text:
BALLISTIC MISSILE INFRARED SIGNATURE: TOWARDS A SURROGATE MODEL Rialland Valerie

(1) , Nicole Aurelie (1) , Antoni Alomar Sitjes (1) , Guy Aurelien (1) and Lefebvre Sidonie

(1) (1) ONERA, BP80100, 91123 Palaiseau CEDEX, Email:valerie.rialland@onera.fr KEYWORDS: Infrared signature, simulation, sensitivity analysis, reduced order model

ABSTRACT:

The multi-disciplinary project SIMBA (acronym for Ballistic Missile Signature in French) was conducted by ONERA from 2014 to 2018 to study and develop an infrared signature (IRS) model. A detailed experimental study was performed at the exhaust of the MASCOTTE test facility to validate our simulation tools, which include LES (Large Eddy Simulation) and RANS (Reynolds-Averaged Navier-Stokes) fluid dynamic solvers, and a radiative transfer code. Then a Proper Orthogonal Decomposition (POD) model was derived from the LES results: the objective was to develop a preliminary Reduced Order Model (ROM). Finally, a sensitivity study on the in-flight test-case of the sounding rocket Black Brant was performed, as a first step towards a simplified multifidelity infrared signature metamodel.

INTRODUCTION

The infrared signature (IRS) modelling of rocket plumes is a challenging problem involving rocket geometry, propellant composition, combustion modelling, trajectory calculations, fluid mechanics, atmosphere modelling, gas and particles radiative properties, and radiative transfer through the atmosphere. ONERA decided to tackle this complex problem through a common project involving several research teams: SIMBA (French acronym for Ballistic Missile Signature). We developed a chain of simulation tools in order to achieve the infrared signature prediction of rocket plumes. This chain, named PRECISE (Plateforme de Recherche pour l'Evaluation de la CInématique et des Signatures d'Engins), encompasses several in-house codes: first, COPPELIA is a thermodynamic equilibrium code that computes the motor specific impulse, the temperature and the gaseous species composition in the combustion chamber as a function of the propellant composition and the nozzle expansion ratio. The chamber temperature, pressure and gaseous composition, the rocket speed, altitude and geometry are used to initialize ONERA Computational Fluid Dynamics (CFD) code CEDRE for the plume flow field computation. CEDRE [START_REF] Chevalier | CEDRE:development and validation of a multiphysic computational software[END_REF] is a multiphysics computational tool for numerical simulation in the field of energetics, with particular emphasis on propulsion applications. The aerothermochemical cartography of the plume computed by CEDRE is transposed on a structured mesh for the last step of the modelling chain: the radiative transfer computation. Our infrared signature computation tool, named SIR, takes as input the pressure, temperature, mass fraction of H 2 O, CO 2 , CO, HCl, alumina particle density and temperature. It can perform radiative transfer computation in a hot non-scattering medium with either a line-by-line model or a statistical narrow band model called RGM3000 [START_REF] Rialland | Infrared signature modelling of a rocket jet plumecomparison with flight measurements[END_REF]. The scattering media are dealt with using the SHDOM solver [START_REF] Evans | The Spherical Harmonics Discrete Ordinate Method for Three-Dimensional Atmospheric Radiative Transfer[END_REF]. The PRECISE chain was used to predict the infrared signature of a solid rocket motor with aluminized propellant, the Black Brant sounding rocket (maximum thrust 77 kN). The calculation case reproduces the conditions of an experimental rocket launch, performed at White Sands in 1997, during which DRDC Valcartier recorded high quality infrared spectral imagery data [START_REF] Moyers R L | Ground-Based Signature Measurements of a Black Brant Sounding Rocket[END_REF] [START_REF] Schwartz | The SERTS-97 Rocket Experiment to Study Activity on the Sun : Flight 36.167-GS on[END_REF]. The simulated results were compared to the measured signatures of an in-flight rocket plume and achieved quite a good agreement [START_REF] Rialland | Infrared signature modelling of a rocket jet plumecomparison with flight measurements[END_REF]. However, other plume IRS predictions evidenced some discrepancies with measurements, especially for front views, where the plume is partially obscured by the missile body. Detailed analyses pointed out that the estimated plume aperture was not large enough. That is the reason why we decided to put some emphasis on the modelling of the mixing between exhaust gases and the outer atmospheric flow field, which is driven by turbulence. In order to improve the knowledge of the reactive flow field which expands into the air environment downstream of the nozzle exit, a detailed experimental and numerical study was performed at the exhaust of the MASCOTTE test facility developed by ONERA [START_REF] Vingert | MASCOTTE, a test facility for cryogenic combustion research at high pressure[END_REF]. The results of this experiment and the corresponding LES simulation will be presented in section 2. The CFD simulations require computer-intensive calculations in order to model the complex physical phenomena involved in the rocket plume infrared signature. This is why we decided to apply a Proper Ortogonal Decomposition (POD) on the LES simulation results in order to develop a Reduced Order Model (ROM), detailed in section 3. We also performed a sensitivity analysis presented in section 4 on several key input parameters in order to identify the most influent variables. Then a simplified model will be derived which describes the infrared signature evolution along the missile trajectory in propulsion phase.

MASCOTTE EXPERIMENTATION AND SIMULATIONS

Experimentation

A detailed experimental study was performed at the exhaust of the MASCOTTE test facility developed by ONERA. Several time-resolved in situ optical diagnostics obtained at high repetition rates were used to characterize the afterburning plume zone: stereoscopic particle image velocimetry (2D-3C PIV), laser induced fluorescence images of OH radical (OH-PLIF) and spontaneous emission images of excited OH*. The aerodynamics of the supersonic plume is visualized using the PIV measurements, and the afterburning zone is characterized through the OH-PLIF technique as well as the excited OH* emission measurements. A prototype fast Fouriertransform spectroradiometer was used for recording infrared emission spectra at several locations in the plume. A medium-wave (3-5 µm) infrared camera and a short-wave (0.7-1.6 µm) infrared camera were set to get full images of the plume. More details about the experimental setup can be found in [START_REF] Ristori | Caractérisation expérimentale de la couche de mélange dans un jet de post-combustion et comparaison aux simulations LES[END_REF][8] [START_REF] Rialland | Ballistic Missile Infrared Signature: Numerical and Experimental Study[END_REF].

Computer Fluid Dynamic Simulations

All the measurements were used to assess the numerical models of our code CEDRE [START_REF] Chevalier | CEDRE:development and validation of a multiphysic computational software[END_REF], and our radiative transfer code (called SIR). In order to investigate the reactive plume structure and dynamics, a reactive Large Eddy Simulation (LES) was performed. Indeed, this simulation approach enables the description of the turbulent structures and their development in the exhaust plume. The final LES mesh contains 34 million of tetrahedral elements, and is only 1 m long and 0.1 m wide. The nozzle exit and the mixing layer are carefully meshed: the mesh size at the nozzle lip is 0.01D, corresponding to 630 cells in the azimuthal direction. The large eddy simulation was performed over 7 ms, which corresponds to around 1000 D⁄U where U is the velocity at the nozzle exit (U=2700 m/s). The simulation was performed thanks to a GENCI (Grand Équipement National de Calcul Intensif www.genci.fr) allocation of 1 million CPU hours, on CEA's Curie supercomputer. For more details about the MASCOTTE LES computation, please refer to [START_REF] Rialland | Experimental and numerical study of a supersonic plumes with afterburning for plume infrared signature prediction[END_REF][9] [START_REF] Nicole | Experimental and numerical investigation of a reactive plume for a rocket-engine exhaust[END_REF].

Figure 2: OH mass fraction LES snapshot

A RANS (Reynolds-Averaged Navier-Stokes) simulation was also performed with CEDRE and compared to the LES calculations in order to quantify the error induced by the average turbulence model. The same chemical kinetic scheme was used for both LES and RANS computations. The RANS turbulence model used was k-epsilon modified for axisymmetry.

Infrared measurements and simulations

Infrared instruments include one infrared camera (MWIR 3-5 µm) with a 60-cm diameter field of view, and a high frequency spectrometer developed by ONERA Microspoc (2.5-5.2 µm) with a 2-cm diameter field of view. The MWIR camera was operated at 100Hz with an integration time of 200µs. Microspoc was operated at 245 Hz for 8 s with an integration time between 0.75 and 3 ms according to the firing conditions, and it aimed at two different locations during the trials: 23cm and 75cm from the nozzle exit plane. All three instruments were looking at the plume with an aspect angle of 90°. A subset of 32 snapshots was extracted from the LES simulation. These snapshots, sampled with a time interval of 6.5 µs, cover a duration of 208µs, which corresponds to the MWIR camera integration time. The IR radiance cartography and the spectral intensity were computed for each snapshot and for the time-averaged flowfield, over the spectral band 2000-4000 cm-1 (2.5 -5 µm). The radiative species considered are H2O, CO2 and CO. The radiative transfer code used is a Narrow Band Statistical Model based on Curtis-Godson approximation [START_REF] Godson | The evaluation of infrared radiative fluxes due to atmospheric water vapour[END_REF], which takes into account the spectral correlations in case of multiple layers of gas with different physical conditions. Figure 3 shows the spectrally-integrated radiance cartography for one snapshot (left), for the average of the 32 flow fields (centre) and for the RANS simulation (right). Because of the structure movements, the average cartography presents lower radiance maxima than the snapshot cartographies. Figure 4 presents the comparison between the apparent spectral intensity measured by Microspoc spectrometer, aiming at a point on the plume axis located at 23 cm from the nozzle exit plane, with a 2-cm diameter field of view and with a targetsensor distance of 2m (purple line) and the predictions in the same geometrical configuration: averaged apparent spectral intensities over the 32 snapshots (blue line), apparent spectral intensities computed over the averaged flow field (red line) and the RANS simulation (green line). On this reduced field of view, the intensity computed on the averaged flow field is higher than the averaged intensities. Predictions seem to underestimate the measured radiation: a possible explanation is that the predicted temperature field is also underestimated. Please refer to [START_REF] Rialland | Experimental and numerical study of a supersonic plumes with afterburning for plume infrared signature prediction[END_REF][9] for more detailed results.

PROPER ORTHOGONAL DECOMPOSITION APPLIED TO MASCOTTE LES SIMULATION

Introduction

Reduced order models (ROMs) are models that mimic the behaviour of the original flow field, but using less information. The two general defining properties of a ROM are 1) that it reduces the size (in terms of amount of information), and 2) that it provides accurate approximations of the original system. A spatio-temporal ROM has been tested upon the MASCOTTE LES simulation. The spatial reduction side of the ROM has been achieved by proper orthogonal decomposition (POD). POD is a statistical tool based on an eigenvalue decomposition of the flow field autocorrelation function. A fundamental property of POD is that, when the POD modes are ordered in terms of decreasing energy, the n th rank reconstruction is the best linear approximation of rank n of the original flow field. This makes POD an efficient tool to develop ROMs, by simply taking a reduced number of the leading POD modes. The frequencydomain version of POD, usually called spectral POD, is especially useful when the flow field has temporal and/or spatial symmetries. In such cases, the initial POD can be decoupled into lower dimensional POD problems through a Fouriertransform along the symmetric directions [START_REF] Nobach | Handbook of experimental fluid mechanics. Chapter 22: Review of Some Fundamentals of Data Processing[END_REF] and leads to an even more efficient reduction [START_REF] Gudmundsson | Instability wave models for the near-field fluctuations of turbulent jets[END_REF][14].

