Jing Zhao

Yanan Zhu

Xuehong Song

Yuanyuan Xiao

Guowei Su

Xinyue Liu

Zhangjie Wang
email: wangc5@rpi.edu

Yongmei Xu

Jian Liu

David Eliezer

Trudy F Ramlall

Guy Lippens

James Gibson

Fuming Zhang

Robert J Linhardt

Dr Lianchun Wang
email: lianchunw@health.usf.edu

Dr Chunyu Wang
email: wangc5@rpi.edu.

3-O-Sulfation of Heparan Sulfate Enhances Tau Interaction and Cellular Uptake

Prion-like transcellular spreading of tau in AD is mediated by tau binding to cell surface heparan sulfate (HS) and the glycan determinants of this interaction are beginning to be decoded. In a microarray of structurally-defined HS oligosaccharides, an additional 3-Osulfo group (3-O-S) resulted in significantly increased tau binding. SPR assays showed that an HS dodecasaccharides (12-mer) with one additional 3-O-S inhibited tau-HS interaction with a ~5-fold lower IC 50 than an HS 12-mer without 3-O-S. In Hs3st1 -/-(3-Osulfotransferase-1 knockout) cells, reduced 3-O-S levels of HS diminished cell surface binding and internalization of tau. An NMR titration mapped the 3-O-S recognition site in tau to PRR2 and R2 domains. Treatment of cells with the 3-O-S HS 12-mer reduced both tau-HS interaction and tau cellular uptake. This study established the important role of 3-O-S in tau-HS interaction, suggesting that 3-O-S represents a pharmacophore for glycan-based drug discovery targeting the spread of tau pathology.

Alzheimer's disease (AD) pathology is characterized by amyloid plaque and neurofibrillary tangles (NFTs). NFTs are composed of microtubule-associated protein tau (MAPT), whose normal functions include bundling and stabilizing microtubules (MTs) in neurons. Continued failure of anti-amyloid compounds in clinical trials has shifted the focus of AD research towards tau. In AD, tau becomes hyperphosphorylated, dissociates from microtubule and aggregates to form NFTs. In contrast with amyloid plaques, NFTs pathology correlates well with cognitive decline in AD [START_REF] Arriagada | Neurofibrillary tangles but not senile plaques parallel duration and severity of Alzheimer's disease[END_REF] . Recently, mounting evidence from cell culture [START_REF] Wu | Small misfolded tau species are internalized via bulk endocytosis and anterogradely and retrogradely transported in neurons[END_REF][START_REF] Frost | Propagation of Tau misfolding from the outside to the inside of a cell[END_REF] , animal models [START_REF] Liu | Trans-synaptic spread of tau pathology in vivo[END_REF][START_REF] De Calignon | Propagation of Tau Pathology in a Model of Early Alzheimer's Disease[END_REF][START_REF] Clavaguera | Transmission and spreading of tauopathy in transgenic mouse brain[END_REF] and human pathology [START_REF] Cope | Tau burden and the functional connectome in Alzheimer's disease and progressive supranuclear palsy[END_REF] has established that tau NFTs spread through neural networks in an orderly and 'prion-like' manner, mediated by transcellular movement of tau [START_REF] Brettschneider | Spreading of pathology in neurodegenerative diseases: A focus on human studies[END_REF][START_REF] Goedert | Like prions: The propagation of aggregated tau and α-synuclein in neurodegeneration[END_REF][START_REF] Guo | Cell-to-cell transmission of pathogenic proteins in neurodegenerative diseases[END_REF] (Fig. 1A). Because NFTs directly correlate to cognitive deficits, inhibiting the prion-like spread of tau is likely a viable strategy to slow down cognitive decline and the progression of AD in patients. Thus, there is a pressing need to understand the molecular mechanisms of NFT spread. A key step in tau transcellular movement is tau binding to heparan sulfate proteoglycans (HSPGs) [START_REF] Holmes | Heparan sulfate proteoglycans mediate internalization and propagation of specific proteopathic seeds[END_REF][START_REF] Holmes | Proteopathic tau seeding predicts tauopathy in vivo[END_REF][START_REF] Rauch | Tau Internalization is Regulated by 6-O Sulfation on Heparan Sulfate Proteoglycans (HSPGs)[END_REF][START_REF] Stopschinski | Specific glycosaminoglycan chain length and sulfation patterns are required for cell uptake of tau versus -synuclein and -amyloid aggregates[END_REF] on cell surface (Fig. 1B), followed by the endocytosis of tau. HSPGs are HS glycosaminoglycan (GAG) chains covalently linked to a protein core. HS is a linear, polyanionic GAG composed of disaccharide repeats of uronic acid (glucuronic acid or iduronic) and glucosamine with sulfation on the 3-OH, 6-OH and -NH of the glucosamine residue, and the 2-OH of the uronic acid residue (Fig. 1C). Specific sulfation patterns are required for the recognition of HS by its protein binding partners [START_REF] Gama | Sulfation patterns of glycosaminoglycans encode molecular recognition and activity[END_REF][START_REF] Soares Da Costa | Sulfation of Glycosaminoglycans and Its Implications in Human Health and Disorders[END_REF] . In a previous study, we have identified the 6-O-sulfo groups as an important determinant in tau-glycan interaction [START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF] , which was later confirmed by others with a variety of approaches, including the knockout of 6-O-sulfotransferases, HS biosynthetic enzymes responsible for carrying out cellular 6-O-S sulfation of HS [START_REF] Rauch | Tau Internalization is Regulated by 6-O Sulfation on Heparan Sulfate Proteoglycans (HSPGs)[END_REF][START_REF] Stopschinski | Specific glycosaminoglycan chain length and sulfation patterns are required for cell uptake of tau versus -synuclein and -amyloid aggregates[END_REF] . The 2-O-sulfo group is not critical for tau-HS interaction, while controversial data exist regarding the role of N-sulfo groups [START_REF] De Calignon | Propagation of Tau Pathology in a Model of Early Alzheimer's Disease[END_REF][START_REF] Brettschneider | Spreading of pathology in neurodegenerative diseases: A focus on human studies[END_REF][START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF] . The role of 3-O-S, a rare sulfation site in HS, has not been studied. Only six proteins are known to rely on the 3-O-S for binding specificity [START_REF] Thacker | Expanding the 3-O-Sulfate Proteome -Enhanced Binding of Neuropilin-1 to 3-O-Sulfated Heparan Sulfate Modulates Its Activity[END_REF][START_REF] Wang | Synthesis of 3-O-Sulfated Oligosaccharides to Understand the Relationship between Structures and Functions of Heparan Sulfate[END_REF][START_REF] Alavi Naini | Heparan Sulfate as a Therapeutic Target in Tauopathies: Insights From Zebrafish[END_REF] . In the human, 3-O-sulfation of HS is catalyzed by seven isoforms of 3-O-sulfotransferase (HS3ST): HS3ST1, 2, 3A, 3B, 4, 5 and 6. HS3ST1, 2, and 5 are only expressed in the brain based on a tissue-based map of human proteome [START_REF] Uhlén | Tissue-based map of the human proteome[END_REF] , and a recent study showed that Hs3st2 and Hs3st4 were overexpressed in AD hippocampus [START_REF] Huynh | Glycosaminoglycans from Alzheimer's disease hippocampus have altered capacities to bind and regulate growth factors activities and to bind tau[END_REF] , suggesting the involvement of 3-O-sulfation in AD pathology. However, how 3-O-sulfation in HS contributes to AD is unknown.

Here, utilizing structurally defined HS oligosaccharide microarray, surface plasmon resonance (SPR), nuclear magnetic resonance spectroscopy (NMR), and cellular binding and uptake assays, we report for the first time that 3-O-S is a crucial determinant in tau-HS interaction and tau uptake. Our results provide molecular details of the link between 3-O-sulfation of HS and AD, pointing towards novel strategies for tau-targeted AD therapy.

Results

3-O-S enhances tau binding to HS in glycan array analysis.

Previous interaction studies of tau/glycan have relied on heparin as a substitute for HS but important structural and functional differences exist between heparin and HS. In this studies, tau/glycan interaction has been examined using HS. Structurally defined HS oligosaccharides were synthesized by a chemoenzymatic method as previously described [START_REF] Wang | Synthesis of 3-O-Sulfated Oligosaccharides to Understand the Relationship between Structures and Functions of Heparan Sulfate[END_REF][START_REF] Xu | Synthetic oligosaccharides can replace animal-sourced lowmolecular weight heparins[END_REF] and were then immobilized on a microarray chip, creating the low molecular weight HS (LMHS) array. Full-length tau binding (or lack thereof) to the HS array was visualized by fluorescently-labeled tau remaining on the chip after incubation and washing. As shown in Fig. 2, high fluorescence intensity was observed for a HS heptasaccharide (7-mer) on spot 4 (oligo-4), and three HS dodecasaccharides (12-mers) in spot 18,19 and 20 (oligo-18, -19 and -20). Remarkably, oligo-4 which only differs from oligo-5 by a single additional 3-O-sulfo group, exhibits ~ 10-fold higher fluorescence intensity than oligo-5, indicating that the presence of 3-O-S increases the binding of tau protein. The significance of 3-O-S is also underscored from the binding of tau to longer oligosaccharides as demonstrated by the microarray analysis. HS 12-mer oligo-18 and oligo-19, containing two and one 3-O-S, respectively, displayed higher binding to tau compared to oligo-20, a HS 12-mer lack of 3-O-S. Oligo-21, which is not sulfated, exhibited negligible fluorescence. Complete results of the LMHS array can be found in Fig. S1 and S2.

