Dr Pauline Lejault

Dr Katerina Duskova

Dr Claire Bernhard

Dr Ibai E Valverde
email: ibai.valverde@u-bourgogne.fr

Dr Anthony Romieu
email: anthony.romieu@u-bourgogne.fr

Dr David Monchaud
email: david.monchaud@cnrs.fr

The scope of application of macrocyclic polyamines beyond metal chelation

Keywords: polyazamacrocycles, molecular platform, multivalency, theranostics, bioactive compounds

Recent advances in the use of radiometals for both imaging and therapy has spurred on the development of an original chemistry that endows radionuclide-chelating molecular cages with ever sharper physicochemical properties. Macrocyclic polyamines (MPAs) such as cyclen and DOTA are among the most frequently encountered cages for the design of new radiotracers, owing to their versatile chemistry that makes them customizable molecular tools. The idea of using MPAs for alternative purposes has recently emerged, with an eye towards benefiting from their unique topology, versatility, symmetry and water-solubility. This review summarizes strategies that have been recently implemented in which MPAs are used as multivalent molecular platforms for constructing sophisticated suprastructures that found applications in various fields, from material chemistry to chemical biology. These original approaches are invaluable in that they successfully expand the scope of applications of MPAs far beyond their restricted roles of metal chelating appendages.

Introduction

Chemistry is the art of playing with complex molecular scaffolds to diversify their uses in a creative and virtually unlimited manner. The capability of chemists to modulate ad libitum the nature of chemical objects allows them for optimizing the properties of selected compounds for intended purposes (e.g., structure-activity relationship studies) or endowing chemicals with new functions, thereby opening new scopes and fields of application. Many examples of the latter approach can be cited, including the chemical modification of natural nutrients for cancer-directed applications, owing to the known avidity of malignant cells: for instance, the modification of glucose into 2-deoxy-2-[fluorine-18]fluoro-glucose ( 18 FDG) allows its use as an effective probe for imaging various cancers via positron emission tomography integrated with computed tomography (PET/CT); [1] also, the repurposing of vitamin B9 (folic acid) as a cancerspecific carrier of drugs (e.g., maytansine, camptothecin) was thoroughly exploited in an approach referred to as small-molecule drugs conjugates (SMDCs). [2] In fewer cases, chemists have also strived to repurpose fully synthetic compounds initially designed to fulfill precisely defined tasks, to open new chemical landscapes. In the present review, we focus on the example of macrocyclic polyamines (MPAs), [START_REF]For selected reviews about the chemistry of MPAs[END_REF] which comprise a class of nitrogen-containing heterocyclic compounds that have found many applications in medicinal chemistry. [4] The most emblematic MPA is certainly the 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (or DOTA) (Figure 1). [5] This macrocycle has been thoroughly exploited for its ability to firmly chelate metal ions, thanks of the presence of 4 nitrogen atoms (embedded in the macrocyclic structure) and 4 surrounding carboxylic moieties (belonging to its 4 acetic acid pendant arms). This eightfold valency has made DOTA and DOTA-like molecules invaluable tools for multiple applications such as waste-water treatment, hydrometallurgy, and medicine. [3a] In the medical field, the use of metal complexes of DOTA is closely connected to molecular imaging and, increasingly, to internal radiation therapy, or radioendotherapy. Gadolinium(III) complexes of DOTA and similar macrocyclic chelators are the perfect example of successful inorganic drugs that have become commonplace in medicinal practice in the last decade. Thanks to their high relaxitivity and stability in physiological media, they have become the gold standard contrast agents for magnetic resonance imaging (MRI). [6] However, gadolinium-based contrast agents used in the clinic are not disease-specific; as a matter of fact, the clear delineation of soft tissues they provide relies on their wide, non-specific, distribution in the body that requires the use of large amounts of metallic complex. In sharp contrast, DOTA-metal complexes can also be used for specific detection of diseases with trace amounts of imaging agent. In a classical approach, DOTA and DOTA-like molecules can be conjugated to biological vectors of interest (peptides, proteins, antibodies) prior to chelating a radiometal of interest (e.g., gallium-68, indium-111, yttrium-90, lutetium-177). [7] The resulting, highly thermodynamically stable complexes can thus be used in vivo for diagnosis, via the use of a broad variety of imaging modalities (positron emission tomography (PET), single photon emission computed tomography (SPECT), Cerenkov luminescence imaging (CLI), etc.), multimodality approaches, [8] or therapeutic purposes, through radioendotherapy using electron (b -decay)-or alpha (a)-particle emitting radiometals, or both (the so-called theranostic approach). [9] The unique complexation properties of DOTA and, beyond this, of many MPAs, and their medical uses thereof, are regularly covered by authoritative reviews the reader is invited to refer to. [3a, 4, 6, 8, 10] Here, we focus on original strategies that have been devised and implemented over the past few years to exploit another, lesser-known aspect of MPAs, unrelated to metal chelation.

DOTA encodes an interesting topological information, due to the programmable positioning of its four, easily derivatizable acetic acid arms, which has not received the attention it deserves. Beyond its chemical stability, inherent polarity and marked aqueous solubility, DOTA can be used as a molecular platform to allow for assembling up to four compounds of interest in a single scaffold, and possibly modulate the physico-chemical properties of the resulting multi-component molecular architecture (Figure 1). This approach has led to the design, synthesis and studies of original, highly functionalized MPAs, which can be either symmetrical (fourfold derivatization) or not (tailored derivatization for endowing MPAs with multiple distinct molecular fragments and functionalities). As further detailed in the next sections, these exquisite molecular tools have found applications in various chemical fields, from soft matter to chemical biology. This review is not mainly dedicated to the synthetic aspects related to MPAs since the vast majority of molecular tools showed below are readily prepared through conventional N-alkylation and/or peptide-like coupling reactions, taking advantage of well-established protecting group manipulations. HPLC purifications are often privileged for their isolation in pure form (often as trifluoroacetic acid salts), due to the marked polarity and large molecular size of these sophisticated multivalent conjugates.

Nevertheless, for some examples of functionalized MPAs, more specific information related to their synthesis/purification which we consider to be relevant for the reader will be provided throughout the text.

Symmetrical MPAs

Full-N-functionalization of readily available tetraazacycloalkanes (i.e., cyclam, cyclen and TACN, vide infra) with the same molecular arm may be regarded as one of the most straightforward and simple way to access to multivalent compounds with specific structural features and tailored properties. It is therefore not surprising that the first applications of MPAs beyond metal chelation were based on use of such symmetrical architectures.

Soft matter and chirality sensing

In the early 2000s, Michinobu, Tsukube and co-workers have synthesized a DOTA conjugated to four chiral cholesterol units (one per arm), through tetra-N-alkylation of 1,4,7,10tetraazacyclododecane (or cyclen) with cholesterol chloroacetate (1, Figure 2). [11] This derivative self-assembles in aqueous ethanol solutions (20-30%) as chiral aggregates (critical aggregation concentration: 4 µM), due to the intrinsic chirality of the cholesterol unit that is spread over the whole supramolecular structure upon self-association. This asymmetry was exploited to sense amino acids fluorescently labeled with an environment-sensitive fluorophore, namely dansyl, in solution, discriminating for instance between dansyl-L-leucine and dansyl-D-leucine by both the fluorescence enhancements (triggered by the hydrophobic pocket provided by the cholesterol units, 6.5-versus 4.9-fold, respectively, i.e., 1.3-fold difference) and the blue-shifts of emission maxima (from 532 to 505 and 507 nm, respectively). [12] Furthermore, at the air-water interface, compound 1 leads to the formation of a stable monolayer (molecular area: 1.6 nm 2 ; collapse pressure: 50 mM.m -1 ), owing to its resolutely amphiphilic nature (hydrophobic cholesterol versus hydrophilic MPA on the other hand) (Figure 2). The resulting chiral monolayer was exploited to sense unlabeled amino acids, discriminating L-leucine versus D-leucine by their binding constants (K) measured via surface pressure (p-A) isotherm measurements (K = 85.2 versus 1063.0 M -1 , respectively, i.e., 12.5-fold difference at 1 mM.m -1 pressure). [13] Of note, in these investigations, the presence of Na + ion is mandatory, as a trigger for the chiral folding the cholesterol-armed DOTA via its octacoordination at the very heart of the conjugate.

