Richard Pasquetti
email: richard.pasquetti@unice.fr

Francesca Rapetti

Cubature points based triangular spectral elements: An accuracy study

Keywords: Spectral element method, simplicial meshes, cubature points, Fekete points, isoparametric mappings AMS Subject Classifications: 65 Chinese Library Classifications: O175.27

We investigate the cubature points based triangular spectral element method and provide accuracy results for elliptic problems in non polygonal domains using various isoparametric mappings. The capabilities of the method are here again clearly confirmed.

Introduction

Extending the capabilities of the quadrangle based spectral element method to the triangle based one, say from the QSEM to the TSEM, has received a considerable attention in the last twenty years. The relevant choice of interpolation points for the triangle has thus motivated a lot of works, see e.g. the Review paper [START_REF] Pasquetti | Spectral element methods on simplicial meshes[END_REF] and references herein. Several sets of points have indeed been proposed, some of them showing the advantage of simplicity in their generation, thus allowing an easy extension to the tetrahedron, e.g.the so-called warp & blend points [START_REF] Warburton | An explicit construction for interpolation nodes on the simplex[END_REF], whereas some other ones are more satisfactory from the theoretical point of view, e.g.the celebrated Fekete points of the triangle, but much more difficult to compute [START_REF] Taylor | An algorithm for computing Fekete points in the triangle[END_REF].

With respect to the QSEM, based on the use of the tensorial product of Gauss-Lobatto-Legendre (GLL) nodes, such interpolation points are however not quadrature points, so that the so called spectral accuracy gets lost if not using for the quadratures a separate set of points, as e.g.done for the Fekete-Gauss approach [START_REF] Pasquetti | Spectral element methods on unstructured meshes: comparisons and recent advances[END_REF]. Using two separate sets of points shows however some drawbacks, because the mass matrix is then no longer diagonal. Thus, when solving an evolution problem with an explicit time scheme, one has at each time step to solve a mass matrix algebraic system. Also, a diagonal mass matrix can be useful to set up high order differentiation operators [START_REF] Minjeaud | High order C 0 -continuous Galerkin schemes for high order PDEs, conservation of quadratic invariants and application to the Korteweg-De Vries model[END_REF]. This is why it is of interest to design a TSEM that makes use of a single set of points showing both nice quadrature and interpolation properties. This was the goal of the cubature points based TSEM, as developed in the last few years [START_REF] Cohen | Higher order triangular finite elements with mass lumping for the wave equation[END_REF][START_REF] Giraldo | A diagonal mass matrix triangular spectral element method based on cubature points[END_REF][START_REF] Liu | Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling[END_REF][START_REF] Mulder | New triangular mass-lumped finite elements of degree six for wave propagation[END_REF].

Another difficulty with SEMs, and more generally with high order FEMs, is to maintain the accuracy when the computational domain is no longer polygonal. Several strategies have been proposed to handle curved elements, from transfinite mappings [START_REF] Gordon | Construction of curvilinear co-ordinate systems and applications to mesh generation[END_REF] to PDEs based transformations, e.g.the harmonic extension.

The present work follows two anterior studies:

• In [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF], using the Fekete-Gauss TSEM we compared different strategies for curved triangular spectral elements, i.e. when isoparametric mappings are required to correctly approximate with curved spectral elements the presence of a curved boundary.

• In [START_REF] Pasquetti | Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes[END_REF], for computational domains of polygonal shape we compared the cubature TSEM, as proposed in [START_REF] Liu | Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling[END_REF], and the Fekete-Gauss one. In terms of accuracy for elliptic problems, it turned out that these two TSEMs compare well. With non Dirichlet or non homogeneous Neumann conditions, i.e. as soon as boundary integrals are involved, some care is however needed if using the cubature TSEM.

Here the goal is to extend the results obtained in [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF] to the case where the cubature TSEM is used. As in [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF][START_REF] Pasquetti | Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes[END_REF] we only focus on elliptic problems, but keep in mind for future works the inherent difficulties associated to constrained operators, see e.g. [START_REF] Ahusborde | Physics-conforming constraintsoriented numerical method[END_REF].

Cubature points based TSEM

For the sake of completeness, let us recall that [START_REF] Pasquetti | Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes[END_REF]:

• If two different sets of points are used for interpolation and quadrature, then the space P N ( T) of polynomials of maximal (total) degree N, defined on the reference triangle T = {(r,s) : r ∈ (-1,1),s ∈ (-1,-r)}, is usually used as approximation space. The cardinality of this space equals n=(N+1)(N+2)/2, that can be associated to n interpolation points if using Lagrange polynomials as basis functions. If 3 of these nodes coincide with the vertices of the element, then 3N of these n points should belong to the edges of T and the remaining (N -1)(N -2)/2 are the inner nodes. Usually, the edge nodes proposed in the literature coincide with the GLL points. Since one does not know an explicit formulation of the Lagrange basis functions, say ϕ i (r,s), 1 ≤ i ≤ n, to compute their values or those of their derivatives at given point one generally makes use the orthogonal Kornwinder-Dubiner (KD) basis [START_REF] Dubiner | Spectral methods on triangles and other domains[END_REF], for which explicit formula exist. Gauss points for the triangle and the corresponding quadrature formula may be found in the literature, up to degree M ≈ 20 if a symmetric distribution of the points is desired. In practice, one may choose M=2N, so that both the stiffness and mass matrix are exactly computed, since their entries are polynomials of degree 2N and 2N -2, respectively. For details on the implementation of the Fekete-Gauss approach, see e.g. [START_REF] Pasquetti | Spectral element methods on unstructured meshes: comparisons and recent advances[END_REF].

• If using a single set of points, as before 3N of the interpolations points must belong to the triangle boundary with 3 of them at the vertices. As demonstrated in [START_REF] Helenbrook | On the existence of explicit hp-finite element methods using Gauss-Lobatto integration on the triangle[END_REF][START_REF] Xu | On Gauss-Lobatto integration on the triangle[END_REF], such a strong constraint forbids the possibility of finding a set of cubature points providing a sufficiently accurate cubature formula, if looking for basis functions that span the space P N . To overcome this difficulty, as first developed in [START_REF] Cohen | Higher order triangular finite elements with mass lumping for the wave equation[END_REF], the idea is then to enrich the space P N by polynomial bubble functions of degree N ′ >N. This indeed allows to include new cubature points inside the triangle while keeping the element boundary nodes number equal to 3N. In the reference triangle T, this may be achieved by introducing the polynomial space P N ∪b×P N ′ -3 , where b is the (unique) bubble function of P 3 ( T), namely b(r,s) = (r+1)(s+1)(r+s). The cardinality of this space then equals n ′ = 3N +(N ′ -1)(N ′ -2)/2. Now, to compute the Lagrange polynomials at a given points one should use an extended KD basis, composed of the usual KD basis of P N completed by those KD polynomials of P N ′ -3 which once multiplied by the bubble function b are of degree strictly greater than N. Of course, N ′ should be chosen as small as possible to avoid a useless increase of the inner nodes number: In [START_REF] Cohen | Higher order triangular finite elements with mass lumping for the wave equation[END_REF] and posterior works, N ′ is chosen such that it exists a cubature rule exact for polynomials of degree N + N ′ -2. The determination of N ′ , together with the cubature points and weights gives rise to a difficult optimization problem, see [START_REF] Liu | Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling[END_REF] for details. It turns out that N ′ -N increases monotonically with N:

N ′ = N +1, for 1 < N < 5, N ′ = N +2 for N = 5 and N ′ = N +3 for 5 < N < 10.
It should be noticed that with the cubature TSEM, neither the mass matrix nor the stiffness matrix are exactly computed, since their entries are of degree 2N ′ and 2N ′ -2, respectively.

Our in house Fekete-Gauss and cubature codes make use of the condensation technique, i.e. one first computes the unknowns associated to the edges of the elements and then reconstructs the numerical solution inside locally. Thus, the algebraic systems that result from the two TSEM approximations are exactly of same size, and so the computational times compare well. They are simply solved by using a standard conjugate gradient method, with Jacobi preconditioner in a matrix free implementation [START_REF] Lazar | Fekete-Gauss spectral elements for incompressible Navier-Stokes flows: The two-dimensional case[END_REF].

A difficulty however arises when the boundary conditions are not of Dirichlet or homogeneous Neumann type, i.e. when the weak formulation involves boundary integrals. In case of the Fekete-Gauss TSEM, such boundary integrals can be easily computed since the edge Fekete nodes coincide with the GLL points. On the contrary, the edge cubature points are not of Gauss type. In [START_REF] Pasquetti | Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes[END_REF],

• it is pointed out that for the Robin condition ∂ n u+αu = g, g being a given function and α a coefficient possibly zero, using a quadrature rule based on the boundary cubature points is not satisfactory,

• it is suggested to approximate these integrals by using on each element edge of the boundary a Gauss quadrature rule, e.g.the one based on the GLL points.

Since the restrictions of the Lagrange polynomials ϕ i at the element edges of the boundary are polynomials of degree N, one can span this polynomial space with the Legendre polynomials, say L i (r) with r ∈ [-1,1], for the reference edge, and 0 ≤ i ≤ N. Then, one can set up the Vandermonde matrices of size (N+1)×(N+1) based on the cubature and GLL points, say V Cub and V GLL . One has e.g.(V Cub ) ij = L j (r i ), with r i ∈ [-1,1] for the edge cubature points. Then, the matrix V GLL V -1 Cub allows to compute at the GLL points quantities known at the cubature points. Especially, each column of this matrix provides the values of the edge Lagrange polynomials at the GLL points.

Another difficulty arises with curved spectral elements. Indeed, for straight triangular elements, the edge Jacobian determinant is constant on each edge and proportional to its length. On the contrary, when considering curved triangular elements, some care is needed for a relevant computation of the edge Jacobian determinants at the GLL points from those at the cubature points. Thus, once the entries of the Jacobian matrix have been computed at the edge cubature points, one can

• compute the edge Jacobian determinant and then use the polynomial interpolation to get the Jacobian at the GLL points,

• use the polynomial interpolation to get the Jacobian matrix entries at the GLL points and then compute the Jacobian determinant.

Because the edge Jacobian determinant is generally a polynomial of degree greater than N, the results of these two approaches slightly differ. There is indeed no interpolation error for the Jacobian matrix entries but there is such an error for the Jacobian matrix determinant. This is why in our cubature points based solver, it is the second approach which is implemented, even if a little more expensive than the first one.

