Bryan C Mounce

Teresa Cesaro

Gonzalo Moratorio

Jan Peter

Anna Hooikaas

Scott W Yakovleva

Everett Clinton Werneke

Enzo Z Smith

Etienne Poirier

Matthieu Simon-Loriere

Prot

Enzo Z Poirier

Everett Clinton Smith

Carole Tamietti

Sandrine Vitry

Etienne Simon-Loriere

Romain Volle

Cécile Khou

Matthieu Prot

Marie-Pascale Frenkiel

Kenneth A Stapleford

Anavaj Sakhuntabai

Francis Delpeyroux

Nathalie Pardigon

Marie Flamand

Giovanna Barba-Spaeth

Monique Lafon

Mark R Denison

Marco Vignuzzi
email: marcovignuzzi@pasteur.fr

Inhibition of polyamine biosynthesis is a broad-spectrum strategy against RNA viruses

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Emerging viruses present an extraordinary threat to human health, given their sudden and unpredictable appearance and the potential for rapid spread among the human population. Recent emergence of chikungunya virus (CHIKV) in the Americas 1 , Middle East respiratory syndrome coronavirus (MCoV) in the Arabian peninsula [START_REF] Holmes | MERS-CoV enigma deepens as reported cases surge[END_REF] and Ebola virus in Western Africa 3 highlight the struggles to contain outbreaks. A significant hurdle is the availability and implementation of antiviral therapies to treat the infected or protect at-risk populations, such as family members and healthcare workers. While several compounds show promise in vitro and in vivo, these recent outbreaks underscore the need to accelerate drug discovery, as well as to explore therapeutic avenues of broad antiviral activity. In this report, we describe the antiviral effects of difluoromethylornithine (DFMO, eflornithine), a potent suicide inhibitor of ornithine decarboxylase (ODC1) [START_REF] Metcalf | Catalytic irreversible inhibition of mammalian ornithine decarboxylase (E.C.4.1.1.17) by substrate and product analogs[END_REF] , a critical enzyme in polyamine synthesis. We show that DFMO is active against diverse families of RNA viruses. Our data show that polyamines are a general requirement for viral RNA synthesis. DFMO is bioavailable and currently used in treating trypanosomiasis [START_REF] Milord | Efficacy and toxicity of eflornithine for treatment of Trypanosoma brucei gambiense sleeping sickness[END_REF] and hirsutism [START_REF] Wolf | Randomized, double-blind clinical evaluation of the efficacy and safety of topical eflornithine HCl 13.9% cream in the treatment of women with facial hair[END_REF] , and given its tolerance in humans [START_REF] Carbone | Bioavailability study of oral liquid and tablet forms of αdifluoromethylornithine[END_REF] , may be an immediately available and viable option for controlling infection during outbreaks of significant concern.

Polyamines are small, positively-charged molecules involved in several cellular processes, including proliferation [START_REF] Gerner | Polyamines and cancer: old molecules, new understanding[END_REF] , apoptosis [START_REF] Schipper | Involvement of polyamines in apoptosis. Facts and controversies: Effectors or protectors? Semin[END_REF] , ion channel regulation [START_REF] Williams | Interactions of polyamines with ion channels[END_REF] , DNA conformation [START_REF] Thomas | Polyamine-mediated conformational perturbations in DNA alter the binding of estrogen receptor to poly(dG-m5dC).poly(dG-m5dC) and a plasmid containing the estrogen response element[END_REF] , and transcription [START_REF] Law | Polyamine regulation of ribosome pausing at the upstream open reading frame of S-adenosylmethionine decarboxylase[END_REF][START_REF] Frugier | Synthetic polyamines stimulate in vitro transcription by T7 RNA polymerase[END_REF] . The biosynthesis of polyamines is regulated by several enzymes, but the conversion of ornithine into putrescine by ornithine decarboxylase (ODC1) is the bottleneck step 14 . Although early work shows that polyamines are included in virions [START_REF] Gibson | Compartmentalization of spermine and spermidine in the herpes simplex virion[END_REF][START_REF] Lanzer | Polyamines in vaccinia virions and polypeptides released from viral cores by acid extraction[END_REF][START_REF] Fukuma | Polyamines in bacteriophage R17 and its RNA[END_REF] or facilitate viral replication [START_REF] Hodgson | Ornithine decarboxylase activity in uninfected and vaccinia virus-infected HeLa cells[END_REF][START_REF] Isom | Stimulation of ornithine decarboxylase by human cytomegalovirus[END_REF] , their general role in viral infection is not established for RNA viruses [START_REF] Tuomi | Inhibition of Semliki Forest and herpes simplex virus production in alpha-difluoromethylornithine-treated cells: reversal by polyamines[END_REF][START_REF] Pohjanpelto | Polyamine depletion of cells reduces the infectivity of herpes simplex virus but not the infectivity of Sindbis virus[END_REF] . We utilized CHIKV to study the role of polyamines in alphavirus infection. CHIKV titers were significantly reduced (p=0.010) in BHK-21 cells treated for four days with 500 μM DFMO and completely rescued with the addition of exogenous polyamines (Fig. 1a). The complete phenotypic reversal with exogenous polyamines suggests that DFMO treatment was non-toxic to cells, which we corroborated with viability assays (Supplementary Fig. 1). The biogenic polyamines putrescine (Put) and spermidine (Spd) also fully rescued viral titers when added individually, but the polyamine precursor, ornithine (Orn), did not (Supplementary Fig. 2), indicating that the biogenic polyamines are required for robust viral replication. Additionally, CHIKV titers were not enhanced with polyamine treatment alone, indicating that viral replication is maximized with endogenous levels of polyamines (Supplementary Fig. 3). We observed the same phenotype in Aedes albopictus C6/36 cells (Fig. 1b), primary C57/Bl6 murine embryonic fibroblasts (Fig. 1c), and green monkey kidney Vero-E6 cells (Fig. 1d). For Sindbis virus (SINV), a closely-related alphavirus, we also observed reduced titers (p=0.002) with DFMO treatment and full rescue with exogenous polyamines (Fig. 1e).

To confirm that DFMO was reducing polyamine content of treated cells, we performed immunofluorescence with an antibody directed against the biogenic polyamines (spermine, spermidine, and putrescine). BHK-21 cells were treated with DFMO and subsequently infected with CHIKV containing mCherry-tagged nsp3 [START_REF] Kümmerer | Construction of an infectious Chikungunya virus cDNA clone and stable insertion of mCherry reporter genes at two different sites[END_REF] to visualize replication compartments. Upon DFMO treatment, polyamine signal was significantly reduced (Fig. 1f). With CHIKV infection, no gross difference was noted in polyamine content or localization, and polyamines did not appear to localize precisely with replication compartments. In addition, we directly visualized individual polyamines within untreated or DFMO-treated cells by thin-layer chromatography [START_REF] Madhubala | Polyamine Protocols[END_REF] .

DFMO treatment reduced the total amount of polyamines by approximately 73% (Fig 1g). As a further confirmation that polyamines are critical to CHIKV replication, we used another ODC1 inhibitor, POB, and observed similar reduction in viral titers (Fig. 1h).

DFMO-mediated knockdown of viral titers of Semliki Forest Virus relied on a four-day pretreatment [START_REF] Tuomi | Synthesis of Semliki-forest virus in polyamine-depleted baby-hamster kidney cells[END_REF] . For CHIKV, BHK-21 cells required a 48-hour pretreatment to significantly impact titers (p=0.038), further reduced with 72-or 96-hour pretreatment (Fig. 1i). This pretreatment was effective at MOI 0.1 and 1, but not 10 for both CHIKV and SINV (Supplementary Fig. 4).

Previous reports described a role for polyamines in herpes simplex virus-1 [START_REF] Wallace | The Effect of Polyamines on Herpes Simplex Virus Type 1 DNA Polymerase Purified from Infected Baby Hamster Kidney Cells (BHK-21/C13)[END_REF] , Semliki Forest virus [START_REF] Tuomi | Synthesis of Semliki-forest virus in polyamine-depleted baby-hamster kidney cells[END_REF] , and hepatitis C virus [START_REF] Korovina | Biogenic polyamines spermine and spermidine activate RNA polymerase and inhibit RNA helicase of hepatitis C virus[END_REF] polymerase activity or RNA replication, and human cytomegalovirus viral assembly [START_REF] Gibson | L-alphadifluoromethylornithine inhibits human cytomegalovirus replication[END_REF] . Entry of CHIKV was not impacted, as viral RNA was equivalent (p=0.282) in untreated and DFMO-treated cells at 2 hours post infection (Fig. 2a). Furthermore, we observed significant inhibition of RNA synthesis for both genomic (p=0.001) and subgenomic (p=0.039) messengers at 24 hours (Fig. 2a,b). SINV viral genomes were similarly reduced (Fib. 2c). Although polyamines did not specifically localize with replication compartments as assayed by immunofluorescence (Fig. 1f), we asked whether polyamines interact with the replication complex or with viral RNA. BHK-21 cells were infected for 16 hours, lysed and immunoprecipitated with an anti-polyamine antibody to analyze coimmunoprecipitation of replication components. The viral nsp2 (helicase, methyltransferase), nsp3 and nsp4 (polymerase) were indeed found to coimmunoprecipitate (Fig. 2d). To provide additional evidence of this interaction, we performed RNA immunoprecipitation with the same anti-polyamine antibody. Both genomic and subgenomic RNA co-immunoprecipitated with polyamines (Fig. 2e), further implicating them in viral RNA replication.

To test whether polyamines directly stimulate viral transcription, we measured polymerase activity of both CHIKV and SINV using an in vitro replication (IVR) assay with replication complexes purified from infected cells. Membrane fractions from infected cells were incubated in buffer alone, or buffer containing exogenous polyamines, and polymerization was measured by radionucleotide incorporation after a 3-hour incubation. Samples incubated with polyamines exhibited a significant increase (p=0.021 and p=0.015 for CHIKV and SINV, respectively) in viral RNA synthesis (Fig. 2f, quantitated in Fig. 2g,h). Similar analyses by qRT-PCR and using the CHIKV replicon system exhibited the same phenotype (Fig. 2i). In these assays, polyamines could be either directly stimulating the replication complex, or stabilizing templates and nascent genomes. To discern between these hypotheses, viral RNA was incubated in IVR reaction mixtures using membranes from uninfected cells, in the presence or absence of polyamines. Rather than stabilizing viral RNA, we observed significant degradation of viral genomes when incubated with polyamines (Supplementary Fig. 5). Taken together, our data support that polyamines are directly stimulating replication complexes activity.