Medicinal chemistry and multivalency

A possible way to improve the efficiency of therapeutics is to assemble multiple units in a same scaffold (the so-called multivalency approach) [14] via covalent linking to a molecular platform. Recent studies seem to indicate that ligand hetero-or homo-multimerization provides increase in half-life in vivo, circulation time and receptor avidity. Thorough studies were performed with cyclic arginine-glycine-aspartic acid (RGD) peptides c(RGDfK) or c(RGDyK), which targets integrin α v β 3 , [15] among others. This receptor affects tumor growth, local invasiveness, metastatic potential and is lowly expressed on the surface of nonmalignant cells while being overexpressed on tumor cells in need of neovasculature. Such expression profile constitutes a unique therapeutic target. [16] Furthermore, it has been demonstrated that integrin heterodimers are prone to receptor clustering upon cell activation, resulting in increased ligand avidity. [17] Thus, strategies of multimerization of an additional glutamic acid unit). [18] Both derivatives show improved integrin binding affinity and cellular uptake, lending credence to this strategy. Similarly, Boturyn and co-workers reported on the synthesis of a Cy5.0-labeled c(RGDfK) tetramer based on a cyclic decapeptide scaffold (RAFT) that displayed improved selectivity for tumor xenografts overexpressing the α v β 3 receptor in comparison with its monomeric counterpart. [19] Cheng and co-workers further explored it, exploiting the unique versatility of the DOTA platform to construct monomeric to tetrameric c(RGDfK) conjugates (DOTA-P1, -P2, -P3 and -P4, respectively, with P for peptide) (Figure 3). [20] Of note, the easy-to-implement synthetic protocol described here, based on the aminolysis of N-hydroxysulfosuccinimidyl ester of DOTA (DOTA-sulfo-NHS) by fully deprotected peptide c(RGDyK) in aqueous buffer, was devised to rapidly obtain RGD multimers. The four compounds were obtained during a single coupling reaction conducted with a large excess of DOTA-sulfo-NHS, and recovered in a pure form by reversed-phase HPLC purification, but neither in large amounts nor in optimized yields. This study confirmed the better integrin affinity of DOTA-Ps, evaluated through competitive binding assays against 125 Iechistatin (IC 50 = 380, 37 and 13 nM for DOTA-P1, -P2 and -P3, respectively), but also highlighted that the DOTA tetra-functionalization might be chemically challenging especially via amidation reactions performed in aqueous buffer (pH 8.5-9.0), given that DOTA-P4 was not isolated in quantities suited to in vitro evaluations. structures in a single scaffold, with the hope of decreasing conformational variability. [21] However, the resulting cyclic c(DOTA-RGD) and c(DOTA-RGDf) (Figure 3 (DOTPI(RGD)4, isolated yield = 68%) (Figure 3). [22] The use of the peptide coupling reagent O-(7-azabenzotriazol-1-yl)-N,N,N',N'-tetramethyluronium hexafluorophosphate (HATU) allows for achieving chemoselective amidation reactions without protection of the phosphinate moieties, making the synthesis of DOTPI(RGD)4 particularly straightforward. This conjugate displayed a higher integrin affinity, evaluated by ELISA using cilengitide as internal standard, with IC 50 = 1330 and 109 pM for monomeric c(RGDfK) and DOTPI(RGD)4, respectively (i.e., 12.2-fold difference). The same research group also explored the grafting of four prostatespecific membrane antigen (PSMA) inhibitors KuE (Lys-urea-Glu) to DOTPI platform via click chemistry (both copper-catalyzed and copper-free azide-alkyne cycloadditions, CuAAC [23] and SPAAC, [24] respectively, to assess whether Cu(II) precatalyst can be used or not in the context of molecular platform with marked copper chelating ability). PSMA, being a membrane-bound zinc hydrolase overexpressed in prostate cancers, is a high-value target (being subjected to 190 clinical trials, 23 of them being currently active). [25] Obtained multimers DOTPI(Trz-KuE)4

and DOTPI(DBCO-KuE)4 (Trz for triazole, DBCO for dibenzocyclooctyne) (Figure 3) display a higher PSMA affinity than monomeric KuE, along with high tumor uptake and blood clearance. [26] Of note, in these investigations, radiometals were subsequently sequestered at the very heart of both DOTA-Ps and DOTPIs to allow for tracking biodistribution of the resulting complexes in vivo through nuclear imaging.

Chemical genetics and biomimicry

The fourfold symmetry of DOTA was also exploited for the construction of chemicals targeting fourfold symmetrical targets. Quadruplex-DNA and RNA (or G4-DNA and G4-RNA, respectively) fold from guanine (G)-rich nucleic acid sequences. [27] The structure of this higherorder DNA/RNA architecture is rather peculiar, given that its stability arises from the formation of fourfold symmetrical G-quartets (i.e., coplanar and cyclic arrangement of four guanines held together via 8 hydrogen bonds) that self-stack to form stable DNA/RNA structures (Figure 4). Quadruplexes (or G4s) are now recognized as key players in genetics, owing to their involvement in critical cellular events, chief among them replication and transcription. [28] Their targeting of G4s by ad hoc chemicals (G4-ligands) has attracted considerable attention, notably for gaining control over the cellular processes they are involved in. Hundreds of candidates have been studied as G4-interacting compounds, the overwhelming majority of them binding to the accessible external G-quartet of G4s. [29] Figure 4. Schematic representation of a G-quadruplex structure (with an emphasis on the chemical structure of both guanine and G-quartet) and its interaction with a G4-ligand (upper panel). Adapted from ref.

[30b] The smart G-quadruplex ligand PNA DOTASQ, under its 'open' (left) and 'closed' conformations (right), the latter being triggered by its interaction with a G-quadruplex only.

Given the fourfold symmetry of this privileged binding site, DOTA-based G4-ligands were designed. A synthetic guanine was inserted on each DOTA arm to allow the resulting compound for forming an intramolecular synthetic G-quartet. This compound named DOTASQ (for DOTA-templated synthetic G-quartet) uniquely interacts with G4 according to a biomimetic process (i.e., the self-recognition of two G-quartets, one from the ligand and one from the G4), thus being the first prototype of biomimetic G4-ligand. [30] A second generation of DOTASQ was reported, in which the simple guanines of DOTASQ were changed for peptidic nucleic acid (PNA)-guanine monomers, in which the presence of protonable amine side-arms make the resulting PNA DOTASQ cationic at physiological pH (Figure 4). The wreath of cationic charges around its intramolecular G-quartet governs and improves its interaction with native G-quartets (surrounded by negative charges from the phosphodiester linkages). [31] PNA DOTASQ is a better ligand than the neutral DOTASQ, for which the presence of metal ion (terbium, Tb driven by its interaction with G4s (demonstrated by NMR), thus being the first prototype of smart G4-ligand.

Non-symmetrical MPAs

A greater demand for multifunctional biomolecular devices, especially for applications in chemical biology, drug discovery and theranostics, has also led chemists to explore multiple functionalization of MPAs with different entities via sophisticated synthetic strategies. Some examples illustrating the use of DOTA derivatives as heteromultifunctional scaffolds will be discussed in the next sections.

MPAs with multiple functionalities

To further exploit the unique opportunity offered by MPA-based multimerization, Schultz, Nazare and co-workers described an elegant chemical strategy in which they insert on a DOTA platform up to three active biomolecules (collagen targeting peptides) along with a fluorescent reporter (i.e., the near-infrared fluorescent Cy5.5 dye). [32] The use of DOTA mono-, di-or tri-tert-butyl ester in combination with Fmoc/Boc protecting group strategy enables a facile and effective synthesis of these fluorescently-labeled multi-peptide conjugates through sequential peptide coupling-type coupling reactions performed in solution (i.e., with DMF as solvent). Small-molecules targeting diseased cartilaginous tissues are indeed scrutinized as promising molecular tools to remediate cartilage breakdown, responsible for osteoarthritis. [33] The targeting of one of the cartilage constituents, here the type II collagen, by N-acetyl- Val-Val-Sta-Ala-Sta, Iva for isovaleryl, Sta for statyl, with statine (3S,4S)-4-amino-3-hydroxy-6methylheptanoic acid) on DOTA. Pepstatin A is a known inhibitor of cathepsin D, [33] responsible for glycan loss-mediated cartilage degradation. The resulting conjugates comprise either 1 Ac-WYRGRL and 1 pepstatin A (1P1I, P for peptide, I for inhibitor), 1 Ac-WYRGRL and 3 pepstatin A (1P3I) or 3 Ac-WYRGRL and 1 pepstatin A (3P1I) (Figure 5). Though less active in vitro (IC 50 = 6.2 and 3.3 nM for 1P1I and 3P1I, respectively, versus 1.4 nM for free pepstatin A;

WYRGRL
1P3I being insoluble in the condition of the assay), these conjugates were found more active than pepstatin A in ex vivo experiments performed with cartilage explants, notably 3P1I that maintains a notable inhibitory activity (18%) after 48 h. These results demonstrate that peptide ligand multimerization improves the efficiency of cartilage targeting and, beyond this, the strategic interest of DOTA as drug carrier platform. This approach was further exploited by Brönstrup and co-workers through the use of multivalent siderophore-DOTA conjugates for targeting bacteria. [34] The introduction of three O-acetyl-2,3-dihydroxybenzoic acid units on the DOTA scaffold via amide linkages made the resulting conjugate capable of capturing and firmly chelating iron (i.e., acting as a siderophore after hydrolysis of its acetate moieties by bacterial esterases and may be regarded as an enterobactin analog). [35] This strategy is therapeutically efficient given that coupling antibiotic agents with iron-binding motif drives conjugated xenosiderophores within bacteria through their iron transportation machinery. Here, the fourfold valency of DOTA allows for introducing an additional functionality (Figure 5): either the antibiotic ampicillin that results in a conjugate with an antibacterial activity lower against wild-type E. Coli (IC 50 = 30.2 versus 4.3 µM for ampicillin used as control) but enhanced against enterobactin receptor-deficient mutants (IC 50 = 3.3 versus 6.2 µM for ampicillin), implying that DOTA is recognized as iron carrier that may enter bacteria via various transporters, which brings significant therapeutic dividends for tackling resistance issues. Additionally, the tris-siderophore-substituted DOTA was labeled with a Cy5.5 fluorophore leading to the successful detection of bacterial infection in vivo through optical imaging in a group of mice subcutaneously injected with P. aeruginosa (here, at 20 µg.kg -1 via a monitoring performed between 0.6-24 h). Again, these results highlight the strategic interest of DOTA as multivalent drug carrier platform. [38] copyright (2019), with permission from Oxford University Press.

C-functionalization of MPAs

For some applications, the chemical differentiation and orthogonal derivatization of the four acetic acid pendant arms of a DOTA platform is not relevant or suited to obtain targeted multicomponent conjugates. In this context, another way for introducing an additional functionality on DOTA, while keeping the global symmetry of the conjugate, is to chemically modify the DOTA scaffold itself. The C-functionalization of cyclen has been reported as a way to introduce an aminomethyl appendage on cyclen poised to be conjugated through conventional peptide-type coupling chemistry. [36] This approach was exploited to insert a pyrene moiety on DOTASQ (vide supra) for making the resulting terbium complex [Tb.Pyro-DOTASQ] 3+ (Figure 6), a luminescent ligand readily immobilizable on graphene surface. [37] The insertion of pyrene was found to improve the G4-binding properties of the complex (evaluated via FRET-melting assay, with DT 1/2 = 15.3 and 9.3 °C for [Tb.Pyro-DOTASQ] 3+ and [Tb.DOTASQ] 3+ , respectively), likely due to its steric hindrance that might facilitate the spatial orientation of the four guanine arms on the same side of the DOTA scaffold. Upon irradiation at 308 nm, the complex was found to efficiently sense the presence of G4s (with a 4-fold enhancement of the luminescence signal at 545 nm in presence of 10 molar equivalents G4s, versus no modifications with duplex-DNA).

