 0.001). There was no significant difference in the secondary outcome between the two groups. The follow-up showed a nonsignificant difference in mortality at one and six months.

Conclusion

An individualised strategy based on a ScVO2 threshold of 70% allows for a more restrictive RBC transfusion strategy with no incidence on postoperative morbidity or six-month mortality.

Institution in which the work was performed: Department of Anaesthesiology and Critical

Care Medicine, Amiens University Hospital, F-80054 France and Department of Anaesthesiology and Critical Care Medicine, Caen University Hospital, F-14000 France

Editor's Key Points

• Whether haemoglobin levels are a justified trigger for red blood cell (RBC) transfusion in cardiac surgery is under discussion.

• This randomised study evaluated transfusion guided by central venous oxygen saturation (ScVO2) as alternative for haemoglobin-guided transfusion.

• A transfusion strategy based on ScVO2 reduced the number of patients receiving at least one RBC transfusion versus a strategy based solely on haemoglobin levels.

• ScVO2-guided transfusion was not associated with an increase in hospital morbidity or mortality.

• This study is supportive for a more physiological approach for RBC transfusion in perioperative care.

Introduction

Red blood cell (RBC) transfusion is widely used in various settings in medicine to increase oxygen delivery to tissues but is associated with adverse reactions. [START_REF] Carson | Indications for and Adverse Effects of Red-Cell Transfusion[END_REF] Among the most frequent recipients of RBC transfusions are patients scheduled for cardiac surgery. Large high-evidence trials have shown the non-inferiority of a restrictive strategy relative to a generalised strategy in terms of postoperative mortality. [START_REF] Murphy | Liberal or restrictive transfusion after cardiac surgery[END_REF][START_REF] Mazer | Restrictive or Liberal Red-Cell Transfusion for Cardiac Surgery[END_REF] However, no haemoglobin threshold is mentioned in the latest European guidelines of blood management in cardiac surgery, which, nonetheless, highlight the necessity of considering the condition of the patient and the balance between O2 delivery and O2 consumption. [START_REF] Boer | EACTS/EACTA Guidelines on patient blood management for adult cardiac surgery[END_REF] Indeed, the application of an arbitrary threshold using the haemoglobin value for all patients is questionable, as it does not consider the O2 consumption (VO2)-to-delivery (DO2) ratio. This ratio can be determined from blood samples obtained from a central venous catheter by measuring central venous oxygen saturation (ScVO2), as ScVO2 = SaO2-(VO2/DO2). Thus, ScVO2, as a component of goal-directed therapy, has been shown to improve early outcomes in septic-shock patients. [START_REF] Rivers | Early Goal-Directed Therapy in the Treatment of Severe Sepsis and Septic Shock[END_REF] After optimization of oxygenation and cardiac output, ScvO2 records individual metabolic tolerance to anaemia and could be used as an individualised and physiological transfusion indicator. [START_REF] Vallet | Venous oxygen saturation as a physiologic transfusion trigger[END_REF] In spite of a physiological rational, the clinical utility of RBC transfusion using individual ScVO2 threshold has been scarcely reported in randomized study. [START_REF] Zeroual | Restrictive Transfusion Strategy after Cardiac Surgery[END_REF] The main endpoint of this study was to assess the feasibility of such a strategy in decreasing the incidence of patients receiving at least one RBC transfusion. The secondary endpoints were to assess the safety of such a strategy in terms of clinical outcomes and mortality.

Materials and methods

Ethics and population study

The postoperative individualised transfusion threshold trial was an open-label, randomised, controlled, superiority trial conducted in two French academic hospitals (Amiens University Hospital and Caen University Hospital). The PITT trial was approved by the local institutional review board (CPP Nord Ouest II, Amiens, France; IRB identifier: 2016-A00880-51, clinicaltrials.gov registration NCT 02963883) in accordance with the Declaration of Helsinki and French law on clinical research. [START_REF] Toulouse | French legal approach to patient consent in clinical research[END_REF] Each participant provided written consent.