3-O-S promotes inhibition of tau-HS interaction by oligosaccharides

as demonstrated by SPR analysis. Binding kinetics and affinity between HS and tau have not been measured before. Here, HS from three different sources, porcine brain, porcine spine and porcine intestine, were prepared, biotinylated, and immobilized on a SA sensor chip for binding studies using full-length tau. Brain, spinal and intestinal HS exhibited similar binding pattern to tau, with a binding affinity (K D ) of 0.02 μM (Fig 3A and Fig. S3), showing similar behavior in tau interaction of HS from these three different sources. The more accessible porcine intestinal HS was then used to further characterize the role of 3-O-sulfation in tau-HS binding, which likely resembles endogenous HS from brain tissues. Three synthesized HS 12-mers, oligo-19, oligo-20 and oligo-21 (the oligosaccharides in spots 19, 20, and 21 of the LMHS array, for chemical structure see Fig. S1B) were tested by a solution/surface competition SPR assay (Fig. 3B) to examine their ability to inhibit tau-HS interaction. Full-length tau protein was individually pre-mixed with each of three HS 12-mer and then flowed over a chip with surface-immobilized HS. The tau protein binding to 12-mer in solution diminishes its interaction with the HS immobilized on the chip surface (Fig. 3B). With increasing 12-mer solution concentrations, less and less binding to the surface was detected. An IC 50 of 0.9 μM and 4.9 μM for the inhibition of tau-HS interaction were obtained for oligo-19 and oligo-20, respectively (Fig. 3C and3D). Observed lower IC 50 value for oligo-19 is consistent with the stronger binding of tau to oligo-19 in HS microarray analysis. This ~ 5-fold lower IC 50 indicates oligo-19 is much more effective in the inhibition of the tau-HS interaction. In contrast, oligo-21 showed very little inhibition of tau-HS interaction, with an IC 50 higher than 700 µM (Fig. 3E), also consistent with the negligible fluorescence signal for oligo-21 in LMHS array. The significantly lower IC 50 of oligo-19 compared with that of oligo-20 and the lack of inhibition by oligo-21 demonstrates that sulfation is required for the ability of HS 12-mer to inhibit the tau-HS binding, and that 3-O-S greatly enhances this inhibition. Hs3st knockout reduces tau cell surface binding and cellular uptake.

Based on the microarray and SPR data, we hypothesized that 3-O-S in HSPGs may play an important role in tau binding to the cell surface and its subsequent internalization. To test this hypothesis, we next carried out tau cell surface binding and cellular uptake assays using a pair of wild type (WT) and Hs3st1 knockout (Hs3st1 -/-) mouse lung endothelial cell (MLEC) lines. The selection of Hs3st1 was based on the expression profiles of HS 3-O-sulfo transferases in primary mouse cerebral cortex neurons determined by RNA-seq, with the highest expression level observed for Hs3st1 among all Hs3sts (Fig. S4). The Hs3st1 -/-MLEC line was derived from the WT parent line using CRISPR-Cas9 gene-editing and expressed normal levels of NS, 6-O-S and 2-O-S (Fig. S5A), but reduced level of 3-O-S (confirmed by significantly reduced cell surface binding to antithrombin III requiring a 3-O-S for binding, Fig. S5B) [START_REF] Qiu | A mutant-cell library for systematic analysis of heparan sulfate structure-function relationships[END_REF] .

Biotinylated-tau was generated and incubated with cells, followed by washing and detection of surface-bound tau with streptavidin-HRP. Tau bound strongly to the surface of WT MLECs surface, while the binding was greatly diminished on Hs3st1 -/- MLECs surface, showing that 3-O-S strongly enhances HS binding of tau on the cell surface (Fig. 4A). We next incubated both WT and Hs3st1 -/-cells with Alexa488 labeled full-length tau (tau-Alexa) for 12 hrs., followed by detection with both flow cytometry (Fig. 4B) and confocal imagining (Fig. 4C) to further investigate the effects of 3-O-S deletion on the cellular uptake of tau. Large amounts of tau were internalized into the WT MLECs, but internalization was greatly reduced in the Hs3st1 -/-MLECs, indicating that 3-O-S indeed enhances HSPG-mediated tau internalization. Here, we demonstrate another role for cell surface 3-O-S in tau pathology, in which it specifically recognizes extracellular tau and mediates efficient cellular uptake.

Oligosaccharides with 3-O-S blocks tau cell surface binding and internalization.

Interfering with tau-HS interaction using heparin (HP, a highly sulfated analog of HS) or its mimetics can block tau transcellular spreading in cell culture and animal models [START_REF] Holmes | Heparan sulfate proteoglycans mediate internalization and propagation of specific proteopathic seeds[END_REF] . Designing glycan-based compound to disrupt the tau-HS interface represents a novel strategy to develop effective therapeutics for tauopathy in AD. We asked whether 3-O-sulfated oligosaccharides could be more effective at blocking tau cell surface binding and internalization than counterparts without 3-O-S. As expected, HP potently inhibits tau cell surface binding and internalization (Fig. 5).

3-O-S is recognized by tau PRR2 and R2 regions in NMR titration.

We next determined which regions of tau are responsible for the recognition of 3-O-S in HS.

The primary sequence of the longest tau isoform (441 residues) features the N-terminal projection region (N1 and N2), the proline rich region (PRR1 and PRR2), and the microtubule binding region (MTBR) and the C-terminal region (Fig. 6C). The MTBR includes four internal repeat motifs (R1-R4), which mediates tau interactions with MTs [START_REF] Gustke | Domains of τ Protein and Interactions with Microtubules[END_REF][START_REF] Butner | Tau protein binds to microtubules through a flexible array of distributed weak sites[END_REF] and other proteins [START_REF] Mandelkow | Biochemistry and cell biology of Tau protein in neurofibrillary degeneration[END_REF] , as well as tau aggregation [START_REF] Frost | Propagation of Tau misfolding from the outside to the inside of a cell[END_REF] . We use full-length tau to map the binding sites of 3-O-S. Shorter HS oligosaccharides, i.e. oligo-4 (HS 7-mer with 3-O-S) and oligo-5 (HS 7-mer without 3-O-S), were used in the experiment, because tau preferably binds to oligo-4 from the microarray analysis. Oligo-4 and oligo-5 were individually added to [START_REF] Gama | Sulfation patterns of glycosaminoglycans encode molecular recognition and activity[END_REF] N labeled tau and the refocused two-dimensional (2D) 1 H- [START_REF] Gama | Sulfation patterns of glycosaminoglycans encode molecular recognition and activity[END_REF] N heteronuclear single quantum coherence (HSQC) NMR spectra of tau were recorded before (blue peaks in Fig. 6A) and after the addition of the HS oligosaccharides (green and red peaks in Fig. 6). Significant chemical shift perturbations (CSPs) in tau were observed upon addition of both oligo-4 (resonance in red) and oligo-5 (resonance in green) titration (Fig. 6). As expected, oligo-4 caused much larger CSPs than oligo-5, due to the stronger binding conferred by the 3-O-S modification. Several isolated peaks with large CSP are highlighted in Fig. 6B. The CSP differences (∆CSP) between CSP due to oligo-4 and CSP due to oligo-5 were plotted against the residue number (Fig. 6C) to map the binding site of 3-O-S in tau (Fig. 6C). Significant ∆CSPs were located at the PRR2 and R2 domains, in which residues V226, L243, and Q276 exhibit the largest ∆CSPs, indicating a specific interaction between 3-O-S and the PRR2 and R2 of tau.

The hexapeptide 275 VQIINK 280 in R2, which contributes to tau aggregation and MTs association, was previously identified as the main site of contact with HP [START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF][START_REF] Smet | Accepting its random coil nature allows a partial NMR assignment of the neuronal Tau protein[END_REF] . PRR regions of tau are not only important for MTs binding [START_REF] Goode | Functional interactions between the proline-rich and repeat regions of tau enhance microtubule binding and assembly[END_REF] , but also hot spots for tau phosphorylation 29,30 and protein interactions [START_REF] He | The proline-rich domain of tau plays a role in interactions with actin[END_REF][START_REF] Lasorsa | Structural basis of tau interaction with BIN1 and regulation by tau phosphorylation[END_REF] . The recognition of 3-O-S in HS by both PRR2 and R2 suggests HS interaction may modulate both tau aggregation and phosphorylation.

Discussion

Growing evidence has established that tau NFTs pathology propagates in a "prion-like" manner [START_REF] Goedert | Alzheimer's and Parkinson's diseases: The prion concept in relation to assembled Aβ, tau, and α-synuclein[END_REF][START_REF] Mudher | What is the evidence that tau pathology spreads through prionlike propagation?[END_REF] . While the mechanisms underlying the intercellular spread of tau are not completely understood, a required step in this process is that tau binding to HSPGs on the recipient cell surface [START_REF] Holmes | Heparan sulfate proteoglycans mediate internalization and propagation of specific proteopathic seeds[END_REF] . HS interactions with proteins are mainly driven by electrostatic forces, between positively charged side chains on proteins and negatively charged sulfo groups on HS [START_REF] Capila | Heparin -Protein interactions[END_REF] . Although charge-based association is relatively nonspecific, many HS-binding proteins require specific sulfation patterns in the glycan, e.g., heparin/antithrombin III (ATIII) interaction requiring a pentasaccharride sequence with a 3-O-sulfo group in its central residue. In contrast to the less stringent requirements for sulfation pattern reported for α-synuclein and Aβ binding to HS [START_REF] Stopschinski | Specific glycosaminoglycan chain length and sulfation patterns are required for cell uptake of tau versus alpha-synuclein and betaamyloid aggregates[END_REF] , tau requires more specific sulfate moieties [START_REF] Rauch | Tau Internalization is Regulated by 6-O Sulfation on Heparan Sulfate Proteoglycans (HSPGs)[END_REF][START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF][START_REF] Stopschinski | Specific glycosaminoglycan chain length and sulfation patterns are required for cell uptake of tau versus alpha-synuclein and betaamyloid aggregates[END_REF] . In previous work, we were the first to report that 6-O-S, but not 2-O-S, is required for tau binding, using structurally heterogeneous polysaccharides [START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF] .