To understand the sensitivity of CHIKV to DFMO, we infected BHK-21 cells treated with a range of concentrations, from 1 μM to 10 mM and determined the IC 50 to be 35.55 µM (13.05 to 96.08 μM) (Fig. 3a), which is near the measured plasma concentration in patients treated with oral DFMO [START_REF] Carbone | Bioavailability study of oral liquid and tablet forms of αdifluoromethylornithine[END_REF] . At concentrations above 100 μM, titers were significantly reduced (p<0.002 for each), and no virus was recovered with 10 mM treatment. Similar results were obtained for SINV (Supplementary Fig. 6).

Additionally, a 2013 Caribbean strain of CHIKV exhibited significant sensitivity to DFMO that was completely reversed with exogenous polyamine treatment (Fig. 3b).

While the required pre-exposure treatment may be a viable option for susceptible populations during an outbreak, such as medical professionals treating infected individuals or cohabitants of individuals with communicable diseases, treating the broader population prior to infection is impractical for alphaviruses. To test whether DFMO could reduce viral titers if given after infection, we infected BHK-21 cells with CHIKV at a MOI of 0.0001 (100 viral particles), to mimic a more natural infectious dose, and treated cells with 1 mM DFMO just after infection. CHIKV titers were significantly reduced (p=0.0004) by 32 hours and remained significantly suppressed (p<0.003) through 72 hours (Fig. 3c). To further investigate potential clinical applications of DFMO, we examined whether it could be combined with another antiviral pharmaceutical, ribavirin [START_REF] Beaucourt | Ribavirin: a drug active against many viruses with multiple effects on virus replication and propagation. Molecular basis of ribavirin resistance[END_REF] . We found that DFMO synergizes with 400 μM ribavirin to significantly reduce CHIKV titers (p=0.038 and 0.0553) in BHK-21 cells beyond either of the antivirals individually (Fig. 3d).

Polyamines are ubiquitous molecules and as such, we wished to determine whether their requirement, and the effects of DFMO that we observed for alphaviruses, were more broadly applicable. Thus, we explored several RNA viruses from different taxonomic families: the positive-sense coronavirus Middle Eastern respiratory syndrome virus (MCoV, Fig. 3e); the positive-sense picornaviruses coxsackievirus B3 (CVB3, Fig. 3f), poliovirus (PV, Fig. 3g), and enterovirus-71 (EV-71, Fig. 3h); the positive-sense flaviviruses dengue fever virus-1 (DENV1, Fig. 3i), Zika virus (ZIKV, Fig. 3j), Japanese encephalitis virus (JEV, Fig. 3k), yellow fever virus (YFV, Fig. 3l), and West Nile virus (WNV, Fig. 3m); the negative-sense rhabdoviruses vesicular stomatitis virus (VSV, Fig. 3n) and rabies virus (RABV, Fig. 3o); and the negative-sense, segmented bunyavirus Rift Valley fever virus (RVFV, Fig. 3p). Despite the diversity in viral family and cell types, DFMO treatment significantly reduced viral titers for all viruses (p<0.05 for all), and in all cases the infection phenotype was rescued by the addition of exogenous polyamines. These results reveal that polyamines may be a general requirement for the replication of all RNA viruses.

Our results uncover a universal role of polyamines in RNA virus replication and a broad antiviral activity of DFMO against every RNA virus we tested. Although the relatively long pretreatment time required to knockdown endogenous polyamines precludes the use of DFMO in most situations of acute infection, we propose DFMO as a potential preventative or early-response therapeutic in particularly severe outbreaks. Given that DFMO is already clinically approved for treating African sleeping sickness in humans [START_REF] Milord | Efficacy and toxicity of eflornithine for treatment of Trypanosoma brucei gambiense sleeping sickness[END_REF][START_REF] Pepin | Difluoromethylornithine for arseno-resistant Trypanosoma brucei Gambinese sleeping sickness[END_REF] , the rapid implementation of DFMO during serious outbreaks may warrant immediate attention. Specifically, this relatively well-tolerated drug could provide added protection for at-risk populations, such as healthcare workers or family members of afflicted individuals, to prevent spread of disease. Furthermore, since many RNA virus infections are characterized by several days of incubation before onset of symptoms, treatment of individuals soon after suspected exposure may delay replication or reduce titers enough, in favor of the mounting immune response, to reduce mortality. Derivatives of DFMO and other molecules that manipulate the polyamine biosynthetic pathway have been developed as anticancer agents [START_REF] Casero | Recent advances in the development of polyamine analogues as antitumor agents[END_REF] as well as for the treatment of leishmaniasis [START_REF] Singh | Antileishmanial effect of 3-aminooxy-1-aminopropane is due to polyamine depletion[END_REF] . These drugs should also be examined as potent inhibitors of RNA viruses.

Figure 1 .

 1 Figure 1. DFMO exhibits antiviral activity against alphaviruses. Chikungunya virus (CHIKV) titers in (a) baby hamster kidney (BHK) fibroblasts, (b) Aedes albopictus (C6/36) cells, (c) C57/Bl6 murine embryonic fibroblasts, or (d) Vero-E6 epithelial cells treated for four days with 500 μM DFMO or in combination with exogenous polyamines and infected for 24 h. (e) Sindbis virus (SINV) titers in BHK fibroblasts treated for four days with 500 μM DFMO. (f) Representative immmunofluorescence against polyamines (green) and mCherry-tagged viral nsp3 in untreated and DFMO-treated (500 μM, four days) mock-or CHIKV-infected BHK cells for 8 h. (g) Representative thin layer chromatography analysis of cellular lysates from BHK cells treated with 500 μM DFMO or in combination with exogenous polyamines. Individual polyamines are labeled for putrescine (put), spermidine (spd), and spermine (spm). (h) CHIKV titers in BHK cells treated with the ODC1 inhibitor, POB (200 μM, four day pretreatment, 24 hpi). (i) CHIKV titers from DFMO-treated BHKs with increasing pretreatment times. * P ≤ 0.05, ** P ≤ 0.01, and *** P ≤ 0.001 versus untreated control or as indicated, one-tailed Student's T-test, n=3. Error bars represent mean ± one standard deviation. Immunofluorescence images and chromatograph are representative of three and two independent replicates, respectively.

Figure 2 .

 2 Figure 2. Polyamines stimulate RNA-dependent RNA polymerase activity. (a) Time-course of CHIKV genomes upon four-day 500 μM DFMO treatment (n=3). (b) CHIKV subgenomes and (c) SINV genomes as quantitated by qRT-PCR, following four-day 500 μM DFMO treatment and 24-h infection (n=4). (d) Western blot of coimmunoprecipitation of nsp2, nsp3, and nsp4 with polyamines (representative of two independent replicates). (e) RNA immunoprecipitation of CHIKV genomes and

Figure 3 .

 3 Figure 3. DFMO is broadly antiviral. (a) CHIKV titers at 24 hpi following four-day pretreatment with increasing concentrations of DFMO in BHK cells (n=3). (b) Caribbean-isolated CHIKV titers in BHK cells following DFMO pretreatment and 24-h infection (n=3). (c) CHIKV titer time-course following inoculation at MOI 0.0001 (10 PFU) and DFMO treatment 1 hpi at 1 mM (n=3). (d) Effect of DFMO pretreatment, ribavirin treatment, and combined treatment, on CHIKV titers (n=2). (e-p) Virus titers following DFMO treatment and rescue with exogenous polyamines. (e) Middle East respiratory syndrome coronavirus (MCoV) at 24 hpi in Vero81 cells (f) Coxsackvirus B3 (CVB3) titers at 24 hpi in HeLa cells (g) Poliovirus (PV) at 24 hpi in HeLa cells (h) Enterovirus-A71 (EV-A71) after 24-h infection of HeLa cells (i) Dengue virus-1 (DENV1) at 24 hpi in BHK-21 cells (j) Zikavirus (ZIKV) at 24 hpi in BHK-21 cells (k) Japanese encephalitis virus (JEV) at 24 hpi in BHK-21 cells (l) Yellow fever virus (YFV) at 96 hpi in BHK-21 (m) West Nile virus (WNV) at 24 hpi in BHK-21 cells (n) Vesicular stomatitis virus (VSV) at 16 hpi in BHK-21 cells at MOI 0.1. (o) Rabies virus (RABV) somatic inclusions measured in fluorescent intensity per cell at 24 hpi in primary cortical neurons (p) Rift Valley fever virus (RVFV) at 24 hpi in BHK-21 cells. * P ≤ 0.05 versus untreated control. Error bars represent mean ± one standard deviation. * P ≤ 0.05, ** P ≤ 0.01, and *** P ≤ 0.001 versus untreated control or as

Figure 3

 3 Figure 1

Acknowledgments

This work was supported by the European Research Council (ERC Starting Grant no. 242719), the French Government's Investissement d'Avenir program, Laboratoire d'Excellence "Integrative Biology of Emerging Infectious Diseases" (grant n°ANR-10-LABX-62-IBEID). the United States Public Health Service awards R01 AI108197 (M.R.D.) and U19 AI109680 (E.C.S) from the National Institutes of Health. We thank Andres Merits for nsp3-mCherry construct and Gorben Piljman for the CHIKV replicon. We thank Benjamin tenOever, Britt Glaunsinger, Vera Tarakanova, and Antonio Borderia for scientific discussions.


Alexandre Nicolas
email: alexandre.nicolas@polytechnique.edu

Lptms

Jörg Rottler
email: jrottler@physics.ubc.ca

Orientation of plastic rearrangements in two-dimensional model glasses under shear

The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional (2D) athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20 • about the direction of maximal local shear. The distributions of sizes and orientations of shear transformations display no substantial sensitivity to the shear rate. These results can notably be used to refine the description of rearrangements in elastoplastic models.

I. INTRODUCTION

Polydisperse foams, highly concentrated emulsions, molecular glasses, and bulk metallic glasses exhibit microscopically heterogeneous mechanical properties. As a result, these disordered solids do not deform affinely under shear. Instead, their deformation features bursty rearrangements of small groups of particles embedded in an otherwise elastically deforming medium. It is now well accepted that these microscopically localized shear transformations (ST) are the elementary carriers of plastic deformation in sheared amorphous solids [1,2]. By straining its surroundings, each ST gives rise to a characteristic long-range deformation halo around it [3,4], which mediates most collective effects in the material, such as cascades of rearrangements [5,6].