Participants

Participants were at least 18 years of age, underwent cardiac surgery with cardiopulmonary bypass (CPB), and had a postoperative haemoglobin measurement < 9 g dl -1 . The exclusion criteria were active postoperative bleeding, defined as chest tube production over 1.5 ml kg -1 h -1 for six consecutive hours or necessitating reintervention within 24 h for persistent bleeding, implantation of mechanical circulatory support, complex aortic surgery, emergency surgery, sepsis, patient refusal to be transfused (religious belief), patients under guardianship, renal failure with dialysis treatment, minor patients or those under court protection, and pregnant or breastfeeding woman.

Intra operative transfusion

The management of transfusion during surgery was at the discretion of the physician and independent of the study.

Postoperative management

Postoperative care was delivered within the first hours after surgery to ensure normothermia (temperature over 36.5°C), including mechanical ventilation, assessment of surgical blood loss, and coagulation tests (anti-Xa heparin activity < 0.2 UI ml -1 , fibrinogen level > 2 g l -1 , platelet count > 50,000 mm -3 , activated partial thromboplastin time > 50%, and activated clotting time < 240 s).

Circulatory support using fluid therapy, vasopressor, and inotrope drugs was delivered to ensure a mean arterial pressure > 65 mmHg, a cardiac index > 2.5 ml min -1 m -2 , diuresis > 0.5 ml kg -1 min -1 , and arterial lactate < 2 mmol l -1 .

Interventions

All patients were screened for haemoglobin values as soon as the haemoglobin value fell < 9 g dl -1 throughout the intensive care unit stay following surgery. In the haemoglobin group, the patient systematically received a transfusion with one unit of RBCs. If haemoglobin remained < 9 g dl -1 , the patient received another unit of RBCs until the haemoglobin value was > 9 g dl -1 .

In the individualised group, the patient received a transfusion with one unit of RBCs according to the ScVO2 value. If the ScVO2 was < 70%, after exclusion of hypoxemia and hypovolemia (a new ScVO2 measurement was performed after correction for these parameters if necessary), the participant received one unit of RBCs. If the ScVO2 was ≥ 70%, the participant did not receive one unit of RBCs, unless the haemoglobin value was < 7.5 g dl -1 , for safety concerns.

The patient was weaned from the protocol at ICU discharge once the central venous line was removed.

Clinical and biological monitoring was performed for 24 h for both groups and included arterial blood pressure monitoring, haemoglobin, and ScVO2 control and screening for complications, as defined in the data collection section. ScvO2 was determined by point-of-care blood gas analysis (ABL800 FLEX; Radiometer, Copenhagen, Denmark).

Physicians were aware of the ScVO2 in both groups. Physicians could contravene the allocated group but had to document the reason for contravention. Similarly, physicians could permanently discontinue adherence to the assigned group, but such discontinuation did not constitute withdrawal of the participant from the study and the data were continuously collected, in accordance with the intention-to-treat analysis.

Endpoints Primary endpoint

The main outcome was the number of patients receiving a transfusion with at least one unit of RBCs from inclusion to hospital discharge.

Secondary endpoints

The secondary endpoints were the presence of the following complications from inclusion to hospital discharge: acute kidney injury, stroke, myocardial infarction, acute heart failure, mesenteric ischemia, 15-day mortality, one-month mortality, six-month mortality, intensive care unit stay (days), and hospital stay (days).