Here, we demonstrate that the 3-O-sulfation strongly enhances the tau-HS interaction and cellular uptake of tau, using LMHS microarray, SPR, cellular binding and uptake assays, and NMR. Structurally defined HS 7-mer and 12-mer with additional 3-O-S exhibited significantly stronger binding to tau in LMHS array (Fig. 2). This was then confirmed in SPR competition assays showing that an HS 12-mer with one additional 3-O-S (oligo-19) inhibits tau-HS interaction with ~5-fold lower IC 50 value than the same HS 12-mer without 3-O-S (oligo-20) (Fig. 3). The reduced cell surface binding and internalization of tau in Hs3st1 -/-cells indicates that 3-O-sulfation significantly enhances the cellular uptake of tau (Fig. 4). These data conclusively demonstrate that 3-O-S modification plays a crucial role in tau-HS interaction and tau cellular uptake. Our data provide a mechanistic rationale for the recent observation that the expression of Hs3st2 and Hs3st4 is elevated in AD brain and that HS containing GAGs isolated from AD brain exhibit enhanced tau binding [START_REF] Huynh | Glycosaminoglycans from Alzheimer's disease hippocampus have altered capacities to bind and regulate growth factors activities and to bind tau[END_REF] .

To date, tau is only the seventh protein shown to specifically recognize 3-O-S in HS [START_REF] Thacker | Heparan sulfate 3-O-sulfation: A rare modification in search of a function[END_REF] . Heparin/ATIII interaction has been the prime example of the specific interaction mediated by 3-O-S. Interestingly, 3-O-S also facilitates cellular entry of Herpes simplex virus (HSV-1), which has been linked to AD [START_REF] Carbone | Herpes virus in alzheimer's disease: Relation to progression of the disease[END_REF][START_REF] Itzhaki | Herpes simplex virus type 1 in brain and risk of Alzheimer's disease[END_REF][START_REF] Devanand | Viral Hypothesis and Antiviral Treatment in Alzheimer's Disease[END_REF] . 3-O-S enhances HS interaction with viral envelop glycoprotein D (gD) [START_REF] Shukla | A novel role for 3-O-sulfated heparan sulfate in herpes simplex virus 1 entry[END_REF][START_REF] Tiwari | Role for 3-O-Sulfated Heparan Sulfate as the Receptor for Herpes Simplex Virus Type 1 Entry into Primary Human Corneal Fibroblasts[END_REF] . Thus, both Herpes virus and tau entry into a cell are enhanced by the 3-O-S functional group, raising the possibility of mechanistic crosstalks between the spread of tau pathology and Herpes infection in the AD brain.

By establishing the critical role of the rare 3-O-S HS modification in tau-HS interaction, we provide one of the most important insights for developing HS-based therapies against the spread of tauopathy: to efficiently inhibit cellular uptake of tau, a 3-O-sulfo group is required. In this work, efficient inhibition of tau-HS interaction has been achieved with a HS 12-mer containing 3-O-S (oligo-19) with an IC 50 of 0.9 µM, in a SPR competition assay (Fig. 3C). Significant inhibition of cellular binding and uptake of tau was also observed (Fig. 5) by the same oligo-19. Based on these data, we propose that the 3-O-S and tau interface represents a novel target for AD disease-modifying therapy to block tau trans-cellular propagation in AD. As 3-O-sulfotransferases are overexpressed in AD brain [START_REF] Huynh | Glycosaminoglycans from Alzheimer's disease hippocampus have altered capacities to bind and regulate growth factors activities and to bind tau[END_REF] , inhibiting the expression or activity of 3-Osulfotransferases may represent another avenue for inhibiting the propagation of NFT pathology.

NMR mapping shows 3-O-S (Fig. 6C) preferably bind to the PRR2 and R2 domain of full-length tau, which are the crucial regions for aggregation [START_REF] Sibille | Structural characterization by nuclear magnetic resonance of the impact of phosphorylation in the proline-rich region of the disordered Tau protein[END_REF] , MTs association [START_REF] Goode | Functional interactions between the proline-rich and repeat regions of tau enhance microtubule binding and assembly[END_REF][START_REF] Mandelkow | Tau domains, phosphorylation, and interactions with microtubules[END_REF] , and interaction with heparin [START_REF] Zhao | Glycan Determinants of Heparin-Tau Interaction[END_REF][START_REF] Sibille | Structural impact of heparin binding to full-length Tau as studied by NMR spectroscopy[END_REF] and other proteins [START_REF] He | The proline-rich domain of tau plays a role in interactions with actin[END_REF][START_REF] Lasorsa | Structural basis of tau interaction with BIN1 and regulation by tau phosphorylation[END_REF] . 6-O-S also binds to the R2 domain as previously studied. Taken together, we suspect there may be a synergistic effect between 3-O-S and 6-O-S that enhances the binding of HS to tau. Similarly, in ATIII-heparin interaction both 3-O-S and 6-O-S modification are critical for inducing the conformational change in ATIII [START_REF] Devanand | Viral Hypothesis and Antiviral Treatment in Alzheimer's Disease[END_REF] needed for anticoagulant activity of heparin. Unlike ATIII, tau is an IDP without a fixed 3D structure, rendering it a more challenging system for conventional structural characterization. More work is needed to delineate the specific HS motifs (the combination of chain length, monosaccharide composition and precise sulfation pattern) required for tight binding to tau in human brain and in Alzheimer's disease, and to understand the structural basis of the specific interactions between 3-O-S and tau residues at atomic resolution.

In summary, our results demonstrate the key role of 3-O-S in the tau-HS interaction and cellular uptake of tau, uncovering a unique structural requirement of HS recognition by tau. This work represents a major step forward in our understanding of the mechanism of tau-HS interaction, with important implications for 3-O-S as a pharmacophore targeting the spread of tau pathology in the development of effective AD therapy.

Methods

Materials.

The overexpression and purification of full-length tau protein were performed as previously described [START_REF] Barre | Structural transitions in tau k18 on micelle binding suggest a hierarchy in the efficacy of individual microtubule-binding repeats in filament nucleation[END_REF][START_REF] Qi | The Study of Posttranslational Modifications of Tau Protein by Nuclear Magnetic Resonance Spectroscopy: Phosphorylation of Tau Protein by ERK2 Recombinant Kinase and Rat Brain Extract, and Acetylation by Recombinant Creb-Binding Protein[END_REF] . Chemoenzymatic synthesis of low molecular weight heparan sulfate (LMHS) was completed according to methods published previously 50 51 . Heparan sulfate extracted from porcine intestine is a commercial product obtained as a side stream in the manufacture of porcine intestinal heparin [START_REF] Griffin | Isolation and characterization of heparan sulfate from crude porcine intestinal mucosal peptidoglycan heparin[END_REF] .

Heparan sulfates from porcine brain and spine were purified and characterized as previously described [START_REF] Liu | Glycosaminoglycans of the porcine central nervous system[END_REF] .

The wildtype and Hs3st1 -/-MLEC lines were developed in our lab recently using Crispr-Cas9 or conditional Cre-LoxP gene editing technologies [START_REF] Qiu | A mutant-cell library for systematic analysis of heparan sulfate structure-function relationships[END_REF] . The Hs3st1 deletion selectively reduces 3-O-S and correspondingly, can be applied to specifically determine the requirement of 3-O-S in interaction with a protein ligand, respectively, in a cellular setting.

The binding preference of tau to HS using microarray assay. Full-length tau protein was labeled with fluorescence dye Alexa Fluor 488 5-SDP Ester (Life Technologies) according to the supplier's instructions. The degree of labeling (DOL) was 1-2 moles/mole of protein. A series of structurally defined HS oligosaccharides are immobilized on a microarray chip using a robotic printer as previously described [START_REF] Yang | Construction and characterisation of a heparan sulphate heptasaccharide microarray[END_REF] . The fluorescently labeled tau protein is incubated with the slide for 1 h at room temperature and then washed. The wash process was repeated twice before analyzing the slide Tau internalization assay. MLECs (5 × 10 5 ), including wildtype and Hs3st1 -/-cells, were seeded at 600 μl /well DMEM containing 10%FBS, 100 U/ml penicillin and 100 μg/ml streptomycin in a 12 well plate. After culturing overnight, the cells were washed with DPBS twice and then incubated with 500 μl/well DMEM containing BSA (2 μg/ml),

Tau-Alexa (2 μg/ml) or Tau-Alexa (2 μg/ml) mixed with heparin (10 μg/ml), oligo-19 (2.5 μg/ml), oligo-20 (2.5 μg/ml) or oligo-21 (2.5 μg/ml) at 37 °C for 3 h. Followingly, the cells were processed for image or flowcytometry analyses. For image analysis, the cells were covered with mounting medium DAPI and examined for internalized tau under confocal microscope for flowcytometry analysis, the cells were trypsinized and resuspended in DPBS containing 2 mM EDTA, 1% BSA and PI which stain dead cells, and then measured for internalized tau-Alexa with flow cytometer.

3-O-S

Figure 1 .

 1 Figure 1. Cellular uptake of tau is mediated by HSPGs on cell surface. (A) Prionlike spread of tau pathology (represented by blue color) in AD brain. (B) Uptake of tau mediated by the binding to heparan sulfate proteoglycans (HSPGs). Microtubules are

Figure 2 .

 2 Figure 2. Low molecular weight heparan sulfate (LMHS) array shows the crucial role of 3-O-sulfo group (3-O-S) in tau binding. Fluorescence intensity on each spot of array was shown in a bar graph, with the monosaccharide composition/sulfation pattern drawn for the HS oligosaccharides with high fluorescence intensity (tau binding).

Figure 3 .

 3 Figure 3. HS 12-mer oligo-19 and oligo-20 inhibit full-length tau-HS binding with an IC 50 of 0.9 μM and 4.9 μM, respectively. (A) Binding affinity of full-length tau-HS interaction was measured to be 0.02 µM by SPR binding kinetic assay for the first time. The association and dissociation curve of different tau concentrations were fitted (black line) by a 1:1 Langmuir kinetics model in Bio-evaluation. HS from three sources (porcine brain, porcine spine and porcine intestine) were tested (Fig. S3) and only porcine intestinal HS binding is shown here. (B) Scheme for Competition SPR. (C) Oligo-19 inhibits tau-HS binding with an IC 50 of 0.9 μM. (D) Oligo-20 inhibits tau-HS binding with

Figure 4 .

