Maxime Vergès

Vinod Kumar

Po-Hung Lin

Stéphane Mangin
email: stephane.mangin@univ-lorraine.fr

Chih-Huang Lai

Affiliations

Role of induced exchange bias in zero field spinorbit torque magnetisation switching in Pt/[Ni/Co]/PtMn

Current induced magnetisation switching is of particular interest to develop non-volatile magnetic memories (MRAM). We studied spin orbit torque (SOT) switching in a Pt/ferromagnet/antiferromagnet Pt/[Co/Ni]2/PtMn Hall cross. For the as-deposited sample which showed no exchange bias effect, SOT switching is observed only under an in-plane applied field. In this case, when the in-plane applied field tends to zero, the current switching required diverges and the Hall voltage signal generated by the switching tends to zero. However, the same sample annealed under a perpendicular to the plane and then under an in-plane applied field demonstrated in zero magnetic field both square Hall voltage versus current hysteresis loops but also a moderate switching current. This procedure induces an out-of-plane exchange bias with strengthen Perpendicular Magnetic Anisotropy (PMA) and an in-plane exchange bias which induces zero field SOT switching. The study of the SOT switching for both annealing procedures as a function of the injected current and the in-plane field is shown. Those results could impact the design of future spintronics devices such as SOT-MRAM.

I. INTRODUCTION

Current-induced magnetisation switching studies allowed developing new spintronics devices such as Spin Transfer Torque (STT)-MRAM which are now on the market 1,2, 3 . Over the past 10 years, lots of attention has been focused on spin-orbit torque (SOT) that provides a reliable way to reverse magnetisation of ferromagnets (FM) 4, 5 . Indeed inplane charge current injected in heterostructures which exhibit both characteristic inversion structural asymmetry and significant spin-orbit interaction results in an out-of-plane spin current which generates a torque known as the SOT 6,7 . The SOT may have two components called damping-like torque and field-like torque which both interact with the FM magnetisation

8

. If the FM layer has Perpendicular Magnetic Anisotropy (PMA), an external field applied in-plane is generally necessary in order to achieve deterministic current-induced SOT switching. Indeed it is understood that symmetry needs to be broken to allow the magnetisation reversal 9 .

Recently, it has been shown that if the FM magnetic layer is replaced by a FM/AFM exchange coupled bilayer, SOT switching can be obtained under zero in-plane applied field. It is understood that the presence of the AFM can induce an exchange bias field acting on the FM layer which results in a field shift on the FM hysteresis loop. Exchange bias or exchange anisotropy has been discovered decades ago thanks to the exchange biased effect induced system but also helps to understand how relevant the crystalline structure of the AFM is for a reliable magnetisation switching 26 . Note that in those systems, the AFM-FM exchange coupling can provide a better thermal stability for future SOT-MRAM 27 .

In our paper, we explore SOT switching in a Pt/FM/AFM bilayer system where the FM and AFM layers consist in [Co/Ni]2 and PtMn, respectively. The dominant source of spin current originates from the Pt bottom layer showing a large Spin Hall angle as in the Pt/Co/IrMn structure studied in ref 27 . We intend to obtain zero field SOT switching as in Fukami's work 12 but also to keep strong PMA to maintain square Hall voltage versus current hysteresis loops. To do this we induced both an inplane and out-of-plane exchange coupling between the two layers. This was done by a double annealing procedure starting with an out-of-plane field annealing followed by an in-plane field annealing.

II. EXPERIMENTAL SECTION

The system SiO2 // Ta (5 nm)/Pt (4 nm)/Co (0.3 nm)/[Ni (0.6 nm)/Co (0.3 nm)]2/PtMn (10 nm)/Ta (3 nm) studied is sketched in Fig. 1(a). By working with an ultrahigh-vacuum magnetron sputtering system, the PtMn/[Co/Ni]2 system has been deposited on thermally oxidized Si substrates without any magnetic sources according to the corresponding order: substrate // Ta (5 nm) / Pt (4 nm) / Co (0. respectively. By using a Vibrating Sample Magnetometer (VSM), we investigated the most suitable ferromagnet for our study and we confirmed that sheet-films involving PtMn exhibit the coexistence of Perpendicular Magnetic Anisotropy (PMA) and out-of-plane exchange bias. Once we managed to get the magnetic properties, the samples have been patterned into a Hall cross (5 µm or 10 µm by 10 µm) and/or into a bar (5 µm by 10 µm) by photolithography, magnetron sputtering and liftoff process. The same method has been used to set up the Ta(10 nm)/Pt(100 nm) electrodes in a second round of patterning.

III. RESULTS AND DISCUSSIONS A. Magnetic Properties

The magnetic properties of the sample were obtained by measuring its magnetisation as a function of the applied field with a VSM with different annealing procedures as shown in Fig. 2. Fig. 2(a) and Fig. 2(b) present the hysteresis loops obtained on the as-grown sample for field applied perpendicular to the film plane and in-plane respectively whereas Fig. 2(c) and Fig. 2(d) show the hysteresis loops obtained after the double annealing procedure. The sample is heated at 583K then a magnetic field of 0.9T is applied along the direction perpendicular to the film plane (z axis) during the first 25 minutes and it is then applied along an in-plane direction (x axis) during the last 35 minutes before cooling down to room temperature. This provides a significant hysteresis loop shift both in the in-plane and the out-of-plane directions without damaging the PMA, i.e. maintaining nice square loops. Out-of-plane VSM measurements for annealed films exhibit square loops with a coercive field HC = 22mT and an out-of-plane exchange bias of 9mT. In addition, in-plane measurements show an in-plane exchange bias of 20mT. The saturation magnetisation, for annealed films, reaches 0.927MA.m -1 with an anisotropy field of 500mT

(5 000Oe), that is to say an effective magnetic anisotropy Keff = 0.23MJ.m -3 .

It should me mentioned that for a single step annealing at 583K under a field of 0.9T along the out-of-plane direction (z axis) during 60 minutes, no in-plane exchange bias is induced as shown on Fig. 3(a). Then, we performed Magneto Optical Kerr Effect (MOKE) measurements in polar configuration using the experimental set-up described in Fig. 1(c) to get SOT switching curves on single-wire annealed only in the direction perpendicular to the plane to demonstrate that no zero field SOT switching is observed as shown on Fig. 4. On the other hand, if the annealing is performed with inplane field only, no strong PMA is observed as shown in Fig. 3(b).

B. Anomalous Hall Effect measurements

We performed Anomalous Hall Effect (AHE) measurements using the experimental set-up described in Fig. 1(d) to get SOT switching curves on Hall-crosses for both as-deposited and annealed systems. We applied pulse current starting from -60mA to + 60mA (with a pulse profile corresponding to Fig. 1(b)) under a permanent in-plane magnetic field ranging from -30mT to +30mT. Fig. 5(a,c) shows SOT loops for double annealed devices. The polarity switching occurs at HX,SWITCH = -1.5mT for annealed devices due to the symmetry breaking. However, we demonstrated (see Fig. 5(b,d)) a polarity switching at HX,SWITCH = 0mT for non-biased devices. Note that the full current switching is observed only for applied field showing an absolute value larger than 10mT.

The amplitude of the AHE voltage variation generated by the SOT magnetisation switching decreases as the field reaches the polarity switching field (HX,SWITCH). In the case of the as-deposited sample at zero applied field HX = 0mT, the critical current tends to diverge and no switching can be observed since the switching voltage amplitude tends to zero. However, a significant switching voltage variation is observed under zero applied magnetic field after a double annealing procedure for a moderate current. Moreover, the Hall voltage versus current remains a square loop.

The critical switching current IC is plotted as a function of the in-plane field HX in Fig. 6. For the asdeposited sample the evolution of the critical current is symmetric i.e. similar behaviour is observed for positive and negative in-plane field. In the case of double annealed sample the evolution is asymmetric. In first approximation the IC versus HX is now centred around HX,SWITCH = -1.5mT.