Methodology

In the present test case, where the goal is to compute the infrared radiation emitted by the jet, it is necessary to capture the high temperature and mass fraction fields of the chemical species, which extend well downstream of the potential core. The domain considered is located between 4D and 30D along the jet axis and up to 6D in radius. It covers 234000 cells and 2078 snapshots. In order to focus into the frequency range of interest for the ROM, a low-pass frequency filter has been applied prior to performing the spatial and temporal reductions. A cut-off frequency St filt = 0.4St Nyq = 0.2 St samp has been used. This frequency is too low to resolve a significant portion of the energy spectrum in the potential core region, but it is high enough to resolve the entire spectrum downstream of the potential core. Prior to performing POD, the temporal means of each individual row are subtracted from the data matrix, leaving a purely stationary flow field. In order to include variables in the POD analysis with different physical units, each In this spectral POD, the Fourier transform along the azimuthal symmetric direction is taken prior to applying the POD algorithm:

𝑓 𝑖𝑚 (𝑥, 𝑟, 𝑡) = ∑ 𝑓 𝑖 (𝑥, 𝑟, 𝜃 𝑘 , 𝑡)𝑒 𝑗𝑚𝜃 𝑘 𝑁𝜃 𝑘=1 , 𝑚 = - 𝑁 𝜃 2 , ⋯ , 𝑁 𝜃 2 ,
The transformed flow field can be encapsulated in the following data matrices, for every azimuthal mode m: . The Fourier transform can also be applied to the time variable, assuming a homogeneous time behavior of the plume during the 2078 snapshots. Then a temporal reduction can be achieved.

𝑋 𝑚 = ( 𝑓 1𝑚 (𝑥 1 , 𝑟 1 , 𝑡 1 ) ⋮ 𝑓 1𝑚 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝑡 1 ) ⋯ ⋯ ⋯ 𝑓 1𝑚 (𝑥 1 , 𝑟 1 , 𝑡 𝑆 ) ⋮ 𝑓 1𝑚 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝑡 𝑆 ) ⋮ ⋮ ⋯ ⋯ ⋮ ⋮ 𝑓 𝑅𝑚 (𝑥 1 ,

Results

The POD was applied to the variables required for infrared signature computation: the static pressure and temperature, and the mass fraction of CO 2 , H 2 O and CO. For completeness, the three components of the velocity (u, v, w) and the mass fraction of OH have also been included. Examples of a reconstructed temperature snapshot from the complete spatio-temporal ROM using 80 POD modes are shown in Figure 7. More details about this work can be found in [START_REF] Alomar | Reduced order model of a reacting, turbulent supersonic jet based on proper orthogonal decomposition[END_REF]. The next step consists in calculating the infrared signature (IRS) on reconstructed snapshots and comparing it to the IRS of the LES snapshots.

BLACK BRANT SIMULATIONS: ALTITUDE AND SPEED SENSITIVITY STUDY

The final goal of our study is to produce realistic infrared signatures of ballistic missiles in order to design surveillance sensors. Therefore we need to estimate not only a realistic value at a given altitude and speed, but also evaluate the evolution of the signature along the missile trajectory.

Because LES or even RANS simulations cannot be run at every kilometer, we need to develop a simplified model that characterizes the major trends in the signature evolution. This model must rely upon high fidelity calculations, performed with RANS simulations. We decided to take as a reference the Black Brant test case mentioned in the introduction and described in [START_REF] Rialland | Infrared signature modelling of a rocket jet plumecomparison with flight measurements[END_REF], which was validated against DRDC in-flight measurements at 7.9km altitude. Then we modified the altitude and speed according to the cases detailed in table Figure 8 displays the temperature cartography for the three speed values: we note that the plume seems to be shorter and wider for the slowest case. On the contrary, the plume appears longer and narrower for the fastest case. The evolutions look monotonous around the reference case. The rocket speed plays an important role in the mixing of the exhaust gases with the external flow field. Figure 9 displays the temperature cartography for the three altitude values. The variation with altitude is less dramatic than with speed, however we notice that the higher the plume the colder. Also, the plume tends to be a little longer and wider with altitude: the lower pressure of high altitude enables a better expansion of the exhaust gases.

The infrared signature was calculated with our code SIR for every sensitivity case. Since the Black Brant used an aluminized propergol, the plume simulation comprises alumina particles. Therefore, we used the SHDOM solver [START_REF] Evans | The Spherical Harmonics Discrete Ordinate Method for Three-Dimensional Atmospheric Radiative Transfer[END_REF] to take into account the scattering on alumina particles. The spectral intensity was computed in the same geometrical configuration and on the same spectral band as in the reference test case [START_REF] Rialland | Infrared signature modelling of a rocket jet plumecomparison with flight measurements[END_REF], but without atmospheric attenuation (because no comparison is done to the measurements). Figure 10 displays the spectral intensity over the whole spectral band [1900-5000 cm-1] for every case. We focused our analysis on three spectral bands: 2000-2500 cm-1: spectral band with the peak emission of CO 2 and H 2 O at 4.3 µm 3100-3800 cm-1: spectral band with the emission of H 2 O at 2.7 µm 4400-4600 cm-1: spectral band with no gas emission, where only the "grey body" particle continuum can be observed. The analysis of the spectra shows that the order of the calculations in magnitude is different in each spectral band. To better quantify the evolution, Figure 11 represents the intensity integrated in each spectral band. ) with no atmospheric propagation for every sensitivity case. The analysis of Figure 11 shows that intensity increases with altitude for gas emission spectral bands. This can be explained by the longer and wider plume due to the lower pressure of high altitude: the growth of the emitting surface contributes to the rise of intensity. Conversely, intensity decreases with altitude for the particle spectral band. This may be explained by the decrease of the atmospheric temperature, which cools the particles faster. Intensity increases with speed for gas emission bands: this may come from the longer afterburning zone that can be observed on Figure 8. It is more difficult to conclude for the particle spectral band, because both the faster and slower cases produce a higher intensity than the reference case. At lower speed, the particle temperature and axial velocity remains close to the gas, whereas thermal and mechanical disequilibrium is observed at higher temperature. This effect may be the cause for this non monotonous behavior.

CONCLUSION

ONERA developed a chain of simulation tools in order to achieve the infrared signature prediction of rocket plumes. The CFD code CEDRE can perform RANS or LES simulations. Both models are computer-intensive, especially LES, which is the reason why we studied several reduced models in order to define a simplified plume IRS model along the missile trajectory. Our approach consisted in 1) validating our accurate models on in-flight (Black Brant) or test bench (MASCOTTE) measurements, in order to ensure the realism of our simulations, 2) developing a reduced order model so as to identify correlations between infrared signature input variables, and 3) building a simplified model of the plume infrared signature evolution, starting with an altitude and speed sensitivity study. For the first time at ONERA, a LES simulation of a supersonic reactive plume was computed on a mesh, rather large in view of the number of transported species. This computation comprises several challenges because it should describe correctly the dynamics of a supersonic jet but also the afterburning of a specific flame. The computation was performed on a tetrahedral mesh with 34 million elements thanks to an allocation of CPU time by GENCI. The experimental campaign on the MASCOTTE test bench was performed successfully during the summer of 2015, and resulted in a large experimental database for the validation of numerical simulations, for the aerodynamics but also the combustion. A spatio-temporal Reduced Order Model of a turbulent, reacting, over-expanded supersonic jet obtained from LES simulation based on POD (spatial reduction) and Fourier (temporal reduction) has been presented and assessed. The two fundamental properties of POD have been used: the optimal low-rank reconstruction, which leads to efficient spatial reductions, and the interpretation of the leading POD modes as the energetically dominant coherent structures. The next step consists in calculating the infrared signature (IRS) on reconstructed snapshots and comparing it to the IRS of the LES snapshots.

The altitude and speed sensitivity study is just the beginning of the simplified model for the plume IRS evolution. A multifidelity metamodel will be developed based on high fidelity points (such as the sensitivity study simulations) and low fidelity points. The low fidelity points may be nonconverged or less refined mesh for CEDRE computations, or a more simple CFD code adapted to jet plume such as REP [START_REF] Cousins | Calculation of conditions in an axisymmetric rocket exhaust plume: the REP3 computer program[END_REF].

Figure 1 :

 1 Figure 1: Experimental setup for PIV

Figure 3 :

 3 Figure 3: Infrared radiance cartography for snapshot 1 (left)), radiance cartography for the time-average of all 32 flow fields (centre), and for the RANS simulation (right). Same colour scale and field of view for all graphs.

Figure 4 :

 4 Figure 4: Averaged apparent spectral intensity for every snapshot (blue), for the averaged flow field (red) and for RANS simulation (green) calculated on the spectrometer field of view, Microspoc measured apparent spectral intensity (purple)

, 2 . 1 2𝜋∑

 21 𝑟 1 , 𝑡 1 ) ⋮ 𝑓 𝑅𝑚 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝑡 1 ) ⋯ ⋯ ⋯ 𝑓 𝑅𝑚 (𝑥 1 , 𝑟 1 , 𝑡 𝑆 ) ⋮ 𝑓 𝑅𝑚 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝑡 𝑆 )) The size of this matrix is N x x N r x S. The eigenvalue decomposition of the auto-correlation matrix 𝑋 𝑚 * 𝑋 𝑚 is equivalent to a singular value decomposition of X m : 𝑋 𝑚 = 𝑈 𝑚 Σ 𝑚 𝑉 𝑚 * . The left singular vectors forming U m are the spatial modes (topos), while the right singular vectors forming V m are the temporal modes (chronos). The diagonal matrix  m is equal to the square root of the matrix  m ( mi = ² mi , for i = 1,…, S), where  mi corresponds to the energy of each mode (intensity of the mode fluctuations). The eigenvalues and corresponding POD modes are usually ordered in decreasing order  m1 >  m2 > … >  mS > 0, which is equivalent to ordering the POD modes by their intensity of fluctuations. An optimum approximation of the data matrix X m is directly obtained using n POD modes: 𝑋 𝑚 ≈ 𝑋 𝑚𝑛 = 𝑈 𝑚𝑛 Σ 𝑚𝑛 𝑉 𝑚𝑛 *where U mn , V mn and  mn are obtained by retaining only the n leading columns. Then an optimum approximation of the data matrix X can be obtained with a reduced number of azimuthal modes: 𝑓 𝑖 (𝑥, 𝑟, 𝜃, 𝑡) ≈ 𝑓 𝑖𝑚 (𝑥, 𝑟, 𝑡)𝑒 -𝑗𝑚𝜃 𝑀 𝑚

Figure 5 (

 5 left) displays the energy fraction of the POD and azimuthal modes. Due to the large set of variables included in the decomposition and the large region considered, containing both the potential core and the downstream self-similar region, the total fluctuating energy of the jet is largely distributed among the POD modes. This leads to a relatively large POD basis required for an accurate reconstruction. The analysis of the frequency spectra of the leading chronos corresponding to the three most energetic azimuthal modes evidenced dominant frequencies of 70 Hz for m=0, 690 Hz for m=1 and 410 Hz for m=2.

