Francois Sanson

Nadège Villedieu

Francesco Panerai
email: panerai@vki.ac.be

Olivier Chazot

Pietro Marco Congedo

Thierry E Magin

Quantification of uncertainty on the catalytic property of reusable thermal protection materials from high enthalpy experiments

Keywords: Uncertainty Quantification, Catalysis, Thermal Protection Systems

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

cility at the von Karman Institute for Fluid Dynamics provides a test environment to analyze gas-surface interactions under effective hypersonic conditions. In this study, we develop an uncertainty quantification methodology to rebuild values of the gas enthalpy and material catalytic property from Plasmatron experiments. A non-intrusive spectral projection method is coupled with an in-house boundarylayer solver, to propagate uncertainties and provide error bars on the rebuilt gas enthalpy and material catalytic property, as well as to determine which uncertainties have the largest contribution to the outputs of the experiments. We show

Introduction

Many achievements in rocket science have been made since Apollo, but the prediction of the heat flux to the surface of spacecraft remains an imperfect science, and inaccuracies in these predictions can be fatal for the crew or the success of exploration missions. This quantity is estimated during the design phase of the heat shield used to protect payload and astronauts during the spacecraft atmospheric entry. Predicting the heat flux with accuracy is a rather involved exercise, due to complex multi-physics phenomena typical of hypersonic flows, in particular gas-surface interactions. In order to properly size a Thermal Protection System (TPS) and verify design margins, nominal values determined from ground testing are required, and also their associated uncertainties. It is difficult to rigorously quantify "error bars" on heat-flux predictions. Usually, engineers resort to safety factors to determine the heat shield thickness. This approach is often too conservative, at the expense of a reduced mass of the embarked payload, whereas it can also lead in some conditions to "lucky" heat shield design with barely enough safety margins. Some famous examples are the design of Apollo, Galileo, and Huygens TPS [START_REF] Park | Frontiers of aerothermodynamics[END_REF].

As opposed to safety factors, Uncertainty Quantification (UQ) is a more systematic approach to establish the variability of a given quantity of interest (QOI) due to the system uncertainties. At the interface of physics, mathematics, and statistics, UQ tools aim at developing rigorous methods to characterize the impact of "limited knowledge" on a QOI such as the heat flux. This limited knowledge arises from uncertainties related to the inputs of any computation attempting to represent a physical system. The uncertainties are naturally associated to the choice of the physical models and to the specification of the input parameters required for performing the analysis. As an example, numerical simulations require the precise specification of boundary conditions and typically only limited information is available from corresponding experiments. Note that numerical errors associated to the translation of a mathematical formulation into a numerical algorithm (and a computational code) are not considered here as uncertainties (see [START_REF] Iaccarino | Quantication of uncertainty in ow simulations using probabilistic methods[END_REF] for more details).

Several examples of UQ techniques (Monte Carlo sampling, Polynomial Chaos, Bayesian methods, etc.) applied to the analysis of complex multiphysics experiments/simulations can be found in the literature [START_REF] Upadhyay | Uncertainty quantification of a graphite nitridation experiment using a bayesian approach[END_REF][START_REF] Urzay | Uncertainty-quantification analysis of the effects of residual impurities on hydrogenoxygen ignition in shock tubes[END_REF][START_REF] Sai | Uncertainty quantification and robust predictive system analysis for high temperature kinetics of hcn/o2/ar mixture[END_REF]. Upadhyay [START_REF] Upadhyay | Uncertainty quantification of a graphite nitridation experiment using a bayesian approach[END_REF] et al. used a Bayesian method to quantify the uncertainty of a laboratory reactor experiment, investigating the nitridation of graphite. Using UQ, the authors obtained a larger reaction efficiency than that deterministically obtained from the modeling of the experimental setup. Reference [START_REF] Urzay | Uncertainty-quantification analysis of the effects of residual impurities on hydrogenoxygen ignition in shock tubes[END_REF] documents an uncertainty quantification analysis of ignition times in H 2 /O 2 mixtures, determined from computations and shocktube experiments. The authors used Monte Carlo sampling to show an increase in the contribution of H-impurities at higher dilution and lower pressures, as well as a negligible effect of kinetic uncertainties compared to the H-impurities, except for air at high temperature for which the role of kinetic uncertainties is dominant.

A Bayesian method was used by Cheung et al. to quantify the uncertainties in the modeling of the HCN/O 2 /Ar mixture kinetics.

In this work, we develop an uncertainty quantification methodology to rebuild values of the gas enthalpy and the catalytic property of a reusable TPS material from Plasmatron experiments conducted at the von Karman Institute for Fluid Dynamics (VKI). The knowledge of the catalytic property, often referred to as effective catalytic recombination coefficient or catalycity, is essential for the development of a reusable heat shield. It can be defined as the probability of a flow-surface system to promote recombination reactions of dissociated species that come from the gas phase and diffuse to the wall. Due to the exothermic nature of these reactions, the catalytic property significantly contributes to the heat transferred to the wall. The methodology for characterizing catalytic gas-surface interactions in the VKI Plasmatron facility is based on experimental measurements and their numerical rebuilding using Computational Fluid Dynamics (CFD) simulations. The goal of this paper is to identify the main uncertainties from experiments on ceramic matrix composites [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF] and to quantify, based on a non-intrusive spectral projection method, how these uncertainties propagate into the numerical rebuilding of the plasma flow enthalpy and the catalytic property of the TPS material sample.

The work is structured in three sections. The first part recalls the main concepts of the methodology used to determine the catalytic properties from Plasmatron experiments. The second section describes the rigourous uncertainty quantification methodology implemented in this study and its novel features compared to a more conservative engineering approach used to compute error bars. The last section presents the results obtained applying the UQ framework to the Plasmatron test campaign.

Enthalpy rebuilding and catalytic property determination

The Plasmatron facility provides an ideal test environment for investigating catalysis effects on TPS materials. The inductively-coupled technology for plasma generation produces an impurity-free flow, ideal to study gas-surface interaction phenomena. Figure 1 shows a typical picture of Plasmatron experiment, where a stagnation-point probe holding a TPS material sample is immersed in the core of a plasma jet and heated to high temperatures. A water-cooled calorimetric probe that is used for calibrating the flow conditions stands in the foreground of the picture.

The Plasmatron facility generates a subsonic, high-enthalpy flow. The testing methodology is based on the simulation of the chemically reacting boundary layer in the stagnation region of a hypersonic body. Aerothermochemical condi-tions similar to those encountered at hypersonic regimes are reproduced around a representative model of the TPS material. The subsonic-hypersonic similarity can be described by means of the Local Heat Transfer Simulation theory [START_REF] Kolesnikov | Conditions of simulation of stagnation point heat transfer from a high-enthalpy ow[END_REF][START_REF] Barbante | Accurate and Efficient Modelling of High Temperature Nonequilibrium Air Flows[END_REF][START_REF] Barbante | Flight extrapolation of plasma wind tunnel stagnation region flowfield[END_REF], which is based on the Fay and Riddell [START_REF] Fay | Theory of Stagnation Point Heat Transfer in Dissociated Air[END_REF] and Goulard [START_REF] Goulard | On catalytic recombination rates in hypersonic stagnation heat transfer[END_REF] formulae for the heat flux at the stagnation point of a body immersed in a chemically reacting flow. Built upon this theory, a methodology has been consolidated at VKI in order to evaluate the catalytic property of a TPS material by combining experimental measurements from the Plasmatron facility and CFD simulations [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF][START_REF] Barbante | Flight extrapolation of plasma wind tunnel stagnation region flowfield[END_REF][START_REF] Marschall | Oxidation of ZrB 2 -SiC Ultrahigh-Temperature Ceramic Composites in Dissociated Air[END_REF], as shown in the schematic in Figure 2. Two steps are involved: the first one aims at calibrating certain flight conditions to be simulated in the experimental facility, the second one aims at determining the catalytic property of the tested material, under these conditions. In Figure 2 the QoIs for the two steps are highlighted in blue. Flight conditions are defined by the boundary-layer edge enthalpy h e , corresponding to the flight speed, and pressure P s , corresponding to the flight altitude. The quantity P s is directly measured, therefore it is not considered to be a QoI, but rather an input uncertainty. The catalytic property of the material surface are described by a global, phenomenological catalytic recombination coefficient γ, which quantifies the amount of catalytic heating transferred to the TPS material surface under the prescribed flights conditions.

The determination of flight conditions, that is the rebuilding of enthalpy h e at the bounday layer edge, can be summarized in the following steps:

• Plasmatron testing conditions are determined by controlling the gas (air in the cases analyzed herein) mass flow ṁ, the electrical power P W and the chamber static pressure P s . The gas mass flow is controlled using a calibrated rotameter. The electrical power dissipated into the plasma is a frac- tion (typically ≈40%) of the generator power setting. The pressure P s is measured by an absolute pressure gauge and adjusted to the required value by means of vacuum pumps and by-pass flow regulation.

Enthalpy rebuilding

Flight conditions

Catalytic property

Catalycity rebuilding

• Testing conditions are calibrated based on cold-wall heat flux q cw measurements, performed with a water-cooled calorimetric probe, and the determination of the total pressure P tot at the TPS sample location. The total pressure is obtained from the dynamic pressure P d measured by means of a Pitot probe and the static pressure P s . Both heat flux and Pitot probes have the same geometry (radius R p ) as the TPS probe.

• The following assumptions are made: Local Thermodynamic Equilibrium (LTE) conditions hold at the boundary layer edge [START_REF] Cipullo | Investigation of freestream plasma flow produced by inductively coupled plasma wind tunnel[END_REF], the temperature of the water-cooled calorimeter is T cw ≈ 350 K, and its copper surface has a known catalytic recombination coefficient γ ref of large magnitude (lower than one) relative to recombination of O and N atoms.

• Magneto-hydrodynamic (MHD), axisymmetric computations of the Plasmatron environment are performed to extract Non-Dimensional Parameters (NDPs) that characterize the plasma flowfield at the edge of the boundary layer. For these simulations, the Plasmatron settings are provided as input conditions (mass flow ṁ, electrical power P W , and chamber static pressure P s ).

• Stagnation-line flow computations are performed using a chemical nonequilibrium boundary layer code. The code solves non-equilibrium boundary layer equations, yielding the cold-wall, catalytic heat-flux at the calorimetric probe surface q cw . It is iteratively called by a rebuilding code based on Newton's method that iterates over the boundary-layer edge temperature T e until the computed heat flux is equal to the one measured experimentally.

