Abdou Rachid Thiam
email: thiam@ens.fr

Elina Ikonen

Lipid Droplet Nucleation

Keywords: Lipid droplet biogenesis, phase transitions, seipin, membrane curvature, neutral lipids, membrane chemistry

acyltransferase 1/sterol O-acyltransferase 1 (ACAT1/SOAT1), belonging to the membranebound O-acyl transferase superfamily. Their cryo-electron microscopy structures show interesting similarities in the proposed catalytic mechanism [START_REF] Qian | Structural basis for catalysis and substrate specificity of human ACAT1[END_REF][17][18][START_REF] Ma | Crystal structure of a membrane-bound O-acyltransferase[END_REF]. They have an intramembrane catalytic chamber to which there are entrances from the cytoplasmic and the lateral, intramembrane side (Fig. 1a). The acyl-CoA enters via the cytoplasmic tunnel and diacylglycerol (for DGAT1) or cholesterol (for ACAT1) may enter through the lateral, transmembrane side (Fig. 1a). The reaction product, TG, leaves laterally, i.e. inside the bilayer, and this may also be the case for SE [START_REF] Qian | Structural basis for catalysis and substrate specificity of human ACAT1[END_REF][17][18]. The synthesized NLs mix with phospholipids (PLs) and are diffusible in the ER bilayer [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF].

These enzymes have isoforms, namely DGAT2 and ACAT2, that also catalyze the esterification reaction generating NLs, although DGAT2 is evolutionarily unrelated to DGAT1.

The structures of these isoforms are not yet resolved but they may mediate the synthesis of specific NL pools under precise physiological stimulations [START_REF] Nguyen | DGAT1-dependent lipid droplet biogenesis protects mitochondrial function during starvation-induced autophagy[END_REF][21][START_REF] Hung | Dgat1 and Dgat2 regulate enterocyte triacylglycerol distribution and alter proteins associated with cytoplasmic lipid droplets in response to dietary fat[END_REF]. ACAT2 is predominantly expressed in enterocytes and hepatocytes and esterifies dietary cholesterol [START_REF] Chang | Immunological quantitation and localization of ACAT-1 and ACAT-2 in human liver and small intestine[END_REF]. DGAT2 localizes around LDs, probably mediating LD-ER contacts [START_REF] Mcfie | Diacylglycerol acyltransferase-2 contains a c-terminal sequence that interacts with lipid droplets[END_REF], and may synthesize and incorporate TG directly into LDs. DGAT2 is also capable of esterifying ceramides into acylceramides to be stored in LDs [START_REF] Senkal | Ceramide is metabolized to acylceramide and stored in lipid droplets[END_REF]. Hence, DGATs and ACATs may esterify other hydrocarbons with alcohol functions to generate NLs other than TG and SE.

The assembly steps of lipid droplets.

How are NLs diffusible in the ER bilayer assembled into LDs? In vitro, when the concentration of NLs reaches a critical level, a spontaneous condensation of NLs by phase separation can occur, leading to the formation of an oil blister within the hydrophobic bilayer region [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF][START_REF] Hamilton | Interactions of triglycerides with phospholipids: incorporation into the bilayer structure and formation of emulsions[END_REF][START_REF] Kassan | Acyl-CoA synthetase 3 promotes lipid droplet biogenesis in ER microdomains[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]: this first step of LD assembly is termed nucleation (Box1). Spontaneous nucleation is also likely to happen in cells.

The second step is growth: following nucleation principles, the oil blister has to grow, by adsorbing more NLs to become an LD or to resorb [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]29,[START_REF] Kelton | Nucleation in condensed matter: applications in materials and biology[END_REF]. If many LDs are nucleated in parallel, it is unfavorable for all of them to grow, unless they are stabilized against Oswald ripening [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF][START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF]. TGs diffuse in tubules roughly at the same rate as PLs, ~4 µm 2 /sec [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF],

implying that a TG molecule can explore two LDs that are 2 µm apart in a second. If LDs are not stabilized against ripening, the equilibrium state requires that only one LD, the larger one, grows at the expense of the others that resorb [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF][START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF].

The third step consists of the budding of a spherical LD into the cytosol [START_REF] Walther | Lipid droplet biogenesis[END_REF][START_REF] Olzmann | Dynamics and functions of lipid droplets[END_REF]. This step requires maintaining the PL and protein coverage of the cytosolic monolayer tighter than in the luminal face [START_REF] Chorlay | Membrane Asymmetry Imposes Directionality on Lipid Droplet Emergence from the ER[END_REF]. Such asymmetry guarantees that the cytosolic leaflet remains of lower surface tension, promoting LD emergence in this direction [33]. If proteins bind strongly to emerging LDs from the ER lumen, LDs fail to fully emerge. This happens when lipidated apolipoprotein B100 is overexpressed in the ER lumen of hepatocytes where it keeps LDs in contact with the lumen [START_REF] Ohsaki | Lipid droplets are arrested in the ER membrane by tight binding of lipidated apolipoprotein B-100[END_REF].

The fourth step is likely a protein-assisted stabilization of LD-ER contacts or a potential detachment of the LD from the ER bilayer. In either case, the budded LDs remain closely tethered to the ER bilayer by several tethering proteins [START_REF] Bohnert | Tethering Fat: Tethers in Lipid Droplet Contact Sites[END_REF][START_REF] Henne | Spatial compartmentalization of lipid droplet biogenesis[END_REF][37][START_REF] Xu | Rab18 promotes lipid droplet (LD) growth by tethering the ER to LDs through SNARE and NRZ interactions[END_REF].

Thermodynamics of lipid droplet nucleation.

We previously detailed the thermodynamics of phase transition in the context of LD nucleation [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]. Briefly, NLs within the ER bilayer can spontaneously demix from the PLs and condense into a lens when a critical nucleation concentration (CNC) is reached [START_REF] Choudhary | A conserved family of proteins facilitates nascent lipid droplet budding from the ER[END_REF] (Fig. 2a,

Figure I Box.2).
The existence of a CNC is common to all phase separation phenomena [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]29]; in the context of detergents, it is the critical micellar concentration. Nucleation is associated with an energy barrier, Enucleation, that needs to be overcome to generate stable NL condensates (Figure I Box.2) [START_REF] Jarc | A twist of FATe: Lipid droplets and inflammatory lipid mediators[END_REF]. The CNC for triacylglycerols (TG) in a flat 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine bilayer is estimated as 3-5% (TG/PL) (Fig. 2a) [START_REF] Hamilton | Interactions of triglycerides with phospholipids: incorporation into the bilayer structure and formation of emulsions[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] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF].

