domain: spi phys math info

text:
Mengmeng Zhang
email: mengmeng.zhang@airinnova.se

Nathalie Bartoli
email: nathalie.bartoli@onera.fr

Aidan Jungo
email: aidan.jungo@cfse.ch

Wim Lammen
email: wim.lammen@nlr.nl

Erik Baalbergen
email: erik.baalbergen@nlr.nl

Mark Voskuijl
email: m.voskuijl@tudelft.nl

Data Fusion and Aerodynamic Surrogate Modeling for Handling Qualities Analysis

In the modern aircraft design process numerical simulation is one of the key enablers. However, computational time increases exponentially with the level of fidelity of the simulation. In the EU Horizon 2020 project AGILE different computation tools relative to different levels of fidelity are used. One of the challenges is to reduce the computational time -e.g. to facilitate an efficient optimization process -by processing the analysis data of various fidelity levels in a global surrogate model. This paper focuses on data fusion via an automatic iterative process embedded in the MDA chains as applied in AGILE. Surrogate

modeling techniques are applied, taking into account the optimal sampling and the corresponding fidelities of the samples. This paper will detail the different steps of the proposed approach. As a test case handling qualities analysis of the AGILE reference conventional aircraft is performed, by fusing the computed aerodynamic coefficients and derivatives. A full spreadsheet of aerodynamic data computed either with different levels of fidelity or with only a low-fidelity tool has been derived and evaluated. By applying the data set with multiple levels of fidelity, the accuracy of the flight performance analysis was significantly improved especially for the transonic region in which the low fidelity aerodynamic method is not reliable. Moreover, the test case shows that by using a surrogate model based data fusion technique, the fidelity of the analysis data can be significantly improved with maximum RMSE less than 5% with minimum computation effort. 1. Problem statement and background

Problem statement

The modern aircraft design philosophy emphasizes on the collaborations and integrations, where the driving force is to build a smooth flow chain to carry out the MDA (Multi-Disciplinary Analysis) process. For the analysis carried out by each single discipline, there are multi-fidelity tools to do the analysis which yield multi-fidelity outputs. One major discipline -addressed in the paper -concerns the aerodynamic database construction for stability and control analysis.

Assessment of aircraft maneuverability and agility at the conceptual design stage brings great challenges in the design process regarding the stability and control analysis over the entire flight envelope. A large lookup table of forces and moments must be constructed by Computational Fluid Dynamics (CFD) while we have to address the computational cost: a useful look-up table for stability and control analysis, the so-called aerodynamic database, needs thousands of entries because of the high dimensionality of the parameter space.

"Brute-force" calculation would be far too costly. But there are ways to reduce the computational time. The first step is to use different CFD methods, from Large-Eddy Simulation (LES) via Reynolds-Averaged Navier-Stokes models, down to potential flow models, or even empirical methods from handbooks.

Using the simplest method and geometry compatible with the level of accuracy required for each flight state can dramatically reduce the computational cost.

The whole spectrum of computational models is widely used in modern aerospace industry. In order not to lose too much accuracy while saving computational cost, the simplifying assumptions made to solve the standard Navier-Stokes equations should be acceptable for each single entry. For example, if one is flying at low speed and non-accelerated small angles of attack, the incompressible potential flow models can give acceptable predictions with significant time saving compared with Euler or RANS equations solving.

The Aircraft design deals with several different disciplines, each having their own focus. During this process, data need to be exchanged. Managing the interconnections is complex and error-prone. Adoption of a standardized, datacentric scheme for storage of all data improves consistency and reduces risks of misconceptions and errors in the process. It however requires an initial effort to make interfaces between analysis modules and the data archive. The CPACS (Common Parametric Aircraft Configuration Schema) [START_REF] Böhnke | Towards a collaborative and integrated set of open tools for aircraft design[END_REF][START_REF]CPACS -a common language for aircraft design[END_REF] is widely used in the frame of AGILE.

The RCE integration environment and workflow manager [START_REF] Seider | Open source software framework for applications in aeronautics and space[END_REF] implements the sequence of analysis modules and manages the data transport and translation as well as logging the process. RCE makes it easy to set up and run a workflow also using modules in which the engineers are not discipline-experts. It is done via Brics [START_REF] Baalbergen | Streamlining cross-organisation product design in aeronautics[END_REF], which allows to "call" a module or a tool (and so produce results) remotely on "the specialist" computer. The remote specialist receives a request to proceed some calculation or analysis. The input is generally a CPACS file containing all the information required. The new data generated are added to the CPACS file and are sent back to the requester. More details about the AGILE collaborative approach can be found in [START_REF] Moerland | Collaborative architecture supporting the next generation of MDO within the AGILE paradigm[END_REF][START_REF] Van Gent | Knowledge architecture supporting the next generation of mdo in the AGILE paradigm[END_REF].

Data fusion aims to handle the large amount of data to be computed for

where the aerodynamic variables are α the angle of attack, β the sideslip angle,

Alt the flight altitude. The data set is denoted by D.

Surrogate modeling has two distinct steps, first the training to produce the g-function, and second, the use of the generated g-function. The data set D is the training set. In this paper y represents the computations of forces, moments, structural deformations and stresses, etc., associated with a particular flight state of a defined aircraft configuration which is the x. Evaluation of y requires at least a flow solution, and possibly a complete aero-servo-elastic simulation.

The training should produce a RSM compliant with maximal accuracy and with minimal cost for producing the training set. This is done by the choice of f (multi-fidelity modeling characterized by fidelity level, L0-L3) and by the choice of a training set. Much effort has been devoted to design algorithms for the choice of an optimal training set, as described in [START_REF] Lefebvre | Methodological enhancements in MDO process investigated in the AGILE European project[END_REF].

Evaluation of a surrogate model requires the input x and the corresponding results of the training, e.g. a set of polynomial coefficients, or a look-up table with the whole flight envelope (flight states, or x), processed in to the function g:

ŷ(x) = g(x, D) (2)
It is assumed that the evaluation will be made for many (thousands) values of

x for a single D. The training, including the choice of the training set, is an iterative process. In a single iteration k, an algorithm M increments/fuses the training set with a set {x, y} k and updates D:

D k+1 = M (D k , {x, y} k ) (3)
For the new D, another algorithm S suggests new samples for testing the accu-racy requirements:

{x} k+1 = S(D k+1 ). ( 4
)
Both the M and S algorithms make frequent use of g.

A typical RSM kit contains computer codes for an RSM evaluator g, data fuser algorithm M and sampling algorithm S, plus a proviso (see Section 4.1) to evaluate f . A developed instance, the data fusion process, which is ready to run, and improved on further, will contain g, M , S and the data set D. Fig. 1 shows an example of a module-independent data fusion workflow exchanging data using Brics. It should be noted that sending D via Brics for each call is impractical in general, due to the size of D. Therefore, in the standard use cases, D is built on one partner's network/machine, and then made available. The f -samples however can easily be sent using Brics since the large discretization and solution files (CFD mesh, finite element mesh for CSM) are usually only stored locally.

However, for the purpose of tracking possible bugs, etc., the parameters used in mesh generation and simulation should be accessible also "after the fact" to the network. S may involve some proprietary tools which raises IP and access issues, and as D embodies information about a design, it also has distribution and access 140 restrictions. Within AGILE a specific Surrogate Model repository (SMR) was developed that deals with theses issues, see [START_REF] Baalbergen | Methods supporting the efficient collaborative design of future aircraft[END_REF] and Section 5.2.

Theoretical Basis for Constructing a Surrogate Model

Kriging and Co-Kriging

Theory. Kriging is a method for scattered data interpolation which sees the data to be predicted as a stationary stochastic field with correction of the predictions depending only on their relative location. Details about Kriging or Gaussian Process can be found in [START_REF] Rasmussen | Gaussian processes for machine learning[END_REF][START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF]. Assume that a set of n design sites are available for d independent variables x, with corresponding observations (responses) y with q dependent variables:

x = [x i j ], i = 1, ..., n, j = 1, ..., d, ∈ R n×d (5)
y = [y i j ], i = 1, ..., n, j = 1, ..., q, ∈ R n×q (6)
The correlation function has value 1 for coinciding locations and vanishes with distance with a length-scale. The estimation of length-scales depends strongly on the data to be interpolated. Also the estimated variance -interpreted as mean square error -is predicted. The Kriging predictor is then the smallest variance, linear, unbiased estimator F(β, x) of ŷ at a point x * from ex-

isting data y = y(x i ), i = 1, 2, • • • , n. It guarantees the interpolation property ŷ(x i ) = y i : ŷ(x * ) = F(β, x * ) + ψ T Ψ -1 (y -F) ( 7
)
where y is the observed data, F is the mean value obtained by the regression model, ψ is the correlation between the x i and the point x * , and Ψ is the n × n correlation matrix of all the designs x. A new prediction at x * , ŷ(x * ), can be computed with the Eq. ( 7). The estimated mean square error in this prediction is given by:

MSE: ŝ2 (x * ) = σ2 1 -ψ T Ψ -1 ψ + + 1 -1 T Ψ -1 ψ 1 T Ψ -1 1 ( 8
)
where σ2 is obtained by the regression model as F.

The co-Kriging process provides a "data fusion" technology for the multifidelity results where a great quantity of low-fidelity data is coupled with a small amount of high-fidelity data to enhance the accuracy of a surrogate model. The approximation is obtained by updating the correlation ψ and the correlation matrix Ψ to the co-variance c and co-variance matrix C between the low (cheap)

and high-fidelity (expensive) observations. The co-Kriging estimation ŷ at x * is:

ŷco (x * ) = F(β, x * ) + c T C -1 (y -F) (9)
Where F is the mean value obtained by the regression model predicted in the same pattern as Kriging, by considering both lo-fi and hi-fi samples. If the prediction is made at the ith high-fidelity points, and the lo-fi data have m c design sites, then c is the m c + ith column of C. Equation ( 9) is an interpolator of the hi-fi data just like ordinary Kriging, but will in a well defined sense regress the lo-fi data unless it coincides with the expensive observations y e .