A more detailed explanation is provided in Figure 2. Once the temperature T e is determined, the flight conditions (enthalpy h e and pressure P s ) are known, as well as the plasma composition since the LTE assumption holds at the boundary-layer edge.

The determination of the catalytic property γ of the TPS material follows a procedure similar to the rebuilding of the flight conditions. In this case, for solving the stagnation line flowfield, the rebuilt conditions are imposed as boundary condition at the boundary layer edge and hot-wall measurements are used to define the wall boundary conditions. A radiative equilibrium boundary relation is imposed at the wall, equating the incoming heat flux (diffusive + convective contributions) to the one re-radiated by the surface. The heat loss by conduction into the material is neglected. Measurements at the Plasmatron are performed using a thin-wall TPS sample (∼2-5 mm thickness) backed by a thick refractory insulation (∼3 cm). Steady state is achieved during a test and the back insulation allows to have an equilibrium temperature that limits the heat exchange at the back of the sample, supporting the adiabatic hypothesis. In summary:

• Boundary layer edge conditions are rebuilt following the steps previously described.

• Hot-wall temperature T w and emissivity ε are measured for a TPS sample model of radius R p , under the same total pressure P tot and boundary-layer edge enthalpy h e .

• The rebuilding code identifies the catalytic property γ of the tested TPS surface, by matching the heat flux computed at the wall temperature T w to the measured value q w ,inferred from the measured temperature and emissivity according to the Stefan-Boltzmann law q w = σ T 4 w , where quantity σ is the Stefan-Boltzmann constant.

While the described methodology, and analogous reference methods [START_REF] Scott | Catalytic Recombination of Nitrogen and Oxygen on High-Temperature Reusable Surface Insulation[END_REF][START_REF] Pidan | Recombination Coefficients and Spectral Emissivity of Silicon-Carbide-Based Thermal Protection Materials[END_REF], have been extensively applied in the literature [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF][START_REF] Kolesnikov | Conditions of simulation of stagnation point heat transfer from a high-enthalpy ow[END_REF][START_REF] Marschall | Oxidation of ZrB 2 -SiC Ultrahigh-Temperature Ceramic Composites in Dissociated Air[END_REF], the sensitivity of enthalpy rebuilding to a reference catalytic value γ ref is a known and accepted limitation.

Other efforts have been devoted to develop alternative methods using subtraction of the convective contribution, obtained from a correlation, from the total measured heat flux [START_REF] Massuti-Ballester | Recent catalysis measurements at {IRS}[END_REF] or near-surface diagnostic techniques [START_REF] Fletcher | Surface catalyzed reaction efficiencies in oxygen plasmas from laser-induced fluorescence measurements[END_REF].

In the present study, we apply non-intrusive UQ techniques to the rebuilding code coupled with the boundary-layer code. The uncertain inputs to the problem considered are highlighted in red in Figure 2. We focus on the following uncertain inputs:

• Controlled parameters: static pressure P s and cold-wall heat flux q cw .

• Measured quantities: dynamic pressure P d and hot-wall temperature T w and emissivity ε.

• Assumptions: cold-wall temperature T cw and reference (copper) catalytic property γ ref .

The model geometry is standard and repeated in every test, hence it is not considered as an uncertainty.

Determination of error bars

In this section, a methodology is developed to quantify the uncertainties on the QoIs: gas enthalpy h e and material catalytic property γ. The goal is to understand which are the main uncertain contributions to the values of h e and γ rebuilt from Plasmatron experiments, rank them, and then compare the error bars calculated by using a UQ method to those obtained based on a more conservative engineering approach. In the following section, the sources of uncertainties are described, then in Section 3.2, the main features of the engineering approach are reviewed, while a more advanced UQ method is presented in Section 3.3.

Sources of uncertainties

First, let us classify the sources of uncertainty identified in Section 2 [START_REF] Oberkampf | Investigation of evidence theory for engineering applications[END_REF] into two different categories.

• Experimental data from the Plasmatron are considered aleatory uncertainties (variables describing the inherent random nature of the physical system). It is conventional to model these as realizations of a zero mean Gaussian random variable, as the errors come from the accumulation of small errors in the physical system. The variance of that random variable is given by the available error bar from the experimental measurement. The six aleatory variables considered in this study are summarized in Table 1 with their respective relative uncertainty.

Variable

Distribution Relative uncertainty

P d [Pa] Gaussian 6% P s [Pa] Gaussian 4% q cw [W/m 2 ] Gaussian 10% T cw [K] Gaussian 10% T w [K] Gaussian 2% ε [-] Gaussian 5%
• The wall catalytic property for the reference calorimeteric probe γ ref is treated as epistemic uncertainty. The lack of knowledge is ascribed to the complex composition and to the poorly known chemistry of the watercooled copper surface exposed to an oxygen-rich plasma. A legacy practice [START_REF] Kolesnikov | Conditions of simulation of stagnation point heat transfer from a high-enthalpy ow[END_REF] consists in assuming that the reference calorimetric probe as fully catalytic (γ ref =1). This provides a conservative catalytic property for the tested TPS material. Nonetheless, studies from both arcjet and induction plasmatron facilities found values on the order of 10 In Section 4, we perform an uncertainty analysis at discrete values of γ ref ranging from 0.05 to 1, in order to understand its influence on the QoIs.

Further contributions to uncertainties in the described problem are related to the choice of the models for the plasma reactive flow and for the gas-surface interactions at the TPS wall. There are five categories of modeling uncertainties that can be identified:

• Non-dimensional parameters. As explained in section 2 a set of NDPs is used to characterize the hydrodynamics of the plasma flow at the boundary layer edge. These parameters are calculated from thermo-chemical equilibrium solutions of the Plasmatron (torch + test chamber with probe) flow field. For a given inlet swirl angle, the solution depends on the inlet mass flow, the pressure level and the coupled plasma power (which in turn depends on the Plasmatron generator efficiency η) that are used during a certain experiment. In order to properly quantify NDPs uncertainties, UQ techniques shall be applied to the dedicated CFD code that allows to solve the Plasmatron flow field. This is a complex undertaking that would require coping with the complexity of the physical models involved, the computa-tional cost of MHD simulations and the difficulty in identifying sources of uncertainty to the specific problem. A sensitivity analysis to the NDPs was performed in [START_REF] Panerai | Aerothermochemistry characterization of thermal protection systems[END_REF], using a database of multiple CFD simulations at different combinations of static pressure, mass flow and power, within the Plasmatron operating envelope. It was shown that, for a given mass flow and pressure, variations of NPDs computed at generators efficiencies between η = 40 and 60% yield variations in h e and γ of less than 0.6%. Based on this analysis, it can be concluded with confidence that NPDs are negligible in the present problem.

• Thermodynamic and transport properties of the plasma flow. Since the highest-fidelity models, with the best data currently available in the literature are used [START_REF] David Bottin Benoît | Thermodynamic and transport properties for inductive plasma modeling[END_REF][START_REF] Thierry | Transport properties of partially ionized and unmagnetized plasmas[END_REF], thermodynamic and transport models can be considered as certain.

• Gas chemistry model. Uncertainties in the gas chemistry model are due to both the number of species used to approximate the test gas, and the selected reaction rates. In [START_REF] Panerai | Aerothermochemistry characterization of thermal protection systems[END_REF], a comparison of 5, 7 and 11-species models for air mixture conducted on series of test cases at different pressures, showed that

for Plasmatron experiments at relatively low enthalpies ( 25 MJ/kg), both and are nearly insensitive to the number of species. A small sensitivity (on the order of ≈5%) was observed for γ ref values below 10 -3 , which however are highly unlikely. A similar behavior was observed when changing from the baseline Dunn and Kang [START_REF] Dunn | Theoretical and Experimental Studies of Reentry Plasmas[END_REF], rates to those of Park [START_REF] Park | Nonequilibrium hypersonic aerothermodynamics[END_REF] and Chung [START_REF] Chung | Chemically Reacting Nonequilibrium Boundary Layer[END_REF] • Surface chemistry model. The boundary layer code used in the present study adopts a very simplified engineering model that accounts for only O and N-atom recombination into O 2 and N 2 , respectively, at equal rates. Nitric oxide production, which was demonstrated to occur on quartz surfaces [START_REF] Dušan A Pejaković | Nitric oxide production from surface recombination of oxygen and nitrogen atoms[END_REF][START_REF] Dušan A Pejaković | Direct detection of no produced by high-temperature surface-catalyzed atom recombination[END_REF] from room temperature to 1200 K, is not included. Oxidation reactions, which are fundamental to the analysis of silica forming surfaces as those in • Boundary-layer edge thermo-chemical state. Local thermo-chemical equilibrium (LTE) conditions are assumed at the boundary-layer edge. This assumption has been validated using spectroscopy measurements [START_REF] Cipullo | Investigation of freestream plasma flow produced by inductively coupled plasma wind tunnel[END_REF] for the test conditions analyzed in the present work. Recent numerical investigations [START_REF] Zhang | Analysis of non-equilibrium phenomena in inductively coupled plasma generators[END_REF] suggest nonetheless that LTE may not hold under different conditions (e.g. lower mass flows). In such a circumstance this shall be considered as an additional source of uncertainty.

As we intend to focus on experimental uncertainties and on how they propagate through the rebuilding procedure, the listed modeling uncertainties are ne-glected. Their influence shall be further studied in a dedicated UQ analysis beyond the scope of the present study.

Engineering approach

In [START_REF] Marschall | Oxidation of ZrB 2 -SiC Ultrahigh-Temperature Ceramic Composites in Dissociated Air[END_REF], Marschall et al. showed independent effects of temperature T w , hot wall heat flux q w (emissivity) and enthalpy h e on the final value of the catalytic property γ. A ±10% assumption on the relative uncertainty of h e was adopted, emissivity ε uncertainties were taken as +0.1/-0.2 and the measurement error on the temperature was set to the quoted instrument uncertainty. Uncertainties on the calorimetric probe catalytic property γ ref and wall temperature T cw were neglected, and each input uncertain variable was considered separately.

Following this approach, variability ranges for enthalpy and catalytic property values from Plasmatron experiments can be computed. Below, the technique is applied to a reference case (sample S12 in [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K) used in the following sections to determine error bands for both

QoIs h e and γ:

• Nominal (measured) values of heat flux, static pressure, dynamic pressure and, wall temperature and emissivity are denoted as q * cw , P * s , P * d , T * w and ε * , respectively.