Endpoint definition and data collection

The primary endpoint was the total number of patients receiving a transfusion with at least one unit of RBCs per group. The secondary endpoints were defined according to standard definitions of postoperative outcomes established by the European Society of Anesthesia. [START_REF] Jammer | Standards for definitions and use of outcome measures for clinical effectiveness research in perioperative medicine: European Perioperative Clinical Outcome (EPCO) definitions: a statement from the ESA-ESICM joint taskforce on perioperative outcome measures[END_REF] Acute kidney injury was defined according to kidney improving global outcomes (KDIGO) criteria as an increase in serum creatinine of > 27 μmol l -1 within 48 h or diuresis < 0.5 ml kg -1 h -1 . [START_REF] Kellum | Diagnosis, evaluation, and management of acute kidney injury: a KDIGO summary (Part 1)[END_REF] Stroke was defined as an embolic, thrombotic, or haemorrhagic cerebral event with persistent residual motor, sensory, or cognitive dysfunction (e.g., hemiplegia, hemiparesis, aphasia, sensory deficit, impaired memory) diagnosed by cerebral CT. Myocardial infarction was defined as an elevation in cardiac troponin above the 99 th percentile combined with at least one of the following symptoms of acute myocardial ischemia: new ischemic electrocardiographic changes, development of pathological waves, imaging evidence of the new loss of viable myocardium or a pattern of new regional wall motion abnormality consistent with an ischemic aetiology, and identification of a coronary thrombus by angiography, including intracoronary imaging or by autopsy. [START_REF] Thygesen | Fourth universal definition of myocardial infarction (2018)[END_REF] Acute heart failure was defined as evidence of fluid accumulation in the alveoli due to poor cardiac function. Mesenteric ischemia was defined as necrosis of the small intestine during laparotomy. Mortality was screened during the hospital stay and at the one-and six-month follow-ups.

The following preoperative data were included: age, body-mass index, male sex, medical history, chronic medications, logistic Euroscore, preoperative left ventricular ejection fraction, and preoperative creatinine and haemoglobin levels. The following intraoperative data were collected: type of surgery, duration of CPB, duration of aortic clamp, and number of RBC transfusions during CPB. The following data were included at inclusion: heart rate, systolic arterial pressure, diastolic arterial pressure, proportion of patients receiving norepinephrine, proportion of patients receiving dobutamine, ScVO2, cardiac troponin level, PaO2, haemoglobin level, platelet count, and activated partial thromboplastin time.

Follow up

Follow-up consisted of contact with the participants by telephone six months following randomization to inquire whether a secondary outcome or another serious adverse event had occurred and to determine the health resources used since discharge.

Randomisation

Patients were randomly assigned to one of two groups at a 1:1 ratio using a concealed centralized, web-based system stratified according to centre and haemoglobin value at the time of inclusion using the minimization method. Randomisation was performed on the day that the participant met the inclusion criteria and after checking for the absence of exclusion criteria.

Sample size and statistical analysis

We expected to show a difference in absolute risk of 15% for patients receiving at least one RBC transfusion. In total, 73 patients in each group (individualised and liberal groups) were required with a power of 90% and a two-tailed alpha risk of 5%. Considering a 10% loss to follow-up, 164 patients were enrolled in the study. The prespecified primary analysis of the primary outcome was intention-to-treat analysis, which included all participants who had undergone randomisation, except for patients who withdrew consent, in accordance with French laws. No intermediate analysis was planned in the trial. Data are presented as means (standard deviations), medians [interquartile range], or numbers (percentage). The primary endpoint was assessed using Fisher's exact test. Stratification of the centre and haemoglobin value was performed using logistic regression. Secondary endpoints were assessed using chi-2 or Fisher's exact tests for qualitative variables and the Wilcoxon rank sum test for quantitative variables. Differences in absolute risk were calculated with a 95% confidence interval. To assess if RBC transfusion at a threshold of 8 g dl -1 is beneficial for the patients, we performed a sensitivity analysis with the selection of patients with a postoperative haemoglobin < 8 g dl -1 and applied the study protocol with the same value of ScVO2. All analyses were performed using SAS software, version 9.4

Results

Participants

In total, 2,536 patients underwent cardiac surgery at the two centres between January 30, 2017, and October 4, 2019. Among them, 164 patients were included, and 160 were analysed: 77 in the individualised group and 80 in the haemoglobin group (Fig. 1). A protocol violation concerned one patient in the individualised group.

