Alexander Kuzmin

Philipp Orekhov

Roman Astashkin

Valentin Gordeliy

Ivan Gushchin
email: ivan.gushchin@phystech.edu

| Philipp Orekhov

Structure and dynamics of the SARS-CoV-2 envelope protein monomer

Keywords: envelope protein, glycosylation, membrane curvature, membrane protein, molecular dynamics, palmitoylation, SARS-CoV-2 ORCID

| INTRODUCTION

Coronaviruses (CoVs) (order Nidovirales, family Coronaviridae, subfamily Coronavirinae) are enveloped viruses with a positive-sense, singlestranded RNA genome of $30 kb, one of the largest among RNA viruses. 1 CoVs infect birds and mammals, causing a variety of fatal diseases. They can also infect humans and cause diseases ranging from the common cold to acute respiratory distress syndrome. Highly pathogenic human coronaviruses include Severe Acute Respiratory Syndrome Coronavirus (SARS)-CoV, Middle Eastern Respiratory SyndromeCoronavirus (MERS)-CoV, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). 2,3 The outbreaks of SARS-CoV in 2002/3 and MERS-CoV in 2012 led to epidemics. SARS-CoV-2 emerged at the end of December 2019 causing a pandemic of the coronavirus disease 2019 (COVID- 19), which is a novel lifethreatening form of atypical pneumonia. 4 Antiviral strategies may be roughly divided into two classes: the measures aimed at prevention of the spread of infections, and treatment of patients who have already contracted the disease. The development of both kinds of strategies benefits greatly from understanding the virus physiology, and in particular the structure and function of viral proteins. Structural biology studies of SARS-CoV-2 have seen rapid progress since the beginning of the pandemic. 5 Whereas most of the key information was obtained using experimental techniques, such as cryo-electron microscopy, x-ray crystallography, or nuclear magnetic resonance (NMR), computational approaches were key for some of the findings. 6,7 Among the most notable examples are detailed simulations of dynamics of the most important viral proteins 6,8,9 or even the whole virion, 10 early generation of atomic models for all SARS-CoV-2 proteins, 11 and high-throughput virtual ligand screening of viral protease inhibitors. 12,[START_REF] Consortium | COVID moonshot: Open Science discovery of SARS-CoV-2 Main protease inhibitors by combining crowdsourcing, high-throughput experiments, computational simulations, and machine learning[END_REF] The genomes of all coronaviruses encode four major structural proteins: the spike (S) protein, the nucleocapsid (N) protein, the membrane (M) protein, and the envelope (E) protein. [START_REF] Masters | The molecular biology of coronaviruses[END_REF] The S protein is involved in host recognition, attachment, and cell fusion. The N protein is involved in the packaging of the RNA genome and the formation of the nucleocapsid. The M protein directs the assembly process of virions through interactions with the other structural proteins and defines the shape of the viral envelope. The E protein is possibly the most mysterious of them since it is associated with the assembly of virions, effective virion transfer along the secretory pathway as well as a reduced stress response by the host cell. Generally, it promotes virus fitness and pathogenesis. [START_REF] Nieto-Torres | Severe acute respiratory syndrome coronavirus envelope protein ion channel activity promotes virus fitness and pathogenesis[END_REF] Overall, coronaviral E proteins are small, integral membrane proteins of 75-109 amino acids, which have at least one helical transmembrane domain (TMD) and a long amphiphilic region comprising one or two α-helices at the C-terminus. [START_REF] Ruch | The coronavirus E protein: assembly and beyond[END_REF][START_REF] Schoeman | Coronavirus envelope protein: current knowledge[END_REF] SARS-CoV-2 E protein consists of 75 amino acids, and its sequence is 95% and 36% identical to those of SARS-CoV and MERS-CoV E proteins, respectively. Given the sequence identity and the available data, SARS-CoV and SARS-CoV-2 E proteins appear to be very similar in their structure and function, and most of the findings about the former proteins likely apply to the latter as well. The general properties of the SARS-CoV-2 E protein presumably match those of other coronaviral E proteins.

It was shown previously that E proteins may undergo co-translational and/or posttranslational modifications (CPTMs), [START_REF] Ruch | The coronavirus E protein: assembly and beyond[END_REF][START_REF] Schoeman | Coronavirus envelope protein: current knowledge[END_REF] but the role of these modifications is still not fully clear. The prominent examples of other viral proteins that may be also modified by palmitoylation are the coronaviral S protein, haemagglutinin (HA) protein of the influenza virus, Env proteins of retroviruses and filoviruses, and vaccinia virus 37 kDa major envelope antigen (p37). [START_REF] Petit | Palmitoylation of the cysteine-rich endodomain of the SARS-coronavirus spike glycoprotein is important for spike-mediated cell fusion[END_REF][START_REF] Fujiwara | Structural basis for the membrane association of ankyrinG via palmitoylation[END_REF][START_REF] Soboci Nska | Protein palmitoylation and its role in bacterial and viral infections[END_REF][START_REF] Boscarino | Envelope protein palmitoylations are crucial for murine coronavirus assembly[END_REF] Some results indicate that conserved cysteines of the SARS-CoV E protein and, presumably, their palmitoylation are functionally important for the stability of the E protein and the overall virus production. [START_REF] Lopez | Importance of conserved cysteine residues in the coronavirus envelope protein[END_REF][START_REF] Yuan | Biochemical and functional characterization of the membrane association and membrane permeabilizing activity of the severe acute respiratory syndrome coronavirus envelope protein[END_REF] On the other hand, glycosylation shields viral proteins from recognition by the immune system. [START_REF] Grant | Analysis of the SARS-CoV-2 spike protein glycan shield reveals implications for immune recognition[END_REF][START_REF] Marth | Mammalian glycosylation in immunity[END_REF] It is closely linked to the protein topology as modification can happen only in the lumen of endoplasmic reticulum. SARS-CoV and SARS-CoV-2 E proteins are predominantly inserted in the membrane with their C-termini in the cytoplasm and are not modified [START_REF] Yuan | Biochemical and functional characterization of the membrane association and membrane permeabilizing activity of the severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Nieto-Torres | Subcellular location and topology of severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Duart | SARS-CoV-2 envelope protein topology in eukaryotic membranes[END_REF][START_REF] Duart | The SARS-CoV-2 envelope (E) protein has evolved towards membrane topology robustness[END_REF] ;am i n o r f r a c t i o nc a nb eg l y c o s y l a t e du n d e rc e r t a i nn o n -n a t i v ec o n d i t i o n s . [START_REF] Yuan | Biochemical and functional characterization of the membrane association and membrane permeabilizing activity of the severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Duart | SARS-CoV-2 envelope protein topology in eukaryotic membranes[END_REF] The role of this possible glycosylation of E proteins is not clear. [START_REF] Schoeman | Coronavirus envelope protein: current knowledge[END_REF] Only a small fraction of the E protein expressed during infection is incorporated into the virion envelope; the rest is localized at the intracellular trafficking endoplasmic reticulum (ER)-Golgi region and mostly at the intermediate compartment between ER and ER-Golgi intermediate compartment (ERGIC). [START_REF] Lopez | Importance of conserved cysteine residues in the coronavirus envelope protein[END_REF][START_REF] Nieto-Torres | Subcellular location and topology of severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Boson | The SARS-CoV-2 envelope and membrane proteins modulate maturation and retention of the spike protein, allowing assembly of virus-like particles[END_REF][START_REF] Cohen | Identification of a Golgi complextargeting signal in the cytoplasmic tail of the severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Godet | TGEV corona virus ORF4 encodes a membrane protein that is incorporated into virions[END_REF][START_REF] Venkatagopalan | Coronavirus envelope (E) protein remains at the site of assembly[END_REF] ERGIC is composed of tubulovesicular membrane clusters, with many curved membrane regions. [START_REF] Appenzeller-Herzog | The ER-golgi intermediate compartment (ERGIC): in search of its identity and function[END_REF] CoVs assemble and bud at the ERGIC, where the E protein may induce membrane curvature or aid in membrane scission. [START_REF] Ruch | The coronavirus E protein: assembly and beyond[END_REF][START_REF] Schoeman | Coronavirus envelope protein: current knowledge[END_REF] Indeed, various recombinant CoVs lacking the gene for E exhibit an aberrant morphology, from which it can be concluded that the function of E is to induce membrane curvature of the viral envelope, thus allowing CoV particles to acquire their characteristic spherical shape and morphology. [START_REF] Cohen | Identification of a Golgi complextargeting signal in the cytoplasmic tail of the severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Ortego | Absence of E protein arrests transmissible gastroenteritis coronavirus maturation in the secretory pathway[END_REF][START_REF] Fischer | Analysis of constructed E gene mutants of mouse hepatitis virus confirms a pivotal role for E protein in coronavirus assembly[END_REF] E protein was also shown to colocalize and interact with the M and N proteins [START_REF] Corse | The cytoplasmic tails of infectious bronchitis virus E and M proteins mediate their interaction[END_REF][START_REF] Tseng | SARS-CoV envelope protein palmitoylation or nucleocapid association is not required for promoting virus-like particle production[END_REF] as well as with the N-terminus of nsp3. [START_REF] Alvarez | The envelope protein of severe acute respiratory syndrome coronavirus interacts with the non-structural protein 3 and is ubiquitinated[END_REF] It increases the expression of the M and S proteins [START_REF] Xu | Construction of SARS-CoV-2 viruslike particles by mammalian expression system[END_REF] and, together with M, affects the processing, maturation, and localization of S. [START_REF] Boson | The SARS-CoV-2 envelope and membrane proteins modulate maturation and retention of the spike protein, allowing assembly of virus-like particles[END_REF] Finally, it can also interact with cellular proteins Bcl-xL, 40 PALS1, [START_REF] Teoh | The SARS coronavirus E protein interacts with PALS1 and alters tight junction formation and epithelial morphogenesis[END_REF][START_REF] Toto | Comparing the binding properties of peptides mimicking the envelope protein of SARS-CoV and SARS-CoV-2 to the PDZ domain of the tight junction-associated PALS1 protein[END_REF] and others such as CWC27, AP3B1, ZC3H18, SLC44A2, BRD2, and BRD4. [START_REF] Gordon | A SARS-CoV-2 protein interaction map reveals targets for drug repurposing[END_REF] In the host membranes, E proteins oligomerize to form ionconductive pores [START_REF] Verdiá-Báguena | Coronavirus E protein forms ion channels with functionally and structurallyinvolved membrane lipids[END_REF][START_REF] Parthasarathy | Structural flexibility of the pentameric SARS coronavirus envelope protein ion channel[END_REF][START_REF] Surya | MERS coronavirus envelope protein has a single transmembrane domain that forms pentameric ion channels[END_REF][START_REF] Tomar | SARS-CoV-2 E protein is a potential ion channel that can be inhibited by gliclazide and memantine[END_REF] that may be inhibited by hexamethylene amiloride (HMA) and amantadine. [START_REF] Wilson | Hexamethylene amiloride blocks E protein ion channels and inhibits coronavirus replication[END_REF][START_REF] Pervushin | Structure and inhibition of the SARS coronavirus envelope protein ion channel[END_REF][START_REF] Torres | Conductance and amantadine binding of a pore formed by a lysineflanked transmembrane domain of SARS coronavirus envelope protein[END_REF][START_REF] Mandala | Structure and drug binding of the SARS-CoV-2 envelope protein transmembrane domain in lipid bilayers[END_REF][START_REF] To | Chapter eight-targeting the channel activity of Viroporins[END_REF] Similar small proteins (60-120 residues), which oligomerize and form hydrophilic transmembrane pores or channels and disrupt a number of physiological characteristics of the cell, are called viroporins. [START_REF] Nieva | Viroporins: structure and biological functions[END_REF] They are known to contribute to the release of infectious enveloped virus particles from infected cells and/or to facilitate the penetration of the viruses into the cell. The most famous representative viroporins of highly pathogenic RNA viruses are human immunodeficiency virus type 1 (HIV-1) Viral protein U (Vpu) protein, hepatitis C virus p7 protein, and influenza A virus matrix protein 2 (M2), which are involved in diverse processes such as virus entry, trafficking, assembly, inflammation, and apoptosis. [START_REF] Nieva | Viroporins: structure and biological functions[END_REF] The significant contribution of viroporins to the life cycle of viruses makes them a target for therapeutic interventions. In particular, M2 can be targeted by FDA-approved inhibitor rimantadine. [START_REF] Jefferson | Amantadine and rimantadine for preventing and treating influenza a in adults[END_REF] Investigations have shown that SARS-CoV viruses, in which the channel activity is inhibited, were much less infectious and pathogenic. [START_REF] Nieto-Torres | Severe acute respiratory syndrome coronavirus E protein transports calcium ions and activates the NLRP3 inflammasome[END_REF] Currently, several experimental structures of the E protein fragments are available. [START_REF] Surya | MERS coronavirus envelope protein has a single transmembrane domain that forms pentameric ion channels[END_REF][START_REF] Pervushin | Structure and inhibition of the SARS coronavirus envelope protein ion channel[END_REF][START_REF] Mandala | Structure and drug binding of the SARS-CoV-2 envelope protein transmembrane domain in lipid bilayers[END_REF][START_REF] Li | Structure of a conserved Golgi complex-targeting signal in coronavirus envelope proteins[END_REF][START_REF] Surya | Structural model of the SARS coronavirus E channel in LMPG micelles[END_REF] In particular, it was shown that the protein contains a TM (transmembrane) α-h e l i xa n do n e( w h e ni n monomeric form and in detergent [START_REF] Li | Structure of a conserved Golgi complex-targeting signal in coronavirus envelope proteins[END_REF] )o rt w o( w h e ni np e n t a m e r i c form [START_REF] Surya | Structural model of the SARS coronavirus E channel in LMPG micelles[END_REF] ), amphipathic α-helices. Yet, the experimental structure of the full-length wild-type protein is not available at the moment, and the influence of CPTMs on it has not been studied. Moreover, there is little data on the behavior of monomeric E protein prior to its assembly into pentameric channels. In the present study, we applied molecular dynamics simulations to study the behavior of monomeric E protein from SARS-CoV-2 and identified the effects of CPTMs on the protein behavior. We have also observed that the protein induces curvature in the membranes, and is attracted to the curved regions. These findings may be helpful in development of anti-SARS-CoV-2 medications, and for understanding the function of viroporins in general.