• The ∆ uncertainty on each variable is based on the values reported in Table 1 and defines upper and lower limits for the variable, which are denoted with the superscripts * , + and -, respectively. For example, for a wall temperature T w of 1600 K and ∆T w = 2% relative uncertainty, the upper and the lower values are T - w = 1568 K and T + w = 1632 K, respectively.

• The numerical rebuilding detailed in Section 2 is performed for the nominal, lower and upper value of each variable, the others being fixed to their nominal value for each simulation.

A summary of the results obtained for the sample S12 from [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF] is provided in Table 2. Upper and lower margins are highlighted in red and blue respectively. As expected, one can notice that higher values of enthalpy h e result from a positive relative uncertainty on the heat flux q + cw , and negative relative uncertainty on the static and dynamic pressures, P - s and P - d . The dissociation of a plasma is enhanced at lower pressures P s , its enthalpy being higher. Assuming a constant total enthalpy, a lower dynamic pressure results in a higher static enthalpy. Similarly, lower values of enthalpy h e are given by the bounds q - cw , P + s and P + d . Obviously, the enthalpy does not depend on the hot wall temperature T w and emissivity ε, which are properties of the sample.

Lower values of the TPS catalytic property are given by the bounds q + cw , P + s , P + d , T - w , and ε -. For a positive error in q cw , a higher wall heat flux is obtained at a given surface catalytic property and at given temperature (in the q w versus T w plot in Figure 2 the iso-γ curves shift upwards). Therefore, for the same sample temperature and emissivity, a lower γ is obtained from the rebuilding. Similarly, for a negative error on the wall temperature T w or on the emissivity ε, the reradiated heat flux is lower, hence a lower γ is determined.

In order to estimate the final error bar a further rebuilding is performed combining the marginal inputs giving a similar effect, therefore yielding the highest and lowest possible values for each QoI. The computed error bars ∆h e = [h - e , h + e ] for the enthalpy and ∆γ = [γ -, γ + ] are shown in Table 3.

T + w - 0.00997 ε * - 0.00862 ε - - 0.00719 ε + - 0.01013
Table 3: Maximum and minimum values of h e and γ based on engineering approach for reference case (sample S12 in [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K)

QoI and input combination Value

h - e = h - e (q - cw , P + s , P + d ) 14.66 MJ/kg

h + e = h + e (q + cw , P - s , P - d ) 18.92 MJ/kg γ -= γ -(q + cw , P + s , P + d , T - w , ε -) 0.00457 γ + = γ + (q - cw , P - s , P - d , T + w , ε + ) 0.01522

Uncertainty quantification method

In this section, the generalized Polynomial Chaos (gPC) method is presented as a rigorous UQ method for computing error bars on the QoIs for the described problem. It was originally developed by [START_REF] Xiu | The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations[END_REF]. The gPC stochastic expansion provides with a method to build a polynomial approximation of a function of stochastic variables. Let us define f as the square integrable function of interest that takes the random vector (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) of n known distributions as input, n being the dimension of the input space. The generalized polynomial chaos (gPC) theory asserts that f can be approximated by an orthogonal polynomial with respect to the input space (Ξ, p ξ 1 ,ξ 2 ,ξ 3 ,..ξn ), with a converging error in the mean-square sense [START_REF] Le Maître | Spectral Methods for Uncertainty Quantification[END_REF]. The classical gPC construction provides us with with a polynomial of order N denoted as

P N (ξ 1 , ξ 2 , ξ 3 , ..ξ n ), i.e. f (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) P N (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) = i α i Ψ i (ξ 1 , ξ 2 , ξ 3 , ..ξ n ). (1)
Here, Ψ i is the polynomial basis, which is orthogonal with respect to the probability measure associated to the uncertain inputs. For Gaussian distributed uncertainties, the polynomial basis is built using the tensorisation of n one-dimensional Hermitian polynomials (six in the present case). Besides L 2 (Ξ, p ξ 1 ,ξ 2 ,ξ 3 ,..ξn ), the space of square integrable functions is a Hilbert space with the following scalar product:

u, v = Ξ u(ξ 1 , ξ 2 , ξ 3 , ..ξ n )v(ξ 1 , ξ 2 , ξ 3 , ..ξ n )p(ξ 1 , ξ 2 , ξ 3 , ..ξ n )dξ 1 dξ 2 dξ 3 ..dξ n , (2)
where p(ξ 1 , ξ 2 , ξ 3 , ..ξ n ) is the product of n one dimensional Gaussian distributions.

Then, it follows that

Ψ i , Ψ j = Ψ i , Ψ i δ i,j , (3)
for any i and j. In order to compute α i , the orthogonality property from Eq. 3 can be used by projecting f on each component of the basis. From Eq. 1 it follows that

α i = f (ξ 1 , ξ 2 , ξ 3 , ..ξ n ), Ψ i (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) Ψ i , Ψ i . (4)
Therefore the computation of P N (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) consists in computing the α i and therefore evaluating an integral according to Eq. 4. In our case, we used the Hermite Gauss quadrature rule described in [START_REF] Le Maître | Spectral Methods for Uncertainty Quantification[END_REF]. As no modifications to the deterministic code computing f are needed, the method is non intrusive. Only evaluations of the function at several collocation points are required for the quadrature rule.

In order to evaluate the results of the gPC analysis, the Sobol indices [START_REF] Tang | Global sensitivity analysis for stochastic collocation expansion[END_REF] can be computed to study the sensitivity of f (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) to each random variables.

Sobol indices compare the variance of the conditional expectation V ar

ξ i [E(y|ξ i )]
against the total variance V ar(y), where E denotes the expected value. The Sobol index S i for the variable ξ i is defined as:

S i = V ar ξ i [E(y|ξ i )] V ar(y) . (5)
Sobol indices quantify the contribution of each source of uncertainty to the variance of the ouputs. Once the coefficient of the polynomial are computed, the statistical moments of f (ξ 1 , ξ 2 , ξ 3 , ..ξ n ) and the Sobol indices are readily available from the coefficients of the polynomial [START_REF] Le Maître | Spectral Methods for Uncertainty Quantification[END_REF]. The built polynomial provides a cheap metamodel that can be evaluated multiple times at low computational cost, enabling to rebuild an estimation of the Probability Distribution Function (PDF)

and Cumulative Distribution (CDF) of the output.

In the next section, the results obtained with the gPC are presented. While not reported here, the convergence of the stochastic method is systematically checked for each one of the cases analyzed. In particular, an increasing polynomial order is considered, showing that orders 2 and 3 are always sufficient to attain convergence. Both expansions yield very accurate results at the quadrature points where the actual function is evaluated, thus validating the statistics estimation.

Results

In this section, we present the results obtained based on the gPC theory. First, the influence of the reference catalytic property γ ref on the resulting uncertainty on the TPS sample catalytic property γ is discussed. Eleven values of γ ref ranging from 0.05 to 1 are selected, and the uncertainty analysis is carried out at those points for one exemplary condition corresponding to case S8 in [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF] (q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K). Later the influence of the mean measured quantities on the rebuilt gas enthalpy h E and material catalytic property γ are discussed for several test cases from [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF]. The mean values for the rebuilt quantities are presented in Figure 5 with ∓σ error bars, for increasing γ ref .

The plots show that for γ ref values higher than 0.2 there is only a slight variation in the rebuilt quantities. This is a well-know behavior, commonly observed on the "S-shaped" curves that plot the variability of rebuilt quantities with γ ref .

An example is provided in Figure 6 for h e . For a given heat flux value, a lower reference catalytic property yields a higher enthalpy due to the lower effectiveness of the surface in recombining atoms [START_REF] Ihor | A method for determining catalytic efficiency of surfaces[END_REF]. The "S-shaped" plot highlights that for a nearly non-catalytic reference surface (γ ref 10 -4 ), or a nearly fully-catalytic one (γ ref 10 -1 ), there is a very small variation on the rebuilt h e . Conversely for partial reference catalycity values, a small variation in γ ref produces a large variation in the rebuilt quantities. In order to further investigate the influence of each experimental uncertainty on the QoI error bars, the Sobol indices of the aleatory variables are presented in Figure 7 for the enthalpy, and in Figure 8 for the sample catalytic property, at Similarly, the sample catalytic property γ uncertainty is significantly affected by the cold-wall heat flux q cw (80% of the error). The emissivity ε and temperature T w of the test sample, that define the re-radiated heat flux from the surface, account for the remaining 20% of the error. Unlike in the case of the gas enthalpy, a reduction of the q cw Sobol index for γ is noticed in Figure 8 for low γ ref values.

Therefore, the decrease in uncertainty previously observed in Figure 5, can be explained by the reduced contribution of cold-wall heat flux q cw to the sample catalytic property variance. q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K).

Comparison of UQ and engineering approaches for reference case (sample

S12 in [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K)

We now compare the error bars obtained based on the UQ methodology to those computed using the engineering approach. As described in section 3, the errors estimated with the engineering approach are defined as the range between the two extreme cases. Using the UQ approach, error bars can be accurately computed, and provided together with the correspondent Confidence Interval (CI).

The results are summarized in Table 4, for the same experimental case (S12 from [], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K) analyzed in Table 2. The mean values for the QoIs obtained with both methods are closely similar. For the gas enthalpy h e , the engineering methodology results in a ±25% accuracy, while the UQ analysis predicts 13% and 17% uncertainty with a confidence level of 95 and 99% respectively. For the catalytic property γ, larger error bars are computed using both methods. This is due the strong non-linearity of the problem, as opposed to the enthalpy that instead varies linearly with the measured heat flux. As shown in Figure 9, in the case of γ rebuilding the engineering approach performs poorly by overestimating the uncertainty of more than one order of magnitude. The UQ analysis predicts 39% and 51% uncertainty with a confidence level of 95 and 99%, respectively. The example underlines the need of a rigorous UQ tion of the three main variables responsible for the catalytic property uncertainty contribute to a similar extent to the total variance. An increase in the sample temperature leads to an increase in the contribution to the sample catalytic property variance from variables measured during the second reconstruction step. Now more than half the variance is explained by the catalytic property rebuilding step.

This observation is also correlated with a relatively high sample catalytic property at 8.7e-03. This behavior was not observed for previous cases in this study. This analysis can be extended to more samples and eventually serve as a reference for further experiments. When setting the experimental setup, one could get an estimation about which variable would yield an important contribution being in the vicinity of cases a1, a2, a3 or a4.

