Elnaz Nazemi
email: elnaz.nazemi@usherbrooke.ca

Walid M Hassen
email: mohamed.walid.hassen@usherbrooke.ca

Eric H Frost
email: eric.frost@usherbrooke.ca

Jan J Dubowski
email: jan.j.dubowski@usherbrooke.ca

Growth of Escherichia coli on the GaAs (001) surface

Keywords: GaAs-based biosensor, Photocorrosion, Self-assembled monolayer, Antibody, Escherichia coli, Bacterial growth

Detection of pathogenic bacteria and monitoring their susceptibility to antibiotics are of great importance in the fields of medicine, pharmaceutical research, as well as water and food industries. In order to develop a photonic biosensor for detection of bacteria by taking advantage of photoluminescence (PL) of GaAs-based devices, we have investigated the capture and growth of Escherichia coli K12 on bare and biofunctionalized surfaces of GaAs (001) -a material of interest for capping different semiconductor microstructures. The results were compared with the capture and growth of Escherichia coli K12 on Au surfaces that have commonly been applied for studying a variety of biological and biochemical reactions. We found that neither GaAs nor Aucoated glass wafers placed in Petri dishes with nutrient agar inoculated bacteria inhibited bacterial growth, regardless of the wafers being bare or biofunctionalized. However, the capture and growth of bacteria on biofunctionalized surfaces of GaAs and Au wafers kept in a flow cell and exposed to different concentrations of bacteria and growth medium revealed that the initial surface coverage and the subsequent bacterial growth were dependent on the biofunctionalization architecture, with antibody-coated surfaces clearly being most efficient in capturing bacteria and offering better conditions for growth of bacteria. We have observed that, as long as the GaAs wafers were exposed to bacterial suspensions at concentrations of at least 10 5 CFU/mL, bacteria could grow on the surface of wafers, regardless of the type of biofunctionalization architecture used to capture the bacteria. These results provide important insight towards the successful development of GaAs-based devices designed for photonic monitoring of bacterial reactions to different biochemical environments.

Introduction

Evaluating growth of bacteria to determine antibiotic susceptibility and metabolic traits is essential to diagnostic microbiology [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF]. Monitoring the viability, growth and cellular metabolism of bacteria also plays an important role in yielding bacterial products in industrial-or small-scale experiments [START_REF] Sonnleitner | Biomass determination[END_REF][START_REF] Nayak | Detection of microorganisms using biosensors-A smarter way towards detection techniques[END_REF][START_REF] Garneau | Bacteriophages of lactic acid bacteria and their impact on milk fermentations[END_REF][START_REF] Schuler | Real-time monitoring and control of microbial bioprocesses with focus on the specific growth rate: current state and perspectives[END_REF][START_REF] Kee | Plasmonic nanohole arrays for monitoring growth of bacteria and antibiotic susceptibility test[END_REF]. Conventionally, bacterial growth has been investigated by [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF] plate counting where colony forming units (CFU) are determined [START_REF] Sonnleitner | Biomass determination[END_REF], and (2) visualization of growth in broth either by eye or by nephelometry [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF][START_REF] Freitas | Study of carbohydrate influence on protein-tannin aggregation by nephelometry[END_REF][START_REF] Joubert | Laser nephelometry applied in an automated microplate system to study filamentous fungus growth[END_REF]. Broth microdilution and Kirby-Bauer disk diffusion are widely applied in clinical laboratories to evaluate the antibiotic susceptibility of bacteria [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF][START_REF] Poupard | Antimicrobial Susceptibility Testing[END_REF]. These techniques are timeconsuming and labour intensive and, typically, they are not able to provide same-day monitoring [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF][START_REF] Kee | Plasmonic nanohole arrays for monitoring growth of bacteria and antibiotic susceptibility test[END_REF][START_REF] Chiang | Innovative antimicrobial susceptibility testing method using surface plasmon resonance[END_REF]. Polymerase chain reaction (PCR) [START_REF] Versalovic | Manual of Clinical Microbiology[END_REF][START_REF] Rolain | Real-time PCR for universal antibiotic susceptibility testing[END_REF][START_REF] Cotto | Quantitative polymerase chain reaction for microbial growth kinetics of mixed culture system[END_REF], surface plasmon resonance (SPR) [START_REF] Chiang | Innovative antimicrobial susceptibility testing method using surface plasmon resonance[END_REF] and fluorescence-based assays [START_REF] Roth | Bacterial viability and antibiotic susceptibility testing with SYTOX green nucleic acid stain[END_REF][START_REF] Boi | Evaluation of Escherichia coli viability by flow cytometry: A method for determining bacterial responses to antibiotic exposure[END_REF] have been introduced for rapid evaluation of growth and antimicrobial sensitivity of bacteria. However, the cost of PCR [START_REF] Mwaigwisya | Emerging commercial molecular tests for the diagnosis of bloodstream infection[END_REF] and SPR systems [START_REF] Lazcka | Pathogen detection: A perspective of traditional methods and biosensors[END_REF] and technical complexity of using fluorescent dyes are inhibitory factors that limit the application of these methods in clinical laboratories. Photoluminescence (PL) emitting semiconductors hold a great potential for biosensing applications due to the sensitivity of the PL signal to the surface localized phenomena [START_REF] Adamowicz | Photoluminescence characterization of air exposed AlGaAs surface and passivated ex situ by ultrathin silicon interface control layer[END_REF][START_REF] Gfroerer | Photoluminescence in Analysis of Surfaces and Interfaces[END_REF][START_REF] Lebedev | Role of sulfide ion solvation in the modification of GaAs surface electronic structure[END_REF][START_REF] Moumanis | Aging and detergent washing effects of the surface of (001) and (110) GaAs passivated with hexadecanethiol[END_REF][START_REF] Tomkiewicz | Surface electronic properties of sulfur-treated GaAs determined by surface photovoltage measurement and its computer simulation[END_REF]. Electrically charged molecules, if immobilized at the surface of such semiconductors, could affect their PL by modifying bending of their energy bands near the surface [START_REF] Seker | Surface chemistry of prototypical bulk II-VI and III-V semiconductors and implications for chemical sensing[END_REF][START_REF] Zhang | Band bending in semiconductors: chemical and physical consequences at surfaces and interfaces[END_REF]. PL of some semiconductors has been used for chemical sensing [START_REF] Seker | Surface chemistry of prototypical bulk II-VI and III-V semiconductors and implications for chemical sensing[END_REF] and detection of biomolecules [START_REF] Budz | Photoluminescence model for a hybrid aptamer-GaAs optical biosensor[END_REF]. We have demonstrated a successful detection of electrically charged viruses [START_REF] Dubowski | Quantum dot template for fast and simultaneous detection of different infectious agents[END_REF], Escherichia coli K12 bacteria [START_REF] Duplan | A photoluminescence-based quantum semiconductor biosensor for rapid in situ detection of Escherichia coli[END_REF][START_REF] Nazemi | GaAs/AlGaAs heterostructure photonic biosensor for rapid detection of Escherichia coli in phosphate buffered saline solution[END_REF] and, more recently, Legionella pneumophila [START_REF] Aziziyan | Photonic biosensor based on photocorrosion of GaAs/AlGaAs quantum heterostructures for detection of Legionella pneumophila[END_REF] by taking advantage of PL emission of GaAs/AlGaAs (001) nano-heterostructures. The major advantage of the GaAs/AlGaAs based biosensors, in comparison to a variety of biosensors employing Au surfaces, is their low cost. Note that GaAs (001) denotes a specific, technologically important surface of a zinc blende crystal structure GaAs material [START_REF] Ohtake | Surface reconstructions on GaAs(001)[END_REF][START_REF] Labella | Arsenic-rich GaAs(001) surface structure[END_REF] that is well-known in the production of optoelectronic devices [START_REF] Wada | Optoelectronic integration based on GaAs material[END_REF][START_REF] Mokkapati | III-V compound SC for optoelectronic devices[END_REF]. While a ubiquitous presence of GaAs/AlGaAs microstructures in light emitting diodes and other commercial devices suggests that they should be relatively inexpensive, an additional attractive feature of the GaAs/AlGaAs based biosensor is the inexpensive hardware required for reading the biosensor PL signal. We have recently demonstrated that PL emission of GaAs/AlGaAs microstructures could be employed to monitor the growth and antibiotic susceptibility of Escherichia coli immobilized on the surface of such microstructures [START_REF] Nazemi | Monitoring growth and antibiotic susceptibility of Escherichia coli with photoluminescence of GaAs/AlGaAs quantum well microstructures[END_REF]. One of the key elements in the development of this innovative biosensing platform is to investigate the mechanisms of interaction between bacteria and the GaAs (001) compound used for capping PL emitting GaAs/AlGaAs microstructures, as well as to determine conditions for the optimized immobilization and growth of bacteria.

Growth of bacteria on solid surfaces can be affected by biocompatibility of the substrate. Some metal surfaces such as silver (Ag) are well-known to have antimicrobial activity and prevent bacterial colonization [START_REF] Golubovich | Kinetics of growth inhibition by silver ions[END_REF]. Silver coating is widely applied for reducing bacterial contamination of medical tools and minimizing nosocomial infections related to operating rooms and other sections of hospitals [START_REF] Casey | Microbiological comparison of a silver-coated and a non-coated needleless intravascular connector in clinical use[END_REF]. Some gold (Au)-coated nanoparticles were found toxic to bacteria [START_REF] Zhou | Antibacterial activities of gold and silver nanoparticles against Escherichia coli and bacillus Calmette-Guerin[END_REF], whereas others were not [START_REF] Williams | Evaluation of the microbial growth response to inorganic nanoparticles[END_REF].

Furthermore, arsenic (As) and gallium (Ga) have been reported to affect bacterial viability [START_REF] Harvey | The effect of As(III) on the growth of Thiobacillus ferrooxidans in an electrolytic cell under controlled redox Potentials[END_REF][START_REF] Podol'skaia | Effect of arsenic on bacterial growth and plasma membrane atpase activity[END_REF][START_REF] Rzhepishevska | The antibacterial activity of Ga 3+ is influenced by ligand complexation as well as the bacterial carbon source[END_REF][START_REF] Deleon | Gallium maltolate treatment eradicates Pseudomonas aeruginosa infection in thermally injured mice[END_REF][START_REF] Mukhopadhyay | Microbial arsenic: from geocycles to genes and enzymes[END_REF]. Here, we report on the results of a systematic study of the growth of E. coli K12 on bare and biofunctionalized surfaces of bulk GaAs (001). We have compared these results with the growth of E. coli K12 on Au surfaces that have been known for their common use in biosensor research [START_REF] Lazcka | Pathogen detection: A perspective of traditional methods and biosensors[END_REF].