Below this threshold, TGs diffuse and form short-lived clusters, which size, lifetime, and appearance frequency increase with the TG concentration [START_REF] Jarc | A twist of FATe: Lipid droplets and inflammatory lipid mediators[END_REF]. Beyond the CNC, some TG clusters can overcome Enucleation and transit into blisters or nascent LDs (Figure

I Box.2) [1-4],
even though a residual fraction of TGs still mixes with the bilayer PLs [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] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF][START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF] for entropic reasons [START_REF] Jarc | A twist of FATe: Lipid droplets and inflammatory lipid mediators[END_REF]. These nucleated LDs reduce the concentration of NLs in the bilayer to below the CNC, and thereupon diminish the appearance frequency of new clusters [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]29]. In a uniform protein-free bilayer, these steps happen stochastically (Fig. 2a). In cells, the compositional and structural heterogeneities of the ER membrane will induce local alterations of the energy barrier and dictate where LDs nucleate [START_REF] Thiam | The why, when and how of lipid droplet diversity[END_REF][START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF] (Fig. 2b,2c).

Role of membrane chemistry in lipid droplet nucleation.

The chemical potential of NLs in a compartment represents the variation in free energy per added NL molecule. The difference in chemical potentials between the condense phase and the dilute phase quantifies how favorable it is for NLs to stay in contact with the membrane components as opposed to be into a nucleated LD [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]. The higher the chemical potential in the bilayer, the less favorable it is for NLs to remain in contact with the membrane components, and the higher the nucleation probability [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]. Therefore, the chemical potential depends on the physicochemical properties of the membrane, which implies that the CNC and Enucleation also depend on these physicochemical parameters, such as membrane proteins and PLs [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF] (Figure II Box.2). Changing the membrane PL composition indeed alters the level of free TG within a bilayer [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF][START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF] and, consequently, the nucleation efficiency of TG blisters [START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF]. In particular, increasing dioleoylphosphatidyl ethanolamine, cholesterol, or diacylglycerol (DAG), which are negatively curved lipids, promote the nucleation of TG blisters [START_REF] Adeyo | The yeast lipin orthologue Pah1p is important for biogenesis of lipid droplets[END_REF][START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF]. Thus, the local enrichment of these lipids in the ER may help determine LD nucleation sites. How exactly these lipids would promote LD nucleation is unclear [START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF] but they may alter the bilayer physical properties, such as local curvature, surface pressure or packing [START_REF] Marsh | Lateral Pressure Profile, Spontaneous Curvature Frustration, and the Incorporation and Conformation of Proteins in Membranes[END_REF]. Generating PL packing defects exposes TGs to water, likely increases chemical potential and favors TG condensation [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. In any case, these observations support the idea that local transient alterations in lipid composition can decrease the CNC and energy barrier to promote nucleation. Conversely, changes in ER PL composition could also lead to excessive accumulation of NLs in the ER membrane [START_REF] Adeyo | The yeast lipin orthologue Pah1p is important for biogenesis of lipid droplets[END_REF], and eventually to the nucleation of abnormally large LDs.

The neutral lipid chemistry impacts nucleation.

PLs and proteins are considered as major factors for LD assembly and NLs are often viewed as "inert" apolar molecules with no impact on LD assembly. Instead, the NL chemistry determines the interactions with the membrane constituents and sets the chemical potential.

TG and SE are the most abundant NLs in eukaryotes but many others exist in specific cells from plants to animals [START_REF] Senkal | Ceramide is metabolized to acylceramide and stored in lipid droplets[END_REF][START_REF] Van Wijk | Plastoglobuli: plastid microcompartments with integrated functions in metabolism, plastid developmental transitions, and environmental adaptation[END_REF][START_REF] Ajat | Hepatic stellate cells retain the capacity to synthesize retinyl esters and to store neutral lipids in small lipid droplets in the absence of LRAT[END_REF] (Fig. 1c-d). These diverse NLs are probably able to spontaneously condense and nucleate LDs, as shown for example for phthiocerol dimycocerosate [START_REF] Augenstreich | The conical shape of DIM lipids promotes Mycobacterium tuberculosis infection of macrophages[END_REF]. Their contrasted chemistry proffers different chemical potentials, CNCs, and nucleation energy barriers. Differences in chemical potential are partially reflected by differential interactions with water, since the oil-water interfaces of NLs have different surface tensions and propensities to recruit proteins [START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF]. The relevance of the NL chemistry for LD nucleation is well illustrated by the capacity of TG to condense into droplets more efficiently than SE in a DOPC bilayer [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF], or by the abnormal accumulation of TG in the ER when DG synthesis is inhibited [START_REF] Adeyo | The yeast lipin orthologue Pah1p is important for biogenesis of lipid droplets[END_REF]; squalene, which is a hydrocarbon and not an ester, tends to accumulate in membranes and likely has a much higher CNC, resulting in fewer and larger LDs [START_REF] Ben M'barek | ER Membrane Phospholipids and Surface Tension Control Cellular Lipid Droplet Formation[END_REF]47]; likewise, retinol palmitate assembles into fewer and larger LDs than TG [START_REF] Molenaar | Lecithin: Retinol Acyl Transferase (LRAT) induces the formation of lipid droplets[END_REF]. In short, based on several in vitro characterizations [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF][START_REF] Zoni | Lipid droplet biogenesis is driven by liquid-liquid phase separation[END_REF][START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF][START_REF] Molenaar | Lecithin: Retinol Acyl Transferase (LRAT) induces the formation of lipid droplets[END_REF]49], NLs differently interact with membrane components (water, PLs, and proteins) and have different chemical potentials. This suggests that specific ER membrane settings, e.g. in PL and protein composition or curvature, may be required to trigger the condensation of a given NL into LDs. Consequently, the NL composition would determine the nucleated LD phospholipidome and proteome [START_REF] Thiam | The why, when and how of lipid droplet diversity[END_REF][START_REF] Chorlay | Neutral lipids regulate amphipathic helix affinity for model lipid droplets[END_REF][START_REF] Molenaar | Lecithin: Retinol Acyl Transferase (LRAT) induces the formation of lipid droplets[END_REF][50][START_REF] Davidi | Proteome analysis of cytoplasmatic and plastidic β-carotene lipid droplets in Dunaliella bardawil[END_REF][START_REF] Fei | The size and phospholipid composition of lipid droplets can influence their proteome[END_REF][START_REF] Meyers | The protein and neutral lipid composition of lipid droplets isolated from the fission yeast, Schizosaccharomyces pombe[END_REF][START_REF] Meyers | Lipid droplets form from distinct regions of the cell in the fission yeast Schizosaccharomyces pombe[END_REF][START_REF] Vrablik | Lipidomic and proteomic analysis of Caenorhabditis elegans lipid droplets and identification of ACS-4 as a lipid droplet-associated protein[END_REF].

