Marine Henry

Laurent Debarbieux
email: laurent.debarbieux@pasteur.fr

Tools from viruses

Keywords:

Tools from viruses: bacteriophage successes and beyond.

1°) Early applications

Amongst the earliest applications of viruses, their use as live or attenuated particles to develop vaccines during the 19 th century was very important as it represented the beginning of taming viruses for our purposes, but is beyond the scope of this review. Beside this major contribution to human health, exploitation of viruses ramped up with the discovery of viruses infecting bacteria named bacteriophages. One of the earliest applications of these bacterial viruses was proposed by F. d'Herelle, who demonstrated almost 100 years ago that bacteriophages were able to cure human bacterial infections (d'Herelle, 1917). This therapeutic approach, bacteriophage therapy, rapidly developed globally until the industrial production of antibiotics was launched in the 1940's [START_REF] Summers | Bacteriophage therapy[END_REF]. Around the same time, Delbrück and colleagues chose bacteriophages as model organisms to understand the genetic basis of virus-host interactions [START_REF] Luria | Mutations of Bacteria from Virus Sensitivity to Virus Resistance[END_REF]. Soon after, the larger scientific community adopted these viruses and their hosts, and studies performed during the following 40 years yielded a tremendous amount of literature (Figure 1), allowing major discoveries notably in both DNA and RNA processes shared by living organisms. Altogether, these findings led to the development of the first molecular tools and ultimately to the advent of a new discipline, now called molecular biology [START_REF] Summers | Félix d'Herelle and the origins of molecular biology[END_REF].

It is remarkable that such a vast array of discoveries were founded on studies performed on a very limited number of bacteriophages (T4, T7, P1, Mu, PhiX174, Lambda and few others but probably less than 20). For example, to our knowledge, the Lambda bacteriophage, one of the best studied temperate bacteriophages, was once isolated almost inadvertently from E.coli and never again from an environmental source, and numerous genetic tools have been derived from this unique virus [START_REF] Hendrix | Bacteriophage Lambda and its Genetic Neighborhood. In "The Bacteriophages, Second Edition[END_REF]. Transduction, described by Lederberg in the 1950's, was amongst the first techniques exploiting bacteriophage abilities to recombine with host DNA [START_REF] Zinder | Genetic exchange in Salmonella[END_REF]. Since then, bacteriophage recombinases have been extensively studied leading to the classification of these enzymes into two families: the lambda integrase group (with a conserved tyrosine residue) and the serine recombinase group (with a conserved serine residue) which includes the phiC31 integrase [START_REF] Smith | Site-specific recombination by phiC31 integrase and other large serine recombinases[END_REF]. In both groups, some of these enzymes were further used to develop tools to manipulate genomes not only within their original host but also outside the bacterial world. For instance, recombination genes of Lambda led to the development of in vitro techniques to perform directed gene replacement in fungi [START_REF] Chaveroche | A rapid method for efficient gene replacement in the filamentous fungus Aspergillus nidulans[END_REF]. A recent development of the use of PhiC31 integrase in the long-term expression of transgenes in mammalian cells may become an important tool for human gene therapy [START_REF] Chavez | Therapeutic Applications of the PhiC31 Integrase System[END_REF][START_REF] Keravala | Long-term transgene expression in mouse neural progenitor cells modified with phiC31 integrase[END_REF]. After the huge contribution of a very limited number of different bacteriophages in the unveiling of numerous molecular mechanisms conserved through cellular life, the current development of viral metagenomics is likely to increase the number of applications exploiting viral genes [START_REF] Schoenfeld | Functional viral metagenomics and the next generation of molecular tools[END_REF]. In this article we review some of the most recent applications covering viral proteins, virion structures, full viruses and highlight some future directions.

2°) Exploiting the specificity

One of the main hallmarks of viruses is their specificity for their target. In many environments, viruses are exposed to a plethora of hosts and their capacity to infect only a limited number of them drives their population expansion and maintenance. This outstanding property has therefore been exploited in numerous applications among which bacteriophage typing was the first to be widely used. The susceptibility to different bacteriophages provides an easy way to classify closely related bacterial strains. Bacteriophage typing was introduced in the 1940's and despite the development of molecular techniques, it is still being used, for example, by the Health Protection Agency (UK) to type Salmonella and Staphylococcus aureus strains (http://www.hpa.org.uk/). This is in fact not so surprising since molecular techniques based on the presence / absence of DNA fragments do not take into consideration the expression of proteins coded by these fragments, as well as the activity of these proteins. In contrast, bacteriophages rely on the presence / absence of molecular motifs expressed at the surface of bacteria and remain useful tools to provide a rapid answer, generally within a day, which is valuable in an outbreak situation [START_REF] Sechter | Twenty-three years of Klebsiella phage typing: a review of phage typing of 12 clusters of nosocomial infections, and a comparison of phage typing with K serotyping[END_REF]. However, it may not be long before the price of the latest sequencing technologies drops to the point where a full genome sequence will become available within a couple of days, thus rendering obsolete the bacteriophage typing activity.

It is clear that the rapid and accurate identification of bacterial pathogens is vital in order to prevent the spread of infections and limit their consequences by implementing appropriate control strategies. This is a particularly important concern for hospitals, care centres and in the food industry. Several bacteriophages have been exploited for technology development to enable the rapid detection of bacteria in complex environments, in particular through the use of bacteriophage based probes [START_REF] Hagens | Application of bacteriophages for detection and control of foodborne pathogens[END_REF][START_REF] Rees | Phage for rapid detection and control of bacterial pathogens in food[END_REF][START_REF] Ripp | Bacteriophage-Based Pathogen Detection[END_REF][START_REF] Singh | Bacteriophage based probes for pathogen detection[END_REF][START_REF] Smartt | Pathogen detection using engineered bacteriophages[END_REF]. However, very few diagnostic kits for the detection of pathogens in human samples such as the FASTPlaqueTB assay and the MRSA/MSSA Blood Culture Test have yet reached the market [START_REF] Stanley | Development of a new, combined rapid method using phage and PCR for detection and identification of viable Mycobacterium paratuberculosis bacteria within 48 hours[END_REF], (http://www.microphage.com/technology/). The current applications of bacteriophages in pathogen detection, can be divided into two groups: those based on inert bacteriophage particles or isolated bacteriophage proteins and those that require an on-going infectious cycle.

Both systems have been developed targeting E.coli 0157:H7, a major food pathogen. One of them, based on the specificity of a bacteriophage tail protein, is already available on the market (VIDAS UP E. coli O157, Biomérieux). Briefly, in this assay, a bacteriophage specific for E. coli 0157:H7 was isolated, its tail fiber protein was identified and produced as a recombinant peptide, labelled with a fluorescent dye and included into the VIDAS sandwich assay technology. Another ingenious device using infective particles this time was also designed. Combining horseradish peroxidase-labelled bacteriophage with a serogroup-specific immunomagnetic separation system and enrichment broth, it allows pre-amplification of the pathogen before its detection by a luminometer [START_REF] Willford | Luminescence based enzymelabeled phage (Phazyme) assays for rapid detection of Shiga toxin producing Escherichia coli serogroups[END_REF]. Among the viral proteins exploited for the detection of hosts, we can distinguish between tail fiber proteins as mentioned above, required for the early step of the infectious cycle, and endolysins used for bacteriophage release, the last step of the cycle. The use of tail fiber proteins relies on the specificity of a bacteriophage protein towards its bacterial receptor. Other examples of such proteins in pathogen detection include the receptor binding protein (RBP) of a Campylobacter bacteriophage and the P22 tailspike protein conjugated to nanoaggregate embedded beads [START_REF] Tay | Silica encapsulated SERS nanoprobe conjugated to the bacteriophage tailspike protein for targeted detection of Salmonella[END_REF].

Endolysins, participate in the lysis of the host cell by degrading specific bonds within the bacterial peptidoglycan in order for the bacteriophage progeny to be released at the end of the lytic cycle. Endolysins reported to date are either globular or modular. Modular endolysins display at least one N-terminal catalytic domain and a C-terminal cell wall binding domain [START_REF] Fischetti | Bacteriophage lysins as effective antibacterials[END_REF][START_REF] Loessner | Bacteriophage endolysins--current state of research and applications[END_REF]. The cell wall binding domain (CBD) of a specific endolysin shows high specificity and affinity for its ligand on the cell wall of its host, readily accessible in Gram positive bacteria. This specificity has been exploited in various techniques, in particular for detection. One example is an assay in which CBDs of Listeria monocytogenes, Bacillus cereus or Clostridium perfringens were coated onto paramagnetic beads, allowing a better separation and recovery of bacterial cells than with standard techniques [START_REF] Kretzer | Use of high-affinity cell wall-binding domains of bacteriophage endolysins for immobilization and separation of bacterial cells[END_REF].

Applications requiring an infectious particle may use labelled particles as described above but may also be based on genetically modified bacteriophages leading to the expression of a reporter gene that is highly expressed upon bacteriophage infection. Examples of these reporter bacteriophages include those carrying luminescence genes such as, the Listeria bacteriophage A511 in which Vibrio harveyi luxAB genes were inserted immediately downstream of the gene encoding the major capsid protein, or bacteriophages for Yersinia pestis and Bacillus anthracis in which a similar approach proved efficient in detecting these two pathogens, whose rapid diagnosis is crucial in the fight against bioterrorism [START_REF] Loessner | Construction of luciferase reporter bacteriophage A511::luxAB for rapid and sensitive detection of viable Listeria cells[END_REF][START_REF] Schofield | Bioluminescent' reporter phage for the detection of Category A bacterial pathogens[END_REF]. Other types of reporter genes can also be inserted in bacteriophage genomes, such as a hyperthermophilic β-glycosidase gene used for the detection of Listeria cells [START_REF] Hagens | Reporter bacteriophage A511::celB transduces a hyperthermostable glycosidase from Pyrococcus furiosus for rapid and simple detection of viable Listeria cells[END_REF]. The main advantage of the latter is that the overtime signal amplification goes on as long as the substrate is provided, long after the host has been lysed.