| RESULTS

| Structure of the monomeric E protein

E protein from SARS-CoV-2 is a 75 amino acid-long protein that may be palmitoylated and glycosylated in vivo (Figure 1A). To assess the overall conformational space available to the protein, we conducted first an extensive coarse-grained (CG) simulation of unmodified E protein, followed by atomistic simulations of unmodified protein and CG simulations of the protein with modifications (Table S1). CG simulations are known to faithfully reproduce the major physicochemical properties of the studied macromolecules while providing a considerable speedup compared to atomistic simulations. [START_REF] Marrink | Lipids on the move: simulations of membrane pores, domains, stalks and curves[END_REF][START_REF] Buslaev | Effects of coarse graining and saturation of hydrocarbon chains on structure and dynamics of simulated lipid molecules[END_REF] In accordance with expectations, the simulations revealed that the protein is very flexible with no particular tertiary structure (Figure 1B). Principal component analysis (PCA) shows that the first two components describe most of the structural variation ($64%, Figure 2) and correspond to motions of the helices H2 and H3 relative to each other and TMD near the membrane surface.

Atomistic simulations are considerably more computationally demanding, and thus the exhaustive sampling of the conformational space can take a prohibitively long time. Consequently, we simulated a number of atomistic trajectories starting from representative conformations from the CG simulation. We divided the CG trajectory snapshots into four clusters and used the centroids of the clusters as the starting structures for atomistic simulations. For each starting structure, we obtained six trajectories of the E protein: three with the protein embedded in the model membrane containing POPC, and three with the membrane mimicking the natural ERGIC membrane (50% POPC, 25% POPE, 10% POPI, 5% POPS, and 10% cholesterol). No qualitative differences were observed between the simulations conducted in these membranes. Overall, PCA shows that the atomistic simulations correspond to the CG simulation and display roughly the same conformational space available to the E protein (Figure 2B).

Conformations observed in atomistic simulations are shown in Figure S1.

Atomistic simulations also show that while the secondary structure of the E protein is largely conserved, the amphipathic α-helices H2 and H3 may partially unfold, with H2 being more disordered (Figures 3 andS2). We observed both unfolding and refolding events.

Overall, this observation is in agreement with NMR experiments. 56,57

| Position of the E protein elements relative to the membrane

Figure 4 shows the average positions of the secondary structure elements of the E protein relative to the membrane surface. In all of the simulations, the TMD remained embedded in the membrane. H2 is deeply buried in the lipid headgroup region, whereas H3 is slightly removed from the membrane border, while still remaining in contact with it. In some atomistic trajectories, partial unbinding of H3 from the membrane is observed (Figure S3). Interestingly, TMD, despite being a single transmembrane α-helix, has a preferable orientation in the membrane (Figures 5 andS4). It is tilted at the angle of 25

-40 in all of the simulations and has a strong orientational (azimuthal) preference, with phenylalanines Phe20, Phe23, and Phe26 orie n t e dt o w a r dt h eN -t e r m i n a ls i d e .N o robust effects of CPTMs modifications on the orientation of TMD were observed (Table S2).

H2, as an amphipathic helix, also has a preferred orientation (Figures 6 andS5). Its three cysteines, Cys40, Cys43, and Cys44, may be palmitoylated in vivo, which would change the physicochemical properties of the helix. To probe the effects of all possible combinations of these PTMs in an efficient manner, we employed CG simulations. We found that palmitoylation, on average, leads to the rotation of H2 around its axis (Figure 6, Table S2). The strongest effect on the H2 orientation is observed when Cys40 and Cys44 are palmitoylated simultaneously: the helix is rotated by $32.2 relative to its position in the unmodified protein. Other palmitoylated variants have intermediate orientations; the effects of palmitoylation of the three cysteine residues are not additive (Table S2). Finally, whereas the position of H3 was not significantly affected by palmitoylation, it was affected by glycosylation (Supporting Text and Figure S6). To check whether the curvature is indeed induced by H2 and H3, we conducted additional CG simulations of artificial proteins consisting of only TMD or only H2 and H3 (Figure 7B,C). Isolated TMD was tilted in a way similar to that observed in the simulations of the full-length protein. The membrane was perturbed and thinned near the α-helix (Figure 7B), presumably because of the polar residues on the respective sides (Glu8, Thr9, Thr11, Asn15, Ser16 at the N-terminal side, Thr30, Thr35 at the C-terminal side). Isolated H2 and H3 curved the membrane in the same way as the full-length protein (Figure 7C). Thus, we conclude that the structural elements responsible for curvature induction by the E protein are the amphipathic helices of the C-terminal domain.

| Dynamics of the E protein within curved membranes

Having observed the induction of curvature by the E protein, we were also interested to check whether it has a preferable position in membranes that are already curved, such as the native ER, Golgi, and ERGIC membranes, especially during the budding of virus-like particles (VLPs). As a test system, we used artificially buckled membranes. [START_REF] Boyd | Buckling under pressure: curvaturebased lipid segregation and stability modulation in Cardiolipincontaining bilayers[END_REF][START_REF] Elías-Wolff | Computing curvature sensitivity of biomolecules in membranes by simulated buckling[END_REF][START_REF] Baoukina | Curvatureinduced sorting of lipids in plasma membrane tethers[END_REF][START_REF] Madsen | Entropic forces drive clustering and spatial localization of influenza a M2 during viral budding[END_REF] Given the size of the systems (Table S1), the simulations were conducted in CG representation. Irrespective of the starting positions, E protein monomers redistribute in the membranes so that the C-termini localize to the convex regions (Figure 8). The effect was observed both in the membranes buckled in a single direction (nonzero mean curvature, zero Gaussian curvature, Figure 8A) and in the membranes buckled in both directions (nonzero Gaussian curvature, Figure 8B). Thus, we conclude that the monomeric E protein is curvature-sensitive.

| Properties of the pentameric E protein

To see whether the pentameric E protein can also generate and/or sense curvature, we conducted additional CG simulations (Figure 9). Using the computational model by Heo and Feig 11 or the more recent NMR model [START_REF] Mandala | Structure and drug binding of the SARS-CoV-2 envelope protein transmembrane domain in lipid bilayers[END_REF] (for TMD) as a starting structure, we obtained similar conformational ensembles. The C-terminal helices do not have a fixed position (Figure 9A). Both H2 and H3 are slightly removed from the membrane in simulations of the pentameric E protein (Figure S9) S3). However, palmitoylation of Cys43 or Cys44 shifts the distribution of H2 positions $2 Å closer to the membrane (Figure S9). In all of the simulations of the pentameric E protein, we also observed bending of the membrane around it (Figure 9B). The mean curvature induced by the pentameric protein is roughly two times

| DISCUSSION

Coronaviruses have relatively large genomes harboring tens of different genes. Understanding of their structures could help in development of efficient antiviral measures. Yet some of the CoV proteins are transmembrane, and some contain intrinsically disordered regions, [START_REF] Giri | Understanding COVID-19 via comparative analysis of dark proteomes of SARS-CoV-2, human SARS and bat SARS-like coronaviruses[END_REF] at least until they become a part of a larger assembly. E protein has both properties: it has a TM segment, and it lacks tertiary structure in the monomeric form, while becoming more ordered in the pentameric assembly. Its flexibility and numerous CPTMs pose many problems for experimental studies, especially of the monomeric E protein. However, because it is small, and its properties are governed by basic physicochemical principles, it is a good subject for simulations.