Isoparametric mappings

For the cubature TSEM, hereafter we make use of the isoparametric mappings that we discussed in [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF]:

• The bending procedure that we introduced in [8];

• The transfinite interpolation discussed for the triangles in [START_REF] Perronnet | Triangle, tetrahedron, pentahedron transfinite interpolations. Application to the generation of C 0 or G 1 -continuous algebraic meshes[END_REF];

• The harmonic extension;

• The linear elasticity approach, see e.g. [START_REF] Persson | Curved Mesh Generation and Mesh Refinement using Lagrangian Solid Mechanics[END_REF].

Moreover, local mappings are used, i.e. we simply distort the elements at the boundary.

As in [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF], we assume to have at hand a parametric description of the boundary of Ω, i.e. , Γ is defined by a vector function, say x Γ (t) = (x Γ (t),y Γ (t)), where t ∈ [t min ,t max ]. Let A 1 A 2 A 3 be a triangular element at the boundary, with A 1 the inner node and A 2 and A 3 on the boundary. Then, for all the four approaches it is assumed that the boundary nodes, i.e. the interpolation points of Γ, are at the intersection of the lines joining the inner vertex A 1 and the interpolation points of the straight line A 2 A 3 , i.e. the edge of the element, say T, provided by the piecewise linear P 1 mapping. This requires one to solve, in general using a simple numerical procedure, N -1 (number of nodes of an edge without the end points) generally non-linear equations. Then, it remains to define n ′ p inner interpolation points, with n ′ p = n ′ -3N = (N ′ -1)(N ′ -2)/2, for the cubature TSEM. For the paper to be self contained, let us briefly describe the previously mentioned isoparametric mappings [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF]:

• The bending procedure: Assume that F is the interpolation point obtained with the affine P 1 mapping. Let G and G be the points at the intersections of A 1 F with the line A 2 A 3 and the boundary Γ, respectively. Then, the bending procedure [START_REF] Lazar | Fekete-Gauss spectral elements for incompressible Navier-Stokes flows: The two-dimensional case[END_REF] consists of stating that F is homothetic to F by the homothety of center A 1 and of ratio A 1 G/A 1 G, so that:

A 1 F = A 1 G A 1 G A 1 F and d ≡ FF = ( A 1 G A 1 G -1)A 1 F
where d stands for displacement. One notices that for this bending procedure, only the point G of Γ influences the location of the interpolation point F. In order to define the inner interpolation points, one has numerically to solve n ′ p equations.

• The transfinite interpolation: For the triangle, the method makes use of the barycentric coordinates, say (λ 1 ,λ 2 ,λ 3 ). Recall that λ i =0 stands for the edge opposite to the vertex i, λ i =Constant to a line parallel to this edge and that vertex i belongs to λ i =1.

General transfinite interpolation formula are given in [START_REF] Perronnet | Triangle, tetrahedron, pentahedron transfinite interpolations. Application to the generation of C 0 or G 1 -continuous algebraic meshes[END_REF] (different approaches are however possible, see e.g. [START_REF] Demkowicz | Computing with hp-adaptative finite elements[END_REF]). For the triangle, if the displacement d vanishes at the two edges A 1 A 2 and A 1 A 3 , again assuming that ⌢ A 2 A 3 is the curved edge, one has:

d(λ 1 ,λ 2 ,λ 3 ) = λ 2 d(0,1-λ 3 ,λ 3 )+λ 3 d(0,λ 2 ,1-λ 2 ).
This means that two points of the boundary Γ influence the location of an inner interpolation point F. They are those at the intersections of Γ with the lines parallel to A 1 A 2 and A 1 A 3 and passing by the point F. One notices that the method requires solving 2n ′ p equations.

• Harmonic extension: The goal is here to define the inner interpolation points by solving, for each curved element T, the weak form of the Laplace Dirichlet problem:

∆d = 0 in T, d| ∂ T = g
with g given on A 2 A 3 and g=0 on the two other sides. To resolve this vector Laplace problem, that in fact yields two uncoupled scalar problems, one has to set up the differentiation matrices, say D x and D ỹ that allows one to compute derivatives in T. To this end, one makes use of the differentiation matrices D r and D s and applies the chain rule. Since the mapping from T to T is affine, the Jacobian matrix and Jacobian determinant are constant. For the same reason, one may solve directly for the interpolation point coordinates. Finally, one should invert a matrix of size n ′ p ×n ′ p , in order to compute the coordinates of the inner interpolation points. The approach is thus rather simple and in practice not costly. In where global mappings are considered, it is however outlined that the harmonic extension may fail to define a mapping.

• Linear elasticity: Here the curved domain is viewed as the deformation of triangles, that is governed by the equation of linear elasticity. Introducing the Lame coefficients λ and µ, the displacement field is governed by the Navier-Cauchy equation:

µ∆d+(λ+µ)∇(∇•d) = 0 in T, d| ∂ T = g.
There is now a coupling between the components of the displacement field. Using the ingredients previously described for the harmonic extension, the weak form of this elasticity problem yields a matrix system of size 2n ′ p . The solution of this system provides the displacements of the inner interpolation points. Again, one can also compute directly their coordinates. Because the forcing term is zero, the mapping is here parametrized by the ratio µ/(λ+µ) = 1-2η, where η ∈ (-1,0.5) is the so called Poisson ratio.

Accuracy study

First, one of the test-cases introduced in [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF] has been revisited. Using the cubature TSEM we solve the Poisson equation, -∆u = f , with exact solution u ex = cos(10x)cos(10y), so that f = 200u ex , and Dirichlet boundary conditions, in the computational domain and mesh (the so-called medium mesh of [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF]) presented in Fig. 1 (left). For the elasticity isoparametric mapping, the Poisson ratio is taken equal to 0.2.

For the different isoparametric mappings, the max norm of the error, obtained from the errors at the cubature points, is shown in Fig. 2 (left). The curve labeled "polygon" is the one obtained for the domain defined by the P 1 mesh, i.e. no isoparametric mapping is involved in this case. Such results compare well with those obtained with the Fekete-Gauss TSEM, recalled in Fig. 2 (right). Again, one observes that the best results are obtained with the harmonic extension or with the linear elasticity approach, i.e. with the isoparametric mappings based on PDEs rather than transfinite interpolations. As in [START_REF] Pasquetti | Cubature versus Fekete-Gauss nodes for spectral element methods on simplicial meshes[END_REF], one observes that a loss of accuracy occurs for N = 9. It is due to a slight lack of accuracy of the cubature rule [10]. Rather than the Dirichlet condition, we now use the Robin condition ∂ n u+u=g, with g derived from the exact solution u ex =cos(10x)cos(10y). Results obtained with the Fekete-Gauss solver and with cubature points based solver are compared in Fig. 3, using the PDEs based isoparametric mappings (harmonic extension and linear elasticity). Clearly, the results obtained with the Fekete-Gauss and the cubature TSEM compare well. Thus, even if curved elements are involved, if the boundary data are correctly handled [START_REF] Pasquetti | Comparison of some isoparametric mappings for curved triangular spectral elements[END_REF] then the cubature approach proposed in [START_REF] Liu | Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling[END_REF] is quite satisfactory (at least for N ≤ 8).

To extend the present study we consider the computational domain and P 1 -mesh shown in Fig. 1 angle θ:

x = cosθ (1+0.3 cos(7θ)) y = sinθ (1+0.2 cos(7θ)).

The P 1 -mesh is generated from 50 boundary nodes, defined by θ∝2π/50, and the number of elements equals 174. Isoparametric mappings based on the harmonic extension and linear elasticity approaches are used. Till now, the linear elasticity isoparametric mapping was characterized by a Poisson ratio η = 0.2. Then, it is of interest to carry out a sensitivity study to this parameter. For isotropic materials one has η ∈ (-1,0.5), most materials are such that η ∈ (0,0.5), and for typical engineering materials η ∈ (0.2,0.5). Hereafter we make computations with the following Poisson ratio η = {0.1,0.2,0.4}.

For one particular element of the mesh and a polynomial approximation degree N=6, Fig. 4 shows the distribution of the cubature nodes obtained from the P 1 -mapping and from the isoparametric P 6 -mapping, when using the harmonic extension or the linear elasticity mappings associated to the different Poisson ratio.

We make use of the cubature TSEM and the exact solution u ex = cos(10x)cos(10y) to set up the source and boundary terms, f and g, of the following elliptic PDE -∆u+u= f . Accuracy tests are made using Dirichlet conditions, i.e. u = g at the boundary nodes, and also the Robin condition ∂ n u+u = g. The results obtained for these Dirichlet and Robin problems are shown in Fig. 5, at left and at right, respectively.

One observes that: curve being then the closest to the harmonic extension one. Note that this is surprising, since if η → 0.5 then µ → 0.

• The decrease of the error for the Robin problem is exponential, whereas this is less obvious in the Dirichlet case. In fact, the convergence curves show two parts, below and beyond a critical value of the polynomial degree. Roughly speaking, for the smallest values of N the convergence rate is governed by the approximation of the solution in the bulk of the domain, whereas for the largest ones it is enforced by its approximation at the boundary. This is why, see Fig. 5, for small N the convergence curves coincide with those obtained when using as computational domain the polygon obtained from the 50 boundary nodes, but differ for N larger than threshold values, say, for the present P 1 of the star-shaped domain,

Figure 1 :Figure 2 :

 12 Figure 1: Computational domains and corresponding P 1 meshes.

Figure 3 :

 3 Figure 3: Max norm of the error vs the polynomial degree N for the Poisson-Robin problem using the cubature TSEM and the Fekete-Gauss TSEM.

Figure 4 :

 4 Figure 4: Distribution of the cubature nodes before and after the isoparametric mapping: Harmonic extension (top left), elasticity with η = 0.1 (top right), η = 0.2 (bottom left) and η = 0.4 (bottom right)

Figure 5 :

 5 Figure 5: Max norm of the error vs the polynomial degree N, using the cubature TSEM for an elliptic problem in the star domain, with Dirichlet (at left) and Robin (at right) conditions.

•

  For the linear elasticity isoparametric mapping, the sensitivity to the Poisson ratio η is low. With the Robin condition, all curves coincide. With the Dirichlet condition, one can discern a slight improvement for the largest value η = 0.4, the convergence

	-0.45		-0.45
		Before		Before
	-0.46	After	-0.46	After
	-0.47		-0.47
	-0.48		-0.48
	-0.49		-0.49
	-0.5		-0.5
	-0.51		-0.51
	-0.52		-0.52
	-0.53		-0.53
	0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89	0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89
		Harmonic Extension		Elasticity eta=0.1
	-0.45		-0.45
		Before		Before
	-0.46	After	-0.46	After
	-0.47		-0.47
	-0.48		-0.48
	-0.49		-0.49
	-0.5		-0.5
	-0.51		-0.51
	-0.52		-0.52
	-0.53		-0.53
	0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89	0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89
		Elasticity eta=0.2		Elasticity eta=0.4

Acknowledgments

The P 1 FEM meshes have been generated with the free software "Triangle". We are grateful to Dr Youshan Liu, Chinese Academy of Sciences, Beijing, for transmitting us the cubature points and weights used in [9].