Finally, one may simply use the lytic nature of the bacteriophage as the "sensor" to detect of the presence of the host. This is the principle of the FASTPlaqueTB assay for the detection of Mycobacterium tuberculosis in sputum in which bacteriophages infecting the slow-growing tubercle bacillus are subsequently detected when forming plaques on a fast-growing strain [START_REF] Rees | Phage for the detection of pathogenic bacteria[END_REF]. This technique can also be coupled to a molecular tool for higher specificity as in the phage-IS900 technique used to detect viable Mycobacterium avium paratuberculosis in dairy products, a pathogen thought to have a role in Crohn's disease pathogenesis [START_REF] Botsaris | Rapid detection methods for viable Mycobacterium avium subspecies paratuberculosis in milk and cheese[END_REF].

By definition, these detection systems are designed to be disposable and single use kits, therefore the nature of the key components (sometimes genetically modified) does present safety issues, and their usage will have to be constrained within an appropriate waste management protocol. In addition, these systems often developed for one particular host can be adapted for many others upon identification of the corresponding genes or proteins in bacteriophage genomes, which nevertheless, can be sometimes difficult when working with a new bacteriophage (typically a new bacteriophage possesses over 70% of ORFs that do not match any ORFS present in genomic databank) Apart from pathogen detection applications, the viral specificity may also be used for targeted delivery such as gene delivery to a target cell for therapeutic purposes. Genetically engineered bacteriophages used as vectors for nucleic acids may target bacterial or eukaryotic cells. For example, non-lytic filamentous bacteriophages can be used to deliver genes encoding proteins that are toxic to their bacterial host, such as the delivery of "addiction toxins" triggering programmed cell death via M13 phagemid system [START_REF] Hagens | Genetically modified filamentous phage as bactericidal agents: a pilot study[END_REF][START_REF] Westwater | Use of genetically engineered phage to deliver antimicrobial agents to bacteria: an alternative therapy for treatment of bacterial infections[END_REF]. The use of a non-lytic bacteriophage presents the advantage of killing the bacterial cell while leaving it intact, thereby limiting the release of bacterial endotoxins and decreasing the resulting inflammation [START_REF] Hagens | Therapy of experimental pseudomonas infections with a nonreplicating genetically modified phage[END_REF].

Among virus-derived applications of gene delivery to eukaryotic cells, one can cite adeno-associated virus AAV works towards therapy for lung cancer via the delivery of the CD40L gene, or studies using Herpessimplex virus for the transfer of the C3 transferase gene to indirectly promote axonal regeneration [START_REF] Wu | Adeno-associated virus mediated gene transfer into lung cancer cells promoting CD40 ligand-based immunotherapy[END_REF][START_REF] Zhou | HSV-mediated gene transfer of C3 transferase inhibits Rho to promote axonal regeneration[END_REF]. Bacteriophages also have a potential in gene therapy via transfection of genes toxic for cancer cells. This could be a promising future strategy for treating advanced lung and colon cancer, combining gene transfer with chemotherapeutic agents [START_REF] Rama | E phage gene transfection associated to chemotherapeutic agents increases apoptosis in lung and colon cancer cells[END_REF].

3°) Exploiting bacteriophages for biocontrol purposes

In the environment, viruses play a major role as biocontrol agents for their hosts and do so through either one of the two life cycle strategies they use. A bacteriophage will either infect its host to immediately produce its progeny leading to the death of the host (virulent cycle), or it may delay the progeny production by staying silent within its host genome for a number of generations (temperate cycle). For obvious reasons, bacteriophages displaying a temperate nature are not suitable for use in the development of biocontrol strategies. Strictly lytic viruses, however, are very much appropriate for biocontrol downstream applications.

The process of infecting and efficiently killing their bacterial hosts has been refined over billions of years of evolution and shows a great versatility in overcoming possible resistance mechanisms that a bacterium could evolve [START_REF] Labrie | Bacteriophage resistance mechanisms[END_REF]. This type of bacteriophage has indeed been broadly exploited for the biocontrol of bacteria for human, industrial or ecological interests.

The alarming problem of the increasing occurrence of antibiotic resistant bacteria has recently revived the interest in bacteriophage therapy. Despite the fact that human bacteriophage treatment has been carried out over the last 80 years in Eastern Europe, the evolution of safety and regulation standards in Western countries during the last 30 years is currently preventing the development of large scale clinical trials due to the lack of recent data on both efficacy and safety (Maura and Debarbieux, 2011). Nevertheless, within the last decade, an increasing number of proof of concept studies were achieved using animal models. As for human testing, one phase II clinical trial using the Biophage-PA bacteriophage preparation towards antibiotic-resistant Pseudomonas aeruginosa in 24 patients with chronic otitis was published, concluding to its safety and efficacy [START_REF] Wright | A controlled clinical trial of a therapeutic bacteriophage preparation in chronic otitis due to antibiotic-resistant Pseudomonas aeruginosa; a preliminary report of efficacy[END_REF]. Another trial, supported by the Nestlé Nutrition Corporate and involving the oral administration of T4 bacteriophages in young children with diarrhea due to ETEC/EPEC infections, is currently being carried out and is due to completion in 2014 (Clinical Trial Identifier NCT00937274).

Biocontrol of pathogens in food products may represent an economically viable field for bacteriophage-based biocontrol. This topic was extensively reviewed [START_REF] Garcia | Bacteriophages and their application in food safety[END_REF][START_REF] Goodridge | Phage-based biocontrol strategies to reduce foodborne pathogens in foods[END_REF][START_REF] Hagens | Bacteriophage for Biocontrol of Foodborne Pathogens: Calculations and Considerations[END_REF][START_REF] Mahony | Bacteriophages as biocontrol agents of food pathogens[END_REF]. Many studies reported success in decreasing the bacterial load (for Listeria, Salmonella and E. coli species among others) on food surfaces (cheese and meat), hard surfaces and also cattle hide [START_REF] Anany | Biocontrol of Listeria monocytogenes and Escherichia coli O157:H7 in Meat by Using Phages Immobilized on Modified Cellulose Membranes[END_REF][START_REF] Coffey | Assessment of Escherichia coli O157:H7-specific bacteriophages e11/2 and e4/1c in model broth and hide environments[END_REF][START_REF] Guenther | Biocontrol of Salmonella Typhimurium in RTE foods with the virulent bacteriophage FO1-E2[END_REF][START_REF] Viazis | Reduction of Escherichia coli O157:H7 viability on hard surfaces by treatment with a bacteriophage mixture[END_REF][START_REF] Viscardi | Isolation and characterisation of two novel coliphages with high potential to control antibiotic-resistant pathogenic Escherichia coli (EHEC and EPEC)[END_REF]. Several systems have already been approved by authorities for use on food products such as ListShield™ (Intralytix) or LISTEX™ (Micreos) for the control of L. monocytogenes (both FDA-and USDAapproved), EcoShield™ (FDA-cleared) targeting E. coli O157:H7 and SALMONELEX™ against Salmonella which also beneficiated from a Temporary Use Exemption by the Dutch Medicine Evaluation Board for the currently ongoing field trials. Bacteriophages were also found to be efficient for the decontamination of livestock raised for the food industry, therefore limiting the risk of pathogens reaching the food chain, or to detect the presence of pathogens in animal-derived alimentary products. Bacteriophages have shown success in control of plant pathogens too with recent examples including the development of a bacteriophage-based biocontrol technique for Dickeya solani, a bacterium which causes potato plants to waste, and the effective prevention of wilting using a cocktail of three lytic bacteriophages for the bacterium Ralstonia solanacearum [START_REF] Adriaenssens | T4-related bacteriophage LIMEstone isolates for the control of soft rot on potato caused by 'Dickeya solani[END_REF][START_REF] Fujiwara | Biocontrol of Ralstonia solanacearum by Treatment with Lytic Bacteriophages[END_REF]. The company Omnilytics developed the bacteriophage product "Agriphage" for the control of bacterial spot caused by Xanthomonas campestris or bacterial speck caused by Pseudomonas syringae (www.omnilytics.com). The effectiveness of this product in protecting the crops against these pathogens is reflected by the report of a marked increase in yield. However, early suggestions that bacteriophage interaction with plants might actually decrease plant growth or not show improvements compared to regular treatments are also reported, highlighting the need for further evaluation of possible biocontrol strategies before implementation is considered [START_REF] Gill | Bacteriophage ecology and plants[END_REF][START_REF] Jones | Bacteriophages for plant disease control[END_REF][START_REF] Kocharunchitt | Use of bacteriophages as biocontrol agents to control Salmonella associated with seed sprouts[END_REF][START_REF] Ye | Evaluation of a Biocontrol Preparation Consisting of Enterobacter asburiae JX1 and a Lytic Bacteriophage Cocktail To Suppress the Growth of Salmonella Javiana Associated with Tomatoes[END_REF].

Finally bacteriophages are currently being investigated for their potential as natural biocontrol agents for environmental issues. Their natural presence in the environment would suggest a lower risk of natural ecology disturbance, making them an attractive alternative to chemicals as antibacterial agents. In this field, works have been carried out in the context of wastewater treatment and sludge processing. Only a few studies have been conducted so far but encouraging results in foam, sludge volume or biomass bulking reduction were reported [START_REF] Choi | Bacteriophage-based biocontrol of biological sludge bulking in wastewater[END_REF][START_REF] Kotay | Biocontrol of biomass bulking caused by Haliscomenobacter hydrossis using a newly isolated lytic bacteriophage[END_REF][START_REF] Petrovski | Genome Sequences and Characterization of the Related Gordonia Phages GTE5 and GRU1 and Their Use as Potential Biocontrol Agents[END_REF].

Besides the use of entire bacteriophage particles, the use of isolated proteins has also raised interest lately. The use of single gene products by-passes the difficulties of using infective particles and tends to reassure the community by eliminating the risk of genetic recombination and general instability linked to the idea of using viruses while keeping the benefit of the main hallmark of the bacteriophage, that is to say its specificity.

