Kristian Torbensen

Anisha Patel

Agnès Anne
email: anne@univ-paris-diderot.fr

Christophe Demaille
email: demaille@univ-paris-diderot.fr

Laure Bataille

Thierry Michon
email: thierry.michon@inra.fr

Eric Grelet

Arnaud Chovin

Immuno-Based Molecular Scaffolding of Glucose Dehydrogenase and Ferrocene Mediator on fd Viral Particles Yields Enhanced Bioelectrocatalysis ACS Paragon Plus Environment

Keywords: bioelectrocatalysis, enzyme nanocarriers, bioelectrocatalytic viral particles, pyrroloquinoline quinone dependent glucose dehydrogenase, bioscaffolding

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

Introduction

Enhancing the catalytic activity of electrode-immobilized glucose oxidizing enzymes is key to the design of more sensitive glucose biosensors, and more powerful biofuel cell anodes. [START_REF] Bollella | Enzyme Based Amperometric Biosensors[END_REF][START_REF] Meredith | Biofuel Cells: Enhanced Enzymatic Bioelectrocatalysis[END_REF] The glucose oxidase (GOx), and the much more active, and oxygen insensitive, pyrroloquinoline quinone (PQQ)dependent glucose dehydrogenase (PQQ-GDH), are amongst the most widely used redox enzymes for these important applications. A promising way to enhance their bioelectrocatalytic activity is to immobilize these enzymes on nanostructured electrode surfaces. [START_REF] Holzinger | Nanomaterials for Biosensing Applications: A Review[END_REF][START_REF] Zhu | Electrochemical Sensors and Biosensors Based on Nanomaterials and Nanostructures[END_REF][START_REF] Zhao | Nanostructured Material-Based Biofuel Cells: Recent Advances and Future Prospects[END_REF][START_REF] De Poulpiquet | New Trends in Enzyme Immobilization at Nanostructured Interfaces for Efficient Electrocatalysis in Biofuel Cells[END_REF][START_REF] Milton | Tailoring Biointerfaces for Electrocatalysis[END_REF] The expectation is that mastering the surface architecture at the nanometer scale will provide a more-enzyme friendly environment, avoiding immobilization-induced denaturation. In addition, this may also improve the electrical communication between the redox enzymes and the electrode, notably if the enzyme can undergo direct electron transfer (DET) with the electrode material. [START_REF] De Poulpiquet | New Trends in Enzyme Immobilization at Nanostructured Interfaces for Efficient Electrocatalysis in Biofuel Cells[END_REF][START_REF] Milton | Tailoring Biointerfaces for Electrocatalysis[END_REF] Similarly, for integrated systems, [START_REF] Heller | Electrical Wiring of Redox Enzymes[END_REF] where the enzyme and its redox mediator are co-immobilized onto the electrode surface, nanostructuring can enhance the rate at which the mediator shuttles electrons from the electrode to the enzyme.

In seminal works regarding integrated systems, the catalytic activity of nanostructured electrode materials combined with hydrogel composites entrapping both enzymes and redox centers has been assessed. [START_REF] Gao | Engineering Hybrid Nanotube Wires for High-Power Biofuel Cells[END_REF][START_REF] Cortez | Effect of Gold Nanoparticles on the Structure and Electron-Transfer Characteristics of Glucose Oxidase Redox Polyelectrolyte-Surfactant Complexes[END_REF][START_REF] Aquino Neto | Co-Immobilization of Gold Nanoparticles with Glucose Oxidase to Improve Bioelectrocatalytic Glucose Oxidation[END_REF] It has notably been shown that depositing GOx-containing redox hydrogels on carbon nanotubes microfiber networks, instead of on regular (non-nanostructured) carbon fibers, resulted in biofuel anodes displaying increased power density. [START_REF] Gao | Engineering Hybrid Nanotube Wires for High-Power Biofuel Cells[END_REF] An enhanced catalytic response was also observed by "dopping" with gold nanoparticles the electron conductivity of GOx containing redox-hydrogels. [START_REF] Cortez | Effect of Gold Nanoparticles on the Structure and Electron-Transfer Characteristics of Glucose Oxidase Redox Polyelectrolyte-Surfactant Complexes[END_REF][START_REF] Aquino Neto | Co-Immobilization of Gold Nanoparticles with Glucose Oxidase to Improve Bioelectrocatalytic Glucose Oxidation[END_REF] Other works considered carbon nanotubes [START_REF] Callegari | Functionalised Single Wall Carbon Nanotubes/Polypyrrole Composites for the Preparation of Amperometric Glucose Biosensors[END_REF][START_REF] Nazaruk | Enzymatic Electrodes Nanostructured with Functionalized Carbon Nanotubes for Biofuel Cell Applications[END_REF][START_REF] Deng | Wiring" Glucose Oxidase in Supramolecular Architecture[END_REF] and ZnO nanoparticles [START_REF] Haddad | Novel Ferrocene-Anchored ZnO Nanoparticle/Carbon Nanotube Assembly for Glucose Oxidase Wiring: Application to a Glucose/Air Fuel Cell[END_REF] functionalized by ferrocene moieties as redox mediators for polymer-entrapped GOx. Another type of nanostructured integrated system, consisting of a mesoporous enzyme electrode, where ferrocene molecules were trapped in nanopores capped with GOx, was also described. [START_REF] Trifonov | Enzyme-Capped Relay-Functionalized Mesoporous Carbon Nanoparticles: Effective Bioelectrocatalytic Matrices for Sensing and Biofuel Cell Applications[END_REF] Recently, PQQ-GDH has been covalently functionalized by a ferrocene mediator and immobilized on a quantum dot-decorated electrode, and a photo-electrocatalytic response was evidenced. [START_REF] Riedel | Connecting Quantum Dots with Enzymes: Mediator-Based Approaches for the Light-Directed Read-out of Glucose and Fructose Oxidation[END_REF] In search of nanostructures offering a microenvironment potentially more enzyme-favorable than inorganic nanoparticles or porous electrodes, integrated systems based on DNA material have been developed. [START_REF] Nguyen | DNA Redox Hydrogels: Improving Mediated Enzymatic Bioelectrocatalysis[END_REF][START_REF] Piperberg | Control of Bioelectrocatalytic Transformations on DNA Scaffolds[END_REF][START_REF] Van Nguyen | Improved Bioelectrocatalytic Oxidation of Sucrose in a Biofuel Cell with an Enzyme Cascade Assembled on a DNA Scaffold[END_REF] DNA hydrogels, incorporating GOx and a ferrocene mediator have notably been reported. [START_REF] Nguyen | DNA Redox Hydrogels: Improving Mediated Enzymatic Bioelectrocatalysis[END_REF] DNA strands were also used as bio-scaffolds to assemble GOx and ferrocene relays. [START_REF] Piperberg | Control of Bioelectrocatalytic Transformations on DNA Scaffolds[END_REF][START_REF] Van Nguyen | Improved Bioelectrocatalytic Oxidation of Sucrose in a Biofuel Cell with an Enzyme Cascade Assembled on a DNA Scaffold[END_REF] Even though many of the above works reported valuable results, new nanostructuring or scaffolding strategies have to be designed to improve further the catalytic performances of integrated enzyme electrodes. This is evidenced by the fact that, for every integrated system reported in literature, the apparent enzymatic turnover, i.e. the current generated per enzyme molecule, falls behind the turnover of the enzymes in solutions. This may result from the electron transport between redox relays being rate limiting, or from partial inactivation of the enzyme.

In that context, the aim of our work is to explore the possibility of using an original bottom-up scaffolding approach for improving the catalytic performances of electrode-supported glucose oxidizing enzymatic systems. This strategy makes use of viral particles as electrode-immobilized bio-scaffolds. The specific interest of using virus particles arises from their availability as perfectly monodisperse nanometer-sized particles and their highly ordered architectures enabling the topologically controlled assembly of enzyme molecules. Moreover, since the introduction of the concept of using viral particles as enzyme nanocarriers, [START_REF] Carette | A Virus-Based Biocatalyst[END_REF][START_REF] Cardinale | Virus Scaffolds as Enzyme Nano-Carriers[END_REF] preserved or improved catalytic performances for virus-supported or virusencapsulated enzymes, have been repeatedly reported, albeit almost exclusively for viral scaffolds dispersed in solution. [START_REF] Minten | Catalytic Capsids: The Art of Confinement[END_REF][START_REF] Aljabali | Controlled Immobilisation of Active Enzymes on the Cowpea Mosaic Virus Capsid[END_REF][START_REF] Patterson | Virus-like Particle Nanoreactors: Programmed Encapsulation of the Thermostable CelB Glycosidase inside the P22 Capsid[END_REF][START_REF] Pille | General Strategy for Ordered Noncovalent Protein Assembly on Well-Defined Nanoscaffolds[END_REF][START_REF] Rurup | Viruses as Model Nanoreactors to Study Enzyme Kinetics[END_REF][START_REF] Cuenca | Nanonets Derived from Turnip Mosaic Virus as Scaffolds for Increased Enzymatic Activity of Immobilized Candida Antarctica Lipase B[END_REF][START_REF] Timmermans | Self-Assembled Nanoreactors Based on Peptides and Proteins[END_REF] The possibility of using viral particles as enzyme carriers for enhancing the catalytic response of electrode-supported enzymatic systems has, at the opposite, been little explored. In pioneering works, Wege et al. reported that adsorbing GOx-functionalized tobacco mosaic virus nanotubes onto a sensor electrode surface did not actually enhance O2-mediated catalysis, but significantly improved enzyme loading and sensor reusability. [START_REF] Koch | Modified TMV Particles as Beneficial Scaffolds to Present Sensor Enzymes[END_REF][START_REF] Bäcker | Tobacco Mosaic Virus as Enzyme Nanocarrier for Electrochemical Biosensors[END_REF][START_REF] Koch | Penicillin Detection by Tobacco Mosaic Virus -Assisted Colorimetric Biosensors[END_REF] The design of a bioanode bearing a random mesh of M13 bacteriophage particles decorated with GOx has also been reported, but in that case the viral particles were "mineralized" by being gold coated in order to promote direct electron transfer (DET). [START_REF] Blaik | Gold-Coated M13 Bacteriophage as a Template for Glucose Oxidase Biofuel Cells with Direct Electron Transfer[END_REF] Using an original immuno-based process, our group previously assembled, a non-integrated GOxbased system on fd bacteriophage particles adsorbed on gold electrodes. [START_REF] Patel | Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis[END_REF] What we address here is the benefit of scaffolding a much more complex, integrated, system on electrode-supported viral particles, by co-immobilizing a redox ferrocene mediator and the redox enzyme PQQ-GDH onto fd bacteriophage particles. Even though multi-enzymatic constructs on viral particles, [START_REF] Koch | Modified TMV Particles as Beneficial Scaffolds to Present Sensor Enzymes[END_REF][START_REF] Patterson | Encapsulation of an Enzyme Cascade within the Bacteriophage P22 Virus-like Particle[END_REF][START_REF] Besong-Ndika | Towards the Reconstitution of a Two-Enzyme Cascade for Resveratrol Synthesis on Potyvirus Particles[END_REF][START_REF] Brasch | Assembling Enzymatic Cascade Pathways inside Virus-Based Nanocages Using Dual-Tasking Nucleic Acid Tags[END_REF] and virus particles decorated by redox moieties, have already been reported, [START_REF] Steinmetz | Decoration of Cowpea Mosaic Virus with Multiple, Redox-Active, Organometallic Complexes[END_REF][START_REF] Nault | Electrochemical Atomic Force Microscopy Imaging of Redox-Immunomarked Proteins on Native Potyviruses: From Subparticle to Single-Protein Resolution[END_REF][START_REF] Aljabali | Redox-Active Ferrocene-Modified Cowpea Mosaic Virus Nanoparticles[END_REF] this is the first time that viral particles are endowed with functionally coupled redox and enzymatic properties.