Based on this picture at the particle scale, mesoscale elastoplastic models of amorphous plasticity have been formulated, which divide the material into small regions (blocks) that are loaded elastically until they fail plastically [7]. The failure of a block is described as an ideal ST which partly dissipates the local stress and partly redistributes it to the other blocks. For an ST aligned with the principal direction of the macroscopic shear in d-dimensional space, the Green's function G for the nonlocal redistribution of the shear stress satisfies

G(r, θ) C cos[4θ + 2θ pl ]/r d (1)
in the plane of the transformation, with a dimensiondependent prefactor C, where (r, θ) are the polar coordinates in the frame centered on the plastic block and θ pl (defined precisely in Eq. ( 3)) refers to the orientation of the individual ST. The far field limit of this expression for G matches Eshelby's solution for a spherical inclusion endowed with a spontaneous strain [8], and was shown to suitably describe the disorder-averaged response of an amorphous solid to an ideal ST in atomistic simulations [9].

Mesoscale models, however, rest on several assumptions concerning the STs, including their idealized "Eshelby" nature, their equal size, and their orientation along the direction of maximal local shear [10,11], or even along the macroscopic shear direction in scalar models [12,13] (in this regard, ref. [14] is an exception). To give them stronger footing, experimental and numerical efforts have been made to characterize plastic rearrangements, as exposed in Sec. II. In particular, much attention has been paid to their shape and their size [1,[15][16][17], while the question of their orientation has remained largely unexplored, despite its obvious relevance for the buildup of spatial correlations between individual STs [18,19]. In this contribution, we simulate the shear deformation of a two-dimensional (2D) athermal model glass (described in Sec. III) with molecular dynamics in order to study the statistical properties of actual rearrangements for different shear rates. Strong emphasis is placed on their angles of failure. To this end, we propose (in Sec. III) and compare (in Sec. V) several numerical methods to extract these angles. We find that these angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20 • . Overall, the sizes and orientations of the detected rearrangements are fairly insensitive to the shear rate, but many of them actually differ from ideal STs. Even when the ideal ST description works reasonably well, local methods relying exclusively on the displacements (or forces) of the most active rearranging particles give poor estimates of the ST orientation; the latter is recovered if a broader selection of particles near the ST is considered.

II. PREVIOUS ENDEAVORS TO CHARACTERIZE PLASTIC REARRANGEMENTS

Leaving aside Schwarz's early attempts to classify rearrangements in a 3D foam at rest [20], Argon and Kuo were the first to report localized rearrangements in a disordered system, more precisely a 2D foam ('bubble raft') that was used as a model system for metallic glasses [1]. Interestingly, they mentioned two types of STs: sharp slips of rows of about 5 bubbles in length and more diffuse cooperative rearrangements of regions of 5 bubbles in diameter. In the 1980's, Princen studied the swap of neighbors between four bubbles (in 2D) to account for some rheological properties of foams and concentrated emulsions [21]; the detailed dynamics of this swap process were investigated much later in clusters of 4 bubbles [22]. In slowly sheared colloidal glasses, STs were directly visualized using confocal microscopy and their core was observed to be around 3 particle diameters in linear size [15]. In metallic glasses, direct visualization of STs cannot be achieved experimentally but estimates for their volumes can be obtained indirectly (e.g., via nanoindentation tests and their sensitivity to the shear rate) and typically correspond to a few dozen atoms (∼ 30 in the Zr-based glass studied with nano-indentation tests in [23]), with a possible dependence on the sample morphology (for instance, for a Ni-Nb metallic glass, the ST size was reported to decrease from 83 atoms to 36 atoms when the material was cast into a µm-thin film [16]).

Numerically, the most comprehensive characterization of rearrangements to date was performed by Albaret et al. [17] on a 3D atomistic model for amorphous bulk silicon under quasi-static shear. Rearrangements were detected by artificially reverting the applied strain increments at every step and deducing the irreversible changes that took place; the detected rearrangements were then modeled as a collection of Eshelby inclusions, whose sizes (or volumes V 0 ) and eigenstrains were fitted to best reproduce the displacement field measured during the actual strain increment. These inclusions were shown to account for all plastic effects visible in the stress-strain curves of these materials and the effective volume γ V 0 (where γ is the maximal shear component of ) was found to be exponentially distributed, with a typical size of 70 Å3 , while both dilational and contractional volumetric strains were observed. The evolution of the effective volume γ V 0 during the transformation was computed in [24] by detecting the saddle point; the value of the effective volume at this saddle point, called activation volume, was found to amount to around 20% of the final γ V 0 .

III. NUMERICAL MODEL AND METHODS

A. Model and simulation protocol

In order to get information on the morphology and orientation of STs, we perfom molecular dynamics simu-lations of an amorphous material (a glass) under simple shear, in 2D and in the athermal limit. The model glass is a binary mixture of A and B particles, with N A = 32500 and N B = 17500, of respective diameters σ AA = 1.0 and σ BB = 0.88, confined in a square box of dimensions 205σ AA × 205σ AA , with periodic boundary conditions. The system, at density 1.2, was prepared by quenching an equilibrated configuration at temperature T = 1 with a fast quenching rate dT dt = 2 • 10 -3 , at constant volume. The particles, of mass m = 1, interact via a pairwise Lennard-Jones potential,

V αβ (r) = 4 αβ σ αβ r 12 - σ αβ r 6 ,
where α, β = A, B, σ AB = 0.8, AA = 1.0, AB = 1.5, and BB = 0.5. The potential is truncated at r = 2.5σ AA and shifted for continuity. Simple shear γ is imposed at rate γ by deforming the (initially square) box into a parallelogram and remapping the particle positions. After an initial transient (20% strain), the system reaches a steady state, which is the focus of the present study.

In the athermal limit, the equations of motion read

dr i dt = v i ; m dv i dt = - i =j ∂V (r ij ) ∂r ij + f D i .
The dissipative force f D i experienced by particle i is computed with a Dissipative Particle Dynamics scheme, viz.,

f D i = - j =i ζw 2 (r ij ) v ij • r ij r 2 ij r ij (2)
where

w(r) ≡ 1 -r rc if r < r c ≡ 3σ AA , 0 otherwise.
Here, v ij ≡ v iv j denotes the relative velocity of particle i with respect to j, r ij ≡ r ir j , and ζ = 1/τ LJ controls the damping intensity (the effect of the damping was studied in [25]). Equations ( 2) are integrated with the velocity Verlet algorithm with a time step dt = 0.005. In all the following, we use τ LJ ≡ mσ 2 AA / as the unit of time and σ AA as the unit of length.

B. Detection of rearrangements

As expected, the simulations display fast localized rearrangements. Several measures are available to identify them and are known to yield comparable results [26]. In Fig. 1, we compute three of these diagnostics of nonaffinity on a typical snapshot of a simulation at shear rate γ = 10 -4 . These diagnostics are based on the displacements δu j of particles j during a short time interval [t, t + δt], with δt = 2. Panel (a) shows the amplitude of the minimized mean-square difference between the actual displacements δu j of particles j in a circular region C around a given particle r 0 and any set of affine displacements, i.e., displacements resulting from a uniform displacement gradient G during δt [2]. This measure of the nonaffine residual strain has become a quasi gold standard for identifying plastic rearrangements in amorphous solids. Panel (b) shows a simpler measure, namely the amplitude of the average kinetic energy of a particle averaged over δt. The motivation is that in an athermal system, only particles undergoing a rearrangement are expected to have large marginal velocities. Lastly, in panel (c) we consider the magnitudes of the (linearized) forces f

d 2 min = min G rj ∈C [δu j -δu 0 -G • (r j -r 0 )] 2
(H) i = -j H ij (t) • δu j ,
where

H ij (t) = ∂ 2 V
∂rirj is the Hessian matrix at time t. These are the forces that effectively drive plastic rearrangements. As discussed by Lemaître [19], they also localize in regions of high non-affine strain.

Figure 1 confirms that the three methods studied give very similar results. Accordingly, for convenience, we choose to use a criterion based on kinetic energies to detect rearrangements. More precisely, particles with a kinetic energy larger than an arbitrary threshold e min are considered to be rearranging; the threshold value is lowered to 3 /4 e min for the neighbors of rearranging particles, in order to obtain more compact ST shapes, where two particles are defined as neighbors if they are separated by a distance smaller than 2. Finally, rearranging particles are partitioned into clusters of neighbors, each corresponding to an individual ST (clusters with fewer than 3 particles were discarded). The distributions p(S) of sizes of the resulting clusters for distinct thresholds e min and distinct shear rates γ are represented on Fig. 3; neither the threshold nor the shear rate seem to considerably alter the seemingly slower-than-exponential (but fasterthan-power-law) decay of p(S). In the following, we shall see that all our results are fairly insensitive to these parameters e min and γ. We have also checked (though inexhaustively) that the distributions of orientations of rearrangements detected on the basis of the linearized forces

C. Methods to measure ST orientations

In order to study ST orientations, a rearrangement is likened to a circular Eshelby inclusion with an eigenstrain , i.e., a region whose stress-free state is not reached for a deformation (r) = 0, but for (r) = (if it were unconstrained). The eigenstrain can be split into a deviatoric part, associated with shape change, and a volumetric part, associated with local dilation, viz.,

= sin 2θ pl cos 2θ pl cos 2θ pl -sin 2θ pl + v 1 0 0 1 (3)
with 0. We define the ST orientation as the angle of failure θ pl ∈] -90 • , 90 • ]; it is thus the angle between the elongational principal direction of the ST and that of the macroscopic shear, as sketched in Fig. 2.

Fit to an Eshelby inclusion

We are now left with the problem of determining in practice. Drawing inspiration from Albaret et al. [17], we exploit the elastic field induced by an inclusion à la Eshelby. For homogeneous isotropic elastic media, the deformation in within any embedded elliptical inclusion will be constant. It naturally follows that, for a circular inclusion, the principal directions of in and will be identical, owing to symmetry arguments. Outside the circular inclusion (of radius a and centered at r = 0), the induced displacements δu are given by [27]

δu 1 (r) = x 1 8(1 -ν) ã2 2(1 -2ν) + ã2 ( 11 -22 ) + 2ã 2 ( 11 + 22 ) + 4 1 -ã2 x2 1 11 + x2 2 22
(4)

+ x 2 8(1 -ν) ã2 • 2 12 2(1 -2ν) + ã2 + 4 1 -ã2 x2 1 δu 2 (r) = x 2 8(1 -ν) ã2 2(1 -2ν) + ã2 ( 22 -11 ) + 2ã 2 ( 11 + 22 ) + 4 1 -ã2 x2 1 11 + x2 2 22 + x 1 8(1 -ν) ã2 • 2 12 2(1 -2ν) + ã2 + 4 1 -ã2 x2 2 ,
where r = (x 1 , x 2 ) and tildes denote distances rescaled by the norm of r (viz., x1 = x 1 /r).