As mentioned earlier, endolysins cleave peptidoglycan bonds enabling them to lyse Gram positive bacteria when applied externally. The potential use of these proteins as antimicrobial agents has been extensively reviewed [START_REF] Coffey | Phage and Their Lysins as Biocontrol Agents for Food Safety Applications[END_REF][START_REF] Fenton | Recombinant bacteriophage lysins as antibacterials[END_REF][START_REF] Fischetti | Bacteriophage lysins as effective antibacterials[END_REF][START_REF] Fischetti | Bacteriophage endolysins: A novel anti-infective to control Gram-positive pathogens[END_REF][START_REF] O'mahony | Lysins to kill -a tale of viral weapons of mass destruction[END_REF]. More recently, the production of recombinant lysins (engineered or chimeric lysins) has also been achieved in a number of studies [START_REF] Pastagia | A Novel Chimeric Lysin Shows Superiority to Mupirocin for Skin Decolonization of Methicillin-Resistant and -Sensitive Staphylococcus aureus Strains[END_REF][START_REF] Resch | A stable phage lysin (Cpl-1) dimer with increased antipneumococcal activity and decreased plasma clearance[END_REF][START_REF] Schmelcher | Chimeric Phage Lysins Act Synergistically with Lysostaphin To Kill Mastitis-Causing Staphylococcus aureus in Murine Mammary Glands[END_REF]. Their antimicrobial potential against S. aureus, B. anthracis, Streptococcus pneumoniae, Enterococci, L. monocytogenes or Clostridium difficile to cite only a few, is well documented [START_REF] Kikkawa | Characterization of the catalytic activity of the gamma-phage lysin, PlyG, specific for Bacillus anthracis[END_REF][START_REF] Mayer | Molecular characterization of a Clostridium difficile bacteriophage and its cloned biologically active endolysin[END_REF][START_REF] Rashel | Efficient elimination of multidrug-resistant Staphylococcus aureus by cloned lysin derived from bacteriophage phi MR11[END_REF][START_REF] Rodriguez-Cerrato | Pneumococcal LytA autolysin, a potent therapeutic agent in experimental peritonitissepsis caused by highly beta-lactam-resistant Streptococcus pneumoniae[END_REF][START_REF] Yoong | Identification of a broadly active phage lytic enzyme with lethal activity against antibiotic-resistant Enterococcus faecalis and Enterococcus faecium[END_REF]Zhang et al., 2012a). Most recent advances in the field of chimeric lysins led to the design of a hybrid protein targeting Gram negative pathogens, whose structure is templated on a bacterial toxin called pesticin. It is composed of T4 lysozyme fused to the domain of pesticin targeting FyuA, an outer membrane transporter but also a major virulence factor for some Yersinia and pathogenic E. coli strains. This hybrid lysin has therefore the potential to cross the outer membrane of pathogens to gain access to the peptidoglycan, and was shown to be able to kill specific Yersinia and pathogenic E. coli strains [START_REF] Lukacik | Structural engineering of a phage lysin that targets gram-negative pathogens[END_REF]. Following infection, the bacteriophage quickly hijacks the host cellular machinery to its own profit in order to redirect it to the production of the proteins that will constitute its progeny. To do so more efficiently, bacteriophages often encode early proteins inhibiting the processing of the host proteins. Several of these early proteins have been identified by different groups and their implication in antibacterial compounds investigation has been reviewed by [START_REF] Sau | Inactivation of indispensable bacterial proteins by early proteins of bacteriophages: Implication in antibacterial drug discovery[END_REF][START_REF] Sau | Inactivation of indispensable bacterial proteins by early proteins of bacteriophages: Implication in antibacterial drug discovery[END_REF]. Examples of such proteins include peptides inhibiting bacterial replication by interacting with the host DNA replication proteins, peptides inhibiting the cell wall synthesis such as the Kil proteins in coliphages Mu or Lambda and peptides interfering with bacterial transcription by inhibiting the synthesis of the host proteins however preserving the synthesis of their own [START_REF] Nechaev | The elusive object of desire -Interactions of bacteriophages and their hosts[END_REF].

When the bacteriophage protein does not have a bactericidal action in itself, it can also be fused to a bactericidal agent in order to direct the latter to its target. This approach was used successfully by Scholl et al., who fused the O-antigen-specific bacteriophage tail spike gene identified in the genome of the O104:H4 E. coli strain, to a Pseudomonas pyocin to obtain an engineered bacteriocin displaying a specific activity against the O104:H4 serotype [START_REF] Scholl | Genome Sequence of E. coli O104:H4 Leads to Rapid Development of a Targeted Antimicrobial Agent against This Emerging Pathogen[END_REF].

4°) Exploitation of bacteriophage structural properties

Due to their high level of organisation, viruses represent elaborate nanomachines. In particular, filamentous bacteriophages, that can be easily genetically manipulated, have been the focus of many studies and allowed the development of bacteriophage display techniques (Figure 2). An increasing number of applications in the field of nanotechnology is driving many researchers to exploit bacteriophage properties among which we can distinguish their use as vectors or as matrices for new nanotechnological devices with a wide array of applications in nanomedicine [START_REF] Fan | The progress of nanomedicine inspired by bacteriophage[END_REF][START_REF] Hemminga | Viruses: incredible nanomachines. New advances with filamentous phages[END_REF][START_REF] Hyman | Bacteriophages and nanostructured materials[END_REF][START_REF] Rakonjac | Filamentous Bacteriophage: Biology, Phage Display and Nanotechnology Applications[END_REF].

A. Viral/Phage display.

Phage display, the principles of which are detailed in several reviews involves the engineering of the bacteriophage in order for the virus to carry foreign molecules on its surface through translational fusion with a surface protein, or through conjugation techniques [START_REF] Pande | Phage display: Concept, innovations, applications and future[END_REF][START_REF] Sidhu | Phage display for selection of novel binding peptides[END_REF].

The use of a bacteriophage to display foreign peptides was first reported in 1985 by Smith and since then, the relevance of this now famous system has found numerous applications in different domains including epitope identification, antigen delivery, drug discovery, vaccine design, targeting of eukaryotic cells, bioimaging and biosensing, enzyme display or nanomaterials design [START_REF] Adda | Random sequence libraries displayed on phage: identification of biologically important molecules[END_REF][START_REF] Ahmadvand | Biological targeting and innovative therapeutic interventions with phage-displayed peptides and structured nucleic acids (aptamers)[END_REF][START_REF] Collins | Engineered Enzymatically Active Bacteriophages and Methods of Uses Thereof[END_REF][START_REF] Gao | Phage display and its application in vaccine design[END_REF][START_REF] Li | Viruses and their potential in bioimaging and biosensing applications[END_REF][START_REF] Molek | Peptide Phage Display as a Tool for Drug Discovery: Targeting Membrane Receptors[END_REF][START_REF] Prisco | Filamentous Bacteriophage Fd as an Antigen Delivery System in Vaccination[END_REF][START_REF] Seker | Material Binding Peptides for Nanotechnology[END_REF][START_REF] Smith | Filamentous Fusion Phage -Novel Expression Vectors That Display Cloned Antigens on the Virion Surface[END_REF][START_REF] Szardenings | Phage display of random peptide libraries: applications, limits, and potential[END_REF].

Numerous viral platforms are used for displaying molecules at the surface of a virus particle, either through molecular manipulation or through chemical modification. These include eukaryotic viruses systems such as the cowpea mosaic and potato X viruses, TMV, turnip yellow mosaic virus or bacteriophage based systems with M13, Qβ, Lambda, T7 or T4 [START_REF] Banerjee | Multivalent Display and Receptor-Mediated Endocytosis of Transferrin on Virus-Like Particles[END_REF][START_REF] Chatterji | Cowpea mosaic virus: From the presentation of antigenic peptides to the display of active biomaterials[END_REF][START_REF] Dunn | Assembly of Functional Bacteriophage-Lambda Virions Incorporating C-Terminal Peptide or Protein Fusions with the Major Tail Protein[END_REF][START_REF] Pande | Phage display: Concept, innovations, applications and future[END_REF][START_REF] Ren | Phage display of intact domains at high copy number: A system based on SOC, the small outer capsid protein of bacteriophage T4[END_REF][START_REF] Smith | Display of Peptides on the Surface of Tobacco Mosaic Virus Particles[END_REF][START_REF] Sokoloff | The interactions of peptides with the innate immune system studied with use of T7 phage peptide display[END_REF][START_REF] Steinmetz | Potato Virus X as a Novel Platform for Potential Biomedical Applications[END_REF][START_REF] Sternberg | Display of Peptides and Proteins on the Surface of Bacteriophage-Lambda[END_REF][START_REF] Zan | Polyvalent display of RGD motifs on turnip yellow mosaic virus for enhanced stem cell adhesion and spreading[END_REF].

Principles: display through molecular manipulation or chemical modification

Molecular engineering of the bacteriophage genome is widespread and has been implemented for display in four main bacteriophage systems: T4, T7, Lambda, and filamentous bacteriophages [START_REF] Beghetto | Lambda-display: a powerful tool for antigen discovery[END_REF][START_REF] Gupta | High-density functional display of proteins on bacteriophage lambda[END_REF][START_REF] Hemminga | Viruses: incredible nanomachines. New advances with filamentous phages[END_REF][START_REF] Kehoe | Filamentous phage display in the new millennium[END_REF][START_REF] Kurzepa | Molecular modification of T4 bacteriophage proteins and its potential application -review[END_REF][START_REF] Meng | Advances of development of phage display systems[END_REF][START_REF] Rakonjac | Filamentous Bacteriophage: Biology, Phage Display and Nanotechnology Applications[END_REF][START_REF] Teesalu | Mapping of vascular ZIP codes by phage display[END_REF]. In this approach, the gene introduced into the bacteriophage genome codes for a peptide that is expressed as a protein fusion on the bacteriophage surface. This technique is widely used in numerous fields of science for its potential of large scale screening as the inserted genetic information can be randomly generated to produce a library, achieve targeted delivery to specific locations or study molecule interactions. This display approach has been extensively applied to the M13 filamentous bacteriophage. M13 is a 880nm long rod shaped, single-stranded DNA virus. Its viral capsid is composed of 2700 copies of helically arranged major coat protein (pVIII) and 5-7 copies of pIII, pVI, pIX and pVII, located at either of its ends [START_REF] Petrenko | A library of organic landscapes on filamentous phage[END_REF][START_REF] Smith | Phage Display[END_REF].