Figure 5 :

 5 Figure 5: (Left) Energy fractions of the POD modes for a given azimuthal mode (Right) Global cross-products of all variable pairs (red = strongly correlated, green= partially correlated).

Figure 6 :

 6 Figure 6: Color maps of the real part of the 3 leading topos corresponding to the m = 0 (up) and m=1 (down) components of the axial velocity, temperature, Y OH , Y CO2 and Y H2O . The topos for m=0 and m=1 are represented on Figure 6. One can notice that the turbulent structures look very similar for temperature, Y OH , Y CO2 and Y H2O . The global cross-products between all variable pairs (Figure 5 right) show that 1) T is strongly correlated to Y OH , Y H2O , Y CO , Y CO2 , v and quite correlated with u, 2) u and v are correlated with every variable except P and w, 3) w is not correlated with any variable. Since strongly correlated variables have similar POD decompositions, this reduces even more the amount of needed information for the ROM.

Figure 7 :

 7 Figure 7: Unsteady temperature snapshot (a), sample after the low-pass filter (b), reconstruction with 80 POD modes (c), and reconstruction using

Figure 8 :

 8 Figure 8: Temperature for case v/2 (left), reference (center), 2v (right). Nozzle is at the top of the graph.

Figure 9 :

 9 Figure 9: Temperature for case 5 km (left), reference (center), 10km (right). Nozzle is at the top of the graph.

Figure 10 :

 10 Figure 10: Spectral intensity (W/sr/cm -1

Figure 11 :

 11 Figure 11: Integrated intensity (W/sr) with no atmospheric propagation for every sensitivity case.

  variable is normalized by the square root of the average global energy of the variable. The resulting value of the flow variable i at the spatial location (x, r, ) and time instant t is f i (x, r, , t). The flow field includes R variables, the cylindrical grid is formed of N x x N r x N  cells and the flow field is sampled at S time instants. The flow field can be encapsulated in the data matrix:

		𝑓 1 (𝑥 1 , 𝑟 1 , 𝜃 1 , 𝑡 1 ) ⋮	⋯ ⋯	𝑓 1 (𝑥 1 , 𝑟 1 , 𝜃 1 , 𝑡 𝑆 ) ⋮
	𝑋 =	𝑓 1 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝜃 𝑁𝜃 , 𝑡 1 ) ⋮ ⋮ 𝑓 𝑅 (𝑥 1 , 𝑟 1 , 𝜃 1 , 𝑡 1 ) ⋮	⋯ ⋯ ⋯ ⋯ ⋯	𝑓 1 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝜃 𝑁𝜃 , 𝑡 𝑆 ) ⋮ ⋮ 𝑓 𝑅 (𝑥 1 , 𝑟 1 , 𝜃 1 , 𝑡 𝑆 ) ⋮
	(	𝑓 𝑅 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝜃 𝑁𝜃 , 𝑡 1 )	⋯	𝑓 𝑅 (𝑥 𝑁𝑥 , 𝑟 𝑁𝑟 , 𝜃 𝑁𝜃 , 𝑡 𝑆 ))

Table 1 :

 1 1. Simulated conditions for Black Brant sensitivity study.

		Reference	V/2	2V	5 km	10 km
	Speed	646.79 m/s	323.39 m/s	1293.58 m/s	646.79 m/s	646.79 m/s
	Altitude	7.9 km	7.9 km	7.9 km	5 km	10 km
	Atmospheric	36117 Pa	36117 Pa	36117 Pa	54019 Pa	26436 Pa
	pressure
	Atmospheric	237 K	237 K	237 K	256 K	223 K
	temperature

ACKNOWLEDGEMENTS

This work was granted access to the HPC resources of TGCC under the allocation made by GENCI in 2015.


Jérôme Belen Gutierrez

Wong Ng

Lun Cui

Christophe Becavin

David Bikard
email: david.bikard@pasteur.fr

Jérôme Wong Ng

Genome-wide CRISPR-Cas9 screen in E. coli identifies design rules for efficient targeting

Keywords: CRISPR-Cas9, Escherichia coli, antimicrobial, genome-wide screen

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

Introduction

The Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) -associated protein 9 (Cas9) has been repurposed as a tool for a variety of applications including genome editing, transcriptional repression or activation, epigenetic modifications, chromosomal loci tagging and more [START_REF] Hsu | Development and Applications of CRISPR-Cas9 for Genome Engineering[END_REF]. In most Eukaryotic cells, Cas9 breaks can be efficiently repaired by templateindependent non-homologous end joining (NHEJ), which introduces small indels and can be conveniently used to knockout genes. Conversely, the main outcome of Cas9 cleavage in the chromosome of bacteria is cell death [START_REF] Bikard | CRISPR Interference Can Prevent Natural Transformation and Virulence Acquisition during in Vivo Bacterial Infection[END_REF][START_REF] Bikard | Exploiting CRISPR-Cas Nucleases to Produce Sequence-Specific Antimicrobials[END_REF][START_REF] Citorik | Sequence-Specific Antimicrobials Using Efficiently Delivered RNA-Guided Nucleases[END_REF][START_REF] Gomaa | Programmable Removal of Bacterial Strains by Use of Genome-Targeting CRISPR-Cas Systems[END_REF]. Most bacteria lack a NHEJ system, but even in species that do carry such repair pathway, it seems unable to efficiently repair Cas9 break under laboratory conditions (T. Xu et al. 2015;[START_REF] Bernheim | Inhibition of NHEJ Repair by Type II-A CRISPR-Cas Systems in Bacteria[END_REF]. Bacteria mostly rely on homologous recombination to repair double strand breaks, which is made possible by the fact that several copies of the chromosome are present in the cell under most conditions [START_REF] Dillingham | RecBCD Enzyme and the Repair of Double-Stranded DNA Breaks[END_REF][START_REF] Ayora | Double-Strand Break Repair in Bacteria: A View from Bacillus Subtilis[END_REF].

We recently showed that when Cas9 is guided to target a position in the chromosome, some guide RNAs appear to be less efficient than others. When guided by a weak guide, Cas9 will not cleave all copies of the chromosome simultaneously leaving a copy intact for repair and allowing cells to survive by entering a cycle of DNA cleavage and repair. However, a strong guide will lead to the simultaneous cleavage of all chromosome copies making repair through homologous recombination impossible and leading to cell death [START_REF] Cui | Consequences of Cas9 Cleavage in the Chromosome of Escherichia Coli[END_REF]. This property can be used to select specific mutants or genotypes in mixed bacterial populations or even harnessed to engineer sequence-specific antimicrobials able to kill target antibiotic resistant or virulent bacteria [START_REF] Bikard | Exploiting CRISPR-Cas Nucleases to Produce Sequence-Specific Antimicrobials[END_REF][START_REF] Gomaa | Programmable Removal of Bacterial Strains by Use of Genome-Targeting CRISPR-Cas Systems[END_REF][START_REF] Jiang | RNA-Guided Editing of Bacterial Genomes Using CRISPR-Cas Systems[END_REF][START_REF] Citorik | Sequence-Specific Antimicrobials Using Efficiently Delivered RNA-Guided Nucleases[END_REF]. For all these applications it is critical to understand what makes some guide RNAs better at killing the cell than others. Cas9 cleavage is the result of a process which starts with the formation of the gRNA-Cas9 nucleoprotein complex. Target search then occurs through the recognition of a small protospacer adjacent motif (PAM), followed by R-loop formation through pairing of the guide RNA with the target strand (S. H. [START_REF] Sternberg | DNA Interrogation by the CRISPR RNA-Guided Endonuclease Cas9[END_REF][START_REF] Anders | Structural Basis of PAM-Dependent Target DNA Recognition by the Cas9 Endonuclease[END_REF][START_REF] Jinek | A Programmable Dual-RNA-Guided DNA Endonuclease in Adaptive Bacterial Immunity[END_REF]. Upon successful pairing a conformational shift in the Cas9 protein occurs bringing two catalytic domains, RuvC and HNH, in contact with the DNA and leading to the formation of a double strand break (Samuel H. [START_REF] Sternberg | Conformational Control of DNA Target Cleavage by CRISPR-Cas9[END_REF]Jinek et al. 2014). Each of these steps could be impacted by the sequence of the guide RNA, genomic context, DNA conformation and DNA modifications.

High-throughput screens performed in Eukaryotic systems have enabled to identify sequence features that determine knockout efficiency [START_REF] Doench | Rational Design of Highly Active SgRNAs for CRISPR-Cas9-Mediated Gene Inactivation[END_REF][START_REF] Doench | Optimized SgRNA Design to Maximize Activity and Minimize Off-Target Effects of CRISPR-Cas9[END_REF]H. Xu et al. 2015;[START_REF] Moreno-Mateos | CRISPRscan: Designing Highly Efficient SgRNAs for CRISPR-Cas9 Targeting in Vivo[END_REF][START_REF] Wang | Genetic Screens in Human Cells Using the CRISPR-Cas9 System[END_REF]. However, the features that emerge in these models seem to be very different between experimental setups, and likely result in great part from constrains on the proper expression and stability of guide RNAs, rather than from their impact on Cas9 biochemical activity [START_REF] Haeussler | Evaluation of Off-Target and on-Target Scoring Algorithms and Integration into the Guide RNA Selection Tool CRISPOR[END_REF][START_REF] Moreno-Mateos | CRISPRscan: Designing Highly Efficient SgRNAs for CRISPR-Cas9 Targeting in Vivo[END_REF].

The goal of this study is to elucidate the genetic requirements for efficient CRISPR-Cas9 targeting in the bacterial chromosome. To this end, we performed a high-throughput screen in which we guide Cas9 to cleave ~92,000 different random positions around the chromosome of E. coli MG1655, followed by a "NGG" PAM. Upon Cas9 induction, guides that efficiently kill E. coli are expected to be rapidly depleted from the library, which can be measured through sequencing of the guide RNA library before and after induction of Cas9 expression. We observed large regions along the chromosome (~100 kb) in which the sgRNAs are rapidly depleted from the library while sgRNAs from other regions, are still present several hours after Cas9 induction. Surprisingly, this large-scale pattern is not correlated to cell death, as revealed by time-lapse microscopy. Indeed, cells immediately stop dividing, start to filament and then die after Cas9 induction regardless of the region targeted. We reveal that the pattern observed is rather due to differences in the copy number of the plasmid carrying the guide RNA library that arise after DNA cleavage in different regions of the chromosome. The loss of some genomic regions leads to an interruption of plasmid replication, while the plasmid can still replicate and increase its copy number after cleavage in other regions. The scale and shape of the pattern is determined by the extent of chromosomal DNA being degraded after Cas9 cleavage. After taking this interesting phenomenon into account, one can still observe differences in the efficiency of guide RNAs targeting the chromosome of E. coli. We built a neural network model able to predict this efficiency based on the guide sequence. Model previously build on Eukaryotic datasets have a limited predictive power on our data, highlighting the need to develop specific models of guide RNA activity in bacteria. Our model should directly aid in the design of guide RNA for genome editing and the development of CRISPR antimicrobials. We are making it available as guide RNA design tool at the following address: http://hub13.hosting.pasteur.fr:8080/CRISPRBact/.