Lipid droplet nucleation at tubules vs. sheets.

The ER membrane is made of sheets and tubules whose curvature affects protein and PL sorting, coordinating biochemical reactions and vesicular trafficking [START_REF] Westrate | Form follows function: the importance of endoplasmic reticulum shape[END_REF][START_REF] Voeltz | Sheets, ribbons and tubules-how organelles get their shape[END_REF][START_REF] Lagace | The role of phospholipids in the biological activity and structure of the endoplasmic reticulum[END_REF][START_REF] Tian | Sorting of lipids and proteins in membrane curvature gradients[END_REF]. TG and SE are also differentially sorted by membrane curvature: relative to PLs, individual TG disfavor tubules with increased curvature while SE is more enriched in them [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. Other NLs can also be expected to show differential enrichments in curved vs. flat membranes.

Curvature generates mechanical stresses [START_REF] Marsh | Lateral Pressure Profile, Spontaneous Curvature Frustration, and the Incorporation and Conformation of Proteins in Membranes[END_REF][START_REF] Hossein | Spontaneous curvature, differential stress, and bending modulus of asymmetric lipid membranes[END_REF], which might be enhanced by the presence of NLs. Therefore, the prompted condensation of TG at tubules to nucleate an LD could be a means to resorb bilayer stress. Another view of this scenario is that curvature increases the chemical potential of TG. One aspect of curvature is to pull apart PLs, creating packing defects or decreasing the bilayer surface pressure, hence promoting more contacts between water and the hydrophobic bilayer core. This changes the interaction energy landscape of an NL in the curved membrane. For TG, this interaction profile likely results in an increase in chemical potential, since it preferentially moves to flatter regions or condenses [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. In other words, the CNC and the nucleation energy barrier for TG is smaller in tubules than in flat membranes. As a result, the curvature is a catalyst for the assembly of TG LDs (Figure I-II Box.2), and the frequency of nucleated LDs would follow the abundance of ER tubules [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF] (Fig. 3a).

In contrast to TG, SE in tubules tends to stay as individual molecules diffusing faster than TG [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. Increasing the SE/TG ratio decreases the nucleation efficiency at tubules [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. SE and TG are both hydrophobic. If the spacing of PL by curvature were the sole reason for the condensation of TG, to minimize contact with water, SE would behave similarly, but it does not [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. This suggests that other factors specifically impact SE and not TG. For example, SE could decrease tubule stress when remaining as individual molecules, as opposed to TG. Also, similarly to sterols [START_REF] Dimova | Recent developments in the field of bending rigidity measurements on membranes[END_REF], SE could alter the rigidity and surface pressure of the membrane, to a direction unfavorable for nucleation (Box.2). Finally, relative to PLs, SE and TG may have different orientations in the membrane and different interactions with membrane components. These diverse options reflect the gap in our understanding of how membrane curvature, chemistry, and mechanics impact the condensation of different NLs.

ER membrane shaping proteins regulate nucleation.

The role of curvature in nucleation explains, at least partly, observations made on the impact of ER shaping proteins on LD formation [10,12,[START_REF] Klemm | A conserved role for atlastin GTPases in regulating lipid droplet size[END_REF][START_REF] Falk | Functional Mutation Analysis Provides Evidence for a Role of REEP 1 in Lipid Droplet Biology[END_REF][START_REF] Renvoisé | Reep1 null mice reveal a converging role for hereditary spastic paraplegia proteins in lipid droplet regulation[END_REF][START_REF] Boström | Cytosolic lipid droplets increase in size by microtubuledependent complex formation[END_REF][START_REF] Joshi | Organelle biogenesis in the endoplasmic reticulum[END_REF][START_REF] Hariri | Lipid droplet biogenesis is spatially coordinated at ER-vacuole contacts under nutritional stress[END_REF]. The dysfunction of several of such proteins impedes the number of formed LDs, without necessarily impacting NL levels [12]. This is the case for example for the yeast peroxisomal membrane shaping protein Pex30, or MCTP2 in mammals, [10,12] whose concomitant deletion with seipin generates large ER structures low in curvature and abnormally filled with TG [12]. This is likely because the CNC of TG (relatively to PLs) is high in these structures of zero curvature. Indeed, decreasing the PL/TG ratio by inhibiting the PC synthesis enzyme PCTY1 may enable TG to reach the CNC, and results in the recovery of LDs [12]. In this rescue experiment, fewer and larger LDs were assembled compared to normal cells, as a signature of the higher CNC in flat membranes (Fig. 3a) [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. Similarly to the PEX30/seipin deletion phenotype, when mammalian cells are subjected to hypotonic medium, they make large flat ER structures bearing high amounts of TG and are deficient in LDs [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF].

Knowing the impact of membrane curvature on LD assembly, any ER shaping protein, as recently shown for atlastin, Rabs, reeps, and torsins, or other ER structuring factors, such as microtubules, septins, etc., will impact LD assembly [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF][START_REF] Xu | Rab18 promotes lipid droplet (LD) growth by tethering the ER to LDs through SNARE and NRZ interactions[END_REF][START_REF] Klemm | A conserved role for atlastin GTPases in regulating lipid droplet size[END_REF][START_REF] Falk | Functional Mutation Analysis Provides Evidence for a Role of REEP 1 in Lipid Droplet Biology[END_REF][START_REF] Renvoisé | Reep1 null mice reveal a converging role for hereditary spastic paraplegia proteins in lipid droplet regulation[END_REF][START_REF] Boström | Cytosolic lipid droplets increase in size by microtubuledependent complex formation[END_REF][START_REF] Akil | Septin 9 induces lipid droplets growth by a phosphatidylinositol-5phosphate and microtubule-dependent mechanism hijacked by HCV[END_REF]69]. The dysfunction of several of these proteins is linked to hereditary spastic paraplegia phenotypes [START_REF] Welte | Lipid droplet functions beyond energy storage[END_REF][START_REF] Renvoisé | Reep1 null mice reveal a converging role for hereditary spastic paraplegia proteins in lipid droplet regulation[END_REF], but whether the alteration in LD assembly is anecdotal or relevant for the disease pathogenesis, remains to be elucidated. Finally, the alteration of LD formation by ER shaping proteins might either be due to variations in the ER tubular fraction, promoting LD assembly, and/or to altered NL/PL ratio, since the synthesis of NLs, like that of PLs [START_REF] Schwarz | The endoplasmic reticulum: structure, function and response to cellular signaling[END_REF], might happen at tubules. These two contributions need to be untangled to better understand the impact of ER shaping proteins on NL levels and LD nucleation. from the ER to the nuclear envelope with little curvature, LD assembly happens at the seipin sites [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF]. However, the careful analysis revealed that most of these LDs assembled close to ER tubules adjacent to the nuclear envelope [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF].