The C-functionalization strategy was also implemented to add a biotin tag on DOTASQ, in order to allow the resulting BioTASQ for being used as a bait for capturing G4-DNA/RNA from human cells. [38] Thanks to the well-known biotin/streptavidin affinity purification system, BioTASQ efficiently pulls down G4-RNA from living human cells, prior to sequencing for characterizing isolated G4-RNA sequences. Two biotin appendages were introduced (biotin per se, and PEG 4 -biotin, for BioTASQ v.1 and v.2, respectively, Figure 6), which in both cases decreases its affinity of G4 in vitro (evaluated via FRET-melting assay, with DT 1/2 = 2.4 and 0.4 °C for BioTASQ v.1 and v.2, respectively versus 12.5 °C for the parent PNA DOTASQ), likely due to an intramolecular interaction between biotin and guanine moieties. The interaction with streptavidin-coated particles allows for tackling this issue (hijacking biotin) and makes BioTASQs capture efficiently G4s (G4-RNA precipitation, G4RP) subsequently identified by sequencing (G4RP-seq protocols). [39] This technique, derived from the Chem-seq method, [40] has not only allowed for confirming the transient existence of G4s in functional cells (highlighting their transient formation) but also for assessing the variations in G4 landscapes upon G4-ligand treatment.

MPAs and higher-order chemical architectures

MPAs were also used as platforms for building higher-scale suprastructures. As an example, Yu and co-workers synthesized cyclen-based cationic lipopolymers to serve as gene vectors. [41] The intracyclic nitrogen atoms of the cyclen were used as hydrophilic headgroups whereas the acetate arms were conjugated to small lipids via ring-opening polymerization to build amphiphilic polymers (Figure 7). They display enhanced transfection efficiency (TE) and cellular uptake, notably thanks to the "proton sponge effect" [42] that is based on the protonation of the gene vector within the endosomes, which favors osmotic swelling and endosomal rupture to deliver the nucleic acid partners. The chemical nature of cyclen allows for the formation of linear polymers only, with a rather low degree of polymerization (MW < 5000). These amphiphilic compounds self-assemble in solution into nanometer-size micellar structures (critical micelle concentration: 0.2 mg/mL; average micelle size = 300 nm). These polymers, which displayed low intrinsic toxicity, were used to condensate DNA (with a 2.8 polymer/DNA weight ratio, here the pGL-3 plasmid coding for luciferase as reported gene) and transfect cancer cells with a higher TE (14-fold) than that of commercially available transfection agents (polyethylenimine, PEI). [3a] Of note, the MPA-based gene delivery approach was thoroughly investigated with cyclen [43] but also with alternative MPAs such as [12]aneN 3 [44] or TACN, [45] highlighting again the great versatility of this family of macrocycles. Another approach was reported by Udugamasooriya and co-workers in which they use DOTA to build on-bead combinatorial libraries of DOTA-peptoid conjugates, [46] aimed at being used for screening and discovering novel and multivalent theranostic agents. To this end, one arm of the DOTA was used to immobilize the construct on TentaGel beads (300 µM diameter) via a short Met-(Nmea-Gly)-bAla linker (Met for methionine, Nmea-Gly for N-(2methoxyethyl)glycine and bAla for b-alanine), the three other arms used to introduce 6-mer peptoid units through PEG-type linkers of various lengths (Figure 7). This approach, so called of split-pool synthesis, allowed for generating a library that amounts to >150 000 compounds in a straightforward and efficient manner also exploiting the effectiveness of microwave (MW)-assisted solid-phase peptide synthesis protocols (overall yields >80%). Hudson and coworkers also thoroughly investigated the chemistry of MPA-peptide conjugates, developing a straightforward access via either MPA peralkylation strategies implemented with cyclen to produce DOTA-type conjugates [47] (but also TACN and cyclam derivatives) [48] or click chemistry approach performed with non-symmetrical DOTA derivatives and based on the prior incorporation of a terminal alkyne into the side-chain of tyrosine residue(s) (i.e., propargyl ether moiety). [49] Finally, DOTA was also used, yet more anecdotally, as a "square assembler" in metal-organic frameworks (MOF): [50] in this assembly, DOTA does not chelate metal within its cavity but is surrounded by four uranyl U(IV) cations (UO 2 2+ ), likely due to the excess of metal (i.e., 4 mol. equiv.), which connected the matrix via oxalato bridges (Figure 7). The obtained crystal structure confirmed the square conformation of DOTA, which provides a MOF with 5 x 8 Å pores. Cyclen was also used to assemble suprastructures such as carbon dots (CDs) via a MW-assisted condensation reaction with citric acid followed by a carbonization step. [51] The obtained blue-emitting CDs were further used to coordinate europium (Eu 3+ ) ions to construct a ratiometric fluorescent probe for tetracyclin detection.

Other types of MPA platforms

While most of the examples of multivalent bioconjugates reported in the literature (and discussed above) are built around a cyclen platform, the use of other MPAs has also been exploited. They offer different topological and functional possibilities and their unique chemistry is suited to construct original molecular devices with new applications, notably in the chemical biology area.

Sarcophagine, NOTA and RGD multimerization

Other MPAs than the cyclen/DOTA system were used as molecular platforms: Li, Conti and coworkers have for instance developed a multifunctional sarcophagine template, aimed at tackling in vivo stability of the 64 Cu/MPA complexes. The two pendant amine groups of this bicyclic MPA were derivatized to allow for the grafting of two c(RGDyC) units via maleimide (Mal) linkers. The copper complexes of the resulting Mal 2 Sar-RGD 2 (Figure 8) showed improved in vivo stability and better kinetics as compared to DOTA-c(RGDyC) conjugates in human glioma tumors. [52] Figure 8. Selected examples of mulitvalent bioconjugates based on different MPAs (including sarcophagine, TACN, cyclen, cyclam and cyclal) and phosphonate derivatives of tetraazamacrocycles used as inhibitors of protein tyrosine phopshatases).

A similar c(RGDyC) multimerization approach was followed by Sun and co-workers using a 1,4,7-triazacyclonane-1,4,7-triacetic acid (or NOTA) platform, surrounded by 1 to 3 c(RGDyC) units (named H 3 1, H 3 2 and H 3 3, respectively). [53] The multimeric conjugates were found to have better a v b 3 binding in vitro than the monomeric control (IC 50 = 171, 44 and 15 nM for H 3 1, H 3 2 and H 3 3, respectively, Figure 8) and the c(RGDyC) itself (IC 50 = 204 nM), along with better in vivo properties (higher stability, imaging signal amplification). These two studies brightly highlight and confirm again the aforementioned positive effect of RGD multivalency on both binding affinity and specificity and imaging signal amplification.

Cyclam, cyclal and phosphatase inhibitors

Vovk, Kukhar and co-workers reported on the use of 1,4,8,11-tetraazacyclotetradecane (or cyclam) to assemble effective inhibitors of T-cell protein tyrosine phosphatases (TC-PTP), an enzyme involved in the development of type I diabetes. [54] Known TC-PTP inhibitors include aromatic compounds with phosphonic groups, notably a,a-difluoro-b-ketophosphonates that poison the enzyme active site. [55] Cyclam but also cyclen and 1,4,8,12tetraazacyclopentadecane (or cyclal) were used to bring together four ketophosphonate-type arms within a single molecular scaffold (Figure 8).

TACN and DNA junctions

1,4,7-triazacyclonane (or TACN) was also exploited to benefit from its C 3 -symmetry suited to the construction of chemicals targeting threefold symmetrical targets. Three-way DNA junctions (TWJ) are Y-shaped, higher-order DNA structure at the heart of which a threefold symmetrical cavity is formed (the branch point), ideally suited to accommodate C 3symmetrical ligands. [56] DNA junctions might arise ahead of the replication fork, as a way to relax helical stress that originates in the translocation of the replication machinery along the duplex. If not properly processed (by helicases), these structures act as impediments to DNA transactions, forcing the fork to stall or collapse. [57] Stabilization of TWJ by ad hoc chemicals (TWJ-ligands) is thus a new strategy to create DNA damages and trigger cell death in proliferating cancer cells. [58] A TACN scaffold surrounded by three 2-methylquinoline arms (TACN-Q) (Figure 8) was shown to stabilize folded TWJ (evaluated by FRET-melting assay, with DT 1/2 = 3.8 °C) [59] but, more importantly, promote the formation of TWJ from separated strands (by polyacrylamide gel and TWJ-screen experiments). [60] TACN-Q also exhibit promising anticancer activity (IC 50 = 10.6 µM against melanoma cells).

Conclusions

Through these selected examples, it is evident that the scope of applications of MPAs goes far beyond the limited roles of complexing agents for metal cations (especially radiometals).

As demonstrated here, MPAs are highly versatile molecular tools that prove efficient in many areas, from material science to chemical genetics. Besides their roles as multivalent molecular platforms, MPAs can find other uses that are yet beyond the strict context of this review but are also invaluable to further substantiate their versatility. For instance, different MPA moieties have been incorporated within the core structure of complex bioactive compounds (Figure 9) either as water-solubilizing appendages (which also favors the renal clearance of LLP2 peptide that targets very-late antigen 4 (VLA-4) overexpressed on the surface of cancer cells), [61] or as ATP-binding moieties (both TACN and cyclen were introduced on a dual kinase (EGFR/HER2) inhibitors) [62] in light of pioneering works from Lehn and co-workers on anion receptor polyazamacrocycles. [63] MPAs have also been used for chelating in situ metals: this strategy allows for modulating abnormal metal metabolism such as in Alzheimer's disease in which a high copper concentration triggers neuronal toxicity favoring the formation of pathogenic b-amyloid plaques and reactive oxygen species (ROS). Derivatives of TACN, [64] of cyclam and cyclen [65] were studied, the latter being conjugated with the b-sheet breaker KLVFF peptide [66] or with silica nanoparticles. [67] MPAs have also been embedded as bioactive components per se, the most brilliant example being certainly AMD3100: [68] this bis-cyclam derivative is used as an antagonist of CXCR4 receptors, initially developed as an anti-HIV agent and subsequently repurposed for the mobilization of hematopoietic stem cells in cancer patients, now commercialized as Mozobil® (plerixafor). [69] AMD3100 was also studied for its ability to alter the copper metabolism in Alzheimer's disease (vide supra) [70] and as possible anti-malaria agent. [71] To improve the pharmacological properties of AMD3100, many derivatives have been designed and synthesized (Figure 9), in which the core structure of cyclam was changed for 1,4-dioxaor 1,4-dithia-8,11-diazacyclotetradecane, [72] or for side-or cross-bridged cyclams [73] (also used for building original antimalarial agents) [74] thus expanding the chemistry of MPAs. Similarly, cyclen-and cyclam-based MPAs were investigated to fight against the parasitic diseases leishmaniasis, and it was found that 2 metal complexes (out of 44 tested compounds), i.e., the iron(II) and manganese(II) complexes of a bisbenzylcyclen derivative, displayed the most promising properties as antileishmanial agents. [START_REF] Hubin | Pauline Lejault received her PhD in biochemistry in 2017 from the Natural History Museum[END_REF] Figure 9. Selected examples of compounds bearing one or two MPAs that behave as bioactive moieties per se.