IV. CONCLUSION

In conclusion, we have demonstrated that using a double annealing procedure which consists in annealing the sample with a perpendicular to the plane followed by an in-plane applied magnetic field, we can combine a zero field SOT switching and a sharp out-of-plane switching. Indeed this procedure induces both an in-plane and out-of-plane exchange bias phenomena which allows an in-plane symmetry breaking needed for the SOT switching but also maintains perpendicular magnetisation resulting in square Hall voltage versus current hysteresis loops. This procedure can be implemented to improve the design of future spintronics devices such as SOT-MRAM.

FIG. 1 .

 1 FIG. 1. System structure and description of experimental setups to measure SOT Switching. (a) Sketch of a SiO2 // Ta (5) / Pt (4) / Co(0.3) / [Ni (0.6) / Co (0.3)]2 / PtMn (10) / Ta (3) sample. (b) Current pulse profile used for SOT measurements. (c) Sketch of the experimental set-up to measure the SOT switching curves with P-MOKE configuration in a single-wire (5μm × 10μm). (d) Sketch of the experimental set-up to measure the Anomalous Hall Effect while injecting current in Hall cross (5 or 10μm x 10μm).

FIG. 2 .

 2 FIG. 2. Normalized magnetisation M/Ms as a function of the applied magnetic field. (a) As-deposited structure with the field applied perpendicular to the plane. (b) As-deposited structure with the field applied in the plane. (c) After annealing at 583K under 0.9T with the field applied perpendicular to the plane. (d) After annealing at 583K under 0.9T with the field applied in the plane.

FIG. 3 .

 3 FIG. 3. Normalized magnetisation M/Ms as a function of the magnetic field applied in-plane and out-of-plane. (a) Sample after out-of plane annealing only. (b) Sample after in-plane annealing only.

FIG. 4 .

 4 FIG. 4. Normalized Kerr intensity as a function of the applied voltage in P-MOKE configuration.

FIG. 5 .

 5 FIG. 5. Normalized VAHE as a function of injected current -IC for a SiO2 // Ta (5) / Pt (4) / Co(0.3) / [Ni (0.6) / Co (0.3)]2 / PtMn (10) / Ta (3) sample. (a), (c) As-deposited sample. (b), (d) Sample after double annealing procedure. (a) For various in-plane fields ranging from +30 mT to -1.5 mT leading to one type of SOT switching polarity. (b) For various in-plane fields ranging from +30 mT to 0 mT leading to one type of SOT switching polarity. (c) For various in-plane fields ranging from -1.5 mT to -30 mT leading to the other type of SOT switching polarity. (d) For various in-plane fields ranging from 0 mT to -30 mT leading to the other type of SOT switching polarity.

FIG. 6 .

 6 FIG. 6. Critical current as a function of the in-plane applied field HX for the SiO2 // Ta (5) / Pt (4) / Co(0.3) / [Ni (0.6) / Co (0.3)]2 / PtMn (10) / Ta (3) sample as-deposited (red square) and after annealing following the procedure described in the text (blue circles).

ACKNOWLEDGMENTS

This work was supported partly by the French PIA project "Lorraine Université d'Excellence", reference ANR-15-IDEX-04-LUE, by the "FEDER-FSE Lorraine et Massif Vosges 2014-2020", a European Union Program. Maxime Verges is supported by a Cifre PhD grant from Vinci Technologies.

DATA AVAILIBILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.


Claire Beauchesne

Morgan Chabanon

Benjamin Smaniotto

Benoît Ladoux

Benoit Goyeau
email: benoit.goyeau@centralesupelec.fr

Bertrand David

Benoît Goyeau

Benoît Goyeau

Pr B Goyeau

Channeling Effect and Tissue Morphology in a Perfusion Bioreactor Imaged by X-Ray Microtomography

Keywords: X-ray microtomography, perfusion bioreactor, tissue engineering, channeling effect, tissue morphology

come

Introduction

In the context of tissue engineering, several types of bioreactors have been designed in an attempt to enhance in vitro cell proliferation and differentiation in a dynamic and controlled environment: spinner flasks [START_REF] Vunjak-Novakovic | Effects of mixing on the composition and morphology of tissue-engineered cartilage[END_REF], rotating wall bioreactors [START_REF] Granet | Rotating-wall vessels, promising bioreactors for osteoblastic cell culture: comparison with other 3d conditions[END_REF], and perfusion systems [START_REF] David | A perfusion bioreactor for engineering bone constructs: an in vitro and in vivo study[END_REF][START_REF] Andrew | Tubular perfusion system for the long-term dynamic culture of human mesenchymal stem cells[END_REF]. Yet an associated challenge is to provide homogeneous nutrients and oxygen supply within the whole volume of such scaffold. Perfusion bioreactors have been shown to give good results in this regard [START_REF] Gregory N Bancroft | Fluid flow increases mineralized matrix deposition in 3d perfusion culture of marrow stromal osteoblasts in a dosedependent manner[END_REF][START_REF] Andrew | Bone tissue engineering bioreactors: dynamic culture and the influence of shear stress[END_REF], leading to relatively even cell seeding and growth on the porous scaffold [START_REF] Warren L Grayson | Engineering anatomically shaped human bone grafts[END_REF][START_REF] Warren L Grayson | Optimizing the medium perfusion rate in bone tissue engineering bioreactors[END_REF]. Perfusion bioreactors present a similar basic design consisting of a closed tubing circuit with a culture medium reservoir, a pump, and a growth chamber. They mainly differ in the design of the cell seeded-scaffold residing inside the growth chamber (fiber meshes, beads or cubes stacks, ...) and the scaffold materials (coral, titanium, alginate, starch-based material, calcium-phosphate ceramics, ...) [START_REF] David | A perfusion bioreactor for engineering bone constructs: an in vitro and in vivo study[END_REF][START_REF] Antoni | Three-dimensional cell culture: a breakthrough in vivo[END_REF][START_REF] James | Model of a tubular perfusion bioreactor using computational fluid dynamics[END_REF].

Given the complex culture environment in perfusion bioreactors, where the fluid flow stimulates cell proliferation and tissue growth alters in turn the fluid flow, recent investigations have turned to modeling approaches to optimize their tissue production [START_REF] Sanaei | Curvature-and fluid-stressdriven tissue growth in a tissue-engineering scaffold pore[END_REF].

In hydrodynamic bioreactors, fluid flow alters cell differentiation and proliferation [START_REF] Gregory N Bancroft | Fluid flow increases mineralized matrix deposition in 3d perfusion culture of marrow stromal osteoblasts in a dosedependent manner[END_REF][START_REF] Glowacki | Perfusion enhances functions of bone marrow stromal cells in three-dimensional culture[END_REF] by providing a mechanical stimulation of the cells [START_REF] David | A perfusion bioreactor for engineering bone constructs: an in vitro and in vivo study[END_REF][START_REF] Scaglione | Effects of fluid flow and calcium phosphate coating on human bone marrow stromal cells cultured in a defined 2d model system[END_REF] and enhancing species transport such as nutrients supply and waste removal [START_REF] Scheper | Advances in biochemical engineering/biotechnology[END_REF][START_REF] Martin | The role of bioreactors in tissue engineering[END_REF]. Externally applied forces, such as shear stresses, traction stresses or fluid drag [START_REF] Orr | Mechanisms of mechanotransduction[END_REF], are translated into intracellular biochemical signaling, which results in a modification of the cellular response [START_REF] Ladoux | Physically based principles of cell adhesion mechanosensitivity in tissues[END_REF]. This process, termed mechanosensitivity, is at the origin of many important biological functions, including bone remodeling [START_REF] Reich | Fluid shear stress as a mediator of osteoblast cyclic adenosine monophosphate production[END_REF].