For each rearranging cluster, the equivalent size a and eigenstrain components , v , and θ pl defined in Eq. ( 3) are calculated as the parameters minimizing the squared difference between the particle displacements δu i over δt = 2 and the theoretical expectations of Eq. ( 4), for all particles i that are at a distance between 2a and a large distance d max away from the cluster center; the quality of the fit will be measured by the relative squared difference χ 2 . (Note that the results turned out to be insensitive to the value of d max .) However, unlike ref. [17], the displacements δu i are not extracted from the actual dynamical simulation. Instead, in order to avoid the superposition of many STs, we run an auxiliary simulation for each rearranging cluster so as to measure the response induced only by this cluster. Pragmatically, starting from the configuration at t, we move particles j belonging to the cluster by a fraction α 1 of their actual displacements δu j , pin them to their new positions and obtain the response αδu i of the other particles to this local rearrangement by minimization This strategy, which we refer to as MD/Esh, will be our main method to access the ST morphology. One should nevertheless be aware that the results of the auxiliary simulations display a slight sensitivity to the details of the minimization procedure, but the consistency of our results will prove that this sensitivity can be overlooked.

Azimuthal modes of the displacements induced by the STs

A variant of this method may save us the cost of the fitting step. As mentioned in the introduction, the strain field δ induced by the shear part ( ) of an ST has a fourfold azimuthal symmetry. Therefore, focusing on δ xy for instance, the m = 4 azimuthal mode of δ xy (r) contains all information pertaining to the ST orientation (whereas the m = 2 component results from the dilational part v ). In practice, using the auxiliary simulations described above, we compute the local strain around each particle (i.e. the tensor δ i which minimizes the local non-affine deviations d 2 min introduced in Sec. III B), coarse-grain the xy-shear strain field into boxes of linear size r c = 3 (see Fig. 4), and compute the azimuthal Fourier modes c m of the resulting coarse-grained field δ c xy along a circle of radius r (much larger than the cluster size), viz.,

c m = 2π 0 e -imθ δ c xy (r, θ)dθ. ( 5
)
Calculating c 4 for the quadrupolar strain field and writing it as c 4 = |c 4 |e iφ4 , we find that the angle of failure is related to φ 4 via θ pl = φ 4 /2. We call this method Esh/azi.

Methods exclusively based on the forces or displacements of rearranging particles

The two methods described above involve minimization steps and/or additional (auxiliary) simulations and are therefore numerically costly. To bypass this cost, we will try to get information on the ST by using only the observed displacements δu i of the particles i within the rearranging cluster. A first idea is to compute the internal part σ of the local stress tensor: σ = -V -1 i f i ⊗r i , where V is the cluster size, the sum runs over all particles i in the cluster, each subjected to an average force f i and undergoing a displacement δu i between t and t + δt. The analogue for the displacements is the tensor M = -V -1 i δu i ⊗ r i . Positions r i are expressed relative to the cluster centers of gravity, and the mean force (or displacement) among the ST particles is drawn off the f i (or u i ). A yield angle θ pl can be extracted from these tensors by symmetrising them and writing their deviatoric (traceless) part s dev as

s dev = -α sin 2θ pl cos 2θ pl cos 2θ pl -sin 2θ pl , (6)
with a coefficient α > 0 (the minus sign comes from the sign convention used to define the Cauchy stress). These methods will be referred to as Loc. We have checked that they yield the same result as the inspection of the azimuthal mode c 4 of the response of an isotropic homogeneous elastic continuum to the set of pointwise forces

F i = f i , or F i ∝ δu i for the displacement-based version,
as computed by means of the Oseen-Burgers tensor. (We have underlined the word continuum to insist on the difference with the MD/azi method).

IV. CHARACTERISTICS OF STS

In this Section, we employ the method based on fitting rearranging clusters to Eshelby inclusions in order to unveil key characteristics of the rearrangements. Although STs are often idealized as pure shear transformations, the volumetric deformations are found not to be negligible in practice. In Fig. 5, we report the distributions of the dilational strengths πa 2 v and the shear strengths πa 2 of the STs detected at γ = 10 -5 , where πa 2 is the surface of the inclusion and v and were defined in Eq. ( 3). The corresponding plots at γ = 10 -4 , 10 -3 are very similar. As in ref. [17], we observe an exponential distribution of shear strengths, with a typical value around 0.3 here. One should however note that, since the present simulations are not quasi-static, the detected rearrangements (computed over δt = 2) often do not cover the whole transformation, which lasts for several time units.

Moving on to the ST orientations, we plot the distribution p(θ pl ) of angles of failure obtained at the three shear rates in Fig. 6(a). We observe no significant sensitivity to the shear rate. Besides, the central part of p(θ pl ) can be approximated by a normal distribution with standard deviation δθ pl = 23 • , but p(θ pl ) has heavier tails. If we discard the STs for which the elastic response significantly deviates from the Eshelby fit (Fig. 6(b)), the peak of p(θ pl ) sharpens slightly, but this does not strongly affect its shape.

It is interesting to compare these results with those predicted by a mainstream tensorial elasto-plastic model in simple shear [START_REF] Nicolas | The Flow of Amorphous Solids: Elastoplastic Models and Mode-Coupling Approach[END_REF]. The latter also showed a Gaussianlike distribution p(θ pl ) which was virtually insensitive to the shear rate, but which was by far narrower than the present ones, with standard deviations of 3 -4 • that could increase up to ≈ 7 • if cooperativity in the flow was enhanced by increasing the duration of plastic events or if elasto-plastic blocks were advected along the flow, instead of being static (see Chap. 9.2, p. 111, of [START_REF] Nicolas | The Flow of Amorphous Solids: Elastoplastic Models and Mode-Coupling Approach[END_REF]). In these models, angular deviations from the macroscopic shear direction θ pl = 0 are exclusively due to cooperative effects, whereby the stress redistributed during an ST (Eq. ( 1)) may load other blocks along a direction θ pl = 0, depending on their relative positions. The much broader distribution p(θ pl ) measured in the present atomistic simulations hints at the impact of the granularity of the local medium, which may favor failure along a direction distinct from that of the local loading.

V. COMPARISON BETWEEN DISTINCT METHODS TO MEASURE ST ORIENTATIONS

Having characterized the strengths and orientations of STs, we now discuss to what extent the ST characteristics can be extracted from methods that do not rely on fits to Eshelby inclusions.

A. Azimuthal mode of the induced strain

We start by considering the MD/azi method introduced in Sec. III C 2, which extracts the quadrupolar azimuthal mode of the xy-strain (from the auxiliary MD simulations) on a circle of radius r to determine θ pl . The angles of failure θ pl measured at distinct r (r = 17 and r = 23) are typically within ±10 • of one another (data not shown); there are outliers, but these very generally correspond to STs that strongly deviate from the Eshelby fits. Hereafter, we fix the radius at r = 17. Figure 7(a) shows that the individual MD/azi angles of failure agree relatively well with those determined with the MD/Esh method used so far, with absolute differences smaller than 20 • for STs with reasonable Eshelby fits.

B. Methods based on local forces or displacements

Turning to the results obtained with local methods (Sec. III C 3), we report that we have not found any correlation between the MD/Esh angles of failure and those determined with force-based local methods, whether it be the total force f i or the 'linearized' forces f (H) i (both being averaged over δt). On the other hand, displacementbased local methods broadly agree with MD/Esh, even though this does not immediately transpire from the scatter plot of Fig. 7(b). To prove the overall consistency of the methods despite this large noise, we split the detected STs into 10 • -wide bins depending on their orientation θ pl MD/Esh and, for each bin, plot the average angle θ pl Loc (measured with the displacement-based local method) in Fig. 8. On a technical note, one should mention that, to average over angles θ 1 , ..., θ n , we computed the circular average arg j e iθj . With these averaged data, the two methods are found to be in good accordance [29].

To shed light on the discrepancies in the one-to-one comparison, we extend the local method by including the displacements (measured in the auxiliary simulation) of all particles within a distance R of the center of gravity of the ST, instead of only the rearranging particles, with the expectation that both methods converge when R → ∞. In Fig. 9, we apply this method to STs detected at γ = 10 -5 for which a mismatch between θ pl Loc and θ pl MD/Esh was observed, despite fairly good fits to Eshelby inclusions. The figure suggests a reasonably quick convergence between the two methods, although the radii R at which convergence is reached strongly depend on the ST. This implies that the deficiency of the pristine Loc method stems from its biased selection of too few particles for the computation of the local tensor. . Differences ∆θ pl between the angles of failure found with the local method based on the displacements of all particles within a distance R of the ST center of gravity (in the auxiliary simulation) and the MD/Esh method for four STs that displayed good Eshelby fits (χ 2 < 1) but large discrepancies with the Loc method. For R = 0, the local method makes only use of the rearranging particles as identified by the kinetic energy threshold.

VI. CONCLUSION

This paper has introduced and compared three approaches to extract the size and orientation of STs in sheared amorphous solids. Rearranging particles were grouped into clusters based on a threshold criterion for the kinetic energy, which is reliable for athermal solids, and their displacements over a small time interval were recorded. Once these clusters are extracted, auxiliary simulations are performed in which the particles taking part in a given ST are displaced and the remainder is relaxed via energy minimization. In the first approach, which we consider to be the most general one, the resulting displacment field is then analyzed by fitting to the ideal "Eshelby" solution for the far-field displacements. In the second method, this fitting is avoided by instead computing the azimutal mode of the (coarse grained) strain field resulting from the ST. Angles of failure obtained from these two methods agree well with each other as long as the Eshelby fit itself is reasonable.

A third and purely local method that avoids auxiliary simulations altogether consists in computing the deviatoric part of the displacement (inertia) tensor after the rearranging clusters have been identified. These angles of failure agree less well with those from Eshelby fits in a point by point comparison, but can be shown to be overall consistent after the noise is reduced through averaging. The inclusion of a larger number of particles improves the agreement between the methods considerably. In practice, this extended local method is the most efficient one as long as the STs do not overlap.