Since its beginnings, the phage display technique and its application within the framework of libraries allowed the screening of a wide array of molecules based on their specificity or binding affinity to various compounds and the selection of ligands to virtually any target. Briefly, the antigen of interest is immobilized on a surface and exposed to the engineered bacteriophage library. The bacteriophage particles displaying on their surface a molecule with affinity for the immobilized antigen will therefore bind and the rest of the library will be washed away. The bound fraction can be eluted and amplified resulting in a mixture of bacteriophage particles displaying the relevant molecule. This procedure is repeated in a process called 'biopanning' and allows the identification of molecules with high binding affinity to the antigen of interest. This technique is widely applied and resulted in the identification of numerous molecules of interest with affinity to other peptides, nucleic acid fragments, carbohydrates but also plastic and polystyrene, or inorganic substances with interesting physicochemical properties [START_REF] Adey | Characterization of Phage That Bind Plastic from Phage-Displayed Random Peptide Libraries[END_REF][START_REF] Vodnik | HWGMWSY, an unanticipated polystyrene binding peptide from random phage display libraries[END_REF] However, the bacteriophage library concept also presents limitations. For example, the amplification of the libraries during which bacteriophage candidates are amplified in the bacteria, leads to a certain level of competition between numerous bacteriophage clones thus resulting in the loss of library diversity. This therefore restricts the number of ligands that can be identified in one screen and may represent a severe constraint for targets with multiple binding sites [START_REF] Derda | Diversity of phage-displayed libraries of peptides during panning and amplification[END_REF].

One should also bear in mind that the displayed peptide size and charge should be taken into account as they influence the number of peptides that can be displayed on the surface of a virion. In order to retain a good bacteriophage production during amplification, the normal processing of the bacteriophage coat protein should indeed not be hindered by the fused peptide in order to allow its correct expression and to let the protein fulfil it biological role in the bacteriophage replication process [START_REF] Imai | Effect of protein properties on display efficiency using the M13 phage display system[END_REF]. Following these observations, Merzlyak and Lee published a method using degenerate flanking residues, to express functional but unfavorable peptide motifs on major coat protein pVIII of bacteriophage M13 while limiting the bacterial biological censorship involved in the natural pVIII protein processing during the bacteriophage replication (Merzlyak and Lee, 2009).

Alternatively, viruses can also be "decorated" with molecules by means of chemical modification in a process called bioconjugation [START_REF] Gillitzer | Chemical modification of a viral cage for multivalent presentation[END_REF]. This technique has been utilized for the binding of peptides (CPMV), polymers (adenoviruses), carbohydrates (CPMV) but also proteins and nucleic acids via surface functionalization as for MS2 and Qβ bacteriophages capsids [START_REF] Chatterji | Chemical conjugation of heterologous proteins on the surface of cowpea mosaic virus[END_REF][START_REF] O'riordan | PEGylation of adenovirus with retention of infectivity and protection from neutralizing antibody in vitro and in vivo[END_REF][START_REF] Patel | Surface functionalization of virus-like particles by direct conjugation using azide-alkyne click chemistry[END_REF][START_REF] Raja | Icosahedral virus particles as polyvalent carbohydrate display platforms[END_REF][START_REF] Gupta | Accelerated bioorthogonal conjugation: a practical method for the ligation of diverse functional molecules to a polyvalent virus scaffold[END_REF]. Binding of inorganic molecules such as gadolinium chelate groups (MS2 bacteriophage capsid) was also achieved [START_REF] Anderson | Viral nanoparticles donning a paramagnetic coat: Conjugation of MRI contrast agents to the MS2 capsid[END_REF]. This approach allows the attachment of molecules on the outside but also the decoration of the inside of the protein shell, for example for the use of viral particles for cargo transport [START_REF] Kovacs | Dualsurface-modified bacteriophage MS2 as an ideal scaffold for a viral capsid-based drug delivery system[END_REF]. The use of archaeal viruses, such as SIRV2 whose surface can also be functionalized, represents an interesting option due to the extremophile nature of the hosts conferring these viruses with an outstanding stability in harsh physical conditions (temperature, pH…), making them attractive for applications in nanotechnologies [START_REF] Steinmetz | Site-specific and Spatially Controlled Addressability of a New Viral Nanobuilding Block: Sulfolobus islandicus Rod-shaped Virus 2[END_REF].

Main Applications

Since the display technique was discovered, a tremendous amount of studies have been carried out (Figure 2).

One can observe a marked increase in the published literature for twenty years and then, the plateau could suggest that we may have reached a limit in the number of new applications derived from this technique. This approach is now used in various domains of science such as in antiviral research, novel therapeutics and vaccine design, cancer research, targeted delivery, imaging or nanotechnologies to cite only a few ranging from biology to nanotechnologies [START_REF] Castel | Phage display of combinatorial peptide libraries: application to antiviral research[END_REF][START_REF] Gao | Phage display and its application in vaccine design[END_REF][START_REF] Huang | Development of Anti-Infectives using Phage Display: Biological Agents against Bacteria, Viruses and Parasites[END_REF][START_REF] Hyman | Bacteriophages and nanostructured materials[END_REF][START_REF] Li | Viruses and their potential in bioimaging and biosensing applications[END_REF][START_REF] Ronca | Phage Displayed Peptides/Antibodies Recognizing Growth Factors and Their Tyrosine Kinase Receptors as Tools for Anti-Cancer Therapeutics[END_REF][START_REF] Staquicini | Phage display technology for stem cell delivery and systemic therapy[END_REF][START_REF] Yamashita | Development of anti-tumor blood vessel antibodies by phage display method[END_REF]. Exhaustive information can be found in numerous articles, book chapters or scientific reviews on the technique itself [START_REF] Bratkovic | Progress in phage display: evolution of the technique and its application[END_REF][START_REF] Miller | M13 bacteriophage: Filamentous phage, Nanostructures, Nanotechnology, Lithium-ion batteries, Endonuclease, Cobalt oxide, DNA supercoil[END_REF][START_REF] Rentero | Screening of Large Molecule Diversities by Phage Display[END_REF][START_REF] Smith | Phage Display[END_REF][START_REF] Vodnik | Phage display: selecting straws instead of a needle from a haystack[END_REF]. A selection of applications from different domains is listed in Table 1.

The display technique involving chemical conjugation is widely used for detection purposes through the binding of contrast agents, of biotin-streptavidin systems for conjugation of peptide-displaying bacteriophages to quantum dots or of fluorescent dyes for bioimaging or biosensing purposes [START_REF] Anderson | Viral nanoparticles donning a paramagnetic coat: Conjugation of MRI contrast agents to the MS2 capsid[END_REF][START_REF] Edgar | High-sensitivity bacterial detection using biotin-tagged phage and quantum-dot nanocomplexes[END_REF][START_REF] Li | Viruses and their potential in bioimaging and biosensing applications[END_REF]). To cite one example, T4 heads were used as scaffolds for the conjugation of Cy3 and Alexa Fluor 546 fluorescent dyes in order to design virus based nanoparticles suitable for cell imaging [START_REF] Robertson | Engineered T4 viral nanoparticles for cellular imaging and flow cytometry[END_REF]. This conjugation technique can also be applied to proteins after surface functionalization as demonstrated for MS2 and Qβ VLPs or to DNA as shown for M13 bacteriophage [START_REF] Lee | Amplified Protein Detection and Identification through DNA-Conjugated M13 Bacteriophage[END_REF][START_REF] Patel | Surface functionalization of virus-like particles by direct conjugation using azide-alkyne click chemistry[END_REF]. In some cases, molecular engineering of the bacteriophage genome and chemical modification of its surface can be coupled, as previously demonstrated for EGFdisplaying Qβ particles subsequently conjugated with a fluorescent dye for visualization of cellular attachment and uptake monitoring [START_REF] Pokorski | Cell targeting with hybrid Qbeta virus-like particles displaying epidermal growth factor[END_REF].

Bacteriophages and nanotechnologies

Peptide display by filamentous bacteriophage allowed the identification of molecules able to bind to inorganic materials and eventually, peptides with selectivity for binding to metal surfaces [START_REF] Brown | Metal-recognition by repeating polypeptides[END_REF]. Works by the team of A. M. Belcher show how phage-display libraries can be used to obtain peptides that bind to a range of semiconductor surfaces with high specificity, depending on the crystallographic orientation and composition of the material, in the view of using this principle with materials important in electronics or optics [START_REF] Whaley | Selection of peptides with semiconductor binding specificity for directed nanocrystal assembly[END_REF]. Molecules with such affinities as well as the highly organised structure of the bacteriophage particle are elements extensively exploited in the construction of periodically ordered nanomaterials such as nanometrescale electronic and medical materials. This resulted in the design of a model for the fabrication of a highly ordered composite material from genetically engineered M13 bacteriophage and zinc sulfide nanocrystals [START_REF] Lee | Ordering of quantum dots using genetically engineered viruses[END_REF]. This led to biotechnological advances as varied as the "creation" of films, fibers, or nanowires with applications in the assembly of materials for lithium ion battery electrodes, photochemical devices and even improved catalysts through the templating of nickel, rhodium, and ceria onto the surface of the M13 bacteriophage [START_REF] Huang | Programmable assembly of nanoarchitectures using genetically engineered viruses[END_REF][START_REF] Lee | Fabricating genetically engineered high-power lithium-ion batteries using multiple virus genes[END_REF][START_REF] Mao | Viral assembly of oriented quantum dot nanowires[END_REF][START_REF] Mao | Virus-based toolkit for the directed synthesis of magnetic and semiconducting nanowires[END_REF][START_REF] Merzlyak | Genetically engineered nanofiber-like viruses for tissue regenerating materials[END_REF][START_REF] Nam | Virus-enabled synthesis and assembly of nanowires for lithium ion battery electrodes[END_REF][START_REF] Nam | Stamped microbattery electrodes based on self-assembled M13 viruses[END_REF]Nam et al., 2010a;Nam et al., 2010b;[START_REF] Neltner | Production of Hydrogen Using Nanocrystalline Protein-Templated Catalysts on M13 Phage[END_REF].

Most recently published works on genetically engineered M13 describe the possibility of generating piezoelectric energy as well as nanorods and nanowires ranging from 300 nm to micron sizes which may find uses in nanoelectronics, sensing, and cancer therapy (Lee et al., 2012;Zhou et al., 2012a).