Herein, fd particles, randomly adsorbed on a gold electrode surface, were equipped with redox and enzymatic functions thanks to the sequential immunological assembly on their protein shell (capsid) of PQQ-GDH conjugated antibodies and redox-labeled antibodies. It is shown that confinement of the system's molecular components on the rod-like fd-nanoscaffold facilitates the mediated electronic communication between the enzyme and the supporting electrode, while fully preserving the enzyme activity, so that the electrocatalytic current is solely limited by the enzyme turnover rate. Moreover, confinement also results in shifting the PQQ-GDH kinetic behavior into its most effective cooperative mode. Consequently, the current generated by each of the GDH molecules incorporated in our fdscaffolded system reaches exceptionally high values.

Results and Discussion

Fd bacteriophage is a filamentous virus, and a close cousin of the M13 bacteriophage which is widely used to design virus-based biosensors. [START_REF] Mao | Virus-Based Chemical and Biological Sensing[END_REF][START_REF] Peltomaa | Application of Bacteriophages in Sensor Development[END_REF][START_REF] Bhasin | The Virus Bioresistor: Wiring Virus Particles for the Direct, Label-Free Detection of Target Proteins[END_REF] Fd differs from M13 only by a single-point mutation of the 12 th amino acid of each major coat protein, changing from asparagine (Asn) in M13 to aspartate (Asp) in fd. This results in a more negatively charged phage by about 30%, having similar dimensions, 880 nm in length and 6.6 nm diameter (Figure 1). Fd bacteriophage can be used as an electroinactive rod-like enzyme nanocarrier, which displays the extra advantages of being robust, easy to handle and totally harmless to humans.

Step by step immunological assembly of a PQQ-GDH integrated system on fd particles.

Fd particles were adsorbed from a stock solution prepared in a 10 mM pH 7.4 phosphate buffer onto ultraflat template-stripped (TS) gold surfaces modified by a self-assembled layer of cysteamine (Figure 1). As shown in our previous work, electrostatic attraction at pH 7.4 between the negatively charged fd particles and the positively charged cysteaminated gold surface result in the irreversible adsorption of fd on the surface to form random virus arrays. [START_REF] Patel | Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis[END_REF] Immediately following the adsorption of the fd particles, the surface was protected against non-specific adsorption by a BSA backfilling step. The surface was then exposed to a rabbit antibody (immunoglobulin G, IgG) directed against the coat protein of fd, in order for this IgG to assemble by immunological recognition onto the whole virus capsid.

Then, the surface was sequentially exposed to: a home prepared PQQ-GDH/anti-rabbit IgG conjugate, a commercial anti-GDH rabbit IgG, and finally to a redox-labelled antibody bearing polyethylene glycol (PEG) chains terminated by a ferrocene group (Fc). [START_REF] Anne | Elastic Bounded Diffusion. Dynamics of Ferrocene-Labeled Poly(Ethylene Glycol) Chains Terminally Attached to the Outermost Monolayer of Successively Self-Assembled Monolayers of Immunoglobulins[END_REF] Note that based on our previous experience of immunological assemblies, [START_REF] Bourdillon | Step-by-Step Immunological Construction of a Fully Active Multilayer Enzyme Electrode[END_REF] we kept the concentration of the antibodies and the antigen-antibody reaction times high enough to ensure that a saturating "coating" of the virus particles by the IgGs was formed at every immunological immobilization step. This insures that a largely defect-free multimonolayer immunoconstruct is effectively assembled onto the virus capsid (see Supporting Information).

Besides, as demonstrated earlier, [START_REF] Bourdillon | Step-by-Step Immunological Construction of a Fully Active Multilayer Enzyme Electrode[END_REF] and confirmed here, the antigen-antibody binding was found to be strong enough to confer very high stability to the immunological assemblies (see Methods section). In-situ AFM imaging of the surface allowed decorated fd particles, forming a random array on the gold surface, to be identified (Figure 1).

The virus coverage, fd, was determined by simple counting of the viral particles visible in the AFM image. fd was experimentally adjusted in the 0-2.5 fd/µm 2 range by controlling the concentration of the fd solution used for the adsorption step.

The redox and enzymatic integrated system ultimately assembled on the fd particles can, in principle, be schematically represented as shown in Figure 1. The successively assembled antibodies form concentric layers, color coded in Figure 1, around the virus scaffold. The expected "thickness" of each layer should correspond to the typical size of an IgG, ~10 nm. [START_REF] Pease | Determination of Protein Aggregation with Differential Mobility Analysis: Application to IgG Antibody[END_REF] The enzymatic component of the system, the GDH enzyme, is considered as forming a layer of its own, the third layer, also of about ~10 nm thickness. [START_REF] Oubrie | The 1.7 Å Crystal Structure of the Apo Form of the Soluble Quinoprotein Glucose Dehydrogenase from Acinetobacter Calcoaceticus Reveals a Novel Internal Conserved Sequence Repeat[END_REF] The redox component of the system, the Fc-PEGylated antibody, comes as the last layer forming the outer "shell" of the assembly. Overall, the fd particles supporting the Fc-PEG / PQQ-GDH system should thus display a hemicylindrical geometry ~ 55 nm in radius and ~900 nm in length.

We sought to experimentally confirm this schematic view of the fd-supported antibody construct by finely characterizing its structure and/or functions by an ensemble of techniques, as described below.

We found that AFM imaging alone was not well suited for monitoring the complete step-by-step assembly of the antibody construct on the fd-scaffold, as we observed that the height increment associated with the immobilization of antibody "layers" on the virus tended to become immeasurably small when more than three successive IgG layers were assembled. This result indicates that the multilayered antibody assembly on the virus is too soft to interact in a detectable way with the solid AFM tip. [START_REF] Kuznetsov | Atomic Force Microscopy in Imaging of Viruses and Virus-Infected Cells[END_REF] We thus turned to a more sophisticated local microscopy technique of our own, [START_REF] Anne | High-Resolution Mapping of Redox-Immunomarked Proteins Using Electrochemical-Atomic Force Microscopy in Molecule Touching Mode[END_REF] combining AFM with scanning electrochemical microscopy (SECM) in an original mediator-tethered (Mt ) configuration, for imaging individual virus particles decorated by the Fc-PEG / PQQ-GDH immunoconstruct. We previously demonstrated that this microscopy technique uniquely enables to map the distribution of redox functionalities on viral particles. [START_REF] Nault | Electrochemical Atomic Force Microscopy Imaging of Redox-Immunomarked Proteins on Native Potyviruses: From Subparticle to Single-Protein Resolution[END_REF] Probing the redox function of the decorated fd particles at the single viral particle scale by Mt/AFM-SECM microscopy.

A home-made combined local probe (tip), acting as both a force sensor and a microelectrode, and operating in tapping mode, was used to raster scan the TS gold surface immersed in phosphate buffer.

The probe and surface were biased at potentials respectively largely anodic (Etip = +0.3 V/SCE) and cathodic (Esub = -0.05 V/SCE) with respect to the standard potential of the Fc heads of the PEG chains (E° = 0.15 V/SCE). Simultaneously acquired topography and current Mt/AFM-SECM images of the surface are reproduced in Figure 2. The topography images enabled to identify and locate individual decorated fd particles, and to measure their apparent height (~ 20 nm) and width (~ 150 nm). These values are respectively under-and overestimates of the actual particle dimensions because of tip-sample interactions and convolution artefacts common to all AFM-based imaging techniques. The current images showed electrochemical tip current detection specifically at the location of the particles. This current reflects the electrochemical probing of the Fc-heads by the tip. It is generated by electrons originating from the TS gold surface, propagating along the capsid of the decorated fd and ultimately collected by the tip, as schematized in Figure 2.

Electron propagation over the few tens of nanometers high decorated virus particle is made possible by the swinging motion of the flexible PEG chains, coupled to electron exchange between neighboring Fc heads. [START_REF] Nault | Electrochemical Atomic Force Microscopy Imaging of Redox-Immunomarked Proteins on Native Potyviruses: From Subparticle to Single-Protein Resolution[END_REF][START_REF] Anne | High-Resolution Mapping of Redox-Immunomarked Proteins Using Electrochemical-Atomic Force Microscopy in Molecule Touching Mode[END_REF][START_REF] Anne | Elastic Bounded Diffusion and Electron Propagation: Dynamics of the Wiring of a Self-Assembly of Immunoglobulins Bearing Terminally Attached Ferrocene Poly(Ethylene Glycol) Chains According to a Spatially Controlled Organization[END_REF] Importantly, no current was detected if decorated fd particles lacking the IgG-PEG-Fc were imaged, or if the tip potential was less than the onset oxidation potential of the Fc heads.

These results demonstrate unambiguously the presence of Fc-PEG chains, hence of the Fc-PEG-IgG, on the capsid of the decorated fd particles. The observation that no current was recorded at locations on the surface away from the particles is an indication of the appropriate protection of the surface against nonspecific adsorption of the Fc-PEG-IgG. We also note that tip current was detected all along the length of the decorated fd particles, confirming that the immunoassembly covers the entire capsid of the fd particle. The fact that some sections of the fd particles appear as brighter spots in the current image may indicate the artefactual formation of antibody clusters resulting from the glutaraldehyde fixation of the sample, a required pretreatment step for Mt/AFM-SECM imaging (see Methods section). Finally, it is worth mentioning that all of the fd particles visible in topography images also appeared in the associated current images, showing that the immunological assembly process left no fd-particles un-decorated.

Even though we were able to visualize the Fc-PEG-IgG layer forming the outermost shell of the integrated virus-scaffolded assembly, extra characterization was needed in order to quantify the number of Fc-chains (hence of redox antibodies) decorating each fd particle. For this, we turned to cyclic voltammetry.

Quantifying the number of ferrocene units decorating fd particles by cyclic voltammetry.