In short, the assembly of TG LDs is catalyzed by membrane curvature as otherwise, TG simply fills membranes, incapable of undergoing efficient condensation [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. Consequently, the relative abundance of ER tubules may serve as a proxy for projecting on the capacity of a cell type to handle excessive TG for storage. Cells with a relatively low abundance of ER tubules may generate fewer and larger LDs due to an inefficiency in LD nucleation (Fig. 3a). Such cells could also compensate for the lack of tubules and develop alternative mechanisms to facilitate LD assembly [START_REF] Chapman | Mechanisms of lipid droplet biogenesis[END_REF]. Finally, cells might dynamically shift their ER tubule/sheet ratio pending on metabolic cues, e.g. increase it to generate more LDs (Fig. 3a).

Role of seipin in LD nucleation.

Seipin is an ER membrane protein capable of determining the nucleation sites of TG LDs and localizing at the ER-LD junction [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF][START_REF] Bohnert | Wrapping up the fats-a structure of the lipid droplet biogenesis protein seipin[END_REF][START_REF] Cartwright | Seipin performs dissectible functions in promoting lipid droplet biogenesis and regulating droplet morphology[END_REF][START_REF] Chung | LDAF1 and Seipin Form a Lipid Droplet Assembly Complex[END_REF][79][START_REF] Szymanski | The lipodystrophy protein seipin is found at endoplasmic reticulum lipid droplet junctions and is important for droplet morphology[END_REF] (Fig. 1c). Seipin possesses two transmembrane domains, with both N-and C-termini facing the cytoplasm and a luminal loop bridging the transmembrane domains [START_REF] Bohnert | Wrapping up the fats-a structure of the lipid droplet biogenesis protein seipin[END_REF]. The protein homo-oligomerizes into ring-like structures and the luminal domains of these rings [START_REF] Binns | Seipin is a discrete homooligomer[END_REF][START_REF] Lundin | Membrane topology of the human seipin protein[END_REF], of circa 15 nm in diameter [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF], resolved by cryo-electron microscopy for human, fly, and yeast, consist of 11, 12, and 10 seipin monomers, respectively [START_REF] Henne | Spatial compartmentalization of lipid droplet biogenesis[END_REF][START_REF] Sui | Cryo-electron microscopy structure of the lipid droplet-formation protein seipin[END_REF][START_REF] Yan | Human SEIPIN binds anionic phospholipids[END_REF]. The human and fly monomers possess hydrophobic helices, dipped into the bilayer, and two beta-sheets of four beta-strands each, reminiscent of the sterol-binding protein Niemann-Pick C2 [START_REF] Sui | Cryo-electron microscopy structure of the lipid droplet-formation protein seipin[END_REF][START_REF] Yan | Human SEIPIN binds anionic phospholipids[END_REF]. The luminal and transmembrane domains are sufficient to rescue the LD biogenesis defect in seipin-deficient cells, indicating that they are critical for seipin function in LD formation [START_REF] Cartwright | Seipin performs dissectible functions in promoting lipid droplet biogenesis and regulating droplet morphology[END_REF].

The ER membrane curvature and physical chemistry regulate the CNC and the nucleation energy barrier (Figure I-II Box.2). The oligomeric structure of seipin may locally exacerbate topological and biochemical parameters for further decreasing the CNC or the energy barrier [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]29,[START_REF] Zoni | Seipin accumulates and traps diacylglycerols and triglycerides in its ring-like structure[END_REF]86]. This means that (a) the probability of nucleation will be exponentially much higher at seipins than elsewhere [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF] and (b) it becomes thermodynamically more favorable to drive free TGs in membranes into seipin-nucleated LDs than assembling them into new non-seipin LDs (Fig. 1) [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]. Seipin is enriched at ER tubules/edges of sheets [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF] and likely acts as a membrane curvature sensor or inducer [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF] (Fig. 3b). Induction of a local curvature by seipin could be a mechanism for inducing the nucleation of TG LDs. Swollen cells can present large onion ring-like ER structures, lacking curvature but bearing seipin [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. Under these conditions, NLs remain in the ER membrane, and nucleation is severely impeded [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF].

The seipin oligomer structure can also provide a means to locally exacerbate interactions of seipin with lipids or their synthases [9,87-90], constituting subdomains of higher nucleation probability. In particular, seipin can bind to anionic phospholipids such as PA [START_REF] Yan | Human SEIPIN binds anionic phospholipids[END_REF] via its beta-sandwich fold, and this might locally regulate both PL and NL synthesis to provide a favorable environment for TG condensation (Fig. 2c). Such an environment might prolong the contacts of TG with the oligomer and increase their probability of condensation at seipin (Fig. 2c). In simulations, the luminal domain of human seipin traps individual TGs within its ring structure in a model ER bilayer and catalyzes TG clustering at low TG concentrations, where TGs fail to cluster in the absence of seipin [START_REF] Zoni | Seipin accumulates and traps diacylglycerols and triglycerides in its ring-like structure[END_REF]86] (Figure I Box.2). At a given TG concentration, TG clusters preferably form inside the seipin ring (Fig. 2c). Serine residues in helices associated with the luminal membrane leaflet and delineating the inner opening of the seipin ring appear critical for TG clustering and subsequent LD formation [86].

Since curvature is sufficient to trigger the assembly of TG LDs [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF][START_REF] Chung | LDAF1 and Seipin Form a Lipid Droplet Assembly Complex[END_REF], the enrichment of seipin at tubules would prevent erratic nucleation events triggered by the sole action of curvature [START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. If a seipin oligomer initiates an LD, it will be more favorable for NLs across a certain distance in the tubule to move to this LD (Fig. 2c). Therefore, controlling all LD nucleation events requires that a critical density of seipin oligomers is maintained [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF] (Fig. 3b,3c). If this condition is not met, regions of seipin-deficient phenotypes will appear within the same cell (Fig. 3d). This prediction is demonstrated by experiments where seipin is trapped to the nuclear envelope and LDs forming at seipins have a normal phenotype, while the rest of the ER membrane, with low seipin levels, displays a lipodystrophic phenotype [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF] (Fig. 3d). These observations indicate that the seipin/tubule ratio needs critical regulation to prevent uncontrolled nucleation (Fig. 3c,3d).