Conclusion

The uncertainty quantification method is a powerful tool to analyze experimental results. We demonstrated here that the method helps mitigating overconservative error bars computed in TPS characterization when using an engineering approach , that considers in a separate manner the different input variables to the problem. We quantified with 95% confidence a 13% error in the duplication of actual flight condition (boundary layer edge enthalpy) during Plasmatron experiments and an error of ∼40% in the computed catalytic property of the reusable TPS material.

The analysis embedded in the gPC method provided understanding of the influence of the measurement error on the QoI. The constructed polynomial approximation can be readily used as a cheap metamodel for rebuilding the QoI PDF.

The documented analysis suggests that, in Plasmatron experiments, the mea- sured cold-wall heat flux is the chief contributor to the rebuilt enthalpy. The reconstruction of the PDF showed that the enthalpy is nearly Gaussian distributed.

This behavior comes from the almost linear relationship between the heat flux and the flow enthalpy. We conclude that, reducing experimental errors in heat flux measurements below 10% would enable matching a desired hypersonic condition with less than 10% uncertainty.

Concerning the catalytic property γ of the TPS material, non-linear trends were observed. The cold wall heat flux and the material's emissivity and temperature were identified as main contributors to the rebuilt values of γ. We found that the cold-wall heat flux has a relative contribution of more that 70% to the computed value of γ at temperatures below 1400 K. For higher temperatures (>1600 K) we found an increase in the relative importance of the materials' temperature and emissivity to γ. This suggest that improvements on optical measurements for the detection of surface radiative properties would provide a more accurate estimation of catalytic heating from Plasmatron experiments, particularly at very high temperatures.

Finally, we showed that the catalytic property of the reference material features a significant impact on the QoI determined at the Plasmatron. Experimental and numerical efforts shall be directed at improving techniques that can provide a suitable alternative to copper-base reference probes for the characterization of experimental conditions.

Figure 1 :

 1 Figure 1: TPS material testing in the VKI Plasmatron facility: stagnation-point probe holding a material sample in plasma jet and calorimetric probe outside of plasma.

Figure 2 :

 2 Figure 2: Schematic of enthalpy rebuilding and catalytic property rebuilding methodology.

[ 6 ]

 6 , are also not modeled. Moreover, the model assumes full energy accommodation to the surface. These approximations are indisputably sources of uncertainty to the analysis of Plasmatron experiments. Several, more advanced surface reaction models have been developed for CFD simulations and the work by Marschall et al.[START_REF] Marschall | Surface Chemistry in Non-Equilibrium Flows[END_REF] is a comprehensive reference on the topic. The challenge in applying advanced finite-rate catalysis formulations lies into the availability of high-fidelity recombination coefficients and, when those are available from controlled laboratory experiments, their applicability to more complex environments like the Plasmatron or even a real flight environment. This is still an open field of investigation, and dedicated, future study shall be devoted to quantify the uncertainties of surface chemistry models.

4. 1 .

 1 Figures 3 and 4 show the influence of the reference probe catalytic property γ ref on the QoIs based on both the PDF and CDF of h e and γ. It is observed

Figure 5

 5 Figure 5 also highlights that the probe catalytic property not only influences the mean rebuilt QoI, but it also affects their uncertainty. Interestingly, it is observed that, in the region where γ ref has a larger influence (γ ref 2 • 10 -1 ), the uncertainties in the experimental measurements produce smaller error bars. This effect is more pronounced for γ, where clearly smaller error bars are observed for γ ref < 0.2.

Figure 3 :

 3 Figure 3: Evolution of the PDF for the rebuilt gas enthalpy h e (top) and material catalytic property γ (bottom), as a function of the reference material catalytic property γ ref for reference case (sample S8 in[START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K).

Figure 4 :Figure 5 :

 45 Figure 4: Evolution of the CDF for the rebuilt gas enthalpy h e (top) and material catalytic property γ (bottom) as a function of the reference material catalytic property γ ref for reference case (sample S8 in[START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K).

Figure 6 :

 6 Figure 6: Rebuilt gas enthalpy h e as a function of the reference material catalytic property γ ref forreference case (sample S8 in[START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K).

Figure 7 :Figure 8 :

 78 Figure 7: Contribution (Sobol indices) of cold wall heat flux q cw , dynamic pressure P d , and coldwall temperature T cw measurements to the uncertainty on the rebuilt gas enthalpy h e as a function of the reference material catalytic property γ ref for reference case (sample S8 in [6], q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K)

Table 1 :

 1 Distribution of the aleatory variables

Table 2 :

 2 Rebuilt values of the QoI based on engineering approach for reference case (sample S12 in[START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K). Enthalpy values are rebuilt with a T cw = 350 K surface temperature value. Variation of h e due to T cw are negligible, hence they are not included.

	Input variable Enthalpy h e [MJ/kg] Catalytic property γ
	P * s	16.70	0.00862
	P -s	16.92	0.009603
	P + s	16.49	0.00823
	P * d	16.70	0.00862
	P -d	16.94	0.00868
	P + d	16.47	0.00855
	q * cw	16.70	0.00862
	q -cw	15.04	0.00862
	q + cw	18.38	0.00712
	T * w	-	0.00862
	T -w	-	0.00737

Table 4 :

 4 Comparison of QoI mean values and error bars computed with the engineering and UQ approaches for reference case (sample S12 in[START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K)

	QoI	UQ (mean) Eng. (mean)	UQ (95% CI) (99% CI) (error bar) UQ Eng.
	h e [MJ/kg]	16.75	16.70	13%	17%	25%
	γ [-]	0.00867	0.00861	39%	51%	122%

Table 5 :

 5 Test conditions and error bars of case a1 to a4. The values are take from case S6, S7, S8

	and S12 in [6], respectively
	Case	a1 (sample S6 in [6])		a2 (sample S7 in [6])
		Mean value	Std. Dev. Mean value	Std. Dev.
	P s [Pa]	1320	17.6	1980	26.4
	q cw [W/m 2 ] 360 000	12 000	385 000	12833.3
	P d [Pa]	83	1.333	60	1.667
	T w [K]	1400	4.667	1400	4.667
	ε [-]	0.79	0.01316	0.8	0.01333
	T cw [K]	350	11.667	350	11.667
	Case	a3 (sample S8 in [6])		a4 (sample S12 in [6])
		Mean value	Std. Dev. Mean value	Std. Dev.
	P s [Pa]	3020	40.2	2010	26.8
	q cw [W/m 2 ] 410 000	13 666	735 000	24 500
	P d [Pa]	60	2	115	2.33
	T w [K]	1400	4.667	1600	5.33
	ε [-]	0.88	0.01466	0.85	0.01466
	T cw [K]	350	11.667	350	11.667

Acknowledgment Research of T.E.M. was sponsored by the European Research Council Starting Grant #259354. The work was partly supported by the European Space Agency (ESA) General Support Technology Programme (GSTP) "Plasmatron+" (contract #4000105388/12/NL/SFe).

method for accurately propagating experimental uncertainties through the rebuilding code.

Study of cases matrix for fixed reference catalytic property γ ref

In this section, a more detailed sensitivity analysis is carried out in order to provide insight into how the variance decomposition evolves as the experimental conditions change. The six aleatory uncertainties listed in Section 3.3 are considered. As in [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], we make the assumption of a constant reference material catalytic property γ ref = 0.1. Four characteristic cases with experimental conditions given in Table 5 are considered and denoted as a1, a2, a3, and a4. These correspond to case S6 (q cw = 360 W/m 2 , P s = 1320 Pa, T w = 1400 K), S7 (q cw = 385 W/m 2 , P s = 1980 Pa, T w = 1400 K), S8 (q cw = 410 W/m 2 , P s = 3020 Pa, T w = 1400 K) and S12 (q cw = 735 W/m 2 , P s = 2010 Pa, T w = 1600 K) from [START_REF] Panerai | Characterization of gas/surface interactions for ceramic matrix composites in high enthalpy, low pressure air flow[END_REF], respectively.

The first three cases aim at understanding the influence of the static pressure on the contribution to the total variance. For those cases, the static pressure P s varies from 1320 to 3020 Pa, and the same surface temperature (T w = 1400 K) is obtained by increasing the cold-wall heat flux q cw for increasing static pressure. In Figure 10, the main Sobol indices involved in the determination of the sample catalytic property are plotted. One observes that for a static pressure of 2000

Pa, the contribution of the measured heat flux to the sample catalytic property variance is much lower than for the other conditions. Similarly, the high pressure case is the case where the contribution of the cold-wall heat flux is the highest. This is well explained by the increase in the measurement uncertainty of the heat flux between cases a2 and a3. Case a4 is chosen at a static pressure of P s = 2000 Pa similar to case a2 but at a higher surface temperature. In this case the contribu-


Sébastien Gélis-Jeanvoine

Stephen Lory

Jacques Oberto

Nienke 4 Buddelmeijer

Residues located on membrane-associated flexible loops are essential for the second 1 step of the apolipoprotein N-acyltransferase (Lnt) reaction 2 3

Keywords: lipoprotein modification, Apolipoprotein N-acyltransferase, membrane 21 topology, essential residues, error-prone PCR mutagenesis. 22 23

Apolipoprotein N-acyltransferase (Lnt) is an essential membrane-bound enzyme that 31 catalyzes the third and last step in the post-translational modification of bacterial 32 lipoproteins. In order to identify essential residues implicated in substrate recognition 33 and/or binding we screened for non-functional variants of Lnt obtained by error-prone 34 PCR in a complementation assay using a lnt depletion strain. Mutations included 35 amino acid substitutions in the active site and of residues located on flexible loops in 36 the catalytic periplasmic domain. All, but one mutation, led to the formation of the 37 thioester acyl-enzyme intermediate and to the accumulation of apo-Lpp, suggesting 38 that these residues are involved in the second step of the reaction. A large cytoplasmic 39 loop contains a highly conserved region and two hydrophobic segments. Accessibility 40 analysis to alkylating reagents of substituted cysteine residues introduced in this 41 region demonstrated that the hydrophobic segments do not completely span the 42 membrane. Two residues in the highly conserved cytoplasmic region were shown to 43 be essential for Lnt function. Together, our data suggest that amino acids located on 44 cytoplasmic and periplasmic membrane-associated loops are required for efficient N-45 acylation of lipoproteins. 46 47

2

Isopropyl β-D-1-thiogalactopyranoside (IPTG), hydroxylamine (HA), sulfonatoethyl)-methane thiosulfonate (MTSES), maleimide polyethylene glycol 5000 26 (malPEG). 27