Our results show that monomeric SARS-CoV-2 envelope protein has rich conformational dynamics strongly affected by CPTMs. The protein is organized as an α-helical TMD and two amphipathic α-helices H2 and H3, flanked by short disordered N-and C-termini. Whereas TMD is rigid and remains α-helical throughout the trajectories, helices H2 and H3 may partially unfold. TMD, H2, and H3 mostly move freely relative to each other, so the monomeric E protein can be considered a protein with intrinsically disordered regions. Yet, all of its α-helices have preferred orientations relative to the membrane.

The TM α-helix of the E protein is relatively long (28 amino acids, $43 Å), and there is a mismatch between the length of its hydrophobic segment and the thickness of the hydrophobic region of the relevant membranes. Tilting of TM helices is a common mechanism for accommodating such mismatch. [START_REF] Park | Tilt angle of a trans-membrane helix is determined by hydrophobic mismatch[END_REF][START_REF] Kandasamy | Molecular dynamics simulations of model trans-membrane peptides in lipid bilayers: a systematic investigation of hydrophobic mismatch[END_REF][START_REF] Özdirekcan | On the orientation of a designed transmembrane peptide: toward the right tilt angle?[END_REF][START_REF] Duong-Ly | The conformation of the pore region of the M2 proton channel depends on lipid bilayer environment[END_REF][START_REF] Koehorst | Lipid bilayer topology of the transmembrane α-helix of M13 major coat protein and bilayer polarity profile by site-directed fluorescence spectroscopy[END_REF] Accordingly, we find that E protein TMD is tilted at 25-40 , similarly to TMD in pentameric E protein [START_REF] Surya | Structural model of the SARS coronavirus E channel in LMPG micelles[END_REF] and in other viroporins (Table S3). Besides tilting, the energetic costs of the hydrophobic mismatch can also be lowered by association (packing) of several TM helices. [START_REF] Benjamini | Robust driving forces for transmembrane helix packing[END_REF] In the case of the E protein, this mechanism could promote formation of pentamers. TMD also has a preferred azimuthal rotation angle, similarly to WALP peptides, [START_REF] Holt | Orientation and dynamics of transmembrane peptides: the power of simple models[END_REF][START_REF] Kim | Revisiting hydrophobic mismatch with free energy simulation studies of transmembrane helix tilt and rotation[END_REF] for which the results obtained with MD simulations were found to correspond well to those obtained in experiments. [START_REF] Strandberg | Hydrophobic mismatch of mobile transmembrane helices: merging theory and experiments[END_REF] However, the rotation angle of TMD in a free E protein monomer is opposite to that in the E protein pentamer. This is likely a consequence of the polar residues such as Glu8, Thr9, Thr11, Asn15, Ser16, Thr30, and Thr35 preferably facing the solvent in the monomer and interior of the channel in the pentamer.

One of the most potentially important findings is a strong dependence of the E protein structure on CPTMs. Previously, it was shown that palmitoylation is important for E protein stability and overall assembly of VLPs, whereas the role of glycosylation is more elusive. [START_REF] Schoeman | Coronavirus envelope protein: current knowledge[END_REF] Yet, experimental studies of the effects of CPTMs on protein structure are hindered by difficulties in obtaining homogeneous samples with a desired CPTM pattern; in vivo, palmitoylation is likely to be stochastic. [START_REF] Rodenburg | Stochastic palmitoylation of accessible cysteines in membrane proteins revealed by native mass spectrometry[END_REF] The proteins may be mutated to abolish the particular CPTM, however this may also introduce unintended side effects. On Previous structural studies of the E protein by NMR dealt with unmodified truncated variants. SARS-CoV E protein construct included residues 8-65, a His-tag and a linker; the cysteines were mutated to alanines, Asn66 was missing. [START_REF] Nieto-Torres | Severe acute respiratory syndrome coronavirus E protein transports calcium ions and activates the NLRP3 inflammasome[END_REF][START_REF] Li | Structure of a conserved Golgi complex-targeting signal in coronavirus envelope proteins[END_REF] SARS-CoV-2 construct was even shorter (residues 8-38) and did not include the residues that could be modified. [START_REF] Torres | Conductance and amantadine binding of a pore formed by a lysineflanked transmembrane domain of SARS coronavirus envelope protein[END_REF] Previous computational studies of the E protein also did not focus on the effects of CPTMs. 11,[START_REF] Sarkar | Structural insight into the role of novel SARS-CoV-2 E protein: a potential target for vaccine development and other therapeutic strategies[END_REF][START_REF] Cao | Computational study of the ion and water permeation and transport mechanisms of the SARS-CoV-2 pentameric E protein channel[END_REF] In this work, we found that the average orientation of H2 is strongly dependent on palmitoylation pattern, as the acyl chains act as anchors on the respective H2 cysteines and bring them closer to the membrane core. On the other hand, positioning of H3 is affected by glycosylation as the glycan acts as a buoy on H3 and prevents its interaction with H2. However, most or all of the E proteins in vivo are probably not glycosylated, [START_REF] Duart | SARS-CoV-2 envelope protein topology in eukaryotic membranes[END_REF] so the possible role of this modification remains unclear. We believe that CPTMs are likely to elicit effects in the assembled oligomers similar to those that we observe in monomers.

In the last part of our work, we focused on interactions of the E protein with curved membranes. Overall, membrane curvature is an important factor in cell physiology, [START_REF] Mcmahon | Membrane curvature at a glance[END_REF] being both generated and sensed by the major membrane constituents: lipids and proteins. [START_REF] Graham | Interplay of proteins and lipids in generating membrane curvature[END_REF][START_REF] Baumgart | Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids[END_REF] Some amphipathic α-helices are known to generate curvature by creating the area difference between the two leaflets of the bilayer [START_REF] Jarsch | Membrane curvature in cell biology: an integration of molecular mechanisms[END_REF][START_REF] Campelo | The hydrophobic insertion mechanism of membrane curvature generation by proteins[END_REF] or to act as curvature sensors. [START_REF] Drin | A general amphipathic α-helical motif for sensing membrane curvature. N a tS t r u c tM o lB i o l[END_REF][START_REF] Cui | Mechanism of membrane curvature sensing by amphipathic helix containing proteins[END_REF] Along with experiments, molecular dynamics simulations have also been fundamental in studies of curved membranes. [START_REF] Marrink | Lipids on the move: simulations of membrane pores, domains, stalks and curves[END_REF] Earlier, simulations have been used to study repartitioning of both lipids and proteins in naturally and artificially curved membranes [START_REF] Boyd | Buckling under pressure: curvaturebased lipid segregation and stability modulation in Cardiolipincontaining bilayers[END_REF][START_REF] Elías-Wolff | Computing curvature sensitivity of biomolecules in membranes by simulated buckling[END_REF][START_REF] Baoukina | Curvatureinduced sorting of lipids in plasma membrane tethers[END_REF][START_REF] Madsen | Entropic forces drive clustering and spatial localization of influenza a M2 during viral budding[END_REF] ; a prominent example is enrichment of cardiolipin and cholesterol in the regions with negative curvature. [START_REF] Boyd | Buckling under pressure: curvaturebased lipid segregation and stability modulation in Cardiolipincontaining bilayers[END_REF][START_REF] Baoukina | Curvatureinduced sorting of lipids in plasma membrane tethers[END_REF] Another example is the influenza A М2 protein, for which both experiments and simulations show that its amphiphilic α-helix induces membrane curvature, which is important for VLP budding and membrane scission, [START_REF] Schmidt | Antimicrobial peptides and induced membrane curvature: geometry, coordination chemistry, and molecular engineering[END_REF][START_REF] Rossman | Influenza virus M2 protein mediates ESCRT-independent membrane scission[END_REF] and can act as a curvature sensor. [START_REF] Madsen | Entropic forces drive clustering and spatial localization of influenza a M2 during viral budding[END_REF] Here, we have found that the SARS-CoV-2 E protein can generate membrane curvature, and this function can be ascribed to the amphiphilic C-terminal domain, containing α-helices H2 and H2 that insert into the proximal leaflet and cause its bulging. Such viroporingenerated curvature may stabilize the budding viral particle and promote its formation. [START_REF] Mcmahon | Membrane curvature at a glance[END_REF] We have also found that the E protein can act as a curvature sensor and localize with the C-terminus at the convex regions of the membrane. Given that the C-terminus of E is oriented toward the cytoplasm, [START_REF] Duart | SARS-CoV-2 envelope protein topology in eukaryotic membranes[END_REF] the protein is likely to localize at the VLP budding sites and promote VLP budding. Concentration of the E protein in these curved areas may promote formation of pentameric channels. The assembled channels are also found to be curvaturesensitive due to their umbrella-like shape. 11,[START_REF] Surya | Structural model of the SARS coronavirus E channel in LMPG micelles[END_REF] On the other hand, E protein is expected to be depleted at the concave inner surface of the VLP, in agreement with experimental data. [START_REF] Lopez | Importance of conserved cysteine residues in the coronavirus envelope protein[END_REF][START_REF] Nieto-Torres | Subcellular location and topology of severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Boson | The SARS-CoV-2 envelope and membrane proteins modulate maturation and retention of the spike protein, allowing assembly of virus-like particles[END_REF][START_REF] Cohen | Identification of a Golgi complextargeting signal in the cytoplasmic tail of the severe acute respiratory syndrome coronavirus envelope protein[END_REF][START_REF] Godet | TGEV corona virus ORF4 encodes a membrane protein that is incorporated into virions[END_REF][START_REF] Venkatagopalan | Coronavirus envelope (E) protein remains at the site of assembly[END_REF] Finally, we would like to discuss the limitations of the present study, and the future directions. First of all, we did not examine in detail the behavior of the envelope protein in the pentameric form.