Mechanosensitive mechanisms have been identified such as the activation of stretch-activated ion channels [START_REF] Katsumi | Integrins in mechanotransduction[END_REF][START_REF] Li | Molecular mechanisms of mechanotransduction in integrin-mediated cell-matrix adhesion[END_REF], integrin-initiated cytoskeleton deformations [START_REF] Haswell | Mechanosensitive channels: what can they do and how do they do it?[END_REF][START_REF] Ryan | Influence of shear stress in perfusion bioreactor cultures for the development of three-dimensional bone tissue constructs: a review[END_REF][START_REF] Brosig | Mechanotransduction in fibroblasts[END_REF], and the stimulation of the primary cilia [START_REF] Berbari | The primary cilium as a complex signaling center[END_REF].

More generally, tissue pattern is driven by the complex combination of external signallings [START_REF] Sa Korossis | Bioreactors in tissue engineering[END_REF][START_REF] Ladoux | Mechanobiology of collective cell behaviours[END_REF]: the substrate material and local geometry (either the scaffold or the extracellular matrix), the culture medium (nutrients, growth factors, mitogens, etc...), and external forces (such as those applied by other cells or fluid shear stress). Besides fluid flow enhanced prolifer-ation, the way connective cells colonize the scaffold is of paramount importance. Despite recent progress in the description of connective tissue growth or repair in static conditions [START_REF] Cécile M Bidan | Gradual conversion of cellular stress patterns into pre-stressed matrix architecture during in vitro tissue growth[END_REF][START_REF] Mahmut Selman Sakar | Cellular forces and matrix assembly coordinate fibrous tissue repair[END_REF][START_REF] Rumpler | The effect of geometry on three-dimensional tissue growth[END_REF][START_REF] Sharma | Aligned fibers direct collective cell migration to engineer closing and nonclosing wound gaps[END_REF][START_REF] Kollmannsberger | Tensile forces drive a reversible fibroblast-to-myofibroblast transition during tissue growth in engineered clefts[END_REF], the mechanisms underlying its formation in dynamic conditions are still poorly understood. In particular, the morphology of a tissue growing under perfusion of culture medium as well as the distribution of cells within this tissue are key information for the development of bioreactors for tissue engineering.

Several studies adopted a modeling approach to understand the interplay between tissue growth and fluid flow. Numerical simulations of fluid flow through empty porous scaffolds have been performed in order to determine the shear stress field and predict the preferential locations of cell proliferation at the initiation of cell culture [START_REF] Andrew | Tubular perfusion system for the long-term dynamic culture of human mesenchymal stem cells[END_REF][START_REF] Cruel | Numerical study of granular scaffold efficiency to convert fluid flow into mechanical stimulation in bone tissue engineering[END_REF][START_REF] Shakhawath Hossain | Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor[END_REF]. More complex models have been proposed to simulate the evolution of the fluid flow as tissue grows by addition of cell layers of varying thicknesses [START_REF] Lesman | Modeling of flow-induced shear stress applied on 3d cellular scaffolds: Implications for vascular tissue engineering[END_REF] or by using a moving boundary approach where the interfacial velocity is a function of the local fluid shear stress [START_REF] Nava | A multiphysics 3d model of tissue growth under interstitial perfusion in a tissue-engineering bioreactor[END_REF]. Recently, the experimental evidence that the geometry strongly influences the tissue morphology and growth kinetics in static conditions [START_REF] Rumpler | The effect of geometry on three-dimensional tissue growth[END_REF][START_REF] Cécile M Bidan | How linear tension converts to curvature: geometric control of bone tissue growth[END_REF] motivated the development of new models. Indeed, tissue growth kinetics under perfusion is determined as a function of both the curvature of the tissue growth front and the fluid shear stress [START_REF] Sanaei | Curvature-and fluid-stressdriven tissue growth in a tissue-engineering scaffold pore[END_REF][START_REF] Guyot | Coupling curvaturedependent and shear stress-stimulated neotissue growth in dynamic bioreactor cultures: a 3d computational model of a complete scaffold[END_REF], although these predictions are still to be validated against experimental data at the pore scale. Overall, given the complexity of the biophysical phenomena at stakes in perfusion bioreactors, modeling and numerical simulations in simplified controlled settings, appear as valuable investigative tools.

In this study, we propose to take advantage of a model-system inspired from a perfusion bioreactor for bone tissue engineering [START_REF] David | A perfusion bioreactor for engineering bone constructs: an in vitro and in vivo study[END_REF] in order to describe the morphological evolution of neo-tissue with respect to local flow patterns. Our model system makes use of two main simplifications: (i) murine fibroblasts are chosen for their rapid proliferation rate, mechanosensitivity, and ability to produce connective tissue, and (ii) the scaffold is composed of immobile, impermeable and non-absorbable polyacetal beads in order to use a simple geometry and image the bioreactor by X-Ray micro-tomography. We combine three-dimensional visualization by X-Ray microtomography and computational fluid dynamic to answer the following questions: How does the fluid flow pattern determine the spatial distribution of tissue in the bioreactor? What is the morphology of the tissue as it grows?

2 Materials and Methods

Cells

Fibroblasts NIH-3T3 (ATCC) were cultured in DMEM Glutamax (Life Technologies) supplemented with 10% Fetal Bovine Serum (Pan-Biotech) and 1% Penicillin Streptomycin (Pan-Biotech), at pH 7.4 under standard cell culture conditions (37 • C, 5% CO 2 , 100% humidity).

Following previous tissue engineering studies using murine fibroblasts [START_REF] Chabanon | Discrete model combined with mimetic microfluidic chips to study cell growth in porous scaffold under flow conditions[END_REF][START_REF] Chabanon | Histological method to study the effect of shear stress on cell proliferation and tissue morphology in a bioreactor[END_REF][START_REF] Thibeaux | Assessment of the interplay between scaffold geometry, induced shear stresses, and cell proliferation within a packed bed perfusion bioreactor[END_REF], these cells have been chosen for our model system because they belong to the family of connective tissue cells (like chondrocytes, osteoblasts, ...) [START_REF] Harris | Fibroblasts and their transformations: the connective-tissue cell family[END_REF]. Additionally, they respond to mechanical stimuli [START_REF] James | Mechanoregulation of gene expression in fibroblasts[END_REF],

which is relevant to our perfusion bioreactor model and have a rapid proliferation rate.

Perfusion bioreactor

The perfusion bioreactor (Fig. 1) consists of a closed tubing circuit with a media reservoir, a peristaltic pump, and a perfusion chamber [START_REF] David | A perfusion bioreactor for engineering bone constructs: an in vitro and in vivo study[END_REF][START_REF] David | Reacteur pour la mise en oeuvre d'un procede de culture de tissus osseux[END_REF]. The cylindrical growth chamber (13.8 mm diameter, 5 cm high, made of polycarbonate) is randomly filled by mono disperse polyacetal beads (2 mm diameter). Let us note that bead-based scaffolds have been identified as good candidates for tissue engineering and therefore have been investigated multiple times [START_REF] Andrew | Tubular perfusion system for the long-term dynamic culture of human mesenchymal stem cells[END_REF][START_REF] Cruel | Numerical study of granular scaffold efficiency to convert fluid flow into mechanical stimulation in bone tissue engineering[END_REF][START_REF] Chabanon | Histological method to study the effect of shear stress on cell proliferation and tissue morphology in a bioreactor[END_REF][START_REF] Thibeaux | Assessment of the interplay between scaffold geometry, induced shear stresses, and cell proliferation within a packed bed perfusion bioreactor[END_REF][START_REF] Andrew B Yeatts | Formation of an aggregated alginate construct in a tubular perfusion system[END_REF][START_REF] David | Design of a modular bioreactor to incorporate both perfusion flow and hydrostatic compression for tissue engineering applications[END_REF][START_REF] Nilay | Titanium phosphate glass microspheres for bone tissue engineering[END_REF][START_REF] Nihal | Titanium microbead-based porous implants: bead size controls cell response and host integration[END_REF]. The beads are immobilized by two polycarbonate grids (0.5 cm high), inserted in the growth chamber at the bioreactor inlet and outlet. Polyacetal is semi-transparent to X-rays allowing the reconstruction of three-dimensional images of the tissue on the beads.