It will be interesting to compare the angles of failure of STs to the local configurations prior to failure, in particular the direction of the maximal shear stress and the directional dependence of the local yield stress, which can be measured by deforming a small region embedded in a purely affinely deforming region [START_REF] Patinet | [END_REF]31]. Moreover, our results suggest that mesoscopic elastoplastic models [7] should be refined to better describe the deviations from the idealized Eshelby picture observed at the particle scale, and the sensitivity of their predictions to such microscopic details should be examined.

Figure 1 .

 1 Figure 1. Detection of plastic events via (a) the d 2 min criterion, (b) by the average kinetic energy of a particle and (c) the magnitude of the linearized "Hessian" forces (see text). The scale bar is 10 particle diameter.

Figure 2 .

 2 Figure 2. Representation of the angle of failure θ pl . The orange arrows indicate the elongational and contractional directions of an ideal ST, while the dashed line represents the elongational direction of the macroscopic shear.

Figure 3 .

 3 Figure 3. Distribution of sizes S of the rearranging clusters detected with the kinetic energy based criterion (a) for two different threshold values emin at γ = 10 -5 and (b) for three different shear rates γ with emin = 0.11. The thin dashed line in the top panel is proportional to exp(-S/S0) with S0 = 7.

  those shown below.

Figure 4 .

 4 Figure 4. Elastic reponse computed in the auxiliary MD simulations (see text) to a selection of three STs exhibiting a quadrupolar response. In the left column, particles in the ST are colored in orange, while the colors of the other particles depend on the norms of their displacements δui (warmer colors denote larger displacements). The arrows with wide shafts represent the directions of δui for a random subset of particles, while the (directions of) displacements represented by narrower arrows are the response to the best-fitting Eshelby inclusion. The figures shown are zooms on a 50 × 50 portion of the global system (of size 205×205). The right column presents the coarse-grained strain field δ c xy computed from the associated auxiliary simulations, in a 100 × 100 square around the cluster.

Figure 5 .

 5 Figure 5. Distribution of the dilational strengths πa 2 v (circles) and the shear strengths πa 2 (squares) of the STs detected at γ = 10 -5 (with threshold emin = 0.11). The dashed blue line is proportional to exp(-x/0.3)

Figure 6 .

 6 Figure 6. Distributions of angles of failure θ pl obtained with the MD/Esh method. (a) Comparison of p(θ pl ) between distinct shear rates γ. The dashed line represents a normal distribution with standard deviation δθ pl = 23 • . (b) Distribution p(θ pl ) at γ = 10 -5 before (filled blue) and after (red) removing the STs which substantially deviate from their Eshelby fits (χ 2 > 0.5).

Figure 7 .

 7 Figure 7. Scatter plot of angles of failure θ pl measured at γ = 10 -5 with (a) the MD/Esh method vs. the MD/azi method and (b) the MD/Esh method vs. the displacementbased Loc method. Large (orange) crosses refer to STs with good Eshelby fits, while small (blue) crosses indicate poor fits; more precisely, the sizes of the crosses are inversely proportional to the χ 2 -deviation from the fit.

Figure 8 .Figure 9

 89 Figure 8. Comparison between the angles of failure θ pl MD/Esh and θ plLoc measured with the MD/Esh method and the displacement-based local method, respectively. The STs have been binned into 10 • -wide angular windows, according to the value of θ pl MD/Esh .

ACKNOWLEDGEMENTS

We thank Jean-Louis Barrat for discussions related to this study. JR is being supported by the Discovery Grant Program of the Natural Sciences and Engineering Research Council of Canada. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.


O Lafforgue

N Bouguerra

S Poncet

I Seyssiecq

J Favier

S Elkoun

Thermo-physical properties of synthetic mucus for the study of airway clearance

Keywords: synthetic mucus, cystic fibrosis, rheology, thermo-physical properties

311-315 were experiementally determined. This simulant is mainly composed of a galactomannan gum and a scleroglucan. It was shown that thermophysical properties of synthetic mucus are dependant of scleroglucan concentrations. More importantly and for some scleroglucan concentrations, the syntetic mucus, exhibits, somehow, comparable thermophysical properties to real bronchial mucus. An insight on the microstructure of this simulant is proposed and the different properties enounced previously have been measured for various scleroglucan concentrations and over a certain range of operating temperatures. This synthetic mucus is found to mimic well the rheological behavior and the surface tension of real mucus for different pathologies. Density and thermal properties have been measured for the first time.

INTRODUCTION

Mucus is a complex biological material whose role in human health is to lubricate and protect organs such as lungs, vagina, eyes or gastrointestinal tract among others. It acts as a physical barrier against pathogens and noxious particles [START_REF] Cone | Barrier properties of mucus[END_REF] while preventing tissue dehydration and allowing useful molecules (for example, ions or proteins) to be transferred through.

The present article focuses on the thermophysical properties of a bronchial mucus simulant. Many respiratory diseases such as cystic fibrosis (CF) are related to abnormal compositions of lung mucus related to a default of transfer for certain ions through the epithelial surface. This results in a hyper viscosity of the mucus, impairing the process of mucociliary clearance, and exacerbating inflammations and chronic infections. As reported by Flume et al., [START_REF] Flume | Cystic fibrosis pulmonary guidelines: Airway clearance therapies[END_REF] there is to date, no clear consensus about the most efficient therapy to support the airway clearance and treat adequately patients suffering from CF or chronic obstructive pulmonary disease (COPD). Presently, most physicians used a combination of drugs, [START_REF] Majima | Mucoactive medications and airway disease[END_REF] respiratory physiotherapy (with a therapist and/or an airway clearance device) and regular physical activities.

In addition, some devices were designed to increase mucus secretion volume to help the airway clearance and increase the patient autonomy. Either based on vibrations, percussions or positive expiratory pressures, the functioning of these devices is based on the shear-thinning and thixotropic properties of bronchial mucus. A given shear stress is applied on the chest or during the exhalation phase of the respiratory cycle, increasing mucus fluidity, thus helping patients to expectorate it more easily. One could cite as examples the FrequencerV R , [START_REF] Cantin | Mechanical airway clearance using the Frequencer electro-acoustical transducer in cystic fibrosis[END_REF] which transmits acoustic and mechanical sinusoidal vibrations at different locations inside the chest, or more recently the SimeoxV R , which imposes an oscillatory air depression during the exhalation phase. [START_REF] Benkoussas | Etude exp erimentale de l'influence de la d epression m ecanique sur le transport et le comportement rh eologique du mucus bronchique synth etique dans une trach ee artificielle[END_REF] Mucus exhibits a complex structure with different characteristic scales. 7 It is made of 90-95% water, 2-5% mucins, 1-2% lipids, 1% salts, and 0.02% of DNA and other molecules such as cells debris. [START_REF] Vasquez | Chapter 2: Complex fluids and soft structures in the human body[END_REF] It forms a physical gel structured by a three dimensional mucin matrix. Mucins are high molecular weight glycoproteins (length 0.5-10 lm) insuring a structural protection function. Within the airways, they can be found as two types [START_REF] Thornton | From mucins to mucus: Toward a more coherent understanding of this essential barrier[END_REF] : monomeric and oligomeric mucins, the latter are able to form a gel and are mainly responsible for the complex rheological properties of the mucus gel. In human native mucus, the mucins of the gel-forming type (mainly MUC2, MUC5AC, MUC5B and MUC6) build with other proteins, a three dimensional gel network. These mucins consist in a peptide chain with Oglycosylated regions (branched sugar chain, endowing the gel-forming ability) and cysteine-rich naked regions (non glycosylated or N-glycosylated). The mucins are oligomerized by strong disulfide inter-molecular bonds; there are also disulfide intra-molecular bonds which stabilize the naked domains. These latter branch free domains are hydrophobic and entail the cross-link of two naked mucin regions trying to avoid water. In addition to these weak hydrophobic bonds and the strong disulfide bonds, several interactions play a role in the cross-linked network: entanglements due to the macromolecules large sizes, hydrogen bonds between sugar branches which are weak but numerous and Van der Waals forces between oligosaccharide moieties. [START_REF] King | Mucus and its role in airway clearance and cytoprotection[END_REF] Boat et al. [START_REF] Boat | Biochemistry of mucus[END_REF] have summarized the biochemistry of mucus, while Verdugo [START_REF] Verdugo | Supramolecular dynamics of mucus[END_REF] provided a deep insight into the dynamics of the different mucus components.

At a macroscopic scale, mucus is also a non-Newtonian fluid, exhibiting properties of viscoelasticity, shear-thinning and thixotropy, while, at a microscale, it behaves as a low viscosity fluid. The reader can refer to Rubin [START_REF] Rubin | Mucus structure and properties in cystic fibrosis[END_REF] or Lai et al. 7 and the references herein for a state-of-the-art up to 2009 on the micro-and macro-rheology of different types of mucus, including humans and animal ones. One focuses here only on human bronchial mucus from patients suffering from CF or COPD, for which rheology has been studied starting from the 1960s [START_REF] Denton | Rheology of human lung mucus[END_REF][START_REF] Davis | The rheological properties of sputum[END_REF] and correlated with the mucociliary clearance some years later. [START_REF] Litt | Mucus rheology. Relevance to mucociliary clearance[END_REF] As an example, Puchelle et al. [START_REF] Puchelle | Biochemical and rheological data in sputum. Relationship between the biochemical constituents and the rheological properties of sputum[END_REF] measured the biochemical and rheological properties of bronchial mucus from 21 chronic bronchitic patients without any medical treatment. The rheological properties of sputum are found to be affected by interactions between its different constituents, namely proteins (like the secretory immunoglobulins, serum albumin, transferrin), the mucins and the nucleic acids. For this pathology, other authors 18 also assessed the important role of spinability, together with the ones of viscosity and elasticity, on the mucociliary transport rate. The thixotropic property of bronchial mucus was investigated some years later by the same authors using bronchial mucus and simulants and was interpreted as a modification in the three-dimensional structure at a microscale. [START_REF] Puchelle | Elastothixotropic properties of bronchial mucus and polymer analogs. I. Experimental results[END_REF] Puchelle et al. [START_REF] Puchelle | Rheological properties controlling mucociliary frequency and respiratory mucus transport[END_REF] correlated the mucus viscosity and the mucociliary transport. Beyond an optimal value of dynamic viscosity close to 12 Pa.s, the mucociliary frequency and transport rate decrease. The spinability and adhesiveness of mucus are also supposed to modify/regulate the mucociliary clearance. Rubin et al. [START_REF] Rubin | Collection and analysis of respiratory mucus from subjects without lung disease[END_REF] characterized the bronchial mucus of healthy patients under two shear rates (1 and 100 rad/s) and compared their mechanical impedance and loss tangent with values obtained on other types of mucus sampled from patients suffering from CF, and dogs. Concerning human mucus, they did not notice any difference between men and women nor depending on the age. There was also no significant differences between healthy or CF human mucus nor dogs mucus. Nielsen et al. [START_REF] Nielsen | Elastic contributions dominate the viscoelastic properties of sputum from cystic fibrosis patients[END_REF] performed oscillatory, creep and steady shear rheological measurements over a wide range of characteristic times (from 10 23 to 10 6 s) using 23 mucus samples from CF patients. They confirmed that such bronchial mucus exhibits viscoelastic properties with a significant elastic recovery. At low shear rates, a nearly constant steady viscosity is observed for long shearing times. For given shear rates, the measured viscosities are significantly different from the ones previously reported in the literature, highlighting the high variability of sputum characteristics.