Root mean square deviations of the TM helix heavy atom positions between the available NMR models is above 6 Å. [START_REF] Mandala | Structure and drug binding of the SARS-CoV-2 envelope protein transmembrane domain in lipid bilayers[END_REF][START_REF] Surya | Structural model of the SARS coronavirus E channel in LMPG micelles[END_REF] Simulations performed by other laboratories reveal low stability of the pentameric models and frequent collapses of the pore. [START_REF] Cao | Computational study of the ion and water permeation and transport mechanisms of the SARS-CoV-2 pentameric E protein channel[END_REF][START_REF] Mehregan | Biophysical characterization of the SARS-CoV-2 E protein[END_REF][START_REF] Monje-Galvan | Molecular interactions of the M and E integral membrane proteins of SARS-CoV-2[END_REF][START_REF] Sun | Computational study on the function of palmitoylation on the envelope protein in SARS-CoV-2[END_REF] Thus, behavior of the pentameric envelope protein deserves a very careful consideration. Perhaps, simulation of the pentamer assembly process starting from monomers or oligomers [START_REF] Novitskaia | Assembly of spinach chloroplast ATP synthase rotor ring protein-lipid complex[END_REF] would prove helpful in arriving at a satisfactory model. Furthermore, while we included the representative ERGIC lipids (POPC, POPE, POPI, POPS, and CHOL) in our simulations, and did not observe any specific interactions, there are many more lipid species in the cell membrane that might bind the envelope protein selectively, especially in the pentameric form, where it has larger accessible surface and, possibly, lipid-binding crevices. We also did not probe the interactions of the E protein with other coronaviral or cellular proteins; these interactions might have affected the structure and dynamics of the E protein. Future experimental and computational studies should provide a better picture of the E protein behavior in physiological settings. We hope that our observations will help in understanding the role of the E protein in infection, in particular, by highlighting its membrane deformation abilities that should facilitate the budding of viral particles. The findings also explain the low abundance of the E protein in assembled virions. Finally, the data on the dynamics of the protein in monomeric form should be helpful for studying and elucidating its structure in physiological settings inside the infected cell, especially within the pentameric channels.

| CONCLUSIONS

| METHODS

| Model preparation

As a starting structure for simulations of the monomeric and pentameric SARS-CoV-2 E protein, we used the model prepared by Heo and Feig 11 (https://github.com/feiglab/sars-cov-2-proteins/blob/ master/Membrane/E_protein.pdb, accessed on September 1, 2020).

Atomistic structure was converted into CG Martini 3 representation 90 using martinize. Define secondary structure of proteins (DSSP) [START_REF] Touw | A series of PDB-related databanks for everyday needs[END_REF][START_REF] Kabsch | Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features[END_REF] was used to assign the α-helical secondary structure for TMD, H2 and H3.

The CG model was inserted into the POPC lipid bilayer using insane. [START_REF] Wassenaar | Computational lipidomics with insane: a versatile tool for generating custom membranes for molecular simulations[END_REF] The structure of the monomer with CPTMs was constructed manually using PyMOL. [START_REF] Delano | The PyMOL Molecular Graphics System[END_REF] For further AA (all atom) simulations, CG structures were converted to AA using backward 95 andinsertedintoPOPCorthe native-like mixed bilayer composed of POPC/POPE/POPI/POPS/ CHOL in the proportion 10:5:2:1:2 using CHARMM-GUI. [START_REF] Jo | CHARMM-GUI: a web-based graphical user interface for CHARMM[END_REF] In all simulations, the N-and C-termini, residues Lys, Arg, Asp, and Glu, and lipids POPS and POPI were charged. The membranes were solvated with water; counter ions were added to neutralize the systems.

The simulations were performed using periodic boundary conditions.

All systems were energy minimized using the steepest descent method, equilibrated and simulated using GROMACS 2019.5 (AA) and GROMACS 2020.1 (CG). [START_REF] Abraham | GROMACS: high performance molecular simulations through multi-level parallelism from laptops to supercomputers[END_REF] To generate the buckled membranes, we compressed the bilayers in the X-dimension until reaching the desired strain by fixing the box size in these dimensions, while the membrane pressure coupling was turned off in the X-Y lateral dimensions.

| Simulation details

CG systems were simulated for 0.5, 1.0, or 2.0 μs (total simulation length > 10 μs), whereas each AA system was simulated 3 times for 100 ns (total simulation length 2.4 μs, Table S1). CG and AA simulations were conducted using the leapfrog integrator with time steps of 20 and 2 fs, at a reference temperature of 323 and 310 K, respectively, and at a reference pressure of 1 bar. Temperature was coupled using velocity rescale [START_REF] Bussi | Canonical sampling through velocity rescaling[END_REF] and Nosé-Hoover 99 thermostats with coupling constant of 1ps À1 , respectively. Pressure was coupled with semiisotropic Parrinello-Rahman barostat 100 with relaxation time of 12 or 5 ps, respectively.

| CG simulations

CG simulations were conducted using the beta version of Martini 3 force field with nonpolarizable water and optimized parameters for palmitoylated cysteines 101 and glycosylated asparagine 102 where needed. The center of mass of the reference structure was scaled with the scaling matrix of the pressure coupling. The nonbonded pair list was updated every 20 steps with the cutoff of 1.1 nm. Potentials shifted to zero at the cutoff of 1.1 nm and a reaction-field potential with ε rf = ∞ were used for treatment of the van der Waals and electrostatics interactions.

| AA simulations

AA simulations were conducted using the CHARMM36m force field. 103 The covalent bonds to hydrogens were constrained using the LINear constraint solver (LINCS) algorithm. 104 The nonbonded pair list was updated every 20 steps with the cutoff of 1.2 nm. Force-based switching function with the switching range of 1.0-1.2 nm and particle mesh Ewald (PME) method with 0.12 nm Fourier grid spacing and 1.2 nm cutoff were used for treatment of the van der Waals and electrostatics interactions.

The simulations were performed using JURECA. 105

| Analysis

Visual molecular dynamics (VMD) 106 and in-house scripts were used for analysis of the TMD tilt angle (α) and rotational (azimuthal) angles (β, φ, ψ) of the TMD, H2, and H3. The tilt angle was defined as the angle between the TMD helix axis and the normal to the membrane (axis Z). The rotational angle was defined as the angle between the C α radial vector of a reference residue (Phe23, Cys43, and Asn66) and the X-Z plane; the helix was aligned so that its axis was in the X-Z plane (Figures 567). We used the Ward's method from MDTraj 107 to group the dataset into four clusters based on pairwise root mean square deviation (RMSD) of coordinates of backbone particles. Density distributions of TMD, H2, and H3 atoms were calculated using the density tool from GROMACS. The secondary structure in the E protein was monitored using the Timeline plugin (version 2.3) for VMD. 106 PCA was performed on the positions of the C α atoms (AA simulations) and backbone particles (CG simulations) using the covar and anaeig tools from GROMACS. Average positions of the membrane boundaries and curvature values were calculated using g_lomepro, version 1.0.

FIGURE 1

 1 FIGURE 1 Structure of the SARS-CoV-2 envelope (E) protein monomer with possible co-and post-translational modifications. (A) Schematic model showing a fully palmitoylated and glycosylated E protein. Transmembrane domain is shown in blue and amphipathic helices H2 and H3 are shown in green and red. (B) Conformations of the unmodified E protein observed in coarse-grained simulations. Positions of the transmembrane helix were aligned for clarity; helices H2 and H3 are mobile

2. 3 |

 3 Induction of curvature by the E proteinIn all of the conducted simulations, we observed induction of curvature by the E protein: the membrane bends toward the side where the C-terminus is located in both CG (Figure7A) and atomistic (FigureS8) simulations. The effect is also observed in larger systems containing

FIGURE 2 FIGURE 3 FIGURE 4

 234 FIGURE 2 Comparison of the E protein conformations observed in atomistic (AA) and coarse-grained (CG) simulations using principal component analysis (PCA). (A) The scree plot for the top 10 PCA eigenvalues. First two components describe $64% of structural variations. (B) Comparison of the conformational ensembles observed in AA (colored) and CG (gray) simulations projected onto PC1 and PC2. The data for CG simulations only are shown on the right. Starting conformations for AA simulations are labeled with stars. Trajectories from the first, second, third, and fourth sets of AA simulations are shown in red, blue, green, and orange, respectively. (C) Conformational changes associated with PC1. (D) Conformational changes associated with PC2. The structures are colored from blue to red according to the PC projection value. Approximate membrane position is shown with the dashed lines

FIGURE 5

 5 FIGURE 5 Orientation of TMD in POPC bilayer in coarse-grained (CG) and all atom (AA) simulations. (A) Distributions of the tilt angles. (B) Distributions of the axial rotation angles. Vertical lines indicate average values. (C) Definitions of the tilt (α) and axial rotation (β) angles

FIGURE 6

 6 FIGURE 6 Effects of palmitoylation on orientation of the helix H2 relative to the membrane in coarse-grained simulations. Rotation of Cys43 relative to the membrane plane (Y) viewed from the N-terminus is analyzed. (A, B) Distributions for the Cys43 rotation angles relative to the membrane plane for different PTMs. Vertical lines indicate average values. (C) Schematics showing the H2 orientation with helical wheel projections for selected variants. Palmitoylation affects the orientation of H2 because the respective side chain becomes more hydrophobic

FIGURE 7

 7 FIGURE 7 Induction of curvature by the E protein monomer in coarse grained (CG) simulations. Upward displacement of each membrane boundary is shown in red, and downward displacement is shown in blue. (A) Induction of curvature by the full-length E protein. (B) Membrane deformation by an isolated TMD. The membrane is thinned around the TMD, but no buckling is observed. (C) Membrane deformation by isolated H2 and H3 helices in CG simulation. The membrane is bent toward the α-helices H2 and H3. Each panel shows an exemplary protein position; positions of the membrane boundaries are averaged over the trajectory length

FIGURE 8

 8 FIGURE 8 Monomeric E protein partitions into the curved region with the N-terminus localizing to the concave side independent of the starting position. (A) Simulations with the membrane buckled in one dimension. (B) Simulations with the membrane buckled in two dimensions. The dashed box shows the unit cell of the simulation

FIGURE 9

 9 FIGURE 9 Properties of the pentameric E protein. (A) Conformations of the five protomers within the pentamer in 5 μs CG simulation based on the nuclear magnetic resonance model. 51 (B) Generation of curvature by pentameric E protein: the membrane bends toward the C-terminal helices H2 and H3. Upward displacement of each membrane boundary is shown in red, and downward displacement is shown in blue. Each panel shows an exemplary protein position; positions of the membrane boundaries are averaged over the trajectory length. (C) Repartitioning of the pentameric E protein into the curved region with the N-terminus localizing to the concave side independent of the starting position. The dashed box shows the unit cell of the simulation

  Our simulations show that the SARS-CoV-2 E protein in monomeric form has rich structural dynamics. The transmembrane helix is tilted in the membrane, and amphipathic helices move freely around it. Posttranslational palmitoylation anchors the helix H2 cysteines to the membrane. The E protein induces and senses membrane curvature, both in monomeric and pentameric forms.These findings are in accordance with experimental observations, while providing a detailed description of the E protein structure. Our work showcases MD simulations as an important complementary technique allowing comprehensive inquiry in the case where the experiment is complicated: when the protein is partially disordered and may undergo different combinations of CPTMs.

Figure S1 .

 S1 Figure S1. Conformations of the E protein observed in all-atom simulations. Positions of the

Figure S2 .

 S2 Figure S2. Conservation of the secondary structure of the E protein in AA MD simulations.

Figure S3 .

 S3 Figure S3. Average positions of TMD, H2 and H3 relative to the membrane in CG and AA

Figure S4 .

 S4 Figure S4. Orientation of TMD in POPC bilayer in coarse-grained (CG, trajectory 1) and all

Figure S5 .