Cyclic voltamograms (CVs) were recorded at gold surfaces bearing arrays of fd particles decorated by the Fc-PEG / PQQ-GDH system. The surfaces were mounted in a liquid cell containing 50 mM Tris-HCl buffer pH 7.5 as the electrolyte. A typical raw CV signal, recorded at a potential scan rate of 0.05 V/s, is presented in Figure 3B (red trace). The raw CV displays a pair of peaks superimposed on a large capacitive component that can be easily subtracted to yield the well-defined background-corrected signal shown in green trace in Figure 3B. On the corrected CV, the peak-shaped signal is centered on a potential of ~0.15 V/SCE, corresponding to the standard potential of the Fc heads, and the peak-to-peak potential separation is very small (~10 mV).

Moreover, we verified that the intensity of the peaks was proportional to the scan rate, v (0.01 -0.2 V/s range). All these characteristics evidence that the recorded CV signal corresponds to the response of surface confined Fc heads borne by the Fc-PEG-IgG of the construct, undergoing fast (Nernstian) electron transfer at the gold electrode surface. [START_REF] Laviron | General Expression of the Linear Potential Sweep Voltammogram in the Case of Diffusionless Electrochemical Systems[END_REF] As a result, integration of the anodic peak of the CV yields the surface coverage in Fc-PEG, Fc, which should depend on the number of decorated particles on the surface.

To verify this relationship, we carried out CV measurements for a large number of gold surfaces bearing decorated fd particles, randomly assembled at coverages varying from fd = 0 (no fd particles) to 2.5 fd /µm [START_REF] Meredith | Biofuel Cells: Enhanced Enzymatic Bioelectrocatalysis[END_REF] . In parallel to CVs we also recorded square wave voltammograms (SWVs) at these surfaces (Figure 3C). Indeed, SWV signals display a much lower background component than CVs, making it easier to probe the presence of the Fc heads from raw data (see Supporting Information). As seen in Figure 3C, the intensity of the SWVs was observed to increase with the virus coverage on the surface.

The surface coverage in Fc heads, as determined by CV, obviously showed the same trend, as can be seen in Figure 4A, where experimental values of Fc (number of Fc/µm 2 ) are plotted as a function of fd. One can see that, at low coverages corresponding to fd = 0 -1.5 fd /µm 2 , Fc increases linearly with fd. Also, when no virus is present (fd =0), almost no Fc is detected, demonstrating the absence of nonspecifically adsorbed IgG-PEG-Fc on the surface. At high coverages, corresponding to fd > 1.5 fd /µm 2 , the Fc vs. fd variation is seen to reach a plateau.

The linearity of the Fc vs. fd variation observed for fd < 1.5 fd /µm 2 brings extra evidence that the Fc heads detected in CV and SWV are borne by the fd particles, and also shows that in this low fd region the average number of Fc-PEG chains borne by decorated fd, NFc, does not vary with the virus coverage on the surface. NFc is given by the experimental Fc /fd ratio, and is plotted as a function of fd in the inset in Figure 4A. One can see that ~ 4000 ± 400 Fc heads are decorating each fd particle. Since each redox IgG used in this study bears ~ 24-30 Fc-PEG chains, (see Methods section), one can conclude that as many as 120-180 IgG-PEG-Fc molecules are decorating each fd particles.

The observation of a plateau region in the Fc.vs. fd plot, occurring beyond a threshold value of fd = 1.5 fd/µm 2 , indicates that at higher virus coverages on the gold surface, decoration of the fd particles becomes incomplete. As discussed in our previous work, [START_REF] Patel | Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis[END_REF] this can be attributed to the fact that, above this threshold, a significant fraction of the randomly adsorbed fd particles are intertwined and display limited accessibility for the antibodies. As previously shown, this problem can be fully alleviated by orientating the fd particles, using simple molecular combing techniques. [START_REF] Patel | Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis[END_REF] However, being solely interested in exploring scaffolding effects, we did not attempt this here, and shall therefore only discuss data obtained with electrodes characterized by fd ≤ 1.5 fd/µm 2 .

Having ascertained and quantified the selective redox-immunodecoration of the fd particles by the Fc-PEG chains, it is next necessary to evaluate the ability of the Fc heads to efficiently shuttle electrons from the gold surface toward the enzyme active site and to serve as enzymatic redox mediators.

Catalytic activity of the integrated Fc-PEG / PQQ-GDH system.

Cyclic voltammetry was used to probe the catalytic activity of random arrays of fd particles decorated by the integrated Fc-PEG / PQQ-GDH system. To this aim, glucose was injected in the liquid cell holding the gold surface bearing the decorated fd-nanoarrays, and CVs were recorded at 10 mV/s.

As can be seen in Figure 5B, the injection of glucose resulted in a spectacular increase in intensity of the CV current, accompanied by a remarkable change in shape of the signal: from being dominated by the capacitive component (red trace), the current developed a marked S-shape (blue trace). This change in shape is characteristic of the catalytic response of an integrated system, where both the mediator and the redox enzyme are immobilized on the electrode. In the present case, and as schematically represented in Figure 5A, electrons resulting from the oxidation of glucose by GDH are transferred to nearby oxidized Fc heads (Fc + ), which play the role of enzymatic cofactors. Electrons are then relayed to the electrode surface by a composite charge transport process, implying physical elastic bounded motion of the Fc heads and electron self-exchanges between neighboring Fc/Fc + heads. [START_REF] Anne | Elastic Bounded Diffusion and Electron Propagation: Dynamics of the Wiring of a Self-Assembly of Immunoglobulins Bearing Terminally Attached Ferrocene Poly(Ethylene Glycol) Chains According to a Spatially Controlled Organization[END_REF] The high intensity and well-defined S-shape of the catalytic signal is thus a qualitative indication of the efficient coupling between electron transport and enzymatic catalysis in the fd-scaffolded immunoassembly.

As demonstrated earlier for integrated catalytic system, [START_REF] Anicet | Electrochemical Approach to the Dynamics of Molecular Recognition of Redox Enzyme Sites by Artificial Cosubstrates in Solution and in Integrated Systems[END_REF] in the absence of kinetic limitation due to electron transport, a catalytic voltammogram icat vs. E, solely containing information on enzyme catalysis, can be conveniently obtained by subtracting the signal recoded in the absence of glucose from the catalytic signal obtained in its presence. The resulting subtracted signal, plotted in Figure 5C displays a remarkably well-defined, hysteresis-free S shape, typical of purely catalytic voltammograms. This notably enables accurate determination of the catalytic plateau current, icat,pl.

Values of icat,pl measured for several gold surfaces bearing decorated fd nanoarrays, characterized by differing virus coverages, are plotted as a function of fd in Figure 4B. One can see that icat,pl increases linearly with fd up to fd ~ 1.5 fd / µm 2 , and reaches a plateau for higher fd values. In the absence of viral particles (fd = 0), a negligibly small catalytic current is recorded indicative of a trace amount of nonspecifically adsorbed IgG-PEG-Fc/IgG-GDH immunocomplexes on the electrode. These results evidence that the GDH molecules were specifically assembled on the virus capsid. The data presented in Figure 4B allow the average characteristic catalytic current generated by each individual fd particle, 𝑖 , to be calculated from the expression: 𝑖 = icat,pl /(S fd), where S is the geometric surface area of the electrode. As seen in the inset in Figure 4B, a value of 𝑖 = 100 ± 10 fA per fd particle is found for all of the surfaces examined, independently of their virus coverage.

Assaying the number of GDH enzyme molecules decorating the fd-particles.

Our strategy for "counting" the number of GDH enzyme molecules decorating the fd particles is based on assaying the amount of its PQQ cofactor stripped from gold surfaces decorated by fd-nanorrays at various coverages of fd (see Supporting Information for details). For this, the surfaces were first treated by a 0.1 M pH 2.5 glycine buffer solution, in order to strip the antibodies off the viral scaffolds by disrupting antigen-antibody bonds. The recovered sample solution was then heated to 50 °C in order to trigger the spontaneous release of the non-covalently bound PQQ cofactors from GDH. [START_REF] Witarto | Site-Directed Mutagenesis Study on the Thermal Stability of a Chimeric PQQ Glucose Dehydrogenase and Its Structural Interpretation[END_REF] The concentration of PQQ in the heat-treated sample was then assayed by introducing in solution an excess of apo-GDH. The activity of the thus reconstituted holo-GDH enzyme in solution was finally monitored spectrophotometrically in the presence of glucose and soluble electron donors (see Supporting Information). [START_REF] Shen | Pyrroloquinoline Quinone-Doped Polymeric Nanospheres as Sensitive Tracer for Binding Assays[END_REF][START_REF] Zimmerman | Visual Detection of Single-Stranded Target DNA Using Pyrroloquinoline-Quinone-Loaded Liposomes as a Tracer[END_REF] The PQQ-GDH used herein is a dimer, each monomer containing one PQQ moiety. Hence, 𝑁 , the amount of PQQ-GDH molecules initially present on the surface (i.e. on the fd particles) was derived simply by dividing the amount of assayed PQQ by a factor 2. The interest of this original protocol to quantify the amount of fd-immobilized PQQ-GDH is to be totally independent of the actual activity of the fd-bonded enzyme.

Figure 4C shows the value of the determined amount of PQQ-GDH, converted into an overall GDH coverage on the surface, GDH = 𝑁 /S, and determined for a series of gold surfaces characterized by various fd values. As can be seen, GDH increases linearly with fd for fd < 1.5 fd/µm 2 , indicating that in this low fd region, each fd particle carries on average 𝑁 GDH /fd ~ 230 ± 30 GDH molecules, as

shown in the inset.

The number of 230 GDH per fd particles found here is in fair agreement with the number of ~ 180

GOx molecules that, as showed previously, can be immunologically immobilized on randomly adsorbed fd particles. [START_REF] Patel | Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis[END_REF] Considering that the adsorbed fd particle exposes half of its total capsid area of 18700 nm 2 , 56 and considering ~100 nm 2 as the footprint of an IgG, one would expect that about 100 rabbit antifd IgG can bind to each fd particle. Since the anti-rabbit GDH conjugate is polyclonal, an estimate of 2-3 copies of it can thus possibly bind per anti-fd IgG, resulting in an estimated saturating number of 200-300 GDH molecules per fd. Hence it can be concluded that the packing density of GDH on the fd particles is close to its maximum, i.e. the GDH-IgG conjugate forms a "saturating" layer on the virus capsid. This results confirms our previous observation, [START_REF] Cardinale | Virus Scaffolds as Enzyme Nano-Carriers[END_REF] and is in agreement with other works, [START_REF] Koch | Modified TMV Particles as Beneficial Scaffolds to Present Sensor Enzymes[END_REF][START_REF] Patterson | Encapsulation of an Enzyme Cascade within the Bacteriophage P22 Virus-like Particle[END_REF][START_REF] Grelet | From Soft to Hard Rod Behavior in Liquid Crystalline Suspensions of Sterically Stabilized Colloidal Filamentous Particles[END_REF] showing that affinity binding allows high yield decoration of virus particles by enzyme molecules.

Quantifying the catalytic efficiency of the scaffolded integrated system, on the basis of the current per enzyme molecule parameter.