Lionel Tarrago
email: lioneltarrago@msn.com

Sandrine Grosse

Marina I Siponen

David Lemaire

Béatrice Alonso

Guylaine Miotello

Jean Armengaud

Pascal Arnoux

David Pignol

Monique Sabaty
email: monique.sabaty@cea.fr

Rhodobacter sphaeroides methionine sulfoxide reductase P reduces R-and S-diastereomers of methionine sulfoxide from a broad-spectrum of protein substrates

Keywords: Enzyme kinetics, methionine sulfoxide reductase, microbiology, molybdoenzyme, oxidative stress, periplasm, protein oxidation, proteomics BV, benzyl viologen, DMSO, dimethylsulfoxide, DTT, dithiothreitol, ESI-MS, Electrospray Ionization-Mass spectrometry, H2O2, hydrogen peroxide, HEPES4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid, MES, 2-

Methionine (Met) is prone to oxidation and can be converted to Met sulfoxide (MetO), which exists as R-and S-diastereomers. MetO can be reduced back to Met by the ubiquitous methionine sulfoxide reductase (Msr) enzymes. Canonical MsrA and MsrB were shown to be absolutely stereospecific for the reduction of S-and R-diastereomer, respectively. Recently, a new enzymatic system, MsrQ/MsrP which is conserved in all gram-negative bacteria, was identified as a key actor in the reduction of oxidized periplasmic proteins.

The haem-binding membrane protein MsrQ transmits reducing power from the electron transport chains to the molybdoenzyme MsrP, which acts as a protein-MetO reductase. The MsrQ/MsrP function was well established genetically, but the identity and biochemical properties of MsrP substrates remain unknown. In this work, using the purified MsrP enzyme from the photosynthetic bacteria Rhodobacter sphaeroides as a model, we show that it can reduce a broad spectrum of protein substrates. The most efficiently reduced MetO are found in clusters of amino acid sequences devoid of threonine and proline on the C-terminal side. Moreover, R. sphaeroides MsrP lacks stereospecificity as it can reduce both R-and S-diastereomers of MetO, similarly to its Escherichia coli homolog, and preferentially acts on unfolded oxidized proteins.

Overall, these results provide important insights into the function of a bacterial envelop protecting system, which should help understand how bacteria cope in harmful environments.

Introduction

Aerobic life exposes organisms to reactive oxygen species (ROS) derived from molecular oxygen, such as hydrogen peroxide (H2O2) or singlet oxygen ( 1 O2). Bioenergetic chains are important sources of these intracellular ROS. H2O2, is principally produced during respiration [START_REF] Messner | The identification of primary sites of superoxide and hydrogen peroxide formation in the aerobic respiratory chain and sulfite reductase complex of Escherichia coli[END_REF] and 1 O2 arises from photosynthesis [START_REF] Glaeser | Singlet oxygen stress in microorganisms[END_REF]. In most organisms, these oxidative molecules act as signaling messengers playing major roles in numerous physiological and pathological states. Furthermore, their production and elimination are tightly regulated [START_REF] Ezraty | Oxidative stress, protein damage and repair in bacteria[END_REF]. However, numerous stresses can affect ROS homeostasis and increase their intracellular concentration to excessive values leading to uncontrolled reactions with sensitive macromolecules [START_REF] Imlay | The molecular mechanisms and physiological consequences of oxidative stress: lessons from a model bacterium[END_REF]. For instance, photosynthetic organisms, such as plants or the purple bacteria Rhodobacter sphaeroides can experience photo-oxidative stress in which unbalance between incident photons and photosynthetic electron transfer generate detrimental accumulation of 1 O2 [START_REF] Ziegelhoffer | Bacterial responses to photo-oxidative stress[END_REF]. Moreover, production of ROS could be used advantageously in a defensive strategy against potential pathogenic invaders. For instance, neutrophils produce the strong oxidant hypochlorite (ClO -) from H2O2 and chlorine ions to eliminate bacteria and fungi [START_REF] Ezraty | Oxidative stress, protein damage and repair in bacteria[END_REF]. Because of their abundance in cells, proteins are the main targets of oxidation [START_REF] Davies | The oxidative environment and protein damage[END_REF]. Methionine (Met) is particularly prone to oxidation and the reaction of Met with an oxidant leads to the formation of Met sulfoxide (MetO), which exists as two diastereomers R (Met-R-O) and S (Met-S-O). Further oxidation can then lead to the formation of Met sulfone (MetO2) [START_REF] Sharov | Diastereoselective reduction of protein-bound methionine sulfoxide by methionine sulfoxide reductase[END_REF][START_REF] Vogt | Oxidation of methionyl residues in proteins: tools, targets, and reversal[END_REF]. As opposed to most oxidative modifications on amino acids, the formation of MetO is reversible, and oxidized proteins can be repaired thanks to methionine sulfoxide reductases (Msr) enzymes that principally exist in two types, MsrA and MsrB. These enzymes, present in almost all organisms, did not evolve from a common ancestral gene and possess an absolute stereospecificity towards their substrates. Indeed, MsrA can reduce only Met-S-O [START_REF] Sharov | Diastereoselective reduction of protein-bound methionine sulfoxide by methionine sulfoxide reductase[END_REF][START_REF] Ejiri | Reduction of methionine sulfoxide to methionine by Escherichia coli[END_REF][START_REF] Lowther | The mirrored methionine sulfoxide reductases of Neisseria gonorrhoeae pilB[END_REF][START_REF] Moskovitz | Purification and characterization of methionine sulfoxide reductases from mouse and Staphylococcus aureus and their substrate stereospecificity[END_REF][START_REF] Vieira Dos Santos | The Arabidopsis plastidic methionine sulfoxide reductase B proteins. Sequence and activity characteristics, comparison of the expression with plastidic methionine sulfoxide reductase A, and induction by photooxidative stress[END_REF] whereas MsrB acts only on Met-R-O [START_REF] Lowther | The mirrored methionine sulfoxide reductases of Neisseria gonorrhoeae pilB[END_REF][START_REF] Moskovitz | Purification and characterization of methionine sulfoxide reductases from mouse and Staphylococcus aureus and their substrate stereospecificity[END_REF][START_REF] Vieira Dos Santos | The Arabidopsis plastidic methionine sulfoxide reductase B proteins. Sequence and activity characteristics, comparison of the expression with plastidic methionine sulfoxide reductase A, and induction by photooxidative stress[END_REF][START_REF] Grimaud | Repair of oxidized proteins. Identification of a new methionine sulfoxide reductase[END_REF][START_REF] Kumar | Reaction mechanism, evolutionary analysis, and role of zinc in Drosophila methionine-R-sulfoxide reductase[END_REF]. This strict stereospecificity was enzymatically demonstrated using chemically prepared Met-R-O and Met-S-O from racemic mixtures of free MetO or by using HPLC methods allowing discrimination of both diastereomers. A structural explanation was also provided by deciphering the mirror images of their active sites, in which only one MetO diastereomer can be accommodated [START_REF] Lowther | The mirrored methionine sulfoxide reductases of Neisseria gonorrhoeae pilB[END_REF].

While MsrA can reduce Met-S-O, whether as a free amino acid or included in proteins, MsrB is specialized in the reduction of protein-bound Met-R-O, and both are more efficient on unfolded oxidized proteins [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF][START_REF] Tarrago | Recharging oxidative protein repair: catalysis by methionine sulfoxide reductases towards their amino acid, protein, and model substrates[END_REF]. Eukaryotic Msrs are important actors in oxidative stress protection, aging and neurodegenerative diseases in animals [START_REF] Kim | The methionine sulfoxide reduction system: selenium utilization and methionine sulfoxide reductase enzymes and their functions[END_REF], during environmental stresses and seed longevity in plants [START_REF] Châtelain | Evidence for participation of the methionine sulfoxide reductase repair system in plant seed longevity[END_REF][START_REF] Laugier | Arabidopsis thaliana plastidial methionine sulfoxide reductases B, MSRBs, account for most leaf peptide MSR activity and are essential for growth under environmental constraints through a role in the preservation of photosystem antennae[END_REF]. In bacteria, MsrA and MsrB are generally located in the cytoplasm [START_REF] Ezraty | Oxidative stress, protein damage and repair in bacteria[END_REF], except in Neisseria or Streptococcus species, for which MsrA and MsrB enzymes can be addressed to the envelope [START_REF] Saleh | Molecular architecture of Streptococcus pneumoniae surface thioredoxin-fold lipoproteins crucial for extracellular oxidative stress resistance and maintenance of virulence[END_REF][START_REF] Skaar | The outer membrane localization of the Neisseria gonorrhoeae MsrA/B is involved in survival against reactive oxygen species[END_REF]. They play a role in protecting against oxidative stress and as virulence factors [START_REF] Ezraty | Oxidative stress, protein damage and repair in bacteria[END_REF].

Beside these stereotypical Msrs found in all kinds of organisms, several other enzymes can catalyze MetO reduction, principally in bacteria. For instance, numerous bacteria as well as unicellular eukaryotes, such as Saccharomyces cerevisiae, possess another type of absolutely stereospecific Msr, called free-R-Msr (fRMsr) or MsrC, which is specialized in the reduction of the free from of Met-R-O [START_REF] Le | Functional analysis of free methionine-Rsulfoxide reductase from Saccharomyces cerevisiae[END_REF][START_REF] Lin | Free methionine-(R)-sulfoxide reductase from Escherichia coli reveals a new GAF domain function[END_REF]. As MsrA and MsrB, the fRMsr uses thiol-based chemistry and the reducing power coming from NADPH to reduce its substrate [START_REF] Le | Functional analysis of free methionine-Rsulfoxide reductase from Saccharomyces cerevisiae[END_REF][START_REF] Lin | Free methionine-(R)-sulfoxide reductase from Escherichia coli reveals a new GAF domain function[END_REF].