 S5 Figure S5. Rotation angles of Cys43 relative to the membrane plane viewed from the N-

Figure S6 .

 S6 Figure S6. Effect of Asn66 glycosylation on orientation of the helix H3 relative to the

Figure S7 .

 S7 Figure S7. Induction of curvature by the E protein monomers in the system containing 4

Figure S8 .

 S8 Figure S8. Induction of curvature by the E protein monomer in atomistic simulations. Upward

Figure S9 .

 S9 Figure S9. Average positions of TMD, H2 and H3 relative to the membrane in CG simulations

Figure S10 .

 S10 Figure S10. Quantification of curvature induction by the monomeric (A) and pentameric (B)

Table S1 .

 S1 List of the simulated systems and their properties.

	17 AA	Structure and dynamics of the SARS-CoV-2 envelope protein monomer No PTM (1) Mixture: 34215 Na+(151) 0.1×3	11×11×12
	POPC (100/100), Number of lipids (by leaflet) POPE (50/50), POPI (20/20), Alexander Kuzmin, Philipp Orekhov, Roman Astashkin, Valentin Gordeliy, Ivan Gushchin * Cl-(93) (hexagonal) № Type Protein Number of Number of ions Time, μs Simulation box size, nm 3 18 AA No PTM (2) 32677 Na+(146) 0.1×3 11×11×12 waters (0.15 mM) POPS (10/10), Cl-(88) (hexagonal)
	1, 19 AA CG	No PTM No PTM (3)	POPC (206/221) CHOL (20/20)	7706 32243	Na+(84) Na+(145)	2, 0.5 0.1×3	12×12×11 11×11×12
	E-mail for correspondence: ivan.gushchin@phystech.edu 2	2. 108 Cl-(86) Cl-(87)		(rectangular) (hexagonal)
	3 20 AA CG	CYSP40 No PTM (4)	POPC (205/221)	7711 35190	Na+(84) Na+(155)	0.5 0.1×3	12×12×11 11×11×12
						Cl-(86) Cl-(97)		(rectangular) (hexagonal)
	4 21	CG CG	CYSP43 1D buckled	POPC (206/221) POPC (946/950)	7580 64695	Na+(82) Na+(710)	0.5 1	12×12×11 25×20×21
	,		along X axis			Cl-(84) Cl-(714)		(rectangular) (rectangular)
	22		2×No PTM
	5	CG	CYSP44	POPC (205/221)	7609	Na+(83)	0.5	12×12×11
	23	CG	2D buckled	POPC (759/761)	52249	Cl-(85) Na+(573)	1	(rectangular) 21×21×20
			along X, Y			Cl-(577)		(rectangular)
	6	CG	CYSP40/43 2×No PTM	POPC (206/221)	7599	Na+(83)	0.5	12×12×11
						Cl-(85)		(rectangular)
	24	CG	4×No PTM	POPC (3998/3997) 105411 Na+(10493)	1	50×50×10
	7	CG	CYSP40/44	POPC (205/220)	7605	Na+(83) Cl-(10501)	0.5	12×12×11 (rectangular)
						Cl-(85)		(rectangular)
	25	CG	Pentamer	POPC (374/425)	17252	Na+(185)	5	17×17×12
	8	CG	CYSP43/44 No PTM	POPC (204/221)	7600	Na+(83) Cl-(195)	0.5	12×12×11 (rectangular)
			(Feig lab)			Cl-(85)		(rectangular)
	9 26	CG CYSP40/43/4 CG Pentamer	POPC (205/219) POPC (373/431)	7616 17274	Na+(83) Na+(185)	0.5 5	12×12×11 17×17×12
			4 No PTM			Cl-(85) Cl-(195)		(rectangular) (rectangular)
	10	CG	ASNG66 (Feig lab + NMR TMD)	POPC (202/221)	12709	Na+(139) Cl-(141)	0.5	12×12×15 (rectangular)
	11 27	CG CG	TMD, no PTM Pentamer CYSP43	POPC (222/219) POPC (376/423)	7934 17196	Na+(88) Cl-(86) Na+(184) Cl-(194)	0.5 5	17×17×12 12×12×11 (rectangular) (rectangular)
	12 28	CG CG	H2+H3, no PTM Pentamer CYSP44	POPC (207/225) POPC (375/421)	7654 17240	Na+(82) Cl-(86) Na+(185) Cl-(195)	0.5 5	17×17×12 12×12×11 (rectangular) (rectangular)
	13 AA 29 CG	No PTM (1) 1D buckled 2×Pentamer along X-axis	POPC (174/180) POPC (2184/2185) 135702 31286	Na+(84) Cl-(86) Na+(1484) Cl-(1504)	0.1×3 1	36×30×21 11×11×12 (hexagonal) (rectangular)
	14 AA	No PTM (2) No PTM	POPC (171/179)	31304	Na+(85)	0.1×3	11×11×12
			(Feig lab)			Cl-(87)		(hexagonal)
	15 AA	No PTM (3)	POPC (169/179)	30882	Na+(84)	0.1×3	11×11×12
						Cl-(86)		(hexagonal)
	16 AA	No PTM (4)	POPC (174/179)	31104	Na+(84)	0.1×3	11×11×12
						Cl-(86)		(hexagonal)
				1

Table S2 .

 S2 Average values and standard deviations (σ) of the tilt and rotation angles of TMD and H2 observed in different simulations. See Figures5 and 6for definitions.

	Type	System	Lipid	Mean	σ_α,	Mean	σ_β,	Mean	Δφ, ° σ_φ, °
				α, °	°	β, °	°	φ, °
	CG	No PTM	POPC	26.9	8	34.1	29.4	77.7		22.5
	CG	CYSP40	POPC	26.6	8.9	34.7	31.2	85.4	+7.7	20.5
	CG	CYSP43	POPC	26.7	8.4	32.4	29	79.3	+1.6	19.7
	CG	CYSP44	POPC	27.1	8.3	40.3	28.8	106.6 +28.9 19.1
	CG	CYSP40/43	POPC	27.7	8.9	34.8	30.9	80.4	+2.7	20.4
	CG	CYSP40/44	POPC	26.1	8.6	42.9	26.5	109.9 +32.2 19.6
	CG	CYSP43/44	POPC	26.9	8	36.6	31.1	96.8	+19.1 17.6
	CG	CYSP40/43/44 POPC	26.4	8.3	31.2	30.4	103	+25.3 17.2
	CG	ASNG66	POPC	26.2	8.5	38.7	26.9	78.6	+0.9	22.5
	CG	TMD, no PTM POPC	25.5	7.7	29.4	31.4	-	-	-
	CG	H2+H3,	POPC	-	-	-	-	82.3	+4.6	26.4
		no PTM
	AA	No PTM	POPC	40.2	9.9	48.1	22.6	85.3		49.2
	AA	No PTM	Mix	32.6	11.6	50.5	27.2	83.7		32.6

Table S3 .

 S3 Properties of the TM helices in experimentally determined structures of single-helical viroporins.

	Protein and	Method	Membrane	TM residues	Tilt angle	PDB ID Reference
	virus name		mimetic	(length)
	M2, Influenza A	NMR	DOPC/DOPE	26-46 (21)	32° (N-term)	2L0J	[3]
					22° (C-term),
					pH 7.5
	M2, Influenza A	NMR	DMPC	26-46 (21)	30° (N-term)	2KQT	[4]
					19° (C-term),
					pH 7.5
	M2, Influenza A	X-ray	OG	25-46 (22)	~35° (N-term),	3BKD	[5]
					pH 7.3
	M2, Influenza A	X-ray	OG	25-46 (22)	16° (pH 7.5-8)	3LBW	[6]
					31° (pH 6.5)
					38° (pH 3-4)
	M2, Influenza B	NMR	POPE,	6-28 (23)	14° (pH 7.5)	6PVR,	[7]
			POPC/POPG		20° (pH 4.5)	6PVT
	Monomeric	NMR	DMPC	8-25 (18)	25°	2N28	[8]
	Vpu, HIV-1
	Vpu, HIV-1	NMR	DOPC/DOPG	8-25 (18)	13°	1PI7,	[9]
						1PI8
	E, SARS-CoV	NMR	LMPG	8-35 (28)	~24°	5X29	[10]

ACKNOWLEDGMENTS

We are grateful to Pavel Buslaev for advices on using the Martini force field. The authors gratefully acknowledge the computing time granted through JARA on the supercomputer JURECA at Forschungszentrum Jülich. Ivan Gushchin was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement #075-00337-20-03, project FSMG-2020-0003). Valentin Gordeliy and Roman Astashkin were supported by the Commissariat à l'Energie Atomique et aux Energies Alternatives (Institut de Biologie Structurale) -Helmholtz-Gemeinschaft Deutscher Forschungszentren (Forschungszentrum Jülich) Special Terms and Conditions 5.1 specific agreement.

DATA AVAILABILITY STATEMENT Molecular dynamics trajectories have been deposited to Zenodo and are available using the following links: https://doi.org/10.5281/ zenodo.4740706 (CG simulations of monomeric protein); https://doi. org/10.5281/zenodo.4743386 (AA simulations of monomeric protein); https://doi.org/10.5281/zenodo.5232499 (CG simulations of pentameric protein).

CONFLICT OF INTEREST

The authors declare no competing interests.

AUTHOR CONTRIBUTIONS

Ivan Gushchin designed and supervised the project; Philipp Orekhov and Valentin Gordeliy helped with the project design; Alexander Kuzmin performed simulations with the help of Philipp Orekhov; Alexander Kuzmin and Ivan Gushchin analyzed the results and prepared the manuscript; Philipp Orekhov, Roman Astashkin, and Valentin Gordeliy helped with data analysis and manuscript preparation.

PEER REVIEW

The peer review history for this article is available at https://publons. com/publon/10.1002/prot.26317.

Supporting Information Supporting Text

Supporting Tables S1-S3

Supporting Figures S1-S10

Supporting References

Supporting Text

Effect of glycosylation on helix H3

As shown previously [1,2], E protein may be glycosylated. There are two potential glycosylation sites: Asn48 and Asn66, yet the former is too close to the membrane to be efficiently glycosylated [2], and its mutation to aspartate didn't change the glycosylation pattern [1]. Here, we find that glycosylation of Asn66 has a pronounced effect on dynamics of the helix H3 (Figure S4). In the unmodified protein, we observed two major orientations of H3: the first one with the hydrophobic residues Val62 and Leu65 facing the membrane, and the less frequent orientation almost completely opposite to it, with H3 stacking with H2 while being slightly above it (Figure S4). Glycosylation resulted in abolishment of the second orientation, presumably due to the potential steric conflict between the sugar moiety and H2 (Figure S4A,D); the helix was also slightly rotated in the most frequent orientation (Figure S4A,E).