Baseline characteristics

The baseline characteristics were similar for the two groups in terms of preoperative data, surgical risk, and type of surgery. The intraoperative characteristics, including the duration of CPB and the aortic clamp, were also similar (Tables 1 and2).

Haemoglobin concentrations

The haemoglobin concentrations of patients before surgery were 12.3 (0.4) and 12.2 (0.5) g dl -1 for the haemoglobin and individualised groups, respectively (Table 1). At inclusion, the mean haemoglobin value was similar for both groups (8.2 (0.4) g dl -1 for the haemoglobin group and 8.2 (0.5) g dl -1 for the individualised group; P = 0.990). Baseline ScVO2 did not differ between the groups: 63 (11) % for the haemoglobin group and 62 (11) % (P =0.895) for the individualised groups. The number of patients with an ScVO2 < 70% did not differ between the two groups (Table 2).

Primary endpoint

The number of patients receiving at least one RBC transfusion was significantly lower in the individualised than haemoglobin group (61 [79%] vs 80 [100%)], absolute risk reduction -21%, 95% CI: -32.0 to -14.0, P < 0.001) (Table 3). Kaplan-Meier analysis was used to estimate the risk of receiving RBC transfusion units (Fig. 2). In total, 198 units were administered: 108 for the haemoglobin group and 90 for the individualised group. The median number of units transfused was 1 [1-2] for the haemoglobin group and 1 [1-1] (P = 0.028) for the individualised group.

Secondary endpoints

The occurrence of acute kidney injury, stroke, myocardial infarction, acute heart failure, and mesenteric ischemia did not significantly differ between the two groups during the hospitalization period. The in-hospital mortality rates were 2.7% (2 patients) for the haemoglobin group and 1.4% (1 patient) for the individualised group (absolute risk reduction -1.28%, 95%CI:

-5.82 to 3.26, P = 0.584). The length of the ICU and hospital stays did not differ between the two groups. The mortality rates at the one and six-month follow-ups were similar between the two groups (Table 3).

Sensitivity analysis

We performed sensitivity analysis to assess the number of patients receiving RBCs if the threshold value was 8 g dl -1 instead of 9 g dl -1 . Adapting the same trial protocol (haemoglobin < 8 g dl -1 and ScVO2 < 70%), 22 patients would have received one unit of RBCs in the haemoglobin group and 15 patients in the individualised group (P < 0.001).

Discussion

In this randomised trial involving patients following cardiac surgery, an individualised transfusion strategy based on ScVO2 reduced the number of patients receiving at least one RBC transfusion versus a strategy based solely on haemoglobin levels, without an increase in hospital morbidity or mortality. The six-month follow-up showed similar mortality rates between the two groups.

RBC transfusion is one of the most frequently used therapies worldwide and is associated with clinical benefits, as well as risks and high overall costs. In the cardiac surgery setting, two large studies compared liberal and restrictive transfusion and showed the non-inferiority of a restrictive strategy in terms of postoperative mortality versus a liberal strategy. [START_REF] Murphy | Liberal or restrictive transfusion after cardiac surgery[END_REF][START_REF] Mazer | Restrictive or Liberal Red-Cell Transfusion for Cardiac Surgery[END_REF] Guidelines are not comparable across the globe; the 2018 Frankfurt consensus conference recommended a haemoglobin concentration threshold of 7.5 g dl -1 , [START_REF] Mueller | Patient Blood Management: Recommendations From the 2018 Frankfurt Consensus Conference[END_REF] for RBC transfusion, whereas the American Association of Blood Banks recommends a value of 8 g dl -1 , [START_REF] Carson | Clinical Practice Guidelines From the AABB: Red Blood Cell Transfusion Thresholds and Storage[END_REF] and the French guidelines a value of 7 g dl -1 or 10 g dl -1 if acute coronary disease or cardiac insufficiency is present or if betablockers are used. [START_REF] Has | French national health authority guideline for red blood cell transfusion[END_REF] Indeed, patients administered β-blockers who experienced severe bleeding in the perioperative setting were shown to have a higher mortality and an increased frequency of multiorgan dysfunction syndrome, explaining the higher suggested RBC threshold value. [START_REF] Manach | Impact of perioperative bleeding on the protective effect of β-blockers during infrarenal aortic reconstruction[END_REF] Moreover, a liberal transfusion strategy was shown to be associated with a trend towards fewer major cardiac events and deaths than a more restrictive strategy for patients with symptomatic coronary disease. [START_REF] Carson | Liberal versus restrictive transfusion thresholds for patients with symptomatic coronary artery disease[END_REF] Our study had several strengths. The study population showed stable hemodynamic parameters and oxygenation in the ICU for both groups. A correction for hypovolemia and hypoxemia was performed for the individualised group using ScVO2 before again measuring ScVO2 to guide rather than the 9 g dl -1 used in our study. However, at the time we designed the trial, a haemoglobin value of 9 g dl -1 was the consensual indicator for the need of a RBC transfusion.