Results

Large-scale depletion pattern of sgRNAs after Cas9 cleavage

We previously constructed a library containing 92,000 guides targeting random positions in the genome of E. coli followed by a "NGG" PAM motif [START_REF] Cui | A CRISPRi Screen in E. Coli Reveals a Sequence-Specific Toxicity of DCas9[END_REF]. We introduced this library in E. coli MG1655 carrying Cas9 in the chromosome under the control of a Ptet promoter (strain LC-E19).

Cas9 was induced and the library sequenced before induction and at different time points in order to determine the efficiency of killing of each guide (Fig. 1a). The experiment was performed in triplicates and the depletion of guides in the library was computed as the log2 transformed fold change of read counts normalized to a non-targeting guide RNA. When plotting the results along the chromosome of E. coli, we immediately noticed a large-scale pattern where guides targeting certain regions on a scale of ~100 Kbp are depleted from the population faster than guides targeting other regions. This pattern can be represented as the moving average of log2FC with a sliding window of 6kb, and is especially striking after 4H of induction (Fig. 1b,c).

We initially formulated the hypothesis that some chromosomal regions might be less accessible to Cas9 cleavage or more easily repaired than others. If this was the case, cells targeted in these regions might be able to survive longer and possibly keep dividing for a few generations after the induction of Cas9. To investigate whether the pattern observed through sequencing was indeed a measure of cell survival to Cas9 cleavage, we performed time-lapse microscopy experiments with guide RNA targeting different positions either in strongly depleted or weakly depleted regions. In all cases we observed that cells started to filament within minutes after Cas9 induction. Cells targeted by weakly depleted guides did not show a delayed or weaker response to Cas9 induction.

The number of reads obtained when sequencing the library can be seen as a measure of the abundance of plasmids carrying each guide RNA in the sample, which is typically used as a proxy of the number of cells carrying each guide in pooled CRISPR screen assays. Since the large-scale pattern observed did not seem to be linked to differences in cell survival, we reasoned that it might rather be due to differences in plasmid copy number (PCN). To test our hypothesis, we measured changes in PCN by qPCR and normalized to the number of copies of the chromosome as measured with qPCR probes distant from the cleavage position. We specifically investigated two regions: one centred on position 2.35 Mb in which guides are strongly depleted and one centred on position 2.95Mb in which guides are weakly depleted. We measured a decrease of PCN after Cas9 induction when targeting genes yfaL and glpA in the first region, and an increase of PCN when targeting genes fucI and tcdA in the second region (Fig. 1e). These results support the hypothesis that variations in the number of copies of the plasmid carrying the guide RNAs are responsible for the pattern observed.

Degradation of chromosomal genes that control plasmid replication explains the large-scale pattern

We then sought to understand why targeting specific genomic regions affects plasmid copy number.

We hypothesized that some regions might contain genes necessary for efficient plasmid replication.

Targeting these regions with Cas9 will lead to the degradation of the target DNA and therefore genes in the target region will no longer be expressed. If our hypothesis is correct then it should be possible to restore plasmid replication by cloning genes in the target region on a plasmid that will not be targeted by Cas9. To test our hypothesis we cloned ~13.3 Kbp located in the central part of the peak located around 2.34Mbp in plasmid pBG7 (Fig. 2a). We then targeted different positions inside or just outside of the region and measured PCN after Cas9 induction. As expected, the copy number of the plasmid carrying the guide was higher in the presence of pBG7 than with a control empty vector (pBG10). When a different region in which guides are also strongly depleted was targeted (see target in opgG), pBG7 did not have an effect on the PCN of psgRNA (Fig. 2b). These results support our hypothesis that genes cloned on pBG7 are important for replication of the plasmid carrying the library and that the loss of these genes after Cas9 cleavage results in the interruption of plasmid replication. In order to identify the specific gene responsible for the variations in plasmid copy number, we independently cloned genes or operons present in the 13.3 Kbp region cloned on pBG7 (Fig. 2a). We only observed a substantial increase in PCN when the nrdA-nrdB-yfaE operon was cloned on the plasmid (Fig. 2c, see pBG15). Genes nrdAB encode a ribonucleoside diphosphate reductase involved in pyrimidine deoxyribonucleotides synthesis [START_REF] Kolberg | Structure, Function, and Mechanism of Ribonucleotide Reductases[END_REF]). The loss of these genes might lead to a decreased availability of deoxypyrimidines and consequently an inhibition of DNA replication. This hypothesis is also consistent with the fact that the level of nrdA mRNA strongly dropped 4H after Cas9 cleavage, consistently with the emergence of the pattern (Supplementary Fig. 1). 143 Finally, we performed the Cas9 genome-wide screen again in the presence of plasmid pBG7, pBG15 or the control empty vector. We observed a much weaker depletion of guides targeting the region located around 2.34Mbp in the presence of pBG7 and pBG15 than with the control vector (Fig. 2d).

Interestingly guides in the library that targeted the region cloned on the complementation plasmid showed a stronger depletion than guides targeting just outside of this region (see Supplementary Fig. 2 for a zoom in the region). This is consistent with the fact that these guides will destroy both the chromosomal and plasmidic nrdAB operons, preventing rescue. As an internal control, a mutation was introduced in the PAM motif of one of the target positions carried by plasmid pBG7. As expected the guide targeting this position was much less depleted than surrounding guides (Supplementary Fig. 2).

The shape of the large-scale pattern is determined by DNA degradation speed

Our results therefore indicate that the nrdAB genes might be responsible for the depletion of guides targeting a region of ~100 Kbp with guides further away from the genes being on average less depleted than guides closer to the genes. These results suggest that the extent of DNA degradation determines the shape of the depletion pattern. To investigate this in more details we programmed plasmid psgRNA to target gene yfaL (next to nrdAB) and sequenced the DNA extracted from strain LC-E19 after 30min of induction. Sequence coverage can be used as a measure of the abundance of DNA around the target region in the sample. DNA was degraded over ~50 Kbp away from the target in about half of the cells (Fig. 2e). The scale of DNA degradation matches that of the large-scale guide RNA depletion pattern consistently with our hypothesis.

If DNA degradation determines the shape of the guide RNA depletion pattern, mutants of genes involved in DNA degradation might change it. We repeated the whole genome Cas9 cleavage screen in DrecD and DsbcB mutants. The pattern was indeed strongly affected in these mutants with broader peaks and a stronger overall depletion of guides in the DsbcB mutant and narrower peaks with a weaker overall depletion of guides in the DrecD mutant (Fig. 2f). Consistently with this observation, DNA degradation was faster in the DsbcB mutant and slower in the DrecD mutant.

Altogether, our results demonstrate that the large-scale pattern of guide RNA depletion originates from the effect of degrading some chromosomal regions on plasmid replication and copy number.

A neural network model enables to predict guide RNA efficiency

The large-scale pattern described above accounts for an important part of the variation in the effect of guides, but we also observed a reproducible variability between guides targeting nearby positions. 9

In order to eliminate the large-scale effect of plasmid copy number, we computed for each guide in the library an activity score as the difference between log2FC and the mean log2FC of all the guides the surrounding region in the target. Interestingly bases at the 5'end of the guide RNA impacted the model predictions the most. The presence of thymidine and to lesser extent adenines seems to reduce the efficiency of the guides, while guanines and to a lesser extent cytidines increase it. This observation differs from previous observations in mammalian cells where the PAM-proximal region was more important than the distal region (H. Xu et al. 2015;[START_REF] Moreno-Mateos | CRISPRscan: Designing Highly Efficient SgRNAs for CRISPR-Cas9 Targeting in Vivo[END_REF][START_REF] Doench | Rational Design of Highly Active SgRNAs for CRISPR-Cas9-Mediated Gene Inactivation[END_REF]. Conversely, the presence of a guanine at the last position of the guide has a positive effect in our model, which was also consistently reported in previous studies.

The ability of a simple linear model to obtain good predictions suggests that the determinants of guide efficiency in E. coli are quite simple and can for the most part be inferred from the specific bases present at each position. This model is however not able to encode more complex interactions between positions. The large amount of data collected in this experiments enables to train neural network models which have recently been successfully employed to model sequence data [START_REF] Kim | Deep Learning Improves Prediction of CRISPR-Cpf1 Guide RNA Activity[END_REF][START_REF] Alipanahi | Predicting the Sequence Specificities of DNA-and RNA-Binding Proteins by Deep Learning[END_REF]. The dataset was split into a training, validation and test set. We first used a locally connected neural network to predict guide activity using an arbitrary 60nt window around the target (Figure 3b). The resulting model achieved a Pearson correlation coefficient of 0.66 on the held-out test set (Spearman-r=0.64). In order to investigate the sequence features used by the model to make its predictions we generated a set of 1000 random sequences and measured the impact on the model predictions of mutating each position to all possible bases. The results are consistent with the linear regression model, showing the importance of the 5'end of the guide, while giving little to no importance to positions outside of the 20nt target (Supplementary Figure 4). We thus restricted the inputs of the model to target sequence, 4 bases upstream and 3 bases downstream of the PAM. This simpler model still achieved a Pearson correlation of 0.66 on the test set while reducing overfitting on the training set (Figure 3c).

In order to investigate the interactions identified by the model we further mutated each pair of position to all possible bases for a set of 200 random sequences. We then compared the effect of a double mutation and the sum of the effect the two single mutations. It appears clearly that bases in the guide interact with their direct neighbours, and to a lesser extent with their second and even third neighbours (Figure 3d). Interestingly positions in the first half of the guide seem to interact with each other on a long range, an effect not observed in the PAM-proximal region.

Comparison to other models

We then compared our model to two of the most widely used models for on-target activity prediction. Doench and colleagues modeled the activity of guide RNAs expressed from a U6 promoter on a DNA vector in human cells [START_REF] Doench | Optimized SgRNA Design to Maximize Activity and Minimize Off-Target Effects of CRISPR-Cas9[END_REF] A previous report showed that these two models make very different predictions suggesting that the determinants of guide efficiency strongly depend on the exact experimental setup [START_REF] Haeussler | Evaluation of Off-Target and on-Target Scoring Algorithms and Integration into the Guide RNA Selection Tool CRISPOR[END_REF]. When applied to our data, the model of Moreno-Mateos provides some predictive power, and conversely our model shows some predictive power on the data from Moreno-Mateos. The model of Doench performs weak predictions on the E. coli and zebrafish data. In order to shed light on the specific sequence features that matter in these different datasets, we plotted the impact of having specific bases at each position along the guide RNA, i.e. the difference between the average activity of guides that have this feature and the average activity of guides that do not have it. This analysis reveals that many of the features that impact the activity of guides in E. coli also impact the activity of guides in the zebrafish dataset. Note that because of experimental constrains, the dataset of Moreno-Mateos only includes guides whose first two bases are guanines. In our dataset these two bases are the most important features determining guide activity, but their effect is unknown in the experimental setup of Moreno-Mateos.