These examples further nurture the view whereby MPAs are far more versatile than initially anticipated. We are convinced that the best is still to come, with new generations of chemists eager and poised to decompartmentalize chemical fields to make the best use of the portfolio of advanced molecular tools at their disposal. This will provide genuine new opportunities and open brand new chemical landscapes that are still, at present, beyond imagining.

Graphical abstract

No metal, no cry! Macrocyclic polyamines (MPAs) are important chelating agents for cations, anions and neutral molecules. Most common compounds such as cyclen and DOTA are inseparable from great advances in the field of contrast agents for magnetic resonance or PET/SPECT imaging. Their unique topological and physicochemical properties make them also attractive multivalent molecular platforms for applications that go far beyond the conventional metal chelation. The key topics discussed in this review are the use of MPAs as molecular platforms for applications in material chemistry, medicinal chemistry and chemical biology.

Figure 1 .

 1 Figure 1. Schematic representation of the uses of DOTA either as molecular cage for chelating metals (left panel) or as platform to assemble multivalent molecular tools (right panel), which is the key topic of the review.

Figure 2 .

 2 Figure 2. Structure of the cholesterol-armed cyclen designed by Michinobu, Tsukube and co-workers. Formation of its octadentate Na + complex and subsequent self-assembly to chiral host monolayer (at the interface airwater) for mechanical control of enantioselectivity of amino acid recognition.

c(

  RGDfK) have already been implemented successfully, mostly through the use of trifunctional amino acid-based platforms. As an example, the glutamic acid (E) was used to synthesize both the dimer E[c(RGDfK)] 2 and the tetramer E[E[c(RGDfK)] 2 ] 2 (in which two dimers are linked via

Figure 3 .

 3 Figure 3. Selected examples of macrocyclic chelator-assembled RGD (upper panel) and KuE (center, lower panel) multimers for tumor targeting through PET imaging, as well as merged DOTA and RGD scaffold (both sides, lower panel). Counter-ions (mostly TFA) not shown.

  ) displayed no real improvements, with a lower a v b 3 binding in vitro than the RGD control (IC 50 = 4.7 and 20.4 nM for c(DOTA-RGD) and c(DOTA-RGDf), respectively versus 6.7 nM for RGDf) and lower tumor uptake in vivo (when labelled with 177 Lu and 64 Cu). Notni and co-workers developed an alternative strategy to tackle DOTA derivatization issues, replacing the DOTA platform by the more reactive 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetramethylenephosphinic acid (DOTPI). The tetra-functionalization of DOTPI was performed through the sequential coupling of amino acid PEG 4 linkers (DOTPI(PEG 4 )4, isolated yield = 38%) and fully protected c(RGDfK)(Pbf,tBu) peptide followed by TFA treatment to remove protecting groups

  3+ ) was mandatory to trigger the intramolecular G-quartet folding. This was evaluated via fluorescence resonance energy transfer (FRET)-melting assay, with DT 1/2 = 12.5 and 1.8 °C for PNA DOTASQ and DOTASQ, respectively, versus 9.3 °C for the [Tb.DOTASQ] 3+ complex. The equilibrium between the 'open' (guanines are free) and 'closed' (guanines are embedded in the intramolecular G-quartet) conformations of PNA DOTASQ is actively and solely

  (Ac-Trp-Tyr-Arg-Gly-Arg-Leu-OH) peptides being previously established, this study aimed at showing that the more peptidic arms, the better the cartilage targeting, investigating both (Ac-WYRGRL) 1 -DOTA-Cy5.5 (or 1TP, T for targeting peptide, P for probe) and (Ac-WYRGRL) 3 -DOTA-Cy5.5 (or 3TP) (Figure5). Optical imaging investigations demonstrated that the accumulation of the conjugates in cartilage increased as a function of the number of peptides (11.2-fold and 36.6-fold increase of fluorescence for 1TP and 3TP, respectively, versus non-peptide but Cy5.5-labeled DOTA control). Drug multivalency thus improved cartilage targeting, penetration and retention. The versatility of this approach was further demonstrated via the conjugation of both Ac-WYRGRL and pepstatin A (JVV-Sta-A-Sta or Iva-

Figure 5 .

 5 Figure 5. Selected examples of multivalent drug carrier platforms based on DOTA: cartilage-targeting carrier conjugated to pepstatin A (3P11) or the fluorescent Cy5.5 dye (3TP) (upper panels), and acetyl prodrug of DOTAbased analog of enterobactin conjugated to the fluorescent Cy5.5 dye or the b-lactam antibiotics ampicillin (lower panels). Counter-ions (mostly TFA) not shown.

Figure 6 .

 6 Figure 6. Examples of biomimetic (Pyro-DOTASQ) and smart G-quadruplex ligands (BioTASQs) based on the Cfunctionalized DOTA platform (upper panel). Schematic representation of the use of BioTASQ to fish Gquadruplexes out from human cells via an affinity pull-down strategy (lower panel). Adapted from ref.

Figure 7 .

 7 Figure 7. Selected examples of cyclen-based high-order chemical architectures: amphiphilic polymer for gene delivery (upper panel); on-bead structure of tri-peptoid-DOTA molecule for screening and discovering novel and multivalent theranostic agents (central panel); and uranyl-organic framework in which DOTA acts as a "square assembler" (lower panel).

  Direct N-alkylation of cyclam with the corresponding a,a-difluoro-b-ketophosphonate-functionalized benzyl bromide failed to provide the desired tetra-N-substituted derivative in an effective manner (yield <10% after purification by column chromatography on silica gel). An alternative procedure involving alkylation of MPA with methyl 3-bromomethylbenzoate, followed by cerium(III)-mediated reaction of ester moieties with LiCF 2 P(O)(OEt) 2 and final deprotection of phosphonate ethyl esters with bromotrimethylsilane provided the desired multivalent PTP inhibitors in decent overall yields (6-24% for the three-step procedure). Both the cyclen-(2) and cyclam-based(3) conjugates prove more efficient than the cyclal conjugate (4, with IC 50 = 75, 590 and 91 nM for cyclam-, cyclen-and cyclal-based derivatives, respectively, versus >100 µM for monomeric ketophosphonate used as control), with a better ability to discriminate between various PTP, notably the closely related PTP1B, a negative regulator of insulin signaling (with IC 50 = 1.08, 4.04 and 1.48 µM for cyclam-, cyclen-and cyclal-based derivatives, respectively).

Acknowledgements

. The authors thank the CNRS and the Université Bourgogne Franche-Comté (UBFC) for funding, along with the Agence Nationale de la Recherche (ANR) and the European Research Council (ERC) for grants ID ANR-17-CE17-0010-01 and H2020-MSCA-IF-2016-750368, respectively. This work belongs to the Pharmacoimagerie & agents théranostiques project supported by the Université de Bourgogne and Conseil Régional de Bourgogne (PARI) and the European Union (PO FEDER-FSE Bourgogne 2014/2020 programs).

The authors also warmly thank their colleagues at the ICMUB and CheMatech TM company for stimulating daily discussions, and all scientists worldwide involved in this area to make it a lively field of research (our apologies for any possible omissions).


Antoine Muller
email: antoine.muller@irsst.qc.ca

Charles Pontonnier

Xavier Robert-Lachaine

Georges Dumont

André Plamondon

Motion-based

Keywords: Ground reaction forces and moments, lifting, kinematics, inverse dynamics, L5/S1 joint moment

come

Introduction

The National Research Council (2001) reported that there is a clear relationship between back disorders and physical load. In this context, numerous studies have evaluated back loading in manual materials handling (MMH) [START_REF] Marras | Spine loading as a function of lift frequency, exposure duration, and work experience[END_REF][START_REF] Plamondon | Biomechanical differences between expert and novice workers in a manual material handling task[END_REF][START_REF] Ning | The assessment of material handling strategies in dealing with sudden loading: The effects of load handling position on trunk biomechanics[END_REF][START_REF] Corbeil | Biomechanical analysis of manual material handling movement in healthy weight and obese workers[END_REF][START_REF] Gagnon | A comparison of lumbar spine and muscle loading between male and female workers during box transfers[END_REF]. In most of these studies, back loading was assessed from the L5/S1 joint moments, based on a motion capture system associated to one or more force platforms, usually in a motion analysis laboratory. The use of such devices reduces the ecological aspect of the tasks (i.e. close to workplace conditions) by constraining the analysis area to the force platforms. To remove this barrier, several studies have been proposed that predict the external forces and moments from motion data only. In the great majority of studies, the external forces and moments were limited to the ground reaction forces and moments (GRF&M). They could be estimated by directly solving the inverse dynamics problem [START_REF] Delisle | Kinematic analysis of footstep strategies in asymmetrical lifting and lowering tasks[END_REF][START_REF] Faber | Estimating 3D L5/S1 moments and ground reaction forces during trunk bending using a full-body ambulatory inertial motion capture system[END_REF]. However, this method uses only one global contact since the problem is undetermined with multiple contacts. Three motion-based prediction approaches to solve this indeterminacy have been identified in the literature.

A first approach uses empirical functions to link the motion and associated GRF&M [START_REF] Koopman | An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking[END_REF][START_REF] Dijkstra | Computation of ground reaction force using zero moment point[END_REF]. This approach has only been applied on gait.