Introduction 48 49

Bacterial lipoproteins fulfill a variety of functions that include nutrient uptake, 50 maintenance of cell wall integrity, cell wall growth, adhesion to surfaces and host 51 cells, modulation of inflammatory processes and translocation of virulence factors 52 [START_REF] Kovacs--Simon | Lipoproteins of bacterial 651 pathogens[END_REF][START_REF] Sutcliffe | Lipoproteins of gram--positive bacteria[END_REF]. Although their primary 53 sequences and three-dimensional structures differ to a large extend, they all possess 54 fatty acids at their amino terminus the source of which are membrane phospholipids 55 [START_REF] Lai | Acyl moieties in phospholipids are tha 667 precursors for the fatty acids in murein lipoprotein in Escherichia coli[END_REF]. Modification of lipoproteins occurs in a post-translational fashion 56 by the sequential action of three membrane-bound enzymes: two acyltransferases and 57 one signal peptidase. Lipoproteins are synthesized in the cytoplasm and inserted into 58 the cytoplasmic membrane via the Sec or Tat secretion machinery (Zuckert, 2014, 59 Sugai [START_REF] Sugai | Export of the outer membrane lipoprotein is 709 defective in secD, secE, and secF mutants of Escherichia coli[END_REF][START_REF] Thompson | Investigating lipoprotein biogenesis and function 719 in the model Gram--positive bacterium Streptomyces coelicolor[END_REF]. A specific signature sequence, composed 60 of a signal peptide sequence containing a so-called lipobox (consensus sequence 61 Leu(Ala/Val)-Leu-Ala(Ser)-Gly(Ala)-Cys for lipoproteins in Proteobacteria), allows 62 membrane insertion and recognition by the modification machinery [START_REF] Wu | 737 Posttranslational modification and processing of membrane lipoproteins 738 in bacteria[END_REF]. 63

The invariant cysteine in the lipobox becomes fatty-acid acylated. After complete 64 maturation this cysteine is the first amino acid of mature lipoprotein. The first step in 65 the modification process is catalyzed by prolipoprotein-66 diacylglyceryl:phosphatidylglycerol transferase (Lgt), which attaches a diacylglyceryl 67 from phosphatidylglycerol to the thiol group of cysteine resulting in a thioether linked 68 S-diacylglyceryl group of prolipoprotein [START_REF] Sankaran | Lipid modification of bacterial prolipoprotein. 698 Transfer of diacylglyceryl moiety from phosphatidylglycerol[END_REF]. The second step in 69 lipoprotein maturation is the cleavage of the signal peptide from S-diacylglyceryl 70 prolipoprotein by signal peptidase II (Lsp) resulting in a free α-amino group of S-71 diacylglyceryl-cysteine [START_REF] Hussain | Mechanism of signal peptide 641 cleavage in the biosynthesis of the major lipoprotein of the Escherichia 642 coli outer membrane[END_REF]. The third and last step is catalyzed by 72 apolipoprotein N-acyltransferase (Lnt) that attaches a fatty acid from phospholipids to 73 this α-amino group resulting in mature triacylated lipoprotein [START_REF] Hillmann | Kinetics and phospholipid 634 specificity of apolipoprotein N--acyltransferase[END_REF], 74 Jackowski & Rock, 1986). The mechanism of the Lnt-catalyzed reaction involves a 75 two-step ping-pong mechanism in which, upon hydrolysis of phospholipids, the 76 enzyme is first auto-acylated on the active site cysteine residue resulting in the 77 formation of a thioester acyl-enzyme intermediate and lyso-phospholipid 78 [START_REF] Buddelmeijer | The essential Escherichia coli 624 Apolipoprotein N--acyltransferase (Lnt) exists as an extracytoplasmic 625 thioester acyl--enzyme intermediate[END_REF][START_REF] Hillmann | Kinetics and phospholipid 634 specificity of apolipoprotein N--acyltransferase[END_REF]. In the second step, the α-79 amino group of diacylglyceryl-cysteine of apolipoprotein is acylated. Phospholipids 80 with small polar head groups, preferentially phosphatidylethanolamine (PE), and 81 saturated-and unsaturated fatty acid on sn-1 and sn-2 position, respectively, are the 82 preferred substrates for Lnt of E. coli [START_REF] Hillmann | Kinetics and phospholipid 634 specificity of apolipoprotein N--acyltransferase[END_REF], Jackowski & Rock, 83 1986). Incomplete modification of lipoproteins in γ-proteobacteria, for example 84 through inhibition of Lsp activity by globomycin [START_REF] Inukai | Mechanism of action of 644 globomycin[END_REF] or myxovirescin 85 [START_REF] Xiao | Myxobacterium--produced 740 antiobiotic TA (Myxovirescin) inhibits type II signal peptidase. 741[END_REF], or depletion of genes encoding the modification enzymes (Pailler 86 et al., 2012[START_REF] Robichon | Depletion of 695 apolipoprotein N--acyltransferase causes mislocalization of outer 696 membrane lipoproteins in Escherichia coli[END_REF][START_REF] Xiao | Genetic redundancy, proximity, and functionality of 743 lspA, the target of antibiotic TA, in the Myxococcus xanthus producer 744 strain[END_REF], leads to arrest of cell growth 87 and cell lysis. Accumulation of the abundant outer membrane lipoprotein Lpp 88 (Braun's lipoprotein) in an unmodified form and covalently linked to the cell wall in 89 the cytoplasmic membrane, is the main cause of cell death [START_REF] Hussain | Accumulation of glyceride--637 containing precursor of the outer membrane lipoprotein in the 638 cytoplasmic membrane of Escherichia coli treated with globomycin[END_REF]. 90

However, modification and correct sorting of other essential outer membrane 91 lipoproteins, such as BamD [START_REF] Malinverni | YfiO stabilizes the YaeT complex and is essential for outer 674 membrane protein assembly in Escherichia coli[END_REF]) LpoA and LpoB (Paradis-Bleau 92 et al., 2010[START_REF] Typas | Regulation of 727 peptidoglycan synthesis by outer--membrane proteins[END_REF], is important since deletion of lpp still leads to cell 93 lysis in the absence of Lgt [START_REF] Pailler | 688 Phosphatidylglycerol::prolipoprotein diacylglyceryltransferase (Lgt) of E. 689 coli has seven transmembrane segments and its essential residues are 690 embedded in the membrane[END_REF]. Retention of these outer membrane 94 lipoproteins in the cytoplasmic membrane likely leads to cell death. The lipoprotein 95 modification machinery is conserved in all bacterial species, and although N-acylation 96 occurs in low GC Gram-positive bacteria such as firmicutes and mollicutes, the gene 97 encoding Lnt has not yet been identified in these species [START_REF] Nakayama | Lipoproteins in bacteria: 680 structures and biosynthetic pathways[END_REF]. In 98 these organisms not only does the composition of the N-acyl group vary, but also the 99 length and degree of saturation of the S-diacylglyceryl entity of lipoprotein is variable 100 [START_REF] Asanuma | Structural evidence of α--aminoacylated lipoproteins of 604 Staphylococcus aureus[END_REF][START_REF] Kurokawa | The triacylated ATP binding cluster transporter 659 substrate--binding lipoprotein of Staphylococcus aureus functions as a 660 native ligand for Toll--like receptor 2[END_REF], Kurokawa et al., 2012b, Serebryakova et al., 101 2011). Recent findings suggest that the extent of N-acylation varies depending on 102 growth conditions probably by regulation of lnt expression (Kurokawa et al., 2012a). 103

The role of Lnt in lipoprotein modification has also been studied in high GC Gram-104 positive bacteria (Actinomycetales). In Mycobacterium smegmatis (Tschumi et al., 105 2009) and Corynebacterium glutamicum [START_REF] Mohiman | The ppm operon is essential for acylation and glycosylation 678 of lipoproteins in Corynebacterium glutamicum[END_REF] a palmitoyl group is 106 transferred by Lnt onto apolipoproteins. It was shown recently that lipoproteins in M. 107 bovis also contain N-acyl tuberculostearic acid (C19) [START_REF] Brülle | Lipoproteins of slow--growing 621 Mycobacteria carry three fatty acids and are N--acylated by apolipoprotein 622 N--acyltransferase BCG_2070c[END_REF]. Thus, both 108 the S-diacylglyceryl and the N-acyl moieties of lipoproteins in Mycobacteria contain 109 tuberculostearic acid [START_REF] Tschumi | Identification of apolipoprotein N--acyltransferase (Lnt) in 723 Mycobacteria[END_REF]. Furthermore, several lipoproteins in 110 actinomycetes are modified by sugars, mainly hexose, via O-glycosylation (Brülle et 111 al., 2010[START_REF] Mohiman | The ppm operon is essential for acylation and glycosylation 678 of lipoproteins in Corynebacterium glutamicum[END_REF][START_REF] Sartain | N--Terminal clustering of the O--glycosylation 701 sites in the Mycobacterium tuberculosis lipoprotein SodC[END_REF][START_REF] Garbe | 627 Expression of the Mycobacterium tuberculosis 19--kilodalton antigen in 628 Mycobacterium smegmatis: immunological analysis and evidence of 629 glycosylation[END_REF]. In C. 112 glutamicum apolipoprotein N-acyltransferase (Lnt or Cg-ppm2) and O-113 glycosyltransferase (Cg-ppm1) operate in a common biosynthetic pathway resulting 114 in glycosylated lipoproteins in this organism [START_REF] Mohiman | The ppm operon is essential for acylation and glycosylation 678 of lipoproteins in Corynebacterium glutamicum[END_REF], but N-acylation 115 is not a prerequisite for glycosylation in M. bovis [START_REF] Brülle | Lipoproteins of slow--growing 621 Mycobacteria carry three fatty acids and are N--acylated by apolipoprotein 622 N--acyltransferase BCG_2070c[END_REF]. Two lnt genes 116 were identified in Streptomyces scabies. Lnt1 is the enzyme responsible for N-117 acylation of lipoproteins since lipoproteins are diacylated in lnt1 and lnt1lnt2 mutants. 118

Lnt2 is required for efficient fatty acid acylation of lipoproteins since in its absence 119 lipoproteins are both di-and triacylated [START_REF] Widdick | Dissecting the 734 complete lipoprotein biogenesis pathway in Streptomyces scabies[END_REF]. 120