The co-variance matrix for data combining both low and high-fidelity observations is:

C =   σ 2 c Ψ c (x c , x c ) ρσ 2 c Ψ c (x c , x e ) ρσ 2 c Ψ c (x e , x c ) ρ 2 σ 2 c Ψ c (x e , x e ) + σ 2 d Ψ d (x e , x e )   (10)
The estimated mean square error is similar to the Kriging error (see Eq. 8)

as well [START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF], calculated as:

MSE: ŝ2 co (x * ) = ρ 2 σ2 c + σ2 d -c T C -1 c + 1 -1 T C -1 c 1 T C -1 1 (11)
Details of the derivation are given in [START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF].

Co-Kriging procedures. The co-Kriging can be carried out based on the Kriging prediction. Let the low-fidelity and high-fidelity design sites (i.e., the independent variables, such as Mach number and Angle of Attack), be x c and x e , and the corresponding "dependent" variables be y c and y e , and let the points be predicted at untried sites x * = (x * 1 , x * 2 , ..., x * n ), i.e. the ŷ(x * ) can be predicted through: The co-Kriging prediction in this paper is carried out following the steps described above, by utilizing the DACE [START_REF] Lophaven | Dace: A Matlab Kriging Toolbox[END_REF] Matlab Toolbox, and the Gaussian process in scikit-learn library in Python [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF]. DACE provides various correlation functions (while the scikit-learn library provides the Gaussian process) based on available prior information about the underlying function to be modeled. The correlation parameters (correlation length) are computed by maximizing the likelihood function by solving a non-linear optimization problem [START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF]. The co-Kriging predictor is scripted in both in Matlab and Python with the computed surrogate model coefficients, the predicted response function, and the estimated MSE as outputs.

1. A Kriging predictor K c is built from (x c , y c )

Mixture of Experts

The Mixture of Experts is a technique which combines local surrogate models in order to approximate heterogeneous functions (flat and steep regions, first and zero order discontinuities) dividing the problem space into homogeneous regions.In the context of this paper, the mixture of experts techniques is used to mix multi-fidelity variables as co-kriging. The Mixture of Experts method [START_REF] Bettebghor | Surrogate modeling approximation using a mixture of experts based on EM joint estimation[END_REF][START_REF] Liem | Surrogate models and mixtures of experts in aerodynamic performance prediction for mission analysis[END_REF] for surrogate modeling provided uses a clustering of the training basis into regions where the function to be approximated is expected to be continuous or at least more simple. It strongly relies on the Expectation-Maximization (EM) algorithm for Gaussian mixture models. With an aim of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, cubic, radial basis functions, or different forms of kriging) on each cluster and all the local experts are finally combined using the Gaussian mixture model parameters found by the EM algorithm to get a global model. Two recent kriging-based models [START_REF] Bouhlel | Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction[END_REF][START_REF] Bouhlel | An improved approach for estimating the hyperparameters of the kriging model for highdimensional problems through the partial least squares method, Mathematical Problems in Engineering[END_REF], called KPLS and KPLS-K that accelerate the calculation of the hyperparameters of Kriging, consist on a combination between the Partial Least Squares (PLS) method and the Kriging model, are also proposed as local expert when the dimension increases.

As explained in [START_REF] Bettebghor | Surrogate modeling approximation using a mixture of experts based on EM joint estimation[END_REF], we must predict outputs from inputs to create a model.

In our case, outputs are scalars y i ∈ R (q = 1 in Eq. ( 6)) and inputs are vectors

x i ∈ R d (
as defined in Eq. ( 5)). To perform the clustering, we need n inputs x = (x i ) 1...n and n outputs y = (y i ) 1...n . So we can only know the cluster posterior probabilities of vectors like (x i , y i ) ∈ R d+1 . To predict the cluster posterior probabilities of a sample knowing only its inputs, we must project each multivariate Gaussian function of Gaussian mixture model, trained in dimension d+1, on the inputs hyperplane of dimension d. Thanks to hyperplane projection and linear recombination, inputs cluster posterior probabilities of each cluster can be predicted and local models can be performed. When local models ŷk are known, the global model ŷ(x * ) would be

ŷ(x * ) = K k=1 P(κ = k|x = x * ) ŷk (x * ) ( 12
)
which is the classical probability expression of mixture of experts. In this equation [START_REF] Rasmussen | Gaussian processes for machine learning[END_REF], K is the number of Gaussian components, P(κ = k|x = x * ) denoted by gating network, is the probability to lie in cluster k knowing that x = x * and ŷk is the local expert built on cluster k.

Equation ( 12) leads to two different approximation models depending on the computation of P(κ = k|x = x * ). When choosing the Gaussian laws to compute this quantity, Eq. ( 12) leads to a smooth model that smoothly recombine different local experts. If P(κ = k|x = x * ) is computed as characteristic functions of clusters (being equal to 0 or 1) this leads to a discontinuous approximation model. The number of clusters K is chosen automatically to minimize the generalization error on a validation data set [START_REF] Bartoli | Improvement of efficient global optimization with mixture of experts: methodology developments and preliminary results in aircraft wing design[END_REF].

MOE has been made available to AGILE partners for different applications as a remote service [START_REF] Zhang | Disciplinary data fusion for multi-fidelity aerodynamic application[END_REF][START_REF] Lefebvre | Overview of mdo enhancement in AGILE project: a clustered and surrogate-based mda use case[END_REF]. MOE has also been wrapped using the Brics connection protocols to enable the transfer of models (constructed on data provided by the user) and not only the results of the evaluation of the models.

At this point, different surrogate models have been described to combine several levels of fidelity from an initial dataset. The next step is to select new sampling points with their associated level of fidelity.

Design of Experiments

Smart Sampling Algorithm

The "smart sampling" is employed to determine new sampling locations and to choose the tools (variable fidelity). The smart sampling scheme uses a mixture of sampling methods with the stopping criteria by examining the MSE or the RMSE (Root Mean Square Error). The sampling identifies a number of sampling locations. The response at the sampling points can be evaluated in parallel. Due to the inherent nature of the sampling algorithm S (shown below), it is strongly coupled with the RSM evaluator g, namely, Kriging or co-Kriging surrogate models.

Figure 2 shows the workflow of the smart sampling technology. For each iteration, the new samples (low-fidelity, or lo-fi & high-fidelity, or hi-fi) are merged so that the surrogate model is updated and the RMSE is computed and compared with the defined tolerance, or tol, chosen by the user. If the stopping criteria are met, the iteration ends. Otherwise new samples are suggested according to the listed methods in Fig. 2 and described in the following. The new suggested samples will be computed by the corresponding tools and will be added to the samples to update the surrogate model. The computational tool fidelity is also suggested. The methods used to suggest new samples are described below, and the rules are understood as a hierarchical sequence (from 1 to 5):

1. Borders: only applies when loading the initial samples. Check the "borders" of the DOE domain, if the hi-fi samples are missing at any of the border locations, add them (computed by hi-fi tools). 5. MaxLoc: finds the maximum RMSE locations and new samples will be added there. This method is used only when the maximum RMSE is not significantly improved compared with previous iterations:

RMSE(k + 1) > ν • RMSE(k) ( 13
)
where 0 < ν < 1 is the improvement factor chosen by the user, thus the sampling method shall be "switched" to MaxLoc.

As stated above, except Borders, the new samples suggested by all other methods will be computed by L1 tools (lo-fi) by default. There is a hierarchy of models and the highest fidelity one is considered as the truth, i.e., we have no error estimate between the highest fidelity models and the "reality". We wish to use lower fidelity (lo-fi) models where they give results close to the hi-fi models, so first use lo-fi until error estimate satisfies lo-fi criterion. Then hi-fi points are filled in until the error estimate between response surface and hi-fi is small enough (i.e., fulfills the hi-fi criterion). Note that this may "waste" lo-fi calculations in regions where lo-fi is bad so hi-fi is necessary.

It shall be possible to choose freely between source tools with different fidelity levels. The criteria for going to the next fidelity level and to switch method are:

• If the new suggested samples are already in the hi-fi sampled domain, switch to the next method level. For example, if the MaxMin suggests a new sample that is already in the hi-fi sampled domain, we then use the MaxHessian.

• If the new suggested samples are already in the lo-fi sampled domain but not in the hi-fi sampled domain, upgrade the fidelity.

• If a low fidelity tool fulfills the lo-fi accuracy criteria, for example, if the maximum RMSE is small enough, go to the next fidelity level, namely, L k "upgrades" to L k+1 , where k is the current fidelity level.

• Another indication is that the maximum RMSE is not significantly improved compared with the previous iteration as described with Eq. ( 13).

This means either the methods shall be "switched" or the fidelity shall be improved.

This "smart" sampling algorithm needs now to be associated with a rescaling of the design domain in order to ensure that points are added throughout the domain.

Domain Validity Issues

The problem of fusing the aerodynamic characteristics, it relates the flight envelope identification, or the identification of the domain validity of the surrogate models. Usually, the DOE techniques are designed to work on rectangular (cubic for 3D) domains. Moreover, the inherent characteristics of the CPACS file definition only supports the uniform distribution of the samples. Therefore, the initial samples, are computed with regular sampling. However, the physical flight envelope is just part of the "CPACS envelope" [START_REF] Zhang | Disciplinary data fusion for multi-fidelity aerodynamic application[END_REF]. For instance, the test case which will be used in this paper, the AGILE reference aircraft, as a conventional transport airliner, its physical flight envelope, will not cover, the high angles of attack at high Mach numbers. The parameter space should be chosen as the physical flight envelope, otherwise the sampling rules will fail and the new suggested samples will always locate around the edges of the (rectangular) domains since they are highly non-linear (but not realistic). This section will spell out how to cope with the domain validity issues.

In this paper, the physical domain is defined by the flight mechanics specialist co-author, as the dashed line bounds shown in the Fig. 3a for a two-dimensional parameter space. The sample points on the physical domain will be re-scaled to fit the new domain within the interval [-1,1] in both dimensions, see Fig. 3b.