It is more favorable for TGs to move to seipin-nucleated LDs than to assemble into new seipin-negative ones [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF]. This is because seipin-LDs have already overcome the nucleation barrier. However, because LDs can be heterogeneous in size, moving TG toward larger LD would be more favorable because of their lower internal Laplace pressure [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF][START_REF] Thiam | The biophysics and cell biology of lipid droplets[END_REF]. To ensure that all nucleated LDs grow, NLs need to be directed towards the smaller LDs, combating the Laplace pressure [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF]. Indeed, if seipin is removed from LD-ER junctions, smaller LDs lose TG for larger LDs through the ER bilayer [START_REF] Salo | Seipin facilitates triglyceride flow to lipid droplet and counteracts droplet ripening via endoplasmic reticulum contact[END_REF]. Finally, given the diversity of NLs, it may be that seipin mainly functions in TG LD biogenesis, but not universally for all NLs [START_REF] Molenaar | Lecithin: Retinol Acyl Transferase (LRAT) induces the formation of lipid droplets[END_REF].

Role of seipin co-workers in LD nucleation.

Recent works indicate that seipin co-operates with and forms an LD assembly complex with promethin/LDAF1 (yeast Ldo 16/45) [START_REF] Chung | LDAF1 and Seipin Form a Lipid Droplet Assembly Complex[END_REF][START_REF] Castro | Promethin Is a Conserved Seipin Partner Protein[END_REF][93][START_REF] Eisenberg-Bord | Identification of seipin-linked factors that act as determinants of a lipid droplet subpopulation[END_REF]. Promethin also forms distinct domains in the ER and several of these foci associate with seipin [START_REF] Chung | LDAF1 and Seipin Form a Lipid Droplet Assembly Complex[END_REF]. Seipin complexes synthesized under lipid-poor conditions do not readily associate with promethin but when NL synthesis is initiated, the fraction of seipins associating with promethin increases [86]. This suggests that NLs facilitate the formation of seipin-promethin complexes. LDs form at sites typically occupied by both seipin and promethin, and upon subsequent LD growth, promethin relocates to the LD surface thanks to its hairpin topology [START_REF] Castro | Promethin Is a Conserved Seipin Partner Protein[END_REF], while seipin remains at the ER-LD junction [START_REF] Chung | LDAF1 and Seipin Form a Lipid Droplet Assembly Complex[END_REF].

Additional players defining the nature of the LD forming ER subdomain, and cooperating with seipin in LD formation, are also involved [START_REF] Greer | SEIPIN isoforms interact with the membrane-tethering protein VAP27-1 for lipid droplet formation[END_REF]. In yeast, seipin (Fld1) and nuclear envelope morphology protein 1 (Nem1) localize to the ER, independently of each other, but both mark LD nucleation sites and co-localize to ER-LD contact sites [START_REF] Choudhary | Seipin and Nem1 establish discrete ER subdomains to initiate yeast lipid droplet biogenesis[END_REF]. Nem1 is an activator of the DAG synthesizing Pah1 (mammalian lipin) enzyme. Upon activation of TG synthesis, the association of Fld1 and Nem1 increases, and this recruits the TG synthase Lro1, spatially coupling TG formation and storage sites. Importantly, a catalytically inactive Lro1 does not associate with the Fld1-Nem1 complex, implying that TG is needed for this association. Both Fld1 and Nem1 are required for the subdomains to recruit additional LD biogenesis factors, such as yeast homolog of FIT2 (Yft2), Pex30, and perilipin1 [START_REF] Choudhary | Seipin and Nem1 establish discrete ER subdomains to initiate yeast lipid droplet biogenesis[END_REF].

Concluding Remarks

The fundamental physicochemical concepts that underlie the phenomenon of LD nucleation are based on classical principles of thermodynamics and mechanics. When these are combined with experimental findings from in vitro model membranes, in vivo cell membranes, and in silico computational approaches, a comprehensive understanding of this process is starting to emerge. At present, several outstanding questions remain to be addressed, see Outstanding Questions Box. To start with, most LDs are not constituted by a pure, single NL species but by mixtures of them [START_REF] Van Wijk | Plastoglobuli: plastid microcompartments with integrated functions in metabolism, plastid developmental transitions, and environmental adaptation[END_REF]. We understand little how the complex NL chemistry impacts LD nucleation and if LDs of heterogeneous composition are nucleated from a continuous ER network [START_REF] Thiam | The why, when and how of lipid droplet diversity[END_REF][START_REF] Santinho | Membrane Curvature Catalyzes Lipid Droplet Assembly[END_REF]. In vitro, it is not possible to generate pure SE LDs but in cells, predominantly SE containing NLs can be formed in the presence of excess cholesterol when TG synthesizing enzymes are inhibited. What solubilizes the SE to enable the nucleation of such LDs, is not known. Furthermore, is the role of seipin dedicated to TG, and perhaps SE, LD nucleation? What are the specific functions of seipin partners in LD nucleation and how are the LD assembly protein complexes spatiotemporally assembled in different systems? In this context, we also need to understand how ER organization beyond tubules and sheets, such as 3-way junctions, domains involved in protein translocation and folding, etc., impact NL distribution and LD assembly complexes. This, in turn, is related to more physiological questions of LD nucleation mechanisms in different cell types and metabolic conditions: the process in hepatocytes or enterocytes may differ considerably from that in adipocytes or white blood cells. What is foreseeable is that LD nucleation will keep inciting an increasing array of

Box1. Basic principles of nucleation phenomena.

Nucleation is a century-old thermodynamics principle, thoroughly explored theoretically and experimentally in diverse contexts [START_REF] Kelton | Nucleation in condensed matter: applications in materials and biology[END_REF][START_REF] Sagui | Theory of nucleation and growth during phase separation[END_REF]. Nucleation is the onset of phase separation or unmixing of constituents of a blend, e.g. of liquids, gases, or solids. It happens when it becomes energetically favorable to decrease the contact between foreign molecules within the mixture and it can be triggered by changing a physical chemistry parameter of the mixture. Examples of nucleation phenomena are the onset of salt crystallization upon reducing water concentration, or the condensation of water molecules from a gas state into raindrops, catalyzed by/at dust present in the air. In biology, nucleation emerged during the past decade as a crucial step of phase separating phenomena that govern the homeostasis of organelles [START_REF] Hyman | Liquid-liquid phase separation in biology[END_REF]. It is involved in the assembly of phospholipid bilayer-bounded organelles, such as the Golgi apparatus [98], but also in the biogenesis of monolayer-encircled organelles, such as LDs [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF] or membraneless organelles devoid of phospholipids called condensates [START_REF] Dignon | Biomolecular Phase Separation: From Molecular Driving Forces to Macroscopic Properties[END_REF]. How and where organelle nucleation is triggered has recently become a central question in biology [START_REF] Dignon | Biomolecular Phase Separation: From Molecular Driving Forces to Macroscopic Properties[END_REF].