Cross-analysis of the plots presented in Figure 4, enables to derive the 𝑖 / 𝑁 ratio, which is the value of the catalytic current generated by each GDH molecule incorporated in the fd-scaffolded integrated system, 𝑖 = 0.45 ± 0.09 fA per GDH molecule. Remarkably, this specific current per enzyme molecule is 7 to 15 times higher than the 0.03-0.065 fA specific current that can be calculated for the most effective integrated PQQ-GDH system reported to date. [START_REF] Flexer | Wired Pyrroloquinoline Quinone Soluble Glucose Dehydrogenase Enzyme Electrodes Operating at Unprecedented Low Redox Potential[END_REF] This notable enhancement in specific current shows that electron transport, enzymatic activity and/or their coupling is superiorly efficient in our virus-scaffolded Fc-PEG / PQQ-GDH system compared to all other reported integrated systems.

Note that the performances of integrated enzymatic systems are often discussed in terms of current density, rather than on the basis of the current generated per enzyme molecule as we do here (albeit the notion of current per mg of enzyme has been recently introduced for describing the performance of an enzymatic biofuel cell). [START_REF] Mazurenko | Impact of Substrate Diffusion and Enzyme Distribution in 3D-Porous Electrodes: A Combined Electrochemical and Modelling Study of a Thermostable H2/O2 Enzymatic Fuel Cell[END_REF] In order to achieve high current densities, it is quite common in literature that the equivalent of several hundreds of enzyme monolayers are immobilized on an electrode, meaning that the sub-optimal activity of the immobilized enzyme is artificially compensated by the enzyme loading of the system. We suggest that the current per enzyme criteria, as introduced here, is also used as a figure of merit for comparing integrated enzymatic systems, as it is a test of the ability of the entrapped enzyme to work at its optimal rate. Once optimal enzymatic conditions are defined, high current densities can then be reached with minimal enzyme loading, which is obviously beneficial considering the cost of enzymes. More generally, expressing the performance of a catalytic system as a function of the amount of catalyst involved is common in the field of electrochemical catalysis, [START_REF] Costentin | Towards an Intelligent Design of Molecular Electrocatalysts[END_REF][START_REF] Voiry | Best Practices for Reporting Electrocatalytic Performance of Nanomaterials[END_REF] but strangely enough disregarded in the field of bioelectrocatalysis.

The all-protein microenvironnment experienced by the enzyme in the on-virus immunological assembly, and the large enzyme-electrode separation, probably contribute to make our virus-scaffolded integrated system so catalytically effective. [START_REF] Bäcker | Tobacco Mosaic Virus as Enzyme Nanocarrier for Electrochemical Biosensors[END_REF][START_REF] Bourdillon | A Fully Active Monolayer Enzyme Electrode Derivatized by Antigen-Antibody Attachment[END_REF] In order to reveal in more details what are exactly the beneficial factors at play, a thorough kinetic analysis of its catalytic response was carried out by cyclic voltammetry.

Kinetic analysis of the catalytic activity of GDH in the virus-scaffolded integrated system.

Cyclic voltammograms were recorded at a gold electrode bearing random arrays of fd-particles immunodecorated by the Fc-PEG / PQQ-GDH system for increasing glucose concentrations. As seen in Figure 6A, it was observed that the plateau current of the catalytic signal increased in intensity with increasing glucose concentration, C°g, up to 30 mM, but then decreased when C°g was further increased. i cat,pl as a function of glucose concentration C 0 g for two surface coverages in decorated fd particles, fd. Plain lines are the theoretical fits of Equation 2 to the experimental data using the here-determined kinetic constants reported in Table 1. Scan rate (v = 0.01 V/s).

This behavior is indicative of the well-documented substrate inhibition of PQQ-GDH. [START_REF] Olsthoorn | Negative Cooperativity in the Steady-State Kinetics of Sugar Oxidation by Soluble Quinoprotein Glucose Dehydrogenase from Acinetobacter Calcoaceticus[END_REF][START_REF] Durand | Effect of Substrate Inhibition and Cooperativity on the Electrochemical Responses of Glucose Dehydrogenase. Kinetic Characterization of Wild and Mutant Types[END_REF] As a result, and as observed by others both for PQQ-GDH in solution, [START_REF] Durand | Effect of Substrate Inhibition and Cooperativity on the Electrochemical Responses of Glucose Dehydrogenase. Kinetic Characterization of Wild and Mutant Types[END_REF] or reconstituted as monolayers on electrode surface, [START_REF] Zhang | Heterogeneous Reconstitution of the PQQ-Dependent Glucose Dehydrogenase Immobilized on an Electrode: A Sensitive Strategy for PQQ Detection down to Picomolar Levels[END_REF] the variation of the catalytic plateau current, icat,pl, with the bulk glucose concentration, C°g, is bell-shaped, as seen in Figure 6B.

The kinetics of glucose oxidation catalyzed by the enzyme PQQ-GDH, using single electron ferrocene mediators as co-substrates, has been studied in great details in literature. [START_REF] Durand | Effect of Substrate Inhibition and Cooperativity on the Electrochemical Responses of Glucose Dehydrogenase. Kinetic Characterization of Wild and Mutant Types[END_REF] From these studies, it appears that PQQ-GDH displays a very complex catalytic behavior characterized by the co-existence of two kinetic modes. A non-cooperative mode, where no kinetic interaction exists between the monomers in the dimer constituting this enzyme (each monomer containing a PQQ active site), and a cooperative mode,

where glucose binding by one of the monomeric units accelerates the catalytic action of the other. It was also shown that the non-cooperative and cooperative modes were prevailing at low and high mediator concentrations respectively. Later it was reported that, in either of these modes, the stationary catalytic current generated by PQQ-GDH molecules confined on an electrode surface is given by the following expression: 65

𝑖 ( 1
)
where C°g and Q0 are, respectively, the bulk glucose concentration and the oxidized mediator concentrations locally "seen" by the enzyme. Observation of a well-defined plateau in the catalytic CVs ascertains that glucose consumption is negligible, so that C°g can actually be taken as the bulk glucose concentration. kcat is the catalytic constant of the enzyme, KM the Michaelis constant for glucose, kox the second order rate constant corresponding to the oxidation of the enzyme by the mediator, and Ki the equilibrium constant of the enzyme inhibition by glucose.

It was also shown that the individual values of the kinetic constants appearing in Equation 1 differed greatly between the non-cooperative and cooperative modes.

As reported previously, [START_REF] Anicet | Electrochemical Approach to the Dynamics of Molecular Recognition of Redox Enzyme Sites by Artificial Cosubstrates in Solution and in Integrated Systems[END_REF] for integrated systems, when neither electron transfer from the enzyme to the electrode nor electron transfer at the electrode limit the overall kinetics, Q0 is simply given by Nernst law. Q0 is thus related to 𝐶 , the total concentration of the mediator in both of its redox forms, and as "seen" by the enzyme, and also to the electrode potential E by: 𝑄 𝐶 / 1 exp 𝐹 𝐸 𝐸° 𝑅𝑇 ⁄ .

It thus appears legitimate to tentatively analyze the series of experimental catalytic voltammograms

we recorded on the basis of Equation ( 1), or more conveniently of its reciprocal expression:

1/𝑖 𝐸 ° ⁄ 1 𝐾 𝐶 1 (2)
which is actually a linearized theoretical expression for the catalytic voltammogram.

Thus, as suggested by Equation 2, we plotted reciprocal of the catalytic current icat (E), measured along the experimental catalytic voltammograms for a wide range of E values, as a function of the expression: 1+exp(-xsi), where xsi = F(E-E0)/(RT). As can be seen in Figure 7 panel A, and as predicted by Equation 2, extremely well defined linear variations were then obtained for all of the voltammograms recorded for various glucose concentrations, C°g. Table 1. Sets of kinetic constants, and specific current per GDH molecule, characterizing the catalytic activity of PQQ-GDH in various systems, configurations and kinetic modes as indicated. Columns (I) to (III) (gray background) present data derived herein on the basis of Equation 1, columns (IV) and (V) present data from reference [START_REF] Zhang | Heterogeneous Reconstitution of the PQQ-Dependent Glucose Dehydrogenase Immobilized on an Electrode: A Sensitive Strategy for PQQ Detection down to Picomolar Levels[END_REF] .

Comparing the data presented in Table 1, it appears that the values of both of the kinetic constants kox and kcat measured for our fd-scaffolded integrated system match those corresponding to the cooperative mode of PQQ-GDH in solution. The value found here for Km (14 ± 2 mM) is somewhat higher than reported for the cooperative mode of PQQ-GDH (4.7 ± 0.3 mM), but mostly is ~20 times higher than the Km value reported for the non-cooperative mode of the enzyme. Interestingly, the value of the inhibition constant Ki we find for our system is ~10 and ~3 times lower than reported for the cooperative and noncooperative modes respectively.

Hence, our global observation of a particularly high activity of PQQ-GDH assembled on fdnanoscaffolds can now be understood on the basis of enzyme kinetics: within our virus-scaffolded assembly, the conditions are such that the enzyme spontaneously adopts its cooperative mode. Besides, as an extra (less decisive) benefit, the fd-supported enzyme displays somewhat lower inhibition with respect to glucose than it does in its native state.

The simplest explanation for this unprecedented result is that the dense molecular arrangement of the IgG-PEG-Fc and GDH conjugated antibodies on the fd-scaffold, results in a local concentration in Fc heads sufficiently high to favor the cooperative mode of the enzyme. Actually, one can evaluate from the above data that each GDH molecule is, on average, surrounded by ~18 ± 5 Fc heads. The reason for a lower sensitivity to inhibition by glucose of the fd-scaffolded PQQ-GDH enzyme is not clear at this stage.

Demonstrating that enhanced bioelectrocatalysis is due to scaffolding.

In order to elucidate which part of these catalysis enhancing effects are due to confinement of the integrated system on the fd-scaffold, or to the particular molecular architecture of the immunological construct, we assembled the integrated system as an immunological monolayer on a planar gold surface (see scheme on top of Column (II) in Table 1). For this, the viral scaffold was replaced by a saturated monolayer of rabbit-Fab fragments, as they display approximately the same diameter (~5 nm) [START_REF] Pease | Determination of Protein Aggregation with Differential Mobility Analysis: Application to IgG Antibody[END_REF] as fdparticles. We then fully characterized the catalytic response of the electrode. As can be read in Table 1, bottom line, the current per GDH molecule recorded for such system was of only 0.08 fA, i.e. about 6 times lower than for the virus-scaffolded system. The kinetic constants derived from kinetic analysis were accordingly very low, even lower than expected for the non-cooperative mode of GDH. This latter result indicates that, when the system is assembled on a planar surface, the rate of electron transport, and not only GDH kinetics, contributes to the kinetic control of the catalytic current. Such is expected here since, in a planar monolayer configuration, mere elongation of the 30 nm long fully extended PEG chains cannot allow the Fc + -heads to directly collect electrons from the remote electrode surface. However, the fact that a catalytic current is nevertheless recorded suggests that hinge-like motion of the antibodies constituting the assembly provide an extra degree of freedom to the system, enabling electron transport from the enzyme to the electrode surface by electron hopping/elastic bounded diffusion.