In bacteria, several molybdenum cofactor-containing enzymes were also shown to be able to reduce oxidized Met. Particularly, the biotin sulfoxide reductase BisC, or its homolog TorZ/BisZ, specifically reduce the free form of Met-S-O, in the Escherichia coli cytoplasm and the Haemophilus influenza periplasm, respectively [START_REF] Ezraty | Methionine sulfoxide reduction and assimilation in Escherichia coli: new role for the biotin sulfoxide reductase BisC[END_REF][START_REF] Dhouib | A Novel, Molybdenum-Containing Methionine Sulfoxide Reductase Supports Survival of Haemophilus influenzae in an In vivo Model of Infection[END_REF]. Moreover, E. coli DMSO reductase reduces a broad spectrum of substrates, including MetO [START_REF] Weiner | Purification and properties of Escherichia coli dimethyl sulfoxide reductase, an iron-sulfur molybdoenzyme with broad substrate specificity[END_REF], while the R. sphaeroides homolog was shown to be absolutely stereospecific towards S-enantiomer of several alkyl aryl sulfoxides [START_REF] Abo | Enantioselective deoxygenation of alkyl aryl sulfoxides by DMSO reductase from Rhodobacter sphaeroides f.s. denitrificans[END_REF]. Finally, another molybdoenzyme, MsrP (formerly known as YedY), was recently identified as a key player of MetO reduction in the periplasm [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF][START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF]. MsrP was shown to be induced by exposure to the strong oxidant hypochlorite (ClO -) and to reduce MetO on several abundantly present periplasmic proteins in E. coli [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF] or on a Met-rich protein in Azospira suillum [START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF]. A most striking feature of E. coli MsrP (EcMsrP) is that, contrary to all known methionine sulfoxide reductases, it seems capable of reducing both Met-R-O and Met-S-O [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF]. The cistron, msrP, belongs to an operon together with the cistron encoding the transmembrane protein MsrQ, which is responsible for the electron transfer to MsrP from the respiratory chain. Of note, the cytosolic flavin reductase Fre was proposed as a potential alternative electron-carrier to MsrQ [START_REF] Juillan-Binard | A two-component NOX-like system in bacteria is involved in the electron transfer chain to the methionine sulfoxide reductase MsrP[END_REF]. The operon is conserved in the genome of most gram-negative bacteria suggesting that the MsrP/Q system is very likely a key player for general protection in the bacterial envelop against deleterious protein oxidation [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF][START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF]. R. sphaeroides MsrP (RsMsrP) shares 50% of identical amino acid residues with EcMsrP and transcriptomic analyses evidenced that RsmsrP is strongly induced under high-light conditions, suggesting a putative role in protecting the periplasm against

1 O2 [31].
In this paper, we describe the biochemical characterization of RsMsrP regarding its substrate specificity.

Using kinetic activity experiments and mass spectrometry analysis, we show that RsMsrP is a very efficient protein-bound MetO reductase, which lacks stereospecificity and preferentially acts on unfolded oxidized proteins. Proteomic analysis indicates that it can reduce a broad spectrum of proteins in the R. sphaeroides periplasm, and that Met sensitive to oxidation and efficiently reduced by RsMsrP are found in clusters and in specific amino acids sequences.

Material and methods

Production and purification of recombinant proteins

Recombinant MsrP was produced similarly to the previously described protocol [START_REF] Sabaty | Detrimental effect of the 6 His C-terminal tag on YedY enzymatic activity and influence of the TAT signal sequence on YedY synthesis[END_REF]. Briefly, R. sphaeroides f sp. denitrificans IL106 dmsA -strain carrying the pSM189 plasmid for production of a periplasmic MsrP with a 6-His N-terminal tag was grown in 6-liter culture under semi-aerobic conditions in Hutner medium until late exponential phase. The periplasmic fraction was extracted and loaded on a HisTrap column (GE Healthcare), MsrP was then eluted by an imidazole step gradient. MsrP solution was concentrated using 15-ml Amicon ® Ultra concentrators with 10-kDa cutoff (Millipore), desalted with Sephadex G-25 in PD-10 Desalting Columns (GE Healthcare). The protein concentration was adjusted to 1 mg.ml -1 in 30 mM Tris-HCl pH 7.5, 500 mM NaCl, the Tobacco Etch Virus (TEV) protease was added (1:80 TEV:RsMsrP mass ratio) and the solution incubated overnight at room temperature to remove the polyhistidine tag. Untagged RsMsrP was purified on a second HisTrap column, then concentrated and desalted in 50 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) pH 8.0. Protein solution was then loaded on a Superdex TM 200 10/30 gel filtration column equilibrated with 30 mM Tris-HCl pH 7.5. Main fractions were pooled and applied to a MonoQ TM 4.6/100 PE (GE Healthcare). RsMsrP was then eluted using a linear NaCl gradient (0 to 500 mM). Fractions were analyzed on SDS-PAGE using NuPAGE TM , 10 % Bis-Tris gels with MES-SDS buffer (ThermoFisher). Recombinant MsrA, MsrB, Thioredoxin Reductase (TR) 1, Thioredoxin 1 (Trx1) from Saccharomyces cerevisiae with polyhistidine tags, as well as the glutathione-S-transferase (GST) from Schistosoma japonicum, were produced and purified as previously described [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF]. Protein concentrations were determined spectrophotometrically using specific molar extinction coefficients at 280 nm: 6-His-RsMSRP, 56,380 M -1 .cm -1 ; untagged RsMsrP, 54,890 M -1 .cm -1 ; MsrA, 34,630 M -1 .cm -1 ; MsrB, 24,325 M -1 .cm -1 ; TR1, 24,410 M -1 .cm -1 ; Trx1, 9,970 M -1 .cm -1 ; GST, 42,860 M -1 .cm -1 , bovine β-casein (Sigma-Aldrich), 11,460 M -1 .cm -1 and chicken lysozyme (Sigma-Aldrich), 32,300 M -1 .cm -1 . Protein solutions were stored at -20°C until further use.

Peptides

Ser-Met(O)-Ser, QWGAGM(O)QAEED and TTPGYM(O)EEWNK peptides were obtained from GenScript® (Hong-Kong).

Preparation of oxidized bovine β-casein and its Met-R-O and Met-S-O containing counterparts

For oxidation, bovine β-casein was prepared in Phosphate Buffered Saline (PBS) at 1 mg.ml -1 in the presence of 200 mM H2O2 and incubated overnight at room temperature. H2O2 was removed by desalting using a PD-10 column and the protein solution was concentrated with 10-kDa cutoff Amicon ® Ultra concentrator. Oxidized GST was similarly prepared using 100 mM H2O2. To prepare Met-R-O containing β-casein, a solution of oxidized β-casein was incubated in 30 mM Tris-HCl pH 8 at a final concentration of 6.5 mg.ml -1 (260 µM) in the presence of 25 mM dithiothreitol (DTT) with 10 µM MsrA and incubated overnight at room temperature. The solution was diluted 10-fold in 30 mM Tris-HCl pH 8 and passed over a HisTrap column to remove the his-tagged MsrA. After concentration, the DTT was removed by desalting using a PD-10 column. Met-S-O containing β-casein was prepared similarly replacing the MsrA by the MsrB (14 µM). The protein solutions were concentrated with a 10-kDa cutoff Amicon ® Ultra concentrator and the final concentration was determined spectrophotometrically. Protein solutions were stored at -20°C until further use.

Enzymatic activity and apparent stoichiometry measurements

RsMsrP reductase activity was measured as described in ref. [START_REF] Sabaty | Detrimental effect of the 6 His C-terminal tag on YedY enzymatic activity and influence of the TAT signal sequence on YedY synthesis[END_REF] with a few modifications. Benzyl viologen (BV) was used as an electron donor and its consumption was followed at 600 nm using an UVmc1 ® spectrophotometer (SAFAS Monaco) equipped with optic fibers in a glovebox workstation (MBRAUN Labstar) flushed with nitrogen. We determined the specific molar extinction coefficient of benzyl viologen at 8,700 M -1 .cm -1 in 50 mM 2-(N-morpholino)ethanesulfonic acid (MES), pH 6.0 buffer. Each reaction mixture (1 ml or 0.5 ml) contained 0.2 mM BV reduced with sodium dithionite, and variable concentrations of substrates in 50 mM MES, pH 6.0 buffer.

Reactions were started by the addition of RsMsrP enzyme (10 to 46 nM). Reduction of MetO rates were calculated from the A600 nm slopes respecting a stoichiometry of 2 (2 moles of BV are oxidized for 1 mole of MetO reduced). Thus, the activity values presented as kcat or kobs (s -1 ) represent the number of moles of MetO reduced per mole of enzyme per second.

The apparent stoichiometry was determined similarly, using subsaturating concentrations of substrates:

1-10 μM oxidized β-casein, 1-10 μM Met-R-O containing β-casein and 1.5-15 μM Met-S-O containing β-casein. The amount of oxidized BV was determined 1 hour after the addition of the RsMsrP (46 nM) by subtracting the final A600 nm value from the initial one. Controls were done without the RsMsrP enzyme, or without the MetO-containing substrate. Quantities of MetO reduced were plotted as a function of substrate quantities and the apparent stoichiometry was obtained from the linear regression slope.

MsrA and MsrB activities were measured following the spectrophotometrical consumption of NADPH at 340 nm using the thioredoxin system similarly to the previously described protocol [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF]. Analysis and kinetics parameters determination were done using GraphPad® Prism 4.0 software (La Jolla, CA, USA).

Electrospray ionization/Mass spectrometry analysis of purified proteins

For oxidation, bovine β-casein (5 mg.ml -1 ) in 50 mM HEPES, pH 7.0, was incubated overnight at room temperature with H2O2 (50 mM). H2O2 was removed by desalting using a PD-10 column and the protein solution was concentrated with a 10-kDa cutoff Amicon ® Ultra concentrator. Oxidized β-casein (100 µM) was reduced by addition of 44 nM MsrP in a reaction mixture containing 50 mM HEPES pH 7.0, 0.8 mM BV and 0.2 mM sodium dithionite. After two hours of reaction in the glove-box, the repaired β-casein was analyzed by electrospray ionization/mass spectrometry in comparison to non-oxidized and oxidized β-casein. Analyses were performed on a MicroTOF-Q Bruker (Wissembourg, France) with an electrospray ionization source. Samples were desalted in ammonium acetate buffer (20 mM) and concentrated with a 30-kDa cutoff Amicon ® Ultra concentrator prior to analyses. Samples were diluted in CH3CN/H2O

(1/1-v/v), 0.2% Formic Acid (Sigma). Samples were continuously infused at a flow rate of 3 µL.min -1 . Mass spectra were recorded in the 50-7000 mass-to-charge (m/z) range. MS experiments were carried out with a capillary voltage set at 4.5 kV and an end plate off set voltage at 500 V. The gas nebulizer (N2) pressure was set at 0.4 bars and the dry gas flow (N2) at 4 L.min -1 at a temperature of 190 °C. Data were acquired in the positive mode and calibration was performed using a calibrating solution of ESI Tune Mix (Agilent) in CH3CN/H2O (95/5-v/v). The system was controlled with the software package MicrOTOF Control 2.2 and data were processed with DataAnalysis 3.4.