Box2. The nucleation energy barrier.

An energy barrier needs to be overcome for nucleation to occur. The lower this energy barrier, the higher is the probability to nucleate (Figure I). The height of the energy arises from the competition between antagonist contributions involving chemical potentials and interfacial energies [START_REF] Thiam | The physics of lipid droplet nucleation, growth and budding[END_REF].

Chemical potentials. Molecules constituting a blend tend to demix because mixing generally costs energy. For demixing, the interaction of an NL with the bilayer components has to cost more energy than the interaction between NLs: the chemical potential of an NL within a PL bilayer, µ(NL)bilayer, needs to be larger than that within LDs, µ(NL)LD. If this condition is unmet, entropy is sufficient to keep NLs mixing with the membrane constituents, thereby hampering nucleation. The chemical potential of NLs in membranes µ(NL)bilayer is likely altered as soon as features of the membrane are varied, e.g. the membrane biophysical and physicochemical factors, protein density, and composition, etc. (Figure II).

Increasing µ(NL)bilayer makes the NL-membrane mixing more unfavorable, which decreases the energy barrier and promotes nucleation (Fig. 2a). The gap in chemical potentials modulates the height of the energy barrier.

LD interfacial energies. Membrane mechanics has several inputs into the energy barrier that can work for or against nucleation.

There is for instance an energy penalty coming from the bilayer leaflet deformation during nucleation; for nucleation to occur, the bilayer leaflets have to be unzipped and its monolayers deformed; this can be combated by the rigidity of the leaflets. Reducing rigidity would reduce the cost of deformation energy and facilitate

  The inner nuclear membrane (INM) possesses metabolic activity and can synthesize TG[71,[START_REF] Romanauska | The inner nuclear membrane is a metabolically active territory that generates nuclear lipid droplets[END_REF]. This seems to be the case at least for the phospholipid: diacylglycerol acyltransferase enzyme whose yeast homolog Lro1 has its catalytic activity in the nucleus and mediates TG synthesis in the nucleus [71]. However, the generated NLs flow through the interconnections between the INM and the ER and feed cytosolic LDs [71,73]. Why these TGs do not directly assemble into nuclear LDs? An answer could be the lack of curvature at the INM. The few nuclear LDs, particularly in hepatocytes [74,75], are mostly observed at nuclear membrane invaginations [74] offering curvature. When seipin is artificially trapped

Figure 1 :

 1 Figure 1: a) Schematic illustration of the esterification of diacylglycerol or cholesterol by diacylglycerol O-acyltransferase 1 (DGAT1), or acyl-coenzyme A: cholesterol acyltransferase 1/sterol O-acyltransferase 1 (ACAT1/SOAT1), or membrane-bound O-acyl transferase (MBOAT). The synthesized neutral lipid exits the enzyme through a lateral gate facing the bilayer hydrophobic core. b) Molecular structures of triolein and sterol oleate, the major triglycerides and sterol esters in neutral lipid stores. c) Examples of other neutral lipids with ester functions. d) Examples of other neutral lipids with non-ester functions.

Figure 2 .

 2 Figure 2. Schematic illustration of the condensation of triglycerides (TG) in protein-free (pf), seipin deficient (S-), and in seipin containing conditions (S+). Increasing the concentration of TG per phospholipids, [TG/PL] leads to the formation of transient clusters that are bigger steadier for larger TG concentrations. Nucleation, i.e. TG condensation, happens at a critical concentration around ~5% in protein-free conditions. Proteins, in particular seipin, might decrease the critical nucleation concentration. ER: endoplasmic reticulum, LD: lipid droplet, AH: amphipathic helix, Plin1: perilipin 1, LDAF1: lipid droplet factor 1.

Figure 3 .

 3 Figure 3. a) Illustration of the evolution of TG LD nucleation frequency and LD size pending on ER tubule/sheet ratio. b) Illustration of the enrichment of seipin in tubules vs. sheets. In seipin deficiency, more TG LD nucleation events happen at tubules. c) Evolution of nucleation frequency pending on the seipin/tubule ratio. At low seipin dose, a lipodystrophic phenotype is observed. d) In a single cell, seipin is trapped at the nuclear envelope membrane where a normal LD biogenesis phenotype is observed. In the rest of the cell ("periphery"), a seipin deficient and lipodystrophic phenotype is observed. A critical density of seipin is required throughout the cell to prevent the undesired lipodystrophic phenotype.

Figure adapted from Figure 7 of

 7 Figure adapted from Figure 7 of Salo et al. Developmental Cell 2019 [31].

Acknowledgements

We thank our team members and Dr. Lionel Fôret for critical discussions and advice. This study was supported by the Academy of Finland (grants 282192, 312491, 307415 to E.I.), Sigrid Juselius Foundation (E.I.), and ANR-17-CE11-0003-NANODROP and ANR-18-CE11-0012-01-MOBIL to A.R.T. We apologize to our colleagues whose works could not be cited due to space restrictions.

nucleation. Rigidity is often increased by PL saturation, cholesterol, and possibly sterol esters, which would disfavor nucleation. Another membrane input is surface tension;

increasing the bilayer surface tension, by pulling or stretching on the bilayer, would disfavor bilayer deformation and nucleation [40,41]. In vitro, LD nucleation requires low bilayer tension.

Glossary

Neutral lipids: hydrophobic apolar molecules, lacking charged groups. Usually optimal forms of energy storage rich in carbon. Can differ between cell types and metabolic states.

Triacylglycerols: three fatty acids esterified to each of the three alcohol groups of glycerol.

Most abundant neutral lipids in eukaryotes that serve for energy and membrane lipid storage.

Often referred to as triglycerides. Mostly stored in adipocytes.

Sterol ester: a fatty acid esterified to the alcohol of a sterol. The second most abundant neutral lipid after triglycerides. Ubiquitous in yeast. In mammals, mostly present in macrophages, adrenals and blood low-density lipoproteins as the storage form of cholesterol.