Moreover, we completed a sensitivity analysis with a haemoglobin value at 8 g dl -1 . The number of RBC administered remained lower when combined to ScVO2 use with a value under 70%.

However, we believe that a lower value of ScVO2 could be tolerated before RBC transfusion.

Zeroual et al. chose a value of 65% for ScVO2 before transfusing postsurgical patients and confirmed the safety of such a decision. [START_REF] Zeroual | Restrictive Transfusion Strategy after Cardiac Surgery[END_REF] In our study, the value of 70% came from a previous report of Vallet et al. showing that critically ill patients would receive the most benefit from transfusion in terms of metabolic demand at this value . [START_REF] Vallet | Venous oxygen saturation as a physiologic transfusion trigger[END_REF] The choice of the primary endpoint may have also not been ideal, as it did not assess a robust outcome, such as mortality or clinical outcomes. However, we initially intended to demonstrate the feasibility of ScVO2 as the RBC transfusion trigger without increasing adverse outcomes.

Further large studies are required to assess the clinical outcomes of using an individualised ScVO2-guided strategy versus one based on a haemoglobin value threshold before recommending this strategy.

Finally, the current application of ScVO2 appears to be limited to cardiac surgery, given the necessity of having a central venous line during the early postoperative period. It could be informative to study such an RBC transfusion strategy in a perioperative setting or in non-cardiac surgery or a medical ICU.

Our findings and those of Zeroual et al. [START_REF] Zeroual | Restrictive Transfusion Strategy after Cardiac Surgery[END_REF] suggest that ScVO2 may be appropriate for critically ill patients to reduce the frequency of RBC transfusion and potentially reduce associated adverse reactions.

Conclusion

The PITT trial compared an individualised threshold-based transfusion strategy with one based on a haemoglobin threshold and assessed the length of ICU and hospital stay following cardiac surgery. A transfusion strategy based on ScVO2 allowed a reduction in the number of RBC transfusions and appears to be safe in terms of postoperative outcomes.

Tables and figure legends

Table 1. Preoperative and intraoperative characteristics. Creatinine, µmol l -1

Cardiac troponin, ng ml -1

PaO2, mmHg

Haemoglobin, g dl -1 Haemoglobin between 8 and 9 g dl -1 and ScVO2 < 70%

(

  SAS Institute) and R software version 4.0.3 (R Foundation for Statistical Computing, Vienna, Austria; www.r-projet.org) through the R Studio Interface Version 1.3.1093 -© 2009-2020. The statistical test results were considered significant if P < 0.05 for primary and secondary endpoints.

ACEI:

  angiotensin converting enzyme inhibitor, ARB: angiotensin II receptor blocker, BMI: body mass index, COPD: chronic obstructive pulmonary disease, LVEF: left ventricular ejection fraction, CABG: coronary artery bypass graft, CPB: cardiopulmonary bypass. Data are presented as means ± standard deviations, medians [interquartile ranges], or numbers (percentages).

Fig. 1

 1 Fig. 1 Flow chart of the study

Table 3 .