In addition, the scaffold is immobile and non-absorbable: this allows to study tissue growth for a given bead stack arrangement. Finally, note that since the beads volume fraction remains constant, the local organization and the global height of bead stacks are slightly sample dependent. The chamber is closed by two caps made of polytetrafluoroethylene and a tubing made of silicon (Pharm-Med) connects the bioreactor to the culture medium reservoir. The culture medium pH is kept constant by the constant supply of air enriched with carbon dioxide at 5%.

Dynamic cell culture in perfusion bioreactor

The following procedure has been followed in order to seed the cells on the beads before their introduction into the bioreactor [START_REF] Thibeaux | Assessment of the interplay between scaffold geometry, induced shear stresses, and cell proliferation within a packed bed perfusion bioreactor[END_REF][START_REF] Thibeaux | Using x-ray computed tomography for quantification of cell proliferation within a perfusion bioreactor[END_REF]. First, a suspension of pre-confluent NIH-3T3 cells (10 6 cells/ml) in culture medium was gently poured onto the polyacetal beads previously coated with fibronectin (10 µg/ml, 1 hour at 37 • C), then left overnight in a CO 2 incubator to let the cells adhere to the beads. The seeded scaffold was then gently poured into the perfusion bioreactor and immobilized by two grids to avoid any bead movements during culture medium changes.

The constructs were perfused at a constant flow rate of 20 ml/min or 30 ml/min for one, two or three weeks (two constructs per experimental condition). The culture medium was changed for the first time after one week then twice a week. At the indicated time points, the constructs, still immobilized by the two grids, were washed with PBS prior being fixed with 4% paraformaldehyde (Sigma-Aldrich) in PBS (Pan-Biotech), then washed again with PBS and H 2 O prior being stained with 1% osmium tetroxide OsO 4 (Sigma-Aldrich) in H 2 O. The solution is beforehand gently injected multiple times at the top and bottom of each sample through the peripheral envelop of tissue in order to ensure that the core of the samples are fully immersed in the solution. The samples were then dehydrated through a series of ethanol baths of growing concentrations (50, 70, 90, 95, and 100%) before being dried using hexamethyldisilazane (Sigma-Aldrich). Osmium is a heavy metal that stains cell membranes thereby making cells visible by X-ray microtomography.

Visualization of the cellular phase

The stained cellular phase was imaged by an X-ray tomography system (North Star Imaging, NSI, X50-CT) equipped with a molybdenum target and a CMOS image sensor Dexela 2923.

Two series of scans were performed with the following characteristics:

• Physical voxel length of 17 µm with a height of field view of about 2.8-2.9 cm and centered at mid-height of the bioreactor growth chamber. The voltage was 50 kV and the current 400 µA. 900 projections were obtained from each sample over 360 degrees.

• Physical voxel length of 10.2 µm with a height of field view of about 1.1 cm from the top or the bottom of the bioreactor growth chamber. The voltage was 50 kV and the current 230 µA. 1000 projections were obtained from each sample over 360 degrees.

Image analysis

The reconstruction was performed with efX-software (NSI) and image processing with ImageJ (version 1.51w) [START_REF] Schneider | Nih image to imagej: 25 years of image analysis[END_REF].

The mean intensity, that we define as the mean grey value, is measured on the raw data (16 bits) after subtracting the mean intensity of the background noise, measured outside the bioreactor.

The creation of a Region of Interest (ROI) delimiting the cellular regions in the parietal region and in the core of the bioreactor followed four steps:

Step 1: The mean intensity of the background noise, measured outside the bioreactor wall, was subtracted.

Step 2: The tube was removed by application of an inverted circular mask on all the slices. The mask was created beforehand by drawing two ovals matching the inner perimeter of the tube on the first and last slide of the stack, and adding them to a ROI. The ROI was completed between the first and last slides by interpolation. The associated mask for the tube was then generated and applied to the stack of the samples obtained in step 1.

Step 3: A binary image of the cellular region was obtained in three steps. The thinnest tissue regions were selected by subtracting the background with rolling ball radius set to 1 then 2 pixels on duplicated stacks. Both stacks were added and thresholded to create a binary mask consisting of the regions where the tissue is the thinnest (Step 3a). The largest tissue regions were isolated by thresholding and converted to a mask (Step 3b). Both masks were added in order to obtain the cellular region as binary image (Step 3c).

Step 4: The annular and core regions were delimited by a radius R. A circle of radius R was drawn on the first and last slides with the same center as the centroid of the growth chamber wall and added to a ROI. The ROI was completed between the first and last slides by interpolation. The circular mask of radius R was then generated. For selecting the cellular region close to the bioreactor wall (or in the core), the mask (respectively the inverted mask) was applied to the binarised image defining the cellular region. The cellular region was finally selected with subpixel accuracy and added to a new ROI.

Results and discussion

Fibroblasts NIH-3T3 cells were cultured for one, two or three weeks in the bioreactor for two different perfusion flow rates of culture medium (20 or 30 ml/min). The samples were scanned by X-ray micro-tomography and the tridimensional arrangements of the beads and the tissue were obtained after image reconstruction. Preliminary experiments showed that tissue proliferation on glass and polyacetal bead stacks in static conditions (without flow) was negligible compared to dynamic conditions [START_REF] Chabanon | Histological method to study the effect of shear stress on cell proliferation and tissue morphology in a bioreactor[END_REF][START_REF] Thibeaux | Assessment of the interplay between scaffold geometry, induced shear stresses, and cell proliferation within a packed bed perfusion bioreactor[END_REF], producing too little tissue volume to be resolved by X-ray microtomography. Additionally, mass transport estimates in similar culture conditions and close flow rate indicate that oxygen and nutrient supply is in excess during most of the three weeks of culture [START_REF] Chabanon | Histological method to study the effect of shear stress on cell proliferation and tissue morphology in a bioreactor[END_REF].

Channeling effect locally enhances the perfusion flow rate at the bead stack periphery

After two or three weeks of culture, we observe a preferential proliferation at the periphery of the bead stack where the cells form an external tissue envelope (Fig. 2a,b). The difference between the external and internal cell proliferation is shown in Fig. 3b which represents a slice of the bioreactor with a flow rate of 30 ml/min after three weeks. It can be seen that the tissue close to the bioreactor wall (colored in yellow) is denser than the tissue in the core (colored in blue). This phenomenon, observed in all the experiments, is also clearly illustrated in Fig. 3c where the intensity, that we define as the grey value of a pixel, of the cellular phase is summed over the entire stack. In order to support these observations, we quantify the averaged relative difference of intensity between the tissue in the core of the bioreactor and the envelope for all samples cultured three weeks. Two regions are identified: an annular region corresponding mainly to the tissue envelope previously described, and an inner disk region representing the core of the bioreactor. Due to some heterogeneous arrangement of the beads in the vertical direction, the inner region is defined using two different radii R 1 and R 2 . This corresponds to two regions (annular and disk) per radius. The thickness of the annular region amounts to about either one or two bead radii. We first determine the averaged relative difference of intensity between the tissue in the annular region and the tissue in the disk region considering the first radius R 1 . The results provided in Table 1 are obtained for all samples cultured three weeks. The relative comparison of mean intensity between the core and the periphery are of the order of 50% in most cases. Of particular note, the average of 42.2% is mainly due to the heterogeneous arrangement of the beads in the vertical direction. Indeed, considering the second radius R 2 , this relative difference amounts to 51.3%.

Additional scans of bioreactor inlets and outlets for experiments carried out with a flow rate of 30 ml/min show that the envelope actually encompasses the whole packing of beads (Fig. 4). 1: Averaged relative difference of intensity between the tissue in the annular region and the tissue in the disk region for a radius R 1 of 10.13 mm, for all samples cultured three weeks.