All samples which are left out of the physical domain will be excluded. During the surrogate modeling process, the design domain will firstly be re-scaled and exclude the parameter space which are left out of the physical domain, before building a surrogate model and iterate the sampling procedures. This will provide a better "coverage" of the area of the domains that are typically difficult to model (extreme flight conditions).

Data Fusion Service for AGILE MDO: a process

As described at the beginning of the paper, in overall MDO, some tools may need large amounts of data, for instance, the flight simulation tool used for Stability and Control (S&C) analysis needs a complete aerodynamic-database as its input. Some entries in the database can be computed by high-fidelity analysis modules, but not all of them, therefore we need data fusion between various fidelity levels. The fused database, thereafter, will be delivered to the e.g. flight simulation tool. The data fusion used for AGILE project is implemented as a process, and it calls for other tools to run the process. The whole fusion procedure is iterative.

This section shows how the surrogate-based data fusion is implemented in the MDA chain, and how deployment and application of the surrogate model is facilitated by the Surrogate Model Repository.

Data Fusion within the MDA Chain

Within AGILE frameworks are applied with CPACS as common data format for tools interaction. Usually the workflow (including tools operated by different specialists) is integrated into some workflow environment, such as RCE, with tools callable using Brics. Figure 4 shows the Brics application from within a client workflow and a server workflow, to enable a specialist to respond to a request to run the "Tool", and to accomplish remote tool execution. The (input)

CPACS file is downloaded (from a server of e.g., a customer) using Brics, and it is sent to the "Tool" operated by a local specialist. After execution, the (output) CPACS file is sent back and uploaded (to the customer who calls for this service) using Brics. Since the data fusion service involves many tools those are not operated by a single site, the communication between the tools is made by Brics call as illustrated in Fig. 4. The numbered arrows indicated the actions. First, the input files for the remote service are uploaded to the central data server in a neutral domain [START_REF] Ghoreyshi | Accelerating the numerical generation of aerodynamic models for flight simulation[END_REF]. Next, the remote specialist gets notified

(2), who in response may start the service (3). The service first retrieves the input files from the data server (4), runs the tool that implements the service [START_REF] Seider | Open source software framework for applications in aeronautics and space[END_REF], and uploads the output files to the data server [START_REF] Baalbergen | Streamlining cross-organisation product design in aeronautics[END_REF]. Finally, the output files are downloaded to the clients side [START_REF] Moerland | Collaborative architecture supporting the next generation of MDO within the AGILE paradigm[END_REF], and the client workflow continues. and partner collaboration. The question then arises how to manage, share and deploy these models. Particularly, surrogate models must be applied with care.

The bounds of the allowed input space of the surrogate model need to be clearly specified, e.g. to avoid extrapolation. Furthermore the prediction accuracy of the outputs of the surrogate model must be specified, so that the user has a clear idea of its applicability, quality and limitations. To address these aspects a specific Surrogate Model Repository (SMR) has been developed as part of the AGILE Development Framework. The SMR is a central broker for registration, storage, deployment and usage of surrogate models so that these may be shared and reused in collaborations in a managed way. SMR development details can be found in [START_REF] Moerland | Collaborative architecture supporting the next generation of MDO within the AGILE paradigm[END_REF][START_REF] Baalbergen | Methods supporting the efficient collaborative design of future aircraft[END_REF].

With respect to the sharing of surrogate models two cases have been considered in the frame of AGILE and are supported by the SMR.

• Full share: Share all of the compiled binary code of a surrogate model (SM) to support its use by others. In this case the complete SM implementation (e.g., an executable program such as MOE) is uploaded to the SMR with meta-information describing its usage. The SM may be used by downloading its code and running it.

• Partial share: Share only the usage of a SM, others may use the SM as a service while the code remains at the owners or developers site. In this case only the meta-information of the SM is uploaded to the repository.

The SMR provides a user interface to directly use this SM by calling the remote service.

In addition to the sharing capabilities, the SMR can export a neutral XML format (i.e., CMDOWS [START_REF] Van Gent | Knowledge architecture supporting the next generation of mdo in the AGILE paradigm[END_REF]) that supports usage of the SM as part of a workflow system without further intervention of the SMR. As such the SMR can interface to other components in the AGILE Development Framework. An illustration of this export facility is described in [START_REF] De Wit | Aircraft rudder optimization -a multi-level and knowledgeenabled approach[END_REF]. The SMR may also function as broker with respect to the creation of surrogate models. The user of the SMR may indicate that a specific surrogate model instead of a high-fidelity model must be used in a study. If the desired surrogate model does not exist already, the SMR initiates a surrogate model creation process behind the scenes. The role of the SMR both for sharing and for triggering the creation of surrogate models is depicted in Fig. 6. Section 7.2 will describe an example of SM deployment through the SMR, using a SM that was developed with the Data Fusion service. A partial share is applied: the SM is provided "as a service". This process can be semi-automatic, which is depicted in Figure 7, and facilitated by Brics, a common building block for the realization of collaborative workflows and part of the AGILE Development Framework [START_REF] Moerland | Collaborative architecture supporting the next generation of MDO within the AGILE paradigm[END_REF]. 6. Test Case and Handling Quality Tool Descriptions

Aerodynamic Model Description

The test case aircraft configuration is the AGILE reference aircraft, a regional jet-liner, which was analyzed and simulated using the AGILE MDA system, without experimental data being available. This aircraft does not correspond to an existing one, but it is in the range of an Airbus 320 or Boeing 737.

The reference aircraft is defined in CPACS [START_REF]CPACS -a common language for aircraft design[END_REF] format.

Some previous numerical simulations have been performed for this aircraft to test the data fusion tool [START_REF] Zhang | Disciplinary data fusion for multi-fidelity aerodynamic application[END_REF], however the primary control surfaces were not modeled. In the test case of this paper, the aerodynamic coefficients and derivatives for the longitudinal analysis are computed by L1 and L2 tools, including the elevator deflections. Those computational results are fused as an aerodynamic-database for the longitudinal flight simulation using the flight simulator PHALANX, which will be described in the last part of this section.

The L1 aerodynamic tool used for the data fusion workflow is the Vortex Lattices Method (VLM) code Tornado [START_REF] Melin | Using Internet Interactions in Developing Vortex Lattice Software for Conceptual Design[END_REF]. The L2 aerodynamic tool used is the open-source code SU2 developed by the Stanford University, which is a fluid dynamics solver for solving the incompressible/compressible and inviscid/viscous flows. In this paper the SU2 is used as L2 level, namely, as an Euler equation solver for solving the inviscid compressible flows. Both of L1 and L2 tools have been fully adapted to the CPACS format, integrated onto RCE and are callable using Brics.

As stated in Section 4.2, the initial DOEs from the CPACS files are uniformly distributed, then the valid domain is selected according to the physical flight envelope. Figure 8 spells out the initial DOEs defined in the CPACS files, which consist of two sets of data from both the low-fidelity (L1) and the highfidelity (L2) tools. The parameter space is three-dimensional: the angle of attack α, Mach number and the elevator deflection δ. The flight altitude is fixed at 10km and the sideslip angle is 0 degree. Again, the initial DOEs which are defined/stored in the CPACS files exceed the bounds of the design domain, which means some of the computations (data) are "wasted" and will be ignored in the future fusion process.

The CPACS file of the AGILE reference aircraft is converted into another type of XML definition geometry to be opened with the mesh generator software sumo [START_REF] Tomac | From Geometry to CFD Grids: An Automated Approach for Conceptual Design[END_REF]. A surface mesh is created automatically by sumo and it calls TetGen [START_REF] Si | TetGen: a Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator[END_REF] to create an unstructured Euler mesh. The mesh used for this study has been chosen following a mesh sensitivity analysis performed in [START_REF] Jungo | Benchmarkig new CEASIOM with CPACS adoption for aerodynamic analysis and flight simulation[END_REF]. It is an unstructured mesh with 5.9 million tetrahedrons, see Fig. 9a.

In order to compute the elevator deflections, the SU2 built-in mesh deformation function SU2 DEF is used to deform the mesh around the elevator locations on the horizontal tail. A Free-form deformation (FFD) [START_REF] Sederberg | Free-Form Deformation of Solid Geometric Models[END_REF] box is defined at the elevator locations. With the hinge line location specified, the mesh in the FFD box can be deformed around the hinge line within a certain angle. To avoid high aspect ratio cells (or even negative volume) usually small deflection angle is preferred. According to authors experience, with a deflection angle less than 8 degrees the deformed mesh can give well-converged solutions. In this paper we limit the deflection angle within 4 degrees for high speed flight at the high altitude.

Flight Simulator PHALANX Description

The Performance, Handling Qualities and Loads Analysis Toolbox (PHA-LANX) is a selective fidelity flight mechanics modelling and analysis tool. It is specifically designed to be used in a multidisciplinary design optimization framework [START_REF] Pfeiffer | Implementation of a heterogeneous, variable-fidelity framework for flight mechanics analysis in preliminary aircraft design[END_REF] and to support the analysis of future novel aircraft designs [START_REF] Voskuijl | Flight mechanics modelling of the Prandtl plane for conceptual and preliminary design[END_REF][START_REF] Voskuijl | Controllability of blended wing body aircraft[END_REF].

PHALANX has the capability to automatically construct and analyze aircraft models within an MDO environment [START_REF] Fengnian | Automated Generation of Multiphysics Simulation Models to Support Multidisciplinary Design Optimization[END_REF][START_REF] Foeken | Knowledge-Based Simulation Model Generation for Control Law Design Applied to a Quadrotor UAV[END_REF]. This makes it possible to analyze the flight mechanics of many different variants of novel aircraft and configurations without a user in the loop. The aircraft models are nonlinear simulation models which serve as virtual flight test vehicles. An extensive analysis suite is available to evaluate aircraft performance characteristics, to perform handling assessments and to simulate loads resulting from both intentional manoeuvres and atmospheric conditions. 7. Results The static coefficients are computed by L1 and L2 tools, and the database is generated by co-Kriging, as stated above. However, the dynamic stability derivatives are only computed based on L1 tool Tornado in order to reduce the computation efforts while demonstrating the benefits of the fused data. The aerodynamics are modelled using a database in the form of look-up tables.