Generation of R. sphaeroides 2.4.1 msrP -mutant

The msrPQ operon was amplified from R. sphaeroides 2.4.1 genomic DNA with the primers 5'-AGATCGACACGCCATTCACC-3' and 5'-TCGGTGAGGCGCTATCTAGG-3'. The 2.2 kb PCR product was cloned into pGEMT Easy (Promega). An omega cartridge encoding resistance to streptomycin and spectinomycin [START_REF] Prentki | In vitro insertional mutagenesis with a selectable DNA fragment[END_REF] was then cloned into the BamHI site of msrP. The resulting plasmid was digested with SacI and the fragment containing the disrupted msrP gene was cloned into pJQ200mp18 [START_REF] Quandt | Versatile suicide vectors which allow direct selection for gene replacement in gram-negative bacteria[END_REF]. The obtained plasmid, unable to replicate in R. sphaeroides, was transferred from E. coli by conjugation. The occurrence of a double-crossing over event was confirmed by PCR and absence of the protein from the SDS-PAGE profile.

Preparation of periplasmic samples for proteomics analysis

R. sphaeroides 2.4.1 msrp -mutant was grown under semi-aerobic conditions. Periplasmic extract was prepared as previously described [START_REF] Sabaty | Detrimental effect of the 6 His C-terminal tag on YedY enzymatic activity and influence of the TAT signal sequence on YedY synthesis[END_REF] by cells incubation in 50 mM HEPES pH 8.0, 0.45 M sucrose, 1.3 mM Ethylenediaminetetraacetic acid (EDTA) and 1 mg.ml -1 chicken lysozyme. For Met oxidation, the periplasmic extract (0.7 mg.ml -1 ) was incubated with 20 mM N-Ethylmaleimide (NEM) and 2 mM NaOCl (Sigma-Aldrich) in 50 mM HEPES pH 8.0, 50 mM NaCl for 10 min at room temperature. NaOCl was removed by desalting using a PD-10 column and buffer was changed to 50 mM MES pH 6.0. The protein solution was concentrated with a 3-kDa cutoff Amicon ® Ultra concentrator. Three reaction mixtures were prepared in the glove box containing 35 µl of periplasmic extract, 1 mM benzyl viologen, 2 mM dithionite in 50 mM MES pH 6.0. The protein concentration in each reaction was 2.5 mg.ml -1 . The first reaction contained non-oxidized periplasmic extract, the second and third ones contained oxidized periplasmic extract. For the third reaction (repaired periplasm) 10 µM RsMsrP was added. The reactions were incubated for three hours at room temperature.

Trypsin proteolysis and tandem mass spectrometry

Protein extracts were immediately subjected to denaturing PAGE electrophoresis for 5 min onto a 4-12% Bis-Tris gradient 10-well NuPAGE TM gel (Thermofisher). The proteins were stained with Coomassie Blue Safe solution (Invitrogen). Polyacrylamide bands corresponding to the whole proteomes were sliced and treated with iodoacetamide followed by trypsin as previously recommended [START_REF] Hartmann | Taking the shortcut for high-throughput shotgun proteomic analysis of bacteria[END_REF]. Briefly, each band was destained with ultra-pure water, reduced with DTT, treated with iodoacetamide, and then proteolyzed with Gold Mass Spectrometry Grade Trypsin (Promega) in the presence of 0.01% ProteaseMAX surfactant (Promega). Peptides were immediately subjected to tandem mass spectrometry as previously recommended to avoid methionine oxidation [START_REF] Madeira | Methionine Residues in Exoproteins and Their Recycling by Methionine Sulfoxide Reductase AB Serve as an Antioxidant Strategy in Bacillus cereus[END_REF]. The resulting peptide mixtures were analyzed in a data-dependent mode with a Q-Exactive HF tandem mass spectrometer (Thermo) coupled on line to an Ultimate 3000 chromatography system chromatography (Thermo) essentially as previously described [START_REF] Klein | RNA-binding proteins are a major target of silica nanoparticles in cell extracts[END_REF]. A volume of 10 µL of each peptide sample was injected, first desalted with a reverse-phase Acclaim PepMap 100 C18

(5 µm, 100 Å, 5 mm x 300 µm i.d., Thermo) precolumn and then separated at a flow rate of 0.2 µL.min -1 with a nanoscale Acclaim PepMap 100 C18 (3 µm, 100 Å, 500 mm x 300 µm i.d., Thermo) column using a 150 min gradient from 2.5 % to 25 % of CH3CN, 0.1% formic acid, followed by a 30 min gradient from 25% to 40% of CH3CN, 0.1% formic acid. Mass determination of peptides was done at a resolution of 60,000. Peptides were then selected for fragmentation according to a Top20 method with a dynamic exclusion of 10 sec. MS/MS mass spectra were acquired with an AGC target set at 1.7 10 5 on peptides with 2 or 3 positive charges, an isolation window set at 1.6 m/z, and a resolution of 15,000.

MS/MS spectrum assignment, peptide validation and protein identification

Peak lists were automatically generated from raw datasets with Proteome Discoverer 1.4.1 (Thermo) and an in-house script with the following options: minimum mass (400), maximum mass (5,000), grouping tolerance (0), intermediate scans (0) and threshold (1,000). The resulting .mgf files were queried with the Mascot software version 2.5.1 (Matrix Science) against the R. sphaeroides 241 annotated genome database with the following parameters: full-trypsin specificity, up to 2 missed cleavages allowed, static modification of carbamidomethylated cysteine, variable oxidation of methionine, variable deamidation of asparagine and glutamine, mass tolerance of 5 ppm on parent ions and mass tolerance on MS/MS of 0.02 Da. The decoy search option of Mascot was activated for estimating the false discovery rate (FDR) that was below 1%.

Peptide matches with a MASCOT peptide score below a P value of 0.05 were considered. Proteins were validated when at least two different peptides were detected. The FDR for proteins was below 1% as estimated with the MASCOT reverse database decoy search option.

Ice logo analysis

Ice logo analysis were performed using the IceLogo server (http://iomics.ugent.be/icelogoserver/index.html) [START_REF] Colaert | Improved visualization of protein consensus sequences by iceLogo[END_REF].

Results

The R. sphaeroides MsrP is an efficient protein-MetO reductase

The results showing that the EcMsrP is a protein-bound MetO reductase, able to reduce both R-and S-diastereomer of MetO [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF] prompted us to evaluate whether these properties are conserved for RsMsrP.

As the EcMsrP was determined to be 5-fold less efficient in reducing the Met-S-O than Met-R-O, and knowing that all previously identified MetO reductases were absolutely stereospecific towards one enantiomer, we thought that it cannot be excluded that a protein contamination might explain the apparent ability of the EcMsrP to reduce the Met-S-O [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF]. Such potential Met-S-O reductase contaminant should be able to use benzyl viologen (BV) as electron provider in activity assays and a good candidate is the periplasmic DMSO reductase [START_REF] Weiner | Purification and properties of Escherichia coli dimethyl sulfoxide reductase, an iron-sulfur molybdoenzyme with broad substrate specificity[END_REF][START_REF] Abo | Enantioselective deoxygenation of alkyl aryl sulfoxides by DMSO reductase from Rhodobacter sphaeroides f.s. denitrificans[END_REF]. Thus, we prepared the recombinant RsMsrP from a R. sphaeroides strain devoid of the dorA gene encoding the catalytic subunit of the DMSO reductase [START_REF] Sabaty | Detrimental effect of the 6 His C-terminal tag on YedY enzymatic activity and influence of the TAT signal sequence on YedY synthesis[END_REF]. After purification on Ni-affinity column and removal of the polyhistidine tag, the mature enzyme was purified by gel filtration, followed by strong anion exchange, yielding a highly pure enzyme (Supplementary Figure S1).

After optimal pH determination showing that RsMsrP acts efficiently between pH 5.5 and 8.0 (Supplementary Figure S2), we determined the kinetic parameters of RsMsrP using BV as an electron provider and several model substrates: the free amino acid MetO, a synthetic tripeptide Ser-MetO-Ser and the oxidized bovine β-casein (Table 1). The β-casein contains 6 Met, it is intrinsically disordered, and was shown as an efficient substrate for the yeast MsrA and MsrB, after oxidation [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF] (see also Supplementary Figure S3). Commercial β-casein contains a mixture of genetic variants, appearing as multiple peaks on mass spectrometry (MS) spectra (Figure 1A). After oxidation with H2O2, MS analysis confirmed an increase in mass of 96 Da for each peak, very likely corresponding to the addition of 6 oxygen atoms on the Met residues (Figure 1B). Using the free MetO, we determined a kcat of ~ 122 s -1 and a Km of ~ 115,000 µM, yielding a catalytic efficiency (kcat /Km) of ~ 1,000 M -1 .s -1 (Table 1). With the Ser-MetO-Ser peptide, the kcat and the Km values were ~ 108 s -1 and ~ 13,000 µM, and thus the kcat/Km was ~ 8,300 M -1 .s -1 . Compared to free MetO, the ~ 8-fold increase in catalytic efficiency is due to the lower KM, and thus this indicates that the involvement of the MetO in peptide bonds increases its ability to be reduced by RsMsrP. With the oxidized β-casein, the kcat and the Km were ~ 100 s -1 and ~ 90 µM, respectively. The kcat/Km was thus ~ 1,000,000 M -1 .s -1 . This value, 4 orders of magnitude higher than the one determined with free MetO, indicates that the oxidized protein is a far better substrate for RsMsrP. Moreover, even assuming that all MetO in the oxidized β-casein were equal substrates for the RsMsrP and thus multiplying the KM by 6, the catalytic efficiency obtained (~ 175,000 M -1 .s -1 ) remained ~ 175-fold higher for the oxidized protein than for the free amino acid. These results indicate that the RsMsrP acts effectively as a protein-MetO reductase.

RsMsrP reduces both Met-R-O and Met-S-O of an oxidized model protein

To 3). These three forms, containing either two or only one diastereomer of MetO, were tested as substrate for RsMsrP (Figure 2). We measured a kcat of ~ 45 s -1 with the oxidized β-casein, which decreased to ~ 30 and to 5 s -1 for the β-casein containing the R or the S sulfoxide, respectively. This result shows that RsMsrP can reduce both diastereomers of MetO, but appears 6-fold less efficient to reduce Met-S-O than Met-R-O.

From this result, we postulated that RsMsrP should be able to reduce all MetO in the oxidized β-casein, as this protein was intrinsically disordered and thus all MetO were very likely accessible. We evaluated this hypothesis by mass spectrometry analysis. When incubated with RsMsrP, the mass of the oxidized protein decreased by 96 Da, showing that all MetO were reduced (Figure 1C). Altogether, these results clearly showed that RsMsrP was able to reduce both R-and S-diastereomers of MetO contained in the oxidized β-casein, and thus lacked stereospecificity.