Flow rate

As shown below, this preferential tissue growth is related to the geometrical heterogeneities of the scaffold. These heterogeneities are due to the spatial distribution of the spherical beads at the vicinity of the wall (parietal region). This disordered arrangement in the parietal region is characterized by a local increase of the porosity and permeability values, both being therefore dependent on the radial coordinate. The consequence of these heterogeneities is an increase of the flow rate close to the wall leading to a more intense local flow. This channeling effect [START_REF] Kaviany | Principles of heat transfer in porous media[END_REF] gives rise to an increase of both nutrient transport and local shear stress, which results in a stronger mechanical stimulation of the cells in the parietal region and therefore in an increased proliferation. As a matter of fact, Cruel et al. [START_REF] Cruel | Numerical study of granular scaffold efficiency to convert fluid flow into mechanical stimulation in bone tissue engineering[END_REF] noticed radial heterogeneities of the fluid shear stress at the beads surface for bead granular packings. More specifically, we locate these heterogeneities at the bioreactor periphery. This mechanism can also be described at the bioreactor scale (macroscopic scale) where the averaged filtration velocity V in the direction of the flow (z-component) is governed by Darcy's law [START_REF] Darcy | Les fontaines publiques de la ville de Dijon: exposition et application[END_REF]:

0 = - dP dz - µ K V (1)
In Eq. ( 1), µ is the dynamic viscosity and K is the permeability coefficient in the direction of the flow which depends on the radial coordinate r. For a porous media composed by mono dispersed spherical beads, the permeability is given by the Kozeny-Carman relationship K = [START_REF] Crosbie | Fluid flow through granular beds[END_REF] where ε represents the average porosity and d the diameter of the beads.

ε 3 d 2 /180(1 -ε) 2 [
Therefore, Eq. ( 1) clearly shows that this channeling effect is explicitly dependent on the beads diameter. It is important to recall that Darcy's law is relevant if the local Reynolds number (Re = KV /ν) is lower than 1. This is the case for our bioreactor where ε = 0.35, K = 2 • 10 -9 m 2 and Re = 0.16. This estimation has been done for the maximum flow rate (30 ml.min -1 ). Therefore, according to Eq. ( 1), for a given pressure gradient, the filtration velocity V continuously increases with the permeability K. It is worth mentioning that the thickness of the channeling region is of the order of √ K and that the flow field non-uniformities in this region are negligible if the ratio d/D is very small compared to 1 (with d the beads diameter and D the bioreactor inner diameter) [START_REF] Kaviany | Principles of heat transfer in porous media[END_REF]. In our bioreactors, d/D is of the order of 0.1, which makes necessary to take into account the presence of a channeling effect in the analysis.

The above analysis leads to an important design principle for perfusion bioreactors using beads, or more generally granular scaffolds: the intensity of the channeling effect can be modulated according to specific bioreactor application by adjusting the ratio between the scaffold beads size and chamber diameter. For instance, if one aims to have homogeneous local flow rate across the scaffold, small beads and large chamber diameters should be used. On the contrary, if an application requires a large flow rate at the scaffold surrounding, bigger beads might be more appropriate.

Shear-stress pattern promotes crater-shaped tissue at early culture time

After one week of culture, the experiments show that whatever the flow rates, the tissue partly covers the beads with a crater-like shape. Indeed, we observe tissue overgrowths on the beads around circular areas devoid of cells and located in the narrowed fluid areas (Fig. 5). In order to investigate this formation of craters, we employ computational fluid dynamics to assess the local wall shear stress induced by the flow on the scaffold beads.

We numerically compute the shear stress field for a stationary laminar viscous flow through an idealized three-dimensional arrangement of nine identical spheres in a cylindrical channel.

The radius of the channel is 2.7 mm while the radius of spheres is 1 mm. Flow properties are close to those of water at ambient temperature and the imposed inlet velocity is 0.001 m/s. Under these conditions, the associated Reynolds number is of the order 1 and therefore the fluid flow is laminar. Numerical simulations are performed using Comsol Multiphysics (version 4.3b). Figure 6 represents the isovalues of the shear stress field at the surface of the spheres. As expected, the maxima are located in the narrow fluid regions.

Importantly, we find that the locations and form of the shear stress maxima obtained numerically correspond to the locations and the form of the crater-like tissue observed experimentally.

It is well known that the proliferation of mechanosensitive cells, including fibroblasts, is enhanced by the flow-induced shear stress. But this stimulation is clearly limited by the intensity of the stress. For high intensity values, cell detachment (which is also material-dependent) [START_REF] George | Relationship between 3t3 cell spreading and the strength of adhesion on glass and silane surfaces[END_REF] can be observed but cellular growth is probably prevented before reaching this limit. In the numerical simulations, the higher flow rate (30 ml/min) the maximum shear stress obtained is about 0.1 Pa which is close to the detrimental value (0.

Biomechanical interpretation of tissue morphology evolution

After one week of culture, the tissue has partly covered the beads with a crater-like shape (Fig. 5b,c,d). After two weeks, it clearly appears in Fig. 7b that the tissue grows by building "bridges" between the beads with concave and smooth interfaces. Such shapes are interpreted as the result of curvature minimization [START_REF] Rumpler | The effect of geometry on three-dimensional tissue growth[END_REF][START_REF] Cécile M Bidan | Geometry as a factor for tissue growth: towards shape optimization of tissue engineering scaffolds[END_REF][START_REF] Kollmannsberger | The physics of tissue patterning and extracellular matrix organisation: how cells join forces[END_REF]. In other words, this results from the contribution of a tension line between the anchoring points and due to the acto-myosin cable along the edge of the tissue, balanced by a surface tension which comes from the global contractility of the cells [START_REF] Bischofs | Filamentous network mechanics and active contractility determine cell and tissue shape[END_REF].

Figure 7 also shows that the density of the tissue at the interface with the culture medium is higher than in the center of the "bridges". It seems that this phenomenon is related to the fact that cells in this interfacial region are mechanically stimulated by the shear stress induced by the flow of the medium. Interestingly, Kollmannsberger et al. [START_REF] Kollmannsberger | Tensile forces drive a reversible fibroblast-to-myofibroblast transition during tissue growth in engineered clefts[END_REF] and Granet et al. [START_REF] Granet | Rotating-wall vessels, promising bioreactors for osteoblastic cell culture: comparison with other 3d conditions[END_REF] showed that cell proliferation preferentially occurs at the tissue-medium interface, where a higher mechanical stimulation results in a higher cell proliferation rate [START_REF] Celeste M Nelson | Emergent patterns of growth controlled by multicellular form and mechanics[END_REF]. The graph presented in Fig. 7e shows that this behavior is more pronounced in the parietal region presumably due to the channeling effect (Fig. 7d). Finally, it is worth recalling that cell contractility has also an important impact on the tissue morphology. Indeed, the evolution of the tissue depends on the balance between cell-cell and cell-scaffold interactions. After one week of culture, the formation of a few narrower "rings"

where the tissue is partly ripped off (Fig. 5b,c,d) suggests that the tissue is subjected to considerable tensions. Such tears in the tissue have been observed with keratinocytes [START_REF] Ram | Epithelial bridges maintain tissue integrity during collective cell migration[END_REF] and fibroblasts [START_REF] Olivier M Rossier | Force generated by actomyosin contraction builds bridges between adhesive contacts[END_REF] forming suspended bridges and have been attributed to cell contractility. In addition, images of bioreactors cultured three weeks clearly show that the tissue has a dense sheet-like shape whatever the location in the bioreactors (Fig. 3), presumably as the result of tissue contraction. This phenomenon is also either initiated or complete after two weeks of culture all along the bioreactors (Fig. 7c). The detachment of the tissue from the scaffold suggests that cell adhesion forces to the substrate are too weak to counterbalance the traction forces due to cell contractility.

Conclusion

In this work, we used a combination of tissue engineering, X-ray micro-tomography imaging, and fluid mechanics simulations to relate tissue morphology and local fluid flow conditions in a model perfusion bioreactor. The model bioreactor consisted of fibroblasts cells grown on a scaffold made of a stack of beads in a perfusion chamber.