Surface tension: energy per area cost for exposing two fluids of different nature. Acts to minimize the interface, which is why droplets are spherical. Oil/water surface tension is decreased by the adsorption of amphiphilic molecules, such as phospholipids or amphipathic proteins, masking the interface. Surface tension of a bilayer is close to zero because of their similar inner and outer aqueous phases. For both monolayers and bilayers, the tighter the phospholipid packing, the lower the surface tension.

Surface pressure: the lateral pressure acting on a monolayer or a bilayer. Considers the different interactions at the interface, such as those between phospholipids, phospholipids, and neutral lipids, or phospholipids/neutral lipids and water. Lateral pressure is lower when phospholipids are pulled apart or when surface tension is augmented.

Laplace pressure: the pressure difference across a curved interface. For LDs, proportional to the surface tension of the interface divided by the droplets' curvature. Large droplets have a lower internal pressure than smaller ones, for a given surface tension. Compared with droplets, the Laplace pressure of bilayers is almost zero, because of the low tension.

Ostwald ripening: leakage of materials due to chemical potential differences. Small particles/droplets of large internal pressure spontaneously lose their molecules for bigger particles/droplets of lower internal pressure, through a continuous medium where the molecules are soluble. Ripening leads to LD heterogeneity and the eventual disappearance of small LDs.


PhD Denis E Corpet
email: d.corpet@gmail.com

Why does SARS-CoV-2 survive longer on plastic than on paper?

Keywords: enveloped virus, coronavirus, inactivation, persistence, surface, mechanisms

The Covid-19 coronavirus, SARS-CoV-2, is inactivated much faster on paper (3h) than on plastic (7d). By classifying materials according to virus stability on their surface, the following list is obtained (from long to short stability): polypropylene (mask), plastic, glass, stainless steel, pig skin, cardboard, banknote, cotton, wood, paper, tissue, copper. These observations and other studies suggest that SARS-CoV-2 may be inactivated by dryness on water absorbent porous materials but sheltered by long-persisting micro-droplets of water on waterproof surfaces. If such physical phenomenons were confirmed by direct evidence, the persistence of the virus on any surface could be predicted, and new porous objects could be designed to eliminate the virus faster.

Introduction

The Covid-19 coronavirus, SARS-CoV-2, is inactivated much faster on paper than on plastic: Three hours after being laid on paper, no virus can be detected. In contrast, the virus can still infect cells seven days after being laid on plastic. By classifying materials according to SARS-CoV-2 stability on their surface, the following list is obtained (from long to short stability): polypropylene (mask), plastic, glass, stainless steel, pig skin, cardboard, banknote, cotton, wood, paper, tissue, copper [START_REF] Chin | Stability of SARS-CoV-2 in different environmental conditions[END_REF][START_REF] Van Doremalen | Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1[END_REF][START_REF] Liu | Stability of SARS-CoV-2 on environmental surfaces and in human excreta[END_REF][START_REF] Harbourt | Modeling the Stability of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) on Skin, Currency, and Clothing[END_REF].

The tested items, the methods and criteria are not exactly the same in the above cited studies. Also, the decay of infectious virus is biphasic with long persistence of few virus on smooth surface [START_REF] Chin | Stability of SARS-CoV-2 in different environmental conditions[END_REF]. Several lists can thus be obtained, depending on the ranking criteria. However, differences between these lists are marginal, involve mostly the median items (e.g., cardboard, cotton, wood), and the variations do not change what follows.

Persistence of other enveloped viruses on surfaces also depends on the material. SARS-CoV-1 behaves very much like SARS-CoV-2 [START_REF] Van Doremalen | Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1[END_REF]. Influenza virus also survives longer on plastic and stainless steel (24-48h) than on on paper and tissue (6-8h) [START_REF] Bean | Survival of Influenza Viruses on Environmental Surfaces[END_REF].

-Pragmatically, these differences suggest that, in order to reduce the spread of virus via fomites, paper sheets and bags should be used instead of plastic to wrap, cover and carry objects (books, food, furniture). Similarly, copper alloy should be used instead of stainless steel to make handles and door knobs, as already reported [START_REF] Noyce | Inactivation of Influenza A Virus on Copper versus Stainless Steel Surfaces[END_REF].

-Scientifically, such differences in survival time are puzzling: Why would the virus be "killed" by certain materials, and conversely be "protected" by others? Absorbent products that blotter moisture seem to inactivate the virus. In contrast, smooth and waterproof materials, but copper, seem to protect the virus. Would the virus be killed by lack of water? Such a simple explanation is hard to believe, since a virus is not metabolically active and should therefore not need water. So how could a virus die of "dryness"? This short review suggests a hypothesis explaining why SARS-CoV-2 survives longer on plastic than on paper and examines published evidence on this questions.

Hypothesis

Dryness would inactivate SARS-CoV-2 virus on paper and other porous solids. Conversely, droplets of water remaining on waterproof surfaces would protect the viruses from dryness.

Evaluation of the hypothesis

Firstly, the common belief that viruses do not contain water was challenged long ago. In 1950 Sharp & Beard established by experiments of sedimentation of influenza virus with deuterated water that these viruses contain 60% of water: water corresponds to 150-230% of their dry weight, depending on method and on influenza strain A, B or swine [START_REF] Sharp | Partial Specific Volume and Water Content of Influenza Virus[END_REF]. Since coronavirus and influenza virus are both "enveloped" in a lipid membrane they take from their host cell, one may think that they both take some cytoplasm and that coronavirus also contains approximately two third of water.

Secondly, Cox reported 30 years ago that dehydration could inactivate enveloped viruses: this inactivation would occur by structural changes of the bilayer membrane, that would need water on its both sides to remain stable. Direct contact of enveloped virus with dry air would also lead to oxidation of lipids and Maillard reactions of proteins [START_REF] Cox | Airborne bacteria and viruses[END_REF][START_REF] Cox | Roles of water molecules in bacteria and viruses[END_REF]. Non-porous surfaces, compared with porous surfaces, would be better at preserving coronavirus viability because they do not draw moisture away from adsorbed viruses. Improved virus persistence would be due to the ability of a surface to maintain a moist microenvironment [START_REF] Casanova | Effects of Air Temperature and Relative Humidity on Coronavirus Survival on Surfaces[END_REF]. However, we could not find solid evidence to support these assumptions, and no work has explicitly investigated the physicochemical mechanisms underlying why some surfaces support longer virus persistence.