In addition, inorganic molecules assembled into electronic and magnetic particles led to the construction of biomedically relevant materials such as artificial bone substance created through the mineralization of a nanofiber constituted bundle of M13 bacteriophage or liquid-crystalline film matrices able to control and guide cell behaviour for tissue-regenerating applications [START_REF] Chung | Genetically engineered liquid-crystalline viral films for directing neural cell growth[END_REF][START_REF] He | Nanofibrous bio-inorganic hybrid structures formed through self-assembly and oriented mineralization of genetically engineered phage nanofibers[END_REF][START_REF] Merzlyak | Genetically engineered nanofiber-like viruses for tissue regenerating materials[END_REF][START_REF] Xu | Self-Assembly and Mineralization of Genetically Modifiable Biological Nanofibers Driven by beta-Structure Formation[END_REF].

B. Bacteriophage proteins/scaffold 1. Cargo

The bacteriophage capsid is built from a number of protein subunits assembled together. Already extensively used for the display of molecules or material assembly, this protein scaffold can also be used for its structure i.e. as a cage to entrap biomolecules of interest. An ideal construct needs to deliver relevant biomolecules on command to a specific target while avoiding the neutralization by the immune system. Several of these steps have already been achieved by different groups. For example, the modification of the internal and external surfaces of the bacteriophage MS2 capsid to turn it into an efficient drug delivery system was described [START_REF] Kovacs | Dualsurface-modified bacteriophage MS2 as an ideal scaffold for a viral capsid-based drug delivery system[END_REF]. In this particular study, first, extensive PEGylation of the capsids effectively reduced the neutralization by antibodies. Second, the binding of a ligand (biotin for example) to the distal ends of the polymer chains (PEG) indicated the possibility to attach targeting molecules to direct the cargo to a specific target. This approach could be applied to various ligands with specific tissue targeting properties [START_REF] Weissleder | Cell-specific targeting of nanoparticles by multivalent attachment of small molecules[END_REF]. Third, the encapsidation of large "druglike" molecules was achieved. The synthesis of such modified particles demonstrates the potential of this system for efficient drug delivery. More recently, another study reported the synthesis of MS2 particles that could specifically deliver a number of molecules such as nanoparticles, drugs, siRNAs or toxins to hepatocellular carcinoma cells via the co-display of a targeting peptide and a fusogenic peptide promoting endosomal escape [START_REF] Ashley | Cell-Specific Delivery of Diverse Cargos by Bacteriophage MS2 Virus-like Particles[END_REF]. Finally, controlled release of a high-copy cargo from engineered P22 capsids through morphological changes induced by a change in temperature was described [START_REF] O'neil | Genetically programmed in vivo packaging of protein cargo and its controlled release from bacteriophage P22[END_REF].

Phi29 motor

Phi29 is another example of a virus which has been extensively used in the field of nanosciences (Zhang et al., 2012b). More precisely, the DNA packaging motor of Phi29, required to package double stranded DNA into the procapsid, has been studied in depth at the molecular level. This motor that uses ATP to push DNA into the procapsid requires only three components, the gp10 (connector) and gp16 proteins and a small packaging RNA (pRNA). In vitro association of purified recombinant proteins and artificially synthesized RNA was sufficient to reconstitute an active motor. This system led to the development of a wide variety of applications as the bionanomotor can be turned on and off on demand (absence/presence of ATP). In addition, not only the motor itself but its individual components such as the connector and the pRNA present molecular characteristics (oligomerization) for which several applications in nanotechnologies have been proposed [START_REF] Ye | Current advances in Phi29 pRNA biology and its application in drug delivery[END_REF].

5°) Perspectives

In half a century of research on viral-derived applications, many molecular tools were developed that helped decipher fundamental biological processes. Following this "golden age" (Figure 1), the scientific community's interest shifted towards "more complex" systems. However, in the past decade, two main fields have revitalized the interest for viruses-derived approaches. On one hand, the advent of nanotechnology that showed many promises based on purely chemical processes is now diversifying towards bionanotechnology for which viruses have been the first biological entities to be used. On the other hand, the impressive reduction in the cost of DNA sequencing now allows the production of a massive amount of data from the analysis of environmental samples. The main hurdle to overcome for the identification of viruses from genomic data is the presence of many unknown sequences within new viral genomes, currently preventing an accurate assembly of short reads.

These data are only starting to be exploited for the deciphering of viral variety and progressively uncovering the extent of its diversity. Analysis of these metagenomic studies vastly broadens our current knowledge on viral specimens and lifestyle [START_REF] Krupovic | Microviridae goes temperate: microvirus-related proviruses reside in the genomes of Bacteroidetes[END_REF]. Sequence assembly issues resulting from short reads should shortly be solved by the next generations of sequencing technologies. Meanwhile, much can be learned from proteins identified with improved techniques and through the presence of conserved domains such as in DNA polymerases or endolysins [START_REF] Schoenfeld | Functional viral metagenomics and the next generation of molecular tools[END_REF]. However if a virus has evolved with a different mechanism from those already known, there is a risk that it will be missed by this approach. While these two domains are still being developed, they carry the potential to increase the number of potential virus-derived applications. For example, DNA polymerases with new combination of properties (proofreading, thermostability, helicase…) could be identified. It could also be anticipated that amongst new viruses identified by sequencing, some display enough homology between regions comprising a number of unknown genes, to be grouped. Looking deeper within these conserved regions might suggest ORFs to be studied in priority for a given function, the easiest ones being those related to the hijacking of the host machinery as these proteins are not often specific to one particular host. As well as contributing to reduce the proportion of unknown genes within bacteriophage genomes, cloning these ORFs in model organisms such as E. coli or S. aureus could reveal new antibacterial activities whose mechanisms would inspire the elaboration of new drugs.

The recent discovery of giant viruses has revolutionized the vision of low complexity associated with viruses [START_REF] Koonin | Origin and evolution of eukaryotic large nucleo-cytoplasmic DNA viruses[END_REF][START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF]. Carrying in their genome a large amount of genetic information coding for elements usually hijacked from the host, these viruses could become platforms to further develop new tools able to support a higher degree of complexity than bacteriophages, such as host-independent processes.

The rate of identification of previously unreported organisms increased markedly with the development of metagenomics, suggesting that numerous hosts and their viruses present in the environment are yet to be discovered. To identify them, the use of microfluidic PCR to link viruses to their hosts in environmental samples without cultivating them has been recently developed [START_REF] Tadmor | Probing individual environmental bacteria for viruses by using microfluidic digital PCR[END_REF]. In particular, this approach applied to the human gut could reveal the degree to which viruses and their hosts interplay in this complex polymicrobial environment. Sequencing the viriome of the human gut has already revealed the prominent contribution of prophages to genetic exchanges [START_REF] Reyes | Viruses in the faecal microbiota of monozygotic twins and their mothers[END_REF][START_REF] Reyes | Going viral: nextgeneration sequencing applied to phage populations in the human gut[END_REF]. In contrast, virulent bacteriophages appear underrepresented suggesting that the gut environment may be unfavourable to them. On the other hand, data obtained in a mouse model showed continuous replication of virulent bacteriophages over several weeks suggesting a high level of complexity in the relationship between bacteriophage and host populations in the gut environment (Maura et al., 2011). Several studies have also shown that in vitro polymicrobial biofilms can be reduced by bacteriophages [START_REF] Brussow | Pseudomonas biofilms, cystic fibrosis, and phage: a silver lining?[END_REF][START_REF] Donlan | Preventing biofilms of clinically relevant organisms using bacteriophage[END_REF][START_REF] Siringan | Bacteriophage-Mediated Dispersal of Campylobacter jejuni Biofilms[END_REF]. However these systems are not yet similar enough to real situations, such as in medical and environmental settings, to claim that bacteriophages can efficiently reduce biofilms on their own. One solution may come from a combinatorial approach where a bacteriophage infecting one species may also code for hydrolytic enzymes targeting the extracellular matrix produced by this species or others [START_REF] Lu | Dispersing biofilms with engineered enzymatic bacteriophage[END_REF]. Such complex environments including various cellular types represent a challenge for viruses and one may ask whether, to some extent, this lifestyle developed, as a form of resistance to viral attack.

Combination of activities might be a future direction in which viruses-derived tools versatility could play an important role. In particular, one can imagine designing a virus targeting for example a gram negative host and carrying genes that are toxic for gram positive species (such as endolysins) or fungi. Coupling these different properties may offer the possibility to come up with new highly efficient broad antimicrobial strategies. With the advent of in vitro synthesis of small genomes such approaches are theoretically feasible and, according to progress in synthetic biology, could have a broader impact than currently appraised on the development of future applications [START_REF] Wimmer | Synthetic viruses: a new opportunity to understand and prevent viral disease[END_REF]. However, there are two main limitations to such a concept: 1) an extensive knowledge on viruses intended to be used as platforms should be achieved; 2) specific guidelines should be defined to regulate the use of these viral recombinants. Nevertheless, it might be possible that such chimeric viruses exist or have existed in nature at some point but have been lost due to evolutionary pressure.

The dynamics of the viral world are indeed so high that, to date not a single gene has been identified that is conserved amongst all bacteriophages sequenced [START_REF] Liu | Protein repertoire of double-stranded DNA bacteriophages[END_REF]. Their genome plasticity, one of the trademarks of viruses, is such that they are continuously creating new answers to the recurring problem of the necessity of infecting their host, thus representing a source of pressure for biological innovations that humans are trying to exploit for their own interest. and percentages calculated from the number of hits bearing the term "phage" over 10 year periods).

Figure 2: Rising of phage display and bacteriophage therapy related publications (percentages of the total "phage" publications dedicated to phage display and bacteriophage therapy related topics over the past two decades). (Search in Pubmed performed in September 2012 and percentages calculated from the number of hits bearing the terms "phage display", or "phage" together with "therapy").

Figure 1 :

 1 Figures legend:

Table 1 :

 1 Main applications of Phage display

Identification of peptides able to bind to inorganic materials Applications in electronics and opticalsbacteriohagebased electrodes and batteries -nanotechnologies [START_REF] Whaley | Selection of peptides with semiconductor binding specificity for directed nanocrystal assembly[END_REF] ( [START_REF] Nam | Virus-enabled synthesis and assembly of nanowires for lithium ion battery electrodes[END_REF][START_REF] Nam | Stamped microbattery electrodes based on self-assembled M13 viruses[END_REF]

M13

Peptide


Keywords: Basel III, Regulation, Bank behaviour, Regulatory distortions

The failures of the banking sector to promote sustainable lending and to build strong capital and liquidity buffers prior to the 2008 Financial Crisis addressed the rationale for implementing the banking regulatory regime Basel III. In this paper, we question the fundamental role of this new regulatory regime in promoting bank lending and ensuring the adequate funding structure of the banking sector regarding the introduction of unprecedented international liquidity standards notably. We build a theoretical model of bank behaviour under a regulatory regime à la Basel III which points to two major results. First, Regulatory Authorities need to define the objectives and thus, the underlying tools implemented in order to achieve the optimum-optimurum. Second, we show that the competitive structure of the markets the bank faces is a determinant to take into account for achieving this optimum-optimurum.