A second approach is based on machine learning methods [START_REF] Choi | Ground reaction forces predicted by using artificial neural network during asymmetric movements[END_REF][START_REF] Oh | Prediction of ground reaction forces during gait based on kinematics and a neural network model[END_REF][START_REF] Johnson | Predicting athlete ground reaction forces and moments from motion capture[END_REF]. From data set using force platforms, a neural network establishes a link between the motion and the GRF&M. These methods, based on a learning phase, have the disadvantage of requiring a set of motions close to the one studied and thus are only applicable to standardized motions. In addition, a large motion set is needed for the learning phase to be efficient.

A third approach uses a contact model with optimization techniques [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF][START_REF] Jung | Dynamically adjustable foot-ground contact model to estimate ground reaction force during walking and running[END_REF][START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF], where a set of discrete contact points is defined on a biomechanical model (corresponding to the hypothesized contact points between the subject and the environment). Then, the external forces are calculated as the minimal forces for each contact point while ensuring respect for the dynamics equations. This approach was recently evaluated on MMH tasks [START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF]Muller et al., 2019a) and the results were promising. However, these studies were limited to standardized tasks: loads were carried only using handles and tasks did not require moving the feet. The objective of this study was to evaluate a motion-based prediction method based on a contact model on more ecological MMH tasks. The experimental procedures are detailed below. Based only on motion data, the prediction method estimates the GRF&M and the load contact forces and moments (LCF&M). More specifically, the method evaluation consists in first, comparing the predicted GRF&M to force platform data and, second, comparing predicted back loading with the L5/S1 joint moments to those computed by using the force platform data.

Materials and methods

Experimental procedure

Several studies analyzing MMH tasks have been carried out at the IRSST (Institut de recherche Robert-Sauvé en santé et en sécurité du travail, Montréal, Canada) biomechanical laboratory. They consisted in comparing expert and novice workers [START_REF] Plamondon | Biomechanical differences between expert and novice workers in a manual material handling task[END_REF], analyzing the importance of expertise, lifting height and weight lifted [START_REF] Plamondon | Relative importance of expertise, lifting height and weight lifted on posture and lumbar external loading during a transfer task in manual material handling[END_REF], comparing healthy bodyweight and obese workers [START_REF] Corbeil | Biomechanical differences between obese and healthy-weight workers in manual materials handling[END_REF][START_REF] Corbeil | Biomechanical analysis of manual material handling movement in healthy weight and obese workers[END_REF] and comparing male and female workers [START_REF] Gagnon | A comparison of lumbar spine and muscle loading between male and female workers during box transfers[END_REF]. The parameters studied were kinematic variables such as the upper trunk flexion, horizontal hand distance to L5/S1 or knee flexion and kinetic variables such as the L5/S1 joint moments. The experimental protocol was the same for each and is detailed below.

The cohort was composed of 65 subjects (50 males, 15 females, age: 27±7 years old, height: 177±4 cm, mass: 73±15 kg). The variability of the subjects (men / women, healthy bodyweight / obese, experts / novices) allows to take into account the variability of the handlers in companies. The studies were approved by the local institution's research ethics committee. Each participant signed an informed consent form prior to participation. An Optotrak system (Northern Digital Inc., Waterloo, Ontario, Canada) recorded at 30 Hz the 3-D coordinates of markers located on the subject. As previously done [START_REF] Plamondon | Biomechanical differences between expert and novice workers in a manual material handling task[END_REF][START_REF] Plamondon | Relative importance of expertise, lifting height and weight lifted on posture and lumbar external loading during a transfer task in manual material handling[END_REF][START_REF] Corbeil | Biomechanical differences between obese and healthy-weight workers in manual materials handling[END_REF][START_REF] Corbeil | Biomechanical analysis of manual material handling movement in healthy weight and obese workers[END_REF][START_REF] Gagnon | A comparison of lumbar spine and muscle loading between male and female workers during box transfers[END_REF], twelve clusters of four markers were attached to each subject segment (head, back at C7, T12 and S1, as well as both arms, both forearms, both thighs and both feet). At the beginning of each experiment, the locations of 48 anatomical landmarks were identified in relation to their respective cluster. The GRF were measured by an extended force platform (1.90 × 1.40 m) mounted on six AMTI mini platforms (model MC3A-6-1000; Advanced Mechanical Technology Inc., Watertown, MA, USA). The force platform collected data at 1024 Hz and had been previously validated [START_REF] Desjardins | A force platform for large human displacements[END_REF].

The task consisted in transferring four boxes one by one from a conveyor (height from the ground 12 cm) to a two-wheel hand trolley (height from the ground 2 cm) and back again (Figure 1). The distance between the lifting and deposit locations was 1.5 m. In the initial phase to the hand trolley, the conveyor was slightly inclined so that the boxes moved towards the handler. The four boxes were transferred one by one to be stacked in a pile on the hand trolley. In the return phase to the conveyor, the conveyor was slightly inclined outwards so that the boxes moved away from the handler. No constraint on foot motion was imposed on the subject. 16 repetitions of the initial and of the return phase resulted in 128 boxes handled by each subject (8,320 boxes in total). To be as close as possible to workplace conditions, no lifting technique or comment about the technique used was given to the participant.

As in a workplace, boxes had various characteristics: one 15-kg box, one 23-kg box, one weakened 15kg box and one off-center 15-kg box (center of gravity 27 cm laterally from one side and 8 cm from the other), all of the same dimensions (26 cm deep × 35 cm wide × 32 cm high). The weakened box contained 12 bottles of sand and water and had no cover so as to be deformable. To avoid constraining the grip, no instrumented handle was used. The evaluation of the method on standardized tasks with an instrumented handle was previously done (Muller et al., 2019a).

Estimation of biomechanical variables

The external forces prediction method is detailed in supplementary materials (Appendix A). For clarity, only the principal steps are summarized below.

All data from the prediction method were processed with CusToM (Customizable Toolbox for Musculoskeletal simulation (Muller et al., 2019b)). CusToM is a toolbox developed in Matlab R enabling musculoskeletal analyses based on inverse dynamics approaches with a high level of customization of the analysis.

A biomechanical model, composed of 16 rigid segments linked by 15 joints corresponding to 37 degrees of freedom, was used. The geometrical parameters were subject-specific calibrated using motion capture data and an optimization-based method [START_REF] Muller | A simple method to calibrate kinematical invariants: application to overhead throwing[END_REF]. Body segment inertial parameters (BSIP) were extracted from anthropometric tables [START_REF] Dumas | Adjustments to mcconville et al. and young et al. body segment inertial parameters[END_REF]. From the positions of the 48 anatomical landmarks (estimated from the positions of the 12 rigid clusters), the joint coordinates were computed in an inverse kinematics step [START_REF] Lu | Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints[END_REF] and then filtered with a 4th-order Butterworth low-pass filter with a cutoff frequency of 5 Hz and no phase shift.

During the tasks, the external forces could be applied on the feet (GRF&M) and hands (LCF&M). Thus, a set of discrete contact points was defined on the biomechanical model: N f points under each foot and N h points on each hand. For this study N f = 14 and N h = 11 were chosen. These points were located in order to map the contact area as proposed in previous studies [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF][START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF].

The handling task was composed of four different phases (Figure 1): 1) the pre-grip, from the initial contact between the hands and the load to the final contact between the load and the grip support; 2) the transfer, from the end of the pre-grip to the initial contact between the load and the destination support; 3) the postdeposit, from the end of the transfer to the final contact between the hands and the load; 4) the return, from the end of the post-deposit to the beginning of the pre-grip phase. During the pre-grip and post-deposit phases, the load was in contact with the subject's hands and load support. As no information was available about the contact between the load and its support, it was not possible to predict the external forces in these phases; consequently, they were not taken into account in this study, as discussed in the last section of the paper. Detection of the phases was accomplished manually using video recording.

During the return phase, as only external forces and moments were applied on the feet, the proposed method was a classical GRF&M prediction method. Only the contact points defined under the feet were considered. At each instant, prediction of the external forces and moments was performed through an optimization procedure, which consisted in minimizing the sum of squared contact forces respecting the dynamics equations applied on the subject and additional constraints including Coulomb's law of friction and a maximal force for each contact point.

As the load grasp differed according the subject's technique or the experimental conditions, the orientation of the load in relation to the subject was not known. Thus, the inertial parameters of the load were not taken into account and only its mass was considered by estimating the location of the center of mass in the middle of the subject's wrist. Then, an inverse dynamics step was performed successively by using the predicted forces and moments and the measured values to obtain L5/S1 joint moments. The predicted and measured GRF&M were used in a recursive Newton-Euler algorithm [START_REF] Featherstone | Rigid body dynamics algorithms[END_REF] with a bottom-up approach.

Data analysis

The pre-grip and post-deposit phases were excluded from the analysis and only the transfer and the return phases were considered. Four transfers with the box and three returns without the box were analyzed, totalling 2,080 tasks. For these phases, the method was evaluated by directly comparing the predicted and measured GRF&M and also by comparing the L5/S1 joint moments computed with the predicted and measured GRF&M.

Predicted and measured GRF&M were compared with the Pearson correlation coefficient, computed for each transfer and return of each subject. Root mean squared error (RMSE) and relative RMSE (rRMSE) [START_REF] Ren | Whole body inverse dynamics over a complete gait cycle based only on measured kinematics[END_REF] were computed between the predicted and measured data. In the same manner, L5/S1 joint moments were compared with the Pearson correlation coefficient, RMSE and rRMSE. For the predicted (u 1 ) and the measured data (u 2 ) (instant t varying from 0 to T ), RMSE and rRMSE were computed with Eq. ( 1) and Eq. ( 2), respectively. 1)

RMS E = 1 T T t=0 (u 1 (t) -u 2 (t)) 2 (
rRMS E = RMS E 1 2 2 i=1 max t∈[0,T ] (u i (t)) -min t∈[0,T ] (u i (t)) (2)
For all the analyses, the antero-posterior axis was considered as the axis between the grip and the destination support. GRM were computed at the central point of the force platform.