The RsMsrP preferentially reduces Met-R-O but acts effectively on Met-S-O too

To gain insight into the substrate preference of RsMsrP toward one of the diastereomers of MetO, we performed kinetics analysis using the oxidized β-casein containing the R or S diastereomers of MetO (Table 1; Supplementary Figure S4). With the protein containing only the R-diastereomer of MetO ("β-casein-R-O"), we determined a kcat of ~ 50 s -1 , a Km of ~ 50 µM and thus a catalytic efficiency of ~ 950,000 M -1 .s -1 . In the case of the protein containing only the Met-S-O ("β-casein-S-O"), the kcat and Km were ~ 8 s -1 and of ~ 50 µM, respectively. This yielded a catalytic efficiency of 142,000 M -1 .s -1 . This value, ~ 7 fold lower than the one obtained with the β-casein-R-O, was due to the lower kcat as the Km was not changed. These values seem to indicate that the RsMsrP preferentially reduced the R than the S diastereomer of MetO in the oxidized β-casein. However, as we could not exclude that the proportion of Met-R-O was higher than the proportion of Met-S-O in the protein, we developed an assay to estimate the number of MetO reduced by RsMsrP in the three forms of oxidized β-casein. We measured the total moles of BV consumed for the reduction of all MetO using subsaturating concentrations of the oxidized protein. Practically, the absorbance at 600 nm was measured before and 90 min after substrate addition. As two moles of BV are consumed per mole of MetO reduced, we obtained the apparent stoichiometry of RsMsrP toward the oxidized protein by performing a linear regression on the straight part of the line and taking the slope, which defines the amount of MetO reduced as a function of substrate concentration (Figure S5). The values determined were ~ 4.6, ~ 3.2 and ~ 1.8 for the oxidized β-casein, the β-casein-R-O and the β-casein-S-O, respectively. In the case of the oxidized β-casein, we expected a value of 6 based on the data obtained by mass spectrometry (Figure 1). This may have been due to the heterogeneity of the oxidized β-casein (all Met were not initially fully oxidized) and/or to a too short time of incubation (all MetO were not fully reduced, as indicated by the presence of a peak corresponding to a portion of β-casein not fully reduced in Figure 1C). To compare the catalytic parameters, the data was normalized by multiplying the Km by the apparent stoichiometries, yielding values per reduced MetO, thereby allowing the removal of variation due to the different numbers of reduced Met-R-O or Met-S-O. The catalytic efficiencies were thus 230,000, 300,000 and 80,000 M -1 .s -1 for the oxidized β-casein, the β-casein-R-O and the β-casein-S-O, respectively (Table 1). The highest value was that obtained for the β-casein containing only the R form of MetO, indicating that this diastereomer was the preferred substrate for RsMsrP. However, the value obtained with the β-casein-S-O was only less than 4-fold lower, showing that RsMsrP can also act effectively on the Met-S-O.

RsMsrP can reduce a broad spectrum of periplasmic proteins

To identify potential periplasmic substrates of RsMsrP and gain insight into its substrate specificity, we applied a high-throughput shotgun proteomic strategy. Periplasmic proteins from the msrP -R. sphaeroides mutant were extracted, oxidized with NaOCl and then reduced in vitro with recombinant RsMsrP. Untreated periplasmic proteins, oxidized periplasmic proteins and RsMsrP-treated oxidized periplasmic proteins were analyzed by semi-quantitative nanoLC-MS/MS. All experiments were done systematically for 3 biological replicates and resulted in the identification of 362,700 peptide-to-spectrum matches. From all 11,320 individual peptide sequences, we identified 2,553 unique Met belonging to 720 proteins. The overall percentages of Met oxidation were ~ 35%, ~ 71% and ~ 40% for proteins from the periplasm extract, the oxidized periplasm extract and the RsMsrP-repaired proteins, respectively (Supplementary Table 1). This first result indicates that RsMsrP is very likely able to reduce MetO from numerous proteins and to restore an oxidation rate similar to the one of the periplasmic extract that has not undergone any oxidation.

The identification of preferential RsMsrP substrates requires the precise comparison of the oxidation state of Met residues from periplasmic proteins before and after the action of the enzyme. After tryptic digestion, since most of the Met/MetO-containing peptides were found in low abundance (i.e. with very low spectral counts), we focused on the proteins robustly detected in all samples. We selected the Met-containing peptides for which at least 10 spectral counts were detected in two replicates for each condition (i.e. untreated periplasm, oxidized periplasm and repaired oxidized periplasm) and at least 7 spectral counts were found in the third replicate. This restricted the dataset to 202 unique Met belonging to 70 proteins (Supplementary Table 2). Overall percentage of Met oxidation (calculated as the number of spectral counts for a MetO-containing peptide vs. the total number of spectral count for this peptide) varied from 2% to 87%, from 9% to 100% and from 4% to 91% in the periplasm, oxidized periplasm and repaired oxidized periplasm, respectively. Comparison of Met-O containing peptides between oxidized and RsMsrP treated samples indicates that the percentage of reduction varied from 100 % to no reduction at all. Eleven MetO were not reduced and 22 were reduced at more than 75 % (only 2 at 100 %). The percentage of reduction for the remaining majority of MetO was almost uniformly distributed between inefficient (less than 25 %)

to efficient (75% or more) reduction (Figure 3A).

No clear evidence of sequence or structure characteristic arose from these 70 identified proteins, neither in term of size or in Met content (Supplementary Table 2). The periplasmic chaperone SurA, the peptidyl-prolyl cis-trans isomerase PpiA, the thiol-disulfide interchange protein DsbA, the spermidine/putrescine-binding periplasmic protein PotD and the ProX protein were previously proposed as potential substrates of EcMsrP [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF]. All these proteins contain at least one MetO amongst the most efficiently reduced by RsMsrP (Supplementary Table 2), indicating that they are potential conserved substrates of the MsrP enzymes in E. coli and R. sphaeroides, and very likely in numerous other gram-negative bacteria.

The sensitivity to oxidation of the Met belonging to these 70 proteins, and their efficiency of reduction by RsMsrP show a wide range of variation, from Met highly sensitive to oxidation and efficiently reduced to Met barely sensitive to NaOCl treatment and not reduced by RsMsrP (Supplementary Table 2). Moreover, this diversity could be visible within a single protein, in which all Met may not be uniformly oxidized and reduced. For instance, the ABC transporter DdpA, along with another putative ABC transporter (Figure 3B,C), contained one of the two only MetO found to be fully reduced in the dataset (Met-230 and Met-353, respectively), although DdpA also contained the Met-243 that was neither efficiently oxidized nor reduced. This is also illustrated by the case of the peptidyl-prolyl cis-trans isomerase, which possessed the Met found to have the higher decrease in oxidation in the entire dataset (Met-172) but also a Met almost not reduced by RsMsrP (Met-190) (Figure 3D). The Met-539 of the PQQ dehydrogenase XoxF illustrates the case in which a Met was highly sensitive to NaOCl-oxidation and very efficiently reduced (Figure 3E). Twenty-one

Met were oxidized at 50 % or more and reduced by 50 % or more by RsMsrP (Supplementary Table S2).

To identify potential consensus sequence favorable to MetO reduction by RsMsrP, we performed a precise comparison of the oxidation percentage before and after the action of the enzyme. We thus defined two criteria to characterize the reduction state of each Met: i) the percentage of reduction calculated using the formula described in Supplementary Table S2 and based on the comparison of the oxidation percentages in oxidized versus repaired oxidized periplasm. For instance, a Met found oxidized at 25 % in the oxidized periplasm and at 5 % in the repaired oxidized periplasm was considered enzymatically reduced at 80 %. ii) the decrease in percentage of oxidation by comparison of the 2 samples. For instance, the same Met found oxidized at 25 % in the oxidized periplasm and 5 % in the repaired extract had a decrease in the oxidation percentage of 20 %. This second criterion was used to avoid bias in which very little oxidized Met were considered as efficient substrates (i.e. a Met oxidized at 5 % in the oxidized periplasm extract and at 1 % in the repaired oxidized periplasm was reduced at 80 %, similarly to one passing from 100 % to 20 %, which intuitively appears as a better substrate than the previous one). We selected as efficiently and inefficiently reduced MetO those for which both criterions were higher than 50 % and lower than 10 %, respectively.

Comparison of the sequences surrounding the efficiently reduced MetO to the theoretical proteome of R.

sphaeroides showed no depletion of amino acid, but mainly enrichment of polar amino acids (Gln, Lys, and Glu) around the oxidized Met (Figure 5A). Similar analysis with the inefficiently reduced MetO indicated the enrichment of Thr and Ser in the far N-terminal positions (-5 and -4) and of a Tyr in position -2 (Figure 5B). The C-terminal positions (+ 1 to +5) were mainly enriched in charged amino acids (Gln, Lys, and Glu), similarly to efficiently reduced MetO. This apparent contradiction may indicate that the amino acids in the C-terminal position of the considered MetO did not really influence the efficiency of RsMsrP but were observed simply because of the inherent composition of the overall identified peptides. We then compared the variation of amino acids composition of the MetO-containing peptides between both datasets, using the inefficiently reduced MetO as a negative dataset (Figure 5C). The results were similar to those obtained by comparison with the entire theoretical proteome of the bacterium, i.e. most enriched amino acids were polar (Glu, Gln, Asp and Lys) at most extreme positions (-5, -4 and + 2 to + 5). Of note, the conserved presence of a Gly in position -1, and the presence of several other Met around the central Met. This potential with H2O2 and checked its oxidation state by mass spectrometry (Supplementary Figure S7). Surprisingly, using a protocol similar to the one allowing the complete oxidation of the 6 Met of β-casein, we observed only a weak and incomplete oxidation of the protein. The major peak corresponded to the non-oxidized form and a small fraction had an increase in mass of 16 Da, likely corresponding to the oxidation of one Met.

Nevertheless, we prepared from this oxidized sample, an unfolded oxidized lysozyme by reduction with dithiothreitol in 4M urea followed by iodoacetamide alkylation of cysteines, and both samples (oxidized and unfolded oxidized), were used as substrates for RsMsrP (Figure 6). We also used glutathione-S-transferase (GST) which possesses 9 Met and is highly structured. After oxidation with H2O2, GST was incubated with 4 M of the chaotropic agent urea, a concentration sufficient to induce complete unfolding of the protein [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF]. For both oxidized proteins, we observed a dramatic increase in activity after unfolding. Indeed, the RsMsrP activity increased 7-fold with the unfolded oxidized lysozyme compared to the folded one, and 6-fold in the case of the unfolded oxidized GST compared to the folded oxidized GST (Figure 6). As the unfolded oxidized protein solutions of lysozyme or GST contained a substantial amount of urea, we performed controls in which the urea was added extemporaneously in the cuvette during the measurements, showing that urea did not influence the RsMsrP activity (Supplementary Figure S8).