Experimental methods

Materials

Semi-insulating (SI) undoped GaAs (001) wafers (AXTG108-36) were obtained from AXT Inc. (Fremont, USA). OptiClear, acetone and isopropanol (2-propanol) used for cleaning the GaAs wafers were purchased from National Diagnostics (Mississauga, Canada), ACP Chemicals (Montréal, Canada) and Fisher Scientific (Ottawa, Canada), respectively. Anhydrous ethanol was obtained from Commercial Alcohols Inc.

(Brampton, Canada). Deionized (DI) water with an electrical resistivity of 18 MΩ.cm was obtained with a Millipore purification custom system built by Culligan (Quebec, Canada). Ultra-high purity nitrogen 5.0 UHP (99.999%) used for deoxygenation of the anhydrous ethanol and high purity nitrogen 4.8 HP (99.998%) used for drying the GaAs wafers were both purchased from Praxair Canada Inc. (Mississauga, Canada). Ammonium hydroxide 28% (NH 4 OH) was obtained from Anachemia (Richmond, Canada). Biotinylated polyethylene glycol (b-PEG) thiols were bought from Prochimia Surfaces (Gdansk, Poland). Ammonium sulfide 48% (AS), Luria Bertani (LB) broth, phosphate buffered saline (PBS) solution (10X, pH 7.4), [START_REF] Lazcka | Pathogen detection: A perspective of traditional methods and biosensors[END_REF]

Biofunctionalization of GaAs (001) and Au surfaces

Samples of 2 mm × 2 mm were cleaved from GaAs (001) wafers and cleaned in an ultrasonic bath with OptiClear, acetone and isopropanol sequentially for 5 min each.

Following the cleaning steps, the GaAs samples were dried under a flow of compressed nitrogen and etched in a solution of NH 4 OH (28%) for 2 min at room temperature. Three different bio-architectures have been applied to functionalize the surface of freshly etched GaAs (001) samples, as described below. The Au-coated glass samples, 2 mm × 2 mm, were cleaned in OptiClear, acetone and isopropanol, and then dried with a flow of compressed nitrogen. Dried samples were functionalized with MHDA-EDC/NHS-Ab in the same way as the GaAs samples.

b-PEG-NA-b-Ab functionalization

Freshly etched GaAs samples were rinsed with deoxygenated anhydrous ethanol and immediately incubated for 20 h at room temperature in a 2 mM mixture of b-PEG (1:15) and HDT (14:15) thiols diluted in deoxygenated anhydrous ethanol. After the thiolation step, the GaAs samples were rinsed with deoxygenated anhydrous ethanol and exposed to AS (0.1%) for 15 min. Following this step, the samples were rinsed with DI water and incubated for 2 h at room temperature in PBS (1X) solution containing 200 µg/mL of neutravidin. Thereafter, the neutravidin-coated samples were immersed for 1 h at room temperature in a solution of biotinylated polyclonal antibodies against E. coli diluted in PBS (1X) at 0.1 mg/mL. The antibodies were biotinylated by the manufacturer by covalent attachment of biotin molecules to free amine groups (NH 2 ) in the antibody structure. Figure 1 shows a schematic illustration of bacteria immobilized on the GaAs (001) surface functionalized with an architecture comprising mixed b-PEG and HDT thiols, neutravidin and biotinylated polyclonal antibodies against E. coli (b-PEG-NA-b-Ab). The formation of HDT self-assembled monolayers (SAMs) on the GaAs (001)

surface has been investigated with PL [START_REF] Ding | Fourier-transform infrared and photoluminescence spectroscopies of self-assembled monolayers of long-chain thiols on (001) GaAs[END_REF][START_REF] Kim | Formation dynamics of hexadecanethiol self-assembled monolayers on (001) GaAs observed with photoluminescence and Fourier transform infrared spectroscopies[END_REF][START_REF] Arudra | Enhanced Photonic Stability of GaAs in Aqueous Electrolyte Using Alkanethiol Self-Assembled Monolayers and Postprocessing with Ammonium Sulfide[END_REF][START_REF] Huang | Solvent-mediated self-assembly of hexadecanethiol on GaAs (001)[END_REF], ellipsometry [START_REF] Rosu | Molecular Orientation in Octanedithiol and Hexadecanethiol Monolayers on GaAs and Au Measured by Infrared Spectroscopic Ellipsometry[END_REF], X-ray diffraction [START_REF] Mcguiness | Molecular self-assembly at bare semiconductor surfaces: Characterization of a homologous series of n-alkanethiolate monolayers on GaAs(001)[END_REF] and Fourier transform infrared spectroscopy (FTIR) [START_REF] Arudra | Enhanced Photonic Stability of GaAs in Aqueous Electrolyte Using Alkanethiol Self-Assembled Monolayers and Postprocessing with Ammonium Sulfide[END_REF]. The SAM formation from b-PEG diluted in OH-terminated PEG thiols has also been investigated using FTIR [START_REF] Duplan | Specific immobilization of influenza A virus on GaAs (001) surface[END_REF]. In each case, the intensity and full-width-at-half-maximum of two peaks in the 2800 to 3000 cm -1 region, that are assigned to stretching vibrations of CH 2 in the alkane chains [START_REF] Arnold | Preparation, modification, and crystallinity of aliphatic and aromatic carboxylic acid terminated self-assembled monolayers[END_REF],

are considered as a measure of the quality of formed SAMs. Mixed SAMs comprising different thiols have also been investigated on Au surfaces [START_REF] Folkers | Self-assembled monolayers of alkanethiols on gold: Comparisons of monolayers containing mixtures of short-and long-chain constituents with CH 3 and CH 2 OH terminal groups[END_REF][START_REF] Olbris | Interplay of wetting and adsorption at mixed selfassembled monolayers[END_REF][START_REF] Nelson | Surface characterization of mixed self-assembled monolayers designed for streptavidin immobilization[END_REF][START_REF] Yoshioka | One-step detection of galectins on hybrid monolayer surface with protruding lactoside[END_REF][START_REF] Tarnawski | Amphiphilic gold nanoparticles: Synthesis, characterization and adsorption to PEGylated polymer surfaces[END_REF][START_REF] Mustafa | Adsorption behaviour of PEGylated gold nanoparticles to different surfaces probed by CV monitoring[END_REF], suggesting the feasibility of formation of such architectures on GaAs (001) surfaces as well. We employed the b-PEG-NA-b-Ab architecture to support the growth of bacteria on GaAs samples placed on nutrient LB-agar plates. A similar architecture was previously used by us for detection of E. coli K12 bacteria [START_REF] Duplan | A photoluminescence-based quantum semiconductor biosensor for rapid in situ detection of Escherichia coli[END_REF][START_REF] Nazemi | GaAs/AlGaAs heterostructure photonic biosensor for rapid detection of Escherichia coli in phosphate buffered saline solution[END_REF].

MHDA-EDC/NHS functionalization

Freshly etched GaAs samples were rinsed with deoxygenated anhydrous ethanol and immediately incubated for 20 h at room temperature in a 2 mM solution of MHDA thiol diluted in deoxygenated anhydrous ethanol. Following this step, the GaAs samples were rinsed with deoxygenated anhydrous ethanol and then PBS (1X). Thereafter, the samples were incubated for 30 min at room temperature in a mixture of 400 mM of EDC and 100 mM of NHS diluted in PBS (1X) to activate the COOH group of the MHDA thiol. A schematic illustration of the MHDA-EDC/NHS biofunctionalization procedure applied to immobilize E. coli bacteria on the GaAs (001) surface is presented in Fig. 2. The formation of MHDA SAM on the GaAs (001) surface and activation of COOH group of this thiol with the EDC/NHS step has recently been discussed by Lacour et al. [START_REF] Lacour | Regeneration of a thiolated and antibody functionalized GaAs (001) surface using wet chemical processes[END_REF]. The appearance of a C=O peak at 1741 cm -1 in FTIR absorption spectra of MHDA-coated samples that follows the EDC/NHS exposure, confirms the activation of the COOH group of MHDA thiol [START_REF] Frey | Covalent attachment and derivatization of poly(l-lysine) monolayers on gold surfa es as hara terized y polarizatio -odulatio FT-IR spectroscopy[END_REF]. This process allows direct attachment of bacteria through covalent binding with naturally-occurring NH 2 groups on the bacterial surface [START_REF] Meyer | Immobilisation of living bacteria for AFM imaging under physiologicalconditions[END_REF]. The EDC/NHS activated MHDA SAM architecture has been applied to directly capture E.

coli bacteria on GaAs samples kept in a flow cell.

MHDA-EDC/NHS-Ab functionalization

The fabrication of MHDA-EDC/NHS-Ab bio-architecture on GaAs (001) and Au surfaces included covalent linkage of polyclonal Ab against E. coli to COOH groups of MHDA SAM that had been activated by EDC/NHS, as described in the previous section.

The reaction was carried out for 1 h at room temperature from an antibody solution in PBS (1X) at 0.1 mg/mL. The illustration of the biofunctionalization steps employed in this case is presented schematically in Fig.

Growth of E. coli on GaAs (001) and Au surfaces in contact with nutrient LB-agar plate

Freshly cultured E. coli K12 suspension was prepared by overnight growth of bacteria in LB at 37º C before use the following morning. The concentration of the bacteria was measured with a cell density meter (Fisher Scientific, model 40) operating at 600 nm.