Discussion

Over the last few years numerous studies have led to a detailed understanding of Cas9 target search mechanism, structure, and biochemical activity [START_REF] Gasiunas | Cas9-crRNA Ribonucleoprotein Complex Mediates Specific DNA Cleavage for Adaptive Immunity in Bacteria[END_REF][START_REF] Jinek | A Programmable Dual-RNA-Guided DNA Endonuclease in Adaptive Bacterial Immunity[END_REF]; S. H. B,C) Comparison of the impact of specific bases along the guide sequence between the different datasets, i.e. the difference between the average activity of guides that have this feature and the average activity of guides that do not have it. The following color code is used for bases (Adenine: blue, Thymine: yellow, Guanine: green, Cytosine: red).

12 [START_REF] Sternberg | DNA Interrogation by the CRISPR RNA-Guided Endonuclease Cas9[END_REF][START_REF] Jinek | Structures of Cas9 Endonucleases Reveal RNA-Mediated Conformational Activation[END_REF][START_REF] Szczelkun | Direct Observation of R-Loop Formation by Single RNA-Guided Cas9 and Cascade Effector Complexes[END_REF][START_REF] Anders | Structural Basis of PAM-Dependent Target DNA Recognition by the Cas9 Endonuclease[END_REF][START_REF] Sternberg | Conformational Control of DNA Target Cleavage by CRISPR-Cas9[END_REF]. Despite the impressive amount of knowledge gathered, little is known about how the guide RNA sequence affects the efficiency of Cas9 targeting. Several groups have performed highthroughput screens in eukaryotic cells to measure the activity of thousands of guide RNAs, enabling the development of algorithms that can predict the efficiency with which a guide RNA can knockout a gene [START_REF] Doench | Rational Design of Highly Active SgRNAs for CRISPR-Cas9-Mediated Gene Inactivation[END_REF][START_REF] Moreno-Mateos | CRISPRscan: Designing Highly Efficient SgRNAs for CRISPR-Cas9 Targeting in Vivo[END_REF]H. Xu et al. 2015;[START_REF] Doench | Optimized SgRNA Design to Maximize Activity and Minimize Off-Target Effects of CRISPR-Cas9[END_REF].

Strikingly, these algorithms tend to perform well on some datasets and very poorly on others [START_REF] Haeussler | Evaluation of Off-Target and on-Target Scoring Algorithms and Integration into the Guide RNA Selection Tool CRISPOR[END_REF][START_REF] Labuhn | Refined SgRNA Efficacy Prediction Improves Large-and Small-Scale CRISPR-Cas9 Applications[END_REF]). Some of these differences have been attributed to the specificities of the experimental system and whether the guide RNA is transcribed in vitro from a T7 promoter followed by injection in cells, or in vivo from a U6 promoter on a DNA vector [START_REF] Haeussler | Evaluation of Off-Target and on-Target Scoring Algorithms and Integration into the Guide RNA Selection Tool CRISPOR[END_REF]. For instance, assays based on DNA vectors consistently observed a bias against uracil at the 3'end of the guide RNA sequence, which is due to the propensity of the RNA polymerase III to terminate transcription at uridine-rich sequences [START_REF] Doench | Rational Design of Highly Active SgRNAs for CRISPR-Cas9-Mediated Gene Inactivation[END_REF][START_REF] Wang | Genetic Screens in Human Cells Using the CRISPR-Cas9 System[END_REF][START_REF] Wu | Genome-Wide Binding of the CRISPR Endonuclease Cas9 in Mammalian Cells[END_REF][START_REF] Moreno-Mateos | CRISPRscan: Designing Highly Efficient SgRNAs for CRISPR-Cas9 Targeting in Vivo[END_REF]. These results argue for the necessity to develop guide RNA design tools that are specific to each experimental setup.

Here we measured guide RNA depletion after cleavage in the chromosome of E. coli, enabling the investigation of features that affect Cas9 targeting in a completely different experimental setup than previous reports, and with a lot more data points. In this assay efficient guides kill the bacteria and are rapidly depleted. The most striking feature that explained differences between guide RNAs was their position along the chromosome. Studies in Eukaryotic systems have shown the importance of chromatin structure and accessibility on Cas9 targeting efficiency [START_REF] Kuscu | Genome-Wide Analysis Reveals Characteristics of off-Target Sites Bound by the Cas9 Endonuclease[END_REF][START_REF] Wu | Genome-Wide Binding of the CRISPR Endonuclease Cas9 in Mammalian Cells[END_REF][START_REF] Horlbeck | Nucleosomes Impede Cas9 Access to DNA in Vivo and in Vitro[END_REF][START_REF] Chen | Probing the Impact of Chromatin Conformation on Genome Editing Tools[END_REF]. However, the pattern of guide RNA depletion that we observed here did not match the known structure of the E. coli chromosome [START_REF] Lioy | Multiscale Structuring of the E. Coli Chromosome by Nucleoid-Associated and Condensin Proteins[END_REF].

Rather, we were able to demonstrate that this large-scale pattern emerges from changes in plasmid copy number that occur after the degradation of specific chromosome regions after Cas9 cleavage.

The description of this artefact should serve as a cautionary tale for any pooled genetic screen in which the readout is made by sequencing a guide RNA or any barcode on a plasmid. Note that Cas9 might still be able to kill E. coli more or less efficiently depending on which region of the chromosome is targeted, but a different experimental design will have to be used to investigate this question.

After taking the large-scale depletion pattern into account we could investigate the effect of the guide RNA sequence on the ability of Cas9 to kill E. coli. Our results highlighted the positive effect of a high GC content at the 5' end of the guide RNA, and in particular the negative effect of thymidines in this region. Binding of the 5' end to the target sequence is required for a conformational shift to occur in Cas9 which brings the RuvC and HNH catalytic domains in contact with the target DNA (Samuel H. [START_REF] Sternberg | Conformational Control of DNA Target Cleavage by CRISPR-Cas9[END_REF][START_REF] Jinek | Structures of Cas9 Endonucleases Reveal RNA-Mediated Conformational Activation[END_REF]. This binding might be disfavored by a high thymidine content, making cleavage less efficient. Another possible explanation is that guide RNA transcription might be imperfect for some sequences. It was previously reported that the sequence around the transcriptional start site (TSS) can impact the frequency at which the polymerase will initiate transcription at different positions [START_REF] Vvedenskaya | Massively Systematic Transcript End Readout, 'MASTER': Transcription Start Site Selection, Transcriptional Slippage, and Transcript Yields[END_REF]. In particular, thymidine-rich sequences where shown to favor initiation further away from the -10 element, which in our case would lead to the formation of truncated guide RNAs. The same study also highlighted the fact that poly-T and poly-A stretches after the TSS promote slippage synthesis, which could conversely lead to the formation of longer guide RNAs. Finally, the sequence at the 5' end of the guide might impact its stability in vivo. Moreno-Mateos measured an increased stability and activity of guides with a higher guanine content, and provided evidence that these guides might form G-quadruplexes protecting them against 5'-directed exonucleases. This mechanism could also be at play in our experiments.

Altogether, our results provide insight into the features that determine the ability of Cas9 to efficiently kill E. coli. We provide a model able to predict the most efficient guides with a high accuracy that should be useful for the design of effective guides in genome editing experiments as well as for applications of CRISPR as antimicrobials [START_REF] Jiang | RNA-Guided Editing of Bacterial Genomes Using CRISPR-Cas Systems[END_REF][START_REF] Cui | Consequences of Cas9 Cleavage in the Chromosome of Escherichia Coli[END_REF][START_REF] Bikard | Exploiting CRISPR-Cas Nucleases to Produce Sequence-Specific Antimicrobials[END_REF][START_REF] Citorik | Sequence-Specific Antimicrobials Using Efficiently Delivered RNA-Guided Nucleases[END_REF]. This model is made available online: http://hub13.hosting.pasteur.fr:8080/CRISPRBact/ Methods Bacterial strains and media E. coli strains were grown in Luria-Bertani (LB) broth or LB Agar 1.5% as solid medium. Whenever applicable, media was supplemented with chloramphenicol (20 µg ml -1 ), carbenicillin (100 µg ml -1 ) or kanamycin (50 µg ml -1 ) to select or ensure the maintenance of the plasmids. Lower concentration of kanamycin (20 µg ml -1 ) was used to select for the integration of vectors in the chromosome. All the strains modifications derived from E. coli MG1655. E. coli strain DH5α or MG1655 were used as transformation recipients.

Plasmids and E. coli strains construction

Strain LC-E19 was constructed using the pOSIP system [START_REF] St-Pierre | One-Step Cloning and Chromosomal Integration of DNA[END_REF]) and the backbones were removed using the pE-FLP plasmid [START_REF] St-Pierre | One-Step Cloning and Chromosomal Integration of DNA[END_REF]. The Ptet-Cas9 expression cassette was integrated at the HK022 attB and a gfp (Green Fluorescent Protein) reporter gene under the control the sulA promoter was integrated at λ attB to monitor SOS response. Genes recD and sbcB were deleted from strain LC-E19 using the lambda red recombineering strategy [START_REF] Sharan | Recombineering: A Homologous Recombination-Based Method of Genetic Engineering[END_REF].

Plasmid pKD4 was used as a template to generate linear DNA fragments via polymerase chain reaction (PCR) followed by electroporation into strain LC-E19 carrying plasmid pKOBEG-A [START_REF] Chaveroche | A Rapid Method for Efficient Gene Replacement in the Filamentous Fungus Aspergillus Nidulans[END_REF]. Colonies resistant to kanamycin were selected and the resistance gene was then removed using plasmid pE-FLP. The constructions were verified by PCR and sequencing. All the bacterial strains used in this study are listed in Supplementary Table 1 and the primers used for strain construction in Supplementary Table 2.

Fragments for plasmid constructions were generated by PCR or restriction digestion and assembled through Gibson assembly [START_REF] Gibson | Enzymatic Assembly of DNA Molecules up to Several Hundred Kilobases[END_REF]. Novel guide RNAs were cloned into plasmid psgRNA by golden gate assembly [START_REF] Engler | A One Pot, One Step, Precision Cloning Method with High Throughput Capability[END_REF]. A list of plasmids is provided as Supplementary Table 3, and primers used in plasmid construction as Supplementary Table 4. A list of guide RNA used in the study is provided as Supplementary Table 5.

Genome-wide Cas9 screen

The data shown in figure 1 was generated as follow. The guide RNA library carried on plasmid psgRNA was electroporated into LC-E19, plated in LB with kanamycin 50 μg/ml and incubated at 37°C for 4h. An estimated number of 10 7 clones were recovered, pooled in 10ml LB and stored as 1ml aliquots in DMSO 10% at -80°C. To perform the assay, 1ml of frozen cells were thawed in 400ml of LB with kanamycin 50 μg/ml and cultivated at 37°C, 190 RMP until they reached early-exponential phase (OD600 ≈0.25). Then, aTc 1nM was added and cells were recovered at different time points (0h, 2h, 4h and 6h). Plasmids were extracted from 50 ml of culture using the NucleoSpin Plasmid kit (Macherey-Nagel, Duren, Germany). The whole assay was performed in triplicate.