Fused Aerodynamic Characteristics

These tables are a function of angle of attack, pitch rate and elevator deflection. Figure 14a shows the angle of attack and elevator deflection in trimmed flight for the whole range of Mach numbers at 10 km altitude. One can clearly see that the elevator deflection results start to deviate at higher Mach numbers. This is caused by the differences in the static moment coefficient between the two databases. The required lift coefficient is relatively small and for the this range of lift coefficients, the fused database and L1 database give similar predictions for the angle of attack. As a consequence, the control authority of the elevator at high speed flight is better predicted by the fused database. Table 1 shows the characteristics of the Short Period mode and Phugoid The short period depends to a large extent on the dynamic derivative M q , which is identical for both databases since they are produced by L1 tools for both. The small differences of the results are due to the differences between the 600 static lift coefficient and the static moment coefficient.

Conclusion and Perspectives

The paper represents the surrogate-based data fusion technology used to generate the aerodynamic database for the handling qualities analysis. This data fusion technology is implemented in a MDA worflow, utilizing the existing tools within AGILE, establishing an iterative and collaborative, distributed process.

The surrogate models which are built from the data fusion service can be stored and deployed for reuse with the Surrogate Model Repository (SMR). An example was given for running a surrogate model "as-a-service" through SMR. A regional jet defined within AGILE project as a reference aircraft is used as the test case for the data fusion tool. A full spreadsheet of aerodynamic data computed either with different levels of fidelity or with only a low-fidelity tool has been derived using the data fusion package. It has been shown that the quality of the flight performance simulation was significantly improved especially for the transonic region in which the low fidelity aerodynamic method is not reliable.

The test case shows that by using a surrogate model based data fusion technique, the fidelity of the analysis data can be significantly improved with minimum computation effort.

The data fusion process enabled in the AGILE MDA chain with different tools or modules communicated by Brics can be used as a well-established & ready-to-use service to be applied to any other aircraft for aero-database generation and flying qualities analyses, in order to reduce the computational time and increase the overall prediction accuracy.

  second step concerns all the data obtained by the different CFD methods over the entire flight envelope. In the data base, the dense low-cost & low-fidelity data indicating the trend must be fused with the sparse high-cost & high-fidelity data correcting the low fidelity data values [1]. The multi-fidelity modeling method is concerned with finding the means to navigate the flight state parameter space and cover the entire flight envelope in an effective way. A procedure is devised to integrate the results from different simulation tools based on different methods and having different complexity levels. Building the multi-fidelity model has two main steps: 1. populate the aerodynamic database over the whole flight envelope by the dense low-fidelity data samples; 2. correct the data using the sparse high-fidelity samples. The data fusion package is developed for the purpose stated above by aiming at building a reliable surrogate model of the aerodynamic database using lowfidelity data and with a minimum number (sparse) of the high-fidelity samples including automatically chosen new sample points. The initial starting points are chosen by a regular systematic sampling. The package is used as a "service" in the MDA workflow for innovative aircraft design available from the EU AGILE Project [2]. This paper focuses on the developed data fusion package which can be used in the AGILE project. Section 2 describes the background about the collaborative framework and the different tools used for some aerodynamic computations. Section 3 shows the theoretical basis for constructing a surrogate model. Sections 4 details the data fusion strategy to select new samples at each iteration and build the associated surrogate model. Section 6 focuses on the different modules in the data fusion workflow from the surrogate model to the sampling module. Results are presented in Section 7 and Section 8 summarizes and concludes the work. 1.2. Background AGILE is a EU funded Horizon 2020 project coordinated by the Institute of Air Transportation Systems of the German Aerospace Center (DLR). Its objective is to implement the 3rd generation of multidisciplinary optimization through efficient international multi-site collaboration in overall design teams. The 19 partners bring different knowledge and competences regarding aircraft design and optimization. In this context the use of surrogate models is interesting to assemble results coming from various source and level of fidelity.

Figure 1 :

 1 Figure 1: Workflow for data fusion in the MDA chain, interchangeable modules exchanging data using Brics.

  and evaluated at hi-fi locations x e to give ŷc (x e ) = K c (x e ); 2. Augment the design sites for the hi-fi samples by adding ŷc (x e ) as a new column, i.e., the augmented samples locations are (d + 1) dimensional vectors, xe = (x i e,1 , ..., x i e,d , K c (x e )) with corresponding hi-fi observations y e (x i ) for i = 1, ..., n; 3. The co-Kriging function K co is calculated using the augmented samples xe and the corresponding hi-fi observations y e ; 4. The target sites x * are augmented by the K c predictor ŷc (x * ) = K c (x * ). The augmented samples are x * = (x * , K c (x * )); 5. The co-Kriging prediction is K co (x * , K c (x * )).

Figure 2 :

 2 Figure 2: The "smart sampling" technology workflow.

2 .

 2 MaxMin: finds the local maximum or minimum of the surrogate model and the new samples will be added there. The position of the local maxima or minima is computed by considering the full surrogate model, comparing any function values with all the points inside a sphere of radius previously computed and centered in it. The sphere radius is initially computed as minimum of the Euclidean norms of any two points with all non-equal coordinates. If the function value is bigger or smaller than all the others in the sphere, the point is marked as local maximum or minimum respectively[START_REF] Pronzato | Minimax and maximin space-filling designs: some properties and methods for construction[END_REF]. The "MaxMin" method can at a time recommend n-set of samples (defined by user). The new samples shall be computed by L1 tool (lo-fi) by default if tool fidelity is not specified.3. MaxHessian: finds/computes the maximum curvature of the surrogate model and the new samples will be added there. The new samples shall be computed by L1 tool (lo-fi) by default. Computation details can be found in Appendix in[START_REF] Zhang | Disciplinary data fusion for multi-fidelity aerodynamic application[END_REF]. This method only becomes active if Find MaxMin fails.4. EIF : finds the Expected Improvement Function (EIF) location[START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF] and the new samples will be added there only when the MaxMin and Max-Hessian fail to add the effective samples, i.e., the new samples suggested by previous methods are already or very close to the existing samples via a distance criterion threshold chosen by the user. The new samples shall be computed by L1 tool (lo-fi) by default.

( a )

 a The physical domain. (b) The scaled domain.

Figure 3 :

 3 Figure 3: The initial samples of the domain for the Test Case and its transformation, at altitude 10 km.

Figure 4 :

 4 Figure 4: Schematic overview of Brics application in AGILE from within a client workflow and a server workflow, to accomplish remote tool execution [7].

Figure 5

 5 Figure5shows how the datafusion workflow is executed, the three modules (described later in the paragraph) can be execute at different locations by specialists. This workflow is implemented with RCE which allows to use the Brics plug-in to share information between the main computer and specialist's computer, in the way as Fig.4describes.The data fusion package includes the development/delivery of: (1) the surrogate model builder/fuser M and model evaluator g; (2) the sampling module S;(3) the samples computation module f (aerodynamic module); (4) the graphic feedback module. This package can be used for fusing computed tables of forces and moments for the purpose of aero-dataset construction. Namely, it can be used for fusing the aerodynamic coefficients data from different tools (sources) and fidelities, and storing the surrogate models.

Figure 5

 5 Figure 5 spells out the data fusion service in the MDA chain. It has three core modules shown below, the graphic feedback module can be used separately and is not included in the MDA chain. • Preparation Module: It prepares the training data storing in the CPACS

Figure 5 :

 5 Figure 5: Data fusion service in the MDA chain with 3 stages.

Figure 6 :

 6 Figure 6: The Surrogate Model Repository as library for sharing surrogate models and as broker for creating surrogate models on demand.

Figure 7 :

 7 Figure 7: Depiction of the under the hood process for an as a service calculation.

Figure 8 :

 8 Figure 8: Initial DOE defined in the CPACS files. Black dot: low-fidelity data; blue cross: high-fidelity data.

  (a) The volume mesh of the test case. (b) The Cp contour from Euler solutions.

Figure 9 :

 9 Figure 9: (a) The unstructured volume mesh with 5.9 million cells of the test case configuration, created by sumo [29] and TetGen [30]; (b) the Cp contour of the horizontal tail of the test case aircraft from Euler solutions computed by SU2, Mach=0.78, α = 0 • with elevator deflection δ = 4 • . The elevator deflection is modeled by deforming the mesh defining by FFD.

Figure 10 shows

 10 Figure 10 shows the fused C L , C D and C m aero-coefficient results of the AG-ILE reference aircraft model from the both fidelities with the elevator deflection δ = 0 • over the flight envelope. The dot sign (•) represents the lo-fi samples and the cross sign (×) represents the hi-fi samples. Figures 10a, 10c and 10eshow the response surfaces from the surrogate models as well as the sampled data over the flight envelope in the three-dimensional space. Figure10b, 10dand 10f represent the two-dimensional cuts for Mach number 0.5 (black), 0.8 (blue) and 0.9 (red) from the response surfaces, and their corresponding sampled data. Note that for M = 0.8 there are no hi-fi samples computed, instead there are hi-fi samples computed at M = 0.78, which are shown and marked in the figures.Figures10a and 10bshow the surrogate models (response surfaces) for C L .The co-Kriging predicts the non-linear behaviors at higher angles of attack, as the hi-fi samples indicate.

( a )

 a Lift coefficient C L surface and the sampled data. (b) Fused lift coefficient C L for Mach number 0.5, 0.8 and 0.9. (c) Drag coefficient C D surface and the sampled data. (d) Fused drag coefficient C D for Mach number 0.5, 0.8 and 0.9. (e) Pitch moment coefficient Cm surface and the sampled data. (f) Fused pitch moment coefficient Cm for Mach number 0.5, 0.8 and 0.9.