Bacteria were then centrifuged in LB for 25 min at 3000 rpm. After that, the medium was removed and the pellets were suspended in PBS (1X) and centrifuged at 3000 rpm for 15 min. Finally, PBS (1X) was removed and the pellets were resuspended in PBS (1X) and diluted to give 10 5 CFU/mL. A group of 8 b-PEG-NA-b-Ab functionalized and 8 bare GaAs (001) samples were placed upside down on a nutrient agar plate that had been inoculated evenly with 100 µL of the bacterial suspension at 10 5 CFU/mL in analogous fashion to a Kirby-Bauer disk diffusion antibiotic sensitivity test [START_REF] Bauer | Antibiotic susceptibility testing by a standardized single disk method[END_REF]. Assuming homogenous distribution of bacteria on the nutrient agar plate, the initial coverage of the agar plate with bacteria was around 2 bacteria/mm 2 . This number was calculated by dividing the total number of bacteria used to inoculate the agar plate (10 4 bacteria) by the total area of the agar plate (45.6 cm 2 ). Figure 4

Growth of E. coli on the surface of GaAs (001) and Au in a flow cell

In this approach, growth of E. coli K12 bacteria on biofunctionalized GaAs (001) and Au surfaces was investigated for samples kept in an ULTEM TM

Microscopic enumeration of bacteria

Biochips were removed after each experiment and placed on glass slides, with the bacteria exposed surface facing up, for microscopic analysis. Without fixation, washing, or staining, bacteria were observed with an optical microscope (Zeiss, Axiotech) using overhead illumination. Bacteria were readily observed through a 100X lens and with a supplemental 10X digital enlargement. Total concentration of bacteria adhered to the surface in each experiment was estimated by analyzing several optical images at magnification of 1000X (each image with the surface area of ~3500 µm 2 per field) collected at different sites of the sample and reported per mm 2 .

Statistical methods

Similar sets of experiments, either for flow cell or Petri dish tests, were repeated at least 3 times to determine experimental error. This allowed us to calculate mean values of surface coverage with standard deviations.

Results and discussion

Growth of E. coli K12 on the surface of GaAs (001) and Au samples in contact with a nutrient agar plate

The growth of E. coli K12 was observed on both bare and b-PEG-NA-b-Ab functionalized surfaces of GaAs (001) biochips placed on nutrient agar plates. Not only was there no inhibition zone around the biochips as has been observed in similar experiments with silver nanoparticles [START_REF] Naqvi | Combined efficacy of biologically synthesized silver nanoparticles and different antibiotics against multidrug-resistant bacteria[END_REF], but neither bare nor functionalized GaAs samples prevented bacteria from multiplying. Figure 6 shows an optical image of an E.

coli inoculated Petri dish with two GaAs chips (indicated by arrows) that remained in contact with the bacteria growth medium at 37 °C during a 24 h exposure. This experiment, inspired by the Kirby-Bauer disk diffusion antibiotic sensitivity test [START_REF] Bauer | Antibiotic susceptibility testing by a standardized single disk method[END_REF],

indicates that GaAs does not inhibit the growth of E. coli as it can be seen that bacteria grew abundantly next to the contact with the GaAs chips. bacteria. However, after 6 hours, in both cases, the surface coverage with bacteria reached a saturation number of around 3×10 3 bacteria/mm 2 . The saturation effect might be related to the stationary phase of bacterial growth when the rates of bacterial growth and bacterial death are equal [START_REF] Akerlund | Analysis of cell size and DNA content in exponentially growing and stationary phase batch cultures of Escherichia coli[END_REF][START_REF] Fujikawa | Modeling surface growth of Escherichia coli on agar plates[END_REF].

The data in Fig. 7(a), fitted with exponential curves, suggest that the number of bacteria doubled every 31 and 44 min on the surface of bare and antibody functionalized GaAs, respectively. This compares to the ability of E. coli to double every 20 min under ideal conditions of temperature, oxygen concentration and a rich liquid nutrient medium [START_REF] Berg | coli in Motion[END_REF].

However, for comparable growth rates of bacteria in the exponential phase in liquid and solid environments (agar plates), the longer latency phase of bacteria on solid media could explain the lower rate of bacterial growth on solid substrates than in liquid environments [START_REF] Fujikawa | Modeling surface growth of Escherichia coli on agar plates[END_REF]. This test demonstrates the feasibility of growing E. coli bacteria on GaAs (001) biochips placed on agar plates.

Growth of E. coli K12 on GaAs (001) and Au surfaces in a flow cell

Figure 8 presents the initial surface coverage (after 30 min exposure to a bacterial suspension) and the coverage after a 4.5-h incubation in LB medium for GaAs biochips functionalized with MHDA-EDC/NHS and MHDA-EDC/NHS-Ab (See related data included in Supplementary Material). For the set of bacterial suspensions ranging from 10 5 , 10 6 , 10 7 and 10 8 CFU/mL, each experiment was performed at least in triplicate.

Examples of optical images for a biochip functionalized with MHDA-EDC/NHS-Ab and exposed to bacterial suspension at 10 6 CFU/mL, before and after incubation in LB, are shown in Figure 9. We noted that the size of the bacteria before and after growth was in good agreement with literature data, indicating increased bacterial length after entering the growth phase [START_REF] Trueba | Changes in cell diameter during the division cycle of Escherichia coli[END_REF]. All bacteria appeared to be immobilized on the surface and not free in the film of LB medium that surrounded the sample because no bacteria could be seen moving by Brownian or flagella-assisted movement, nor were any partially out of the plane of focus as would be observed if the bacteria were free in the film of LB medium above the wafer surface. Theoretically, it would have been possible for bacteria to grow in the medium and then attach to the surface. This is very unlikely in this experiment as the flow cell was abundantly washed to remove unattached bacteria at the beginning of the experiment. If a few remaining bacteria had grown, subsequent attachment is quite inefficient. Indeed, when we add 10 6 bacteria to the flow cell, only 176±20 and 112±24 attach for MHDA-EDC/NHS-Ab and MHDA-EDC/NHS architectures respectively, so the majority of these bacteria would have still been floating in the LB medium and thus moving out of focus. For these reasons, we attributed increased coverage with surface growth rather than with growth free in the medium and subsequent attachment. The fact that no bacterial movement was observed during microscopic analysis cannot be explained by the bacteria being dead as even dead bacteria move extensively by Brownian movement. Since no heating was applied for fixation of bacteria to the surface, the bacterial immobility must be a result of attachment via antibodies.

The average growth index of bacteria was calculated for each bio-architecture and for each concentration of bacteria, and is presented in Table 1. The average growth index of bacteria was calculated using the following formula:

(

where and correspond to the surface coverage with bacteria before and after bacterial growth, respectively, and is the duration of the experiment, which is equal to 300 min.

We systematically observed a greater initial surface coverage with E. coli using the EDC/NHS-Ab capture method compared with the direct EDC/NHS method for comparable concentrations of bacteria. The difference between the two bio-architectures in terms of the initial surface coverage was more noticeable for lower concentrations of bacteria. This might be related to a limitation in the number of bacteria that the antibodycoated surface is able to capture and saturation of this surface at higher bacterial concentrations. Due to the higher efficiency of antibody-coated surface in initial capture of bacteria, the surface coverage after bacterial growth (see Figure 8), and the bacterial growth index (see Table 1) were higher compared with the EDC/NHS functionalized surface for each concentration of bacteria. It is also possible that the lower number of bacteria on the EDC/NHS functionalized surface compared with antibody-coated surface, might be related to the reduced capture of growing bacteria directly on the EDC/NHS functionalized surface due to the inactivation of COO-NHS groups following their reaction with free NH 2 groups of proteins in the LB medium. In addition to the better conditions that antibody-coated surfaces offer for bacterial growth, they possess other advantages over EDC/NHS functionalized surfaces. In general, polyclonal antibodies, which were employed in MHDA-EDC/NHS-Ab bio-architecture, identify multiple epitopes on one antigenic macromolecule, therefore, they provide high affinity with bacteria. Besides that, application of GaAs samples functionalized with antibodies enables us to investigate growth of specific bacteria, while MHDA-EDC/NHS captures We were not able to observe the growth of bacteria on either of the investigated architectures for bacterial concentration of 10 4 CFU/mL. A minimum threshold concentration for bacterial growth might be related to the toxicity of Ga and As ions that are known to affect the viability and/or growth of bacteria [START_REF] Harvey | The effect of As(III) on the growth of Thiobacillus ferrooxidans in an electrolytic cell under controlled redox Potentials[END_REF][START_REF] Podol'skaia | Effect of arsenic on bacterial growth and plasma membrane atpase activity[END_REF][START_REF] Rzhepishevska | The antibacterial activity of Ga 3+ is influenced by ligand complexation as well as the bacterial carbon source[END_REF][START_REF] Deleon | Gallium maltolate treatment eradicates Pseudomonas aeruginosa infection in thermally injured mice[END_REF][START_REF] Mukhopadhyay | Microbial arsenic: from geocycles to genes and enzymes[END_REF]. The release of these ions is a consequence of GaAs corrosion according to the following formula [START_REF] Ruberto | The laser controlled micrometer scale photoelectrochemical etching of III-V semiconductors[END_REF]:

It is possible that for bacterial concentrations below 10 5 CFU/mL, the amount of Ga and/or As ions released per bacteria could reach a toxic dose [START_REF] Podol'skaia | Effect of arsenic on bacterial growth and plasma membrane atpase activity[END_REF][START_REF] Diorio | An Escherichia coli chromosomal ars operon homolog is functional in arsenic detoxification and is conserved in gram-negative bacteria[END_REF] and, thus, affect bacterial viability and growth. Moreover, the growth of bacteria might also be inhibited by the antibodies used to capture bacteria in MHDA-EDC/NHS-Ab bio-architecture [START_REF] Lin | Inhibition of in vitro growth of coliform bacteria by a monoclonal antibody directed against ferric enterobactin receptor FepA1[END_REF][START_REF] Chalghoumi | Adhesion and growth inhibitory effect of chicken egg yolk antibody (IgY) on Salmonella enterica serovars Enteritidis and Typhimurium in vitro[END_REF].