Thirdly, water droplets may stay for days on plastic, glass and stainless steel, not on copper. Using photos taken under a microscope every hour Kumar et al. demonstrated that droplets condensed from human breath first shrink rapidly on a smooth surface leaving residues of a few micrometers [START_REF] Kumar | Droplet evaporation residue indicating SARS-COV-2 survivability on surfaces[END_REF]. Then, these resulting micro-drops persist without further decrease in size for more than 24 hours on plastic and glass. They are smaller on stainless steel than on plastic and glass, and they quickly disappear from a copper surface. These micro-drops are 10 to 100 times larger than a coronavirus, which is enough to shelter the virus particles, insulating them against heat and dryness. Kumar et al. explain fast disappearance of drops on copper surface by its high thermal conductivity, while drops are protected from the subsurface heat on more insulating surfaces like stainless steel, glass and plastic [START_REF] Kumar | Droplet evaporation residue indicating SARS-COV-2 survivability on surfaces[END_REF]. The disappearance of drops on paper or cotton was not studied, but we can assume that they quickly disappear from such absorbent supports, leaving viruses exposed and unprotected to dry air, thus leading to their inactivation.

However, the hypothesis that dryness would inactivate SARS-CoV-2 seems in contradiction with experimental studies showing higher reduction in coronaviruses number at 80% relative humidity than at 20% humidity [START_REF] Aboubakr | Stability of SARS-CoV-2 and other coronaviruses in the environment and on common touch surfaces and the influence of climatic conditions: A review[END_REF][START_REF] Biryukov | Increasing Temperature and Relative Humidity Accelerates Inactivation of SARS-CoV-2 on Surfaces[END_REF] and with epidemiological studies suggesting that wet climates reduce Covid-19 transmission [START_REF] Ward | Humidity is a consistent climatic factor contributing to SARS-CoV-2 transmission[END_REF]. The effect of high humidity is not the scope of this article. Briefly, the wet conditions appear to discourage aerosol transmission of influenza virus, but may increase virus survival in droplets on surfaces [START_REF] Paynter | Humidity and respiratory virus transmission in tropical and temperate settings[END_REF]. Moreover, 90% of all Covid-19 cases in the world were detected in places where absolute humidity was between 4 and 8 g/m 3 [START_REF] Bukhari | Will Coronavirus Pandemic Diminish by Summer?[END_REF]. SARS-CoV-2 transmission thus seems reduced in both wet and dry climates, the latter being compatible with our hypothesis.

These studies thus support the hypothesis that dryness inactivates SARS-CoV-2 virus on paper and other cellulose-based porous solids. Conversely, the droplets of water that stay for days on plastic and other waterproof surfaces would protect the viruses. An alternative hypothesis would be that cellulose chemically inactivates the virus: we think it is unlikely. In addition let us examine below two outliers at both ends of the above cited list: copper and face masks.

Outliers

Copper is an outlier in the above cited list of materials. It is the only smooth and waterproof surface on which the virus persists less than a day. One may accept Kumar et al.

explanation that copper conductivity leads to the fast evaporation of protective droplets. However, copper also holds antiseptics properties on influenza virus and common cold coronavirus 229E. Exposure to copper destroys the viral genome, disintegrates envelope and disperses spikes. Cu(I) and Cu(II) moieties are responsible for the inactivation, which is enhanced by reactive oxygen species generation on alloy surfaces [START_REF] Noyce | Inactivation of Influenza A Virus on Copper versus Stainless Steel Surfaces[END_REF] [START_REF] Warnes | Human Coronavirus 229E Remains Infectious on Common Touch Surface Materials[END_REF]. Silver has not yet been tested with SARS-CoV-2. Like copper, it has a high thermal conductivity and is a powerful antiseptic. We therefore suggest that the Covid-19 coronavirus is not stable on silver.

Finally, coronavirus persists for a particularly long time on face masks. The mask inner layer is made of a specific plastic material, polypropylene, which holds permanent electrostatic charges and is thus an "electret" [START_REF] Eguchi | On the permanent electret[END_REF][START_REF] Heaviside | Electromagnetic induction and its propagation. Electrization and electrification[END_REF]. The stability of viruses on this material may be linked to the strong bond between the electret and the viral particles (See [START_REF] Castaño | Fomite transmission and disinfection strategies for SARS-CoV-2 and related viruses[END_REF] Fig. 3). Virus adsorption on a surface would stabilize them [START_REF] Vasickova | Issues Concerning Survival of Viruses on Surfaces[END_REF]. For instance, survival of viruses in soil is linked to their adsorption onto soil particles [START_REF] Hurst | Effects of environmental variables and soil characteristics on virus survival in soil[END_REF]. This has not, however, yet been demonstrated for coronavirus on mask electret.

Implications

The direct demonstration of the hypothesis remains however to be done experimentally, notably for porous blotting material like paper. A simple approach to this demonstration would be to test the persistence of SARS-CoV-2 on a range of papers with various blotting ability in dry or moist atmospheres. Such demonstration would be of scientific interest, regarding the physical mechanisms of disappearance of lipid bilayer enveloped viruses on blotting surfaces. It would also have practical applications.

First, it would make it possible to predict whether the enveloped viruses may persist on materials that have not been tested yet. For instance, our hypothesis predicts that enveloped viruses, should be quickly inactivated on absorbent products like bread crumb, "suede" leather, salt and chalk. Conversely these viruses should be relatively stable on non absorbent products like glossy paper, polished marble or fruit skin, and possibly more stable on wet products like fresh meat.

Finally this would help to design objects and surfaces that eliminate coronavirus faster that paper and tissue. Many materials are more absorbent than paper tissue, for instance super-absorbent polymers from cellulose (e.g., wood pulp, carboxymethylcellulose), from petroleum (e.g., acrylamide, acrylic acid), and mineral desiccant (e.g., silica aerogel, montmorillonite "nano-clay") [START_REF] Hubbe | Enhanced Absorbent Products Incorporating Cellulose and Its Derivatives: A Review[END_REF]. Objects made of, or covered with such material would be expected to reduce the survival of coronaviruses on their surface. Direct spread of saliva, aerosol diffusion, and contact with fomites are three ways of coronavirus spread. The increased use of water absorbent objects might thus reduce the fomite way of Covid-19 spread.

Acknowledgements

Thanks are due to Adrien Chopin who helped me to solve the paradox of wet climates, and to Virginie Courtier-Orgogozo and Claire Wiart who reviewed the manuscript and made helpful suggestions.

No funds were necessary for this work.

Conflict of interest statement

The author declares no competing interest.