Results and discussion

GRF&M estimation

The Pearson correlation coefficient between predicted and measured GRF&M are detailed in Table 1. A direct comparison of the results with those reported in the literature was not possible since different tasks were performed, only the orders of magnitude were compared. The minimal correlations were found along the vertical axis where the level of effort was higher. In comparison to the methods based on a contact model, except for the vertical GRF, correlations were higher. In comparison to the methods using machine learning, overall, the proposed method yielded lower correlations for the GRF (particularly on the vertical axis).

Table 2 and Table 3 show the RMSE and rRMSE between the predicted and measured GRF&M. Also, the mean RMSE was 39 N (±11), 17 N (±6.5) and 14 N (±5.2) respectively for the vertical, antero-posterior and medio-lateral GRF and 24 Nm (±10), 17 Nm (±6.7) and 7.7 Nm (±2.4) respectively for the sagittal, frontal and transverse GRM. Considering the vertical axis (concerned with the highest force magnitudes), even if contact models were added on each hand, a comparison of results shows the same magnitude as in the literature with the same type of method. Higher errors are only observed in [START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF] where large dynamic motions were studied. Considering the other directions, the correlations were higher than or comparable to those reported in the literature. However, the variety of motions studied in the different papers makes it difficult to directly compare results. Contrary to other tasks, MMH tasks have no preferred direction within a large movement area. For example in the case of GRF, the correlation was higher, whereas the RMSE was the same magnitude or higher than reported in the literature. The mean RMSE for GRM was higher overall than the literature results; however, the corresponding rRMSE was lower since the amplitude of the GRM was more important in the current study. The large amplitude is explained by the large displacements made during the MMH tasks.

L5/S1 joint moment estimation

The results of comparison of L5/S1 joint moments with predicted and measured GRF&M is detailed in Table 4. Higher correlation was observed on the sagittal axis (corresponding to the flexion/extension) where the moment values were the most important. By comparing a bottom-up and a top-down approach during lifting tasks, Larivière and Gagnon (1998) reported uncertainties of 15 Nm, 8 Nm and 8 Nm for the L5/S1 joint moment estimation along the same respective axis. In a similar study, [START_REF] Plamondon | Validation of two 3-D segment models to calculate the net reaction forces and moments at the L5S1 joint in lifting[END_REF] observed uncertainties of 4 Nm, 4 Nm and 5 Nm along the same axis. [START_REF] Kingma | Validation of a full body 3-d dynamic linked segment model[END_REF] reported uncertainties in the range of 3.9 Nm to 23.7 Nm on the sagittal axis, 5.4 Nm to 20.5 Nm on the frontal axis and 1.9 Nm to 15.2 Nm on the transverse axis. Given the tasks studied and models used, the uncertainties in the literature varied greatly. However, the errors found were comparable to the estimation uncertainties reported by [START_REF] Larivière | Comparison between two dynamic methods to estimate triaxial net reaction moments at the L5/S1 joint during lifting[END_REF] and were in the range of uncertainties reported by [START_REF] Kingma | Validation of a full body 3-d dynamic linked segment model[END_REF].

Considering the transfer and return phases separately, the RMSE were 14.0 Nm (±6.9) and 14.1 Nm (±6.5) for the sagittal axis, 10.0 Nm (±4.0) and 9.0 Nm (±4.0) for the frontal axis and 10.0 Nm (±4.0) and 8.0 Nm (±3.5) for the transverse axis. Thus, compared to a classical GRF&M prediction method with no box, taking into account a load does not add any error in the estimation of L5/S1 joint moments.

Generally, phases where prediction had poorer results were observed when the proposed contact model was the least representative of the performed movement. Two recurrent observations were noted. First, several subjects threw the load before contact with the destination support, whereas the model assumes that the load is always between the subject's hands. Second, in several cases, there was contact between the load and a body part other than the hands (in most cases the belly). For these situations, the model differs considerably from the experimental conditions and the predicted data reveal more significant errors.

Table 1: Pearson correlation coefficient r (±SD) between predicted and measured GRF&M along each direction computed and averaged for each transfer and return phases. Results of the proposed method are compared to those detailed in the literature: three methods based on a contact model [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF][START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF][START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF], and two methods based on machine learning [START_REF] Oh | Prediction of ground reaction forces during gait based on kinematics and a neural network model[END_REF][START_REF] Johnson | Predicting athlete ground reaction forces and moments from motion capture[END_REF]. For the studies of [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF], [START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF] and [START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF], the results for the different types of motions were averaged. V: vertical; AP: antero-posterior; ML: medio-lateral; S: sagittal; F: frontal; T: transverse.

Motions

General discussion

On the basis of these results, the proposed method is very encouraging. It allows MMH tasks to be studied without the use of force platforms, which increases the ecological aspect of the tasks. In this paper, the predicted external forces and moments were used to estimate the L5/S1 joint moments. However, the method can also be used to compute several biomechanical variables permitting assessment of handling tasks, for example destabilizing and stabilizing forces to assess equilibrium [START_REF] Duclos | Destabilizing and stabilizing forces to assess equilibrium during everyday activities[END_REF] or glenohumeral joint moments to assess shoulder loading (which cannot be estimated using only force platforms on asymmetrical tasks). Compared to previous studies, the current method was evaluated under experimental conditions representative of the workplace: variability of the subjects (men / women, healthy bodyweight / obese, experts / novices), transporting boxes from a conveyor to a hand trolley, no constraint on foot motion, and no particular instructions given. Even if machine learning methods have overall better results, they require a learning phase using a data set corresponding to external forces and moments on the standardized motion, which is not the situation studied here. In the context of MMH tasks, machine learning seems difficult to adapt since the tasks vary widely, i.e. variability of movement, handling techniques and carried loads. The learning phase would require a very large data set [START_REF] Halilaj | Machine learning in human movement biomechanics: best practices, common pitfalls, and new opportunities[END_REF].

The results obtained appear satisfactory despite several hypotheses where no specific parameters were chosen for the different models. First, the load model was simplified since its inertial parameters and the specific location of the center of mass of the off-center box and the weakened box were not taken into account. Using only the mass of the load therefore simplifies the method development in an ecological context by us-ing various loads. For example, for order picking in a bonded warehouse, the mass of the load could easily be obtained from the order tracking data. Second, the BSIP were based on a regression method [START_REF] Dumas | Adjustments to mcconville et al. and young et al. body segment inertial parameters[END_REF] even though some of the cohort were obese workers (greater than 50 th percentile). Moreover, using only regression methods allows a simplification of the experimental protocol where only the subject mass is used, which facilitates use of the method in an applied ergonomics context.

Limits and perspectives

The current method has several limitations. First, it was based on an optoelectronical motion capture system which is usually only available in motion analysis labs. Where the aim is to improve the ecological aspect of the experiments, wearable motion capture systems could be used. For example, inertial motion capture systems [START_REF] Vignais | Innovative system for real-time ergonomic feedback in industrial manufacturing[END_REF][START_REF] Robert-Lachaine | Validation of inertial measurement units with an optoelectronic system for whole-body motion analysis[END_REF][START_REF] Faber | Continuous ambulatory hand force monitoring during manual materials handling using instrumented force shoes and an inertial motion capture suit[END_REF] or depth cameras (Plantard et al., 2017a,b) have already been proposed for workstation ergonomic posture assessments. More recently, in the laboratory, the use of 2D images associated to deep learning methods were also developed to estimate pose during lifting tasks [START_REF] Mehrizi | A deep neural network-based method for estimation of 3D lifting motions[END_REF]. The extension of the proposed method to include this type of technology is one important means to complete an ergonomics assessment in the workplace. Second, the phases of the MMH tasks were identified manually by using video recordings, which requires a timeconsuming post-treatment. The addition of sensors (for example on the load or on the hands) or the use of an automatic identification method could decrease the post-treatment time. Third, acquisition frequency has a direct impact on the computation of dynamic quantities and therefore on prediction forces. If very dynamic Table 2: Averaged RMSE (±SD) and rRMSE (±SD) between predicted and measured GRF along each direction. Results of the proposed method are compared to those detailed in the literature: four methods based on a contact model [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF][START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF][START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF]Muller et al., 2019a) and one method based on machine learning [START_REF] Oh | Prediction of ground reaction forces during gait based on kinematics and a neural network model[END_REF]. For the studies of [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF], [START_REF] Skals | Prediction of ground reaction forces and moments during sportsrelated movements[END_REF] and [START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF], the results for the different types of motions were averaged. The results are presented first normalized by body weight and second divided by the subject's mass, which improves comparison to the literature where results are available. -refers to unavailable data. V: vertical; AP: antero-posterior; ML: medio-lateral. phases (pre-grip, grip, deposit or post-deposit phases) are of interest, an acquisition frequency higher than 30 Hz may be necessary. In addition, in these phases, a more detailed modelling of the hypothesized contact points would improve prediction. Fourth, a more detailed modelling of the discrete contact points would improve prediction method. In the current study, the contacts points were chosen to map uniformly the hand surface, with a similar density to the ones on the feet. A sensitivity study to determine the optimal number of points to use and their location on the hand would improve the model. Finally, since the method is based on a contact model, the pre-grip and post-deposit phases were not taken into account. Given the tasks studied, assessing these phases could be of interest. In this case, the addition of sensors on the ground or on the load appears necessary.

Motions

Conclusion

The proposed method showed that external forces and moments and back loading can be estimated during manual material handling tasks from only motion data on a wide variety of subjects (experts / novice, men / women, healthy bodyweight / obese). This method improves the ecological aspect of the tasks by not constraining the movement area or the handling techniques. Handler follow-up could thus be improved by assessing the ergonomics of MMH tasks that are as representative as possible of those performed in the workplace.

Table 3: Averaged RMSE (±SD) and rRMSE (±SD) between predicted and measured GRM along each direction. The proposed method results are compared to those detailed in the literature: three methods based on a contact model [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF][START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF]Muller et al., 2019a) and one method based on machine learning [START_REF] Oh | Prediction of ground reaction forces during gait based on kinematics and a neural network model[END_REF]. For the studies of [START_REF] Fluit | Prediction of ground reaction forces and moments during various activities of daily living[END_REF] and [START_REF] Larsen | Estimation of spinal loading using inertial motion capture and ground reaction force prediction: A validation study[END_REF], the results for the different types of motion were averaged. The results are presented first normalized by body weight times height and second divided by the subject's mass, which improves the comparison to the literature according to the available results.refers to unavailable data. S: sagittal; F: frontal; T: transverse.