During the course of the study we realized that leaky expression of Cas9 in strain LCE-19 might lead to the introduction of biases in the library as clones that mutate the CRISPR-Cas9 system or the target might be selected before induction with aTc. To avoid this problem, we used modified experimental design for the data shown in figure 2 and figure 3. Plasmid psgRNA carries a cos site enabling its packaging in phage lambda capsids. The library was transformed in strain CY2120 which carries a temperature sensitive lysogenic lambda prophage with its cos site deleted [START_REF] Cronan | Improved Plasmid-Based System for Fully Regulated off-to-on Gene Expression in Escherichia Coli: Application to Production of Toxic Proteins[END_REF].

Upon induction at 42°C, lambda capsids are produced and the psgRNA packaged. Cosmid particles can then be purified as described previously [START_REF] Cronan | Improved Plasmid-Based System for Fully Regulated off-to-on Gene Expression in Escherichia Coli: Application to Production of Toxic Proteins[END_REF]. Briefly, strain CY2120 carrying psgRNA was diluted 100-fold from an overnight culture in LB supplemented with 50 mM Tris-HCl buffer (pH 7.5) and grown at 30°C until OD600 ≈ 0.5. The culture was then incubated at 42°C for 20 minutes and then at 37°C for 4 hours. Cells were harvested by centrifugation at 4000g for 5 minutes, washed in lambda dilution buffer (Tris-HCL pH 7.5 20mM, NaCl 0.1M, MgSO4 10mM) with 1/20 of the culture volume, centrifuged and re-suspended again in the same volume of lambda dilution buffer. To purify the cosmid particles chloroform was added (20 vol%), samples vortexed for 15 seconds and incubated at 37°C for 15 minutes with shaking. Cosmids were harvested after centrifugation at 12,000g for 1.5 minutes. This cosmid library was then used to transduce strain LC-E19 induced to produce Cas9 as follow. An overnight culture of strain LC-E19 was diluted 100-fold in fresh LB, 0,2% arabinose and aTc 1nM and grown until OD 600 ≈ 0.6. The psgRNA library was transduced at a MOI (Multiplicity of Infection) of 0.2 and incubated at room temperature for 30 minutes. Cells were then grown 4h at 37°C, 190 RPM with kanamycin 50 μg/ml to inhibit the growth of cells that were not transduced. Cells were recovered and plasmids extracted from 15 ml of culture using NucleoSpin Plasmid kit (Macherey-Nagel, Duren, Germany). Transduction in strain MG1655, which does not carry Cas9, was used as a control.

To measure the relative abundance of guide RNAs in each sample, the library of guide RNA was sequenced following the method described by Lun Cui et al. [START_REF] Cui | A CRISPRi Screen in E. Coli Reveals a Sequence-Specific Toxicity of DCas9[END_REF]. Two nested PCR reactions were used to generate the sequencing library with primers described in Supplementary Table 6. The 1 st PCR adds the 1 st index. The 2 nd PCR adds the 2 nd index and flow cells attachment sequences. Sequencing is then performed using primer LC609 as a custom read 1 primer. Custom index primers were also used: LC499 reads index 1 and LC610 reads index 2. Sequencing was performed on a NextSeq 500 benchtop sequencer. The first 2 sequencing cycles read bases common to all clusters and were set as dark cycles, followed by 20 cycles corresponding to the guide RNA.

We report here the log2 transformed fold change in the number of reads obtained for each guide RNA, normalized by the total number of reads obtained for the sample and the number of reads obtained for a control guide RNA which does not have a target position in the genome of E. coli MG1655. Reads were counted only if they showed a perfect match to the sequence of a guide in the library.

Determination of plasmid copy numbers

Pre-cultures of LCE-19 carrying a plasmid with a single guide RNA were incubated at 37°C in triplicate at 190 RPM shaking overnight. The appropriate antibiotics (kanamycin 50 μg/ml or chloramphenicol 20 μg/ml) were used to maintain the plasmids. Pre-cultures were diluted 100-fold in fresh LB and grown in the same conditions until they reached early-exponential phase (OD 600 ≈ 0.25). Cas9 expression was then induced with aTc 1nM. Cells were recovered before and after 4 hours of induction. Total DNA was extracted using the Wizard Genomic DNA Purification Kit (Promega, Madison, USA). Quantitative Polymerase Chain Reaction (qPCR) was carried out in triplicate for each extraction using the FastStart Essential DNA Green Master (Roche Diagnostics, Mannheim, Germany) in accordance with the manufacturer's specifications in a LightCycle 96 system (Roche Diagnostics).

The plasmid copy number was determined as described by [START_REF] Millan | Positive Epistasis between Co-Infecting Plasmids Promotes Plasmid Survival in Bacterial Populations[END_REF]. The efficiencies of the reactions were calculated from a standard curve generated by performing qPCR with five 10-fold dilutions of template DNA in triplicate (10 ng/μl-1pg/μl). Primers BG114 and BG115 were used to perform the qPCR with a concentration of template DNA of 0.1 ng/μl. To determine the average PCN per chromosome, we used primers BG116 and BG117 to amplified gene rpoB. Primers are listed in Supplementary table 7. The amplification conditions were: initial denaturation for 10 min at 95°C, followed by 45 cycles of 10 s at 95°C, 20 s at 55°C and 10 s at 72°C. The following formula described by San Millan et al. (San Millan, Heilbron, and Maclean 2013) was used:

where cn is the plasmid copy number per chromosome, S c and S p are the sizes of the chromosomal and plasmid amplicons (in bp), E c and E p are the efficiencies of the chromosomal and plasmid qPCRs (relative to 1), and Ctc and Ctp are the threshold cycles of the chromosomal and plasmid reactions, respectively. Fold change values in plasmid copy number after 4H of Cas9 induction and normalized to a non-targeting control are reported.

Quantification of gene expression

Overnight cultures were diluted 100-fold and grown until they reached early-exponential phase (OD 600 ≈ 0.25). Then aTc (1nM) was added and cells incubated for 4h. RNA was extracted from 10 ml of culture at OD 600 ≈ 0.25, and from 2ml after 4h of induction using Direct-zol TM RNA Miniprep kit (Zymo Research). All the RNA samples were first treated with DNase (Turbo DNase free kit, Ambion) and then 1 μg of RNA for each sample was reverse transcribed into cDNA using the Transcriptor First strand cDNA synthesis Kit (Roche). qPCR was performed using 1 μL of the reverse transcription reaction with the Faststart essential DNA green master mix (Roche) in a LightCycle 96 (Roche). Probes and PCR primers are listed in Supplementary Table 7. Relative gene expression was computed using the ΔΔCq method [START_REF] Schmittgen | Analyzing Real-Time PCR Data by the Comparative CT Method[END_REF].

Quantification of DNA degradation after

S c S p

Strain LC-E19 carrying plasmid psgRNA programmed to target gene yfaL was diluted 100x from on overnight culture and grown until OD 600 ≈ 0.25. Cas9 expression was induced by addition of aTc 1nM followed by 30min of incubation at 37°C with shaking. Total DNA was extracted using the Wizard Genomic DNA Purification Kit (Promega, Madison, USA) and fragmented with a Covaris E220 ultrasonicator. Sequencing libraries were prepared using the NEXTflex PCR-free DNA-Seq kit (Bioo Scientific Corporation), and sequenced on a MiSeq v3 PE300 flowcell. Sequencing reads were mapped to the genome of E. coli LC-E19 using bowtie2 [START_REF] Langmead | Fast Gapped-Read Alignment with Bowtie 2[END_REF] and sequence coverage computed with samtools [START_REF] Li | The Sequence Alignment/Map Format and SAMtools[END_REF]). The plot of figure 2e shows a moving average of the coverage normalized between 0 and 1, with a window of 10kb.

Microscopy

LC-E19 cells were transformed with plasmid psgRNA carrying different guides. Overnight cultures were diluted 100-fold in fresh LB and incubated at 37°C for 1h. Cas9 expression was induced with aTc 1nM and cells transferred to LB pads with 1% UltraPure TM agarose (Invitrogen), kanamycin 50 μg/ml and aTc 1nM. Cells were imaged using an inverted microscope (TI-E, Nikon Inc.) equipped with a 100x phase contrast objective (CFI PlanApo Lambda DM100x 1.4NA, Nikon Inc.). Images were taken every 5 min during 8 h with an exposure of 100 ms using a sCMOS camera (Orca Flash 4.0, Hamamatsu)

with an effective pixel size of 65 nm.

Machine learning

For each guide of the library, we computed a sgRNA activity score as the difference between its log2FC and the mean log2FC of all the guides within 6 Kbp, normalized between 0 and 1. The activity score of guides was computed as the mean activity from 4 independent assays measured in strain LC-E19 using the cosmid transduction assay.

After splitting the dataset into a training, validation and test sets, we implemented a neural network (Fig 3b) using Keras and TensorFlow. We used a model architecture inspired from our previous work [START_REF] Cui | A CRISPRi Screen in E. Coli Reveals a Sequence-Specific Toxicity of DCas9[END_REF]) and consisting of 2 locally-connected layers of size 20 and 8, with kernel sizes of 4 and 7, followed by 2 dense layers of size 14 and 8. The layers sizes and kernel sizes were optimized to minimize the loss on the validation set using a grid search approach. We used the rectified linear unit (ReLU) activation function for all the neurons of these layers. Finally a densely connected single neuron predicted the sgRNA efficacy using a linear combination of the last dense layer. The network was trained to minimize the mean square error of the log2FC prediction with L2 regularization using the Adam optimizer [START_REF] Kingma | Adam: A Method for Stochastic Optimization[END_REF]. Training was interrupted when loss on the validation set ceased do decrease for more than two epochs.

Figure 1 .

 1 Figure 1. Genome-wide Cas9 killing screen reveals large-scale depletion pattern. a) A genome-wide library of guide RNA was introduced in E. coli strain LC-E19 carrying a cas9 under the control of a Ptet promoter. Cells were grown in the presence of 1nM aTc and the guide RNA library sequenced before and after a few hours of induction. b) Scatter plot showing the log2FC of guides around the genome. The black line represents the moving average with a window size of 6kb (outer line of circle: log2F=2, centre of circle: log2F=-6). c) Moving average of guide RNA depletion around the genome after 2H, 4H and 6H of aTc induction. d) Time lapse microscopy after Cas9 induction in the presence of different guide RNAs. e) Fold change of plasmid copy number normalized to a non-targeting control as measured by qPCR. Points show independent biological replicates, the black bar shows the median.

Figure 2 .

 2 Figure 2. The large-scale pattern is explained by the degradation of chromosomal regions carrying genes necessary for replication. a) Genes at the centre of a depletion peak were cloned on a set of vectors. b) Fold change in the copy number of the plasmid carrying the guide RNA in the presence of plasmid pBG7 or the control empty vector pBG10, after cleavage with guides targeting genes yfaL, yfaU, glpA in the region, and opgG outside of the region. c) Fold change in the copy number of the plasmid carrying the guide RNA in the presence of various complementation plasmids and the control (pBG10), after 4H of induction with a guide targeting glpA. d) Moving average of guide RNA depletion in the genome-wide Cas9 killing screen performed in the presence of various complementation plasmids (window size of 6kb). e) Sequence coverage after 30min of Cas9 induction to cut position yfaL in strain LC-E19 (wt), a DrecD mutant and a DsbcB mutant (moving average with a window size of 10kb. f) Moving average of guide RNA depletion in the genome-wide Cas9 killing screen performed in DrecD and DsbcB mutants (window size of 6kb).

  within 6 kbp. The sgRNA activities were extremely consistent across experiments, showing on average Pearson correlation between replicates of 0.92 (Supplementary Fig 3). We then sought to model guide activity based on the one-hot-encoded target sequence (4 bases upstream, target, PAM and 3 bases downstream). A simple linear model with L1 regularization was able to predict guide activity in cross-validation with a Pearson correlation of 0.58. The coefficient of the features in the regression are plotted as a heat map in Figure 3a. The model uses positions in the guide RNA but not

Figure 3 .