As a control, we investigated the growth of E. coli on Au substrates functionalized with MHDA-EDC/NHS-Ab. Following the methodology applied for GaAs samples, the biofunctionalized Au samples were kept in the flow cell and exposed to the bacterial suspension at 10 5 CFU/mL and then to LB medium. The initial coverage of Au samples exposed for 30 min to the bacterial suspension and for 4.5 h to LB medium was at 17±5 and 98±25 bacteria/mm 2 , respectively. The average bacterial growth index of 0.019 min -1 on these samples was slightly higher than that of 0.016 min -1 on MHDA-EDC/NHS-Ab functionalized GaAs samples, suggesting that for the 10 5 CFU/mL solution, the GaAs substrate had only a minor negative effect on bacterial growth in comparison to the Au substrate. We note that the Petri dish experiments with GaAs (001) and Au substrates in contact with nutrient agar plates inoculated with bacteria at ~ 2 bacteria/mm 2 , revealed comparable growth rates of bacteria on both bare GaAs and Au substrates. This suggests that the concentration of As and/or Ga released to the Petri dish was not sufficient to affect bacterial growth, or that the agar growth medium neutralized any toxicity. Given that some toxicity has been observed for Au in an ionic form [START_REF] Williams | Evaluation of the microbial growth response to inorganic nanoparticles[END_REF], our inability to observe bacterial growth on both Au and GaAs substrates kept in the flow cell, when initial concentrations of bacteria were below 10 5 CFU/mL, could be due to comparable toxicity of the Au and GaAs substrates. Nevertheless, these results have revealed that the GaAs surface provides conditions satisfactory for the growth of bacteria in a flow cell, which potentially is attractive for photonic monitoring in situ of the growth and reaction of bacteria to different biological environments and particularly antibiotics.

Conclusion

In our endeavour to develop a GaAs-based photonic biosensor for monitoring reaction of bacteria to different biochemical conditions, we have investigated the capture and growth of E. coli K12 on surfaces of GaAs (001). The experiments with bare GaAs and Au in contact with nutrient agar plates inoculated with bacteria at ~ 2 bacteria/mm 2 suggested that neither of these substrates inhibited the growth of bacteria. However, the experiments in a flow cell revealed that the initial coverage, and the subsequent bacterial growth were dependent on the biofunctionalization architecture used to capture bacteria. Antibody biofunctionalized surfaces exhibited significantly higher capture efficiencies, especially at lower concentrations of bacteria. For suspensions containing bacteria at less than 10 5 CFU/mL, we were not able to observe the growth of bacteria, regardless of the biofunctionalization architecture. This threshold might be related to the toxicity of As and/or Ga released from the GaAs samples. While different methods could be investigated to address this issue and reduce the potential effect of toxicity of As and/of Ga ions, we note that a similar shortcoming characterizes matrix-assisted laser desorption ionization time of flight mass spectrometry (MALDI-TOF MS) which requires 10 4 -10 5 cells per assay [START_REF] Van Belkum | Rapid clinical bacteriology and its future impact[END_REF], yet is about to revolutionize clinical diagnostic laboratories. Whereas MALDI-TOF MS does not determine antibiotic sensitivity, our approach does [START_REF] Nazemi | Monitoring growth and antibiotic susceptibility of Escherichia coli with photoluminescence of GaAs/AlGaAs quantum well microstructures[END_REF] and could thus complement MALDI-TOF MS in the same time frame. However, it is expected that by increasing the initial surface coverage with bacteria we could observe bacterial growth at concentrations lower than 10 5 CFU/mL. The reason is that by increasing the number of bacteria immobilized on the surface, the ratio of Ga and/or As per bacteria decreases and, consequently, the dose might not reach the toxic levels.

Increasing the surface coverage with bacteria could be achieved by improving surface functionalization techniques, or by applying some methods such as chemotaxis [START_REF] Hassen | Chemotaxis for enhanced immobilization of Escherichia coli and Legionella pneumophila on biofunctionalized surfaces of GaAs[END_REF],

filtration [START_REF] Wu | Rapid Detection of Pathogenic Bacteria from Fresh Produce by Filtration and Surface-Enhanced Raman Spectroscopy[END_REF] or electrophoresis [START_REF] Bossi | Capillary electrophoresis coupled to biosensor detection[END_REF].

Fig. 1

 1 Fig. 1 Schematic illustration of a GaAs (001) surface functionalized with a biotinylated PEG-neutravidin-biotinylated antibody architecture for immobilization of E. coli bacteria.

Fig. 2

 2 Fig. 2 Schematic illustration of the biofunctionalization steps employed for non-specific immobilization of E. coli bacteria on the surface of GaAs (001). Following formation of MHDA SAM on the freshly etched surface of GaAs (001) (a), COOH group of MHDA thiol is activated with EDC/NHS (b), which allows immobilization of E. coli via naturally-occurring NH 2 groups on the bacterial surface (c).

Fig. 3

 3 Fig. 3 Schematic illustration of the biofunctionalization steps applied for immobilization of E. coli bacteria with antibody on the surface of GaAs (001). Following formation of MHDA SAM on the freshly etched surface of GaAs (001) (a), COOH group of MHDA thiol is activated with EDC/NHS (b), followed by immobilization of E. coli antibodies whose NH 2 groups react with the EDC/NHS activated carboxyl sites (c), and antibody specific immobilization of E. coli bacteria (d).

  schematically illustrates the top and side views of the experimental setup. The plate with GaAs samples was then kept at 37° C for up to 8 hours.Every hour, one of the bare samples and one of the biofunctionalized samples were removed from the agar plate and adherent bacteria were counted with an optical microscope following the procedure discussed in the Microscopic enumeration of bacteria section. These measurements allowed us to investigate the dynamics of the immobilization process on the surface of both samples. As a control experiment, a series of experiments was also carried out for bare Au samples following the methodology applied for GaAs (001) samples. The principle of studying the growth of bacteria on GaAs and Au samples in contact with bacterial cultures on Petri dishes can be compared to a Kirby-Bauer antibiotic sensitivity test[START_REF] Versalovic | Manual of Clinical Microbiology[END_REF][START_REF] Poupard | Antimicrobial Susceptibility Testing[END_REF] where paper disks containing different types of antibiotics are placed on Petri dishes to allow evaluation of the impact of the antibiotics on bacterial growth.

Fig. 4

 4 Fig. 4 Top view (a) and side view (b) of the setup for studying the growth of E. coli in proximity of GaAs samples. The nutrient agar plate was inoculated evenly with 100 µL of E. coli K12 bacteria (red ovals in (b)) at 10 5 CFU/mL. Biofunctionalized and bare GaAs (001) samples were placed upside down. The same setup and procedure was applied for bare Au samples.

Fig. 5

 5 Fig. 5 Schematic illustration of the flow cell setup. The biofunctionalized GaAs (001) or Au biochips were placed in the flow cell and exposed to bacterial suspension (red ovals) and LB, sequentially. The bacteria and LB were injected into the flow cell at a flow rate of 0.1 mL/min using the peristaltic pump.

Fig. 6

 6 Fig.[START_REF] Kee | Plasmonic nanohole arrays for monitoring growth of bacteria and antibiotic susceptibility test[END_REF] Optical image of a Petri dish inoculated with E. coli. Two GaAs wafers (indicated with arrows) were placed on the surface. After 24 h of growth at 37°C, the Petri dish was photographed showing that bacteria grew abundantly next to the GaAs wafers.

Figure 7 (

 7 Figure 7(b) illustrates the time dependent surface density of E. coli bacteria immobilized on bare GaAs and Au samples. The number of bacteria immobilized on bare Au samples increased from 8±2 bacteria/mm 2 at 1 h to 2955±341 bacteria/mm 2 at 8 h. Fitted with the exponential curve, the number of bacteria in this case doubled every 35 min, which compares to the 31 min required by bacteria to double on the surface of bare GaAs. Thus, the similar growth rates of bacteria on bare GaAs and Au samples indicate that GaAs was no more inhibitory to the growth of E. coli bacteria than Au for the biochips placed on nutrient agar Petri dishes inoculated with bacteria.

Fig. 7

 7 Fig. 7 Time dependent surface density of E. coli bacteria immobilized on bare and b-PEG-NA-b-Ab functionalized surfaces of GaAs (001) (a) and on bare Au surfaces compared to those of bare GaAs (b). Each experiment was repeated in triplicate to obtain the mean values with standard deviation.

1 N 2 NTFig. 8

 128 Fig. 8 Growth of E. coli on GaAs biochips functionalized with EDC/NHS-Ab (a), and EDC/NHS without antibody (b), detected by measuring initial (after 30 min exposure to a bacterial suspension) and final (after 4.5 h in LB) bacterial surface coverage for different concentrations of bacteria. Standard deviations were calculated based on experiments repeated in triplicate.

Fig. 9

 9 Fig. 9 Examples of microscopic images of E. coli K12 bacteria immobilized on the MHDA-EDC/NHS-Ab functionalized surface of GaAs (001) exposed for 30 min to a 10 6 CFU/mL solution (a), and after 4.5 h exposure to a growth medium (b). The scale bars correspond to 10 µm.

Table 1

 1 Growth indices of bacteria on functionalized surfaces of GaAs (001) for different bacterial concentrations.

	Bacterial

concentration (CFU/mL) Growth index with EDC/NHS-Ab capture method (min -1 ) Growth index with EDC/NHS capture method (min -1 ) 10 5

	10 6 10 7 10 8	0.0157± 0.0010 0.0231±0.0003 0.0213±0.0006 0.0287±0.0056	0.0148±0.0000 0.0180±0.0009 0.0160±0.0008 0.0180±0.0011

Acknowledgements

We thank Dr. Khalid Moumanis and the technical staff of the Interdisciplinary Institute for Technological Innovation (3IT) for their assistance. We are also indebted to Dr.

François Malouin of the Department of Biology, Université de Sherbrooke for kindly supplying E. coli K12.

Funding

This work was supported by the Canada Research Chair in Quantum Semiconductors Program (Grant No 950-220304) and the Fonds de recherche Nature et Technologie du Québec (FRQNT) project (Grant number 2015-PR-184056).