The main issues in analyzing bronchial mucus properties can be listed as follows:

1. The difficulty to collect it: on one hand, the collecting method often entails changes in the properties of concern (e.g., saliva contamination, hypersecretion of mucins in response to the collecting tool). 7 On the other hand, the collectable amount is limited and requires to establish clinical studies. 2. Its huge variability in terms of mucin size, type and concentration. They depend indeed on many factors: patient, pathology (disease conditions, 9 severity 23 ) and daily practices (food, smoker/non smoker, [START_REF] Kollerstrom | A difference in the composition of bronchial mucus between smokers and non-smokers[END_REF] practice of physical activities). . .

Hence, many studies are performed on mucus simulants that are engineered in accordance with the properties to be probed (bulk rheology, surface tension, diffusivity. . .). These mucus models can be produced by cell cultures, which provides a great relevance compared to native mucus but are still limited in quantity, or by the formulation of synthetic gels made of polymeric materials which can be produced in large amounts but hardly gather all mucus properties. [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF] Most of the studies to date on synthetic mucus used either guar gum [START_REF] King | On the transport of mucus and its rheologic simulants in ciliated systems[END_REF] or locust bean gum. [START_REF] Hasan | Effect of artificial mucus properties on the characteristics of airbone bioaerosol droplets generated during simulated coughing[END_REF][START_REF] King | Clearance of mucus by simulated cough[END_REF][START_REF] Hassan | Clearance of viscoelastic mucus simulant with airflow in a rectangular channel, an experimental study[END_REF] Madsen et al. [START_REF] Madsen | A rheological evaluation of various mucus gels for use in in-vitro mucoadhesion testing[END_REF] compared four commercial simulants of mucus, Sigma or Orthana mucin types. Banerjee et al. [START_REF] Banerjee | Effect of phospholipid mixtures and surfactant formulations on rheology of polymeric gels, simulating mucus, at shear rates experienced in the tracheobronchial tree[END_REF] investigated the influence of three therapeutic surfactants on the viscosity of mucus simulant mainly composed of gum tragacanth. Such polymeric gel was preferred for the presence of fucose, used to simulate fucomucins. The mucus exhibits a shearthinning behavior with a flow index inferior to unity. Shah et al. [START_REF] Shah | An in vitro evaluation of the effectiveness of endotracheal suction catheters[END_REF] developed a simulant based on a polyethylene oxide with addition of resin to test the efficiency of endotracheal suction catheters. Hamed et al. [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF] developed a mucus simulant with a complex composition based on pig gastrin mucins to mimic native tracheal mucus in terms of rheology and surface tension.

The main objective of the present article is to fully characterize the thermophysical properties of a synthetic mucus for different mucin concentrations and operating temperatures. The empirical correlations and different measured properties could then be used for a better understanding of the respiratory diseases impacting the composition of mucus. It could be used to develop better adapted treatments or improve existing numerical models dedicated to the simulation of airway clearance in human lungs, and go a step forward toward the development of numerical lungs as a predictive tool for medical diagnosis. To the best of the author's knowledge, this experimental study is the first to propose the characterization of the thermal properties and an insight into the structure of a synthetic mucus.

The article is organized as follows: The materials and the preparation of the mucus simulant are described in Section "Measurement Preparation". The techniques used to measure the dynamic viscosity, the density, the surface tension, the heat capacity, the thermal diffusivity and the thermal conductivity are presented in Section "Measurement Techniques". The results are discussed in Section "Results and Discussion" for different mucins concentrations over a given range of temperature before some conclusions in Section "Conclusion".

MATERIALS AND PREPARATION

Materials

Viscogum TM FA (Cargill TM ), a galactomannan gum derived from locust beans and Actigum TM CS 6 (Cargill TM ), a scleroglucan obtained by aerobic fermentation of a Sclerotium fungus were kindly provided by the company Laserson (Etampes, France). Viscogum TM is composed of galactose and mannose (average of 1 galactose unit for 4 mannose residues). A chain of mannose is branched with galactose sugars irregularly distributed in smooth and substituted zones. Actigum TM consists in a glucose chain branched every three units by an additional glucose forming a three dimensional (triple helix) structure. Figure 1 shows the molecular structure of these two components. Sodium chloride a.r. (99.81% NaCl) and di-sodium tetraborate 10aq a.r. buffer substance (99.51% Na 2 B 4 O 7 .10H 2 O) were purchased from Chem-Lab NV (Zedelgem, Belgium). Distilled water used in all preparations were obtained from a settling tank (GFL 2012).

Preparation of synthetic mucus

Mucus simulants were prepared within glass bottles filled with 200 mg of distilled water. Each component was then very slowly poured into the solution stirred using a magnetic stirrer (IkamagV R RET) at room temperature (around 218C). The following protocol taken from Ref. 33 and adapted from Ref. 1 consists in the addition, in the following order, of 0.9 wt % of NaCl, 0.5 wt % of Viscogum TM FA (galactomannan) and a chosen fraction of Actigum TM CS 6 (scleroglucan). To approach the diversity of real mucus, seven different gels with scleroglucan concentration from 0.5 to 2 wt % (by increments of 0.25%) were prepared. The mixture was kept under agitation for 48 h at room temperature. After this period, a mass corresponding to 0.2 mL per 10 mL of di-sodium tetraborate at 0.02 M (buffer component) was added to cross-link the galactomannan chains. The high molecular weight branched macromolecules of sugar, once cross-linked, build a gel matrix that mimicks the mucin network patterning the native mucus. The concentration of tetraborate (around 4 3 10 24 mol/L) remains in the range [2.5 3 10 24 -7 3 10 24 ] mol/L found in the literature. [START_REF] Zahm | Role of simulated repetitive coughing in mucus clearance[END_REF][START_REF] Hasan | Effect of artificial mucus properties on the characteristics of airbone bioaerosol droplets generated during simulated coughing[END_REF][START_REF] Zahm | Tests effectu es avec l'appareil SIMEOX[END_REF] It is notewothy that higher concentrations, as proposed by Ref. 27 (4 3 10 23 mol/L) or more, lead to a gel with a jelly aspect. The agitation is kept for a few hours before storing the final mixture at 48C. Before performing the measurements, the gel is allowed to recover at room temperature and is fractionated into several 30 mL plastic vials.

Figure 2 presents the microstructure of the simulant using both an optical microscope and a scanning electron microscope for a solution of 2 wt % in Actigum TM . For the optical microscopy, droplets of mucus simulant were placed between two glass plates and loaded in an optical microscope (Leica DMRX, Germany) equipped with a 103 lens and different objectives (Fluotar, Germany) from 53 to 633. For scanning electron microscopy, small amounts of simulant were sampled and dehydrated by series of alcohol washings before being critical-point-dried. The dried samples were then metalized with a gold/palladium alloy before being observed with a scanning electron microscope (Hitachi S-4700) operating at 2.0 kV.

The microstructure is very similar to the one of bronchial mucus with a complex tangled network of worm-like filaments. [START_REF] Suk | Rapid transport of muco-inert nanoparticles in cystic fibrosis sputum treated with n-acetyl cysteine[END_REF][START_REF] Manzenreiter | Ultrastructural characterization of cystic fibrosis sputum using atomic force and scanning electron microscopy[END_REF][START_REF] Schuster | Nanoparticle diffusion in respiratory mucus from humans without lung disease[END_REF] From Figure 2, the filaments appear as linear chains at a larger scale (top) but at a smaller scale (bottom), they tangle to form a low viscosity network as reported by Voynow and Rubin [START_REF] Voynow | Mucins, Mucus, and Sputum[END_REF] for bronchial mucus. At the macroscale, the length of the filaments remains here of the order of 200 lm, while their thickness is rather constant and equal to 2.4 lm. At the microscale, the medium pore size is hardly accurately measurable with accuracy but it remains in accordance with the literature on human bronchial mucus: between ten and hundreds of nm. For example, Kesimer et al. [START_REF] Kesimer | Molecular organization of the mucins and glycocalyx underlying mucus transport over mucosal surfaces of the airways[END_REF] reported for real bronchial mucus that the typical length of mucins ranges between 0.2 and 1.5 lm depending on the type of mucins, while their typical width varies from 7 to 12 nm. Nevertheless, in some respiratory diseases, such as severe asthma, there is an intermolecular cross-linking between mucin chains making the structure more complex and the length of some mucin chains much longer. [START_REF] Voynow | Mucins, Mucus, and Sputum[END_REF] A secondary polymer structure consisting of DNA and filamentous actin copolymers may coexist with the mucin chains for CF patients. This structure consists of thicker and longer polymer bundles dissociated from the mucin network and induces a decrease in elasticity compared to pure mucins. As shown in, [START_REF] Voynow | Mucins, Mucus, and Sputum[END_REF] the characteristic length of such a structure is close to the one observed in Figure 2 (top). More surprisingly, such longer bundles of fiber-like mucus strands have been observed for the stomach mucus from rabbits. [START_REF] Bansil | The influence of mucus microstructure and rheology in Helicobacter pylori infection[END_REF] It will be shown in Section " Results and Discussion", that such simulant mimic the main properties of bronchial mucus for CF patients. Increasing the concentration in Actigum TM (not shown here) leads to higher density regions without modifying the microstructure. One can attribute this to an unavoidable shrinkage happening during the drying process, as also reported in the literature. [START_REF] Kesimer | Molecular organization of the mucins and glycocalyx underlying mucus transport over mucosal surfaces of the airways[END_REF]

MEASUREMENT TECHNIQUES

Rheological measurements

The experiments were performed on a stress-controlled rheometer AR 550 (TA Instruments) equipped with a 50 mm/ 28 steel cone. Temperature was regulated by a Peltier plate. Dehydration was prevented by using a wet steel cover insuring a water saturated atmosphere around the sample. All the tests were realized at 208C and 378C. No significant differences were noted depending on the temperature. Thus, series of isothermal experiments were performed at 208C to limit dehydration issues.