 3 Figure 3. Predicting guide RNA efficiency. (A) A linear model with L1 regularization was trained to predict guide activity using the primary sequence as the only input feature. The heat map shows the coefficients attributed to each base. Position 0 is the first base of the guide, position N refers to the undetermined base of the PAM (NGG), position +1 refers to the first base after the PAM. (B) Architecture of the locally connected neural network trained to predict guide activity from the one-hot-encoded sequence. (C) Predictions of the model plotted as a function of the measured guide activity on a held-out test set. (D) Level of interaction between positions along the target that is seen by the model.

  , while Moreno-Mateos and colleagues modeled the activity of guide RNAs expressed in vitro from a T7 promoter and injected into zebrafish embryo (Moreno-Mateos et al. 2015).

Figure 4 .

 4 Figure 4. Comparision between models. (A) Heat map of Spearman correlation coefficient between activity scores predicted by models and datasets. The score given for the performance of models on their own training set corresponds to the performances on a test set in cross-validation. The other correlations are computed on the whole dataset. (B, C) Comparison of the impact of specific bases along the guide sequence between the different datasets, i.e. the difference between the average activity of guides that have this feature and the average activity of guides that do not have it. The following color code is used for bases (Adenine: blue, Thymine: yellow, Guanine: green, Cytosine: red).

Acknowledgements

We thank Gizem Ozbaykal for the help with the fluorescence and phase-contrast microscopy. DNA sequencing after Cas9 cleavage was performed by Cédric Fund from the Institut Pasteur Genomics Platform, a member of "France Génomique" consortium (ANR10-INBS-09-08). This work was supported by the European Research Council (ERC) under the Europe Union's Horizon 2020 research and innovation program (grant agreement No [677823]); the French Government's Investissement d'Avenir program; Laboratoire d'Excellence 'Integrative Biology of Emerging Infectious Diseases' [ANR-10-LABX-62-IBEID]; the Pasteur-Weizmann consortium, and a Ramon Areces Fellowship to B.G.

Data Access

The screen results are provided as Supplementary Dataset 1 and Supplementary Dataset 2. Other relevant data supporting the findings of the study are available in this article and its Supplementary Information files, or from the corresponding author upon request. An online version of the model is provided here: http://hub13.hosting.pasteur.fr:8080/CRISPRBact/

To identify the positions used by the model to make its predictions we generated a set of 1000 random sequences, mutated each position in silico, and computed the effect of each mutation on the model prediction (Supplementary Figure 4). To measure the level of interaction between positions we generated all possible pairs of mutations for each sequence in a set of 200 random sequences, and compared the effect of individual mutations to that of pairs of mutations. Positions are interacting if the effect of a double mutation (Eij) is different from the sum of the effect of the single mutations (Ei+Ej). The heat map shows the average Euclidean distance between Eij and Ei+Ej for all pairs of positions (Figure 3).

Model comparisons

The Fusi/Doench algorithm (from Doench 2016) was recoded from explanations provided in the article. In order to have a fair comparison with our model, all the features detailed in Doench 2016 were used except the cutting position and the amino acid percentage position. We then performed a 5-fold cross validation using a boosted regression tree on the FC+RES dataset from the same paper and obtained a Spearman coefficient similar to what was reported. In order to test the prediction capabilities of the Fusi/Doench algorithm on other datasets, we re-trained the algorithm on the whole FC+RES dataset and computed the correlation between the model predictions and the actual sgRNA activity.

Similarly, we recoded the Moreno-Mateos algorithm. Features far from the guide sequence that were used in the Moreno-Mateos were not kept as their value was not easily accessible for the FC+RES data. Removing them did not hurt the predictions. We then used a lassoCV regression and performed a 5-fold cross validation on the Moreno-Mateos dataset (obtained from Haeussler and colleagues [START_REF] Haeussler | Evaluation of Off-Target and on-Target Scoring Algorithms and Integration into the Guide RNA Selection Tool CRISPOR[END_REF]). We obtained similar prediction performance than described in their original paper (Spearman coefficient = 0.46). In order to test the prediction capabilities of the Moreno-Mateos algorithm on other datasets, we retrained the model on the whole Moreno-Mateos dataset and computed the correlation between the model predictions and the actual sgRNA activity.

Author contributions


Sebastien Meineri
email: sebastien.meineri@univ-ubs.fr

Mickaël Dupré

Nicolas Guéguen

Boris Vallée

Keywords: social responsibility, reciprocity, Helping behavior, Altruism

.

Other Papers

Polish Psychological Bulletin 2017, vol. 48(3) 375-379 DOI -10.1515/ppb-2017-0043 "One of the key human characteristics is our willingness to help others in need" (Warneken, 2013;p. 431). However, this willingness could be reinforced by contextual elements such as the attribution of success following the completion of a task (Clark & Waddell, 1986), being smiled at [START_REF] Solomon | Anonymity and helping[END_REF][START_REF] Guéguen | The effect of smiling on helping behavior: Smiling and Good Samaritan behavior[END_REF][START_REF] Vrugt | Effects of a smile on mood and helping behavior[END_REF], finding coins on the shelf of a phone box or on the ground (Batson, Coke, Chard, Smith, & Talaferro, 1979;[START_REF] Isen | Effect of feeling good on helping: cookies and kindness[END_REF][START_REF] Levin | Further studies on the effect of feeling good on helping[END_REF] or being offered a piece of cake, a drink or help, beforehand [START_REF] Harris | Mood and Helping[END_REF][START_REF] Isen | Effect of feeling good on helping: cookies and kindness[END_REF][START_REF] Regan | Effects of a favor and liking on compliance[END_REF][START_REF] Berkowitz | Affecting the salience of the social responsibility norm: Effects of past help on the response to dependency relationships[END_REF]. According to the authors' theoretical hypothesis, induced positive mood [START_REF] Isen | Affect, accessibility of material in memory, and behavior: A cognitive loop[END_REF] or the respect of the standard of reciprocity [START_REF] Gouldner | The norm of reciprocity: A preliminary statement[END_REF] or of social responsibility [START_REF] Berkowitz | Responsibility and dependency[END_REF] could explain the observed effect. This manuscript focuses specifically on this second set of interpretations by questioning an inconsistency in research.

Proposed by [START_REF] Gouldner | The norm of reciprocity: A preliminary statement[END_REF] as a universal principle governing the exchanges between individuals, the norm of reciprocity first prescribes the acceptance of a favor from someone and second, the duty to return the favor. Within the framework of a so-called study on artistic judgement, [START_REF] Regan | Effects of a favor and liking on compliance[END_REF] brought two individuals into a room: a confederate and a naive subject. During the break, the confederate left the room, then based on the condition either returned with two cans of soda and offered one to the participant, or returned empty-handed. At the end of the experiment, he asked the participant to buy some raffle tickets. The results reveal that the preliminary drink offer statistically increases the number of raffle tickets sold. Replications in quasi-identical experimental contexts reveal that the returned favor remains observed in the absence of the solicitor [START_REF] Burger | The norm of reciprocity as an internalized social norm: Returning favors even when no one fi nds out[END_REF], or when the latter is unable to know of the participant's actual behavior (Whatley, Webster, Smith, & Rhodos, 1999), but on condition that the lapse of time separating the initial gift from the final request does not exceed a few hours [START_REF] Burger | Effects of time on the norm of reciprocity[END_REF]. On the contrary, the reciprocity effect disappears if the target request is of an antisocial nature [START_REF] Boster | The effectiveness of an altruistic appeal in the presence and absence of favors[END_REF]. Furthermore, although the hypothesis was not specifically tested by the authors, the results of [START_REF] Regan | Effects of a favor and liking on compliance[END_REF][START_REF] Burger | Reciprocal favor exchangeand compliance[END_REF]Sandoval (2006, exp. 3) suggest that the reciprocity effect can be observed only in regard to a single person: the initial donor.

The internalization of the norm [START_REF] Gouldner | The norm of reciprocity: A preliminary statement[END_REF] is the privileged interpretation of the observed effects. In reference to [START_REF] Schwartz | A normative decision-making model of altruism[END_REF] model, reciprocity, considered as a personal standard, is assumed to be activated by the preliminary gift and puts the individual under the moral obligation to return what he has received so as not to feel guilty. However, a second explanation underlining not the moral character of the behavior but the consequences in terms of social evaluation has been put forward. In agreement with self-presentation theory [START_REF] Pendleton | Self-presentation and the door-inthe-face technique for inducing compliance[END_REF][START_REF] Baumeister | A self-presentational view of social phenomena[END_REF], the image that individuals wish to display to others guides their behavior in public. Counter-normative behavior would place the individual in a deviant situation with social disapproval as a consequence. Those who violate the norm of reciprocity are qualified by [START_REF] Cialdini | Infl uence et Manipulation[END_REF] as "Ungrateful" or "free-loaders" (p. 32). On the contrary, pro-normative behavior would earn the individual a favorable social evaluation.

The norm of reciprocity is classically distinguished from the norm of social responsibility [START_REF] Berkowitz | Responsibility and dependency[END_REF]. The latter also aims to account for helping behavior but by prescribing that, "People must help those who are dependent upon them" (Berkowitz & Daniels, 1964, p. 275). [START_REF] Berkowitz | Responsibility and dependency[END_REF] invited pairs of individuals -a participant and a confederate acting as a supervisor -to jointly carry out a task. Based on the condition, the participant was either told that his performance would determine the evaluation of the "supervisor" for a possible reward, or the participant was told nothing at all. The results reveal that the relation of induced dependence significantly increases the participant's performance.

However, certain experiments would tend to bring the two norms closer [START_REF] Staub | Instigation to goodness: The role of social norms and interpersonal infl uence[END_REF]. [START_REF] Berkowitz | Affecting the salience of the social responsibility norm: Effects of past help on the response to dependency relationships[END_REF], wishing to demonstrate that contextual elements could also activate the norm of social responsibility reproduced their original experiment by asking the participants to first carry out a task supposedly unrelated to the following. During this experiment, a confederate other than the supervisor either offered help to the participant or did not. The results reveal that the preliminary assistance coupled with the relation of dependence with the supervisor significantly increases the participant's performance. Based on the same protocol, [START_REF] Goranson | Reciprocity and responsibility reactions to prior help[END_REF], also demonstrated that the participant's performance was higher when the confederate's help was presented as spontaneous compared with help that was planned within the protocol and announced in advance, or compared with a refusal to help (help planned in the protocol but refused by the confederate). The participant's performance is nonetheless greater when the initial help comes from the supervising confederate. Finally, results from [START_REF] Greenglass | Effect of prior help and hindrance on willingness to help another: reciprocity or social responsibility[END_REF] reveal that the participant's performance, having benefited from the help of the supervising confederate, is significantly higher when he had been previously helped by a confederate other than the supervisor than when he hadn't been helped (help not planned in the protocol) or when he had been put in a difficult situation by this confederate (help planned and announced in the protocol but refused by the latter). These results are observed whether the supervisor appears similar or dissimilar to the confederate from the first phase (this variable was manipulated through responses obtained from a questionnaire presented to the participant).