Figure 10 :

 10 Figure 10: The co-Kriging surrogate model results of AGILE reference aircraft for C L , C D and Cm, with elevator deflection δ = 0 deg. Notations: dot: lo-fi samples; cross: hi-fi samples; line: the response surfaces. Figures (a), (c) and (e): the response surfaces and sampled data over the flight envelope.Figure (b), (d) and (f): the cuts for Mach number 0.5 (black), 0.8(blue) and 0.9 (red) from the response surfaces, and their corresponding sampled data.

Figure 11 :

 11 Figure 11: Final DOEs for building the surrogate models, viewed in a 2D space.

Figure 12 :

 12 Figure 12: Meta information of an example surrogate model available through the SMR. In the text, its is mentioned that this is a SM resulting from the test / experiments.

7. 3 .

 3 Prediction of Flying Qualities from Fused Data 555 The flight performance and flight dynamics are analyzed by PHALANX and compared between the fused data (by co-Kriging from L1 and L2 tools) and the

Figure 13 :

 13 Figure 13: SMR user interface for the "as a service" calculations with the surrogate model

  The propulsion system (thrust and fuel consumption) is modelled based on engine performance maps which are a function of Mach number, altitude and throttle setting. The resulting nonlinear simulation model is used to assess the trim condition (e.g. the prediction of flight envelope limits and power required as function of Mach number) and a handling qualities assessment. The analysis results for various flight conditions and aircraft configurations are written in the CPACS file.

Figure 14b shows the

  Figure 14b shows the throttle setting in trimmed flight as a function of Mach number. The fused data shows a shape which is to be expected. The L1 results are completely wrong at high Mach numbers since it is rather obvious that Tornado cannot predict C D properly at high Mach numbers due to the presence of the wave drag.

( a )

 a Angle of Attack and elevator deflection. (b) The throttle setting.

Figure 14 :

 14 Figure 14: Angle of attack, elevator deflection and the throttle setting between the L1 data and the fused data in the horizontal trimmed flight at 10 km altitude, as a function of Mach number.

Figure 15 :

 15 Figure 15: A step input on the elevator and its dynamic motion for a single Mach number M=0.7.

  each design cycle in the Multidisciplinary Design Optimization (MDO) process by constructing surrogate models from the data produced by variable fidelity analysis tools in the MDO framework. Methods like Kriging, co-Kriging, and adaptive modeling techniques are used for fusing the outputs of each tool. This technique is well established (see for instance the recent review[START_REF] Fernández-Godino | Review of multi-fidelity models[END_REF]) and constitutes its own challenges in applying multi-fidelity MDA in AGILE.

	of data fusion. In AGILE the surrogate models are constructed by different
	methods provided by partners. In the context of this paper the RSM function
	is specified as:
	[force and moment coefficients] = RSM(α, β, Alt, M ach, ..., D)
	In this paper when "multi-fidelity" is referred, we always use the nomencla-
	ture L* to indicate the fidelity Level:
	L0: empirical or handbook method;
	L1: linearized-equation method, e.g. linear aerodynamics, or vortex lattice
	method (VLM) in aerodynamic point of view;
	L2: higher fidelity equation solvers with less simplifications, nonlinear-equation
	methods (e.g. Euler equations solvers);
	L3: highest fidelity equation solvers (e.g. RANS equations).
	To demonstrate a proof of concept, partners in AGILE have formed teams
	to apply data fusion as part of RCE workflows via Brics, which will provide
	data fusion solutions for the whole AGILE MDA system.
	2. Surrogate Models for Data Fusion: the Overall Road Map
	A surrogate model is a cheap-to-evaluate function ŷ = g(x) approximation
	to the exact but expensive-to-evaluate function y = f (x). Another name is
	Response Surface Model (RSM). A used-to-be-well-known example is the table of
	logarithms which reduces arduous exact manual multiplication to much quicker
	approximate calculations by repeated table lookup, interpolation, and addition.
	Data fusion means the integration of results from different simulation models
	into a single surrogate model. Building a surrogate model is a particular form

Table 1 :

 1 The characteristics of short period and phugoid modes comparison between L1 and the fused data for Mach =0.7 at altitude 10 km.

	-	L1	Fused
	ω sp [rad/s] 2.7063 2.3476
	z sp [-]	0.2319 0.2656
	ω ph [rad/s] 0.0766 0.0632
	z ph [-]	0.0084 0.0591

file design study branch, or in two separate column-based csv files;

• Surrogate Modeling Module: The surrogate model builder is provided by different tools/partners. This module also includes the "sampling service". The surrogate modeling techniques are (1) co-Kriging [START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF] provided by Airinnova AB in Matlab based on the DACE toolbox [START_REF] Lophaven | Dace: A Matlab Kriging Toolbox[END_REF], or its alternative Python's built-in persistence Model (scikit-learn), containing the co-Kriging model parameters corresponding to the co-Kriging surrogate trained with incoming training data as described in Section 3.1. The resulting Model file (both Matlab-based and Python built-in) can be read by Python and used by the Py scikit-learn toolbox. So that it can be stored, transferred, shared and re-produced by partners without Matlab license.

(2) Mixture of Experts (MOE) method for surrogate modeling provided by ONERA [START_REF] Bartoli | Improvement of efficient global optimization with mixture of experts: methodology developments and preliminary results in aircraft wing design[END_REF] as an executable file. It will output one (binary) file containing the MOE model parameters corresponding to the MOE surrogate trained with incoming training data. The MOE strategy [START_REF] Bettebghor | Surrogate modeling approximation using a mixture of experts based on EM joint estimation[END_REF][START_REF] Liem | Surrogate models and mixtures of experts in aerodynamic performance prediction for mission analysis[END_REF] recalled in Section 3.2 has been made available to AGILE partners for different applications [START_REF] Lefebvre | Overview of mdo enhancement in AGILE project: a clustered and surrogate-based mda use case[END_REF][START_REF] Lefebvre | Methodological enhancements in MDO process investigated in the AGILE european project[END_REF][START_REF] Bartoli | Robust nacelle optimization design investigated in the AGILE european project[END_REF].

• Aerodynamic Module: In this module the new samples are computed by aerodynamic tools. In this paper, the L1 aerodynamic data are provided by Tornado, which is a Vortex Lattice Method code [START_REF] Melin | Using Internet Interactions in Developing Vortex Lattice Software for Conceptual Design[END_REF]; L2 aerodynamic data are provided by SU2 tool [START_REF] Economon | SU2: An open-source suite for multiphysics simulation and design[END_REF] which is a computational fluid dynamics simulation software. Both of the tools are operated by different specialists at different sites. Other aerodynamic tools can be integrated into this MDA chain by modifying their API to the data fusion package.

Surrogate Model Repository

Many surrogate models of various types have been created in the AGILE project, e.g. to support reuse of knowledge and models, efficient optimization


Margaux Renvoisé

Ludovic Bonhomme

Marlène Davanture

Benoît Valot

Michel Zivy

Claire Lemaire

; Benoit Valot

Quantitative variations of the mitochondrial proteome and phosphoproteome during fermentative and respiratory growth in Saccharomyces cerevisiae

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

Introduction

Mitochondrion is an organelle with multiple functions, the most important of which being to provide energy to the rest of the cell in the form of ATP by oxidative phosphorylation,a process catalyzed by the respiratory enzymes organizedin supercomplexes in the mitochondrial inner membrane [START_REF] Schagger | Supercomplexes in the respiratorychains of yeast and mammalian mitochondria[END_REF][START_REF] Acín-Pérez | Respiratory active mitochondrialsupercomplexes[END_REF]. In humans, deregulation of mitochondrial functions, in particular of the respiratory chain, is associated with several pathologies, including neurodegenerative diseases [START_REF] Su | Abnormal mitochondrial dynamics and neurodegenerative diseases[END_REF][START_REF] Winklhofer | Mitochondrial dysfunction inParkinson's disease[END_REF],neuromuscular diseases [START_REF] Dimauro | Mitochondria in neuromuscular disorders[END_REF], type II diabetes [START_REF] Maechler | Mitochondrial function in normaland diabetic beta-cells[END_REF]and cancer [START_REF] Verma | Proteomicanalysis of cancercell mitochondria[END_REF].In response to metabolic demand or various stresses, theactivity of the respiratory enzymes may be adjusted andseveral levels of regulation could be conceived such as change in the expression level of proteins, reversible inter-action with effectors, or post translational modifications suchas phosphorylation. In plants, phosphorylation was shown to play a regulatory role in response to light conditions by inducing change in the supramolecular organization and the activity of photosynthetic apparatus of the chloroplast,an energyconverting organelle that is related to the mito-chondrion [START_REF] Takahashi | Identificationof the mobile light-harvesting complex II polypeptides forstate transitions inChlamydomonas reinhardtii[END_REF]. The steadily increasing number of known mitochondrial phosphoproteins, kinases and phosphatases suggests that reversible protein phosphorylation could be an important level of regulation in mitochondria [START_REF] Bodenmiller | Phosphoproteomic analysis reveals interconnectedsystem-wide responses to perturbations of kinases andphosphatases in yeast[END_REF]and couldbe partly responsible for an adaptation to environmental change as it is the case for chloroplasts [START_REF] Schonberg | Signal integration by chloroplastphosphorylation networks: an update[END_REF].Testing such hypothesis cannot be considered without quantitative data on the variations of mitochondrial protein amounts and their level of phosphorylation under several growth conditions.The yeast Saccharomyces cerevisiaeis a powerful tool to study various energetic and physiological states as it is a facultative aerobe which can grow either on fermentative substrate such as glucose or galactose or on respiratory substrate such as lactate. Few global quantitative phosphoproteomic and proteomic studies have been carried on yeast grown on different carbon sources but mostly on whole cell extracts [START_REF] Oliveira | Regulation of yeast central metabolism by enzymephosphorylation[END_REF][START_REF] Griffin | Complementary profiling of gene expression at thetranscriptome and proteome levels in Saccharomycescerevisiae[END_REF]and the lack of subfractionation limited the access of information on mitochondrial proteins. Two qualitative studies focused on a subset of mitochondrial proteins, but the use of 2D gel electrophoresis [START_REF] Ohlmeier | Theyeast mitochondrial proteome, a study of fermentative andrespiratory growth[END_REF][START_REF] Ohlmeier | Protein phosphorylationin mitochondria. A study on fermentative and respiratorygrowth of Saccharomyces cerevisiae[END_REF]limited the access to hydrophobic orbasic proteins and to those of very high or very low molecular weight. In this paper, we present for the first time a quantitative study of both protein abundance and phosphorylation levels in isolated yeast mitochondria, under respiratory (lactate medium)or fermentative conditions with two different substrates(glucose and galactose). We performed a subcellular fraction-ation to focus our analysis specifically on the mitochondrial proteins and used LC-MS/MS to overcome the limitations of 2D gel electrophoresis [START_REF] Pflieger | Systematic identification of mitochondrial proteinsby LC-MS/MS[END_REF][START_REF] Sickmann | The proteome ofSaccharomyces cerevisiae mitochondria[END_REF][START_REF] Reinders | Toward the complete yeast mitochondrial proteome:multidimensional separationtechniques for mitochondrialproteomics[END_REF]. Protein abundances were quantified using a label free method. The quantitative analysis of the phosphoproteome was carried out by using the multiplex stable isotope dimethyl labeling procedure [START_REF] Boersema | Multiplex peptide stable isotope dimethyl labeling forquantitative proteomics[END_REF]. Forall quantified phosphopeptides, protein abundance measurements were performed allowing normalization of the data and providing a way to analyze the specific variation of phosphorylation status independent of the protein abundance changes.