Our results highlight the heterogeneous distribution of the cells as the consequence of a channeling effect in the bioreactor. Because of the particular arrangement of the bead packing and the subsequent higher porosity and permeability at the periphery of the bioreactor, the flow is more intense in the channel at the periphery. In our model bioreactor, this effect results in a preferred proliferation around the bead stack and the formation of a very dense envelope of tissue. The dimensions of the beads and bioreactor determine the importance of these boundary effects: a small bead to bioreactor diameter ratio means a weak channeling effect.

Furthermore, we identify crater-shaped tissue patterns at early culture times. We show that this morphology resembles the distribution of fluid shear stress on beads, highlighting the importance of local fluid flow on tissue development.

Finally, we find that after one, two and three weeks of culture, the tissue adopts very distinct morphologies, and attribute these observations to the simultaneous growth and contraction of the connective tissue as it grows.

By providing insights into the coupling between tissue development and fluid flow in a perfusion bioreactor, this work has potential implications in the effective design of bioreactors relying on hydrodynamic stimulii for tissue engineering.

Figure 1 :

 1 Figure 1: Schematic representation of the experimental set-up.

Figure 2 :

 2 Figure 2: 3D views obtained by X-ray micro-tomography of the tissue on the scaffold after two weeks (a) and three weeks (b) of culture at a flow rate of 20 ml/min. The beads appear in dark grey (dashed arrow) and the tissue in light grey (black arrow). Scale bar, 2 mm.

Figure 3 :

 3 Figure 3: Visualization obtained by X-ray micro-tomography of the tissue on the scaffold after three weeks of culture at a flow rate 30 ml/min. (a) 3D side view. (b) 2D representative slide (intensity normalized with respect to the maximum intensity). (c) Sum over the whole stack of pixel intensity in the cellular region (relative to the maximum intensity).

Figure 4 :

 4 Figure 4: 3D views obtained by X-ray micro-tomography of the tissue on the scaffold at fluid inlet after three weeks of culture at a flow rate of 30 ml/min. (a) 3D side view. (b) 3D bottom view.

3

 3 Pa) obtained by Truskey and Proulx[START_REF] George | Relationship between 3t3 cell spreading and the strength of adhesion on glass and silane surfaces[END_REF] for fibroblasts NIH-3T3 seeded on glass. Note that this value is of the same order of magnitude as the detrimental shear stress obtained for osteoblasts by Leclerc et al.[START_REF] Leclerc | Study of osteoblastic cells in a microfluidic environment[END_REF]. Although our numerical simulations ignore the presence of tissue on the beads, they provide useful insights into the determination of the spatial distribution of the tissue by the shear stress field in the perfusion bioreactor. Keeping the global flow rate constant through the growth chamber, the coupling of tissue growth with the laminar flow would lead to an intensification of the flow and an expected increase of the fluid shear stress.

Figure 5 :

 5 Figure 5: 3D views obtained by X-ray micro-tomography of the tissue on the scaffold after one week of culture at flow rate of 30 ml/min. (a) 3D side view. (b)(c)(d) Close-up views.

Figure 6 :

 6 Figure 6: Numerical simulation of a laminar flow around a symmetrical arrangement of nine beads for an inlet velocity of 0.001 m.s -1 . (a) Norm of the fluid shear stress on the beads surface. (b) Norm of the fluid velocity vector.

Figure 7 :

 7 Figure 7: Visualization obtained by X-ray micro-tomography of the tissue on the scaffold after two weeks of culture at a flow rate 20 ml/min. (a) 3D side view. (b) 2D representative slide (intensity normalized with respect to the maximum intensity Im). (c)(d) Close-up views (e) Variation of the relative intensity I/I m associated to each pixels along the yellow line drawn on (d).

Acknowledgments

This work has been financially supported by the French Agence Nationale de la Recherche through the Investissements d'avenir program (ANR-10-EQPX-37 MATMECA Grant) and the Fondation pour la Recherche Médicale (FRM FDT201805005480).

We thank Pascal Silberzan (Institut Curie) for kindly providing the NIH-3T3 cell line and Stéphane Roux (LMT, ENS Paris-Saclay) for his kind help regarding image post-processing.

Conflict of interest

The authors have no conflict of interest to declare and all co-authors confirm agreement with the final statement. All authors have been appropriately disclosed according to the policy of the Journal.

Ethical statement

There are no animal experiments carried out for this article.


Mikaël Jacquemont
email: jacquemont@lapp.in2p3.fr

Thomas Vuillaume

Alexandre Benoit

Gilles Maurin

Patrick Lambert

Single Imaging Atmospheric Cherenkov Telescope Full-Event Reconstruction with a Deep Multi-Task Learning Architecture

The Cherenkov Telescope Array (CTA) is the next generation ground-based observatory for γ-ray astronomy. It will be used to study γ-ray sources, allowing to better understand the Universe. One order of magnitude more sensitive than the current generation of experiments, CTA will propose unseen challenges to standard reconstruction methods. The GammaLearn project offers to apply deep learning as a part of the analysis of CTA data. Its goal is to separate the γ photons from cosmic particles, and reconstruct the γ photon parameters (energy and arrival direction) from noisy unconventional images, with expected better performance and faster reconstruction than standard methods. Here we present a complete reconstruction of IACT events using state-of-the-art deep learning techniques. The network is then applied in the single telescope context of the LST1, the first CTA telescope prototype built on the Northern hemisphere site (La Palma, Canary Island). We show that the full event reconstruction is possible with a single multi-task network, reducing the computing needs.

Introduction

Imaging Atmospheric Cherenkov Telescopes (IACT) detect the Cherenkov light induced by particle showers generated by cosmic rays and gamma rays entering the atmosphere. A complex data analysis is then required to reconstruct the direction, energy and type of the incoming particle from the telescope images. Since the 2012 ImageNet breakthrough, deep learning advances have shown dramatic improvements in data analysis across a variety of fields. Convolutional neural networks look particularly suited to the task of analyzing IACT camera images for event reconstruction as they provide a way to reconstruct the interesting physical parameters directly from calibrated images, skipping the preprocessing steps of standard methods, such as image cleaning and image parametrization. Moreover, despite demanding substantial computing resources to be trained and optimized, neural networks show very good performance during inference in a production setup. Some effort has been made to explore deep learning techniques for IACT data analysis, especially to perform gamma event reconstruction of CTA data [START_REF] Nieto Castaño | 35th International Cosmic Ray Conference[END_REF][START_REF] Mangano | IAPR Workshop on Artificial Neural Networks in Pattern Recognition[END_REF] or other IACTs [START_REF] Shilon | [END_REF]. Although these papers present promising results, especially for gamma/proton classification, they all handle the different reconstruction problems as single tasks, without considering their strong interdependence. 1 2. γ-PhysNet for Full Event Reconstruction γ-PhysNet is a multi-task learning (Caruana 1997) architecture that performs full-event reconstruction with a single neural network, exploiting the interdependence of the parameters to reconstruct. It is composed of two parts. The first one is a very deep backbone (the convolutional part of the ResNet 56 [START_REF] He | CVPR2016[END_REF])) augmented with Dual Attention (Sun et al. 2020). The attention blocks help the model focus on the relevant part of the feature maps to extract a meaningful latent representation of the input data. This representation is then fed to a multitask block inspired by the physics knowledge. This block is divided into two paths, a global path to reconstruct the energy and a local path to perform gamma/proton separation, direction reconstruction and virtual impact point reconstruction as an auxiliary task. Multi-task learning helps improve the generalization ability of the model, and so the reconstruction performance by reducing the degeneracy introduced by the monoscopic detection by a single IACT. To automatically balance the tasks during the learning process, we use an adaptive method relying on the modeling of the homoscedastic uncertainty of each task [START_REF] Kendall | Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition[END_REF]). In addition, in order to prevent protons from disturbing the learning of the energy and direction reconstruction of gamma events, we use a masked loss strategy. γ-PhysNet is implemented with indexed convolution (Jacquemont et al. 2019) to apply deep learning directly to the hexagonal pixel images of the LST1, thus reducing the number of preprocessing steps. Besides, γ-PhysNet inference rate on an NVIDIA V100 is compatible with data acquisition rates, making it a potential solution for real-time analysis.