Motions

Figure 1 :

 1 Figure 1: Different phases of the experimental task consisting in transferring four boxes one by one from a conveyor to a hand trolley and back again.

Table 4 :

 4 Comparison of L5/S1 joint moments along each direction computed with predicted and with measured GRF&M using the Pearson correlation coefficient r (±SD) and the RMSE (±SD), where r was computed and averaged for each transfer and return phases.

		S	F	T
	r	0.947 (0.072) (0.111) (0.136) 0.875 0.794
	RMSE (Nm)	14.1 (6.7)	9.6 (4.3)	9.1 (4.1)
	rRMSE (%)	5.3 (2.5)	5.9 (2.7)	8.0 (3.3)

S: sagittal; F: frontal; T: transverse.


Trinh Dinh

Aurélie Tran

Danielle Joubert

Sylvain Venditti

Thierry Durecu

Olivier Meunier

Emmanuel Le Bihan

Laurence Fiani

Le Coq

Characterization of Polymer Waste Containing Nano-fillers Prior its End-of-Life Treatment

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Martin Prochazka

Univerzita Karlova

From a Corrupt Eden to Bio-power: War and Nature in the Henriad 1

In the Henriad, nature and war coexist and their closeness implies deep changes of their conventional understanding. Representations of nature in Shakespeare's mature works differ from those in the works of his predecessors and contemporaries. A crucial distinction is the absence of a Neoplatonic perspective, which informs the works of Edmund Spenser (Waller, 1994: 76-77) and considerably influences also those of other early modern poets, such as

http://www.new-faces-erasmusplus.fr/ their being doe dilate: / And turning to themselues at length againe, / […] / […] they raigne ouer change, and doe their states maintaine" 7.7.58).

In contrast to this discourse relating nature permanently to its divine origin, the representation of nature in the Henriad is subject to "the revolution of the times," in the course of which "chance's mocks / And changes fill the cup of alteration / With divers liquors"

(2 Henry IV, 3.1, 45, 51-2). 3 Anticipating theories of chaos, this representation emphasizes fortuitous temporality pervading nature seen as a universal process, which, envisaged in human dimensions, acquires a deterministic character. Warwick's "history in all men's lives" can be grasped as a cumulative representation of the past, a set of diverse temporal processes and events ("Figuring the natures of the times deceas'd;"), whose respectful understanding ("The which observed") can reveal future potentialities of historical development based on general probability -"the main chance of things / As yet not come to life, who in their seeds / And weak beginnings lie intreasured" (2 Henry IV,. 4 Even though the passage may draw on Renaissance typology, where the past events prefigure the future ones, it completely abstracts from the metaphysical framework of this typology, the Divine Providence. The book which King Henry longs to read is neither the Scripture, nor even the Book of Nature, but "the book of fate " (3.1.44).

The probabilistic as well as determinist framework of universal "history" in 2 Henry IV informs the representations of nature in the whole Henriad. These are characterized by the growth of their pragmatic character: the shift from Nature as an ideal, which is the source of perfection as well as the objective of all existence, to nature as a power which has to be controlled and exploited for political and military purposes.

In Richard II nature is identified with the symbolic authority and "the body politic" 5 of the monarch ("This royal throne of kings, this scepter'd isle" Richard II, 2.1.40), yet this http://www.new-faces-erasmusplus.fr/ "body politic" is no longer "a theological idea" (Kantorowicz, 1957: 8ff). It is a presented as a fiction to be unravelled in the course of the play. As Victoria Kahn points out: "Kantorowicz appears more interested in the way Shakespeare imaginatively anticipated the unraveling of the fiction of the king's two bodies" especially in the moment when "the fiction of the oneness of the [fictive] body breaks apart" (Kahn 2009: 86;Kantorovicz 1957: 31) 6 The "duplications" characteristic of the "two bodies of the king" also influence the verbal aspects of the representation of nature: "This fortress built by nature for itself" (2.1.43; emphasis added) and its cognates: "This royal throne of kings (…) /(…) / This other Eden" (2.1.40, 42; emphasis added). In this way, seemingly equivalent or "adequate" 7 notions are played "off against each other," confused or balanced again (Kantorowicz,. As a result, Platonic and Aristotelian principles of mimesis are unsettled and "the idea of a legislator" shifts "from the imitator of nature to the creator of laws ex nihilo" (Kahn,idem: 87). The last changes mentioned had in most cases led to the glorification of poets and affirmation of the independence of their creation, often called "second nature." 8 These features, however, do not characterize the representations of nature in Richard II. Here, nature as the corrupt "Eden" (2.1.42; "now bound with shame" 3.1.63) and the representation of the gradual loss of Richard's royal power ("the blushing discontented sun" shaded by "the envious clouds" 3.1.62, 64) is replaced by the allegory of a "garden (…) full of weeds" (3.4.44-45), which can no longer represent good government as a model 9 ("Showing as in a model our firm estate" 3.4.42).

Although John of Gaunt still believes that nature's "fortress" can protect "against infection and the hand of war " (2.1.43, 44), war evidently prevails, being identified with a disease, an "infection" (2.1.44) wasting the body politic, caused by the corruption of the king and his advisors. In this way, nature can no longer serve as a bond between the "two bodies of "usefulness" consists precisely in dislocating power "from one particular place and one particular body" (Kahn,idem: 95).

Anticipated by Kantorowicz, this solution is discussed at some length by Claude Lefort, who suggests that "democracy" is the only form of government representing power as "an empty place" and thus maintaining "a gap between the symbolic and the real," in order to show that power belongs to no one; that those who exercise power do not possess it; that they do not, indeed, embody it; that the exercise of power requires a periodic and repeated contest; that the authority of those vested with power is created and re-created as a result of the manifestation of the will of the people (Lefort, 1988: 225).

Lefort has also shown that this condition is not new but rather results from a process common to all changes of the representations of political and social power, namely the transfer "from one register to another (…) intended to ensure the preservation of a form which has since been abolished" (idem, 255). This, among others, implies two rather fatal flaws of democracy:

First, the reactivation of the religious fiction, whose "efficacy is no longer symbolic but imaginary, (…) at the weak points of the social" (ibidem), where it can generate violent symbolic practices, such as those typical of nationalism or racism. Secondly, this internal instability of democracy appears to be, in Lefort's words, "the unavoidable -and no doubt ontological -difficulty democracy has in reading its own story" (ibidem) leading to the fundamental weakness of its political ideologies, where the notions like "n/Nature," or "the people" lose their meaning and performative power. It can almost be said that the ominous http://www.new-faces-erasmusplus.fr/ aspect of Lefort's approach consists in his effort to re-establish the "Theologico-Political" as an underlying pattern of all forms of government. In this way, the essential vulnerability of democracy and the imminence of civil war may almost appear as a 'natural' feature of somehow absurdly repeating history, where "falseness" and corruption grow to demand a radical response, 10 "the inward [i.e., civil] wars" (2 Henry IV, 3.1.102), as King Henry fears.

In the introductory monologue of the king in 1 Henry IV the link between nature and war becomes imminent and threatening. "The other Eden" invoked by John of Gaunt (Richard II 2.1.42) is not only corrupted, but also destroyed. Personified by a disfigured female body or face, where the mouth is as a mere opening gorged with blood 11 ("No more the thirsty entrance of this soil / Shall daub her lips with her own children's blood" 1 Henry IV 1.1.5-6), the land is drained ("channelled"1.1.7) and mutilated by "trenching war" (1.1.7). 12 The polarization of the body politic reaches down to the level of strife between individuals ("Those opposèd eyes" 1.1.9). As a consequence, the body politic is no longer that of the king but of the nation, and its near destruction is associated with a cosmic disaster ("like the meteors of a troubled heaven /All of one nature, one substance bred / Did lately meet in the intestine shock" 1.1.10-12). The last line of the passage represents the violence of civil wars by means of the image of a fierce hand-to-hand combat ("furious close of civil butchery" 1.10.13). The metaphor of war as "infection" in Richard II (2.1.44) is intensified in 1 Henry IV: the birth of one of the rebel leaders and the representative of the exotic, 'barbaric' and demonized culture, the Welsh king Owain Glyndŵr, is described as a violent outbreak ("eruption") of disease ("Diseasèd nature oftentimes breaks forth / In strange eruptions" 3.1. [25][26]. Despite all effort to rectify the stereotyping of Wales and the Welsh in 3.1, the threat of acculturation [START_REF] Howard | Introduction" to 1 Henry IV[END_REF](Howard, : 1149)), is looming large over the civil war in 1 Henry IV and intensifies its catastrophic representations.

http://www.new-faces-erasmusplus.fr/ The imagery of war as a disease inaugurates also the scenes of the battle of Shrewsbury ("The day looks pale / At his distemp'rature." 5.1.2-3). Metaphors of the disturbance of cosmic order are repeated in the exchange of the King and Prince Harry with the Earl of Worcester, one of the leaders of the rebels. The metaphorical image of the Earl represents him (andsynecdochically -the whole rebellion) as a star, which was moving "in [an] obedient orb" and giving "a fair and natural light" but has turned into "an exhaled meteor, / A prodigy of fear, and a portent / Of broachèd mischief to the unborn times " (5.1.16-21). This parallel between the disintegration of the body politic and the disruption of the macrocosmic order is extended beyond the limits of the present and near future. War represented as a cosmic disorder becomes a powerful omen of evil haunting "the unborn times."

The representation of war is further monumentalized in Hotspur's speech to his allies which uses the words "instruments," "embrace" and "courtesy" as syllepses, meaning both "musical instruments" and "weapons"; "friendly hug" and "grip in a close man-to-man fight"; "graciousness" and "chivalrous combat"; and ascribes them a cosmic ("heaven to earth") dimension: "Sound all the lofty instruments of war, / And by that music let us all embrace, / For, heaven to earth, some of us never shall / A second time do such a courtesy" (5.2.97-100).