Mass spectrometry analysis showed that the RsMsrP was able to completely reduce the oxidized lysozyme in these conditions (Supplementary Figure S7), suggesting that observed differences of repair between the folded-and unfolded-oxidized lysozyme were not due to the incapacity of RsMsrP to reduce some MetO, but were due to kinetic parameters. We thus determined the kinetics of reduction of these proteins by RsMsrP (Table 1, Supplementary Figure S8). For the oxidized lysozyme, the kcat and the Km were ~ 4 s -1 and ~ 900 µM, respectively. Using the unfolded oxidized lysozyme, the kcat increased to ~ 7 s -1 and the Km decreased to ~ 100 µM. The catalytic efficiency determined with the unfolded oxidized lysozyme was thus ~ 18-fold higher than the one determined using the oxidized lysozyme before unfolding (70,200 vs. 4,000 M -1 . s -1 ). Similar results were obtained with GST. Indeed, with the oxidized GST, we recorded kcat and Km values of ~ 8 s -1 and ~ 640 µM, respectively. Whereas for the unfolded oxidized GST, the kcat was slightly higher (~ 12 s -1 ), and the Km was ~ 6-fold lower (~ 100 µM). The catalytic efficiency was 10-fold Supplementary Figure S6). To our knowledge, the presence of a Thr close to a MetO was not previously shown to influence any Msr activity, but the presence of a Pro was shown to decrease or totally inhibit MetO reduction by the human MsrA and MsrB3, depending on its position [START_REF] Ghesquière | Redox proteomics of protein-bound methionine oxidation[END_REF].

The presence of oxidation-sensitive Met efficiently reduced by the RsMsrP in clusters on polar parts of proteins should facilitate the oxidation/reduction cycle aiming to scavenge ROS as previously proposed for canonical Msrs [START_REF] Luo | Methionine in proteins defends against oxidative stress[END_REF]. This is also illustrated by the methionine-rich protein MrpX proposed as main substrate of the A. suillum MsrP, which is almost only composed of Met, Lys, Glu and Asp [START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF]. The presence of numerous MetO on a single molecule of protein substrate should increase the RsMsrP efficiency as one molecule of the substrate allows several catalytic cycles, potentially without breaking physical contact between the enzyme and its substrate.

Comparison of the RsMsrP activity using folded or unfolded protein substrates (lysozyme and GST)

showed that it is far more efficient to reduce unfolded oxidized proteins (Figure 6). Similar results were found for canonical Msrs [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF]. In the case of MsrB it was because more MetO were accessible for reduction whereas for MsrA this increase was independent of the number of MetO reduced. Here, the use of lysozyme containing only one MetO (Supplementary Figure S7) undoubtedly showed that the increase in activity is not related to the unmasking of additional MetO upon protein denaturation (Table 1; Figure 6). This could indicate that the RsMsrP has better access to the MetO in the protein or that the MetO is more easily accommodated in the active site of the enzyme because of increased flexibility. This should provide a physiological advantage to the bacteria during oxidative attacks, which could occur during other stresses such as acid or heat, hence promoting simultaneous oxidation and unfolding of proteins. Particularly, hypochlorous acid, which was shown to induce msrP expression in E. coli [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF] and A. suillum [START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF], has strong oxidative and unfolding effect on target proteins [START_REF] Winter | Bleach activates a redox-regulated chaperone by oxidative protein unfolding[END_REF].

Finally, previous work indicated that the E. coli MsrP lacks stereospecificity and can reduce both R-and S-diastereomers of MetO chemically isolated from a racemic mixture of free L-Met-R,S-O [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF]. This discovery is of fundamental importance as it breaks a paradigm in Met oxidation and reduction knowledge, and very likely for all enzymology as non-stereospecific enzymes were very rarely described. Indeed, to our knowledge, all previously characterized enzymes able to reduce Met sulfoxide or related substrates were shown to be absolutely stereospecific. This was the case for the canonical MsrA and MsrB, which reduce only the S-diastereomer and the R-diastereomer, respectively [START_REF] Sharov | Diastereoselective reduction of protein-bound methionine sulfoxide by methionine sulfoxide reductase[END_REF][START_REF] Ejiri | Reduction of methionine sulfoxide to methionine by Escherichia coli[END_REF][START_REF] Lowther | The mirrored methionine sulfoxide reductases of Neisseria gonorrhoeae pilB[END_REF][START_REF] Moskovitz | Purification and characterization of methionine sulfoxide reductases from mouse and Staphylococcus aureus and their substrate stereospecificity[END_REF][START_REF] Vieira Dos Santos | The Arabidopsis plastidic methionine sulfoxide reductase B proteins. Sequence and activity characteristics, comparison of the expression with plastidic methionine sulfoxide reductase A, and induction by photooxidative stress[END_REF][START_REF] Grimaud | Repair of oxidized proteins. Identification of a new methionine sulfoxide reductase[END_REF][START_REF] Kumar | Reaction mechanism, evolutionary analysis, and role of zinc in Drosophila methionine-R-sulfoxide reductase[END_REF], as well as for the free Met-R-O reductase [START_REF] Le | Functional analysis of free methionine-Rsulfoxide reductase from Saccharomyces cerevisiae[END_REF][START_REF] Lin | Free methionine-(R)-sulfoxide reductase from Escherichia coli reveals a new GAF domain function[END_REF] and for the DMSO reductase [START_REF] Weiner | Purification and properties of Escherichia coli dimethyl sulfoxide reductase, an iron-sulfur molybdoenzyme with broad substrate specificity[END_REF][START_REF] Abo | Enantioselective deoxygenation of alkyl aryl sulfoxides by DMSO reductase from Rhodobacter sphaeroides f.s. denitrificans[END_REF] and BisC/Z molybdoenzymes [START_REF] Ezraty | Methionine sulfoxide reduction and assimilation in Escherichia coli: new role for the biotin sulfoxide reductase BisC[END_REF][START_REF] Dhouib | A Novel, Molybdenum-Containing Methionine Sulfoxide Reductase Supports Survival of Haemophilus influenzae in an In vivo Model of Infection[END_REF]. To evaluate the potential lack of stereospecificity of the RsMsrP, we chose to use a different strategy than the one used for E. coli MsrP [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF] and prepared oxidized β-casein containing only one or the other MetO diastereomer using yeast MsrA and MsrB to eliminate the S-and the R-diastereomers, respectively. Activity assays and kinetic experiments using a highly purified RsMsrP demonstrated that it can efficiently reduce the β-casein containing only the R-or the S-diastereomer (Table 1; Figure 2 and Supplementary Figure S4). Moreover, this lack of stereospecificity was undoubtedly confirmed by the ability of the RsMsrP to reduce all 6 MetO formed on the oxidized β-casein (Figure 1). These results, consistent with Gennaris and coworkers finding, indicate that this lack of stereospecificity is very likely common to all MsrP homologs. Together with the apparent ability of the enzyme to repair numerous unrelated oxidized proteins, the capacity to reduce both diastereomers of MetO, argues for a role of MsrP in the general protection of envelope integrity in gram negative bacteria. However, it raises questions regarding the structure of its active site as the enzyme should be able to accommodate both diastereomers. From this, we wondered whether the RsMsrP could reduce the Met sulfone, which can be imagined as a form of oxidized Met containing both R-and S-diastereomers, but we did not detect any activity (Supplementary Figure S9). Although it could be because of an incompatibility in redox potential, it may indicate that this form of oxidized Met cannot reach the catalytic atom. The three-dimensional structure of the oxidized form of E. coli MsrP indicated that the molybdenum atom, which is supposed to be the catalytic center of the enzyme, is buried 16 Å from the surface of the protein [START_REF] Loschi | Structural and Biochemical Identification of a Novel Bacterial Oxidoreductase[END_REF]. The next challenge will be to understand the MsrP reaction mechanism and will require the determination of the enzyme structure in its oxidized and reduced forms bound to its MetO-containing substrates. B) The same oxidized peptides were analyzed using the peptides containing a non-oxidized Met from the same samples (periplasm and oxidized periplasm extracts). Amino acids are colored according to their physiochemical properties. with oxidized and unfolded oxidized GST, respectively. Data presented are averages of three replicates. ± S.D.

  A 500-µl reaction cuvette contained 200 µM NADPH, 2 µM TR1, 25 µM Trx1 and 5 µM MsrA or MsrB and 100 µM oxidized β-casein. Production of Met was calculated respecting a stoichiometry of 1 (1 mole of NADPH is oxidized for 1 mole of Met produced).

  determine whether the RsMsrP can reduce both MetO diastereomers, we chose the oxidized bovine β-casein as a model substrate because it was efficiently reduced by the yeast MsrA and MsrB indicating the presence of both R and S diastereomers of MetO [15]. After oxidation with H2O2, we treated the protein with MsrA and MsrB, taking advantage of their stereospecificity, to obtain protein samples containing only the Met-R-O ("β-casein-R-O") or the Met-S-O ("β-casein-S-O"), respectively. The absence of one or the other diastereomer of MetO was validated by the absence of remaining Msr activity (Supplementary Figure

  corresponding of the non-oxidized β-casein, showing the ability to reduce all MetO in this protein. Note the presence of a peak with an increase of 16 Da (*, mass of 23999.4 Da) compared to the main reduced peak, indicating an incomplete reduction of the total protein pool. Main peaks masses: 1, 23983.0 Da; 2, 24022.4 Da; 3, 24037.1 Da; 4, 24075.0 Da; 5, 24091.0 Da; 6, 24128.2 Da; 7, 24143.7 Da.

Figure 2 .

 2 Figure 2. RsMsrP activity using oxidized β-casein, β-casein-R-O and β-casein-S-O as substrates. The

Figure 3 .

 3 Figure 3. Characteristics of MetO reduction sites and oxidation state of Met in representative

Figure 4 .

 4 Figure 4. IceLogo representation of enriched and depleted amino acids around the sites of Met

Figure 5 .

 5 Figure 5. IceLogo representation of enriched and depleted amino acids around the sites of MetO

Figure 6 .

 6 Figure 6. Relative RsMsrP activity using unfolded oxidized proteins. The RsMsrP activity was

TableTable 1 .