 4 Figure 4. Deletion of Hs3st1 diminishes tau cell surface binding and internalization. (A) The Hs3st1 -/-cells showed less (46.3% reduction) tau cell surface binding, compared with WT. After fixing and incubating with biotinylated full-length tau (500 ng/ml, 100 μl/well) for 90 min at RT, the cell surface bound tau was measured after incubating with Streptavidin-HRP and color development. (B) The Hs3st1 -/-cells showed significantly less internalization of tau-Alexa (500 ng/ml) assessed by flow cytometry. (C)

Oligo- 19

 19 and oligo-20, but not oligo-21, inhibit tau cell surface binding and internalization with similar pattern as to HP. Compared with oligo-20, oligo-19 exhibits significantly greater inhibition of the cell surface binding and internalization of tau, underscoring the crucial role of 3-O-sulfation for effectively blocking tau-HS interaction on cell surface and tau internalization. The addition of 3-O-S modification may lead to more potent HS-based therapeutics for tauopathy.

Figure 5 . 3 -

 53 Figure 5. 3-O-S modification enhances the inhibitory potency of HS oligo on taucell interaction and tau cellular uptake. (A) HP, oligo-19 and oligo-20 inhibit tau cell surface binding by 46.3%, 28.0% and 13.0%, respectively. After fixing and incubating with biotinylated tau (500 ng/ml, 100 μl/well) without or with HP (50 ng), HS oligos (25 ng) for 90 mins at RT, the cell surface bound tau was measured after incubating with Streptavidin-HRP and color development. Oligo19 has a stronger inhibitory potency than oligo-20. Oligo-21 has no inhibition. (B) HP, oligo-19 and oligo-20 inhibit tau-Alexa (500 ng/ml) internalization assessed by flow cytometry. (C) HP, oligo-19 and oligo-20 inhibit tau internalization assessed by confocal images. The cells were incubated with tau-Alexa (2 μg/ml, 500 μl/well) without or with HP (10 μg/ml), HS oligo (2.5 μg/ml) at 37 ℃ for 3 h. Oligo-19 has a stronger inhibitory potency than olig-20. Olig-21 has no inhibition. The data shown are representative of 2-4 independent experiments.

Figure 6 .

 6 Figure 6. Chemical shift perturbation difference (∆CSP) reveals specific interactions between 3-O-S and PRR2 and R2 domain of full-length tau. (A) Overlay of 1 H-15 N HSQC spectra of full-length tau before (blue) and after 1:0.6 molar ratio addition of HS 7-mer oligo-5 (green) and HS 7-mer oligo-4 (red). (B) Zoomed-in NMR spectra of residues with biggest CSPs. (C) CSP differences (∆CSP) reveals specific interaction between 3-O-S and tau PRR2 and R2 domain. Construct of tau is shown above the figure, PRR = proline-rich region, MRBR = microtubule binding region.

Fig. S5 .

 S5 Fig. S5. The Hs3st1 -/-MLEC line expressed normal levels of NS, 6-O-S and 2-O-S (A), but reduced cell surface binding to antithrombin III (B).

  using the excitation wavelength of 488 nm on a GenePix 4300 scanner (Molecular Dynamics). Resolution was set at 10 μm. The array images were analyzed by GenePix Pro 7.2.29.002 software. Spots were automatically found and spot deviations were manually fit to correct. Mean median fluorescence intensities of arrays were obtained by Array Quality Control of software.Characterization of tau-HS interaction by SPR assays.Preparation of the HS biochip. Biotinylated HS was prepared by reacting sulfo-Nhydroxysuccinimide long-chain biotin (Thermo Scientific, Waltham, MA) with free amino groups of unsubstituted glucosamine residues in the polysaccharide chain according to a published procedure[START_REF] Hernaiz | Enzymatic modification of heparan sulfate on a biochip promotes its interaction with antithrombin III[END_REF] . The biotinylated HS was immobilized to a SA chip based on the manufacturer's protocol. In brief, a 20 μL solution of the HS-biotin conjugate (0.1 mg/mL) in HBS-EP running buffer (0.01 M HEPES, 0.15 M NaCl, 3 mM EDTA, and 0.005% surfactant P20 (pH 7.4)) was injected over flow cell 2 (FC2) of the SA chip at a flow rate of 10 μL/min. Successful immobilization of HS was confirmed by the observation of an ~250 resonance unit increase in the sensor chip. The control flow cell (FC1) was prepared by a 1 min injection with saturated biotin. Binding affinity of HS-tau interaction. Lyophilized full-length tau protein was resuspended in HBS-EP buffer. Different concentrations of the protein (0.1 μM, 0.25 μM, 0.5 μM, 1.0 μM, and 2.0 μM) were injected at a flow rate of 30 μL/min for 3 min. At the end of the sample injection, HBS-EP buffer was flowed over the sensor surface to facilitate dissociation. After a 3 min dissociation time, the sensor surface was regenerated by injection with 30 mL of 2 M NaCl. The response was monitored as a function of time (sensorgram) at 25 °C. Competition assay of 12-mer. Competition SPR experiments were performed to study how the presence of 3-O-S impacts the inhibition of 12-mer on tau-HS interaction. Tau protein was premixed with three different 12-mer, separately, and flowed over the HS chip at a flow rate of 30 μL/min. After each injection, dissociation and regeneration were performed as described above. For each set of competition experiments on SPR, a control experiment (with only tau protein and no 12-mer) was performed to confirm that the surface was completely regenerated and that the results obtained between runs were comparable. A series of concentrations of 12-mer was tested and IC 50 was obtained by fitting the data using the '[Agonist] vs. normalized response' equation in GraphPad Prism 8 software, Y=100*X H /(IC 50 H + X H ), where Y is the normalized binding of tau to HS biochip, X is the concentration of 12-mer, and H is the Hill slope describing the steepness of the curve. Cell surface tau binding assay. ELISA was performed to determine cell surface tau binding. In brief, 3 × 10 4 MLECs, including wildtype and Hs3st1 -/-cells, were seeded at 200 μl/well in DMEM containing 10% FBS, 100 U/ml penicillin and 100 μg/ml streptomycin in a 96 well plate. After culturing overnight, the cells were washed with DPBS (3 times x 5 min) and then fixed with 4% PFA (15 min, RT), washed with DPBS (3 times x 5 min) and blocked with DPBS containing 1% BSA (90 min, RT), the cells were incubated with 100 μl DPBS containing BSA (50 ng), biotinylated Tau (50 ng/ml), or biotinylated Tau (50 ng) mixed with heparin (50 ng), oligo-19 (25 ng), oligo-20 (25 ng) or oligo-21 (25 ng) for 90 min at RT. Following, the cells were washed with DPBS (3 times x 5 min), incubated with Streptavidin-HRP (1:2000 dilution in DPBS containing 1% BSA, 30 min, RT), and then cell surface bound tau (represented by HRP activity) was measured using an Ultra TMB-ELISA kit (34028, Thermo Scientific) according to the manufacturer's protocol.

  Binding site mapping by NMR. NMR experiments with oligo-4 (HS 7-mer with 3-O-S) and oligo-5 (HS 7-mer without 3-O-S) were performed on full-length tau to map the binding site of 3-O-S on tau. 1 H-15 N HSQC spectra were recorded on an 150 μM fulllength tau sample before and after the adding of a 1:0.6 ratio of oligo-4 and oligo-5, separately. Normalized chemical shift perturbation (CSP) of tau for amide 1 H and 15 N chemical shifts upon HS 7-mer addition were calculated using the equation = √100 × ∆ + ∆ , where ∆ and ∆ are the differences between the chemical shifts of the free and bound forms of tau, respectively. As the only difference between oligo-4 and oligo-5 is an additional 3-O-S, a CSP difference (∆CSP) calculated by CSP (due to oligo-4) minus CSP (due to oligo-5) was plotted against the residue number to map the binding site of 3-O-S in tau.

Acknowledgement

The research was supported by NIH (5R01HL093339, R56AG062344 and U01CA225784 to L.W.).

Supporting Information

Competing Financial Interests Statement

No competing financial interests.


Mathilde Veron

Anselmo Peñas
email: anselmo@lsi.uned.es

Guillermo Echegoyen

Somnath Banerjee

Sahar Ghannay

Sophie Rosset

A Cooking Knowledge Graph and Benchmark for Question Answering Evaluation in Lifelong Learning scenarios

Keywords: Question Answering, Lifelong Learning, Evaluation resources

In a long term exploitation environment, a Question Answering (QA) system should maintain or even improve its performance over time, trying to overcome the lacks made evident through the interactions with users. We claim that, in order to make progress in the QA over Knowledge Bases (KBs) research field, we must deal with two problems at the same time: the translation of Natural Language (NL) questions into formal queries, and the detection of missing knowledge that impact the way a question is answered. The research on these two challenges has not been addressed jointly until now, what motivates the main goals of this work: (i) the definition of the problem and (ii) the development of a methodology to create the evaluation resources needed to address this challenge.

Introduction

Since every human domain is dynamic and evolves over time, in the mid-long term, any Knowledge Base (KB) will become incomplete or, at least, it won't we able to satisfy user demands of information. In a long term exploitation environment, QA systems must deal with the challenge of maintaining their performance over time and try to overcome the lacks made evident through the interactions with the users. In other words, we need to provide QA systems with Lifelong Learning mechanisms. The first step is the detection of such situations. QA systems must distinguish the reason why the system cannot answer a question: either the problem is in the translation of the Natural Language (NL) question into a formal query, or the problem is a lack of knowledge that prevent the system from giving an answer. If the reason is the latter, the system must trigger a learning process to overcome this limitation and update its previous knowledge.

Unfortunately, most of the current research in QA over KBs works with datasets of questions that can always be answered by the KB [START_REF] Lopez | Evaluating question answering over linked data[END_REF][START_REF] Höffner | Survey on challenges of question answering in the semantic web[END_REF]. That is to say, the research focus is on the problem of how to translate a NL question into a formal query. However, working under the assumption that there exists an answer to the question according to the KB leads researchers to a set of solutions that will not work in a real scenario.

We claim that, in order to make progress in the QA research field, we must deal with both problems at the same time: the translation of NL into formal queries, and the detection of lacks of knowledge that impact the way questions are answered. To the best of our knowledge, the effort done in this direction has not been significant. Therefore, the main goals of this work are (i) the definition of the problem and (ii) the development of a methodology to create the evaluation resources needed to address this challenge.