Abbreviations


Amélie Aussel
email: amelie.aussel@loria.fr

Laure Buhry

Louise Tyvaert

Radu Ranta

Keywords: Hippocampal oscillations, Conductance-based neurons, Sleep-wake cycle, Sharp-Wave Ripples, Theta-nested gamma oscillations, Acetylcholine

come

A detailed anatomical and mathematical model of the hippocampal formation for the generation of sharp-wave ripples and theta-nested gamma oscillations

Amélie Aussel, Laure Buhry, Louise Tyvaert, Radu

A detailed anatomical and mathematical model of the hippocampal formation for the generation of Sharp-Wave Ripples and Theta-nested Gamma oscillations

Introduction

The hippocampus can exhibit different oscillatory rhythms within the sleep-wake cycle, each of them being involved in cognitive processes. For example, theta-nested gamma oscillations, consisting of the coupling of theta (4-12Hz) and gamma (40-100Hz) rhythms, are produced during wakefulness and are associated with spatial navigation and working memory tasks ([O' Keefe and Recce, 1993], [START_REF] Axmacher | Cross-frequency coupling supports multi-item working memory in the human hippocampus[END_REF]), whereas Sharp-Wave-Ripple (SWR) complexes, consisting of fast oscillatory events occurring during low frequency waves (≤ 0.5Hz), are produced during slow-wave sleep and quiet waking and play an important role in memory consolidation ( [START_REF] Girardeau | Hippocampal ripples and memory consolidation[END_REF], [Buzsáki, 2015]). Models exist to reproduce and explain the generation of each of these rhythms individually: for Sharp-Wave Ripples, see [START_REF] Taxidis | Modeling sharp wave-ripple complexes through a ca3-ca1 network model with chemical synapses[END_REF] or [START_REF] Traub | A model of high-frequency ripples in the hippocampus based on synaptic coupling plus axon-axon gap junctions between pyramidal neurons[END_REF] and for theta-nested gamma oscillations, see [START_REF] Pastoll | Feedback inhibition enables theta-nested gamma oscillations and grid firing fields[END_REF], [Fukai, 1999], or [START_REF] Bartos | Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks[END_REF]. However, to the best of our knowledge, there is at the moment no model capable of generating both rhythms and functionally switching between them.

The transitions between these rhythms suggest a change in the functional connectivity of the hippocampus. Some authors ( [Hasselmo, 1999], [START_REF] Platt | The cholinergic system, {EEG} and sleep[END_REF], see also [START_REF] Tiesinga | Computational model of carbachol-induced delta, theta, and gamma oscillations in the hippocampus[END_REF]) propose that this phenomenon may be due to a neuromudulator, Acetylcholine (Ach), whose concentration is higher during active wakefulness than sleep, modulating synaptic transmissions. Ach concentration can also vary rapidly during wakefulness (see [START_REF] Ruivo | Coordinated acetylcholine release in prefrontal cortex and hippocampus is associated with arousal and reward on distinct timescales[END_REF] and [START_REF] Sarter | Phasic acetylcholine release and the volume transmission hypothesis: time to move on[END_REF] for studies in rodents), and therefore it could also possibly account for the SWRs that are seen in quiet awake individuals [START_REF] Foster | Reverse replay of behavioural sequences in hippocampal place cells during the awake state[END_REF]). But though we understand the influence of Ach on individual cells for different receptor types and locations [START_REF] Drever | The cholinergic system and hippocampal plasticity[END_REF]), its quantitative effects on the whole hippocampal network remain unclear.

In this context, we have built a computational model of the hippocampal formation that exhibits characteristic rhythms of wakefulness and slow-wave sleep, considering the varying concentration of Ach. In order to simulate the complete hippocampal formation, our model uses point neural models (single-compartment) but having realistic dynamics (conductance-based Hodgkin-Huxley neurons). Among these neurons, some have one of the membrane channel's conductance directly linked to the level of Ach (CAN, see [START_REF] Giovannini | The can-in network: A biologically inspired model for self-sustained theta oscillations and memory maintenance in the hippocampus[END_REF]). The microscopic anatomy of the neurons was approximated by two compartments (the simplest shape able to generate a relatively realistic LFP through a dipolar electric field [START_REF] Pettersen | Extracellular spikes and csd[END_REF]), while the macroscopic anatomy of the hippocampal structure was reproduced by positioning and connecting the neurons in an anatomically realistic manner. Based on the model proposed in [Hasselmo, 1999], the network's functional connectivity was changed between wakefulness and slow-wave sleep. Moreover, the stimulation entry of the network was derived from real sEEG measurements recorded during wake/sleep in the human prefrontal cortex (projecting on the entorhinal cortex). In order to compare our results with in vivo signals from the human hippocampus, we also simulated the signals recorded by a realistic macroscopic sEEG electrode placed within the network.

Our main finding is that our model can indeed reproduce both theta-nested gamma oscillations and SWR complexes in humans by changing the level of Ach, with but little influence of the input stimulus. The network connectivity seems to determine the high frequency component of the rhythms, whereas individual neurons channel conductance seem to determine its low frequency component.

In the following section, we describe our model in terms of individual neuron equations, synapses, topology, and electrode simulation, and we highlight the connectivity parameters that were changed to represent slow-wave sleep and wakefulness. We then present and analyze the oscillatory patterns we obtain.

Materials and Methods

Experimental data

The LFP data we used was obtained from a patient suffering from refractory epilepsy, implanted with intracranial electrodes for surgery planning at the Neurology Service of the University Hospital (CHU) from Nancy, France. The patient gave his informed consent and the study was approved by the ethics committee of the hospital. The SEEG electrodes (Dixi Medical R , France) had a diameter of 0.8mm, with 2mm-long contacts and 1.5mm inter-contact distance. The patient was notably implanted in the prefrontal cortex, the temporal lobe and the hippocampus (see Figure 1 for an MRI image of the implatation of an electrode in the hippocampus), but the epileptogenic zone was located in another region. The position of the electrodes in the patient's brain was automatically ascertained using a procedure described in [START_REF] Hofmanis | Automatic depth electrode localization in intracranial space[END_REF].

Signals were recorded using Micromed R , Italy acquisition system. The sampling frequency was 1024 Hz. All signals were labelled by a neurologist to identify the different stages of the sleep-wake cycle (based on EEG signal) as well as to exclude any epileptic phenomena from the data (interictal or seizures). Therefore we assumed that, when no seizure or epileptic spike occurred, the signals from these regions were similar to that of healthy people. We used signals from wakefulness and slow-wave sleep states.

Computational model

Neuron dynamics models

The neurons in our network were simulated using a single compartment conductancebased model derived from Hodgkin-Huxley's ([Hodgkin and Huxley, 1952]). The temporal evolution of each neuron membrane potential V m followed a differential equation of the form:

C m dV m dt = -I leak - I channel -I syn E -I syn I + η (1)
where I leak is a leakage current, each I channel is the membrane current associated with the ion channel channel, I syn E and I syn I are the excitatory and inhibitory synaptic input to the cell, respectively, and η is a random gaussian noise accounting for unknown entries.

Our principal excitatory neurons were pyramidal cells modelled with the following ion channels: fast sodium (I N a ), potassium (I K ), low-threshold calcium current (I Ca ), and potassium M-current (I M ) . Some pyramidal cells were also added a Calcium-Activated-Nonspecific (CAN) cationic channel, with corresponding current I CAN . In the following, these two types of pyramidal cells are referred to as non-CAN and CAN respectively. Interneurons were modelled with the following ion channels : fast sodium (I N a ), and potassium (I K ).

The complete expressions for all these ionic channel currents are detailed in [START_REF] Giovannini | The can-in network: A biologically inspired model for self-sustained theta oscillations and memory maintenance in the hippocampus[END_REF].

The leakage currents obey the following equation :

I leak = (g leak × A) × (V m -E leak ) (2)
where g leak is the maximum leaking conductance, A is the area of the neuron membrane and E leak is the channel reversal potential. The I K , I M and I CAN currents follow a set of equations of the form :

I channel = (g channel × A) × m k × (V m -E channel ) (3)
where m is a gating variable defined by :

dm dt = m ∞ -m τ m
For I K and I CAN , the m ∞ and τ m parameters depend on two functions α m and β m :

m ∞ = α m α m + β m τ m = 0.2 α m + β m
Similarly, the I N a and I Ca currents follow a set of equations of the form :

I channel = (g channel × A) × m k × n × (V m -E channel ) (4)
with two gating variables m and n, such as :

dm dt = m ∞ -m τ m dn dt = n ∞ -n τ n m ∞ = α m α m + β m n ∞ = α n α n + β n τ m = 0.2 α m + β m τ n = 0.2 α n + β n
0.1mS/cm 2 E leak -90mV g K 9mS/cm 2 E K -65mV k K 4 α m,K 0.01 V M +34mV 1-e -0.1(V M +34mV ) β m,K 0.125 e -V M +44mV 80mV g N a 35mS/cm 2 E N a 55mV k N a 3 α m,N a 0.1 V M +35mV 1-e -0.1(V M +35mV ) β m,N a 4 e -V M +60mV 18mV α n,N a 0.07 e -V M +58mV 20mV β n,N a 1 e 1-0.1 * (V M +28mV )
Finally the gating variable of I CAN depends on the calcium concentration inside the neuron, [Ca] 2+ i , defined by :

d[Ca] 2+ i dt = γ(I Ca ) + ([Ca] 2+ ∞ -[Ca] 2+ i ) τ [Ca] 2+ γ(I Ca ) = -k u × I Ca 2 × F × depth × A
where τ [Ca] 2+ = 1s represents the rate of calcium removal from the cell, [Ca] 2+ ∞ = 0.24mol/L is the calcium concentration if the calcium channel remains open for a duration ∆ T → ∞, k u = 10 4 is a unit conversion constant, F is Faraday's constant and depth = 1µm is the depth at which the calcium is stored inside the cell.

The amplitude of the noise η (Equation 1) simulating random unknown inputs to our network was set to 500pA.

The full expression of all the parameters defined here can be found in Table 1 and Table 2 for interneurons and pyramidal neurons, respectively.

Synaptic models

The interactions between neurons were modelled as AMPA and GABA-A synapses, with I syn E and I syn I currents for excitatory and inhibitory connections respectively. These currents are described by the following bi-exponential differential equations:

I syn I,E = g I,E (V m -E I,E ), ( 5
) dg I,E dt = (-g I,E + h I,E ) 1 τ g I,E , dh I,E dt = -h I,E 1 τ h I,E
. Whenever a pre-synaptic spike occurs, the value of g I or g E in the post-synaptic neuron is increased by a fixed amount g max E or g max I .