The viscoelastic properties of the simulant unbroken structure were investigated through a series of dynamical shear experiments (Small Amplitude Oscillatory Shear). The results were interpreted from the evolution of the elastic and viscous moduli and the loss angle (G 0 , G 00 , d) in response to the sinusoidal load input. The stress dependency of the structure was observed via stress amplitude sweeps at a constant frequency (1 rad.s 21 ). More detailed rheological measurements will be presented in a further article.

Densimetry measurements

Density measurements have been performed using the DMA 5000 M manufactured byAnton Paar GmbH. A 1 mL sample is placed in an U-shaped tube made in borosilicate glass, which is electronically oscillated at its characteristic frequency. This frequency varies with the density of the sample, which is deduced from the accurate measurement of the new characteristic frequency (U-shaped tube 1 sample) from a simple mathematical formula. The oscillations are measured by optical sensors. Temperature is controlled by a built-in Peltier thermostat. Two platine Pt 100 probes are used to measure the temperature of the sample, with an accuracy of 0.018C. For high viscosity samples, corrections are applied to avoid errors due to viscosity. It leads to highly repeatable and accurate density measurements: the standard deviations on the repeatability and accuracy of the density measurements are 10 26 and 5 3 10 26 g/cm 3 respectively. The experimental protocol has been validated using distilled water with a standard deviation of 5 3 10 26 g/cm 3 compared to the expected values between 198C and 418C.

Surface tension measurements

The surface tension of the mucus simulant was measured by means of the du No€ uy ring method using a semiautomatic tensiometer (Surface Tensiomat 21, Fisher Scientific). A platinum-iridium du No€ uy ring (circumference 5.93 cm, radius ratio between the ring and the wire R/ r 5 53.2) suspended to a counter-balanced lever arm was immersed in the mucus simulant samples before being driven upward by a torsion wire (radius 0.007 00 ) until the fluid film carried by the ring broke down. The apparent surface tension is determined from the force necessary to induce the breakage. Each measurement was repeated at least three times at room temperature (238C). This method was found to be more accurate than the Wilhelmy plate balance method described by Hamed and Fiegel. [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF] To validate the experimental protocol, preliminary tests have been performed using distilled water, acetone and toluene as calibration samples. For all these samples, the relative standard deviations and the repeatability remain better than 0.5%.

Thermal diffusivity and conductivity measurements

Both thermal conductivity and diffusivity were measured using the THW-L1 Liquid Thermal Conductivity System from Thermtest Thermophysical Instruments. It measures simultaneously the thermal conductivity, k, and the thermal diffusivity, a, based on the Transient Hot Wire (THW) method. Coupled with a system controlling the temperature (heat exchanger 1 thermostat bath circulator), this device allows a complete characterization of the thermal conductivity and diffusivity within the range 2408C to 2008C. The main advantage of this method for its application to complex fluids is its capacity to experimentally eliminate the error due to natural convection. The principle of the hot-wire method is based on an ideal and constant heat generation source, an infinitely long and thin continuous line, dissipating the heat into an infinite test medium. A constant current is supplied to a platinum wire (diameter 0.1 mm, length 35 mm) to generate the temperature rise. The wire serves as both the heat source and the temperature sensor. Heating the wire by Joule effect causes the variation of its resistance, thus its temperature is measured as a function of time using a Wheatstone bridge and a data acquisition system. A PT100 platinum resistance thermometer enables to measure independently the temperature of the sample. The THW sensor including the sample cell is made of stainless steel. The required sample volume is 50 mL. The thermal conductivity value is determined from the heating power and the slope of temperature change in a logarithmic time scale. The thermal diffusivity is then evaluated through the thermal conductivity, temperature and heating power at a given time.

To validate the experimental protocol, preliminary tests have been performed using distilled water as the working fluid between 208C and 508C. For both thermal conductivity and diffusivity, the repeatability remains better than 1%. The relative standard deviations for k ranges between 0.1% at 208C and 0.17% at 40.58C, while for a, its remains at 0.1% for this range of temperatures.

RESULTS AND DISCUSSION

Rheological properties

Bronchial mucus is a complex biologic material with viscoelastic properties and a non-linear and time-dependent rheological behavior. 7 These rheological properties have been widely observed qualitatively on real native, pathological or simulant mucus. [START_REF] Rubin | Mucus structure and properties in cystic fibrosis[END_REF][START_REF] Denton | Rheology of human lung mucus[END_REF][START_REF] Davis | The rheological properties of sputum[END_REF][START_REF] Litt | Mucus rheology. Relevance to mucociliary clearance[END_REF][START_REF] Puchelle | Biochemical and rheological data in sputum. Relationship between the biochemical constituents and the rheological properties of sputum[END_REF][START_REF] Puchelle | Spinability of bronchial mucus. Relationship with viscoelasticity and mucous transport properties[END_REF][START_REF] Puchelle | Elastothixotropic properties of bronchial mucus and polymer analogs. I. Experimental results[END_REF][START_REF] Puchelle | Rheological properties controlling mucociliary frequency and respiratory mucus transport[END_REF][START_REF] Rubin | Collection and analysis of respiratory mucus from subjects without lung disease[END_REF][START_REF] Nielsen | Elastic contributions dominate the viscoelastic properties of sputum from cystic fibrosis patients[END_REF][START_REF] Puchelle | Rheological and transport properties of airway secretions in cystic fibrosisrelationships with the degree of infection and severity of the disease[END_REF] In the present Section, the objective is to demonstrate that the present mucus formulation exhibits similar properties.

Figure 3 displays a typical rheogram obtained from continuous shear stress ramps (shear stress ramps of 6 12.5 Pa.s 21 ) for a 2 wt % concentration in Actigum TM at 208C. A continuous shear stress up and down ramp test has been performed using different geometries (Couette, plate and cone) leading to similar results. A progressive departure from an elastic behavior to a shear-thinning behavior is observed beyond a stress threshold. This observation is the manifestation of the progressive yielding of the gel structure. The experimental data (up curve or down curve) are well fitted by a Herschel-Bulkley model with a flow index lower than 1. Nevertheless, one has to keep in mind that the result of this experiment is subjected to the timedependent behavior of the material. The yield stress observed here is not an inherent property of the material since the structural strength of the gel is time-dependent. As a consequence, in such a non steady flow measurement, the up curve apparent yield stress is above the down curve apparent yield stress. The characterization of such a non steady-state flow curve constitutes a first step toward a more complete characterization accounting for the steady state flow curve and the time-dependent behavior as well. The thixotropic property of the mucus simulant is simply highlighted, on a purely qualitative manner, by the hysteresis loop in Figure 3 (yellow area).

Small Amplitude Oscillatory Shear (SAOS) sweep tests for a 2 wt % concentration in Actigum TM obtained at 208C and a constant frequency of 1 rad.s 21 have also been performed. Figure 4 presents the variations of the elastic G 0 and viscous G 00 moduli and the loss factor (tan d) as a function of the oscillating stress amplitude. A yield point, denoted s y , that delimits the linear viscoelastic domain can be deduced from a 5% departure from the plateau behavior of G 0 . This is the stress limit above which the measurements no longer reflect the native structure since a structural breakdown starts to occur. Beyond the yield stress, the moduli are no longer constant due to the breakdown of the gel network. Just above this critical point, the stress is large enough to initiate the structure breakdown but too small to allow flowing. A flow point (s f ) is then identified as the shear stress corresponding to the moduli crossover, that is, the point above which the material becomes more viscous than elastic due to a critical structure breakdown.

Above the yield stress, the viscous modulus shows an overshoot before decreasing. According to Mezger 40 this is a common phenomenon in gels. The increase of deformation energy inducing the overshoot could be related to a progressive collapse of the network due to structure components with some freedom of motion. The resulting friction would thus be responsible for the high dissipated energy (increase in G 00 ) until the final breakdown occurs when G 00 displays a peak (s peak ). This kind of behavior has been classified as a Type III ("weak strain overshoot") behavior by Hyun et al. [START_REF] Hyun | Large amplitude oscillatory shear as a way to classify the complex fluids[END_REF] A review of Hyun et al. [START_REF] Hyun | A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (laos)[END_REF] emphasizes the very diverse possible structural causes of this behavior depending on the class of the soft material and claims the necessity to perform LAOS (Large Amplitude Oscillatory Shear sweep test) study to probe the meaning of this behavior.

Identical stress sweep tests have been performed on mucus simulants for the whole range of concentrations in Actigum TM . Similar curves are obtained for all concentrations (data not shown here) and the characteristic values are summarized in Table I. Viscous and elastic moduli and yield stresses all increase according to the polymer concentration. The overshoot is also observed at higher stress amplitudes for more concentrated samples. One could interpret this by the fact that more concentrated samples have a stronger network, which requires more energy to collapse. When the collapse begins, friction occurs and energy dissipation expresses itself by the G 00 overshoot. The peak height is also amplified by the Actigum TM concentration. When the structure starts collapsing, friction occurs between structural components. A more concentrated sample is expected to dissipate more friction energy as a result of its higher network density entailing more chain promiscuity and entanglements.

The plateau values of G 0 and G 00 shown in Figure 4 or in Table I agree

Surface tension

Surface tension of synthetic mucus with concentration in Actigum TM varying between 0.5 and 2 wt % has been measured by a du Nouy ring tensiometer at 238C. The results are compared to former results obtained on real mucus [START_REF] Albers | Ring distraction technique for measuring surface tension of sputum: Relationship to sputum clearability[END_REF][START_REF] Bush | Mucus properties in children with primary ciliary dyskinesia: Comparison with cystic fibrosis[END_REF][START_REF] Daviskas | Effect of mannitol and repetitive coughing on the sputum properties in bronchiectasis[END_REF][START_REF] Bennett | Effect of a single 1200 mg dose of MucinexV R on mucociliary and cough clearance during an acute respiratory tract infection[END_REF] or mucus simulants [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF][START_REF] Schenck | Tensiometric and phase domain behavior of lung surfactant on mucus-like viscoelastic hydrogels[END_REF] in Table II. The surface tension is particularly interesting since it is closely related to the wettability and adhesiveness of bronchial mucus on the epithelium surface. It directly influences the efficiency of ciliary and cough clearance on the mucus transport. At low concentrations in Actigum TM , the present values are close to that of pure water, whose surface tension slightly decreases from 72.8 mN.m 21 at 208C to 70 mN.m 21 at 378C. As already reported by Hamed and Fiegel, [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF] surface tension increases with cross-linking due here to an increase of the concentration in Actigum TM . Albers et al. [START_REF] Albers | Ring distraction technique for measuring surface tension of sputum: Relationship to sputum clearability[END_REF] also observed higher surface tensions for more solid-like sputum surfaces. The values reported here are significantly different from those obtained for native mucus, which contains surface-active molecules. This kind of surfactant considerably lowers the surface tension of mucus down to 30-34 mN.m 21 approximately. [START_REF] Hof | In vivo determination of surface tension in the horse trachea and in vitro model studies[END_REF] For high concentrations, the results have to be considered with special care as the du Nouy ring method requires some corrections to account for the complex shape of the meniscus during the ring detachment. As discussed in, [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF] such a correction exists only for Newtonian fluids and cannot be applied here leading to less reliable values of surface tension.