Although the mechanism of apolipoprotein N-acyltransferase is likely to be conserved 121 among bacteria, differences in substrate specificity result in different types of 122 lipidation. This led us to ask the question of how Lnt recognizes and interacts with its 123 substrates, phospholipid and apolipoprotein, and what residues are involved in the two 124 steps of the reaction. Here we identified various essential residues in Lnt of E. coli 125 that are located on flexible loops and are predicted to be membrane-associated. Our 126 results suggest that amino acids located on the cytoplasmic-and on the periplasmic 127 side of the cytoplasmic membrane are involved in the transfer of the acyl group onto 128 the apolipoprotein substrate. Topology studies with Lnt from E. coli using reporter fusions with cytoplasmic β-137 galactosidase and periplasmic alkaline phosphatase showed that this enzyme spans the 138 cytoplasmic membrane via six transmembrane segments (TMS) with both its amino-139 terminus and carboxy-terminus facing the cytoplasm [START_REF] Robichon | Depletion of 695 apolipoprotein N--acyltransferase causes mislocalization of outer 696 membrane lipoproteins in Escherichia coli[END_REF]. Lnt 140 contains a large cytoplasmic loop (R 114 -R 193 ) (CL-2) between TMS-IV and TMS-V, 141 with two hydrophobic sequences (TMS-IVa and TMS-IVb) and a highly conserved 142 sequence (T 144 GFPWL 149 ) (Fig. 1). 143

In order to identify residues in Lnt involved in substrate recognition and/or binding 144 we performed random PCR mutagenesis on full-length lnt using a two-step PCR 145 protocol where in the first step long complementary oligos were synthesized using 146 error-prone DNA polymerase and in the second step the entire plasmid was 147 synthesized using the mutagenized oligos. The PCR conditions were chosen such that 148 on average one to three mutations would occur per kilobase (kb) of target DNA. The 149 lnt gene is 1.5 kb in length and between 1 and 5 mutations were expected. 150 Functionality of the mutated Lnt-s was addressed in a complementation assay using 151 the lnt depletion strain [START_REF] Robichon | Depletion of 695 apolipoprotein N--acyltransferase causes mislocalization of outer 696 membrane lipoproteins in Escherichia coli[END_REF]. In this strain endogenous lnt is under 152 control of an arabinose-inducible promoter. In the presence of L-arabinose lnt is 153 expressed, in the absence of L-arabinose lnt is not expressed and cells are depleted for 154

Lnt. The newly created plasmids were, either transformed directly into the lnt 155 depletion strain and selected for growth under permissive conditions (with L-156 arabinose), or lnt was first re-cloned into a new vector backbone and then transformed 157 into the lnt depletion strain. Gene expression was not induced by IPTG and 158 complementation was observed due to basal expression levels of lnt mutants. Colonies 159 that did not grow in the absence of L-arabinose, and thus express non-functional 160 variants of lnt, were analyzed further. We screened 450 colonies from two 161 independent rounds of mutagenesis and 34 of those did not complement the lnt 162 depletion strain (Table S1). The lnt gene from mutants obtained after direct screening 163 for non-complementation of the lnt depletion strain was also re-cloned into a new 164 vector backbone to exclude plasmid-linked mutations. Several mutants contained 165 substitutions on C387 of the Lnt active site (E267-K335-C387), and some had stop 166 codons. More than two substitutions were frequently observed and in several cases 167 multiple mutations resulted in non-functional variants (Table S1). Among those, 168 several mutants contained substitutions located in the first transmembrane segment of 169 Lnt (Fig. 1) [START_REF] Robichon | Depletion of 695 apolipoprotein N--acyltransferase causes mislocalization of outer 696 membrane lipoproteins in Escherichia coli[END_REF] and five mutations in NB24 map in TMS-VI. This 170 suggests that membrane insertion of Lnt was probably affected in these cases. Most 171 mutants possess substitutions of amino acids located in both CL-2 and the periplasmic 172 catalytic domain. We have shown that Lnt is a low abundant enzyme, about 100-200 173 molecules exist per cell [START_REF] Hillmann | Kinetics and phospholipid 634 specificity of apolipoprotein N--acyltransferase[END_REF]. Single mutations that only slightly 174 affect Lnt function may not be found because higher protein levels due to expression 175 from a high-copy plasmid may overcome a functional defect. This might explain why 176 several mutations are required to observe a strong phenotype in our screen. 177

Mutants that contained one or two substitutions and produced Lnt protein were 178 analyzed in more detail. Re-cloning of lnt from NB8 (L183R, T404S), NB10 (R123C, 179 I126N), NB14 (W192R, I211T) led to restoration of growth of the lnt depletion strain 180 in the absence of L-arabinose suggesting that additional mutations had occurred either 181 on the plasmid or on the chromosome. Reconstruction of Q155R from NB34 (Q155R, 10 T315N) was not successful, perhaps due to a dominant negative phenotype of this 183 mutation, but T315N alone did not affect Lnt function. 184

The substitutions in mutants NB12 (F358V, T481R), NB22 (N244I, Y406C) and 185 NB31 (P353S, L392H) were constructed individually by site-directed mutagenesis 186 and analyzed for functionality in the lnt depletion strain. A spot dilution assay was 187 used as a complementation assay that allowed comparison of the various mutants. A 188 single colony from a fresh plate containing L-arabinose was inoculated in liquid 189 medium without L-arabinose and cells were grown for two hours to deplete Lnt. Cells 190 were serial diluted and spotted on plates containing or not L-arabinose and/or IPTG. 191

The lnt depletion strain shows a slight growth defect on L-arabinose when a non-192 functional copy of Lnt is present (Fig. 2). Depletion of Lnt in these strains probably 193 resulted in loss of viability prior to plating. The results show that both F358V and 194 T481R result in non-functional Lnt. L392H is functional. When combining P353S and 195 L392H into a single protein, a non-complementing phenotype is again observed. 196

Complementation was also observed with G447S but the strain has a mucoid 197 morphology. Both N244I and Y406C (from NB22) resulted in functional enzyme 198 (data not shown). 199

Previous studies identified W237 and E343 as essential for Lnt function and were 200

shown to be located on flexible loops in the catalytic domain (Vidal-Ingigliardi et al., 201 2007). Two substitutions, P361A (NB30) and M362I (NB28), are found close to F358 202 and P353. Construction of M362I resulted in non-functional Lnt (Fig. 2). NB30 203 contains several substitutions including P147L that results in non-functional Lnt (see 204 below). We have previously shown that when highly conserved residues P340 or 205 P346, located closely to E343, resulted in functional Lnt (Vidal-Ingigliardi et al., 206 2007). P361A was therefore not analyzed separately. 207

Addition of IPTG resulted in restoration of growth in the absence of arabinose in non-208 functional Lnt variants T481R and P353S/L392H and to a lesser extend in F358V and 209 M362I, suggesting that the enzymes are less efficient and that increase in enzyme 210 concentration compensates for their reduced activity. All variants produced protein, 211 although less in the case of T481R, as judged by Western blotting (Fig. S1). 212

In conclusion, the essential residues identified here are located in the catalytic 213 Several mutants contained multiple substitutions as described above (Table S2). 234

Conserved residues E136 and R139 were replaced separately by alanine using site-235 directed mutagenesis. Lnt with R139A partially complements the lnt depletion 236 mutant, but Lnt containing E136A was functional (Fig. 2). We previously showed that 237

Lnt in which conserved residue P147 was substituted by alanine was still functional 238 [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. NB30 contained P147L among others substitutions 239 (Table S1) and was reconstructed and analyzed separately. Lnt with P147L was not 240 functional, but addition of IPTG restored growth in the absence of L-arabinose (Fig. 241 2). Both R139A and P147L result in a mixed-colony phenotype. Substitution of P147 242 by leucine increases the overall hydrophobicity of the region containing TMS-IVa and 243 T 144 GFPWL 149 and probably results in an orientation of CL-2 relative to the 244 membrane that leads to inactive Lnt. Thus, R139 is essential and P147 is important for 245 Lnt function. 246 247 TMS-IVa and TMS-IVb do not completely span the cytoplasmic membrane 248 249 CL-2, with 79 amino acids in length, is a relative long cytoplasmic loop for a bacterial 250 membrane protein. Furthermore, although not always predicted, the two hydrophobic 251 regions in CL-2 are putative transmembrane segments, where TMS-IVa is less 252 hydrophobic then TMS-IVb. We used the substituted cysteine accessibility method 253 (SCAM) to determine whether TMS-IVa and TMS-IVb are real transmembrane 254 segments such that CL-2 is exposed to the periplasm [START_REF] Bogdanov | Transmembrane protein 613 topology mapping by the substituted cysteine accessibility method 614 (SCAM): applications to lipid--specific membrane protein topogenesis. 615 Methods[END_REF], Pailler et 255 al., 2012). Single cysteine substitutions were constructed in previously identified 256 cytoplasmic and periplasmic loops and between the putative membrane-spanning 257 segments TMS-IVa and TMS-IVb (Fig. 1). The substitutions were introduced by site-258 directed PCR mutagenesis in lnt encoding both an active variant and an inactive 259 variant that has active site cysteine 387 replaced by serine (C387S). To facilitate 260 determination of membrane topology by SCAM, all constructs have cysteine 23 and 261 cysteine 62 replaced by alanine. These substitutions do not affect Lnt function 262 [START_REF] Buddelmeijer | The essential Escherichia coli 624 Apolipoprotein N--acyltransferase (Lnt) exists as an extracytoplasmic 625 thioester acyl--enzyme intermediate[END_REF]. The cysteine substitutions in active Lnt were used to 263 test the biological activity in a complementation assay with the lnt depletion mutant 264 [START_REF] Robichon | Depletion of 695 apolipoprotein N--acyltransferase causes mislocalization of outer 696 membrane lipoproteins in Escherichia coli[END_REF]. All variants restored growth of the lnt depletion mutant under 265 restrictive growth conditions, in the absence of L-arabinose, indicating that all Lnt 266 cysteine mutants are functional enzymes (data not shown). 267

The second series of cysteine substitutions in inactive Lnt was used to determine 268 membrane topology. Whole cells were first treated with EDTA to permeabilize the 269 outer membrane. Cells were then treated with or without membrane-impermeable 270 alkylating reagent MTSES and subsequently labeled with a second alkylating reagent 271 maleimide polyethylene glycol (malPEG). The PEG buffer contains urea, SDS and 272