 3 Primary and secondary endpoints.RBC: red blood cell, AKI: acute kidney injury, ICU: intensive care unit, NA: non-applicable

Table 2 . Patient characteristics.

 2 SAP: systolic arterial pressure, DAP: diastolic arterial pressure, ScVO2: central venous saturation in oxygen, aPTT: activated partial thromboplastin time, SOFA: sequential organ failure assessment. Data are presented as means ± standard deviations, medians [interquartile ranges] or numbers (percentages).

HR: heart rate,

Table 3 . Primary and secondary endpoints.

 3

RCT: red cell transfusion, AKI: acute kidney injury, ICU: intensive care unit, NA: non-applicable

Table 2 . Patient characteristics at inclusion and following RBC transfusion. HR: heart

 2 rate, SAP: systolic arterial pressure, DAP: diastolic arterial pressure, ScVO2: central venous saturation in oxygen, aPTT: activated partial thromboplastin time, RBC: red blood cells, SOFA: sequential organ failure assessment. Data are presented as mean ± standard deviation, median [interquartile range] or number (percentage).

	Characteristics	Haemoglobin group (n = 80)	Individualised (n = 77) group	P value
	At inclusion time
	Hemodynamic data
	HR, bpm	86 ± 17	85 ± 15	0.625
	SAP, mmHg	120 ± 14	121 ± 14	0.715
	DAP, mmHg	58 ± 9	58 ± 10	0.813
	Cardiac output, l min -1	4.8 ± 1.6	5.2 ± 1.8	0.276
	Catecholamine use, n (%)
	Dobutamine	3 (4)	4 (5)	0.661
	Norepinephrine	24 (30)	15 (20)	0.127
	SOFA
	ScVO2, %
	ScVO2<70%, n (%)
	Arterial lactate, mmol l -1

Funding

This study was supported by the Amiens University Hospital

RBC transfusion if the value remained < 70%. No patients showed sepsis, which could modify the interpretation of ScVO2. Finally, the follow-up to ascertain survival was six months following cardiac surgery.

Hence, the results of our study favour a more restrictive RBC transfusion strategy, along with a reduction in the administration of units, while considering oxygen demand based on ScVO2. Thus, patients who may poorly tolerate anaemia or are at risk of organ damage could be screened through ScVO2 monitoring. Approaches guided by ScVO2 have not been reported until publication of the very recent study of Zeroual et al. [START_REF] Zeroual | Restrictive Transfusion Strategy after Cardiac Surgery[END_REF] In a closed design study setting, the authors also demonstrated a reduction in RBC transfusions of 32% when targeting a ScVO2 of 65%.

Other potential physiological triggers should be considered. Initially, clinical symptoms of anaemia could be used, such as cardiac symptoms (angina or electrocardiographic modifications), pulmonary signs (dyspnoea, polypnea), and neurological disorders (confusion, stroke). However, such symptoms may appear too late to be safely used. Other indicators of metabolic triggers are available, such as blood lactate levels or the veno-arterial CO2 gap, but little data are available concerning their utility as transfusion triggers and they should be interpreted with caution, especially in septic shock patients. A multiparametric approach based on more than one universal transfusion trigger could be used by physicians at the bedside, based on both the clinical context (disease and clinical tolerance) and biological data (i.e., haemoglobin value, ScVO2, and lactate level, for example).

Our study had several limitations. First, our threshold haemoglobin value in the haemoglobin group was higher than that recommended in recent guidelines, which suggest a value of 8 g dl -1 Author contribution: Study conception and manuscript drafting: OAA, PGG, and MOF.

Clinical data collection: PH, CB, MG, KB, and SD. Patient follow up: TC and GB. Statistical analysis: MD. Revision of the manuscript: JLH, HD, and EL. All the authors approved the final version of the manuscript.

Declaration of interest

The authors declare that they have no conflicts of interest.

2,536 patients who underwent cardiac surgery

Eligible (n = 1,748)