For a better understanding of the problem, we chose the context of a real user demand, constructing an imperfect (by definition) Knowledge Graph (KG), and asking real users to pose questions that the QA system has to answer. Then, a set of annotators have tried to translate the real NL questions into formal queries, identifying when the questions can be translated and when they cannot, annotating the reasons why. Examples of annotations can be found in Figure 1.

The form of the Knowledge Base is a Graph (i.e. RDF triples style) for several reasons. First, the updating of the KG with new classes (or types), property names (or relations), instances (or objects), etc. is straightforward and does not affect the previous version. It only requires the addition of new triples. Secondly, working with a graph makes the use of different formalisms and different retrieval engines possible, from using SPARQL over database managers (like Virtuoso) to the use of simple Prolog. That is, in a Lifelong scenario where the systems must evolve over time and continuously update their knowledge, KGs seem to be the most appropriate formalism.

In the following sections, we describe the whole process in detail, together with our learnings and conclusions. The contributions of this work are:

-The definition of the problem; -A methodology for studying it and creating the evaluation resources; -A publicly available Knowledge Graph (in cooking domain) 4 ; -A first version of a set of answerable and unanswerable questions over this KG, for benchmarking system self-diagnostic about the reasons why the question cannot be answered by the KG5 .

2 Previous work

Question Answering with unanswerable questions

We are interested in QA systems with the ability to recognize unanswerable questions. This problem has been addressed lately under the free text assumption and only partially. To the best of our knowledge, it has never been addressed in QA over KBs.

Under the free text paradigm, systems must answer questions whose answer can be found in a given text. Current research is more focused on answer extraction than in the complete QA architecture that includes the recovering or ranking of candidate paragraphs. (as opposed to KG-based QA, where the whole process must be carried out). SQuAD [START_REF] Rajpurkar | Know What You Don't Know: Unanswerable Questions for SQuAD[END_REF], TriviaQA [START_REF] Joshi | TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension[END_REF] and MS Marco [START_REF] Nguyen | MS MARCO: A human generated MAchine reading COmprehension dataset[END_REF] are among the most popular collections for QA over free text featuring empty answers. They are all created following one or various crowdsourcing annotation processes. Current systems competing with these datasets are usually made out of ensembles of pre-trained language models like ALBERT [START_REF] Lan | ALBERT: A Lite BERT for Self-supervised Learning of Language Representations[END_REF] and XLNet [START_REF] Yang | XLNet: Generalized Autoregressive Pretraining for Language Understanding[END_REF].

However, when doing QA over KBs, a more sophisticated process is required. In general, all systems proceed with a multi-step process, comprising a combination of complex steps: Question Analysis, Named Entity Recognition and Linking, Disambiguation and Parsing. There are some surveys detailing these systems, we refer the reader to them [START_REF] Diefenbach | Core techniques of question answering systems over knowledge bases: a survey[END_REF], and [START_REF] Höffner | Survey on challenges of question answering in the semantic web[END_REF]. Over the last years, neural systems have tremendously increased in capability, however in the specific domain of QA over KBs, it has been argued that deep learning does not contribute that much [START_REF] Mohammed | Strong Baselines for Simple Question Answering over Knowledge Graphs with and without Neural Networks[END_REF]. In particular, these systems can, for now, only answer simple questions [START_REF] Bordes | Large-scale Simple Question Answering with Memory Networks[END_REF][START_REF] He | Character-Level Question Answering with Attention[END_REF][START_REF] Lukovnikov | Neural Network-based Question Answering over Knowledge Graphs on Word and Character Level[END_REF]. Furthermore, to solve QA over KBs, the majority of approaches assume that the question can be answered by the KG because the most popular collections like QALD [START_REF] Lopez | Evaluating question answering over linked data[END_REF] or LC-QUAD [START_REF] Höffner | Survey on challenges of question answering in the semantic web[END_REF] do not contain empty answers. Therefore, answering a question is a kind of graph matching against the KG.

In summary, a production system for QA over KBs requires the ability to recognize unanswerable questions, and therefore, we identify the need to correctly define the problem of QA over KBs, but also to develop the necessary resources to train and evaluate systems to solve this problem.

Lifelong learning and Question Answering

This problem has already captured the attention of some researchers such as Mazumder and his colleagues [START_REF] Mazumder | Lifelong and interactive learning of factual knowledge in dialogues[END_REF] although in that work, the problem is only addressed partially. In particular, queries to the system are just single triples, reducing to the trivial case the problem of deciding whether the answer to a question is in the KG or not. It simplifies also the problem of detecting the pieces of knowledge that have to be added to the KG. The option taken for enriching the KG is to ask the user for some missing pieces of knowledge and try to find strategies to infer some others. However, in the general scenario of complex NL QA over KGs these decisions are not trivial. If a system does not get an answer to a question, it could be due to several factors, including some errors in the process of NL interpretation (e.g. Entity Linking).

Cooking Knowledge Graph construction

The KG is a set of triples <arg1, property-name, arg2>, where the first argument must be always an entity and the second one can be both an entity or a literal (number or string). Entities (also mentioned as resources or objects) can refer to type names (or classes, e.g. cookbook:ingredients), instances (e.g. cookbook:milk), or category names (e.g. category:pancake_recipes). Categories refer to groups of recipes according to some criteria given by the original wiki. Thus, a recipe can belong to several categories and this will be encoded through the corresponding triples with the property name recipeCategory. Recipe categories use the prefix category: instead of cookbook: used for the rest of entities. The property names (or relations) used here follow the Recipe schema 6 when it has been possible. The complete set of properties is shown in Table 1.

The KG has been derived from the English wikibook (enwikibooks-20190701pages-articles.xml) related to cooking (name space 102, Cookbook). We have processed both the cookbook pages one by one, and the category links file (enwikibooks-20190701-categorylinks.sql).

The processing of the category links file produced 480 triples among categories, 6935 triples that link recipes to recipe categories, and 4479 type relationships.

With respect to the processing of the Cookbook enwikibook pages, the method has been the following:

1. Consider the mark redirect inside the wiki pages to store which is the canonical uri for each object. 2. Use the title of the page to produce the name and url relations. 3. Identify sections in recipe pages. 4. Process ingredients section and produce the triples for the recipeIngredient and recipeFoodstuff relations. The former one corresponds to the text describing the ingredient, quantity, etc. The latter one, corresponds to the object in the Knowledge Graph associated to the food used as ingredient. 5. Process instructions section to produce a triple that relates the recipe with the list of steps (recipeInstructions relationship). Each element in the list corresponds to the original text describing the step. 6. Process the section of notes and variations, and produce the triple for the recipeNotes between the recipe object and the corresponding text. 7. Process the marks that associate the main types with the page under processing. These main types are: recipes, diets, equipment, ingredients and techniques. Main ingredient subtypes are: cereals, chesses, fruits, herbs_and_spices, meat_and_poultry, nuts_and_seeds, seafood and vegetables. These types and subtypes are the ones defined originally in the wikibook. We observed that, in many cases, there are inconsistencies in the types of the objects. In principle, since the types described are a partition, no objected should have more than one of these main types. However, in the majority of cases it is the type recipes the one that spreads incorrectly over the objects. In these cases, we promote the other types. 8. Process the links in the page with two purposes: (i) to store their text as label for the corresponding objects and (ii) identify that there is an implicit relationship between two objects. In the wiki pages there exist a number of links that relate the current page to another page. In our case, both pages will correspond to objects in the knowledge graph, but we need to infer the appropriate property name that must identify this relationship. Once the types of the source and target objects are solved according to the previous step, then the implicit relationship between them is trivially solved and made explicit. 9. Process the recipe summary according to the corresponding template instructions. This processing produces the triples for recipeCategory, recipeYield (servings), totalTime and difficulty (numeric value from 1 to 5).

Freq. Property name Example

General props

8263

Methodology for dataset creation

This section describes the creation process of the developed dataset. The objective of this dataset is to help the research community to study the following research issues: (i) the translation of NL into formal queries, (ii) the detection of unanswerable questions and (iii) the identification of elements missing in the KG which impact the way questions are answered. We first describe how we collected the user's queries in NL and then how we annotated them.

Collection of queries in natural language

We asked collaborators from our institutions through a web form to write at least 5 queries in natural language in English. The participants were no native English speakers but Spanish and French people. We received 30 responses in 3 days, resulting in 169 queries. The participants needed around 5 minutes to read the guidelines and write at least 5 queries. They were asked to pose any question about the cooking domain. Thus we provided them a non exhaustive list of items they could ask about along with some examples. The query could be posed in any of these four possible ways: interrogative (e.g., "Which herbs go well with mushrooms?"), imperative (e.g., "Give me a soup recipe for tonight"), informative ("I'm looking for the name of the utensil that is used to beat the egg whites"), or propositional (yes/no question e.g. "Is tomato a fruit?") and have to fit in only one sentence.

After collecting the queries in NL, we filtered them by assessing their usability regarding our task 7 . It allowed us to directly discard the queries that couldn't be answered either with the current KG or by adding new elements to the KG. Each question has been annotated as usable or not by two different persons. After filtering, 124 queries were identified as usable (around 73%). The annotations were made using a unique table for each annotator as presented in Figure 1. Using the provided guidelines 7 the annotators had to write the associated Prolog query and to give the result of it, or if it was not possible, to give the elements missing in the KG that made the question unanswerable.

Annotations

We decided to remove from the final dataset all the annotated user's queries where the annotator wrote that more than one element was missing in the KG. The first reason is that in this case, there can be multiple ways to represent the missing knowledge in the KG and to annotate the reasons why the query cannot be answered. In other words, the annotation would be subjective and the dataset would suffer from inconsistencies. Secondly, regarding machine learning algorithms, the tasks of identifying the elements missing will be much more complex if it has to be able to detected when multiple elements are missing for one user's query, as it corresponds to a multi-labelling task. However, we consider that the annotated user's queries that were removed from the dataset, will be useful anyway, either for detecting when a user's query cannot be answered, or in the future when a system will be mature enough.