EDTA that denatures all proteins and renders all unprotected cysteine residues 273 accessible to malPEG. When cysteine residues are accessible to MTSES, and thus 274 exposed to the periplasm, their free thiol groups covalently react with MTSES and as 275 a consequence are blocked for alkylation with malPEG. In the case of cytoplasmic or 276 membrane-embedded cysteine residues, MTSES does not react with thiol groups and 277 proteins are alkylated by malPEG resulting in an increase in molecular weight of 5 278 kDa. Active Lnt and inactive Lnt were not alkylated by malPEG independent of 279 treatment with MTSES since C387 is acylated in both proteins, as a thioester in Lnt 280 and as an oxygen-ester in Lnt C387S (Fig. 3). Substitutions Y31C, G87C and T221C 281 were protected by MTSES and not alkylated by malPEG. S5C, S56C, T120C, S154C, 282 N191C and S513C were not protected by MTSES and therefore alkylated with 283 malPEG (Fig. 3). Alkylation by malPEG of N191C and S513C was less efficient 284 compared to the other cysteines. These results suggest that residues Y31, G87 and 285 T221 are accessible to MTSES and are facing the periplasm and that S5, S56, T120, 286 S154, N191 and S513 are not accessible to MTSES and are located either in the 287 cytoplasm or embedded in the membrane. Similar results were obtained with an 288 inactive variant of Lnt in which C387 was replaced by alanine and thus unable to 289 form an acyl-enzyme intermediate (data not shown) [START_REF] Buddelmeijer | The essential Escherichia coli 624 Apolipoprotein N--acyltransferase (Lnt) exists as an extracytoplasmic 625 thioester acyl--enzyme intermediate[END_REF]. 290

This indicates that the overall membrane topology of Lnt does not change upon auto-291

acylation. 292

Our membrane topology analyses show that S154C is not accessible to MTSES in 293 whole cells and therefore not exposed to the periplasm. Thus the hydrophobic 294 segments TMS-IVa and TMS-IVb do not completely span the membrane (Fig. 1). 295

This indicates that the conserved sequence T 144 GFPWL 149 is located in the cytoplasm 296 and may be in close proximity to the membrane due to the hydrophobic character of 297 TMS-IVa and TMS-IVb. 298 299

Conservation of essential residues in Lnt of other bacterial species 300 301

The Lnt sequence of E. coli was used to retrieve all Lnt orthologous sequences from 302 over 2700 complete bacterial genomes. The workflow included comparison of the Lnt 303 E. coli sequence to itself using BLASTP to determine the maximal bit score then 304 matching the Lnt sequence against sequenced genomes using TBLASTN in a single 305 representative for each genus. Lnt orthologs with a score of 15% or higher were 306 analyzed further using Clustal Omega alignment and the conserved residues were 307 identified (Fig. S2). Known Lnt sequences from high GC gram-positive bacteria fell 308 below this cut-off and were analyzed separately (Fig. S3). 309

Residue G447 is found in Lnt of all bacterial species and P147 and T481 are 310 conserved in γ-proteobacteria (Fig. 4, Fig. S2). R139 is conserved in γ-proteobacteria 311 and is substituted by K in some species. One species (Tolumonas) has M at this 312 position. Position 136 in E. coli Lnt and the corresponding location in the orthologues 313 contains a conserved acidic residue, usually an E and less frequently a D. F358 and 314 M362 are less conserved but are nevertheless shown to be essential in Lnt of E. coli. 315 Interestingly, several Lnt sequences have F358 replaced by valine and M362 replaced 316 by isoleucine, substitutions that lead to inactivation of Lnt of E. coli. Other poorly 317 conserved residues are probably required to act together with F358 and M362 for Lnt 318 to function correctly. In the structural model the carboxyl group of L338 interacts 319 with M362 [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. Substitution of L338 by alanine did not 320 affect Lnt function, since the amino group of L338 does not play a role in the M362-321 L338 interaction [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. P353 is also poorly conserved and is 322 only essential in combination with an additional mutation (L392H). This supports the 323 idea that conformational changes take place in the catalytic domain that involves 324 movement of flexible loops to facilitate binding of substrate. 325 326

Essential residues are located on flexible loops in the catalytic periplasmic domain 327 328

We have previously reported a structural model for the catalytic periplasmic domain 329 of Lnt [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. The α-β-β-α fold is characteristic for members 330 of the nitrilase, or carbon-nitrogen hydrolase, family [START_REF] Pace | The nitrilase superfamily: classification, structure 686 and function[END_REF]. The 331 localization of the essential residues on a revised version of the structural model 332 obtained with PHYRE2 [START_REF] Kelley | Protein structure prediction on the Web: a 649 case study using the Phyre server[END_REF] is shown in Fig. 5A. The less 333 conserved essential residues are located on flexible loops. The structural modeling 334 program I-TASSER [START_REF] Zhang | I--TASSER server for protein 3D structure prediction[END_REF] did not lead to a more precise or different 335 secondary structure prediction than that obtained with PHYRE2 (data not shown). 336 Essential residue T481 is part of a α-helix on top of the α-β-β-α folded structure of 337

Lnt. Replacement of T481 by arginine probably results in a conformational change in 338 this α-helix affecting the overall structure of Lnt. Levels of mutant Lnt (T481R) 339 detected by immunoblotting are lower compared to wild type, suggesting that the 340 mutated protein is less stable (Fig. S1, Fig. 6). G447 and L392 are found close to the 341 active site triad. P353, F358 and M362 are located on a flexible loop β5/β6 (residues 342 N336-L382) facing away from the active site in the model. E343 was previously 343 identified as essential and required for the first step in the reaction. It is located on 344 loop β5/β6 in close proximity to P353, F358 and M362 (Fig. 5A). Essential residue 345 W237 is located on loop β1/α1 [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. Similar structural 346 models were predicted for the catalytic domain of Lnt from C. glutamicum 347 (NCgl_1424), M. smegmatis (MSMEG_3860), M. bovis (BCG_2070c), S. coelicolor 348 (SCO_1014) and S. scabies (SCAB_83111) (Fig. 5B). Whereas P340-E343 is highly 349 conserved, other essential residues located on this loop, including P353, F358 and 350 M362, are not. These residues probably have a role in correctly positioning the 351 conserved residues and/or substrate(s) to efficiently N-acylate lipoproteins. 352 353 Essential residues located on the cytoplasmic loop CL-2 and the β5/β6 periplasmic 354 loop in the catalytic domain are involved in the second step of the Lnt reaction 355 356 A stable thioester acyl-enzyme intermediate is formed as part of the two-step reaction 357 catalyzed by Lnt [START_REF] Buddelmeijer | The essential Escherichia coli 624 Apolipoprotein N--acyltransferase (Lnt) exists as an extracytoplasmic 625 thioester acyl--enzyme intermediate[END_REF]. The effect of the various amino acid 358 substitutions resulting in non-functional Lnt on the formation of the thioester acyl-359 enzyme intermediate was assessed by alkylation of C387 by malPEG. The acyl group 360 bound to C387 can be specifically cleaved by neutral hydroxylamine (HA), after 361 which the free thiol group is accessible for alkylation by malPEG. Whole cells from 362 strains expressing lnt variants from an arabinose-controlled promoter were treated 363 with or without hydroxylamine and after protein precipitation samples were treated 364 with malPEG. Wild type Lnt was alkylated by malPEG after HA treatment, 365 corresponding to the presence of a thioester acyl-enzyme intermediate. Lnt (T481R) 366 was alkylated both in the absence and presence of HA, suggesting that a thioester 367 acyl-enzyme intermediate was not formed (Fig. 6). The amount of Lnt protein in this 368 mutant is lower compared to Lnt. All other mutants tested were only alkylated in the 369 presence of HA and thus all Lnt variants form a stable thioester acyl-enzyme 370 intermediate (Fig. 6). This suggests that the essential residues identified in this study, 371 including those located in CL-2, do not affect the first step of the N-acyltransferase 372 reaction. We analyzed endogenous Lpp in the presence of non-functional Lnt variants 373 in the lnt depletion strain by Western blotting to confirm that accumulation of apo-374

Lpp occurred under restrictive growth conditions. Since basal level expression of lnt-375 myc 2 from a strong pTrc promoter was sufficient to observe complementation in the 376 case of wild type Lnt we did not add IPTG to avoid overexpression effects. The 377 results shown in Fig. 7 We identified essential residues and regions in Apolipoprotein N-acyltransferase (Lnt) 393 of E. coli using random and site-directed PCR mutagenesis. A loop (CL-2) located 394 between TMS-IV and TMS-V containing two hydrophobic segments and a conserved 395 region, is located in the cytoplasm. Secondary structure predictions of CL-2 of Lnt 396 demonstrated that the hydrophobic segments are α-helices with high hydrophobicity 397 and with a length of 18-20 amino acids that resemble transmembrane segments, 398 however, our results demonstrate that these segments do not completely span the 399 cytoplasmic membrane but may partially enter into the lipid bilayer. Reentrant loops 400 are structural motifs that go halfway through the membrane and then turn back to the 401 side of entry [START_REF] Yan | An analysis of reentrant loops[END_REF]. These loops are found in transporters such as ion-402 channels and undergo conformational changes following substrate binding 403 [START_REF] Grunewald | Cysteine--scanning mutagenesis 631 reveals a conformationally sensitive reentrant pore--loop in the glutamate 632 transporter GLT--1[END_REF][START_REF] Yagur--Kroll | Spatial arrangement of the 746 beta--glucoside transporter from Escherichia coli[END_REF]. In general, reentrant loops are 404 shorter and less hydrophobic than transmembrane segments, they have very low 405 hydrophobicity around the turning point and the two sides usually have different 406 secondary structure [START_REF] Yan | An analysis of reentrant loops[END_REF]. Since CL-2 does not have these 407 characteristics, we hypothesize that the α-helices form a tilted fold in the membrane 408 as described for intra-membrane proteases like GlpG in E. coli (Ben-Shem et al., 409 2007). 410

The first hydrophobic segment (TMS-IVa) has a pair of amino acids with opposite 411 charges (E136 and R139 in E. coli), an arrangement found in all Lnt enzymes. 412

Immediately downstream of this hydrophobic segment a conserved sequence 413 (T 144 GFPWL 149 ) was identified. In a previous study we have replaced several of these 414 conserved amino acids by alanine and found that all Lnt variants were functional 415 [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. Here we identified P147 as an important residue for 416

Lnt function since replacement by leucine resulted in an inactive variant. By 417 increasing the hydrophobicity of this region or by eliminating the proline-imposed 418 turn, it is likely that the orientation of CL-2 changed resulting in an inactive 419 conformation. Substitution of R139 by alanine also resulted in non-functional Lnt but 420 no effect was observed when E136 was replaced by alanine. This result was surprising 421 since E136 is as conserved as R139. Association of CL-2 with the membrane 422 positions residues R139 and P147 in close proximity to the lipid bilayer. 423