γ-PhysNet Performance

Experiments. We evaluate γ-PhysNet in the single-telescope context of the LST1. We use the large-scale Monte Carlo production generated by the LST collaboration for the LST1 commissioning, referenced as the LST4 mono-trigger Production (from 2019/04/15). This dataset has been calibrated and integrated with DL1Data-Handler [START_REF] Kim | DL1-Data-Handler: DL1 HDF5 writer, reader, and processor for IACT data[END_REF]. It is separated into a training set, a validating set and a test set. The images have two channels, one for pixel intensity (unit being the number of photoelectrons) and the other containing per-pixel mean arrival time of the photoelectrons. A series of loose selection cuts on image amplitude and truncated showers is applied to the data, resulting in a training set composed of 874k gammas and 506k protons. With the help of the GammaLearn framework (Jacquemont et al. 2019), we train γ-PhysNet on diffuse gamma and proton events scattered over the full field of view of the 4 telescopes of the dataset to provide a more accurate overview of the data variability. The model is evaluated on point-like gamma and proton events detected by the LST1 only.

Results. We compare the performance of the proposed architecture with the widespread Hillas + RF method (Bock et al. 2004) that relies on image Hillas parametrization followed by Random Forest regressions and classifications. We repeat the experiments 10 times for γ-PhysNet, in order to take into account the variability introduced by the network parameter initialization. The resolution curves and the sensitivity presented in Figure 2 and 3 are then drawn as bands to illustrate this variability. Both angular and energy resolution curves and the sensitivity one show that γ-PhysNet outperforms the Hillas + RF method below 1 TeV. The improvement is remarkable at the lowest energies (below 100 GeV), and is especially relevant for the study of extragalactic sources and transient phenomena. In particular, γ-PhysNet improves the direction reconstruction up to 0.3 °at very low energy. Moreover, it has a sensitivity twice better on the same energy range. Besides, we observe a very low variability for the three metrics presented, highlighting the robustness of our architecture. Combined with its computing performances, this approach is therefore a good candidate for offline and online analysis for CTA, although moving from simulations to real data will be challenging.

Conclusion

The results obtained by γ-PhysNet on Monte Carlo simulations show that full-event reconstruction form a single IACT data is possible with a deep multi-task architecture. In a future work, we will probe how this good results transfer to real data by analyzing the data produced by the LST1. We also plan to lean on this good performance in a single telescope context to build a model for stereoscopic data reconstruction.

Figure 1 .

 1 Figure 1. γ-PhysNet, a physically inspired multi-task architecture for single telescope full-event reconstruction.

Figure 2 .

 2 Figure 2. Comparison of γ-PhysNet and Hillas + RF. Angular (left) and energy (right) resolutions representing the 68% containment of the error per energy bin.

Figure 3 .

 3 Figure 3. Sensitivity. Comparison of γ-PhysNet and the widespread Hillas + RF method. The performance of MAGIC (Aleksić et al. 2016) is included for reference.

Acknowledgments. We gratefully acknowledge financial support from agencies and organizations listed here: www.cta-observatory.org/consortium_acknowledgment. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 653477, and from the Fondation Université Savoie Mont Blanc. This work has been done thanks to the facilities offered by the Univ. Savoie Mont Blanc -CNRS/IN2P3 MUST computing center and HPC resources from GENCI-IDRIS (Grant 2020-AD011011577) and computing and data processing ressources from the CNRS/IN2P3 Computing Center (Lyon -France). We gratefully acknowledge the support of the NVIDIA Corporation with the donation of one NVIDIA P6000 GPU for this research.


Dr Daniela Mazzier

Dr Soumen De

Dr Barbara Wicher

Dr Victor Maurizot

Ivan Huc
email: ivan.huc@cup.lmu.de

Prof. I Huc

Parallel homochiral and anti-parallel heterochiral hydrogen-bonding interfaces in multi-helical abiotic foldamers

Keywords: helix bundles, foldamers, tertiary structures, molecular design, structure elucidation

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Parallel homochiral and anti-parallel heterochiral hydrogenbonding interfaces in multi-helical abiotic foldamers

Daniela Mazzier, [a,b] Soumen De, [b] Barbara Wicher, [c] Victor Maurizot [b] and Ivan Huc* [a,b] Abstract: A hydrogen-bonding interface between helical aromatic oligoamide foldamers has been designed to promote the folding of a helix-turn-helix motif with a head-to-tail arrangement of two helices of opposite handedness. This design complements an earlier helix-turnhelix motif with a head-to-head arrangement of two helices of identical handedness interface. The two motifs were shown to have comparable stability and were combined in a unimolecular tetra-helix fold constituting the largest abiotic tertiary structure to date.

Foldamer research has shown that secondary structures such isolated helices or -strands occur in a great variety of synthetic backbones. [1] In contrast, the design of tertiary folds represents a considerable challenge. This challenge is worth pursuing because tertiary folding is the level at which sophisticated functions emerge in proteins and the same may be expected for foldamers. The way is being paved by impressive progress in protein design [2] and increasing mastery in programming binding interfaces between peptidic structures, in particular within peptide helix bundles. [2b, 2c, 3] For instance, helix bundles have been reported in peptidomimetics such as -peptides [4] and -ureas. [5] We have recently introduced the first abiotic tertiary folds, that is, from backbones that do not relate to peptides or nucleotides. [6] We used the stable helices formed by aromatic oligoamides of 8amino-quinolinecarboxylic acid [7] (Q in Fig. 1) and 6-aminomethylpyridine carboxylic acid [8] as well-defined modules and introduced hydroxy groups at precise positions at their periphery (X and Y in Fig. 1) to promote inter-helix hydrogen bonding with amide carbonyl groups (Fig. 2a). Various types of helix bundling were observed, including parallel trimers and dimers, and tilted dimers. [6,9] As opposed to biotic tertiary folds that form in water and are often driven by hydrophobic effects, these folds form in organic solvents. All these assemblies were homochiral, i.e. they involved helices that have the same handedness. Further progress in tertiary structures design will primarily rest on the orchestration of interactions between secondary folds, a far-fromtrivial endeavor. Here we introduce a binding interface between helices of opposite handedness. Unlike what was recently shown in heterochiral peptide bundling, [10] we demonstrate the equivalence of parallel homochiral and anti-parallel heterochiral abiotic helix association. We also show how the two patterns can be combined within the same tertiary fold without having to consider stereochemistry at each unit, as it would in a peptide. Turn unit T1 (Fig. 1) has been shown to promote homochiral parallel helix bundling between two identical helical segments attached at their C-terminus as, for example in sequence 1 (Fig. 1). [6] Molecular modelling was used to design 1: it allowed us to adjust the positions of hydrogen-bond donors and led to the replacement of some X units by Y to avoid possible steric repulsions. A diagram of the helix-helix interface illustrates how the hydrogen-bond donors and acceptors may face each other (Fig. 2c,left). This diagram also shows that hydrogen bonding occurs despite the helices having the same handedness: the slope of the main chain (i.e. the angle between its tangent and a plane perpendicular to the axis) should in principle result in some distance between hydrogen-bond donors and acceptors placed on two helices of identical handedness. Yet the large helix diameter and the resulting moderate slope (ca. 15°) are such that hydrogen bonding takes place. An extension of this observation is that an anti-parallel heterochiral helix dimer (Fig. 2c, right) should not only give rise to a similar hydrogen-bonding pattern, but in fact lead to a better match between the positions of the donors and acceptors due to the fact that the helical chains have their tangent parallel to each other at the interface, i.e. their slopes have opposite signs (Fig. 2c). [11] To test this prediction, we designed turn unit T2 and sequence 2 (Fig. 1). It should be pointed that sequence 2 contains the very same nonameric helix segment as 1 but that one of the two is now attached to the turn at its N-terminus. helices (left) can be transformed in an equivalent array between anti-parallel heterochiral helices (right). In the plane symmetrical central structure, hydrogenbond donors (reciprocally acceptors) face each other and no hydrogen bond forms: inverting either helix handedness or sequence orientation makes hydrogen bonding impossible, whereas changing both is a productive transformation. The C2 axis in the diagram at left is best seen in the crystal structure shown in Fig. 4a.