Introduction

In response to the excessive build-up of risk leverage and the insufficient holdings of liquidity buffer of the banking sector prior to the Global Financial Crisis, the Basel Committee on Banking Supervision (BCBS) had designed a package of reforms under the amendment Basel III. Based on the three-pillar approach of Basel II 1 , Basel III includes tighter rules on capital and liquidity as "the Basel III reforms are central to promoting financial stability" [START_REF] Walter | Basel iii: Stronger banks and a more resilient financial system[END_REF]. Among this set of rules, the Basel Committee strengthens the quantity and quality of the capital base, complements risk-sensitive measures implemented under Basel I and Basel II with a leverage ratio (LR) and introduces two liquidity standards, namely the Liquidity Coverage Ratio (LCR) and the Net Stable Funding Ratio (NSFR).

While the effectiveness of Basel III in achieving its primary goal of financial stability remains a debate of on-going research, we question the fundamental role of this new regulatory regime in promoting bank lending and strengthening the funding structure of the bank. The objective of this paper is twofold: First, we examine the effects of implementing capital and liquidity rules on bank lending in order to raise the key implications of a regulatory environment both capital and liquidity driven such a Basel III on bank lending behaviour. Second, we analyse the impact of this new regulatory environment on the composition of the liabilities of the bank as one objective of Basel III is to promote the adequate funding structure of the banking sector.

Analysing the impact of International Regulatory Standards on bank lending is not new. A large stream of literature supporting the effectiveness of the 1988 Basel Capital Accord shows that banks adopted different strategies to comply with the so-called "Cooke ratio" 2 . The tightening of capital requirements as implemented under Basel III suggests similar strategies 3 . [START_REF] Cohen | Banks and capital requirements: channels of adjustment[END_REF] show that banks from advanced economies 1 Basel II, fully effective in 2008, adopted a three-pillar approach to promote financial stability. These three pillars were "Capital Requirements", "Supervisory Review" and "Market Discipline".

2 The Cooke-ratio, named after one of the past Chairs of the Basel Committee Peter Cooke, defines the first international capital-adequacy standard. Banks were required to hold a minimum capital-torisk-weighted-asset ratio of 8%. For a complete review on bank strategies, see [START_REF] Jackson | Capital requirements and bank behaviour: the impact of the Basle Accord[END_REF] and [START_REF] Bcbs | Basel III: the net stable funding ratio: consultative document[END_REF] 3 Note that we do not mention the literature on the effects of the Basel II regulatory regime on bank lending as the main body of research on this topic focuses on the procyclical character of this regulation.

comply with the Basel III capital requirements through the accumulation of retained earnings and to a lesser extent, shifting to assets with lower risk weights. [START_REF] Cosimano | Bank behavior in response to Basel III: A cross-country analysis[END_REF] examine the impact of the Basel III capital standards on lending rates and growth.

They find that a tightening of capital requirements gives incentives to banks to increase lending rates causing a slowdown in credit supply. This stream of literature remains focused on the effects of capital requirements on bank lending behaviour. However, as documented in BCBS ( 2016) : "Liquidity requirements can affect banks through several channels". For example, [START_REF] King | The Basel III Net Stable Funding Ratio and bank net interest margins[END_REF] disentangles the different banks' strategies to meet the NSFR. Among these strategies, the bank is able to shrink the size of the portfolio of loans (downsizing) or substitute them for more liquid assets (portfolio-shift) modifying thus the composition of their assets and bank lending. [START_REF] Gobat | The Net Stable Funding Ratio: Impact and Issues for Consideration[END_REF] examine the impact and issues raised by the implementation of such a ratio for a large panel of banking systems. They also highlight the potential adverse effect of the NSFR on bank lending especially for large Domestic Systemically Important Banks D-SIBS. Using banks' balance-sheet data, [START_REF] Banerjee | The impact of liquidity regulation on banks[END_REF] study the impact of the Individual Liquidity Guidance-a liquidity ratio close to the LCR-on the UK banking sector. They find that banks did not shrink the size of their balance-sheet but rather modify its composition without causing deleterious effects on bank lending. These types of adjustments were already performed under Basel I when no liquidity standard were set-up suggesting that capital and liquidity requirements may produce similar bank balance-sheet adjustments and thus, have common implications for bank lending behaviour.

To our knowledge, the literature examining the effects of liquidity standards on bank behaviour remains relatively sparse due to the fact that liquidity standards set at international level has been mainly motivated since the implementation of Basel III 4 . We contribute to this emerging literature by developing a theoretical model of bank behaviour subject to capital and liquidity regulatory constraints. Our objective is to examine the key implications of a regulatory framework à la Basel III, i.e. a regulatory framework both capital and liquidity driven on bank behaviour. Our model is derived from [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF]. These authors investigate the impact of the adoption of the first Basel Capital Accord on Japanese banks' behaviour for the period 1990-1993. In particular, they find that banks tended to issue more subordinated debts and to reduce lending following the decrease in the Nikkei index in order to comply with the Basel Capital ratio.

However, as international liquidity requirements were not in place at that time, the model does not provide banks' lending implications when implementing an additional regulatory tool such as liquidity requirements. Nevertheless, the role of these last should not be undermined as an emerging body of literature shows that liquidity requirements modify the composition of banks' balance-sheet and thus have effects on bank behaviour. As a result, further investigation on the impact of a regulation both capital and liquidity driven on bank behaviour is needed.

The remainder of this paper is organised as follows: Section 2 describes the model and Section 3 concludes.

The Model

We develop a theoretical model of banks' behaviour drawn upon [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF].

Their model is suitable to depict and understand banks' behaviour under Basel I and Basel II as the microprudential structure of these two regulatory regimes is capital driven.

However, the introduction of liquidity requirements under Basel III questions the implications of a micro-prudential regulatory structure both capital and liquidity driven on bank behaviour. Our contribution is adding liquidity requirements to the model of [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF] in order to assess the effects of such a new regulatory structure on bank behaviour plus modelling the Risk-Weighted-Asset (RWA) metrics designed under Basel II and Basel III.

The Bank Business Model

We assume the bank buys credits to households and firms whether retail, commercial, wholesale or universal banks5 . Investment banks are not considered as they do not distribute credits and are involved in financial activities such as trading and mergers and acquisitions (M&As). We depict these credits as mortgage, credit cards or commercial loans which are defined through a unique loan portfolio held by the bank. The credit risk related to these loans plays a central role in the model as we focus on the credit activity of the bank. For the sake of simplicity, we consider the bank is government-bond buyer on capital market. Thus, the market risk is nil because government bonds are risk-free assets in the model. We propose this simple bank investment decision problem for two reasons. First, as one of our objective is to study the impact of capital and liquidity rules on the asset composition of the bank, we reduce the bank investment decision problem to two dual assets, one risky asset (loans) for which the bank has to provide sufficient capital and liquidity coverages and one risk-free asset (government bonds) requiring neither capital nor liquidity coverage. Second, defining a risky market portfolio induces introducing additional hypotheses in the model while our research question remains the same. We choose to keep the simplified version following somewhat Ockham's razor spirit even if a more general specification including market risky securities could be developed.

We assume Capital K, Subordinated Debts R and Customer Deposits D funds Loans L and Government Bonds B, where K represents the shareholder's equity issued by the bank. The maturity of capital is infinite and thus greater than the subordinated debt maturity which consists of long to medium term bonds issued by the bank. Finally customer deposits is a resource comprising both non-maturity deposit and term deposit.

In sum, the activity of the bank consists of buying a portfolio of loans L and government bonds B, selling capital K, subordinated debt R and customer deposits D.

We depict the balance-sheet of the bank as follows:

Assets Liabilities L Loans Capital K Subordinated Debts R B Government Bonds Customer Deposits D
We consider the loan activity of the bank as the main source of illiquidity. The portfolio of government bonds defines the total amount of liquid assets the bank can buy. Finally, capital, subordinated debts and customer deposits define the sources of available funding the bank disposes for covering the funding risk induced by the credit activity. The loan decision process of the bank is characterised by the parameter 0 < θ ≤ 1 which is the risk default on loan and the return r L at which the bank charges the loan. Therefore, the product θL defines the credit risk the bank is willing to bear on the loan activity.

Assuming a competitive loan market environment, the bank has to decrease the loan interest rate in order to raise the volume of loans bought by one unit setting r ′ L (L) < 0 6 . The introduction of the parameter θ allows us to better account for the aggregate risk related to the bank lending activity. An exogenous shock may indeed increase the overall credit risk as it has been the case in 2008. This risk parameter is necessary to measure the credit risk assessed in the requirement ratios. The market activity of the bank consists of buying a risk-free portfolio of bonds, typically high-graded government bonds excluded from the regulatory risk-asset base given a risk-free rate r B . Thus, the portfolio of loans defines the total asset risk-exposure of the bank since the market-risk is nil in the model. We suppose the bank takes as given the rate r K at which it issues capital because investors benefit from perfect information on capital market and thus, are perfectly able to assess the cost of equity r K of the bank. As a result, the rate r K is investor-driven, not bank-driven. On the other hand, the bank can increase its capital base by raising R. We assume the bank sells more subordinated debts as it raises its attractiveness via r R implying r ′ R (R) > 0.

Regulatory Requirements

The Basel III measures aim at providing a " global regulatory framework for more resilient banks and banking systems" BCBS (2010). Reforming the Basel II Accords was about " strengthening the global capital framework" and "introducing a global liquidity standard" (ibid.). The introduction of liquidity requirements is the most significant change in the regulatory framework and is a direct consequence of the liquidity crisis faced by the banking industry in 2008 when the subprime mortgage crisis triggered. The theoretical approach we use underlines the impact of these new liquidity requirements both on bank lending and liability composition. In view of this, we propose to transpose the Basel III regulatory ratios.