The above comparative results demonstrate that the optimal catalytic response observed for the virusscaffolded integrated system can unambiguously be attributed to a beneficial nano-scaffolding effect.

In search of the mechanism underlying such an effect, we assembled a non-integrated two-IgG construct comprising solely the anti-fd antibody and the PQQ-GDH conjugate (see Column (III) in Table 1), and we interrogated its activity by cyclic voltammetry, using ferrocene methanol as a soluble mediator.

We restricted our-selves to a low concentration in mediator (3 µM), where the enzyme works in its non-cooperative mode, since previous work showed that for higher mediator concentrations glucose diffusion partially controls the catalytic CV signals, which interferes with kinetic analysis. [START_REF] Zhang | Heterogeneous Reconstitution of the PQQ-Dependent Glucose Dehydrogenase Immobilized on an Electrode: A Sensitive Strategy for PQQ Detection down to Picomolar Levels[END_REF] The kinetic and thermodynamic constants we determined for the non-integrated scaffolded system are reported in Table 1, Column (III). Comparing the data presented in Column (III) and Column (IV) shows that the activity of PQQ-GDH is virtually the same whether the enzyme is scaffolded on the fd particles or free in solution.

This result confirms that the immunological assembly process fully preserves the activity of the enzyme, but also that scaffolding by itself does not enhance the catalytic performances of PQQ-GDH. Hence, we can conclude that the catalytic enhancement effect observed here for the integrated system is due to the confinement of both the enzyme and the redox mediator on the fd-scaffold. Our interpretation is that this effect is rooted in the nanoscale hemicylindrical geometry of the fd-scaffolded assembly which, as represented schematically in Figure 5A, facilitates access to the electrode for the Fc heads, but also accelerates electron transport within the assembly. This not only cancels the kinetic limitations due to electron propagation to/from the enzyme but also, by insuring a high local concentration in Fc heads in the vicinity of the enzymatic sites, drives PQQ-GDH toward its most effective catalytic mode.

We believe that the present work is a rare example where the effect of enzyme nano-scaffolding could be so clearly evidenced, and explained on sound enzyme kinetics and (nano)-topological basis. This is the first time that such an effect is evidenced for a fully integrated enzymatic system.

Conclusion.

It has been shown herein that assembling an integrated enzymatic system on a viral nanoscaffold strongly enhances its catalytic performance compared to non-scaffolded systems. We elucidated the physical reason underlying such a catalytic improvement in the present case: the hemicylindrical arrangement of the system's molecular components on a nanometer-sized rod-like scaffold enhances the rate of mediated electronic communication between the enzyme and the supporting electrode. As a result, the only kinetic limitation to the current generated by the integrated system is enzyme kinetics. As a benefit of the enzyme-friendly microenvironment provided by the immunological assembly, the enzyme PQQ-GDH can remain fully active. Moreover, confinement of the Fc-PEG on the virus scaffold results in a high local mediator concentration, which shifts the enzyme behavior into its most effective cooperative mode. Consequently, the current generated by each of the GDH molecules incorporated in our fd-scaffolded system reaches its maximal, enzyme kinetics limited value, which significantly exceeds the current-per-enzyme molecule generated by other integrated PQQ-GDH systems reported in literature.

More generally, we are not aware of any glucose oxidizing immobilized PQQ-GDH electrode where the enzyme was shown to work in its high-current generating cooperative mode.

Although the present work is of fundamental nature, it sets some rules for improving the performances of PQQ-GDH integrated glucose biosensors and bioanodes, as we showed that optimal current-perenzyme is achievable via virus particle-based nanostructuring of enzyme electrodes. However, for these applications high current densities is also required, which is typically achieved in literature by immobilizing the equivalent of multiple enzyme layers. Hence, a possible development of the present work would be forming multilayers of PQQ-GDH decorated fd particles, using for example layer by layer electrostatic assembly of fd/polyelectrolyte polymers, [START_REF] Yoo | Solvent-Assisted Patterning of Polyelectrolyte Multilayers and Selective Deposition of Virus Assemblies[END_REF] to ensure both optimal enzyme activity and high current density.

Materials and methods

Biological Material.

Virus particles. Fd viruses were grown and purified as described elsewhere. [START_REF] Sambrook | Molecular Cloning: A Laboratory Manual[END_REF] Virus suspensions were then concentrated by ultracentrifugation (200 000 g) and redispersed in a stock solution of about 4 mg/mL as measured by spectrophotometry with an absorption coefficient of 3.84 cm 2 /mg at 269 nm. To control the ionic conditions, the fd suspension was then extensively dialyzed against 10 mM sodium phosphate buffer pH 7.4 and stored at 4°C until further use.

Antibodies. The anti-fd polyclonal antibody (Immunoglobulin G, IgG) produced in rabbit was obtained from Sigma-Aldrich. The anti-rabbit GDH-IgG conjugate was prepared in-house by conjugating PQQ-GDH to a polyclonal goat anti-rabbit IgG, as detailed in Supporting Information. The anti-GDH polyclonal antibody was custom produced in rabbit by Genosphere Biotechnologies using apo-GDH monomers as antigens (see Supporting information). The goat anti-rabbit antibody to be conjugated with GDH or Fc-PEG chains, and the bovine serum albumin (BSA) (IgG-free grade) blocking agent were from Jackson ImmunoResearch Laboratories.

Enzymes. PQQ-GDH to prepare the IgG-GDH conjugate was produced from Acinetobacter calcoaceticus and purified as detailed in Supporting Information. Apo-GDH (GD-2) used for the PQQ assays was acquired form Sekisui enzymes.

Chemicals and solutions. All chemicals were analytical grade Sigma-Aldrich products and used as received, expect for PQQ that was a gift from the group of Dr. Benoit Limoges. All solutions were prepared with double-deionized water (18.2 MΩ cm resistivity, TKA Micro-Pure UV). Two buffer solutions were used: 10 mM phosphate buffer at pH 7.4 (phosphate buffer), and 50 mM Tris-HCl buffer at pH 7.5. Phosphate buffer was used for the preparation of the fd bacteriophage solutions and of the antifd antibody solutions employed for the assembly of the fd-scaffolded integrated system. Phosphate buffer was also the imaging medium for the in-situ AFM and AFM-SECM experiments. Tris buffer was used to prepare the solutions of GDH-IgG conjugate, of anti-GDH IgG and of Fc-PEG-IgG, required for the successive system assembly steps. Tris buffer was also the supporting electrolyte for the CV and SWV experiments. We chose Tris buffer over phosphate for these solutions/experiments since we observed increased stability of PQQ-GDH activity in Tris. All antibody solutions contained 1 mg/ml BSA. 0.01 % sodium azide was added as a preservative to the antibody solutions if used or stored for longer than a few hours at room temperature. All solutions and systems were protected from light with aluminum foil during investigation and storage.

Preparation and characterization of the redox secondary antibody, IgG-PEG-Fc. Fc-PEG chains were covalently conjugated to goat anti-rabbit IgGs by reacting the NHS activated ester of a home synthesized NHS-PEG3500-Fc chain with the amino groups of the IgG species, as previously described. [START_REF] Anne | Elastic Bounded Diffusion. Dynamics of Ferrocene-Labeled Poly(Ethylene Glycol) Chains Terminally Attached to the Outermost Monolayer of Successively Self-Assembled Monolayers of Immunoglobulins[END_REF] The purified IgG-PEG-Fc product used in this study is decorated by a number of Fc-PEG molecules per Preparation of the ultra-flat gold electrodes. Ultra-flat gold surfaces were produced by templatestripping of a 200 nm thick gold layer deposited on mica, as previously described. [START_REF] Huang | Probing Individual Redox PEGylated Gold Nanoparticles by Electrochemical-Atomic Force Microscopy[END_REF] A perforated Teflon adhesive mask was glued onto the surface in order to define a 4 mm diameter disk-shaped electrode. All subsequent surface modification steps were carried out by depositing/rinsing with ~20 µL drops of solutions confined to the electrode area by the hydrophobic Teflon mask.

Preparation of cysteaminated-gold surfaces. A 20 µL drop of a 5 mM cysteamine hydrochloride (HS-(CH2)2-NH3 + , Cl -) solution in water was left in contact with the electrode for 2 h under a water-saturated nitrogen atmosphere. The surface was then thoroughly rinsed by droplet replacement of cysteamine with water (twice) and then with phosphate buffer (twice). Drop replacement was cautiously carried out to avoid drying of the surface. Note, thiol functionalized surfaces were kept under a water-saturated nitrogen atmosphere in all subsequent assembly steps to prevent oxidative desorption of the cysteamine layer from the gold surface.

Adsorption of random fd nanoarrays on cysteaminated gold. A 20 µL solution of phosphate buffer containing fd particles at 0.1 to 1.7 g/mL ((0.4 to 7.0) x 10 10 phage particles /mL) was deposited onto the cysteaminated gold surface for 5 minutes. The surface was then rinsed by two droplet replacement steps and left under phosphate buffer for 10 minutes for desorption of any weakly bound material.

AFM imaging. Tapping mode AFM images were acquired with a Nanowizard II microscope (JPK, Germany). In-situ (i.e. in phosphate buffer) imaging was carried out with V-shaped contact mode probes (MLCT-AUMN or MSNL-10, Bruker, spring constant 0.1 N/m, tip curvature 20 nm).

AFM-SECM imaging. Mt/AFM-SECM images were acquired using the JPK Nanowizard II microscope operated in AFM-SECM mode as previously described. [START_REF] Nault | Electrochemical Atomic Force Microscopy Imaging of Redox-Immunomarked Proteins on Native Potyviruses: From Subparticle to Single-Protein Resolution[END_REF] The AFM-SECM tips were hand-fabricated according to a procedure detailed elsewhere. [START_REF] Abbou | Fabrication of Submicrometer-Sized Gold Electrodes of Controlled Geometry for Scanning Electrochemical-Atomic Force Microscopy[END_REF] The standard JPK electrochemical liquid cell contained 900 µL of filtered phosphate buffer solution, and was equipped with a platinum wire as a counterelectrode, and a micro Ag/AgCl reference electrode. All potentials in this work are reported versus the KCl saturated calomel electrode reference SCE. A home-made bipotentiostat was used to control independently the potential applied to the TS gold surface and to the electrochemical tip, and to measure the tip current. The tip current signal was passed through a 10 Hz low-pass analogue filter. The current images were first order flattened and a light gaussian filter was applied. Images shown in text were processed using the JPK software.