The synthesis of the Fmoc-protected version of T2 is described in the supporting information. For the synthesis of 2a, and in anticipation of the preparation of much longer oligomers, we developed a solid-phase fragment condensation (SPFC) approach (Fig. 3a). Fragments A and B were synthesized using previously reported solid phase synthesis (SPS) methods. [8c,12] Segment A was then cleaved from the resin, purified and coupled to T2-terminated fragment B still on the resin. To prepare 2a, two identical fragments were condensed. Using mild resin cleavage conditions, the oligomer 4 was obtained as a free carboxylic acid with side chains protections still on, and was then converted into the corresponding methyl ester 2a. showing the NH and OH resonances of 1 [9] The 1 H NMR spectrum of 2a in CDCl3 shows two set of signals, suggesting the coexistence of PM and PP/MM conformers in solution (Fig. S1a), as was previously observed for structures containing T1. [6,9] On the contrary, the deprotected sequence 2b shows one set of sharp NMR signals including for OH resonances (Fig. 3c). The spectrum is similar to that of 1 (Fig. 3b) and indicative of a well-folded helix-turn-helix motif. A crystal structure of 2b confirmed the formation of the anti-parallel heterochiral helix dimer (Fig. 4b). The resemblance of the hydrogen-bonding interface in this structure with that of 1 (Fig. 4a), is striking. Despite the change of one helix handedness and orientation, the hydrogen-bond donors and acceptors are found at very similar positions (Fig. S2-3). The stability of the hydrogen-bonding interfaces was then assessed upon monitoring the effect adding DMSO-d6 in CDCl3 solutions. Because of the rigidity of the aromatic helices, chelate effects are observed between the hydrogen-bonding units that results in an all-or-nothing behavior: the six hydrogen bonds are disrupted all at once through a small change of DMSO concentration. Remarkably, this transition occurred with identical amounts of DMSO (ca. 20 % vol/vol, Fig. S4-7) for 1 and 2b, showing comparable strengths of the parallel homochiral and anti-parallel heterochiral hydrogen-bonding interfaces.

Differences from peptide helical bundles may be noted here. In peptides, bundling is mostly known between -helices of identical handedness which, to best match at their binding interfaces, generally coil around one another. Studies on heterochiral peptide helix bundling [10] and in particular some recent work by Gellman [10a,b] et.al., show that homochiral and heterochiral peptide helix interfaces are not equivalent, notably because coil-coiling is not conducive of better complementarity in heterochiral bundles. In contrast, the rigidity of the aromatic helices hampers coiling, at least over short distances, and strictly parallel arrangements form when mediated by turn units such as T1 and T2. However, aromatic helices may slightly change their local curvature, so as to optimize inter-helix interactions: helix curvature in the structures of 1 and 2b is not rigorously constant and identical to that of relaxed helices not involved in bundling.

In compounds 1 and 2b, helix handedness control is relative, not absolute, and guided only by strand orientation as imposed by the turn unit, and by hydrogen-bonding complementarity. This should in principle allow for the combination of both parallel-homochiral and antiparallelheterochiral motifs in the same tertiary structure without having to consider the nature of stereogenic centers at each unit as it would in peptides. We challenged this possibility through the design of sequence 3b (Fig. 1). As shown in Fig. 4d-c, 3b is expected to fold in a sequence of four contiguous helices having either identical or opposite handedness depending on whether they are separated by T1 or T2, with the central YXXQ h Y helical segments each bearing two independent hydrogen-bonding interfaces, one homochiral, and one heterochiral. In the design of 3b, we made use of helices of different length to avoid creating an extended aromatic surface that might promote aggregation and reduce solubility. Similarly, we introduced Q h units with a longer branched alkyl chain inside the sequence to promote solubility (Fig. 1). Oligomer 3a was synthesized combining SPFC (Fig. 3a) and solution phase synthesis for the final coupling of T1 with 5. The 1 H NMR spectrum of protected compound 3a was complex due to the presence of multiple turn units (Fig. S1b) and thus of different conformational stereoisomers (PMMP, PMMM, MMMM, PMPM, PMPP, MMPP and their enantiomers). After removal of the side chain protecting groups, a sharp spectrum with only one set of signals was observed for 3b (Fig. 3d). Even though an unambiguous structure elucidation could not be achieved in solution or in the solid state, these observations altogether suggest that 3b is present in solution in a well-defined folded conformation.

In conclusion, we have introduced a new well-defined abiotic helix-helix hydrogen-bonding interface and showed that tertiary structures combining different interfaces can be designed, resulting in predictable helix-turn-helix structures comprised of helices of different handedness and orientation, a pattern difficult to reach with simple peptides. We currently expand this work to interfaces between tilted, i.e. non-parallel, helix multimers and will report our progress in due course.

Figure 1 .

 1 Figure 1. Structures of units Q, Q h , X, Y, T1, T2 and foldamer sequences. X and Y are the protected precursors of hydrogen-bonding units X and Y. Sequences are labelled 'a' when protected and 'b' when deprotected. Sequences end with an 8-nitro group at their N-terminus: this group is noted in the replacement of the NH group at N-terminal Q units. The T1 unit constitutes an inversion of C→N sequence polarity; sequences that contain T1 thus have two N termini. The arrows indicate the hydrogen-bonding patterns between the helices and point towards the hydrogen-bond acceptor. TMSE = 2trimethylsilylethyl.

Figure 2 .

 2 Figure 2. Hydrogen-bonding patterns involving X (a) and Y (b) units. Double headed arrows indicate the different distances between the two hydrogen bonds for both X and Y units, as represented in c. c Helical net diagrams depicting hydrogen bond interfaces between helices. The arrays of six hydrogen-bond donors (yellow) and acceptors (red) belonging to X (top and bottom) and Y (middle) units are approximated to belong to two planes facing each other. Hydrogen bonds are shown as dotted black lines. Blue and pink rods represent the rims of the helices and are tilted in different directions according to their P or M helix handedness. A hydrogen-bond array between parallel homochiral

Figure 3 .a

 3 Figure 3. a Scheme of synthesis of compounds 4 and 5 via solid-phase fragment condensation (SPFC). Extract of 1 H NMR spectra (500 MHz, CDCl3)showing the NH and OH resonances of 1[9] (b), 2b (c) and 3b(d). The red dots indicate signals corresponding to OH protons.

  Figure 3. a Scheme of synthesis of compounds 4 and 5 via solid-phase fragment condensation (SPFC). Extract of 1 H NMR spectra (500 MHz, CDCl3)showing the NH and OH resonances of 1[9] (b), 2b (c) and 3b(d). The red dots indicate signals corresponding to OH protons.

Figure 4 .

 4 Figure 4. Crystal structures of compounds 1 [6] (a) and 2b (b). Front view (c) and top view (d) of energy-minimized molecular model of 3b. Cartoons indicate helix handedness, C and N-termini. Side chains of Q, Q h , T1 and T2, included solvent molecules and most hydrogen atoms have been omitted for clarity.

Acknowledgements

This work was supported by the European Research Council under the European Union's Seventh Framework Programme (Grant Agreement No. ERC-2012-AdG-320892). It benefited from the facilities and expertise of the Biophysical and Structural Chemistry platform at IECB, CNRS UMS3033, INSERM US001, Université de Bordeaux. We thank Dr. B. Kauffmann for assistance with X-ray data collection and Ms. F. Menke for NMR measurements.