Five Annotators, including PhD students and researchers from our institutions, participated in the annotation process. Each annotator had to know at least about the basis of Prolog. We expected to remove around 10% of the annotated data when multiple elements were missing, so we decided to annotate 110 user's queries to get at the end 100 annotated queries in the final dataset. To make it possible, each annotator had 22 user's queries to annotate. The annotation process was quite long, since the annotators had to check for each element if they exist in the KG and under which name. Depending on the knowledge on Prolog and on the cooking KG, the annotators needed from 5 minutes to 20 minutes to annotate one user's question. This time take into account the corrections needed. At the end one person was responsible of reviewing all the annotations and to correct them in order to have consistent data.

Description of the dataset

The original dataset is provided in the form of an Excel document. It contains all the annotations as presented in Figure 1 with the comments of annotators. The characteristics of the original dataset are presented in table 2. The final dataset is provided in the form of a json file 8 . The questions where more than one element was missing have been removed from this dataset. When a question contained typos, we replaced the question with the corrected one in the final dataset. The characteristics of the final dataset are presented in table 3 3. Final dataset. Proportions of questions among some categories.

Lessons learned through the creation process

We have observed that in the majority of cases, the questions that cannot be answered initially can become answerable after populating the knowledge graph with new entities, property names or triples. So the system can evolve over time. However, there is one situation where the system can't evolve easily: when it affects the structure of the data. For example, in the current version of the KG, the information related to a recipe ingredient is just a triple, but several questions require it to be a tuple with additional information beyond the foodstuff (quantity or amount, possible replacement, textual description, etc.). This problem cannot be overcome by adding some triples, but altering the current structure of the recipe ingredients nodes.

After completing the annotation process we re-evaluate the questions that we annotated as not usable regarding our task. We came to the point that we actually filtered too many questions and determined that only 10% of the questions were not usable (against 27% previously). We also figured out that we underestimated the proportion of questions with more that one element missing (22% against 10% estimated). That is why the final dataset actually contains 86 annotated questions instead of 100.

Conclusion and future work

In a real exploitation environment, usual QA systems would provide an incorrect answer when the question refers to element that are missing in the KB. Thus we state that it is fundamental for lifelong learning QA systems to be able to handle jointly the two following problems: the translation of Natural Language (NL) questions into formal queries, and the detection and identification of missing knowledge that impact the way questions are answered. As no evaluation resources are yet available to address these problems, we presented in this paper a methodology for the creation of these resources. Moreover we publicly share the resulting resources, namely i) A cooking KG and (ii) the first version of a dataset containing a set of questions over the KG with the element missing in the KB if an answer cannot be found.

For future work we plan to collect and annotate more questions by taking advantage of lessons learned though the creation of the first version of the dataset.

Fig. 1 .

 1 Fig. 1. Examples of annotated user's queries. This annotated queries are not part of the dataset.

Table 1 .

 1 Property names in the Cooking KG

			label	baguette label "french bread"
			5214 url	adobo url en.wikibooks.org/wiki/Cookbook:Adobo
			5214 name	frosting_and_icing_recipes name "Frosting"
			5156 type	baking_soda type cookbook:leavening_agents
			21077 recipeIngredient chocolate_mousse recipeIngredient "200 g bitter..."
	Recipe	properties	15616 recipeCategory 12343 recipeFoodstuff chocolate_mousse recipeFoodstuff cookbook:chocolate chocolate_mousse recipeCategory category:dessert_recipes 2419 recipeInstructions chocolate_mousse recipeInstructions ["Melt chocolate..."] 849 difficulty chocolate_mousse difficulty 2 844 totalTime chocolate_mousse totalTime "30 minutes"
			805 recipeYield	chocolate_mousse recipeYield 4
			458 recipeNotes	chocolate_mousse recipeNotes "* This recipe is not the..."

Table 2 .

 2 . Original dataset. Proportions of questions among some categories.

			#questions	86
			typo mistakes	09%
	#questions	110	one element missing	49%
	answerable	40%	type of element missing
	one element missing	38%	entity	43%
	multiple element missing 22%	type name	02%
			property name	24%
			triple	31%
			Table

http://nlp.uned.es/lihlith-project/cook/

https://perso.limsi.fr/rosset/resources/cooking_LL_QA.json

https://schema.org/Recipe

The guidelines can be found here https://perso.limsi.fr/rosset/resources/ cooking_LL_QA.tar.gz

https://perso.limsi.fr/rosset/resources/cooking_LL_QA.json

Acknowledgments

This work has been supported by ERA-Net CHIST-ERA LIHLITH Project funded by ANR (France) project ANR-17-CHR2-0001-03, and AEI (Spain) projects PCIN-2017-085/AEI and RTI2018-096846-B-C21 (MCIU/AEI/FEDER, UE).


Dario Magliacano
email: dario.magliacano@univ-fcomte.fr

Morvan Ouisse

Sergio De Rosa

Abdelkrim Francesco Franco

Abdelkrim Khelif

Computation of acoustic properties and design guidelines of periodic Biot-modeled foams

Keywords: vibroacoustics, Biot, foam, absorption coefficient, transmission loss, design guidelines Nomenclature

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

Introduction

Poro-elastic media are made of a frame with saturated fluid phase, and they attenuate sound energy through viscous and thermal dissipations, which come from fluid-structure interaction [START_REF] Biot | Mechanics of deformation[END_REF]. Poro-elastic materials with high porosity have interesting advantages of low 5 density, high surface area and low manufacturing costs. Open pore foams are widely used for acoustic applications in fields such as civil and industrial engineering, thanks to their capability of dissipating sound energy in a wide frequency range [START_REF] Cao | Porous materials for sound absorption[END_REF]. However, even if foams are commonly used for noise reduction, they suffer from a lack of performances at low frequencies compared 10 to their efficiency at higher ones [START_REF] Allard | Propagation of sound in porous media: Modelling sound absorbing materials[END_REF]. This difficulty is usually overcome by multi-layering [START_REF] Yang | Wave and finite element method for predicting sound transmission through finite multi-layered structures with fluid layers[END_REF]. Anyway, while reducing the impedance mismatch at the air-material interface, the efficiency of such devices still relies on the allowable thickness [START_REF] Weisser | Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach[END_REF][START_REF] Gaborit | A simplified model for thin acoustic screens[END_REF].

A more efficient way to enhance the low frequency response of sound packages consists in embedding periodic inclusions in a poro-elastic layer [START_REF] Groby | Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions[END_REF][START_REF] Xiong | Sound attenuation optimization using metaporous materials tuned on exceptional points[END_REF] in order to create wave interferences or resonance effects that may improve the dynamics of the system. Indeed, structural periodic design is a powerful strategy for lightweight structures achievements [START_REF] Boutin | Acoustics of porous media with inner resonators[END_REF] while remaining a convenient solution for manufacturing guidelines aspects [START_REF] Allard | Propagation of sound in porous media: Modelling sound absorbing materials[END_REF][START_REF] Gosse | Periodic assembly of multi-coupled parallel plates: vibration propagation and acoustic radiation, 16[END_REF], since periodic media exhibit proper dynamic filtering effects that can be smartly used for vibroacoustic design [START_REF] Rumpler | A modal-based reduction method for sound absorbing porous materials in poro-acoustic finite element models[END_REF][START_REF] Rumpler | A residue-based mode selection and sorting procedure for efficient poroelastic modeling in acoustic finite element applications[END_REF][START_REF] Liu | Broadband locally resonant metamaterial sandwich plate for improved noise insulation in the coincidence region[END_REF][START_REF] Liu | Investigation of the sound transmission through a locally resonant metamaterial cylindrical shell in the ring frequency region[END_REF][START_REF] Khelif | Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency[END_REF]. In the work by Groby et al. [START_REF] Groby | Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions[END_REF], the influence of periodic inclusions on the acoustic performances is explained by excitation of additional acoustic modes which dissipate acoustic energy. To this aim, advanced and innovative numerical tools are more and more useful [START_REF] Magliacano | Computation of dispersion diagrams for periodic porous materials modeled as equivalent fluids[END_REF]. Periodic poro-elastic media, generated by uniform spatial repetition of specifically designed unit cells in the 3D domain, are extensively used in noise control applications; examples include polyurethane foams, metal foams, porous asphalt, cotton, hemp synthetic fibers, jute, glass wools, which are widely used in commercial and industrial applications [START_REF] Deshmukh | Design of periodic foam structures for acoustic applications: Concept, parametric study and experimental validation[END_REF]. Over the years, these media have been studied to the aim of their optimization for acoustic performances [START_REF] Allard | Propagation of sound in porous media: Modelling sound absorbing materials[END_REF][START_REF] Doutres | Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model[END_REF]. Open cell or reticulated foams are also used in heat sink, energy absorption, packaging, architecture and even multifunctional applications. Several application-specific requirements exist; for example, in mission-critical applications such as space ones, predictability is a very high priority [START_REF] Deshmukh | Design of periodic foam structures for acoustic applications: Concept, parametric study and experimental validation[END_REF]. The typical process of material choice in these fields includes the characterization of several foams, in order to identify the most suitable one. Anyway, this process is time-consuming, and a systematic design-based approach to obtain the desired macroscale performances is still lacking. In the research performed by Deshmukh et al. [START_REF] Deshmukh | Design of periodic foam structures for acoustic applications: Concept, parametric study and experimental validation[END_REF], some parametric analyses about unit cell geometry, porosity, airflow resistivity, tortuosity, viscous and thermal characteristic lengths are carried out using the Johnson-Champoux-Allard (JCA) model [START_REF] Johnson | Theory of dynamic permeability and tortuosity in fluid-saturated porous media[END_REF][START_REF] Champoux | Dynamic tortuosity and bulk modulus in air-saturated porous media[END_REF][START_REF] Ouisse | On the sensitivity analysis of porous material models[END_REF]. For what concerns the design guidelines, similar investigations are present in the relevant literaure [START_REF] Magliacano | Design guidelines for the acoustic performance improvement of a periodic porous material[END_REF]. The main difference that is proposed herein is constituted by the extension of such parametric analyses to periodic Biot-modeled poro-elastic foams; thus, in this case, also the elastic properties of the frame are considered and analyzed [START_REF] Biot | Mechanics of deformation[END_REF]. In this work, some novelties are introduced to the state of the art regarding the study and the design of Biot-modeled poro-elastic materials [START_REF] Biot | Mechanics of deformation[END_REF], in order to estimate their acoustic performances.