0.01mS/cm 2 E leak -70mV g K 5mS/cm 2 E K -100mV k K 4 α m,K -0.032 V M +40mV e -1-0.2(V M +40mV ) β m,K 0.5 e -V M +45mV 40mV g N a 50mS/cm 2 E N a 50mV k N a 3 α m,N a -0.32 V M +42mV e - V M +42mV 4mV -1 β m,N a 0.28 V M +15mV e - V M +15mV 5mV -1 α n,N a 0.128 e -V M +38mV 18mV β n,N a 4 1+e - V M +15mV 5mV g M 90µS/cm 2 E M -100mV k M 1 m ∞,M 1 1+e - V M +35mV 10mV τ m,M 1 3.3e V M +35mV 20mV +e - V M +35mV 20mV g Ca 0.1mS/cm 2 E Ca 120mV k Ca 2 α m,Ca -0.055 V M +27mV e - V M +27mV 3.8mV -1 β m,Ca -0.94 e V M +75mV 17mV α n,Ca -0.000457e V M +13mV 50mV β n,Ca 0.0065 e - V M +15mV 28mV +1 g CAN 25µS/cm 2 E CAN -20mV k CAN 2 α m,CAN 0.0002 • 3 1.4 [Ca] 2+ i 0.5mol/L β m,CAN 0.0002 • 3 1.4
The values of the synaptic resting potentials E I and E E , and the synaptic time constants of rise and decay τ g E , τ h E , τ g I and τ h I are summed up in Table 3.

Anatomical modelling

At the macroscopic level, our network is composed of two different structures: one representing the hippocampus, and the other representing the entorhinal cortex.

The hippocampus itself is divided into three substructures: the dentate gyrus, CA3 and CA1. A 10:1 ratio between pyramidal neurons and interneurons, as reported in [START_REF] Jinno | Stereological estimation of numerical densities of glutamatergic principal neurons in the mouse hippocampus[END_REF] for dorsal hippocampus, was respected in all regions but the dentate gyrus . The same 10:1 ratio was used between the total number of neurons in CA1 and the total number of neurons in CA3, as reported in humans in [START_REF] West | Unbiased stereological estimation of the number of neurons in the human hippocampus[END_REF].

As for the dentate gyrus, we considered a ratio 100:1 ratio between the pyramidal cells and the interneurons, because of the higher proportion of excitatory cells compared to inhibitory cells in this structure ( [START_REF] Patton | Connection matrix of the hippocampal formation: I. the dentate gyrus[END_REF], [START_REF] Jinno | Stereological estimation of numerical densities of glutamatergic principal neurons in the mouse hippocampus[END_REF]). The number of excitatory cells as well as interneurons are summed up in Table 4. CAN pyramidal neurons were used in the entorhinal cortex, CA3 and CA1, while non-CAN neurons were used in the dentate gyrus.

As our goal is to model realistically the population's extracellular recordings, the position of the entorhinal cortex and the hippocampal structures and the different types of neurons within them were chosen in accordance with human anatomy. A 15mm-thick layer of the hippocampal formation was reproduced in this way, with pyramidal neurons uniformly distributed within the stratum pyramidale (or within the stratum granulosum for the dentate gyrus), and interneurons uniformly distributed within the stratum oriens. For each pyramidal neuron, its projection on the stratum moleculare was also computed as an estimation of the position of its apical dendrites (Figure 2), and thus the orientation of the (neural) elementary dipole used for generating the extracellular recordings. In other words, at the cellular level, the detailed geometry of the pyramidal neurons was simplified to simple current dipoles [START_REF] Pettersen | Extracellular spikes and csd[END_REF]. Moreover, as interneurons contributions to the LFP are very small [START_REF] Mazzoni | Computing the local field potential (lfp) from integrate-and-fire network models[END_REF], their microscopic geometry was neglected (point neurons).

Structural connectivity

As it is commonly accepted that the hippocampal formation receives most of its external inputs through the entorhinal cortex, only these neurons receive external stimulation in our model ( [START_REF] Andersen | The hippocampus book[END_REF]). From this region, the neural activity propagates in the hippocampus through the so-called "tri-synaptic way", going from the entorhinal cortex to the dentate gyrus, from the dentate gyrus to CA3, from CA3 to CA1, and finally from CA1 back to the entorhinal cortex. Fewer connections are also made from the entorhinal cortex directly to CA3 and CA1 ( [START_REF] Andersen | The hippocampus book[END_REF]). The connection probability of any two neurons from different regions is summed up in Table 5.

On the other hand, and as was also done in [START_REF] Taxidis | Modeling sharp wave-ripple complexes through a ca3-ca1 network model with chemical synapses[END_REF], the connection probability p between any two neurons within the same region depends on the distance D between them, following a gaussian-like distribution : p = A.e -D 2 2σ 2 . The width σ of this distribution was set to 2500µm for pyramidal cells, in accordance with [START_REF] Ropireddy | Axonal morphometry of hippocampal pyramidal neurons semi-automatically reconstructed after in vivo labeling in different ca3 locations[END_REF] (which states that hippocampal pyramidal cells make half of their connections within 1.3-1.7mm), and to the value of 350µm for interneurons, in accordance with the values reported in [START_REF] Freund | Interneurons of the hippocampus[END_REF] for hippocampal basket cells (which states that the transverse extent of their axon is between 900 and 1300 µm). The connection probability distributions for each region are then characterized by the probability A of two neurons within a distance D close to zero to be connected, summed up in Table 6 (Sources : [START_REF] Couey | Recurrent inhibitory circuitry as a mechanism for grid formation[END_REF], [START_REF] Patton | Connection matrix of the hippocampal formation: I. the dentate gyrus[END_REF], [START_REF] Taxidis | Modeling sharp wave-ripple complexes through a ca3-ca1 network model with chemical synapses[END_REF], [START_REF] Larimer | Nonrandom local circuits in the dentate gyrus[END_REF], [START_REF] Debanne | Physiology and pharmacology of unitary synaptic connections between pairs of cells in areas ca3 and ca1 of rat hippocampal slice cultures[END_REF], [START_REF] Knowles | Local circuit synaptic interactions in hippocampal brain slices[END_REF]. Note that parameters come from experiments on human or rat hippocampus depending on the availability of the data). Note that the synaptic connectivity within and between different structures of our network is concordant with the two-step memory process described by Hasselmo in [Hasselmo, 1999] for wakefulness and slow-wave sleep.

Network input

In order to represent inputs from the rest of the brain, each of the entorhinal cortex neurons is driven by a Poisson input whose variable firing rate is drawn from the envelope of the real sleep/wake SEEG signals measured in the prefrontal cortex, the lateral temporal lobe and the temporal pole.

More precisely, three groups of 10000 Poisson neurons were defined : each of their firing rates was obtained by first high-pass filtering the LFP from one of these regions above 5Hz, then taking its absolute value, and finally scaling it to a 0-200Hz range. Each of the Poisson neuron group was connected to the entorhinal cortex region with a uniform probability of 0.01 through excitatory synapses with the same conductance as above.

The inputs to the network are later referred to as "wakefulness inputs" or as "slow-wave sleep inputs" (or shortly "sleep inputs") depending on whether SEEG signals from awake or deeply sleeping states were used to compute the input of the network.

Network output: extracellular recordings

The analysed output is the extracellular potential generated by the network, both at microscopic and at macroscopic scales.

The modelling of the LFP follows the approach proposed in [START_REF] Mazzoni | Computing the local field potential (lfp) from integrate-and-fire network models[END_REF]. More precisely, the potential in every point in space was approximated by a weighted sum of the synaptic currents arriving at each pyramidal neuron, and neglecting the influence of the interneurons. Considering the neurons as dipoles, the contribution of a neuron of length L to the extracellular potential at any point in space, at a distance r and an angle θ from the midpoint of the neuron (see Figure 3), writes as:

U = L cos θ 4πσr 2 (I syn E + I syn I ) (6)
where σ = 0.3 S/m is the conductivity of the extracellular medium, which we considered homogeneous. The LFP at one point is the sum of the contributions from all the pyramidal neurons in the entorhinal cortex and the hippocampus (dentate gyrus, CA3, and

CA1

). In order to model the signal recorded by the macroscopic electrode and to compare it with real patient recordings, we averaged the LFP on two sets of 144 points evenly distributed on a cylinder of diameter 0.8mm going through the network, each of them representing a 2mm-long contact, separated by 1.5mm (as was also done in [START_REF] Cosandier-Rimele | A physiologically plausible spatio-temporal model for eeg signals recorded with intracerebral electrodes in human partial epilepsy[END_REF]), and computed the difference between the two resulting signals (see figure 2).

Similarly to what is done by our intracranial EEG recording system, the simulated LFP was also bandpass filtered between 0.15Hz and 480Hz and downsampled to 1024Hz.

Simulation

The aim of this work is to test three main hypotheses for explaining the sleep/wake variations of the signals recorded inside the human hippocampal formation, two of which are directly linked to the concentration of Ach in the system.