Electrochemical analysis. The surface was mounted in a standard JPK electrochemical liquid cell. Cyclic voltammograms (CVs) were recorded with a CHI630C electrochemical workstation, in a three electrode configuration, using the platinum wire counter electrode encased in the JPK cell, and a standard KClsaturated calomel electrode (SCE) inserted in the middle of the cell. Temperature of the air-conditioned room was around 22 °C. Measurements were carried out under ambient atmosphere, PQQ-GDH being insensitive to oxygen. Note, the stock solutions of glucose in Tris buffer were allowed to mutarotate overnight. When not in use the electrodes bearing the Fc-PEG / PQQ-GDH system were stored at 4°C in Tris buffer. Upon one week storage, a maximal loss of ~15 % in catalytic activity was typically observed.

Figure 1 .

 1 Figure 1. Assembly steps of the fd-scaffolded ferrocene-PEG-(Fc-PEG) / PQQ-GDH integrated system on a TS ultra-flat gold electrode surface. Right: In-situ AFM topography control image of a random array of Fc-PEG / PQQ-GDH immunodecorated fd particles on gold.

Figure 2 .

 2 Figure 2. Mt/AFM-SECM images of the individual decorated fd particles. Simultaneously recorded tapping-mode topography and tip current images. The contrast in the current image is generated by the electrochemical detection of the Fc heads by the scanning combined AFM-SECM probe (tip). Tip and TS gold surface potentials were respectively of: E tip = + 0.3 V/SCE, E s = -0.05 V/SCE. Scale bar: 200 nm. Imaging buffer: phosphate buffer.

Figure 3 .

 3 Figure 3. (A) Schematic representation of the electron transfer and transport processes occurring at the gold electrode surface supporting a random array of fd particles decorated by the Fc-PEG / PQQ-GDH system, during the anodic scan of the electrode potential. (B) Cyclic voltammetry (CV) response of the gold electrode supporting an array of the decorated fd particles. The raw and background corrected CVs are plotted in red and green traces respectively. Scan rate, 0.05 V/s. fd = 2.56 fd particles/µm 2 . (C) Square-wave voltammetry signal (SWV) of gold electrodes supporting decorated-fd particles at various coverages as indicated (in fd particles per µm 2 ). Medium: Tris buffer. SWV parameters: Amplitude, 25 mV; frequency, 25 Hz; increment 5 mV.

Figure 4 .

 4 Figure 4. Structural and functional parameters characterizing gold surfaces bearing random arrays of fd particles decorated by the Fc-PEG / PQQ-GDH system, as a function of the fd surface coverage  fd. (A) Fc head surface coverage, Fc as determined by CV. (B) Intensity of the CV catalytic plateau current icat,pl in Tris buffer containing 30 mM glucose. (C) GDH surface coverage as determined by the PQQ stripping method. The insets in (A), (B) and (C) respectively show the number of Fc heads, the intensity of the catalytic plateau current and the number of GDH molecules per fd particle as a function of the fd coverage  fd .

Figure 5 .

 5 Figure 5. (A) Schematic representation of the catalytic oxidation of glucose by PQQ-GDH, coupled to electron transfer and transport processes occurring at the gold electrode surface supporting a random array of fd particles decorated by the Fc-PEG / PQQ-GDH system. (B) Cyclic voltammetry (CV) response of the gold electrode supporting a random array of decorated fd in the absence of glucose (red trace) and in the presence of 30 mM glucose (blue trace). (C) Purely catalytic voltammogram derived from the CVs presented in (B) by subtracting the CV recorded in the absence of glucose from the signal recorded in its presence. Scan rate, 0.01 V/s. fd = 0.85 fd particles/µm 2 . Medium: Tris buffer.

Figure 6 .

 6 Figure 6. (A). Catalytic voltammograms recorded at a gold electrode bearing fd particles decorated by the PQQ-GDH integrated system in Tris buffer containing glucose at the following concentrations: (a) 3 (black), 5 (red), 10 (light green), 30 (blue) mM; (b) 30 (blue), 50 (cyan), 100 (orange), 200 (deep green) mM glucose. (B) Steady-state catalytic plateau currents

Figure 7 .

 7 Figure 7. Kinetic analysis of the catalytic response of the integrated fd-scaffolded Fc-PEG / GDH system. (A) Primary plots where the reciprocal of the catalytic current (icat (E)) is plotted as a function of the 1 exp 𝑥𝑠𝑖 term calculated all along the voltammograms shown in the insets (in the electrode potential region delimited by the double-headed red arrow shown). Each plot corresponds to a different glucose concentration, C°g, as indicated. (B) Secondary plots showing the dependence of : (left) the intercept of the primary plots with 1/C°g, (right) the slope of the primary plots with C°g. Scan rate, 0.01 V/s.  fd = 0.85 fd particles/µm 2 . Medium: Tris buffer.

  IgG protein, n ~ 27 ± 3, as determined by MALDI-TOF MS. Briefly, the IgG-PEG-Fc sample and its starting IgG were (after reconstitution in a 0.1M ammonium acetate buffer) analyzed by MALDI-TOF MS on a UltrafleXtreme mass spectrometer (Bruker Daltonics). Sinapic acid (Aldrich) at a concentration of 45 mM in 50:50 water/acetonitrile (0.05% TFA) was used as a matrix. MALDI-TOF (positive ion mode) m/z data: Starting IgG, Singly charged ion M + 147121, Doubly charged ion M 2+ 73179 -IgG-PEG Fc conjugate, Singly charged ion M + 253675 Doubly charged ion M 2+ 126337. Calculated M + for [IgG + 27.3 PEG3500-Fc] ~ 253600 (knowing that the average molecular mass for the Fc-PEG3500 chain is ~ 3900). Production of GDH, preparation and characterization of the GDH-IgG conjugate. See Supporting Information.

Acknowledgments.

Dr. Nicolas Mano is warmly thanked for providing the pgp492 plasmid used to produce PQQ-GDH.

We thank Drs. Benoit Limoges, François Mavré and Mathieu Branca for the generous gift of a PQQ sample. Vincent Guérineau, www.imagif.cnrs.fr, is thanked for Maldi-Tof mass spectrometry analysis. This work has received financial support from the French "Agence Nationale de la Recherche" (ANR) through "eVIRZYM" (DS0401 -ANR 2014-CE09-0009).

Observation of such linear Lineweaver-Burk-like "primary plots" validates our analysis and initial assumptions. In particular, this result shows that in our integrated system, the overall kinetics of PQQ-GDH can be phenomenologically described by the kinetic Equation 1, even though the kinetic mode adopted by GDH is not yet known.

From Equation 2, it can be seen that the theoretical expression for the slope, s1, and origin, o1, of the primary plots are respectively given by: 𝑠 Determining the value of kox requires that the notion of the local concentration in mediator, 𝐶 , is now clarified. 𝐶 actually corresponds to the average local concentration in Fc heads as "seen" by the enzyme active site. Its value depends on the actual Fc-PEG coverage on the viral particles, on the respective positions of the IgG-PEG-Fc and GDH-IgG conjugate "layers" in the assembly, but also on the elasticity of the PEG chain. As discussed in details in Supporting Information, a reasonable estimate for 𝐶 can be obtained based on our previously introduced elastic bounded diffusion model adapted to describe the behavior of IgG-bound Fc-PEG chains in immunoassemblies. [START_REF] Anicet | Electrochemical Approach to the Dynamics of Molecular Recognition of Redox Enzyme Sites by Artificial Cosubstrates in Solution and in Integrated Systems[END_REF] We thus derived a value of 𝐶 ~ 12 µM, which yielded kox = (2.5 ± 0.6) 10 8 M -1 s -1 .

The set of values obtained here for kox, kcat, KM and Ki for fd-scaffolded integrated system are gathered in Table 1 (Column (I)), and compared to those determined by Limoges et al. for PQQ-GDH, using ferrocene methanol as a mediator, and functioning in both of its kinetic modes in solution (Column (IV)

and Column (V)). [START_REF] Zhang | Heterogeneous Reconstitution of the PQQ-Dependent Glucose Dehydrogenase Immobilized on an Electrode: A Sensitive Strategy for PQQ Detection down to Picomolar Levels[END_REF] Protective BSA backfilling. Fd bearing surfaces were backfilled with a protective BSA layer by adsorption from a 20 µL drop of 2 mg/mL BSA in phosphate for 1 h followed by two 10 minutes rinsing steps by drop replacement with phosphate buffer.

Assembly of the anti-fd antibody. The surface was left in contact for 1h with a 20 µL droplet of a 2 g/mL (~0.8 10 13 molecules/mL) solution of the anti-fd rabbit antibody. After two 10 minutes drop replacement rinsing steps, the surface was stored overnight at room temperature in the dark under a phosphate buffer solution containing 1 mg/ml BSA and 0.01 % (w:v) sodium azide. This overnight storage/desorption step was found to be important for reducing non-specific binding of subsequent antibodies onto the surface.

Assembly of the PQQ-GDH conjugated antibody.

A 20 µL droplet of a 5 µg/ml (~1.2 10 13 molecules/mL) anti-rabbit GDH-IgG conjugate in Tris buffer was left in contact with the surface for 2 h.

Two drop replacement rinsing steps with Tris buffer containing 1mg /mL BSA followed.

Assembly of the anti-GDH antibody. The surface was left in contact for 1h with 20 µL of a 5 µg/ml solution of the rabbit anti-GDH IgG in Tris buffer. Rinsing was then carried out by drop replacement with Tris buffer containing 1mg /mL BSA.

Assembly of the IgG-PEG-Fc antibody. 20 µL of a 20 µg/ml solution of the home prepared anti-rabbit IgG-PEG-Fc in Tris buffer were deposited on the surface, the assembly reaction was left to proceed overnight at 4°C.

When required, the surfaces were stored at 4°C in Tris buffer, being placed in a water-saturated nitrogen atmosphere.

Assaying the amount of PQQ-GDH molecules immuno-scaffolded on fd-particles. The assay protocol developed in this work is fully described in Supporting Information. Briefly, the antibodies of the immunoassembly are stripped off the fd-scaffolds, PQQ is thermally released from the IgG-GDH conjugate and assayed spectrophotometrically by an enzymatic method.

Supporting Information Available

Detailed experimental protocol for assaying the number of enzyme molecules borne by the viral particles.

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Correlation between the ferrocene head coverage on the electrodes, determined by CV, and the intensity of the corresponding SWV signals. Estimation of the concentration of ferrocene heads "seen" by the enzyme. Production of holo-GDH. Preparation and characterization of the GDH-IgG conjugate. This information is available free of charge via the Internet at http: //pubs.acs.org.


Patrice Berthod
email: patrice.berthod@centraliens-lille.org

Cédric Heil

Lionel Aranda

Influence of the morphologic evolution of the eutectic carbides at high temperature on the thermal expansion behavior of refractory cast alloys

Keywords: metals and alloys (A), microstructure (C), thermal expansion (C), mechanical properties (C), computer simulations (D)

Two alloys particularly rich in carbides, a nickel-based one reinforced by chromium carbides and a cobalt-based one strengthened by tantalum carbides were characterized by metallography and their hardness and thermal expansion behavior tested, after alloys had undergone a more or less long aging treatment at high temperature. Aging induces a progressive coarsening and/or fragmentation of these interdendritic carbides, with as first consequence a decrease in hardness. Also due to these morphology changes, aging the alloys on long times leads to a loss of effect of the carbides on the thermal expansion behavior of the alloys. The total thermal expansion, initially lowered by the rigid carbides network, is then free again. Indeed, the high temperature phenomenon of plastic or viscous-plastic deformation in compression of the matrix by the initial continuous carbides network has almost disappeared.