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M Le Gouil

Mériadeg Bactériologie-Virologie

Mme Lelong-Boulouard

Véronique Pharmacologie

M Macrez

Richard Médecine D'urgence

M Mittre Hervé

M Molin

Arnaud Génétique

M Saint-Lorant

Guillaume Pharmacie

M Toutirais

Olivier Immunologie

M Veyssiere

M Villain

Cédric Gériatrie

Maitre De

Universités De Médecine

Générale M Humbert

Xavier Maitres De

Associés Des

Mi-Temps Mme

Armand Audrey Médecine

M Bansard

Mathieu Médecine

M Couette

Noel Mme

Jaegher De

Sophie

M Pithon

M Sainmont

Mme Schonbrodt

Mme Debruyne

Chirurgie maxillo-faciale et stomatologie

A mes parents, Dadou et Mouti qui m'ont transmis à leur façon la passion de la médecine et qui m'ont permis de réaliser mes rêves. Bien gagné la médaille.

A mes frères et soeurs, Alexandre, Charles, Marie-Anne, Sixtine et Sophie, ainsi qu'à leur conjoints, Claire, Margaux, Umberto, Roxane, et Jules, qui n'ont pas toujours compris ce que je faisais mais qui sont quand même contents pour moi. A mes neveux, Léa, Arthur et Auguste, plein de vie et de voix.

A mes grands-parents qui ne sont plus là mais qui veillent sur moi chaque jour.

A ma famille Vouvrillonne qui m'a nourri, consolé et supporté pendant les 7 premières années.

A mon oncle Eric, merci de m'avoir amené à tous mes concours de PACES.

A toute ma famille MICHEL-SANTOSUOSSO et ma future nouvelle famille SAYEGH-DANIEL.

Présentation du sujet

Un accident vasculaire cérébral (AVC) est une perte brutale de la fonction neurologique due à un événement vasculaire intracrânien ischémique ou hémorragique. Chaque année, on estime à 140 000 le nombre de patients hospitalisés en France pour un AVC. C'est la deuxième cause de décès et la première cause de handicap à long terme chez l'adulte.

A un an, on estime que 20% des patients décèdent. Une déficience de la marche survient chez plus de 75% des survivants et 25% ne récupèrent pas à 3 mois.

La marche est un indicateur important des domaines d'activités et de participation de la

Classification Internationale du Fonctionnement, du Handicap et de la Santé (CIF). Retrouver la capacité de marche est un objectif très important pour les patients après un AVC.

La rééducation est un processus complexe qui nécessite une prise en charge multidisciplinaire incluant le patient et ses objectifs, la famille et les amis, les autres soignants, les médecins, les infirmières, les kinésithérapeutes et les ergothérapeutes, les orthophonistes, les animateurs, les psychologues, les nutritionnistes, les assistants sociaux etc. L'entraînement à la marche assisté par robot est utilisé depuis 1980 pour aider les patients souffrant de dysfonctionnement du mouvement causé par des troubles neurologiques. L'entraînement à la marche assisté par des dispositifs électromécaniques et robotiques peuvent être utilisés pour la rééducation de la marche après un AVC et pour l'entraînement aux tâches répétitives.

Les dispositifs électromécaniques peuvent être séparés en deux groupes : les dispositifs à effecteurs terminaux (par exemple le "G-EO System", le "Lokohelp", le "Gait trainer") et les exosquelettes (par exemple le "LOPES" (Lower extremity powered exoskeleton) et le "Lokomat").

Plusieurs études ont montré que les patients qui reçoivent un entrainement à la marche assisté par robot en association avec une rééducation conventionnelle après un AVC ont plus de chances de parvenir à une marche indépendante que les personnes qui reçoivent un entraînement à la marche sans ces dispositifs, mais ne sont pas susceptibles d'améliorer la vitesse de marche ni la capacité de marche. Cependant, le type de robot et la population analysée n'étaient pas clairement définie.

Depuis 2007, le centre de réadaptation de Granville " Le Normandy " est équipé d'un Lokomat (Hocoma, Volketswil, Suisse), qui est un appareil d'entraînement à la marche assisté par robot avec entraînement sur tapis roulant et support du poids du corps. La principale différence avec l'entraînement sur tapis roulant est que les jambes du patient sont guidées par le dispositif robotique contrôlé par un ordinateur.

Des études antérieures, menées en particulier sur le Lokomat, ont donné des résultats mitigés pour la récupération de la marche et n'ont pas trouvé d'effets supérieurs de l'entraînement robotique sur les résultats de la marche par rapport à une thérapie conventionnelle. En revanche, ces études ont montré que le Lokomat pouvait être utilisé en toute sécurité sans nuire aux résultats des patients. L'objectif de cette étude observationnelle était d'évaluer l'effet de la rééducation avec le Lokomat ® sur la capacité de marche des patients hémiplégiques. L'influence de certains facteurs a également été étudiée.

Liste des Abréviations

Liste des Tableaux et figures

Annex 1 : modified Functional Ambulation Category.

Introduction

A stroke is a sudden loss of neurological function due to an ischemic or hemorrhagic intracranial vascular event [START_REF] Emro | Stroke, Cerebrovascular accident | Health topics[END_REF]. Each year, an estimated 140 000 patients in France are hospitalized for a stroke which is the second cause of death and the first cause of long-term disability in adults [START_REF]Accident vasculaire cérébral (AVC) ⋅ Inserm[END_REF].

At one year, it is estimated that 20% of patients die. Walking dysfunction occurs in more than 75% of survivors and 25% do not recover at 3 months (3).

Walking is an important indicator of the activities and participation domains of the International Classification of Functioning, Disability and Health (ICF) [START_REF]International Classification of Functioning, Disability and Health (ICF)[END_REF]. Regaining the ability to walk is a very important goal for patient after stroke.

Rehabilitation is a complex process requiring multidisciplinary care including the patient and their goals, family and friends, other caregivers, physicians, nurses, physical and occupational therapists, speech-language pathologists, recreation therapists, psychologists, nutritionists, social workers, and others [START_REF] Winstein | Guidelines for Adult Stroke Rehabilitation and Recovery[END_REF].

Robotic-assisted gait training (RAGT) has been used since 1980 to assist patients with movement dysfunction caused by neurological disorders [START_REF] Van Vliet | A new challenge--robotics in the rehabilitation of the neurologically motor impaired[END_REF]. Electromechanical-assisted gait training and RAGT can be use in walking rehabilitation [START_REF] Tefertiller | Efficacy of rehabilitation robotics for walking training in neurological disorders: a review[END_REF] and provide repetitive task training (RTT).

Electromechanical devices can be differentiated into end-effector and exoskeleton devices.

Examples of end-effector are "G-EO System", "Lokohelp", "Gait trainer". Examples of exoskeleton are "LOPES" (Lower extremity powered exoskeleton) and "Lokomat" (8) [START_REF] Mehrholz | Electromechanical-assisted gait training after stroke: A systematic review comparing end-effector and exoskeleton devices[END_REF].

Several reviews have shown that people who receive RAGT in combination with physiotherapy after a stroke are more likely to achieve independent walking than people who receive gait training without these devices but are not likely to improve the walking speed nor the walking capacity. However, the type of RAGT and the analyzed population were not clear (10) [START_REF] Bruni | What does best evidence tell us about robotic gait rehabilitation in stroke patients: A systematic review and meta-analysis[END_REF].

Since 2007, the rehabilitation center of Granville « Le Normandy » is equipped with a Lokomat (Hocoma, Volketswil, Switzerland), which is a robotic assisted gait training with treadmill training and body weight support. The main difference with the treadmill training is that the patient's legs are guided by the robotic device controled by a computer.

Previous researches, carried out particularly on the Lokomat, have found mixed results

for gait recovery and have not found superior effects of robotic training compared to conventional therapy on walking outcomes (12) (13) but have shown that Lokomat could be safely used at no detriment to patient outcomes [START_REF] Louie | Efficacy of an exoskeleton-based physical therapy program for non-ambulatory patients during subacute stroke rehabilitation: a randomized controlled trial[END_REF].

The objective of this observational study was to assess the effect of the Lokomat ® rehabilitation on the walking capacity of hemiplegic patients. The influence of certain factors was also studied.

Material and methods

Study design

This was a retrospective, observational study conducted at « Le Normandy » Rehabilitation Center in Granville, France. Patients selected were hospitalized in the center for a rehabilitation after an ischemic or a hemorrhagic stroke between 2007 and 2018.

The inclusions criteria for this study were All vascular hemiplegic patients were eligible to use the Lokomat unless they had one of the following contraindications: obesity (more than 130kg), major cognitive impairment, hemianopia, any co-morbidity or disability other than hemiparesis that would preclude gait training, urinary catheter or gastrostomy or major spasticity.

The training program consisted of 20 sessions of Lokomat, 30 minutes per session, five days a week (from Monday to Friday) for four consecutive weeks. The first session allowed to get familiar with the robotic equipment and take measurements for the installation.

All patients had conventional gait training in addition with the Lokomat. (15)(5)

A trained physical therapist supervised the treatment and adjusted treadmill speed, guidance and body-weight support. Level of body weight support and guidance progressively decreased, and treadmill speed progressively increased [START_REF] Iosa | Driving electromechanically assisted Gait Trainer for people with stroke[END_REF].

Each patient benefited from a clinical examination by a doctor and a physiotherapist on arrival before starting rehabilitation, as part of their care. No additional examination or functional tests were performed if they were not indicated as part of the rehabilitation.

All patients have agreed to undergo the therapy.

The protocol was approved by ethics committee of the university hospital of Caen, France.

Definitions and measurements

Medical data were collected retrospectively from medical records and included: sex, age, type of stroke (ischemic or hemorrhagic), time since the onset, modified Functional Ambulation Categories (mFAC) before rehabilitation, date of the stroke and results of the six minutes walk test (6MWT) before and after rehabilitation.

The 6MWT is commonly used in people with stroke undergoing rehabilitation (17) [START_REF] Cheng | Validation of stroke-specific protocols for the 10-meter walk test and 6-minute walk test conducted using 15-meter and 30-meter walkways[END_REF], to classify a patient into a degree of functional limitation. Patient is asked by his physiotherapist to walk as fast as possible for 6 minutes, with or without walking aide. The reference value is calculated by a formula including gender, height and weight. For an adult, normal range is 407-535meters (19) (20) [START_REF] Arcuri | Validity and Reliability of the 6-Minute Step Test in Healthy Individuals: A Crosssectional Study[END_REF].

The mFAC ( 22) (Annex 1) is a scale that evaluate the capacity of ambulation and the need of technical assistance. Classes 0 and 1 define a patient not able to walk, and classes 2 up to 8 define a walking patient with or without technical assistance.

The mFAC was evaluated before the rehabilitation and was therefore a measure of the initial severity of the stroke about motricity.

Statistical Analysis

Our outcome was the difference between the 6MWT before and after rehabilitation to determine the evolution of the walking capacity and factors associated with an improvement.