In Section 2, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, are introduced. Successively, in Section 3, a nonrigid inclusion test campaign is carried out in terms of absorption coefficient and transmission loss, highlighting the differences between the use of a perfectly rigid inclusion and a rubber inclusion (which is an attempt to simulate an almost rigid one) in three different foams. Then, in Section 4 some guidelines are provided in order to predict at which frequency the 1 st performance peak (related to periodicity effects: half of the wavelength = periodicity dimension) appears, together with its amplitude, as functions of the unit cell dimensions. Conversely, also the link between the unit cell dimensions and the 1 st performance peak amplitude as functions of the design frequency is shown. Furthermore, some additional guidelines are provided in order to predict at which frequency the 1 st performance peak appears, together with its amplitude, as functions of the foam airflow resistivity, tortuosity, viscous and thermal characteristic lengths; moreover, it is shown that frame density, Young modulus and loss factor of the foam constitute less efficient parameters in order to tune the performances of an acoustic package. In Section 5 it is also shown that, even if apparently the insertion of a periodic inclusion pattern in a layer of foam always leads to an absorption coefficient performance decay for the cases of study, instead there is an actual way to improve it without necessarily exploiting the use of Helmholtz resonators. In conclusions, as highlighted in Section 6, the results of this investigation are very promising within the field of applications of periodic poro-elastic media in acoustics.

Definition of the system

This section aims at introducing the properties of the system that represents the object of the present work.

The tested unit cell is constituted by a 3D-periodic cube with side dimension r =2 cm and with a 0.5 cm radius perfectly rigid cylindrical inclusion (Figure 1). For similar cases, some results are available in literature in terms of absorption coefficient [START_REF] Groby | Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating[END_REF]. The characteristics of the poro-elastic media are reported in Table 1; in addition, quantities defined in Biot model of poro-elasticity [START_REF] Biot | Mechanics of deformation[END_REF] are recalled in Appendix A. It should be noted that, even if for most polymeric foams the elastic properties are frequency dependent, here they are not since, during the investigation process, it has been remarked that their frequency dependence is generally quite negligible and, in authors' opinion, does not justify 90 the sensible increase in terms of computational time required to perform a Finite Element (FE) analysis. The size of the cylindrical inclusion is large compared to the typical characteristic length that may be observed on a representative elementary volume describing the macroscopic behavior of the porous material [START_REF] Robin | Measurement of the absorption coefficient of sound absorbing materials under a synthesized diffuse acoustic field[END_REF]. The air parameters are: ρ air = 1.21 kg m 3 (density), c air = 343.3 m s (speed of sound) and K air = 142 kPa (bulk modulus), while the properties of the PU 60 foam are reported in Table 1.

Non-rigid inclusion test campaign

In this section, through the use of the acoustic-structure coupling that comes from the implementation of Biot model [START_REF] Biot | Mechanics of deformation[END_REF], a non-rigid inclusion test campaign that considers some solid (but still non-perfectly-rigid) inclusions in a 3D-modeled unit cell is shown, in terms of absorption coefficient and transmission loss computed at normal incidence. The general definition of the sound absorption coefficient is the fraction of incident energy propagating into a sample material versus the energy propagating out. A part of the incident energy will be absorbed into the sample material, or rather dissipated. Since, in this case, the FE system is modeled in order to be acoustically closed, this must imply that the part of the incident propagating wave that is not reflected by the material must be absorbed, therefore the coefficient of absorption is [START_REF] Groby | Total absorption peak by use of a rigid frame porous layer backed by a rigid multi-irregularities grating[END_REF]:

α = 1 -|R| 2 , (1)
with the reflection coefficient computed from the surface impedances of the material (Z s ) and of the air (Z 0 ) as [START_REF] Groby | Total absorption peak by use of a rigid frame porous layer backed by a rigid multi-irregularities grating[END_REF]:

R = Z s -Z 0 Z s + Z 0 . ( 2
)
Transmission loss is numerically calculated as:

T L = 10log 10 Π incident Π transmitted , (3)
where Π incident and Π transmitted represent the incident and transmitted powers, 100 respectively [START_REF] Kosałan | Calculation models for analysing the sound insulating properties of homogeneous single baffles used in vibroacoustic protection[END_REF]. The analysis is carried out in the frequency range 0 -9000 Hz, and classical Floquet-Bloch periodic conditions [START_REF] Floquet | Sur les équations différentielles linéaires à coefficients périodiques [On the linear differential equations with periodic coefficients[END_REF][START_REF] Bloch | Uber die quantenmechanik der elektronen in kristallgittern [On the quantum mechanics of the electrons in crystal lattices[END_REF] are used along x and y directions. The following results are related to an acoustic package composed by a finite arrangement of five unit cells (Figure 1), whose geometry and properties are described in Section 2, and the poro-elastic properties 105 of the foams are reported in Table 1. In particular, the materials labeled as "Foam 1" and "Foam 2" indicate generic real porous materials which can easily be found on the market. Related results are shown in Figure 2 and Figure 3. It should be noted that the mass variation related to the perfectly rigid inclusion case reported in Table 2 is negative, due to the fact that this case is purely theoretical, being representative of an inclusion with perfect sound-hard boundary walls, but with no matter inside. Additional results are provided from Figure 4 to Figure 7, obtained by carrying out the non-rigid inclusion test campaign also using Foam 1 and Foam 2, described in Table 1. Some interesting considerations may be formulated, based on the results provided herein.

In the context of the studied systems, after appropriate checks, the cause of the macroscopic resonances that are visible in the cases of PU 60 (around 6500 Hz) and Foam 1 (around 5000 Hz) has been addressed to the effect of periodicity (half of the wavelength = periodicity dimension), except from the case related to Foam 2 (around 3000 Hz), where the main visible peak is probably caused by a spring-mass effect. This is confirmed by the fact that, looking at the "Air inclusion" curves from Figure 2 to Figure 5, they do not seem to advert the effect of the inclusion, probably due to the low impedance mismatch between the contact surfaces; instead, in Figure 6 and Figure 7, the peaks are visible also in case of an inclusion filled by air, this being a further clue leading to a spring-mass resonance.

As expected, it should be noted how the sharpness of the performance peaks rises when the structural loss factor of the foam decreases. Moreover, the fact that the periodicity peak shifts backward in frequency from PU 60 case to Foam 1 case, could be explained through the higher tortuosity value of the latter. This behavior is better explained in Section 4, which provides a more detailed discussion and additional results about design guidelines.

Design guidelines

In this section, with reference to a PU 60 foam, some design guidelines are provided.

For some of the investigated quantities (airflow resisitivty, tortuosity, viscous and thermal characteristic lengths), some 3D plots are provided too, in which the two horizontal axes always represent the ranges of frequency and of the considered parameter, while the vertical axis shows the values of absorption coefficient (from 0 to 1) or transmission loss (from 0 dB to 100 dB). Firstly, they are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of the unit cell dimensions. Conversely, also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency is shown. The test campaign is carried out in the 0 -10000 Hz frequency range, through the use of a repetition of five 3D unitary cells constituted by a 2 cm cube with a 0.5 cm radius perfectly rigid cylindrical inclusion (Figure 1), where the dimension of the inclusion changes accordingly to those of the unit cell (the ratio between the unit cell and the inclusion dimensions is kept constant).

According to the results obtained in Figure 8 and Figure 9, and considering that a typical acoustic excitation in aeronautics lays in the range of 20 -2000 Hz [START_REF] Peiffer | Full frequency vibro-acoustic simulation in the aeronautics industry[END_REF], one should choose a unit cell dimension between 0.065 m and 0.1 m in order to obtain a transmission loss improvement of averagely 25% respect to the use of a simple foam layer of the same thickness.

Considering an automotive application, instead, the typical acoustic excita- tion lays in the range of 20 -4000 Hz [START_REF] Mohanty | An overview of automobile noise and vibration control[END_REF], and therefore one should choose a unit cell dimension between 0.035 m and 0.1 m in order to obtain a transmission loss improvement of averagely 35% respect to the use of a simple foam layer of the same thickness. Furthermore, some guidelines are also provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of the airflow resistivity value of the foam. The test campaign is carried out in the 0 -10000 Hz frequency range, by comparing a repetition of five PU 60 unit cells, whose geometry is described in Figure 1 and where the airflow resistivity value is artificially changed. Looking at Figure 10, the static airflow resistivity has negligible impact on the position of the periodicity peak in the frequency range. Instead, one may notice that the airflow resistivity σ has a non-negligible effect on the variation of the nonhomogeneous values, compared to the homogeneous ones, in correspondence of the periodicity peak. In particular, this variation reduces its amplitude at increasing airflow resistivity values, both for absorption coefficient and transmission loss performances. This is probably due to the fact that, as shown in Figure 11 and, in an even more evident manner, in Figure 12, for a homogeneous layer of foam, when σ increases absorption coefficient performances decrease, while transmission loss ones gets better. This is an expected phenomenon, since the airflow resistivity parameter may be considered as an "acoustical hardness" indicator of a foam, in the sense that, the higher it is, the less air permeability there is.

It is evident, then, that the general effect of the presence of any external inclusion in the foam reduces at increasing σ, and the non-homogeneous curves tends to assume the same behavior of the homogeneous one, still maintaining a bias difference in the average value (as it can be clearly seen from Figure 12). Indeed, already starting from σ = 60000 Pa*s m 2 , periodicity peaks are no more precisely identifiable.

For what concerns the tortuosity of the foam, from Figure 13 to Figure 15 it is evident that it has a strong impact on the acoustic performances of the system. In particular, at increasing tortuosity, the periodicity peak shifts backward in frequency, while also weakly reducing its amplitude.