The Capital Requirement Ratio (CRR)

Due to the insufficient build-up of capital coverage during the financial crisis, the Basel Committee proposed to tighten the definition of capital under Basel III. The bank regulatory capital base has been classified into two categories denominated "Tier". We define K

as Tier 1, the best-quality capital which includes Common Equity Tier 1 Capital (CET1)

and Additional Tier 1 Capital (AT1). The liability R is defined as Tier 2 with a lower Risk Absorbing Capacity (RAC) 7 . The regulatory capital of the bank is thus equal to (K + R).

The Basel III Total Capital Ratio (TCR) is the sum of Tier 1 and Tier 2 (Capital plus Subordinated Debts) and complemented regarding the bank asset risk-exposure: TCR = Regutatory capital Risk-weighted assets RWAs are the sum of the risks incurred by the bank. They consist in credit risk, market risk, and operational risk. Since both market and operational risk are nil in our model, the TCR can be rewritten as follows:

7 Note that Tier 3 aiming at covering the market risk under Basel II has been removed in Basel III.

(1)

CRR = (K + R) θL
CRR defines the total amount of capital available to the bank to cover the credit risk and corresponds to the Basel III Total Capital Ratio. The CRR we propose differs from the capital ratio standard developed by [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF] to the extent that we introduce the parameter θ. However, the two regulatory ratios are similar for θ = 18 . The credit risk θL is a positive linear function of L and is measured in units of currency as it is the case for the Value-at-Risk (VaR) which is used to assess RWAs under Basel II and

Basel III. This metric is consistent with the underlying logic of VaR "which is a lower tail percentile for the distribution of profit and loss (P&L)" [START_REF] Berkowitz | How accurate are value-at-risk models at commercial banks?[END_REF].

All things being equal, the higher the aggregate risk related to banks' lending activity, the higher the credit risk. Similarly, the higher the volume of loans bought by the bank, the higher the credit risk9 . This phenomenon complies with Samuelson's "fallacy of large numbers" [START_REF] Samuelson | Risk and uncertainty: A fallacy of large numbers[END_REF] since the "maximum loss" increases with the size of the portfolio of loans.

The Liquidity Requirement Ratio (LRR)

In . This ratio should be equal to at least 100 % on an on-going basis. "Available stable funding" is defined as the portion of capital and liabilities expected to be reliable over the time horizon considered by the NSFR, which extends to one year. The amount of stable funding required is function of the liquidity characteristics and residual maturities of the various assets held by the bank as well as those of its off-balance sheet (OBS)

exposures".

The liabilities taken into account to assess the available stable funding (ASF) are weighted using an ASF factor which is between 100 % (e.g. for Tier 1 liabilities and Tier 2 liabilities with a maturity above one year) and 0 %. Symmetrically, the assets taken into account to assess the required stable funding (RSF) are weighted using an RSF factor which is between 0 % (e.g. for central bank reserves and risk free securities) and 100 % e.g. for "all assets that are encumbered for a period of one year or more" (BCBS (2014), p.11). The NSFR can thus be defined as follows:

NSF R = i L i × ASF i A i × RSF i
Where: L i is the total amount of liabilities which belongs to the category i defining an ASF factor of ASF i , and A i is the total amount of assets belonging to the category i defining an ASF factor of RSF i . Based on this definition, we can write the equivalent of the NSFR ratio in our model. Both K (Tier 1) and R (Tier 2) receive an ASF factor of 100 %. Deposits which are composed of term and non-maturity customer deposits define and ASF factor of 95 % or 90 % under the Basel III framework. For the sake of simplicity we also consider an ASF factor of 100 % for D. As a consequence, AASF equals (K + R + D) in the model. RASF induced by the banking activity are related to each asset held by the bank. Since the market risk is nil for the government bonds B, they define a 0% RSF-factor. Loans have a credit risk parameter equals to θ. Following the Basel III principle that the higher the risk, the higher the RSF factor we assume that loans L receive a RSF factor of θ. The assets with the highest VAR also have a high level of required stable funding: such as the unencumbered residential mortgages (65 % RSF factor) and the other unencumbered performing loans (85 % RSF factor) 10 . This symmetry is respected in our model where the credit risk is set equal to the requirement amount of stable funding for loans.

Applying the former NSFR formula to the model, we obtain the following liquidity requirement ratio:

LRR = (K × 1) + (R × 1) + (D × 1) (L × θ) + (B × 0)
LRR measures the total amount of available funding (total capital plus deposits) the bank disposes of to cover the funding risk induced by the credit activity and can be rewritten as follows:

(2)

LRR = (K + R + D) θL = CRR + D θL
Note that CRR and LRR are not orthogonal by construction and modify the funding

Bank Behaviour under a Regulatory Regime à la Basel III

To analyse the behaviour of the banking firm under Basel III, we consider a representative bank seeking to maximise its profits under a capital and liquidity constrained environment.

The constraints the regulatory authorities implement take the form of incentives and specifically ratios the bank is expected to comply with. These ratios are central to the bank decision process since the bank use them as indicators of profitability. [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF] assume that "the cost of the [regulatory capital] ratio is reduced as the ratio increases while its rate of change is diminished or constant; (C ′ < 0, C ′′ ≥ 0). It means that banks with a low [regulatory capital] ratio can improve profit more by raising the ratio than banks with a high [regulatory capital] ratio" (Ito & Sasaki (1998), p.15). We define L and R among the bank decision variables of the profit maximisation problem as in [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF]. However, deposits D becomes central within our bank decision problem because the NSFR is designed to give incentives to the bank to fund its business activities with stable sources of funding such as customer deposits: " The second objective is to promote resilience over a longer time horizon by creating additional incentives for a bank to fund its activities with more stable sources of funding on an ongoing structural basis. The Net Stable Funding Ratio (NSFR) has a time horizon of one year and has been developed to provide a sustainable maturity structure of assets and liabilities " (BCBS (2010), p.9). As a result, we define the deposit endogeneization of our bank decision problem as regulatory-induced. To picture the importance of collecting deposits, we set the following assumption on customer deposits: r ′ D (D) > 0, meaning the bank raises more customer deposits when increasing its return.

We define the profits of the bank, denoted Π as the sum of its revenues on credit and market activity net of the costs on capital, subordinated debts, deposits and net of the costs induced by the regulation. Increasing the volume of loans bought is costly C ′ L > 0 as the regulatory ratios of the bank are lower reducing thus its ability to cover capital and liquidity losses ceteris paribus. On the other hand, rising the volume of subordinated debts and deposits decreases the costs C ′ R < 0 and C ′ D < 0 as the ratios of the bank are higher increasing thus its RACs:

Π = r L (L).L + r B .B -r K .K -r R (R).R -r D (D).D -C(L, R, D)

Properties of the Cost Function

The cost function C(L, R, D) measures the restriction and opportunity costs a bank may incur for its activity 11 . We consider that a bank with low capital and liquidity ratios incurs an opportunity cost not expanding its business activities as a strong capital base is necessary to support lending 12 and "Deposits are used to fund loans and other earning assets" [START_REF] Spierdijk | How do banks adjust to changing input prices? A dynamic analysis of U.S. commercial banks before and after the crisis[END_REF], p.2) . On the other hand, high ratios are a signal for good bank business opportunities and the bank is thus able to improve its profitability. The cost function C(L, R, D) also measures the management costs related to the intermediation activity of the bank. In particular, the bank incurs a structural funding liquidity risk when funding illiquid assets with liquid liabilities as the banking sector experienced during the 2008 financial crisis 13 . The quality of the management of the liquidity funding risk can be assessed through the banking Asset and Liability Management (ALM) activity which plays a prominent role under Basel III as the NSFR is designed to limit the over-11 A bank satisfying no regulatory standard incurs restriction costs as regulatory authorities monitor certain credit activities of the bank. If there is no regulation, C(L, R, D) = 0 by definition.

12 For example, see BCBS (2010).

13 The funding liquidity risk the bank is willing to bear is different from the aggregate credit risk it takes on its loan portfolio. We define the funding liquidity risk as the inability of the bank "to meet its obligations as they fall due" (BCBS, 2014).

reliance on short-term wholesale funding 14 . Thus, we are able to measure the efficacy of the liquidity regulation through the cost function C(L, R, D). In more details, a high qualitative liquidity regulation should promote an efficient banking ALM which minimises the funding liquidity risk the bank bears and limit the incentive to increase the liquidity gap.

The Bank Profit Maximisation Problem

We reduce the optimisation problem of the bank as an ALM problem in order to assess the impact of the banking regulation on bank lending and the structure of bank liabilities:

max L,R,D Π = r L (L).L + r B .B -r K .K -r R (R).R -r D (D).D -C(L, R, D) s.t. L + B = K + R + D
Solving this profit-maximisation problem with the Lagrangian method gives the following first-order economic conditions:

r L (L) -r R (R) = C ′ L + C ′ R -(r ′ L (L) • L -r ′ R (R) • R), (3) r R (R) -r D (D) = C ′ D -C ′ R + r ′ D (D) • D -r ′ R (R) • R, (4) K + R + D -(L + B) = 0. (5)
Eq.3 means that the difference between the loan and subordinated debt rate -the Net Interest Margin (NIM) -equals the sum of the marginal regulatory costs on loans and subordinated debts (C ′ L + C ′ R ) net of the marginal profit derived from the intermediation activity

(r ′ L (L)•L-r ′ R (R)•R).
Rising the portfolio of loans bought L entails an increase in the NIM (r L (L) -r R (R)) as managing a higher illiquid portfolio of loans is costly. Other things being equal, the bank has to pay a higher price (C ′ L -r ′ L ) for its ALM. Eq.4 states that the funding arbitrage of the bank -the difference between the subordinated debt and deposit rate -equals the marginal regulatory cost difference between deposits and subordinated debts plus the marginal market funding cost on these same liability components. Assuming the funding arbitrage is positive, the bank has an incen- 14 The ALM activity covers other types of risk which turned out to be significant during banking crises. For example, the Saving and Loans Crisis (S&Ls) the US banking sector experienced at the end of the 80s was related to the mismanagement of the repricing gap of the banking sector.

tive to raise deposits D at the expense of subordinated debts R. However, selling more deposits is costly at the margin. Thus, the bank issues deposits to the extent that the marginal cost of issuing it equals the marginal cost of issuing subordinated debt. The implementation of the additional liquidity ratio LRR shows that the bank funding arbitrage is both capital and deposit driven while it is only capital driven under a regulatory environment capital constrained such as Basel I and Basel II15 .