Introduction

For a superalloy in service, remaining a long time exposed to very high temperatures generally induces significant microstructure changes, in presence or not of stresses applied to the pieces. Among the modifications which are usually observed in the microstructure of industrial superalloys, one can give as examples: the establishment of a rafting structure for intermetallic precipitates in γ'-reinforced nickel-based superalloys [START_REF] Sims | The Superalloys[END_REF], coarsening of grains and morphology evolution of carbides [START_REF] Bradley | Superalloys: a technical guide[END_REF], the fragmentation of TaC carbide fibers in eutectic Cobased superalloys directionally solidified [START_REF] Stohr | [END_REF], or the same phenomenon but affecting the interdendritic TaC-carbides [4][5][6] or other MC-carbides [7] with which several equiaxed cast superalloys are strengthened. Since the interdendritic carbides play an important role at high temperature for both the mechanical resistance of the alloys (as reinforcing phases [START_REF] Sims | The Superalloys[END_REF][START_REF] Bradley | Superalloys: a technical guide[END_REF]) and the oxidation/corrosion resistance (grain boundaries = special diffusion paths notably for Cr [START_REF] Kofstad | High Temperature Corrosion[END_REF][START_REF] Young | High Temperature Oxidation and Corrosion of Metals[END_REF]), it appears that such carbides modifications may influence the mechanical / thermomechanical behavior of these alloys, as well as their oxidation rate.

The aim of this work is to learn more about the possible effects of carbides modifications on the thermal expansion of conventionally-cast carbides-rich refractory alloys, between room temperature and 1200°C. This was done by studying the case of a simple carbon-rich nickel alloy and a more complex Co-based alloy containing TaC carbides with high densities, after preliminarily aging treatments at 1200°C performed for different durations.

Experimental details of the study

The studied alloys

Three 100g-ingots of a nickel alloy (targeted composition: Ni(bal.)-30%Cr-1%C in weight percent) and three 100g-ingots of a cobalt-based superalloy (targeted: Co(bal.)-10%Ni-30%Cr-0.5%C-7.5%Ta in wt.%) were cast in the water-cooled copper crucible of a High Frequency induction furnace (CELES). This was achieved under an inert atmosphere of several hundreds millibars of pure argon, by melting pure elements together (purity higher than 99% in mass): Co, Ni, Cr and Ta supplied by Alfa Aesar, and C added as pure graphite. With either 1wt.% C and a high content in chromium, or 0.5wt.% C and 7.5wt.% Ta, chromium carbides or tantalum carbides can be present with high densities in the microstructures, of the nickel alloy and of the cobalt alloy respectively. The two alloys are elsewhere able to resist high temperature oxidation for several tens or hundreds hours (depending on both the temperature and the nature of the corrosive environment), thanks to their 30wt.% of chromium. The role of the 10wt.% of nickel present in the cobalt alloy is the stabilization of the FCC structure of matrix, down to sufficiently low temperatures.

For each alloy, one of three ingots was heated at 20 K min -1 from room temperature to 1200°C, maintained at this temperature during 5 hours, then air-cooled. A similar heat treatment was applied for the second and the third ingots of each alloy, but for longer durations of the isothermal dwell: 25 hours and 100 hours.

Metallographic preparation and microstructure characterization

The ingots were thereafter cut using a Buehler Isomet 5000 precision saw, in order to keep only the zone preserved from possible microstructure modifications possibly caused by high temperature oxidation. One sample per ingot was embedded in a cold resin (Escil CY230 + HY956) and the mounted samples were polished by using SiC paper from 120 to 1,200 grit under water, then with a 1µm-diamond paste.

A Scanning Electron Microscope (SEM, model: XL30 Philips) was used for metallographic observations, essentially in the Back Scattered Electrons mode (BSE) under an acceleration voltage equal to 20kV. The chemical composition of each alloy was analyzed in the bulk on several locations, by using a Cameca SX microprobe in a defocalized mode (magnification: × 400). A diffractometer (Bruker XPERT-Pro) was also used to complete the metallographic characterization, with X-ray diffraction results.

The proportions of carbides were determined by image analysis for the two alloys in their three aged states, by measuring their surface fractions on five BSE micrographs randomly taken in the bulk of each sample. The BSE detector led to different levels of gray, depending on the average atomic number of the phases, allowing a good separation of the matrix (gray), the chromium carbides (darker than matrix) and the tantalum carbides (whiter than matrix). The Photoshop CS software (Adobe ) allowed the measurement of these experimental surface fractions of carbides. The latter ones were supposed to be close to the volume fractions.

Thermal analysis

In order to specify the temperature ranges of melting and of solidification Differential Thermal Analysis (DTA) experiments were performed using a Setaram TGA 92-16.18 apparatus, in order to measure the temperatures of fusion's start and of fusion's end of the alloys. The thermal cycle was composed of a heating rate of 20 K min -1 up to 1200 °C, followed by a slower heating at 5 K min -1 up to 1500 °C for a better accuracy in this zone of temperatures. The cooling was done first at 5 K min -1 down to 1200°C, then at 20 K min -1 down to room temperature. The solidus and liquidus temperatures of the alloys were supposed to be close to the temperatures of fusion's start and fusion's end determined in the heating part of the DTA curve.

Thermodynamic calculations

The theoretical stable microstructure states at 1200°C of the two alloys were determined by using the Thermo-Calc version N software and the SSOL database (SGTE) enriched with the descriptions of the following binary and ternary systems : Ta-C [START_REF] Frisk | [END_REF], Co-Ta [11], Ni-Ta [12], Cr-Ta [13], Co-Ta-C [14], Ni-Cr-Ta [15] (only four ternary systems were still missing in the new database: Co-Cr-Ta, Co-Ni-Ta, Ni-Ta-C and Cr-Ta-C). Calculations were carried out to specify, when the aging duration increases, the degree of convergence of the alloys towards the theoretic stable state at 1200°C, first by comparing the microstructures of the alloys (after each of the three heat treatments) to the metallurgical stable state at 1200°C, and second to compare the temperatures of fusion's start and fusion's end to the theoretic solidus and liquidus temperatures. All calculations were performed by considering the real chemical composition of each ingot.

Hardness measurements

The hardness evolution of the two alloys with the 1200°C-treatment duration was studied by Vickers macro-indentation performed using a Testwell Wolpert apparatus. Five indentations in the bulk of each metallographic sample with a load of 30kg were performed. The average value and the standard deviation were calculated in each case.

Dilatometry runs

Thermal expansion was measured using a Setaram apparatus (model: TMA 92-16.18) on parallelepipeds cut in each ingot. The dimensions of these samples were about 4mm × 4mm (square main faces) × 2mm (direction of the characterized expansion). The heating was performed from room temperature up to 1200°C (rate: 10 K × min -1 ), followed by a dwell of 3600 seconds and finally a cooling down to room temperature (rate: -10 K × min -1 ). Three evolutions of the sample's thickness were studied: the thermal expansion during the heating, the thermal contraction during the cooling, and the dimensional evolution during the 1hourdwell at 1200°C.

Results

Microstructure states of the alloys after the aging treatments

The chemical compositions of the obtained alloys, characterized by Energy Dispersion Spectrometry using the EDS apparatus with which the SEM is equipped, are displayed in Table 1. They are close to the targeted contents and one can also consider that the three ingots of the same alloy (Ni-based or Co-based) have effectively the same compositions.

The microstructures of the two alloys after the three aging treatments are illustrated by the SEM micrographs given in Fig. 1. After the 5h-treatment, the microstructures of the two alloys are still totally analogous to their as-cast microstructures. The Ni-based alloy contains a dendritic matrix of FCC nickel containing a part of chromium and of carbon in solid solution, and an interdendritic network of primary chromium carbides forming a eutectic compound with matrix. Secondary carbides can also be observed in the matrix. After more time spent at 1200°C, there is a progressive morphology change of the primary carbides which are coarsened / rounder than before, while the secondary carbides have disappeared. This is particularly true between the as-cast/5h-aged state and the 100h-aged state. In contrast, no difference was observed concerning the carbides natures: they are still Cr 7 C 3 , even after 100 hours of aging at 1200°C (Fig. 2).

The Co-based alloy, the microstructure of which is already slightly different after 5 hours spent at 1200°C by comparison to its as-cast state, goes on evolving for longer times at 1200°C since the primary tantalum carbides become more and more divided into alignments of small and round TaC carbides. Here too, their nature does not change (Fig. 3). However, spectra of X-ray diffraction tend qualitatively showing that the FCC part of matrix still remaining after cooling to room temperature tends to be more present after 100h-aging than after only 5haging.

Carbide fractions and hardness of the alloys

In order to get more quantitative data about the populations of carbides in the two alloys after the three different aging durations, measurements of the surface fractions of chromium carbides were performed for the Ni-based alloy and of tantalum carbides for the Co-based alloy. The results led to the curves of evolution presented in the two graphs displayed in Fig. 4. The volume fraction of Cr 7 C 3 carbides stays almost constant, independently on the aging duration (even if there is maybe a little tendency to increase), while the volume fraction of TaC carbides obviously decreased during the first tens hours before staying almost constant. Thermodynamic calculations were also performed using Thermo-Calc for the chemical composition of each ingot and the aging temperature. This led to verify that effectively carbides are Cr 7 C 3 and TaC at 1200°C and showed that matrixes were, at this same temperature, FCC in the two cases. The parts of HCP in the matrix of the cobalt-based ingots appeared during the cooling. Volume fractions were obtained from the mass fractions calculated by Thermo-Calc by using the following densities: 8.1 for Ni-based matrix, 8.9 for Co-based matrix, 6.94 for Cr 7 C 3 carbide and 14.5 for TaC carbides (all in g cm -3 ) [16]. There is little difference (taking into account the standard deviation values) between the final volume fraction and the value determined with Thermo-Calc calculations. The TaC volume fraction significantly converged to the equilibrium value, while this was obviously done for the Cr 7 C 3 volume fraction before 5 hours of heat treatment.

Hardness measurements, achieved under 30kg, logically led to values for the three aging states of the Co-based alloy which are higher than for the three aging states of the Ni-based alloy (Fig. 5). In the two cases the Vickers hardness decreases rapidly between the 5h-aged state and the 25h-aged state. This decrease goes on thereafter, but slower, for the cobalt alloy. In contrast hardness seems stabilized after 25h-aging for the Ni-based alloy.