Other properties

To the best of the author's knowledge, the density, heat capacity and thermal diffusivity (or conductivity) of mucus simulants or sputum have not been considered in the literature. As it will be shown below, these properties take different values compared to those of pure water. They have to be measured carefully for the different concentrations u in Actigum TM at the body temperature. From a thermal point, the respiratory system also plays the role of humidifier and heater for the inspired gas. Thomachot et al. [START_REF] Thomachot | Measurement of tracheal temperature is not a reliable index of total respiratory heat loss in mechanically ventilated patients[END_REF] measured the minimal and maximal temperatures in the trachea of 10 healthy patients. For an ambient air temperature around 238C and mean body temperatures equal to 37.88C, temperatures in the upper part of the trachea vary between 30 and 338C. Considering the whole upper airways (nose, mouth, larynx. . .), they can vary between the ambient temperature and 338C. It appears then also important to measure the thermal properties of mucus simulants for a temperature range between 208C and 408C (patients with fever). It will provide a very useful database for future advanced numerical modelings dedicated to the transport of bronchial mucus in the respiratory system by mucociliary clearance or helping clearance devices.

Figure 5 presents the evolution of the density q of mucus simulants as a function of temperature. As for pure water, q decreases quadratically with temperature. For example, for u 5 2 wt %, one gets: [START_REF] Albers | Ring distraction technique for measuring surface tension of sputum: Relationship to sputum clearability[END_REF][START_REF] Bush | Mucus properties in children with primary ciliary dyskinesia: Comparison with cystic fibrosis[END_REF] 81.1-92.4 79.1 Chronic bronchitis [START_REF] Albers | Ring distraction technique for measuring surface tension of sputum: Relationship to sputum clearability[END_REF] 72.1-84.8 Primary Ciliary Dyskenesia [START_REF] Bush | Mucus properties in children with primary ciliary dyskinesia: Comparison with cystic fibrosis[END_REF] 82.9 Bronchestasis [START_REF] Daviskas | Effect of mannitol and repetitive coughing on the sputum properties in bronchiectasis[END_REF] 86 Respiratory Tract Infection [START_REF] Bennett | Effect of a single 1200 mg dose of MucinexV R on mucociliary and cough clearance during an acute respiratory tract infection[END_REF] 86.47 Synthetic mucus [START_REF] Hamed | Synthetic tracheal mucus with native rheological and surface tension properties[END_REF][START_REF] Schenck | Tensiometric and phase domain behavior of lung surfactant on mucus-like viscoelastic hydrogels[END_REF] 53.3-95 72 q T; u52% ð Þ 520:0049T 2 20:0277T11015:8

with T in 8C. Eq. ( 1) is to be compared to the following expression for pure water:

q T; water ð Þ 520:0041T 2 20:0574T11001:1

As expected also, q is also an increasing function of the concentration u in Actigum TM . For the lower concentration, u 5 0.5 wt %, q is increased by around 0.9% compared to pure water at the same temperature. All results are fitted by the following quadratic relationship giving q as a function of the concentration u in Actigum TM for a given prescribed temperature T (8C):

q 8T; u ð Þ5au 2 1bu1c u ð Þ c u ð
Figure 6 presents the variations of thermal diffusivity and conductivity versus the temperature. Both quantities increases linearly with temperature as in the case of pure water. The influence of the concentration u in Actigum TM is almost negligible. The thermal conductivity (resp. diffusivity) of pure water is 0.4% (resp. 0.3%) higher (resp. lower) in average than that for u 5 2 wt %.

The heat capacity at constant pressure has been deduced from the previous measurements through the relation: C p 5 k/(a q). Figure 7 displays the distribution of the heat capacity versus temperature for different values of u. Whatever the concentration in Actigum TM , the heat capacity decreases quadratically with temperature. As expected, taking into account the fact that the heat capacity of Actigum TM is lower than that of pure water, the heat capacity decreases also with u. At a given imposed temperature, C p decreases by 1.6% between pure water and the u 5 2 wt % simulant.

Note that the effect of aging on the heat capacity of mucus simulant has also been considered. There is no noticeable difference between measurements performed with "fresh" simulant or with simulant prepared 4 days before and stored in a fridge at 48C.

CONCLUSION

Bronchial mucus plays a crucial role in the protection of the respiratory system and can be seen as a key-element for better understanding and treatment of chronic respiratory diseases such as severe asthma or cystic fibrosis. The airway clearance function is a complex phenomenon directly linked to the thermophysical properties of the mucus layer coating the airways. The difficulty to collect and exhaustively test samples from a same mucus collection first motivated the choice to work here on mucus simulants. The composition and experimental protocol to prepare this synthetic mucus were proposed by. [START_REF] Zahm | Tests effectu es avec l'appareil SIMEOX[END_REF] This gel is mainly composed of water, NaCl, Viscogum TM FA (galactomannan) and a variable fraction of Actigum TM CS 6 (scleroglucan) to mimic a large range of mucus consistencies.

The rheological properties at rest were investigated using small amplitude oscillatory shear tests. They revealed that mucus simulant behaves as a gel within a defined linear viscoelastic region and as a viscoelastic liquid above the yield stress zone. To characterize the behavior of mucus in response to in vivo shearing, continuous ramp flow tests have also been performed. The flow curves revealed the yield stress and shear-thinning behavior of the mucus simulant as well as a hysteresis loop between the up and down curves that qualitatively accounts for the time-dependent (thixotropic) behavior.

Measurements of the surface tension of mucus simulants also measured here, were in good agreement with previous published data. The present synthetic mucus described as the most appropriate one in the literature, is here shown to mimic precisely the surface tension of real mucus for different pathologies ranging from cystic fibrosis to respiratory tract infection. Future measurements of the contact angle should enable to determine experimentally the adhesiveness of such mucus simulants.

Thermal properties, namely thermal diffusivity, thermal conductivity and heat capacity, are quite comparable to those of pure water in the range of tested temperature (20-408C). Thermal diffusivity and thermal conductivity increases linearly by respectively 6% and 5%, while the heat capacity decreases by only 0.3% between 208C and 408C.

FIGURE 1 .

 1 FIGURE 1. Structural chemical formula of (a) Viscogum TMV R FA and (b) Actigum TMV R CS.

FIGURE 2 .

 2 FIGURE 2. Structure of synthetic mucus (2 wt % of Actigum TM ) using: an optical microscope (top, 103 and 633) and an scanning electron microscope (bottom).

FIGURE 3 .

 3 FIGURE 3. Example of rheogram for a 2 wt % concentration in Actigum TM obtained at 208C. Continuous shear stress ramp (up and down) highlighting a hysteresis loop.

  particularly well with the experimental values for human cystic fibrosis sputum displayed on Figure5ain the review of Lai et al.7

FIGURE 4 .

 4 FIGURE 4. Small Amplitude Oscillatory Shear (SAOS) sweep test for a 1.5 wt % concentration in Actigum TM obtained at 208C and a constant frequency of 1 rad.s 21 . Elastic G 0 and viscous G 00 moduli (Pa) and the loss factor (tan d) as a function of the stress amplitude (Pa).

FIGURE 5 .

 5 FIGURE 5. Influence of temperature and concentration in Actigum TM on the density q of synthetic mucus.

FIGURE 6 .

 6 FIGURE 6. Influence of temperature and concentration in Actigum TM on the (a) thermal diffusivity a and (b) thermal conductivity k of synthetic mucus.

Þ521:41u 2 17

 17

TABLE I .

 I Main Rheological Characteristics as a Function of wt % in Actigum TM Measured at 208C for of 1 rad.s 21 . LVE Refers to the Linear Viscoelasticity Region

	wt% in
	Actigum TM	G 0	LVE (Pa)	G 0	LVE -5% (Pa)	G 00	LVE (Pa)	G 00	peak (Pa)	s y (5%) (Pa)	s f (Pa)	s peak (Pa)
	0.5		5.76		5.48		1.77		2.07	0.24	2.30	1.93
	0.75		14.36		13.64		3.68		5.86	2.43	5.20	4.84
	1		32.47		30.85		6.76		11.49	1.53	5.51	6.10
	1.25		39.57		37.59	12.90		16.01	2.43	8.90	9.66
	1.5	100.86		95.82	15.70		35.03	6.10	15.30	15.32
	1.75	108.35		102.93	18.86		43.34	7.68	18.72	12.17
	2	133.08		126.43	20.22		52.38	1.93	18.10	19.29

TABLE II .

 II Surface Tension as a Function of wt % in Actigum TM Measured at 238C

	wt% in Actigum TM	0.5	0.75	1	1.25	1.5	1.75	2
	Present measurements
	(10 23 N.m 21 )	71.6	72	75.4	78.4	86.1	86.6	89.9
	Cystic fibrosis

LAFFORGUE ET AL.

LAFFORGUE ET AL.

LAFFORGUE ET AL.

ACKNOWLEDGMENTS

O. Lafforgue would like to thank the company Physio-Assist and the Association Nationale de la Recherche et de la Technologie for the CIFRE grant 2014-1287. S. Poncet gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada through the Discovery Grant (RGPIN-2015-06512) and Canadian Foundation for Innovation (Grant 34582) for the provision of most measurement facilities through the John R. Evans Leaders fund.

Contract grant sponsor: Physio-Assist and the Association Nationale de la Recherche et de la Technologie; contract grant number: 2014-1287 Contract grant sponsor: Natural Sciences and Engineering Research Council of Canada; contract grant number: RGPIN-2015-06512 Contract grant sponsor: Canadian Foundation for Innovation; contract grant number: Grant 34582 V C 2017 WILEY PERIODICALS, INC.