Results of mFAC scale was categorized in two groups, ambulatory patients with or without technical assistance (mFAC 2 to 8) and non-ambulatory patient (mFAC 0 and 1).

Modified FAC class 0 means non-walking. We decided that it meant a 6MWT of 0 meters. For other mFAC classes, missing data from the 6MWT were excluded.

Time since stroke was categorized in two groups, described as early rehabilitation (0-3 months) and late rehabilitation (3-6 months) for the acute phase after stroke (23):

Date of stroke was categorized in two periods, before and after 2016. In 2016, the thrombectomy protocol has been generalized and standardized in Caen University Hospital for all our region (24) [START_REF] Braud | Prise en charge de l'AVC ischémique à la phase aiguë en Basse-Normandie : étude descriptive et analyse des facteurs limitant l'accès à la thrombectomie mécanique[END_REF]. We made the hypothesis that more thrombectomies were performed after 2016 possibly leading to a factor of better prognosis of gait rehabilitation.

Categorical data are presented as counts and percentages. For continuous data, normality was tested using the Kolmogorov-Smirnov test and assessment of histograms.

Distributions of all continuous data were skewed and were therefore described with medians and interquartile ranges (IQR) and then compared with the use of the Mann-Whitney test or the Spearman correlation coefficient, as appropriate.

Bivariate analyses were performed to compare, first, the 6MWT before and after rehabilitation using a paired Mann-Whitney test, and then to assess the association between the gain in 6MWT and the following characteristics : sex, age, type of stroke, rehabilitation phase, mFAC before rehabilitation, and period.

We then fitted a multivariable quantile regression model using the modified version of the Barrodale and Roberts algorithm, and confidence intervals for the estimated parameters were produced by inverting a rank test without assuming that the errors were independent and identically distributed. We chose to model the 50% quantile, i.e. the median, that allows us to obtain the adjusted augmentation of the median gain in 6WMT for each variable and 95% confidence interval. Quantile regression model was used instead of an ordinary least squares (OLS) model because OLS residuals were non-normal, highly skewed and heteroskedastic.

The final multivariable model was based on all variables associated with the evolution of the 6MWT in bivariate analysis. P-value was 0.20 for inclusion in the model. Age and sex were forced in the model regardless of their p-value as well as variables of clinical interest, including the type of stroke and the date of the stroke as a proxy of thrombectomy treatment.

All analyses were two-sided with a 5% type I error and were completed in R 4.1.3 software, using « quantreg » package for quantile regression model.

Results

We retrospectively reviewed 268 medical records with stroke in the Lokomat Database between 2007 and 2018.

Thirty three records were excluded because there were not first stroke or first Lokomat session. Patients with incomplete Lokomat sessions were likewise excluded.

A total of 235 patients were included. When the results of the 6MWT before or after rehabilitation was missing, we could not calculate the difference. It was the case for 72 patients and this patient were not included in the analysis (Figure 1).

There were 151 men with a median age of 66 years. Sixty-eight percent had an ischemic stroke, and 73% of patients were in early rehabilitation phase. There were 71% of nonambulatory patients.

The characteristics of the population is summarized in Table 1 We found a median 6MWT before the program of 0 meters (IQR [0-76]) and median 6MWT was 62 meters (IQR [0-169]) after the program, corresponding to a median gain of 18 meters (IQR [0-74,5]) (p<0,01) (Figure 1).

Table 2 shows the results of the bivariate and multivariate analysis. Two factors were significantly associated with the 6MWT gain. No significant difference was observed according to the age, the correlation coefficient of Spearman was -0,15 by years (p=0.064). This result was close to significant.

After adjustment, the association between the evolution of the 6WMT and respectively the rehabilitation phase and severity of stroke before rehabilitation was less strong but remained significant.

74.69)).

There was a decrease of 0.56m per year at the 6MWT, and this result was not significant (95% CI -0.99 ; 0.16).

The others factors were not significant in multivariate analysis.

Finally, no significant interaction between the mFAC before rehabilitation and the rehabilitation phases was found, meaning that the effect of rehabilitation phase on the evolution of the 6WMT was not shown to be different between initially walking patients and non-walking patients.

No significant interaction between the period before or after 2016 and the type of stroke was found. There was no difference of the effect of period on the evolution of the 6MWT between ischemic or hemorrhagic. We inferred that there was no difference in the effect of period on the evolution of 6MWT in ischemic patients.

In Table 3, we compared the group with missing data with the study group. There were significantly more missing data in the group unable to walk at the onset.

Discussion

The aim of this retrospective monocentric study of the effects of robotic gait rehabilitation with Lokomat ® in combination with conventional therapy was to describe the evolution of the 6MWT in patients with stroke.

There were 163 patients included in our study.

At the beginning, the median 6MWT was 0 meters (IQR [0-76]) and after the rehabilitation, we found a median 6MWT of 62 meters (IQR [0-169]). The median gain was 18 meters (IQR [0-74.5]).

The gain was significant (p<0,001) and was greater in patients in the early rehabilitation phase versus in the late rehabilitation phase (21.22 Although we did not find significant differences with the others factor, we did not have any problems with feasibility.

In previous studies, the robotic rehabilitation by Lokomat has not shown a greater effect on walking capacity than conventional rehabilitation (12) ( 13), but has shown than it could be safely used with no harm to patient outcomes [START_REF] Louie | Efficacy of an exoskeleton-based physical therapy program for non-ambulatory patients during subacute stroke rehabilitation: a randomized controlled trial[END_REF]. These studies provide an early look at the efficacy of robotic devices but are limited in the number of participants enrolled. In addition, the details of the training programs of Lokomat were not clear.

In our 11-years study, we have included a large number of patients, and each patient had a conventional therapy and the same protocol of Lokomat and their results were comparable.

At our knowledge, no studies have been conducted analyzing the factors associated with a gain of walking capacity after rehabilitation by Lokomat.

The relevance of an improvement in 6MWT of 18 meters depends on the Minimal Clinically Important Difference (MCID) for 6MWT after a stroke. Fulk (26) calculated MCID of 65 meters as an improvement of a perception of an important change in walking ability estimated by the patient. Although we found an inferior gain, this aims should be interpreted with caution cause their population had a mean of 6MWT at 80 +/-50 meters initially. In our study, 70% of the patients were unable to walk before the rehabilitation and had a median 6MWT of 0 meters IQR [0 -76.0]. It was clinically relevant for a patient to be able to gain 18 meters when they could not walk before rehabilitation (for example, moving around indoors and doing bed-chair transfers) [START_REF] Lyden | Using the National Institutes of Health Stroke Scale[END_REF]. Nevertheless, more than 25% of patient had reached the MCID of 65 meters after the program because the third interquartile range was 74.5 meters.

The gain was better when we compared the early versus the late rehabilitation phases.

These results are consistent with a Cochrane review [START_REF]Electromechanical-assisted training for walking after stroke -Mehrholz[END_REF]. All these results are also associated with the concept of brain plasticity; the best time for boosting brain plasticity is within 3 months after a stroke [START_REF] Wolpert | Principles of sensorimotor learning[END_REF]. The robotic rehabilitation should start as early as possible particularly in early stage of stroke recovery.

We also found that the gain on the 6MWT was higher when the patient was ambulatory at the onset.

In the Cochrane reviews [START_REF]Electromechanical-assisted training for walking after stroke -Mehrholz[END_REF], they found that non ambulatory patient at the start of the study had greater benefits regarding walking speed after rehabilitation by RAGT.

These results are not comparable with ours because walking speed was not calculated on a 6MWT (which assesses walking perimeter) but rather on a 5 or 10-meter walk test (which assesses walking speed).

The motor severity of a stroke was measured by the mFAC scale. Usually, the National Institutes of Health Stroke Scale (NIHSS) score is used to determine the severity of a stroke [START_REF] Lyden | Using the National Institutes of Health Stroke Scale[END_REF]. However this data was not seen in medical records.

Nevertheless, in the randomized controlled trial Schwartz and all (29), they describe an improvement of FAC and NIHSS scores in subacute stroke patient using RAGT in comparison with conventional therapy. These results suggest that these two scores evolve together.

Regarding age, we found a median loss per year of 0.56 meters. Although this result is almost significant 95% CI [-0.99; 0.16], we believe that this loss is not clinically relevant. There were no feasibility problems in each age group.

We did not find a significant difference for Lokomat rehabilitation between males and females.

Although it is generally believed that hemorrhagic stroke survivors have better neurological and functional prognoses than ischemic stroke survivors, a recent study shows that the results are discordant [START_REF]Do stroke patients with intracerebral hemorrhage have a better functional outcome than patients with cerebral infarction?[END_REF]. Only one study compared the walking performance of hemorrhagic and ischemic stroke patients in RAGT rehabilitation and found significant improvement at 6MWT in both groups but the gain was not significantly better in any of them [START_REF]Hemorrhagic versus ischemic stroke: Who can best benefit from blended conventional physiotherapy with robotic-assisted gait therapy? ResearchGate[END_REF]. We also did not find any difference between ischemic and hemorrhagic stroke patient.

There were no feasibility issues for these groups.

The thrombectomy has been shown to improve the prognosis for recovery after an ischemic stroke [START_REF] Wahlgren | Mechanical thrombectomy in acute ischemic stroke: Consensus statement by ESO-Karolinska Stroke Update 2014/2015, supported by ESO, ESMINT, ESNR and EAN[END_REF]. In 2016, in our region, the practice of thrombectomy was generalized and standardized. This meant that patients for whom thrombectomy was indicated, benefited from it more generally than before 2016.

We sought to study whether this generalization of thrombectomy had an effect. We did not find difference but we estimated the practice of thrombectomy in relation to the period and selected only patients admitted to our center for stroke and not patients who received thrombectomy or not cause we did not have the information. Further research is needed in order to evaluate this point.

There were more missing data about the 6MWT in the group unable to walk (mFAC 0-1) at the onset. We have 45 missing data about the 6MWT before the rehabilitation and 56 after; in a total of 72 patients. These patients were not included in the analysis so it is possible that the median gain was overestimated.

This limitation is related to the retrospective analysis. Only a prospective study could answer this question.

Because of the retrospective nature of our study, we do not know if all the patients who met the criteria for using the Lokomat benefited it. The assessment was therapist dependent.

As the years went by, therapists could be less apprehensive about using the Lokomat on a larger population.

Also, the Lokomat was not always available and therefore the use was not possible all the time, for example periods of maintenances and when the schedule was full. Thus, there may have been a selection bias.

It is important for future research to focus on the identification of patients for whom an exoskeleton would truly benefit. Our study adds to the emerging literature surrounding the use of exoskeletons in stroke rehabilitation. It provides information regarding the factors of the patients who had a best gain but a prospective and randomized research is needed to confirm these first results.

Robotic tools are not only used for gait rehabilitation. They also allow for early verticalization of patients thanks to its system of partially or totally body weight support.