Finally, this study allowed us to obtain a reliable description of the adaptation of the yeast mitochondrial proteome and phosphoproteome to different carbon sources.

Material and methods

Cell culture of yeast

The yeast wild strain W303 (aade2-1 ura3-1 his3-11,15 trp1-1leu2-3,112 can1-100) was grown either in 2% glucosemedium (YPGA) to an OD$_{ nm}$= 6, or 2% galactose medium (YPGAL)to an OD$_{600}$ nm= 6 or 2% lactate medium (YLAC) to an OD$_{600}$ nm=4.5 media as described in Lemaire and Dujardin [START_REF] Lemaire | Preparation of respiratory chaincomplexes fromSaccharomyces cerevisiaewild-type andmutant mitochondria: activity measurement and subunitcomposition analysis[END_REF]. Four independent biological replicates were performed in each growth condition, leading to 12 samples in total.

.

Extraction of mitochondria

Extraction of mitochondria was performed using the protocol originally developed by Meisinger et al. [START_REF] Meisinger | Purification ofSaccharomycescerevisiaemitochondria devoid of microsomal and cytosoliccontaminations[END_REF]and widely used in proteomic studies in yeast (see Reinders et al., [START_REF] Reinders | Profiling phosphoproteins of yeastmitochondria reveals a role of phosphorylation in assemblyof the ATP synthase[END_REF]). Briefly, crude mitochondrial fraction was prepared by differential centri fugation and adjusted to a protein concentration of 5 mg/mL in250 mM sucrose/1 mM EDTA/10 mM Mops, pH 7.2. After treat-ment with 10 pestle strokes in a glass-Teflon potter, mitochondria were loaded on top of a three-step sucrose gradient. The proteins were then precipitated by 10% TCA, washed by acetoneandstoredat-20 °C.

Stable isotope dimethyl labeling of trypsic peptides

Trypsic digest of each sample was dried by vacuum centrifugation and re-suspended in 1 mL of 5% formic acid. Trypsic peptides were labeled on column by multiplex stable isotope dimethyl labeling procedure as described in Boersema [START_REF] Boersema | Multiplex peptide stable isotope dimethyl labeling forquantitative proteomics[END_REF]. Briefly the peptides are labeled on their primary amines which are converted to dimethylamines. Several isotopomers of formaldehyde and cyanoborohydride were used to add a specific mass [START_REF] Lagunas | Misconceptions about the energy metabolism ofSaccharomyces cerevisiae[END_REF]32 Twenty four percent of the identified peptides were phosphorylated in the enriched fractions. This result shows that the enrichment was very effective, since only 4 phosphopeptides can be detected in non-enriched samples. Interestingly, 88% of the unphosphorylated peptides contained at least one Asp or Glu, which confirms the known limit of the IMAC methodology with regards to the strong affinity for acidic peptides.

LC-MS/MS analysis

Each sample was resuspended in 20μL of 0.1% formic acid in 2%ACN (solvant E) then 4μLwere loaded at 7.5μL/min on a pre-column cartridge (stationary phase: C18 PepMap 100, particles of 5μm; column: 100μm i.d., 1 cm length; Dionex) using a Nano LC-Ultra system (Eksigent, AB SciEX Massachusetts, USA).Peptides were desalted with solvent E during 3 min and loaded on a separating PepMap C18 column (stationary phase C18PepMap 100, particles of 3μm; column 75μm i.d., 150 mm length; Dionex) prior to gradient chromatography. The buffers used were 0.1% formic acid in water (solvent F) and 0.1% formicacid in ACN (solvent G).

A 37 min-long linear gradient from 5 to30% G at 300 nL/min was used for peptide separation. Including the regeneration step at 95% G and the equilibration step at 95%F; each run took 45 min. Eluted peptides were analyzed with a Q-Exactive mass spectrometer (Thermo Electron, Courtaboeuf, France) using a nano-electrospray interface. Ionization was performed with a 1.3-kV spray voltage applied to an uncoated capillary probe (10μi.d.; New Objective, Woburn, MA, USA). Xcalibur 2.1 interface was used to monitor data-dependent acquisition of peptide ions. This included a full MS scan covering the 300 to 1400 mass-to-charge ratio (m/z) with a resolution of 70,000 and a MS/MS step (normalized collision energy: 30%; resolution: 17,500). The MS/MS step was reiterated for the 8 major ions detected during the full MS scan. The dynamic exclusion was set to 45 s. For the analysis of total protein content, 1μg of digest from each of the 12 samples was directly submitted to LC-MS. The methods were thesame as those described for phosphopeptides, except that the duration of the LC gradient separation was increased to 1 h.

Identification of peptides and phosphorylation sites

Database searches were performed using X!Tandem CYCLONE (http://www.thegpm.org/TANDEM). Cys carboxyamidomethylation and light, intermediary and heavy dimethylation of peptideN-termini and lysine residues were set as static modifications while methionine oxidation and phosphorylation of tyrosine were set as variable modifications. Serine and threonine residues phosphorylation was search as variable modification motifs including phosphate loss. Precursor mass tolerance was10 ppm and fragment mass tolerance was 0.02 Th. Identifications were performed using the Saccharomyces Genome Database, (http://www.yeastgenome.org/, release number: R63-1-1, release date: 20100105, S288C_reference_genome_R63-1-1_20100105) to which common contaminants were added. Identified proteins were filtered and grouped using the X!Tandem pipeline v3.3.0 (http://pappso.inra.fr/bioinfo/xtandempipeline/). Data filtering was achieved according to a peptide E value smaller 0.01. Using such a thre shold, the false discovery rate (FDR) was estimated to 0.5%.

Relative quantification of peptides and proteins

Mass ChroQ [START_REF] Valot | MassChroQ: a versatiletool for mass spectrometry quantification[END_REF] was used for the a lignment of LC-MS runs and peptide quantification by integration of extracted ion current (10 ppm window) in the peak detected at the expected retention time.

Normalization was performed to take into account possible global variations between samples: for each LC-MS run the ratioof all peptide values to their value in a chosen reference LC-MS run was computed, and normalization was performed by dividing peptide values by the median value of peptide ratios. Only peptides which have been quantified in at least 3 replicates per condition were kept for protein quantification.

Only proteins quantified with at least two peptides were kept. Statistic tests were performed on log10-transformed data. The effect of growth condition on each protein was tested by using its normalized peptide values in a mixed model of analysis of variance, with growth conditions as a fixed effect and the peptides and the sample as random effects. We used thefdrtool library of the R package to compute the classical False Discovery Rate [START_REF] Benjamini | Controlling the false discovery rate:a practical and powerful approach to multiple testing[END_REF]. The effect of the growth condition was considered significant when the q-value (False Discovery Rate adjusted p-value) was <0.01.

Relative quantification of phosphopeptides and statistical analyses

As for the analysis of protein abundance, the quantification of phosphopeptides was performed using MassChroQ [START_REF] Valot | MassChroQ: a versatiletool for mass spectrometry quantification[END_REF].The alignment was performed between LC-MS/MS runs originating from the same SCX fraction of the different replicates. In the following, a replicate designates the mix of 3 samples corresponding to 3 different growth conditions, each sample being labeled with a different isotope, and a triplex designates the set of isotopes for a same m/z in the same fraction. As there were 12 SCX fractions, each replicate was represented by12 LC-MS runs. For a given peptide, a triplex in a fraction was quantified only when at least 2 isotopes were detected. For normalization, we used a method similar to the one used forprotein quantification, i.e. based on the principle that the median ratio between isotopic peptides within a replicate (i.e. within amix of 3 samples labeled with different isotopes) must be equal to 1 [START_REF] Bonhomme | Phosphoproteomedynamics upon changes in plant water status reveal earlyevents associated with rapid growth adjustment in maizeleaves[END_REF].Afterlog10-transformation of normalized data, phosphopeptide variations according to the growth condition were determined by using a mixed model of analysis of variance with the treatment (i.e. the corresponding isotope)as a fixed effect and with the triplex and replicate as random effects. Finally, the relative level of phosphorylation of a protein was computed by dividing the phosphopeptide by the unphosphorylated protein content estimated by the twoANOVA models.