 1 Kinetics parameters of RsMsrP reductase activity towards DMSO and various MetO-containing substrates. Da. C) Oxidized β-casein was incubated with RsMsrP (25 nM) in the presence of BV (0.8 mM) and sodium dithionite (2 mM) as electron donors. All major peaks had masses

	Substrates	kcat (s -1 )	Km	kcat/Km
			(µM)	(M -1 .s -1 )
	DMSO a	28 ± 1	61,000 ± 7,000	465
	Free L-Met-R,S-O	122 ± 20	115,000 ± 27,000	1,000
	Ser-MetO-Ser	108 ± 17	13,000 ± 3,400	8,300
	QWGAGM(O)QAEED	479 ± 24	4,530 ± 370	105,700
	TTPGYM(O)EEWNK	> 70	> 5,000	N.D.
	Oxidized β-casein	100 ± 5	93 ± 9	1,075,000
	β-casein-R-O	49 ± 3	51 ± 6	950,000
	β-casein-S-O	8 ± 1	53 ± 10	142,000
	Oxidized lysozyme	4 ± 1	886 ± 349	4,000
	Unfolded oxidized lysozyme	7 ± 1	105 ± 17	70,200
	Oxidized GST	8 ± 2	643 ± 194	12,400
	Unfolded oxidized GST	12 ± 3	99 ± 33	120,000

a From

[START_REF] Sabaty | Detrimental effect of the 6 His C-terminal tag on YedY enzymatic activity and influence of the TAT signal sequence on YedY synthesis[END_REF]

. N.D, not determined.

Acknowledgment:

We are very grateful to Prof. Vadim, N. Gladyshev (Brigham's and Women Hospital and Harvard Medical School) for the gift of pET28a-MsrA, pET21b-MsrB, pET15b-TR1, pET15b-Trx1 and pGEX4T1 expression vectors. We thank Dr. Benjamin Ezraty and the members of his team (Laboratoire de Chimie Bactérienne, Institut de Microbiologie de la Méditerranée) for fruitful discussions. Pascaline Auroy-Tarrago (Laboratoire de Bioénergétique et Biotechnologie des Bactéries et Microalgues, CEA, BIAM) is acknowledged for her help with proteomics analysis.

Funding: This work was supported by the Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA) and by the project METOXIC (ANR 16-CE11-0012).

Altogether, these results show that RsMsrP can reduce a broad spectrum of apparently unrelated proteins (only 11 Met among 202 were not reduced). However, since all MetO were not reduced with similar efficiency, some structural or sequence determinants could drive the ability of MetO to be reduced by RsMsrP.

The nature of the amino acids surrounding a MetO influences the RsMsrP efficiency

Having in hand a relatively large dataset of oxidized and reduced Met prompted us to search for consensus sequences that could favor or impair the oxidation of a Met or the reduction of a MetO by RsMsrP.

For all identified Met, we extracted, the surrounding 5 amino acids on the N-and C-terminal sides to obtain an 11-amino acid sequence with the considered Met centered at the 6 th position. As shown for bacterial MsrB [START_REF] Kim | Structural and kinetic analysis of an MsrA-MsrB fusion protein from Streptococcus pneumoniae[END_REF], this length might be sufficient to encompass the amino acids in physical contact with RsMsrP during reduction. We then performed an IceLogo analysis aiming to identify whether some residues were enriched or depleted around the target Met. The principle is to compare a 'positive' dataset of peptides, to a 'negative' one [START_REF] Colaert | Improved visualization of protein consensus sequences by iceLogo[END_REF]. To find potential consensus sequences of oxidation, we first compared all unique MetO-containing peptides from both the untreated and the NaOCl-oxidized periplasmic extracts (our positive dataset) to the theoretical R. sphaeroides proteome (our negative dataset). The IceLogo presented in Figure 4A shows that MetO-containing sequences were mainly depleted of His and aromatic or hydrophobic residues (Trp, Phe, Tyr, Leu, Ile) and were mainly enriched in polar or charged amino acids (Asn, Gln, Asp, Glu and Lys). This suggests that Met in a polar environment, as commonly found at the surface of proteins, are very likely more susceptible to oxidation than those located in hydrophobic environments such as those in the protein core. We then compared all these unique MetO-containing peptides to all the Met-containing peptides from the same samples (Figure 4B), and we observed that Trp, along with His, Tyr and Cys, were principally depleted around the potentially oxidized Met. Strikingly, the only amino acid significantly more abundant around an oxidized Met was another Met in position -2 and +2. These results indicate that oxidation sensitive Met might be found as clusters. enrichment of Met around an oxidation site is consistent with the result found for the sensibility of oxidation (Figure 4B), and indicates that potential clusters of MetO could be preferred substrates for RsMsrP. We found 16 peptides containing 2 or 3 MetO, reduced at more than 25 % by RsMsrP (Supplementary Table S2). This was illustrated, for example, by the cell division coordinator CpoB which possesses two close Met residues (66 and 69) highly reduced by the RsMsrP, or by the uncharacterized protein (YP_353998.1) having 4 clusters of MetO reduced by the RsMsrP (Supplementary Table S2).

From this analysis, the only depleted amino acids appeared to be Thr and Pro in positions -4 and -3 (Figure 4C). To validate these results, we designed two peptides, QWGAGM(O)QAEED and TTPGYM(O)EEWNK, as representative of most efficiently and most inefficiently RsMsrP-reduced peptide-containing MetO, respectively. We used them as substrates to determined reduction kinetics parameters for RsMsrP (Table 1; Supplementary Figure S6). The results showed that the peptide QWGAGM(O)QAEED was efficiently reduced, with the highest kcat value from all the substrates we tested (~ 480 s -1 ) and a Km of ~ 4,500 µM. This yielded a kcat/Km of ~ 100,000 M -1 .s -1 , which is 2 orders of magnitude higher than the one determined for the free MetO, and 10-fold lower than for the oxidized β-casein (Table 1). On the contrary, the peptide TTPGYM(O)EEWNK was not efficiently reduced by RsMsrP (Table 1; Supplementary Figure S6). Indeed, we could not determine the kinetic parameters as the activity value curve never reached an inflection point using concentrations as high as 5,000 µM. The maximal kcat value was determined at ~ 70 s -1 at 5,000 µM of peptide, which is ~ 3.5-fold less than the one determined with the same concentration of the other peptide (~ 250 s -1 ) (Supplementary Figure S6). These results are in full agreement with the proteomics analysis and confirm that the nature of the amino acids surrounding a MetO in a peptide or a protein strongly influences its ability to be reduced by RsMsrP.

The RsMsrP preferentially reduces unfolded oxidized proteins

To test whether structural determinants affect RsMsrP efficiency of MetO reduction, we compared its activity using oxidized model proteins, either properly folded or unfolded. We started with chicken lysozyme as it is a very well folded protein highly stabilized by four disulfide bonds [START_REF] Ray | An electrospray ionization mass spectrometry investigation of 1-anilino-8-naphthalene-sulfonate (ANS) binding to proteins[END_REF]. We oxidized it higher for the unfolded oxidized GST than for its folded counterpart (Table 1; Supplementary Figure S8). Altogether, these results showed that RsMsrP is more efficient at reducing MetO in unfolded than in folded oxidized proteins. Moreover, as evidenced with lysozyme that contained only one MetO in our conditions, the increase in activity using unfolded substrate is not dependent on the number of MetO reduced.

Discussion

All organisms have to face harmful protein oxidation and almost all possess canonical Msrs that protect proteins by reducing MetO. Bacteria also have molybdoenzymes able to reduce MetO, as a free amino acid for the DMSO reductase [START_REF] Weiner | Purification and properties of Escherichia coli dimethyl sulfoxide reductase, an iron-sulfur molybdoenzyme with broad substrate specificity[END_REF] or the biotin sulfoxide reductase BisC/Z [START_REF] Ezraty | Methionine sulfoxide reduction and assimilation in Escherichia coli: new role for the biotin sulfoxide reductase BisC[END_REF][START_REF] Dhouib | A Novel, Molybdenum-Containing Methionine Sulfoxide Reductase Supports Survival of Haemophilus influenzae in an In vivo Model of Infection[END_REF], but also included in proteins in the case of MsrP [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF][START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF]. Genetic studies and the conservation of MsrP in most gram-negative bacteria indicate that it is very likely a key player in the protection of periplasmic proteins against oxidative stress [START_REF] Gennaris | Repairing oxidized proteins in the bacterial envelope using respiratory chain electrons[END_REF][START_REF] Melnyk | Novel mechanism for scavenging of hypochlorite involving a periplasmic methionine-rich Peptide and methionine sulfoxide reductase[END_REF] However, an in-depth characterization of its protein substrate specificity is still lacking. In this work, we chose the MsrP from the photosynthetic purple bacteria R. sphaeroides as a model enzyme to uncover such specificity. Using purified oxidized proteins and peptides, we showed that RsMsrP is a very efficient protein-containing MetO reductase, with apparent affinities (Km) for oxidized proteins 10 to 100-fold lower than for the tripeptide Ser-MetO-Ser or the free MetO (Table 1). As reported for canonical MsrA and MsrB [START_REF] Tarrago | Methionine sulfoxide reductases preferentially reduce unfolded oxidized proteins and protect cells from oxidative protein unfolding[END_REF], we observed important variations in the reduction kcat of different oxidized proteins, arguing for the existence of sequence and structural determinants affecting the enzyme efficiency (Table 1).

To find potential physiological substrates of RsMsrP and uncover their properties, we used a proteomic approach aiming at comparing the oxidation state of periplasmic proteins after treatment with the strong oxidant NaOCl, followed by RsMsrP reduction of these proteins. We found 202 unique Met, belonging to 70 proteins, for which the sensitivity of oxidation and the ability to serve as an RsMsrP substrate varied greatly (Figure 3, Supplementary Table S2). MetO efficiently reduced by RsMsrP belong to structurally and functionally unrelated proteins, indicating that RsMsrP very likely does not possess specific substrates and acts as a global protector of protein integrity in the periplasm. Interestingly, we observed from our IceLogo analysis that Met sensitive to oxidation are generally presented in a polar amino acid environment and can be found in clusters (Figure 4). These properties might be common to all Met in proteins as similar results were found in human cells [START_REF] Ghesquière | Redox proteomics of protein-bound methionine oxidation[END_REF][START_REF] Hsieh | Oxidation of protein-bound methionine in Photofrin-photodynamic therapy-treated human tumor cells explored by methionine-containing peptide enrichment and quantitative proteomics approach[END_REF] and plants [START_REF] Jacques | Protein Methionine Sulfoxide Dynamics in Arabidopsis thaliana under Oxidative Stress[END_REF]. Moreover, oxidized Met efficiently reduced by the RsMsrP were also found clustered in polar environments and our analysis shows that the presence of Thr and Pro in N-terminal side of a MetO strongly decrease RsMsrP efficiency (Table 1, Figure 5 and