Other essential residues were located in the catalytic periplasmic domain of Lnt and 424 several on flexible loops facing away from the active site triad in the structural model 425 predicted using PHYRE2. The degree of amino acid conservation was high for G447 426 and T481 but low for P353, F358, M362 and L392 in sequences more than 15% 427 identical to Lnt from E. coli. Residues P353, F358 and M362 are located on the 428 flexible loop β5/β6 between N336 and L382. Two other highly conserved residues, 429 W237 and E343, were previously identified as being essential for Lnt activity. E343 is 430 also located on the β5/β6 loop and W237 is found on loop β1/α1 between G229 and 431 G240 [START_REF] Vidal--Ingigliardi | Identification of 730 essential residues in apolipoprotein N--acyltransferase, a member of the 731 CN hydrolase family[END_REF]. All residues, except E343 (Buddelmeijer & 432 Young, 2010), are involved in the second step of the reaction since the thioester acyl-433 enzyme intermediate was formed but apolipoprotein accumulated and mature 434 lipoprotein was not formed. The loops likely adopt a secondary structure upon 435 substrate binding that brings the α-amino group of S-diacylglyceryl-cysteine of the 436 substrate in close proximity to the active site cysteine. We hypothesize that the CL-2 437 region and the catalytic flexible loops are in close proximity and together contribute 438 to efficient transfer of fatty acids onto apolipoprotein. One likely possibility is that the 439 six transmembrane segments surround the partially membrane-embedded periplasmic 440 and cytoplasmic loops adopting a barrel shape where the active site cavity becomes 441 into close contact with the carbonyl group of PE. The bottom of this barrel shape is 442 closed by CL-2 that sticks into the membrane towards the active site. This model 443 suggests that access of the apolipoprotein substrate to the thioester-acyl group of Lnt 444 occurs via lateral opening of the barrel. 445

The CL-2 region was targeted separately in an error-prone mutagenesis approach but 446 essential residues were not identified. Lnt is a low abundant enzyme that we estimated 447 to exist in about 100-200 molecules per cell [START_REF] Hillmann | Kinetics and phospholipid 634 specificity of apolipoprotein N--acyltransferase[END_REF]. This might 448 explain why mutations resulting in slightly less efficient enzyme were not identified 449 and that only mutations leading to a severe phenotype were obtained in our screen. 450

The fact that an increase in protein level of non-functional Lnt enzymes restores 451 growth of the lnt depletion strain supports this hypothesis. 452

Together with the catalytic triad, residues E389 and E343 are conserved even in the 453 more distantly related actinobacterial Lnt-s [START_REF] Widdick | Dissecting the 734 complete lipoprotein biogenesis pathway in Streptomyces scabies[END_REF]. Lipoproteins from 454 C. glutamicum are modified with a N-acyl (C16:0) and S-diacylglyceryl (C16:0, 455 C18:1) moiety like in E. coli [START_REF] Mohiman | The ppm operon is essential for acylation and glycosylation 678 of lipoproteins in Corynebacterium glutamicum[END_REF], whereas lipoproteins in 456 Mycobacteria contain tuberculostearic acid (C19:0) as part of their S-diacylglyceryl 457 moiety and palmitic or tuberculostearic acid as N-acyl group (Brülle et al., 2010, 458 binding of substrate [START_REF] Suree | The structure of the Staphylococcus aureus sortase--713 substrate complex reveals how the universally conserved LPXTG sorting 714 signal is recognized[END_REF] and that the loops are involved in substrate 484 recognition [START_REF] Bentley | Engineering the 609 substrate specificity of Staphylococcus aureus Sortase A. The beta6/beta7 610 loop from SrtB confers NPQTN recognition to SrtA[END_REF]. We hypothesize that the β5/β6 flexible loop in Lnt 485 is involved in recognition of the S-diacylglyceryl-cysteine of apolipoprotein and that 486 binding of substrate leads to conformational changes and a substrate-bound closed 487 form of Lnt similar to sortases. 488

Our data suggest that cytoplasmic and periplasmic membrane-associated loops are 489 required for N-acylation of lipoproteins and that specific amino acids in these loops 490 may be involved in substrate recognition and/or binding. Ongoing three-dimensional 491 structural analyses of full-length Lnt enzymes are expected to highlight differences 492 between various species and to establish how the enzyme interacts with its substrates. S3. Cells were grown in LB medium 499 supplemented with ampicillin (100 µg/ml) when required. Induction of gene 500 expression from a pBAD promoter was obtained by addition of L-arabinose (0.2%) 501 and from pTrc promoter with IPTG (1 mM). 502 503 Standard DNA manipulation 504 505 Silent sites were introduced in lnt flanking the cytoplasmic loop 2 (CL-2) coding 506 sequence using the QuickChange II site-directed mutagenesis protocol (Stratagene). 507

The procedure included a two-step PCR reaction where large oligomers were 508 synthesized in the first PCR reaction that contained only one of the two mutant 509 primers and synthesis of the entire mutated plasmid in the second reaction that 510 contained the large oligomers and DNA template. A PmlI site was introduced at 511 codon 120 (T120) with primers T120-PmlI_for and T120-PmlI_rev, an NheI site at 512 L185 with primers L185-NheI_for and L185-NheI_rev, and a StuI site at A186 with 513 primers Del_StuI-5' and Del_StuI-3' (primers are listed in Table S3). The PmlI and 514 NheI sites were combined in pCHAP9610 and the CL-2 segment was removed by 515 deleting the PmlI-StuI fragment, resulting in pCHAP9609. 516

The gene encoding lnt was amplified by PCR using primers 5'-cutE and lntXbaIrev 517 and was inserted between the EcoRI and XbaI sites of pUC18, the 3' end of lnt is in 518 frame with a double c-myc tag, resulting in pCHAP7547. Site-directed mutagenesis 519 The presence of Lnt orthologs was investigated in all bacteria and separately in the γ-583 proteobacteria taxonomic class using E. coli Lnt (NP_415190) as bait as follows. For 584 each genus, a single representative and sequenced genome originating from the NCBI 585 repository (ftp://ftp.ncbi.nih.gov/genomes/Bacteria/) was selected alphabetically and 586 submitted to TBLASTN analysis with Lnt using an in-house C# script. Taxonomic 587 relationships between individual species were determined with the SyntTax web 588 service [START_REF] Oberto | SyntTax: a web server linking synteny to prokaryotic 682 taxonomy[END_REF]. Normalized genomic BLAST scores were used to measure the 589 degree of orthology as described [START_REF] Lerat | From gene trees to organismal 670 phylogeny in prokaryotes: the case of the gamma--Proteobacteria[END_REF]. The threshold was set 590 empirically at the value of 15% in agreement with the annotations of the selected 591 genomes. Lnt orthologs with a score equal or greater than 15% were collected and 592 submitted to multiple protein sequence alignment using the Clustal Omega web 593 service (https://www.ebi.ac.uk/Tools/msa/clustalo/).

  periplasmic domain of Lnt. 214 215 Conserved residues R139 and P147 in cytoplasmic loop 2 are required for Lnt 216 function 217 218 In the screen for essential residues using full-length lnt described above, we did not 219 identify amino acids located in the cytoplasmic loop 2 (CL-2) region of Lnt. Due to 220 their hydrophobic character, TMS-IVa and TMS-IVb might position the CL-2 with 221 the conserved T 144 GFPWL 149 sequence in close proximity to or associated with the 222 membrane (Fig. 1). Upstream of this sequence a charge distribution is conserved in 223 TMS-IVa (E136 and R139 in Lnt of E. coli) (Fig. 1). To gain additional insights into 224 the role of this loop in Lnt function we performed random PCR mutagenesis targeting 225 the part of lnt encoding CL-2. Restriction sites not affecting the amino acids were 226 created in codons that allowed for exchange of CL-2 encoding fragments between 227 wild type lnt and mutated fragments. Induction of the plasmids was not required to 228 observe full complementation with plasmids expressing wild type Lnt. Deletion of 229 CL-2 resulted in non-functional Lnt, demonstrating that this region is required for Lnt 230 function (data not shown). A total of 200 mutated clones were screened for loss of Lnt 231 activity. All clones restored growth of the lnt depletion strain under restrictive 232 conditions. Efficient mutagenesis was confirmed by sequencing of several clones. 233

  demonstrate that apo-Lpp accumulates in strains where Lnt 378 with R139A, P147L, F358V, M362I, T481R or P353S/L392H substitutions is the 379 only form of enzyme present. Mature Lpp was detected in the presence of Lnt with 380 G447S substitution. This residue probably plays a role in the efficiency of the 381 reaction. This demonstrates that the non-functional variants are affected in the second 382 step of the apolipoprotein N-acyltransferase reaction. one signal peptidase are involved in the post-translational 387 modification of lipoproteins but little is known about the molecular mechanism of the 388 catalytic reactions. In this study we searched for essential residues that are either 389 involved in the first step (auto-acylation of Lnt) or in the second step (N-acylation of 390 apolipoprotein) of the N-acyltransferase reaction with the hope to identify residues 391 involved in recognition or binding of substrate. 392

  are listed in Table

  samples and incubated for 60 minutes at room temperature. Proteins were precipitated 568 with TCA or MeOH/CHCl 3 and analyzed by SDS-PAGE and Western blotting. 569 570Gel electrophoresis and Western blotting 571 572Protein samples were solubilized in SDS sample buffer containing 4 mM DTT or 5% 573 β-mercaptoethanol (β-ME) and were heated at 100°C for 5 minutes. Samples were 574 separated on polyacrylamide gels (Biorad) and transferred onto nitrocellulose 575 membranes. Lnt was detected by chemiluminescence (Pierce) using anti-c-myc 576 antibodies (Sigma) and secondary anti-rabbit antibodies conjugated with horseradish 577 peroxidase (HRP). Lpp was detected with antibodies against Lpp (a gift from H

Fig. 1 .Fig. 2 .Fig. 5 .Fig. 6 .

 1256 Figure legends 757

Acknowledgements 596 597

We thank all members of the Molecular Genetics Unit and Biology and Genetics of 598 the Cell Wall Unit of the Institut Pasteur for their support. We thank Nicolas Bayan 599 and colleagues for helpful discussions and constructive comments on the work. 600