As phosphopeptides and peptides used tomeasure protein abundance are different, the computed ratiodoes not represent a real estimation of the relative level of protein phosphorylation, but this normalization allowed making the phosphorylation value independent from protein amount variation. A simple ANOVA model was used to analyze changes, with only the growth condition as a fixe deffect. It was considered significant when the FDR adjusted p-value was <0.05. The analysis of qualitative variations was based on the detection of MS peaks. A K-means clustering was done on proteins whose abundance changed significantly according to growth conditions. Another was done on phosphorylation sites whose level varied according to growth conditions. For these 2 K-means analyses,the dissimilarity criterion was the Pearson correlation and the maximal iterations were 50.

Results and discussion

Variations of mitochondrial protein abundances during fermentative and respiratory growth

We quantified 724 proteins, of which 75% (544 proteins) were known to be mitochondrial proteins and only these were used for further data treatment (see Supplemental data S1). Theother 25% proteins were essentially from the polysomes (11%)which are known to be bound to mitochondria [START_REF] Margeot | Why are many mRNAs translated to the vicinity ofmitochondria: a role in protein complex assembly? GeneCross-Talk between Nucleus and Organelles[END_REF]. The other contaminants were essentially of cytoplasmic (8%) or nuclear (2%) origin. Among these 724 proteins, the abundance of 368 displayed no change according to the growth medium while 176 proteins varied significantly. A classification was performed on this set of 176 proteins which defined 4 clusters (Fig. 1 and Supplemental data S2).

For each cluster, the different abundance factors relating to the three growth media were compared pair wise (see Table 1). This approach allowed defining two major groups (see Fig. 1andTable 1) showing that the most extreme differences are between glucose and lactate media. One group includes proteins more abundant in glucose than in lactate by a factor varying between 1.9 and 7.5 (cluster 1; 68proteins i.e. 39%). The second group is defined by proteins more abundant in lactate than in glucose (clusters 2 to 4; 108 proteinsi.e. 61%) with an average abundance factor varying from 0.26 to0.42. Interestingly, we highlighted significant differences between the two fermentative substrates studied as, in most ofthe cases (clusters 1 to 3), protein abundance in galactosemedium displays a different pattern than in glucose medium(average abundance factor varying from 0.55 to 2.9). In clusters 1and 3, the galactose medium was intermediary between the glucose and lactate media. In cluster 2, the same pattern is observed for galactose and lactate. Finally, cluster 4 is the onlyone which contained proteins whose abundance in galactose and glucose were almost similar. Few studies have already compared protein amounts between fermentation and respiration at the steady-state level [START_REF] Griffin | Complementary profiling of gene expression at thetranscriptome and proteome levels in Saccharomycescerevisiae[END_REF][START_REF] Futcher | Asampling of the yeast proteome[END_REF][START_REF] Prokisch | Integrative analysis of the mitochondrial proteome inyeast[END_REF]. Moreover these analyses were performed on whole cell extracts and only some few data on mitochondrial proteins were found.

Our study allows for the first time a noverall comparison of mitochondrial protein abundances in fermentation and respiration together with a deeper analysis of differences between two fermentative substrates which suggest that galactose could be finally considered as a substrate displaying an intermediate metabolism between fermentation (glucose medium) and respiration (lactate medium). This is supported by the data indicating that the contribution of respiration has been shown to be larger during growth on galactose than in glucose [START_REF] Lagunas | Misconceptions about the energy metabolism ofSaccharomyces cerevisiae[END_REF] Fig. 1-Significant changes of protein abundances according to the substrate. Pie graph of the clusters built for proteins whose abundance was significantly affected by the substrate (K-means clustering) (G = glucose; Gal = galactose; L = lactate). Box plots are depicted beside their respective shares. The number of proteins associated to each of the four defined clusters is given.

The protein composition of the clusters will be presented and discussed later in the section concerning the comparison between variation of mitochondrial protein abundances and protein phosphorylation according to their metabolic path-ways. To facilitate this comparison, the clusters were defined by their major trend. Cluster 1 was considered as lactate$^-$(LAC$^-$), clusters 2 and 3 were gathered and defined as glucose$^-$ (GLU$^-$) and cluster 4 as lactate$^+$ (LAC$^+$). The mitochondrial phosphoproteome of yeast cultivated in three different sources of carbon was investigated using the multiplex stable isotope dimethyl labeling procedure for relative quantification which labeling efficiency was estimated between 93 and 97.7%. Our mitochondrial phosphoproteome analysis led to the identification of 670 phosphorylation sites, observed in at least one of the 12 samples (Supplemental dataS3, S4 and S5). Ninety eight percent of the spectra that identified the same phosphopeptide were found in at most three SCX fractions and 50% were found in the same fraction. The phosphopeptides were identified in 299 proteins of which 150 displayed one site of phosphorylation, 72, two sites, 27,three sites and 50, four sites or more (http://moulon.inra.fr/protic/yeast_mitochondria,http://www.proteomexchan ge.organd Supplemental data S3). In total, 71% of them were serine,16% were threonine and 0.6% were tyrosine. 12.4% of the residues could not be precisely localized in the peptide sequence.

Mitochondrial protein phosphorylation display qualitative and quantitative variations between fermentative and respiratory growth

We considered here only the 289 phosphosites which were present in at least 3 biological replicates in 1, 2 or 3 conditions (Supplemental data S6 and S7). Among them, 214 were notidentified in previous studies [START_REF] Oliveira | Regulation of yeast central metabolism by enzymephosphorylation[END_REF][START_REF] Reinders | Profiling phosphoproteins of yeastmitochondria reveals a role of phosphorylation in assemblyof the ATP synthase[END_REF][START_REF] Amoutzias | Evaluation and properties of the budding yeastphosphoproteome[END_REF] (Supplemental data S6). Thus our present work enlarges significantly the map of yeast mitochondrial phosphosites.

Variations in the three growth conditions

Among the 289 phosphosites reproducibly quantified in 1, 2 or 3conditions, the majority (238 phosphosites) were reproducibly quantified in the three growth conditions and were subjected to quantitative examination using analysis of variance. To estimate as precisely as possible the variations of protein phosphorylation independent of protein amount variations, all phosphopeptide data were normalized according to protein abundance by dividing the phosphopeptide quantitative values by the protein abundance values. The mean coefficient of variation of the log$_{10}$-transformed ratio was 1.86%.

39 phosphorylation sites significantly varied according to carbon substrate (Supplemental data S8) while 199 displayed no significant change under our experimental conditions (Supplemental data S9). A classification based on the normalized quantification of these 39 phosphorylation sites was performed (Fig. 2 and Supplemental data S10). We could isolate five clusters of phosphorylation sites. Clusters P1 to P4 displayed the same pattern as those observed for the clusters 1 to 4 defined for protein abundances. Indeed, the abundance factors of the phosphopeptides were of the same order of magnitude thanthose of protein abundances for a given cluster (seeTable 2). An additional cluster P5 included three sites that were less phosphorylated in galactose than in glucose (a decrease by a factor 5) and lactate (a decrease by a factor 2.5). This suggests that a specific regulation could occur in galactose, independently from the two other conditions.

Variations in one or two growth conditions

In addition to the 238 sites reproducibly quantified in thethree growth conditions, we also observed 51 sites showing avariation in 1 or 2 conditions as they were absent in the 4biological replicates of the(se) condition(s) (seeTable 3).In the following sections, we gathered phosphorylation sitesdisplaying variations either in one or two growth conditions (51 residues,Table 3) or in the three simultaneously (39 residues, Supplemental data S5). As for the protein abundances, we grouped the sites according to their major trend. The 29 sites detected only in glucose and/or galactose and the 7 sites of cluster P1 were considered as LAC$^-$, the 16 sites detected onlyin lactate and galactose and 24 sites of clusters P2 + P3 as GLU$^-$; the 2 sites only detected in lactate and glucose and the 3 sites of cluster P5 as GAL$^-$ and finally the 4 only detected in lactate andt he 5 sites of cluster P4 as LAC$^+$.

Table 2-Variations of phosphopeptide abundancesaccording to the cluster. The mean and standard deviationof the ratio between the abundance in one condition andthe abundance inthe otherareshown for every comparisonbetween two substrates and for every cluster.

Glucose

Variations of mitochondrial protein abundances and protein phosphorylation according to their metabolic pathways

Proteins whose amounts vary according to conditions wereassociated with the main metabolic pathways (Fig. 3, panel A) according to the MIPS functional classification ((http://mips.helmholtz-muenchen.de/genre/proj/yeast/) and SGD Fig. 2-Significant changes of phosphorylation level according to the substrate for the 39 varying residues quantified in the 3growth conditions. Pie graph of the clusters built for phosphorylation sites whose abundance was significantly affected by thesubstrate (K-means clustering) (G = glucose; Gal = galactose; L = lactate). Box plots are depicted beside their respective shares. The number of phosphorylation sites associated to each of the five defined clusters is given.

(http://www.yeastgenome.org/) The pathways were affecteddifferentially and two major patterns could be identified. Firstly, proteins involved in protein fate, amino acid metabolism, transport, C-compound and carbohydrate, vitamins and cofac-tors metabolism were mainly LAC-. Secondly, proteins involvedin energy, protein synthesis and mitochondria biogenesis were Fig. 3-Regulation of proteins abundance and protein phosphorylation status for different metabolic pathways. Distribution ofvarying proteins (A) and varying phosphorylation sites (B) in their 4 trends of regulation (LAC-, GLU-, LAC+, GAL-) for everymetabolic pathway. For every metabolic pathway, the number of proteins and the number of phosphorylation sites associatedto each trend are precised mostly GLU-. For the other pathways (lipid metabolism, cellrescue, defense and virulence, nucleotide metabolism, cell cycleand DNA processing) the proteins did not appear to be groupedin any specific cluster, or the number of the proteins observedwas too small to reach any significant conclusion. Accordingly, the metabolic pathway displaying the most variation of proteinamount was energy metabolism that included enzymes of therespiratory chain and TCA cycle. They were all GLU-, i.e. moreabundant in lactate and less in glucose, but differed by theirabundance in galactose medium. It was of particular interestto note that the external NADH dehydrogenase Nde1p, theinhibitory peptide of the ATP synthase Inh1p and the TCA cycleenzyme Cit1p are accumulated in galactose medium, contraryto their respective functional homologs Nde2p, Stf1p and Cit3p (78%, 79% and 62% of homology, respectively). This suggests that growth in galactose medium might require the specific function of one specific homolog. Phosphorylation sites whose status changed according tothe carbon substrate were also associated with the metabolicpathway of the protein containing the residue (Fig. 3, panel B). Proteins of energy metabolism show the highest number ofquantified sites displaying different phosphorylation levels. They were mainly dephosphorylated under glucose conditions. The other metabolic pathways did not show a general trend.