Eq.5 simply refers to the balance-sheet equilibrium constraint.

We assume dθ = 0 which means that the bank implements the right screening mechanism and is therefore able to perfectly assess the credit risk of the borrower in the short-run. The bank is unable to raise K to the extent that it remains investor-driven and is thus considered exogenous in the model setting dK = 0. We obtain the following elasticities by totally differentiating Eq.3 and Eq.4 at the third order16 :

(6) dL = δ 2 • dR + δ 3 • dD δ 1 ; (7) dD = δ 4 • dR + δ 6 • dL δ 5 ;
where the coefficients are given by:

δ 1 = r ′′ L (L) • L + 2 • r ′ L (L) - ∂ 2 C ∂L 2 + ∂ 2 C ∂L ∂R ; δ 2 = r ′′ R (R) • R + 2 • r ′ R (R) + ∂ 2 C ∂R 2 + ∂ 2 C ∂R ∂L ; δ 3 = ∂ 2 C ∂D ∂L + ∂ 2 C ∂D ∂R ; δ 4 = r ′′ R (R) • R + 2 • r ′ R (R) + ∂ 2 C ∂R 2 - ∂ 2 C ∂R ∂D ; δ 5 = r ′′ D (D) • D + 2 • r ′ D (D) + ∂ 2 C ∂D 2 - ∂ 2 C ∂D ∂R ; δ 6 = ∂ 2 C ∂L ∂R - ∂ 2 C ∂L ∂D ; (8) dL dR = δ 2 + δ 3 • δ 4 δ 5 δ 1 - δ 3 • δ 6 δ 5 ; (9) dD dR = δ 4 + δ 6 • δ 2 δ 1 δ 5 - δ 6 • δ 3 δ 1
• Totally differentiating Eq.3 and Eq.4 stresses three important results. First, we see that the elasticities are market driven via the conduct of the first and second derivatives of the interest rates r ′ (.) and r ′′ (.) obtained in δ 1 , δ 2 , δ 4 and δ 5 . Second, we note that these elasticities are also regulatory driven. In addition to introducing banking adjustment and marginal regulatory costs as we have seen so far, capital and liquidity requirements adds secondary costs ∂ 2 C ∂(.) 2 and cross-effects

∂ 2 C ∂(.) ∂(.)
potentially. The nature of these secondary costs and cross-effects may modify the structure of the elasticities of the bank and thus its behaviour. As stated in [START_REF] Freixas | Microeconomics of banking[END_REF], if costs are separable, then cross-effects are nil. If cross-effects are not nil then the elasticities are modified and determined depending on the functional form of the cost function. It is crucial to determine the nature of these costs because they may affect the profitability, the NIM, the funding arbitrage and the elasticities of the bank as a whole. Therefore, the regulation may not be neutral. Third, as in [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF], p.18) the signs of these elasticities "may not be uniquely determined." We find that they depend on the costs that the regulation entails and second, the structure of the competition the bank faces on the market. For small enough C ′′ , the signs of the elasticities depends on the structure of this competition and the regulation has only effects on the profitability, the NIM and the funding arbitrage of the bank:

(10) dL dR ≃ δ 2 δ 1 ≃ r ′′ R (R) • R + 2 • r ′ R (R) r ′′ L (L) • L + 2 • r ′ L (L) ; (11) dD dR ≃ δ 4 δ 5 ≃ r ′′ R (R) • R + 2 • r ′ R (R) r ′′ D (D) • D + 2 • r ′ D (D)

•

The sign of the loan-to-subordinated-debt elasticity depends on the condition set on δ 1 and δ 2 . Assuming the competitive pressure on the loan market increases as the bank buys a greater portion of loans (r ′′ L < 0), " the rate of increase accelerates as more subordinated debts being issued" [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF] 17 and the deposit interest rate follows the same pattern than subordinated debts (r ′′ D > 0), it follows:

(12) dL dR > 0 ;

(13) dD dR > 0 •

Conclusion

The insufficient build-up of capital and liquidity buffers of the banking sector prior to the 2008 financial crisis has raised the rationale for implementing the regulatory regime Basel III. The novel aspect of this banking regulation is introducing liquidity requirements aiming at counteracting the massive liquidity disruptions experienced by the banking sector during the 2008 financial crisis. In this paper, we propose to draw a micro-founded analysis of bank behaviour subject to capital and liquidity regulatory constraints in order to raise the key implications of this type of regulation on bank behaviour. To our knowledge, this is the first paper presenting a theoretical approach of bank behaviour under a regulatory regime à la Basel III. Based on [START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF], we define the liquidity constraint as a ratio the bank is expected to comply with in addition to the capital ratio.

We also propose to enhance the definition of the capital ratio the authors introduced in their model by including the credit risk parameter which models the risk-based regulatory capital approaches implemented under Basel II and Basel III. Evidence contained in this paper points to two major results. First, we see that implementing new regulatory rules for a given regulatory structure shed some light on the need to re-consider the design of the micro-prudential architecture. Indeed, introducing an additional rule such as liquidity funding requirement could interfere with the capital requirements and produce non-desirable effects taking the form of distortions on bank behaviour. These distortions could entail the misachievement of the objectives set by Regulatory Authorities because, following the Tinbergen counting rule and [START_REF] Fisher | Microprudential, macroprudential and monetary policy: conflict, compromise or co-ordination?[END_REF], p.2-3): " A necessary condition is that there should be at least as many independent and effective policy instruments as there are independent policy targets.". Thus, the results also question the need to clarify the hierarchy (primary or secondary) of the objectives as well as their nature (complements or substitutes). Second, Regulatory Authorities should identify the nature of the competitive pressure the bank faces for implementing the optimal regulatory regime. The results obtained in this paper show that the sign of the elasticities derived in the model is primarily market-determined and depends on the conditions set on competition. Identifying the costs the bank incurs could be one way to determine this competitive nature.

  addition to strengthening the global capital framework, the Basel Committee designed a new liquidity framework as the banking sector failed to enter the financial crisis with adequate liquidity buffers. More specifically, the Basel Committee emphasised on the need for a better liquidity risk management and published in 2008 "Principles for Sound Liquidity Risk Management and Supervision" which has been complemented by the introduction of two minimum liquidity regulatory standards under "Basel III: International framework for liquidity risk measurement, standards and monitoring" in 2010. While the LCR is designed to improve the short-term resilience of the banking sector to meeting liquidity obligations for 30 days, the NSFR requires to meet funding obligations under a time horizon of one year. This last is designed to promote sustainable sources of funding when banks perform maturity transformation activities such as credit origination. As a result, we choose to model a liquidity ratio close to the NSFR because "Maturity transformation performed by banks is a crucial part of financial intermediation that contributes to efficient resource allocation and credit creation."[START_REF] Bcbs | Basel III: the net stable funding ratio: consultative document[END_REF]. Moreover, we choose to characterise the liquidity aspect of our regulatory environment with the quality of the funding stability the banking sector might produce because as referenced in EBA (2015), the NSFR " is needed in addition to the solvency requirements (capital and leverage ratio) and the LCR, because these existing requirements miss important aspects of structural funding stability." Finally, it is more convenient to distinguish stock measures from flow measures. Therefore, we characterise the regulatory environment with stock measures only. We contribute to the emerging literature by modeling a funding requirement ratio close to the NSFR in order to assess to what extent the adoption of this ratio modifies the funding risk structure of the bank and thus ensures the primary goal of financial stability as set under Basel III. As defined by (BCBS (2014), p.2): "The NSFR is defined as the amount of available stable funding relative[AASF] to the amount of required stable funding[RASF]

  10 BCBS (2014), p.11 choice structure of the bank: a rise in CRR implies a rise in LRR while a rise in LRR does not necessarily entail a rise in CRR. More specifically, raising R increases both CRR and LRR while increasing D only improves LRR. Even though Regulatory Authorities introduce an incentive to raise deposits via the funding requirement, the liability structure of the bank remains capital driven under a regulatory environment à la Basel III because the bank has an incentive to raise R at the expense of D. As a result, we question the efficacy with which such a type of regulatory environment strengthens the liability structure of the bank.

Analysing such aspect of banking regulation is beyond the scope of this paper.4 Note that the Basel Committee published "Sound Practices for Managing Liquidity in Banking Organisations" in 2000. However the unprecedented liquidity crisis experienced by the banking sector in 2008 urged for a better liquidity regulation.

Études et Documents n° 8, CERDI, 2018

Following Freixas & Rochet (2008), we define the bank as a financial intermediary buying and selling financial claims. In particular, we consider the bank funds its lending and market activities through the selling of financial liabilities.

Assumptions on the second derivative of the interest rates will be discussed later on.

[START_REF] Ito | Impact of the basel capital accord on japanese banks' behavior[END_REF] add the term fukumi to the book value of shareholders' equity which is equivalent to mark-to-market valuation.

If the aggregate risk for loans was nil, the VaR would equal zero and thus θ = 0. The market risk is nil in the model as the bank buys risk-free bonds which is equivalent to a zero VaR within the Basel framework.

For further details, see Appendix A.

Note that developing the model at further order is possible. However, we do not do so because the economic interpretation would not be straightforward.

This implies that r ′′ R > 0.

Acknowledgments

We would like to thank Fabien Feschet, Michaël Goujon, Grégoire Rota-Graziosi, Clément Mathonnat and Vianney Dequiedt for their helpful comments and suggestions. All remaining errors are our own and the usual disclaimers apply.

Appendix A Bank Behaviour Under Basel II

We reduce the optimisation problem of the bank as follows: max

Solving this profit-maximisation problem with the Lagrangian method gives the following first-order economic conditions:

Eq.14 means that the difference between the loan and subordinated debt rate -the Net Interest Margin (NIM) -equals the sum of the marginal regulatory costs on loan and subordinated debt plus the marginal profit derived from the intermediation activity as deduced from the Basel III optimisation problem. Rising the portfolio of loans bought increases the NIM as it is costly to manage a higher loan portfolio. Eq.15 states that the funding arbitrage -the difference between the subordinated debt and deposit rate -equals the marginal regulatory and market cost on subordinated debt. The structure of this funding arbitrage remains capital driven as the bank has no incentive to raise deposits.