It also helps to prevent falls [START_REF] Lahrabli | L'hémiplégique vasculaire en milieu rééducatif : quels sont les facteurs de risque de chute : à propos de 30 cas[END_REF] and the complications that can result from them (fractures, post-fall syndrome etc.) [START_REF] Pérennou | Incidence, circonstances et conséquences des chutes chez les patients en rééducation après un premier accident vasculaire cérébral[END_REF].

It allows for a lower intensity of exercise training than conventional physiotherapy. It is proved that RAGT is less energy-consuming and cardiorespiratory stressful than walking without robot-assistance [START_REF] Lefeber | The immediate effects of robot-assistance on energy consumption and cardiorespiratory load during walking compared to walking without robot-assistance: a systematic review[END_REF] and can be used in patient with cardiovascular diseases.

In another study, RAGT has shown to have the potential to improve cardiopulmonary fitness [START_REF] Chang | Effects of robot-assisted gait training on cardiopulmonary fitness in subacute stroke patients: a randomized controlled study[END_REF].

In the future, it would be interesting to study different protocols on well-defined populations in order to offer the most appropriate protocol for the patients.

Conclusion

Our findings suggest that the use of Lokomat associated with conventional physiotherapy should be used for adults after stroke, particularly in ambulatory adults and in the first three months after a stroke.

Larger randomized prospective clinical trials are needed to establish the efficacy of Lokomat training for the recovery of walking after stroke, to identified patient for whom it will be highly effective and to propose differents protocols according to patient characteristics. Ces opinions doivent être considérées comme propres à leurs auteurs ».

A

  Madame le Docteur Anne PESKINE. Vous me faites l'honneur d'avoir encadré et dirigé ma thèse. Merci de m'avoir proposé ce travail. Merci de votre accompagnement et de votre aide précieuse tout au long de sa préparation. A Monsieur le Docteur Alexis RUET. Tu me fais l'honneur de participer à mon jury de thèse. Merci de m'avoir encadré lors de mes stages et pour tout ce que tu m'as appris. A Monsieur le Docteur Philippe BUSSON. Vous me faites l'honneur de participer à mon jury de thèse. Merci d'avoir pu m'enseigner la neurologie entre deux COVID. A Monsieur le Docteur Rémy DE MIL. Merci d'avoir réalisé le dur travail de statistiques et d'avoir relu et corrigé cet article patiemment. Je n'aurais pas pu effectuer ce travail sans vous. A Messieurs Xavier ROPERO et Olivier ARKOUN pour votre travail sur le recueil de donné au cours de votre stage au Normandy. Je dédie ce travail et ces longues années d'étude :

A

  mes témoins Camille et Diane, pour toutes ces soirées potins de La Riche, les escapades Parisiennes et les vacances au camping. Vous êtes un soutien précieux. A mes copains Tourangeaux, bien dispersés à présent et en particulier Jeremy et Mélanie, Adrien, Cornélia et le petit Maël, Dylan et Yohan la ZAD, Quentin, Noé et Olga, Irène, Loïc, Mathias et Nicolas. On ne se voit pas souvent mais c'est comme si c'était hier. A la team MPR et en particulier Anaëlle ma première rencontre. Aux Avranchinais Henri, Sylvain, Antoine, Fanny, Alicia et Raphael et leur chat à 3 pattes. Aux amis Caennais et fans de pizza Cyril, Alix, Arvin, Charlie et Aude. A tous les membres des équipes des centres de rééducation de Aunay sur Odon, du CHU de Caen, et de Granville, ainsi que des services de gériatrie du CHU de Caen et de médecine 2 du CH d'Avranches, qui m'ont tous accueillis avec bienveillance. Et à toi Jimmy, mon soutien de tous les jours depuis notre rencontre. Tu m'as partagé ta détermination et ton ambition tout au long de mon parcours. Merci de ta patience et de tes encouragements. Au passé, à nos beaux jours à venir, et à notre 25 juin. Je t'aime cinquantedeux factoriel et chaque jour un peu plus.

Figure 1 :

 1 Figure 1 : The flow diagram of the study.

Figure 2 :

 2 Figure 2 : Results of the walking test.

-( 1 )

 1 adult age 18 or older -(2) first hemiparetic stroke based on clinical examination or Magnetic Resonance Imaging (MRI) -(3) occurrence of the stroke less than 6 months before rehabilitation -(4) patient should have trained with Lokomat for a first complete program (including 20 sessions), eventual subsequent session were not taken into account The exclusions criteria were -(1) recurrent stroke -(2) non complete session of Lokomat All patients who had a Lokomat session were included in a Lokomat Database stating their pathology.

  Time since onset : Patients in early rehabilitation phase significantly improved their walking distance on the 6WMT compared with patients in late rehabilitation phase (40.0 meters IQR [0-85.0] vs 0 meters IQR [0-20,3] p < 0,001). Severity of stroke : mFAC before rehabilitation was also significantly associated with the evolution of the 6WMT. Initially, ambulatory patients had indeed a better recovery than nonambulatory patients (55.0 meters IQR [22.0-93.0] vs 0 meters IQR [0-50,0] p < 0,001). There are no significant difference of median gain between men and women (24.0 meters IQR [0-68.0] vs 11,5 meters IQR [0-78.8] p=0,4), between ischemic and hemorrhagic strokes (20.0 meters IQR [0-75.3] vs 15.0 meters IQR [0-60.0] p=0,8) and between the pre-2016 and post-2016 periods (13,0 meters IQR [0-71,5] vs 43,0 meters IQR [0-80] p=0,27).

Figure 1 :

 1 Figure 1 : The flow diagram of the study.

Figure 2 : 1 :

 21 Figure 2 : Results of the walking test.

Table 3 :

 3 Range; Q1-Q3 first and third quartiles Comparison of missing data from the 6MWT range; Q1-Q3 first and third quartiles « Par délibération de son Conseil en date du 10 Novembre 1972, l'Université n'entend donner aucune approbation ni improbation aux opinions émises dans les thèses ou mémoires.

Table :

 : Baseline characteristics of the patients.

	Table : Bivariate analysis and Multivariate quantile regression analysis of the gain at 6MWT.
	Table : Comparison of missing data from the 6MWT

  The median gain of the 6MWT for less severe stroke patients (able to ambulate before the program) was 34 meters longer than non-ambulatory patients(34.22 meters (95% CI,

The median gain in 6WMT was indeed greater of 21 meters for patients in early rehabilitation phase compared to patients in late rehabilitation phase

(21.

22 meters (95% CI, 1.86 -44.93)),

  meters (95% CI [1.86 -44.93]), and in ambulatory patients versus non-ambulatory patients at the onset (34.22 meters 95% CI [16.20 -74.69]).

Table 2 :

 2 Bivariate analysis and Multivariate quantile regression analysis of the gain at 6MWT.

	Variable	Bivariate analysis	Multivariate quantile
			regression analysis
		Median Gain
		6MWT [Q1-Q3]

Remerciements

A Monsieur le Professeur Emmanuel TOUZE. Vous me faites l'honneur d'avoir accepté de présider ce jury.

Sommaire Introduction...............................................................................................................................1 Materiel et Methods..................................................................................................................3 Results.....................................................................................................................................6 Discussion................................................................................................................................8 Conclusion..............................................................................................................................11 References.............................................................................................................................12 Annexes.................................................................................................................................15

Annexes

Annex 1 : modified Functional Ambulation Category. Class 0 : Can not walk or needs assistance from more than one person.

Class 1 : Can walk with the permanent assistance of a person. Les données médicales ont été recueillies : sexe, âge, type d'AVC, phase de rééducation, Functional Ambulation Categories modified (mFAC), date de l'AVC et résultat du test de marche de 6 minutes. Le critère de jugement était la différence du test de marche de 6 minutes (TM6) avant et après la rééducation afin de déterminer l'évolution de la marche et les facteurs associés à un gain. Résultats : Nous avons inclus 235 patients. Le gain médian au TM6 était de 18m (p<0,01). Deux facteurs étaient significativement associés au gain du TM6 : phase précoce versus phase tardive (gain de 21m) et patients marchant versus non marchant initialement (gain de 34m). Il n'y avait pas de différence significative de gain entre les hommes et les femmes, entre les types d'AVC et entre les périodes avant et après 2016. Il y avait une diminution de 0,56m par année au TM6, et ce résultat était non significatif. Conclusion : Il y avait un gain significatif du TM6après la rééducation par Lokomat. Ce gain était plus important chez les patients en phase précoce et lorsque le patient était initialement déambulant. MOTS CLES : Rééducation, Accident Vasculaire Cérébral ; Hémiplégie ; Robotique ; Lokomat.

TITRE DE LA THESE EN ANGLAIS :

Effects of robotic gait rehabilitation with Lokomat ® in vascular hemiplegia: a single-center retrospective observational study.

RESUME DE LA THESE EN ANGLAIS :

Introduction : Gait rehabilitation after a stroke is a major concern in physical medicine and rehabilitation. Since 2007, « Le Normandy» rehabilitation center is equipped with robotic assisted gait training named "Lokomat"; vascular hemiplegic patients benefit from it. This study was conducted to investigate the effect of Lokomat on the walking performance of hemiplegic patients after a stroke and to identify the influence of certain factors. Methods: This was a retrospective, observational study conducted at « Le Normandy » rehabilitation center in Granville, France. All adult patients hospitalized between 2007 and 2018 for a first stroke within the last six months who completed a full Lokomat program were included. Medical data were collected : sex, age, type of stroke, time since the onset, modified Functional Ambulation Category (mFAC), date of stroke and results of the six minutes walking test (6MWT) before and after rehabilitation. The outcome was the difference between the 6MWT before and after the rehabilitation to determine the evolution of the walking capacity and factors associated with a gain. Results: We included 235 patients. The median gain on the 6MWT was 18 meters (p<0,01). Two factors were significantly associated with the 6MWT gain : rehabilitation phase and severity of stroke. The median gain was 21.22 meters (95% CI [1.86 ; 44.93]) for patients in early rehabilitation phase versus late rehabilitation phase. The median gain was 34.22 meters (95% CI [16.20 ; 74.69]) for ambulatory patients at the onset compared to non-ambulatory patient. There were no significant difference of median gain between men and women (3.22 meters 95% CI [-11.86 ; 19.48]), between ischemic and hemorrhagic strokes (1.67 meters 95% CI [-10.59 ; 17.03]) and between the post-2016 and pre-2016 periods (6.22 meters 95% CI [-7.99 ; 32.78]) There was a decrease of 0.56 meters (95% CI [-0.99 ; 0.16]) per year at the 6MWT, and this result was not significant. Conclusion : There was a significant improvement in the 6MWT after robotic rehabilitation by Lokomat. This improvement was greater in patients in early rehabilitation phase and when the patient was initially ambulatory. KEY WORDS : Rehabilitation ; Stroke ; Hemiplegia ; Robotic ; Lokomat.