Our analysis gives deeper results on the mitochondrialchanges at both proteomic and phosphoproteomic levelsfor every metabolic pathway. The most regulated metabolicpathway at both proteomic and phosphoproteomic levelswas energy metabolism with 60 proteins exhibiting differentabundances according to conditions and 28 phosphosites (20 phosphoproteins) showing different levels of phosphorylationas a function of growth medium. As the accumulation ofthe respiratory complexes has been shown to be modified infermentescible conditions compared to a respirable one [START_REF] Schagger | Supercomplexes in the respiratorychains of yeast and mammalian mitochondria[END_REF], we particularly focused our attention on the regulation ofproteins involved in the respiratory chain. Interestingly, it mustbe noted that most of the protein chaperones involved in theassembly of the respiratory complexes were not regulatedin the same way as the OXPHOS proteins, as no significantvariation in their amount has been detected on the threedifferent carbon sources (see Supplemental data S1).3.4. Phosphorylation of proteins belonging to the oxidativephosphorylation display major variations between fermentativeand respiratory growth and phosphorylation regulation is site-dependent 31 proteins involved in the respiratory chain were reproduciblyquantified in the 3 growth conditions and showed different abundances according to the condition (Table 4). They are all GLU-, i.e. more abundant in lactate compared to glucose, whichaccount for an increase in the oxidative phosphorylation during growth in respiratory conditions.19 of these proteins were phosphorylated, displaying 37 phosphosites, which suggests an important role of phosphorylation in the regulation of the respiratory chain (Table 4). 12 of these residues located on 7 proteins exhibited a varyinglevel of phosphorylation depending on the carbon source. Formost of them, the level of phosphorylation globally varied inthe same direction as protein amounts, as proteins were more abundant and more phosphorylated in respiratory conditions, except for 2 proteins. Rip1p was more abundant in lactate but more phosphorylated in glucose. Atp2p was also more abundant in lactate, but showed different phosphorylation patterns according to the residue: one residue was more phosphorylated in lactate (T43) but the two others (S35 and T40) were specifically less phosphorylated in galactose. Interestingly, 2 proteins (Cor1p and Atp2p) displayed several phosphorylation sites that were differentially regulated according to the substrate. Thus the variation of phosphorylation according to carbon substrate was site-dependent and not protein-dependent. Considering the position of the phosphosites on thecomplexes, most of the 37 quantified phosphosites are located on the matrix side, where the extra membrane parts of the complexes predominate while only one site, localized on Rip1p, is located in the intermembrane space (Fig. 4).

When it was possible to look at the precise position in the structure, for Atp2p for example, we observed that the phosphorylation sites were at the periphery of the subunit which is in agreement witha good accessibility to kinases. Relations between kinases and their targets are still poorly documented in mitochondria: in particular for the mitochondrial proteins encoded by the nucleus, the question to know if phosphorylation occurs before or after their translocation to the mitochondria can be asked However, some kinases have been shown to be located in the mitochondria (e.g. pyruvate dehydrogenase kinase [START_REF] Muller | Protein phosphorylation in yeastmitochondria: cAMP-dependence, submitochondriallocalization and substrates of mitochondrial proteinkinases[END_REF] and protein kinase B, that phosphorylates Atp2p [START_REF] Bijur | Rapid accumulation of Akt in mitochondriafollowing phosphatidylinositol 3-kinase activation[END_REF]) which seems rather in favor of a regulation within the organelle. Phosphorylation site of Inh1p is not localized in its structure since only bovine structure of Inh1p is available.

We have been able for the first time to quantitatively analyze variations of respiratory chain at proteomic and phosphoproteomic levels during a change in carbon source. Among the 37 phosphorylation sites discussed here, 34 have not been described yet (see Supplemental data S4). The comparison of these modifications suggests an important role for phosphorylation in the regulation of the respiratory complexes and this study is essential to target the phosphorylation sites which may be involved in this process. Some phosphorylation sites, located on Rip1p and Atp2p, are of particular interest since modifications of protein abundances and of phosphorylation levels are not on the same way and further experiments to elucidate the role of these residues are currently under investigation

Conclusions

We performed a combined approach of quantitative proteomic and phosphoproteomic analysis of mitochondria from yeast grown on three different carbon sources: glucose, galactose and lactate. We highlighted significant differences of the proteome between the two fermentative substrates studied which suggest that galactose could be finally considered as a substrate displaying an intermediate metabolism between fermentation (glucose medium) and respiration (lactate medium). Proteins involved in a same metabolic pathway seem to exhibit a specific pattern of accumulation among the carbon source. The most regulated metabolic pathway at both proteomic and phosphoproteomic levels was energy metabolism ant particularly the proteins involved in oxidative phosphorylation. They are all more abundant in lactate and less in glucose but some differs by their abundance in galactose. Their phosphorylation level also varies according to the carbon substrate mostly in the same way as the protein accumulation with a few exceptions. Our extensive study provides for the first time confident quantitative data on mitochondrial phosphosites responses to different carbon substrates. It is a step forward in the analysis of regulation of mitochondrialproteins by phosphorylation.

[

FIG. 4

 4 FIG. 4Localization of phosphorylation sites on yeast OXPHOS proteins whose abundance vary according to conditions. The presented phosphoproteins exhibited different abundance according to growth conditions. Their phosphorylation sites also displayed either a consistent qualitative variation or a significant quantitative variation. Residues represented by a yellow point are those more phosphorylated in respiratory medium. The one in green has a higher level of phosphorylation in glucose medium. Those in gray are less phosphorylated in galactose, specifically. C II = succinate ubiquinone reductase. C III = ubiquinone cytochrome c reductase. C IV = cytochrome c oxidase. C V = ATP synthase. Respiratory complexes presented in their dimeric form are noticed by a subscript 2. Phosphorylation site of Inh1p is not localized in its structure since only bovine structure of Inh1p is available.

Table 1 -

 1 Variations of protein abundances according to the cluster. The mean and standard deviation of the ratio between the abundance in one condition and the abundance in the other are shown for every comparison between two substrates and for every cluster.

		Glucose/lactate Galactose/lactate Galactose/glucose
	Cluster 1	4.7 ± 2.8	2.0 ± 0.58	0.55 ± 0.09
	Cluster 2	0.42 ± 0. 08	0. 92 ± 0.11	2.5 ± 0.67
	Cluster 3	0.26 ± 0.08	0.57 ± 0.09	2.9 ± 0.72
	Cluster 4	0.28 ± 0.12	0. 32 ± 0.11	1.4 ± 0.30

Table 3

 3

		/lactate Galactose/lactate Galactose/glucose
	Cluster P1	4.5 ± 1.5	2.1 ± 0 24	0.60 ± 0.15
	Cluster P2	0.37 ± 0.08	1.1 ± 0.18	3.4 ± 0.67
	Cluster P3	0.44 ± 0.50	0.45 ± 0.18	2.2 ± 0.44
	Cluster P4	0.18 ± 0. 04	0.21 ± 0.06	1.1 ± 0.11
	Cluster P5	2.8 ± 1.1	0. 42 ± 0.0	80. 20 ± 0. 05

Table 4 -

 4 32]Vizcaino JA, Cote RG, Csordas A, Dianes JA, Fabregat A, FosterJM, et al. The PRoteomics IDEntifications (PRIDE) database andassociated tools: status in. Nucleic Acids Res 2013;41:D1063-9. Phosphorylation of OXPHOS proteins whose abundance change according to growth conditions. Phosphorylationsites displaying a significant quantitative variation were noted in bold with 1 asterisk and those displaying a consistentqualitative variation were noted in bold with 2. Positions of the phosphorylated amino acids were determined fromprecursor proteins. Phosphorylation sites unambiguously located on the peptide sequence are indicated in bold and by p inthe sequence. Otherwise, the different possibilities are noted in the sequence.

	ORF	Gene	Phosphorylation site Group of regulation	Phosphopeptide
				for level of phosphorylation
	YML120C	NDI1	S27	pSpTGVENSGAGPTSFK

Acknowledgments

This work has received financial support and encouragements from Pr Marc Le Maire and particularly from Dr Bruno Robert.We are grateful to Dr Francis Haraux for helpful discussions since the beginning of the project and for the design of the yeast respiratory chain presentedin Fig. 4. We thank Mehdi Lembroukand Thierry Balliau for technical assistance and Aurélie Stanislas for the achievement of the preliminary experiments.We acknowledge Dr Patrice Hamel and Dr Andrew Gall for critical reading of the manuscript. We thank Pr Alexander Tzagoloff, Dr Manuel Garrigos and Dr Andy Pascal for their support. We thank Attila Csordas and the PRIDE team for their assistance in making the data available in the PRIDE repository.This work was supported by the International PhD Program forLife Science of CEA (IRTELIS) for which we sincerely thank Dr Christophe Carles.

Appendix A. Supplementary data

All the data on the protein and phosphopeptide identification are available on the following link:http://moulon.inra.fr/protic/yeast_mitochondria (login: mitochondria/password:review) The mass spectrometry proteomics data have been also deposited to the ProteomeXchange Consortium (http://www.proteomexchange.org) via the PRIDE partner repository [32] with the data identifiers PXD000714 and PXD000735 Projectname: Quantitative variations of the mitochondrial proteome and phosphoproteome during fermentative and respiratory growth in Saccharomyces cerevisiae. Supplementary data to thisarticle can be found online athttp://dx.doi.org/10.1016/j.jprot.2014.04.022.