Figure 16 show that also the viscous characteristic length has a measurable impact, in this context. The behavior is the inverse of the one related to tortuosity: at increasing viscous characteristic length, the periodicity peak shifts forward in frequency, while also weakly increasing its amplitude. In addition, a higher value of viscous characteristic length means a less reflecting foam: absorption increases (Figure 17), while transmission loss decreases (Figure 18). Differently from the viscous one, from Figure 19, Figure 17 and Figure 18 it can be stated that the thermal characteristic length has no evident impact on the frequency position of the periodicity peaks, but it has a more intense effect on their amplitude: at increasing thermal characteristic length, the periodicity peak do not shift in frequency, but increases its amplitude. Moreover, as it can be stated from Figure 22, Figure 23 and Figure 24, frame density, Young modulus and loss factor parametric analyses do not provide any evident shifts in terms of absorption coefficient and transmission loss.

Therefore it can be concluded that, for what concerns the acoustic perfor-

1 st peak (data) mances of a periodic arrangement of unit cells, the elastic characteristics of a foam represent parameters that are less meaningful, compared to the ones related to its porous nature, in order to tune the periodicity peak. Instead, the elastic characteristics are strongly linked with the spring-mass effect, whose design guidelines are out of the scope of this work. Summarizing, in order to tune the frequency position of an acoustic performance peak caused by periodicity effects, one should act on:

1 st peak (fitted curve) enhancement (data) enhancement (fitted curve
• the unit cell dimension (discordant trend),

• the tortuosity (discordant trend), instead, to the aim of properly designing its amplitude, one could change:

• the unit cell dimension (discordant trend),

• the airflow resistivity (discordant trend),

• the tortuosity (discordant trend),

• the viscous characteristic length (concordant trend),

• the thermal characteristic length (concordant trend).

Design of absorption coefficient low frequency improvement

The aim of this section is to show that, even if apparently the insertion of a periodic inclusion pattern in a layer of foam always leads to an absorption coefficient performance decay for the cases of study (Figure 2), instead there is an actual way to improve it without necessarily exploiting the use of Helmholtz resonators [START_REF] Groby | Enhancing the absorption properties of acoustic porous plates by periodically embedding helmholtz resonators[END_REF]. If one uses a repetition of sufficiently small unit cells, some oscillations of the absorption coefficient values can be observed at low frequencies, respect to the homogeneous case. In Figure 25, the results are related to Configurations 1, 2 and 3 of Table 2, where the setup is constituted by a repetition of five 3D unit cells (Figure 1), whose side length is 0.01 m. In this situation, the differences between the perfectly rigid inclusion and the rubber inclusion cases are negligible at low frequencies. It can be noticed that the effect described above lays in the range of 550 -1450 Hz, very interesting for acoustic applications, where the average improvement is of about 16 % .

Conclusions

In this work, some novelties are introduced to the state of the art regarding the study and the design of Biot-modeled poro-elastic materials, in order to estimate their acoustic performances. First of all, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, have been introduced. Then, through the use of the acoustic-structure coupling that comes from the implementation of Biot model, a non-rigid inclusion test campaign has been carried out by considering some solid (but still non-perfectly-rigid) inclusions in a 3D-modeled unit cell. In particular, six setups have been discussed. • KB = 2N (ν+1) 3(1-2ν) ;

•

N = |N |(1 + jη) = Y 2(1+ν) ; • P = (1-φ)(1-φ-KB KS )KS+φ KBKS KF 1-φ-KB KS +φ KS KF -2 3 N ∼ = (1 + ν 1-2ν )2N + 1-φ 2 φ KF ; • Q = (1-φ-KB KS )φKS 1-φ-KB KS +φ KS KF ∼ = (1 -φ)KF ; • R = φ 2 KS 1-φ-KB KS +φ KS KF ∼ = φKF ; • Y = |Y |(1 + jη); • γ = φ( ρ 12 ρ 22 -Q R ); • µ i = P δ 2 i -ω 2 ρ 11 ω 2 ρ 12 -Qδ 2 i , i = 1, 2; • ρ a = φρ 0 (α ∞ -1); • ρ 11 = ρ 1 + ρ a + b jω ;
• ρ 12 = -ρ a -b jω ;

• ρ 22 = φρ 0 + ρ a + b jω ;

• ρ = ( ρ 11 -ρ

Figure 1 :

 1 Figure 1: 3D unit cell constituted by a 2 cm cube with a 5 mm radius cylindrical hole (on the left), and a repetition of five of these unit cells (on the right).

Figure 2 :Figure 3 :

 23 Figure 2: Non-rigid inclusion test campaign for PU 60 foam; absorption coefficient.

Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 4567 Figure 4: Non-rigid inclusion test campaign for Foam 1; absorption coefficient.

Figure 8 :Figure 9 :

 89 Figure 8: Absorption coefficient design curves as a function of the unit cell dimension (on the left) and the frequency of the first peak (on the right).

Figure 10 :

 10 Figure 10: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam airflow resistivity.

Figure 11 :

 11 Figure 11: Absorption coefficient value as a function of frequency and foam airflow resistivity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 12 :

 12 Figure 12: Transmission loss value as a function of frequency and foam airflow resistivity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 13 :

 13 Figure 13: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam tortuosity.

Figure 14 :

 14 Figure 14: Absorption coefficient value as a function of frequency and foam tortuosity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 15 :Figure 16 :Figure 17 :

 151617 Figure 15: Transmission loss value as a function of frequency and foam tortuosity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 18 :

 18 Figure 18: Transmission loss value as a function of frequency and foam viscous characteristic length; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 19 :Figure 20 :

 1920 Figure 19: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam thermal characteristic length.

Figure 21 :

 21 Figure 21: Transmission loss value as a function of frequency and foam thermal characteristic length; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right).

Figure 22 :

 22 Figure 22: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam skeleton density.

Figure 23 :

 23 Figure 23: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam Young modulus.

Figure 24 :

 24 Figure 24: Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam loss factor.

Figure 25 :

 25 Figure 25: Absorption coefficient low frequency improvement.

  395 dimension (on the left) and the frequency of the first peak (on the right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam airflow resistivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 11 Absorption coefficient value as a function of frequency and foam airflow resistivity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right). 12 Transmission loss value as a function of frequency and foam airflow resistivity; homogeneous case (on the left) and case 405 with a cylindrical perfectly rigid inclusion (on the right). . . . 13 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam tortuosity. . . 14 Absorption coefficient value as a function of frequency and foam tortuosity; homogeneous case (on the left) and case with 410 a cylindrical perfectly rigid inclusion (on the right). . . . . . . 15 Transmission loss value as a function of frequency and foam tortuosity; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right). . . . . . . . 16 Absorption coefficient (on the left) and transmission loss (on 415 the right) design curves as functions of the foam viscous characteristic length. . . . . . . . . . . . . . . . . . . . . . . . . . 17 Absorption coefficient value as a function of frequency and foam viscous characteristic length; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on 18 Transmission loss value as a function of frequency and foam viscous characteristic length; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 19 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam thermal characteristic length. . . . . . . . . . . . . . . . . . . . . . . . . . 20 Absorption coefficient value as a function of frequency and foam thermal characteristic length; homogeneous case (on the 430 left) and case with a cylindrical perfectly rigid inclusion (on the right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Transmission loss value as a function of frequency and foam thermal characteristic length; homogeneous case (on the left) and case with a cylindrical perfectly rigid inclusion (on the 435 right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam skeleton density. 23 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam Young modulus.

440 24

 24 Absorption coefficient (on the left) and transmission loss (on the right) design curves as functions of the foam loss factor. . 25 Absorption coefficient low frequency improvement. . . . . . . .

Table 1 :

 1 Poro-elastic properties of the tested foams.

		PU 60 Foam 1 Foam 2
	Porosity	0.98	0.96	0.97
	Tortuosity	1.17	1.7	2.52
	Resistivity [Pa*s/m 2 ]	3750	32000	87000
	Viscous char. length [mm] 0.11	0.09	0.037
	Thermal char. length [mm] 0.742	0.165	0.119
	Density [kg/m 3 ]	22.1	30	31
	Young modulus [kPa]	70+j19 733+j73 143+j8
	Shear modulus [kPa]	25+j7	246+j26 55+j3
	Loss factor	0.265	0.1	0.055
	Poisson ratio	0.39	0.387	0.3

Table 2 :

 2

	PU 60	22.1	70(1 + j0.265)	0.39
	Silicon rubber 1100	1e6(1 + j0.4)	0.47

Combinations of inclusions used in the non-rigid inclusions test campaign, with a Biot-modeled PU 60 foam, and mass variations respect to the homogeneous case.

Material

Density [kg/m 3 ] Young m.

[kPa] Poisson r.

Table 3 :

 3 Elastic properties of the materials used in the non-rigid inclusions test campaign, with a Biot-modeled PU 60 foam.

  12 2 ρ 22 ). Non-rigid inclusion test campaign for PU 60 foam; transmission loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inclusion test campaign for Foam 2; absorption coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absorption coefficient design curves as a function of the unit cell dimension (on the left) and the frequency of the first peak (on the right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Transmission loss design curves as a function of the unit cell

	3
	385
	4	Non-rigid inclusion test campaign for Foam 1; absorption co-
		efficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	5	Non-rigid inclusion test campaign for Foam 1; transmission loss.
	6 Non-rigid 390
	7	Non-rigid inclusion test campaign for Foam 2; transmission loss.
	8

• the viscous characteristic length (concordant trend);

the right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Successively, some design guidelines are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of unit cell dimensions, airflow resistivity, tortuosity, viscous and thermal characteristic lengths, frame density, Young modulus and loss factor; conversely, it is shown also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency. The outcome of this investigation is very promising in the context of characterizations and applications of periodic poro-elastic media for aeronautic and automotive acoustic applications, and the presented results are qualitatively applicable beyond the configurations studied herein. Future works can focus on embedding resonant inclusions in a porous layer, which offer an alternative to multi-layering and double porosity materials in the design of sound absorption and insulation packages for low frequency applications.

Appendix A. Quantities defined in Biot model of poro-elasticity

List of Tables