1. The role of the synaptic connectivity: The varying concentration of Ach between wakefulness and slow-wave sleep modulate the synaptic interactions between and within hippocampal subregions. According to [Hasselmo, 1999], high Ach concentration during wakefulness reduces synaptic interactions from CA3 to CA1 and back to the entorhinal cortex, thus promoting short-term memory storage in CA3, and conversely the low concentration of Ach during sleep strengthen these connections and promotes long-term memory formation in the neocortex. More precisely, due to the presence of nicotinic and muscarinic receptors on hippocampal neurons, it has been shown that some synaptic connections are enhanced by a high Ach concentration, such as the inhibitory connections within the dentate gyrus and CA1 ( [START_REF] Jones | Functional nicotinic ach receptors on interneurones in the rat hippocampus[END_REF], [START_REF] Frazier | Acetylcholine activates an α-bungarotoxin-sensitive nicotinic current in rat hippocampal interneurons, but not pyramidal cells[END_REF]), or the excitatory connections from the dentate gyrus ([Cheng and Yakel, 2013], [START_REF] Gray | Hippocampal synaptic transmission enhanced by low concentrations of nicotine[END_REF]), while others are reduced, such as the excitatory connections from the entorhinal cortex ( [START_REF] Heys | Effects of acetylcholine on neuronal properties in entorhinal cortex[END_REF]) or CA3 ( [START_REF] Herreras | Sensory modulation of hippocampal transmission. ii. evidence for a cholinergic locus of inhibition in the schaffer-ca1 synapse[END_REF]). In our simulations, after having tested different sets of parameters, we chose to model this effect by multiplying or dividing by a factor f = 3 the conductance g max E or g max I of these connections to represent higher Ach concentration during wakefulness. These two connectivity settings, summed up in Figure 4, will be called later on in this article "slow-wave sleep connectivity" and "wakefulness connectivity". It is worth noting that other biological mechanisms apart from the varying concentration of Ach could also cause changes in the functional connectivity during the sleep-wake cycle, such as synaptic plasticity ( [START_REF] Tononi | Sleep function and synaptic homeostasis[END_REF]) or differential activity of distinct interneurons subtypes ( [START_REF] Gan | Phase-locked inhibition, but not excitation, underlies hippocampal ripple oscillations in awake mice invivo[END_REF]). 2. The role of CAN currents : As presented in [START_REF] Yoshida | Cholinergic modulation of the can current may adjust neural dynamics for active memory maintenance, spatial navigation and time-compressed replay[END_REF], Ach also plays a key role in the activation of CAN currents in hippocampal pyramidal cells. To account for the low concentration of Ach during slow-wave sleep, we chose to divide by 50 the maximum conductance g CAN of this channel in the corresponding simulations. 3. The role of the input : The last possible factor inducing sleep wake variations that we are investigating here is the (glutamatergic) input of the hippocampal network. Indeed, the inputs the hippocampal formation receives from its afferent structures also vary between wakefulness and sleep, as the whole brain exhibits different oscillatory rhythms. Therefore we chose to change the input stimulation to our network accordingly, by basing it on measured LFP signals measured in the patient's brain either during wakefulness or slow-wave sleep (see Section 2.2.5). Please note that cholinergic inputs (from the medial septum for example) are only represented by changing the two other settings (functional connectivity and CAN currents), and that other non-glutamatergic inputs are not directly modeled here.

All the simulations were performed using the Brian2 libraries for Python ( [START_REF] Stimberg | Equation-oriented specification of neural models for simulations[END_REF]), on the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).

Analysis of the real and simulated signals

Meaningful events were located in the simulated signals with a method close to that of ( [START_REF] Taxidis | Modeling sharp wave-ripple complexes through a ca3-ca1 network model with chemical synapses[END_REF]). First, the root mean square (RMS) of the signal was computed using 10ms-long time windows with no overlap, and its standard deviation (SD) was derived from its whole length. Portions of signal where the RMS was greater than 2xSD, with a peak above 4xSD, were considered as events.

The spectrum of all the events was then analyzed to determine their peak frequency and to identify the type of oscillatory patterns: in the following sections, all filters applied to the signals are Butterworth filters of order 2.

The distribution of the peak frequencies in the different simulations performed were compared using WilcoxonMannWhitney tests (with the purpose of avoiding making assumptions on the shape of the distributions).

In the real SEEG signals, a similar procedure was used to detect SWR, except that the RMS was computed from the 120-250Hz bandpass filtered signal and only events when the peak RMS was above 6xSD were considered.

Results

Network Topology influences the measured LFP

One of the original contributions of this work is the use of an approximation of the real anatomy of the simulated systems. Therefore, regardless and previous to any sleep/wake analysis, one of our first concerns was to check what could be the benefits of using a anatomically realistic topology and connectivity compared to, say, a random one.

Figure 5 and Figure 6 present the simulated LFP with slow-wave sleep and wakefulness parameters respectively in 3 different networks: a first network with topology and connectivity as defined in Section 2, a second network with the same topology but a uniform rather than distance-related connectivity, and a third network where the connectivity was kept but where each structure's topology was replaced with a simple rectangular-shaped column. Other parameters were kept the same across simulations.

What can be seen is that both topology and connectivity influence the results of the simulations for slow-wave sleep parameters. Sharp-wave ripples-like events (see Section 3.2) can only be seen with a distance-related connectivity and not with uniform connectivity. The events obtained with the full topology are closer to the frequency of sharp-wave ripples reported in the literature (see [Buzsáki, 2015]), while those obtained with a simplified topology lie within the gamma band (and there is proportionally more power in the theta and gamma bands compared to the ripple band in this case). Power (V²) D Fig. 5 Comparison of the simulated LFP for slow-wave sleep, with the following topology and connectivity : (a) full topology and distance-related connectivity, (b) full topology but uniform connectivity, and (c) simplified topology and distance-related connectivity. A: 10-second LFP traces for each conformation. B: Peak frequency of the detected events in each LFP simulations, for each conformation, with mean and SD. Statistical comparison shows significant difference between each case (p < 10 -3 ). C: Frequency of occurrence of the events for each conformation, with mean and SD. D: Power in in the oscillations in the Ripple (120-200Hz, yellow), Gamma (30-100Hz, green) and Theta (5-10Hz, blue) frequency bands, with mean and SD, for each conformation.

On the other hand, theta and gamma oscillations can be obtained with all the three networks, though the temporal aspect of the simulated signal is modified by changing either the connectivity or the topology.

A possible explanation as for why the topology and connectivity can affect so much the resulting simulations in the slow-wave sleep case is that it changes the number and sizes of interconnected neuronal clusters and therefore without a detailed topology it is hard to get the same kind of neural synchronization as seen during sharp-wave ripple complexes. To a lesser extent, changing the position of the neurons and their orientation when changing the topology also affects the resulting signal as it affects the way neural activities are summed up when computing the LFP seen by the electrode.

Sharp Wave-Ripples complexes appear with Slow-Wave Sleep parameters

With slow-wave sleep connectivity, slow-wave sleep inputs, and reduced CAN currents, large amplitude events can be seen on the simulated electrode every few seconds (11 events in a typical one-minute-long simulation, with mean duration 156ms), as the one shown on figure 7. Band-pass filtering them between 30 and 400Hz reveals an oscillatory pattern with peak frequency at 161Hz (SD: 9Hz) (see also Figure 13), which is consistent with the literature on sharp-wave ripple complexes for in vivo recordings ( [Buzsáki, 2015]).

The ripples in the simulation also appear to happen with a timing close to that of the sharp-waves ripples in the LFP recorded in the patient's hippocampus, as shown in Figure 8. In ten one-minute-long signals, 228 SWR were found in the measured LFP and 235 in the corresponding simulations. 62% of the simulated events were located within 1 second of a SWR in the corresponding measured signal, the simulated SWRs occurring in average 220ms before a measured SWR (SD:1.8s).

The raster plot and population coherence measure of the different regions reveals that the sharp-wave ripples seen on the LFP come from a synchronized activity of CA1 pyramidal cells that is initiated by a strong inhibitory input from the interneurons in CA3 (followed by excitation from CA3 and then strong inhibition in CA1 itself). During the ripple, interneurons in CA1 and CA3 are relatively silent, and only get strongly synchronized again around 100ms later, possibly causing the termination of the ripple (this inhibitory activity originates from the Dentate Gyrus). This activity is similar to what has been reported for O-LM interneurons in particular (see [START_REF] Somogyi | Temporal redistribution of inhibition over neuronal subcellular domains underlies state-dependent rhythmic change of excitability in the hippocampus[END_REF]). The evolution of a coherence measure of the CA3 and CA1 regions during a ripple (computed as in [START_REF] Wang | Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model[END_REF] on sliding windows of width 50ms with 75% overlap) is shown on Figure 9.

However, almost all of the CA1 pyramidal neurons fire during each of these events, therefore it does not fully respect what was reported in the literature, as in [START_REF] Nádasdy | Replay and time compression of recurring spike sequences in the hippocampus[END_REF]. The direction of the propagation of the ripples in CA1, as well as their original location, varies between events (figure not shown), in accordance with [START_REF] Patel | Local generation and propagation of ripples along the septotemporal axis of the hippocampus[END_REF].

The spectrum of the simulated signal is quite similar to that of the SEEG signal measured in the hippocampus during slow-wave sleep, though the simulated signal shows a stronger power density in the ripple frequency band (see Figure 12). This could be explained by the fact that our simulated neurons only model a small layer of the hippocampus where CA1 pyramidal cells almost all get involved in the SWRs and get highly synchronized, and therefore our simulations don't show enough noise and power in other frequency bands. Also, we do not include in our simulation the LFP generated by neighboring structures and propagated through the extracellular medium, which could increase the energy in the low frequencies of the LFP and therefore could compensate for the apparent high frequency peak that we observe in our simulations.

Theta-nested Gamma Oscillations appear with Wakefulness parameters

Switching the network parameters to the wakefulness ones gives rise to different oscillatory rhythms. Indeed, when applying a similar method of event detection as for slow-wave sleep, that is when looking for portions of the signal with RMS significantly above its standard deviation (see Section 2.3.1), it can be seen that the events' peak frequency is shifted towards the gamma range (53Hz, SD 32Hz). Also, the signal now presents lower frequency oscillations, with a peak in its power spectral density around 7Hz, which corresponds to the theta frequency band (see Figure 10).

More precisely, power in the gamma frequency band (30-100Hz) is mostly located around the peak of the theta oscillations (see Figure 11). On the other hand, the frequency of the gamma oscillations doesn't change significantly depending on the phase of the theta oscillations.

The spectrum of the simulated signal is similar to that of the measured SEEG in the hippocampus (see Figure 12), though it has more power in the theta frequency band, possibly for the same reasons as the one explained earlier in Section 3.2.

Factors influencing the sleep-wake oscillatory rhythms

After having confirmed that slow-wave sleep and wakefulness parameters (input, CAN current and functional connectivity) were associated with sharp-wave ripples and theta-nested gamma oscillations respectively, we tried to modify each of them individually to analyze their influence. Note that among these parameters, two are continuously varying (functional connectivity gain f and CAN channel conductance g CAN , while the third one is binary (sleep/wake input).

A first analysis can actually be done by binarizing all three factors. As we have determined the most plausible values that generate either sleep rhythms (i.e. SWR) or wake rhythms (theta-gamma oscillations), we can choose the respective values for the connectivity gain and the CAN conductance (f={1, 3} and g CAN = {0.5, 25}µS). These values are designated in the following by sleep (f = 1, g CAN = 0.5) and wake (f = 3, g CAN = 25) respectively.