To give an account of this effect, the authors specifically evoked the existence of a mechanism distinct from the norm of social responsibility, namely: generalized reciprocity: "Participants helped by the confederate felt indebted […] This feeling could have been generalized toward the supervisor in that by working hard for this person, they were reciprocating the help they had received" (Berkowitz & Daniels, 1964, p. 281;Goranson & Berkowitz, 1966, p. 228). More recently, Dieckman ( 2004) also refers to a generalized form of reciprocity to account for cooperation, observed under certain conditions, in repeated social dilemmas situations involving several people.

This proposal, which opposes the data of [START_REF] Regan | Effects of a favor and liking on compliance[END_REF] and Burger and Al (2006, exp. 3) presenting a reciprocity effect essentially aimed at the initial donor, motivated the experimental investigation of a generalized form of reciprocity. One could consider that some attempts to test this hypothesis have been already made in the context of the DITF compliance gaining paradigm -which reciprocity is one of the explaining theories -by using two different requesters. Results are not consistent: some succeeding to obtain an effect in the presence of two requesters [START_REF] Terrier | Door-in-the-face: Is it really necessary that both requests be made by the same requester?[END_REF] and some others failing (Cialdini, Vincent, Lewis, Catalan, Wheeler, & Darby, 1975, exp. 2). The context and more precisely the laps of time between the two requests and the final beneficiary of the request were confounded variables, and conditioned the results [START_REF] Dillard | Sequential-request persuasive strategies[END_REF].

To test directly the generalized reciprocity hypothesis, without activating the norm of social responsibility, we conceived a protocol in which the relationship of dependence between individuals was not explained and the preliminary favor was not an act of assistance. Furthermore, and in order to extend the reach, our investigation was carried out in a natural context among solicited passersby in the street. Based on the results of [START_REF] Goranson | Reciprocity and responsibility reactions to prior help[END_REF] and [START_REF] Greenglass | Effect of prior help and hindrance on willingness to help another: reciprocity or social responsibility[END_REF], we expected to observe a generalized reciprocity effect, however on a smaller scale than that of the classic reciprocity effect.

Method

Participants 120 participants (63 women and 57 men 1 ) took part in the experiment. They were directly approached in a pedestrian area in the town center of Lorient in the south of Brittany during the end of the year holidays in 2012.

Procedure

Four female undergraduate experimenters (average age: 21.2 years; standard deviation: 0.7) took part in the experiment, approaching individuals in each of the 3 definite conditions. The participants were randomly assigned. The first met participant was solicited in reference to the first condition script, the following one, in reference to the second condition script, and so on. In the "classic reciprocity" condition, the experimenter approached the passerby by saying, "Hello, I belong to a university association, and we are seeking to promote the University of South Brittany this Christmas season. We are giving away chocolate cake, would you like a piece?" After having accepted the piece of cake, the passerby was solicited for the target request: "Excuse me, would you watch my things 2 while I go to the restroom? I won't be long." The experimenter then pointed to the public restroom that was located a couple of meters away. In the "generalized reciprocity" condition the participant was approached in the same manner as in the previous condition but was let go after taking a piece of cake. A few meters further, a second experimenter, supposedly not related to the operation but carrying several bags, approached the participant with the same target request. Finally in the control condition, this target request was presented to the participant the same way as in the previous conditions, except for the cake offer.

We hypothesized a linear increase in helping behavior across the conditions. More precisely, we envisioned "classic reciprocity" as statistically different from "generalized reciprocity," itself statistically different from the control condition.

Results

The data coming from the 4 experimenters not presenting a difference were aggregated in the analysis. A 2 (participant gender) X 3 (solicitation type) log-linear analysis was carried out on request acceptance. A main effect of solicitation type appears (χ 2 (1, 120) = 34,761; p = .0001 φ = .538). In accordance with our hypothesis, the 2 by 2 comparisons carried out on our data reveal that the "classic reciprocity" condition (37/40) produced a significantly higher acceptance rate than the "generalized reciprocity" condition (28/40) (χ 2 (1, 80) = 6.65, p < .01; φ = .28); and a significantly higher rate than that of the 1 Participant age was not raised in order not the break the ecological context of the experiment. 2 Several bags containing the cakes to be distributed were laid out on the ground near the experimenter. control condition (13/40) (χ 2 (1, 80) = 30.72, p < .0001, φ = .53) (exact Fisher test = p < .0001). In addition, the analyses reveal that "generalized reciprocity" produces significantly higher results than those in the control condition (χ 2 (1, 80) = 11.26, p < .001, φ = .35).

Discussion

Using the results of studies situated on the interface of the norm of reciprocity and the norm of social responsibility [START_REF] Staub | Instigation to goodness: The role of social norms and interpersonal infl uence[END_REF], the objective of our experiment was to investigate the existence of a broadened effect of the norm of reciprocity. In accordance with our hypothesis, the results reveal that an individual being offered a piece of cake is first of all, not only more likely to help the person who had previously given him the gift, but also more likely to help someone who had not been involved compared to a control situation where nothing was offered beforehand. These results replicate those of [START_REF] Regan | Effects of a favor and liking on compliance[END_REF], [START_REF] Whatley | The effect of a favor on public and private compliance: How internalized is the norm of reciprocity?[END_REF], [START_REF] Boster | The effectiveness of an altruistic appeal in the presence and absence of favors[END_REF], [START_REF] Burger | Reciprocal favor exchangeand compliance[END_REF] or [START_REF] Burger | The norm of reciprocity as an internalized social norm: Returning favors even when no one fi nds out[END_REF] concerning the observed reciprocity effect between two individuals and support the proposal of [START_REF] Berkowitz | Affecting the salience of the social responsibility norm: Effects of past help on the response to dependency relationships[END_REF] reiterated by [START_REF] Goranson | Reciprocity and responsibility reactions to prior help[END_REF], [START_REF] Greenglass | Effect of prior help and hindrance on willingness to help another: reciprocity or social responsibility[END_REF], [START_REF] Staub | Instigation to goodness: The role of social norms and interpersonal infl uence[END_REF] and Dieckman (2004) concerning the existence of a generalized reciprocity mechanism.

Compliance rates reported in our experimentation are particularly high, especially those observed in the classic and generalized reciprocity conditions (respectively 92.5% and 70%). Christmas season, when the experimentation took place might explain these levels. [START_REF] Greenberg | On the complementarity of prosocial norms: The case of restaurant tipping during the holidays[END_REF], by analyzing amount of tips leaving in restaurants over two years, reveals that people tend to give more tips during the Christmas holydays than the rest of the year. According to the author, a social norm of generosity and altruism would be salient during this period.

The inconsistency in our data with those of [START_REF] Regan | Effects of a favor and liking on compliance[END_REF] and Burger and Al (2006, exp. 3) presenting a reciprocity effect at the exclusive benefit of the initial donor, could be explained by the specificity of the experimental situations put in place in these two studies. In [START_REF] Regan | Effects of a favor and liking on compliance[END_REF] experiment, the results are obtained on the basis of an initial gift given by the experimenter himself, which moreover justified this by the wish "to make the experience pleasant" (p. 631). Because of this donor's particular status and the context in which participating in the experiment was already the object of financial remuneration, this gift could have been seen by the participant as a complementary remuneration in kind, and thus inhibit a potential broadened effect toward the non-involved confederate. In Burger and Al's (2006, exp. 3) experiment, the experimental situation also moves away from a typical situation since the participant was solicited for the target request by a confederate other than the initial donor while he had just returned the favor to the latter. The absence of effect could then come from the previously returned favor.

In accordance with our hypothesis and with the results of Goranson and Daniels, (1964), [START_REF] Goranson | Reciprocity and responsibility reactions to prior help[END_REF] and [START_REF] Greenglass | Effect of prior help and hindrance on willingness to help another: reciprocity or social responsibility[END_REF], the generalized norm of reciprocity is shown to be statistically less influential than the classic norm of reciprocity. The visibility of the behavior, emphasizing it social evaluation could explain this result. Watley and Al (1999), having demonstrated greater public rather than private reciprocity, consider the difference to be related to an individual's awareness of his own public image [START_REF] Pendleton | Self-presentation and the door-inthe-face technique for inducing compliance[END_REF][START_REF] Baumeister | A self-presentational view of social phenomena[END_REF], which has either been activated or not based on the condition. To the extent that the participant is truly the only one to know that he received a gift beforehand in a generalized reciprocity condition, such awareness would be less significant than in a classic reciprocity condition.

Another mechanism that our data do not make possible to dismiss remains in consideration. In parallel with investigations carried out on reciprocity and social responsibility, several studies have shown that receiving a gift [START_REF] Levin | Further studies on the effect of feeling good on helping[END_REF], finding coins [START_REF] Levin | Further studies on the effect of feeling good on helping[END_REF]Isen & Simmonds, 1978), or being smiled at [START_REF] Vrugt | Effects of a smile on mood and helping behavior[END_REF] could put people in a good mood, capable of increasing the likelihood they would carry out acts of solicited or spontaneous helping behavior in turn [START_REF] Guéguen | The effect of smiling on helping behavior: Smiling and Good Samaritan behavior[END_REF]. It is not excluded that this mechanism also contributed to obtaining our results.

As this is an initial experimental attempt, there are certain limitations that future studies will need to consider. First, studies to come will need to take measures of affect in the different experimental conditions before making the target request in order to evaluate the relative weight of mood in the obtained effects. Also, in order to eliminate interpretation taken in the context of generalized reciprocity, the gift will need to be more disconnected from all considerations relative to assistance. As is, it cannot be excluded that accepting the cake was perceived by certain individuals as a way of helping to promote the university and despite our precautions, could have activated the norm of social responsibility. Finally, but in connection with the above, replication must be carried out in a period of the year less likely to promotes helping behaviors as this is the case during the Christmas period.

In addition to these limitations, the present experiment contributes elements of knowledge related to the implemen tation. While [START_REF] Cialdini | Infl uence et Manipulation[END_REF] cites many examples of reciprocity in real life, the majority of research has been carried out in laboratories and with students. This experiment carried out in the street and with passersby demonstrates that the effect is sufficiently robust to be observed in a context however favorable to the occurrence of parasitic variables. Moreover, it suggests that whatever the experimental condition considered and whatever the theoretical interpretation selected, the preliminary distribution of a low value gift is an effective tool at increasing subsequent submission of individuals to a pro-social request.

Table 1 . Frequencies and percentages of acceptance of the request target in the different conditions

 1

	Conditions	Classic Reciprocity	Generalized Recicprocity	Control
	Acceptance	92.5%a	70%b	32.5%c
	rates	(37/40)	(28 /40)	(13/40)
	Distincts letters indicate a statistical difference at p < .001 between
	conditions.

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