Intervals of fusion and of solidification

Differential Thermal Analysis runs were performed for the two alloys in their three aged states. The DTA curves for the two extreme aged states are displayed in Fig. 6. One can first see that the endothermic peaks (fusion part) are better distinguished after only 5h-aging than after 100h-aging, while the exothermic peaks (solidification part) are logically not dependent on the aging duration. No significant difference can be noted between the measured temperatures of fusion's start and of fusion's end for the two extreme aging states, and the calculated solidus temperatures are in good agreement with the temperatures of fusion's start (Table 2). In contrast this is less true for the liquidus temperatures).

Thermal expansion behaviors

When the samples are heated from room temperature up to 1200°C, their thickness increases more or less regularly, while it decreases thereafter during the cooling. The deformation curves are presented in Fig. 7 for the two extreme aged states of the Ni-based alloy and in Fig. 8 for the Co-based alloy. It appears first that the maximal dilatation is almost the same for the Ni-based alloy and for the Co-based alloy for the same duration of preliminary aging. In contrast, for a same alloy, the expansion when arriving to 1200°C for the 5h-aged state (1.59% and 1.69% for the Ni-based alloy and for the Co-based alloy respectively) is significantly lower than for the 100h-aged states (1.93% and 1.89% respectively). This can be found again for the average thermal expansion coefficients: indeed α 100-1200°C for the 5h-aged state (15.8 and 16.7 × 10 -6 K -1 for the Ni-based alloy and for the Co-based alloy respectively) is significantly lower than for the 100h-aged state (18.4 and 18.3 × 10 -6 K -1 respectively). Another difference between the two aged states is what is occurred during the 1 hour-isothermal dwell: for the 5h-aged alloys there is a contraction at 1200°C, significant for the Ni-based alloy (-0.04%) and particularly important for the Co-based alloy (-0.21%). When alloys were preliminarily aged during 100 hours, the isothermal contraction at 1200°C exists too but is much less important for the Co-based alloy and almost inexistent for the Ni-based alloy. This isothermal contraction, which apparently followed a start of contraction already occurring before the end of heating (especially in the case of the 5h-aged Co-based alloy), is responsible of a significant part of the permanent negative deformation after return to 100°C (-0.16% and -0.27% for the Ni-based alloy and for the Co-based alloy respectively). Near the end of heating and during the beginning of cooling, the alloys were also subjected to a contraction phenomenon which participates thereafter to the total contraction after return to 100°C. The values deduced from these curves are listed in Table 3.

In order to better examine how the contraction acts during the isothermal stage it can be useful to plot the dilatometry results in the {deformation = f (time)} scheme. The corresponding curves for the Ni-based alloy after 5h-aging and 100h-aging are displayed in Fig. 9 and the curves for the Co-based alloy in Fig. 10. In each case an enlargement of the dwell part is added. One can see now that in the three cases of significant contraction during the hour spent at 1200°C, (5h-aged Ni-based, 5h-aged and 100h-aged Co-based alloys), the isothermal contraction is initially fast then it progressively decelerates.

Discussion

During solidification the mechanisms of development of the microstructures do not always allow the alloys to strictly respect the natures, the volume fractions, and also the morphologies of phases with which these alloys could be in metallurgical equilibrium at all the successive temperatures. This is true for the primary carbides the growth mechanisms of which lead to elongated shapes. At room temperature these shapes remain as formed at solidification and they can influence the properties of the alloys. If the latter are heated again up to high temperature, their properties depend in a first time on the still elongated shape of the interdendritic carbides, but they may thereafter progressively change with the morphology evolution of the carbides due to the reduction of interfacial energy. Hence, the high temperature mechanical properties can be logically changed with the coarsening of chromium carbides or with the fractioning of tantalum carbides, since these carbides are important interdendritic reinforcing particles. These morphology changes induce a weakening of the alloy but also improvements of ductility and toughness).

Changes in Young's modulus or ultimate tensile strength are not the sole possible properties modifications resulting from carbides fragmentation [17]. It was for example seen recently for the same alloys [18] that such modifications of the primary carbides, which are present in the grain boundaries along which species involved in the oxidation phenomena (e.g. Cr) diffuse with easiness, can lead to changes in the kinetic of oxidation at high temperature: the longer the aging duration, the faster the mass gain by oxidation (especially at 1200°C).

In this study, one saw in a first time that the aging at high temperature led to a lower fraction of TaC carbides (as well as a slightly higher proportion of FCC phase in matrix) after cooling in the Co-based alloy, while no such changes were seen for the chromium carbides of the Ni-based alloy. The chemical homogenization which resulted from the first hours of aging for the Co-based matrix smoothed the segregations developed during solidification, and the locally too high fractions of TaC were then corrected, and they better fitted the thermodynamic calculations results. This led for this alloy to a decrease in hardness which went on thereafter because of TaC fragmentation (already seen for other TaC-strengthened cobalt based superalloys [17]), although the carbide fraction had become already constant. Another possible effect of the decrease in TaC fractions in the Co-based alloy during the first hours of aging is a slight but global homogeneous enrichment of the matrix in both carbon and tantalum atoms. This possibly led to a better stabilization of austenite at low temperature, which may result in a higher proportion of FCC against HCP for the matrix at the end of cooling, as qualitatively shown by X-ray diffraction. The coarsening of the chromium carbides in the Ni-based alloy, which also favors a loss of continuity for the interdendritic carbides network at constant volume fraction, also induces a decrease in hardness, but much slower than the one due to TaCfragmentation. In contrast, the interval of fusion was not really changed by the microstructure consequences of aging.

Concerning the thermal expansion of the alloys versus the different aging durations, one can first remark that the presence of a significant volume fraction of carbides led to thermal expansions which are slower than usually for nickel or cobalt-based alloys without such quantities of carbides (α ≅ 20 × 10 -6 K -1 ). Indeed, in the 5h-aged state (which is close to the as-cast state), the whole curves have a lower average slope, which is quantitatively found again by considering the average coefficients of thermal expansion (α ≅ 16 or 17 × 10 -6 K -1 ). This is clearly due to both the high carbides fractions and the low thermal expansion coefficients of Cr 7 C 3 (α ≅ 11 × 10 -6 K -1 ) or TaC (α ≅ 6.3 × 10 -6 K -1 ) carbides [START_REF] Samsonov | Plenum Press Handbooks of High-Temperature Materials[END_REF]. The decrease in dilatation which was observed at the end of heating for the two 5h-aged alloys, as well as the progressive contraction during the isothermal dwell, were already observed but for alloys not so rich in carbon and in carbides [START_REF] Berthod | [END_REF]. In addition, in these previous results the dwell duration was only 10 minutes, while it is here 1 hour which allows to observe the contraction progression on longer times and its deceleration. This permits here confirming the mechanisms previously explained [START_REF] Berthod | [END_REF], which can be illustrated by Fig. 11.

All along the heating the matrix tends to undergo a thermal expansion greater than the carbides one. Therefore, since the two phases are mixed together with interpenetration of their networks, the mechanical equilibrium necessarily imposes that matrix is subjected to a more and more intensive compression and the carbide network is in a state of more and more intensive traction. When temperature has become high enough to weaken the metallic matrix, this one begins to be plastically deformed in compression by the carbide network which remained very rigid. This leads to a deceleration of the elongation, and even to its inversion. When temperature arrived at the isothermal dwell, there is now no tendency of thermal expansion and the carbides network continues to viscoplastically compress the matrix, until an equilibrium between the decreased compressive action of the carbides network and the increasing resistance of the plastically deformed matrix is reached.

When a sufficient aging is applied, with as consequence a fragmented state for carbides and then a sufficient loss of continuity for their network, this effect can obviously disappear: 100 hours spent at 1200°C are sufficient to suppress the increasing compressive action of carbides on matrix: global thermal expansion coefficients of the whole alloys are higher, no deceleration of elongation occurs at high temperature and no isothermal contraction acts during the dwell.

Conclusion

The difference of thermal expansion behavior between the metallic matrix and the network of intergranular carbides can induce significant modifications for the thermal elongation of a piece made of the considered alloy. This can be a decrease in average thermal expansion coefficient (which is usually considered as beneficial) but also, if temperature becomes too high, a deformation of the matrix which is responsible of a not so interesting permanent deformation after return to room temperature, with as result a bad geometrical stability. Previous studies [21] showed that new increases in carbide volume fractions enhance the problem, but fortunately it appeared here that a sufficiently long aging can then reduce, and even suppress, the phenomenon by eliminating the carbides network continuity.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Microstructures of the two alloys after each heat-treatment (SEM/BSE micrographs)

Fig. 4 .Fig. 5 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .

 457891011 Fig.4. Evolution of the carbides volume fractions with the aging duration, with comparison with the ones calculated using Thermo-Calc from the real chemical composition of the three ingots used for the three heat-treatments (the 5h-aged cobalt alloy also contains 0.09%vol of M 23 C 6 )

Table 1

 1 Chemical compositions of the studied alloys (SEM/EDS, ± 1wt.%)

	Average	ingot	aged	Co	Ni	Cr	Ta
	± Std deviation
		N°1	5h at 1200°C	/	Bal.	31.4	/
	Ni alloy
		N°2	25h at 1200°C	/	Bal.	29.0	/
	(1.0 wt.%C)
		N°3	100h at 1200°C	/	Bal.	32.7	/
		N°1	5h at 1200°C	Bal.	9.7	31.3	7.5
	Co alloy
		N°2	25h at 1200°C	Bal.	10.0	31.3	7.7
	(0.5 wt.%C)
		N°3	100h at 1200°C	Bal.	10.2	31.1	7.6
			Table 2
	Values of the solidus temperatures and liquidus temperatures determined on the heating part of
			the DTA curves
	Temperatures	Temperature of fusion start	Temperature of fusion end
			/ Solidus temperature	/ Liquidus temperature
			(°C)		(°C)
			Thermo		Thermo
	Alloys		DTA	-	DTA	-
				Calc		Calc
		5h	1320	1316	1373	1341
	Nickel alloy
		100h	1320	1317	1378	1338
		5h	1273	1272	1402	1343
	Cobalt alloy
		100h	1265	1272	1395	1342

Table 3

 3 Values of the solidus temperatures and liquidus temperatures determined on the heating part of the DTA curves

	Temperatures	Average thermal expansion
			coefficients α 100°C-1200°C (×10 -6 K -1 )	∆l / l 0 (%) at 1200°C
	Alloys		α 100°C-1200°C heating	α 1200°C-100°C cooling	end of heating	start of cooling
			final deformation after	isothermal contraction
			return to 100°C
			15.8	14.6	1.594 %	1.551 %
	Nickel alloy	5h	-0.163 %	-0.043 %
			18.4	17.2	1.931%	1.965 %
		100h
			+0.095 %	+0.034 %
			16.7	15.7	1.692 %	1.484 %
		5h
	Cobalt alloy		-0.270 %	-0.208 %
			18.3	15.6	1.887 %	1.853 %
		100h
			+0.101 %

Acknowledgements

The authors thank the Common Service of Microanalysis of the Faculty of Science and Technologies of the University Henri Poincaré Nancy 1 (Electron microscopy) and Pascal Villeger (XRD analyses).