As it can be seen in Figures 13, the high frequency component of the oscillations depends mostly on the functional connectivity, with little effect from the CAN current and almost no effect from the input: slow-wave sleep connectivity produces events within ripple frequency range, while wakefulness connectivity produces peak frequencies within the gamma band. The input type (sleep/wake) does not significantly change these peak frequencies. The CAN conductance has a slightly more important effect, sufficient for changing the peak frequency when the connectivity is low (sleep connectivity). Similar results can also be seen on Figure 14, as whenever the connectivity is set to slow-wave sleep, there is more power in the ripple band than in the gamma band and conversely with wakefulness connectivity. The CAN currents increase the overall power in the signal in every parameter set, and also increase the frequency of occurrence of SWRs seen with slow-wave sleep connectivity, from 0.3Hz (SD 0.1Hz) to 1.6Hz (SD 0.1Hz) with sleep inputs and from 0.13Hz (SD 0.04Hz) to 1.25Hz (SD 0.4Hz) with wakefulness inputs (in each case the p-value is less than 0.01). The power of the signals are much higher with slow-wave sleep connectivity than with wakefulness connectivity, which may be due to the very high neuronal activity seen during our simulated SWRs.

In order to asses more precisely the effect of the CAN conductance variations, we have also modified it gradually between the two extreme values (see Figure 17, left panel; recall that the on/off CAN current labels in Figure 13 correspond to the most extreme cases in Figure 17).

Figure 13 indicates that functional connectivity is the most important factor for changing the peak frequency. The natural question which arises is if this change in the peak frequency is gradual when we vary the connectivity gain f or if there is a switch at some point. This is explored in Figure 15 (left panel). As it can be seen, the peak frequency varies rather continuously with the connectivity, but nonlinearly. Small values of f ensure the generation of ripples, while values greater than 1.5 lower the peak frequencies into the gamma band. For conciseness, we present here the dependency of the peak frequency with f for fixed values of the CAN conductance (to one of the extreme values, namely wake) and the input (wake also), but the results are similar for other combinations.

The low frequency part of the simulated signals seems to be influenced differently by these three factors. Indeed, low-passing the signals below 20Hz and looking at the highest frequency peak in their spectrum shows that the low frequency component of the oscillations seems to be influenced mostly by the CAN current, with smaller effect from the input or the connectivity (see Figure 16). High CAN current (g CAN ≥ 25µS/cm 2 , see Figure 17, right panel) is a sufficient condition for the oscillations to reach the theta band. Similar results can be obtained even if the CAN current is high only in the CA1 and CA3 neuron populations and not in the entorhinal cortex. On the contrary, varying the functional connectivity alone (while maintaining the input and the CAN conductance in wake states) does not significantly alter the low frequency part of the simulated signals (see Figure 15, right panel). Still, theta oscillations can also be generated in the absence of a high CAN current (which thus is not a necessary condition), if both connectivity and input are in the wake state. If one of them (or both) are in the sleep state, the low frequency part remains below the inferior bound of the theta band.

Discussion

In this work, we built a computational model of the hippocampus capable of reproducing both slow-wave sleep sharp-wave ripples and wakefulness theta-nested gamma oscillations. This models takes advantage of a realistic network topology and synaptic connectivity, and includes effects on individual neurons and functional connectivity that are coherent with the varying concentration of Acetylcholine over the sleep-wake cycle. Overall, it is consistent with the theory from [Hasselmo, 1999] stating that Ach could be an important factor in the changes of rhythms observed in the hippocampus in the context of the two-stage model of memory formation. However it should be noted that other mechanisms might be at work than Ach modulation, leading to similar effects (especially regarding the synaptic connectivity).

Our results suggest that the high frequency component of hippocampal oscillations might be governed mostly by network connectivity, whereas the low frequency components could result from individual neuron channel properties. A possible consequence of this idea is that higher frequency, pathological oscillations that are seen in the epileptic hippocampus for example (fast ripples or seizures) might also emerge from an abnormal functional connectivity of the system rather than individual neuron properties. An interesting point to raise is that the glutamatergic inputs given to the network seemed to have little to no influence on the frequency of our model's oscillations, which could indicate that the hippocampus doesn't need an external "pacemaker" such as the medial septum to set its rhythms, but it has its own internal pacemaker, the CAN neurons (for more arguments on that topic, see for example [START_REF] Hangya | Gabaergic neurons of the medial septum lead the hippocampal network during theta activity[END_REF], [START_REF] Kang | Theta-rhythmic drive between medial septum and hippocampus in slow-wave sleep and microarousal: a granger causality analysis[END_REF] or [Buzsáki, 2002]). Still, the external influence cannot be excluded, as our model predicts that theta oscillations can also be generated by the correct combination of the inputs and functional connectivity, as mentioned in the previous section. On the other hand, the inputs seem to influence the timing at which oscillations are generated, which could account for signal encoding, particularly during wakefulness. On portions of the signals, the simulation even showed some similarities with the measurements in the temporal domain and not only in the frequency domain (see Figure 8).

Similarly to what have been proposed by [START_REF] Taxidis | Modeling sharp wave-ripple complexes through a ca3-ca1 network model with chemical synapses[END_REF], our model was able to reproduce different rhythms, and sharp-wave ripples in particular, by using only chemical synapses (and therefore no axo-axonic gap junctions). This further supports the idea that gap junctions may not be necessary for generating high frequency oscillations in the hippocampus.

Finally, our work suggests that the topology of the hippocampal formation should be taken into account in order to improve existing computational models. In particular, such methods could produce a realistic SEEG signal estimation while keeping the simulation complexity low, by solving the differential equations for point neurons only and considering them as dipoles for calculating local field potentials.

Fig. 1

 1 Fig. 1 Coregistered CT-MRI image of the implantation of an SEEG electrode in the patient's hippocampus (coronal view).

Fig. 2

 2 Fig. 2 Topology of the entorhinal cortex and the hippocampus used in the model

Fig. 3

 3 Fig. 3 Diagram of the parameters L, r and θ used to compute the contribution of single neuron to the LFP.

Fig. 4

 4 Fig. 4 Synaptic connectivity for slow-wave sleep and wakefulness. Bold lines indicate increased connectivity, and dotted lines indicate decreased connectivity during wakefulness compared to slow-wave sleep

Fig. 6

 6 Fig.6Comparison of the simulated LFP for wakefulness, with the following topology and connectivity : (a) full topology and distance-related connectivity, (b) full topology but uniform connectivity, and (c) simplified topology and distance-related connectivity. A: 5-second LFP traces for each conformation. B: Peak frequency of the detected events in each LFP simulations, for each conformation, with mean and SD. Statistical comparison shows significant difference between each case (p < 10 -3 ). C: Peak frequency of the LFP filtered in the theta band (5-10Hz), for each conformation, with mean and SD.

Fig. 7

 7 Fig. 7 LFP simulated at the electrode during a ripple, and corresponding 120-250Hz bandpass filtered and 50 Hz lowpass filtered signals.

Fig. 8 AFig. 9

 89 Fig. 8 A : Comparison between the position of sharp-wave ripples in the simulation (red stars) and in the slow-wave sleep recordings of the hippocampus (green stars). The blue line corresponds to the simulated LFP, and the red line to the recorded one. B : Frequency of occurrence of the sharp-wave ripples in the measured and simulated LFP.

Fig. 11 Fig. 12

 1112 Fig. 10 LFP simulated at the electrode during theta-nested gamma oscillations, and corresponding 50-120Hz bandpass filtered and 12 Hz lowpass filtered signals.

Fig. 14 Fig. 15 Fig. 16

 141516 Fig.14Power in the oscillations in the Ripple yellow), green) and Theta (5-10Hz, blue) frequency bands in ten one-minute-long simulations with Sleep or Wakefulness stimulation, Sleep or Wakefulness connectivity, and presence or absence of CAN current, with mean and standard deviation.

Fig. 17

 17 Fig.17Influence of the CAN channel conductance g CAN (in µS/cm 2 ). In green, the value g CAN = 0.5µS/cm 2 corresponds to slow-wave sleep settings and g CAN = 25µS/cm 2 corresponds to wakefulness. Left: Distribution of the peak frequencies of events. Right: Distribution of the low frequency component of the signals (ten simulations in each case).

Table 1

 1 Parameter values of interneurons

	Parameter	Expression
	A	14.10 3 cm 2
	g leak

Table 2

 2 Parameter values of pyramidal neurons

	Parameter	Expression
	A	29.10 3 cm 2
	g leak

Table 3

 3 Parameter values of the biexponential synapses

	Synapse Type

Table 4

 4 Number of excitatory neurons (N E ) and interneurons (N I ) in each region

	Region

Table 6

 6 Maximum probability A of the synaptic connectivity within each region. EC: Entorhinal Cortex, DG: Dentate Gyrus. Py: Pyramidal neuron, In: Interneuron (the first two letters indicates the presynaptic neuron type while the second one indicates the post-synaptic neuron type).

		Py-Py	Py-In	In-Py	In-In
	EC	0	0.37	0.54	0
	DG	0	0.06	0.14	0
	CA3	0.56	0.75	0.75	0
	CA1	0	0.28	0.3	0.7

  Distribution of the peak frequencies of events in ten one-minute-long simulations with Sleep or Wakefulness stimulation, Sleep or Wakefulness connectivity, and presence or absence of CAN current, with mean and standard deviation (N indicates the number of events). Whenever a different connectivity is used, the peak frequency is significantly different (p < 10 -3 ). The number of studied events in each case isN=234, 967, 76, 750, 309, 218, 164 and 272 respectively. The dark blue points correspond to the same set of parameters chosen for the study of the influence of the connectivity in Fig 15.

		175
		150
	Peak frequency(Hz)	75 100 125
		50
		25
	input : connectivity : CAN current : 0	sleep sleep off	sleep sleep on	wake sleep off	wake sleep on	sleep wake off	sleep wake on	wake wake off	on wake wake
	Fig. 13

Information Sharing Statement

All the Python source files used for building the network and running the simulations are accessible on the ModelDB public repositories.