In this way, war becomes an ironical and perverted version of a cosmic dance, which at the This over-inflated image of civil war as the self-destruction of nature, order, representation ("And let this world no longer be a stage") and the body politic can be read as a coda of a specific history of representing based on the disintegration of the King's body politic and its transformation into the collective body of the nation. As Jean Howard has shown, further development of this representation will require "a complex illusion of temporal simultaneity" (idem, 1149). This is also in keeping with Benedict Anderson's definition of nation as an "imagined community" (1991: 6). 13 The emergence of Falstaff in this catastrophic situation does not merely represent the debasement of the unity of the humans with nature symbolised by the "grotesque body," the main agency of the "carnivalesque" which, according to Bakhtin, "is not separated from the rest of the world," and in which "the cosmic, social and bodily elements are given (…) as an indivisible whole" (Bakhtin, 1984: 19). 14 Beyond this symbolic function, Falstaff represents the alienation of common humanity from the unity of nature, when he denies its authority, seeing "no reason in the law of nature" (2 Henry IV 3.2.297) and valuing nature (and "time") only as random processes and opportunities for aggressive or calculating behaviour. 15 At the end of the second part of Henry IV, nature is identified with death. When the king dies, "He's walked the way of nature" opposed to "our purposes" ("and to our purposes he lives no more"), as Warwick dryly states (5.2.4). In other words, the body politic is no longer represented by the body of the king, but defined by the "purposes" of the powerful, or rather, the strategic nature of power. A similar feature characterizes Falstaff's influence on Prince Hal. http://www.new-faces-erasmusplus.fr/ Falstaff's passionate entreaty, which identifies his obese body with the collective "grotesque body" of the carnival, "Banish plump Jack and banish all the world" (2 Henry IV, 2.5.439), is treated by Hal with ironic humour ("I do, I will" 2.5.439), which undermines the carnivalesque subversion of the preceding parodic game.

It can be said that the influence of Falstaff and his companions engenders Hal's pragmatic, strategic approach to politics: "Redeeming time, when men think least I will"

(1 Henry IV,1.2.195). Hal comes to understand fairly soon that an efficient political action cannot be based on political theology but draws from an unscrupulous, even criminal, use of "political technology" (Foucault, 1982: 780). He can "offend to make offence a skill" (1.2.194).

When Hal is enthroned and leads the nation into an aggressive war, his actions acquire the features of modern political technologies leading to genocide in later centuries (Foucault, 1978: 137). 16 When he talks in disguise to his soldiers, Williams and Bates, about justice and war, he denies his responsibility for the deaths of soldiers in his military campaign, comparing his subjects to potential criminals:

Besides, there is no king, be his cause never so spotless, if it comes to the arbitrament of swords, can try it out, with all unspotted soldiers. Some, peradventure, have on them the guilt of premeditated and contrived murder; some of beguiling virgins with the broken seals of perjury; some making wars their bulwark, that have before gorged the gentle bosom of peace with pillage and robbery. Now, if these men have defeated the law and outrun native punishment, though they can outstrip men, they have no wings to fly from God. War is his beadle. War is his vengeance. So that here men are punished for before-breach of King's laws, in now the King's quarrel. (Henry V,emphasis added) Taking war as a just, though extra-legal, punishment for the potential or undetected crimes committed by his subjects, King Harry subscribes to modern strategy, not yet of the http://www.new-faces-erasmusplus.fr/ circulation of power in the network and "network-centric warfare" (Reid, 2003: 7), but to the "strategical model" of power, which has supplanted "the model based on law" (Foucault, 1978: 102;Reid, idem, 13), whose representation was also the body politic of the king. In modernity, wars are not waged for the preservation of the king, but, as Foucault points out, "on behalf of the existence of everyone; entire populations are mobilized for the purpose of wholesale slaughter in the name of life necessity" (Foucault,idem,137): in the latter plays of the Henriad this takes the form of overcoming the threat of civil war. War also becomes an efficient means of policing the population, or in Foucault's terms, managing the "bio-power" (idem, 140ff).

Seen in this context, King Harry's strategies anticipate the ominous dictum of Carl von Clausewitz: "War is the continuation of Politik by other means," where the German word "Politik" means both "politics" and "policy," the latter meaning government control of the population (Foucault, 1988: 158-159). 17 As a result, the existence, which is at stake in modern wars, "is no longer the juridical existence of sovereignty" but "the biological existence of a population" (Foucault, 1978: 137).

It is important not to confuse this condition with that of the totalitarian state. As King Harry says, "Every subject's duty is the King's, but every subject's soul is his own" (Henry V 4.1.164-65), articulating the position of the individual in a liberal society characterized by the responsibility towards the law combined with the freedom of choice. While the first one becomes increasingly problematic (as in Kafka's parable "Before the Law"), the second one is all the more restricted by the allegedly free market.

Works Cited

Abrams, Meyer Howard (1971) The Mirror and the Lamp: Romantic Theory and the Critical Tradition, New York, Oxford UP. Anderson, Benedict (1991), Imagined Communities, second edition, London, Verso. http://www.new-faces-erasmusplus.fr/ 9 "The common-sense relationship between a model and its copy, which is one of cause and priority, is disturbed."

This "mime" (Derrida uses Mallarmé's "Mimique") "delivers activity which is reduplication without origin" (Hobson,idem,136). In this way, "law and form" are no longer "in a due proportion" (Richard II 3.4.42). However, as Derrida shows in The Truth in Painting, the word "model" can also function as a "fetish," that is, as a replacement for something banned or taboo (Hobson,idem,141). In Richard II, the "unweeded garden," whose "herbs," are "swarming with caterpillars" cannot present the unity of the "two bodies of the king" and the representation of truth as adequatio becomes impossible.

10 See Warwick's speech in 2 Henry IV, 3.1.81-87: "Such things become the hatch and brood of time; / And by the necessary form of this / King Richard might create a perfect guess / That great Northumberland, then false to him, / Would of that seed grow to a greater falseness, / Which should not find a ground to root upon, / Unless on you."

In terms of political theology, the fortuitous, chaotic process of history, "the hatch and brood of time" (see above) is represented not only as "necessities" (3.1.87), but also as ongoing corruption ("grow to greater falseness"3.1.85) which must be stopped by force. 11 The ambiguity of the personification derives from the violence of disfiguration which obscures the difference between the face and other body parts. 12 The word "trench" has been used in its modern military meaning since 1500 and appears frequently in Shakespeare. The original etymology of the verb "to trench" is to maim, mutilate, cut off (Online Etymology Dictionary). 13 Instead of imagining the community in a temporal simultaneity ("along time" as Benedict Anderson has it), which includes both the mythical time and the cycles of growth and cultivation (the gardening and planting metaphors as a model for good government in Richard II 3.4.), the country is seen in a "transverse, cross-time" simultaneity, "marked not by prefiguring and fulfilment, but by temporal coincidence" (idem, 24-25). Anderson has pointed out that religious communities, including monarchies based on the authority of sacred kingship, are not imagined at certain historical moments but always with respect to the whole course (and end) of time represented in their sacred texts. Every historical moment is simultaneously a moment in the totality of mythical time, which accounts for the spiritual authority of individuals (priests, kings). The links between individual moments are meaningful only because of this mythical time, providential or sacred history.

beginning of 2

 2 Henry IV changes into a danse macabre in Northumberland's eschatological tirade: Let heaven kiss earth! Now let not nature's hand Keep the wild flood confined! Let order die! And let this world no longer be a stage To feed contention in a ling'ring act; But let one spirit of the first-born Cain http://www.new-faces-erasmusplus.fr/ Reign in all bosoms, that each heart being set On bloody courses, the rude scene may end, And darkness be the burier of the dead! (2 Henry IV, 1.1.153-60)

http://www.new-faces-erasmusplus.fr/ the king." And since the "body politic" of the king can no longer be represented as the actual location of power, political theology itself has to be transformed by means of fiction, whose

http://www.new-faces-erasmusplus.fr/ 2018. (Based on The Complete Works in Verse and Prose of Edmund Spenser, ed. Alexander Balloch Grosart, London and Aylesbury, Hazell, Watson and Viney, 1882). Waller, Gary (1994), Edmund Spenser: A Literary Life, Basingstoke, Macmillan.

1 Research for this paper was supported by the European Regional Development Fund Project "Creativity and Adaptability as Conditions of the Success of Europe in an Interrelated World" (No. CZ.02.1.01/0.0/0.0/16_019/0000734).

2 All quotations are from [START_REF] Spenser | The Faerie Queene, Renascence Editions[END_REF] with emphases added. Numbers of book, cantos and stanzas are in brackets in the text.

3 All quotes from Shakespeare follow [START_REF] Shakespeare | The Norton Shakespeare[END_REF]. Abbreviated titles of plays and numbers of acts, scenes and lines are in parentheses in the text.

4 King Henry's and Warwick's speeches may be said to anticipate the main aspects of recent definitions of chaos: "sensitive dependence on initial conditions" ("the main chance of things / As yet not come to life, who in their seeds / And weak beginnings lie intreasured"), "topological mixing" ("Make […] the continent, / Weary of solid firmness, melt itself / Into the sea" 3.1.46-48) and a number of "dense periodic orbits" ("Figuring the natures of the times deceased"). For mathematical definitions of these aspects see Hasselblatt and Katok (2003: 209-210).

5 Ernst H. Kantorowicz has identified the source of this representation in Edmund Plowden's transformation of the abstract legal concept of Sir John Fortescue. According to Plowden, "the Body politic includes the [king's] Body natural … [and] these two bodies are incorporated in one person" (Kantorowicz, 1957: 9). 6 Kahn has also demonstrated Kantorowicz's interest in the "duplications" revealed in the central scenes of Richard II: "The duplications [are] (…) all one and all simultaneously active in Richard: 'Thus play I in one person, many people' (5.5.31) (…). Moreover, in each one of those three scenes we encounter the same cascading: from divine kingship to kingship's 'Name' and from the name to the naked misery of man" (Kantorowicz,idem,27).

7 On mimesis as "adequatio" ("the measured quality of proportion to a model" -Hobson, 2001: 138) see Derrida (1981: 219).

8 "It is therefore of Poets thus to be conceiued, that if they be able to deuise and make all these things of them selues, without any subiect of veritie, that they be (by manner of speech) as creating gods" (Puttenham, 1904: 2).

" [T]he artist is a God-like creator of a second nature" (Abrams, 1971: 274).