Yann Traonmilin
email: yann.traonmilin@telecom-paristech.fraguerreb@telecom-paristech.fr

Cecilia Aguerrebere

Simultaneous High Dynamic Range and Super-Resolution Imaging Without Regularization

Keywords: super-resolution, high dynamic range, regularization

Modern digital cameras sensors only capture a limited amplitude and frequency range of the irradiance of a scene. A recent trend is to acquire and combine multiple images to raise the quality of the final image. Multi-image techniques are used in high dynamic range processing, where multiple exposure times are used to reconstruct the full range of irradiance. With multi-image super-resolution, the difference between sampling grids caused by the motion of the camera is used to generate a high resolution image. It is possible to combine these two processes into one to generate a super-resolved image with a full dynamic range. In this paper, we study the reconstruction error of high dynamic range super-resolution imaging without regularization, under affine motion hypothesis. From this study, we deduce a strategy for the choice of the number of images and the exposure times which makes the unregularized problem well conditioned. With these acquisition parameters, if the affine motion hypothesis holds and sufficiently long exposure time is available, the recovery of all the amplitude and frequency content of the scene irradiance is guaranteed.

1. Introduction. Limitations of digital cameras sensors restrict the information that a single image can possibly gather. In particular, the spatial sampling and the dynamic range of an image are limited. Restrictions on spatial sampling result in aliased images. Scenes with high dynamic range have over or under-exposed image regions because of the sensor's limited potential well capacity. A way to overcome these two problems is to improve spatial and dynamic range sampling by acquiring and combining several images of the scene. Motion between shots gives a spatial sampling diversity that allows for a high resolution reconstruction of the scene. The process of recovering a high resolution (HR) image from several low resolution (LR) ones is called super-resolution imaging (SR). The dynamic range limit can be extended by using different exposure times or gains between images. This process is called high dynamic range imaging (HDR). These two processes need to be combined in order to recover the high frequency and high dynamic range information of the scene.

Super-resolution algorithms have been reviewed in several works [START_REF] Farsiu | Advances and challenges in super-resolution[END_REF][START_REF] Milanfar | Super-resolution imaging[END_REF][START_REF] Tian | A survey on super-resolution imaging[END_REF]. Most of them can be summarized with a variational approach. The HR image is recovered by minimizing a regularized data-fit functional. This data-fit is usually an L p norm fit. From Tychonov to total variation, many regularization functionals are available. Such regularization is necessary when little information is available (i.e., a small number of images). The resulting interpolation must be considered as an inpainting using a regularity model and not as the recovery of missing high frequency information as the scene might not verify the regularity hypothesis. It has been shown [START_REF] Champagnat | Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework[END_REF][START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF] that regularization becomes less useful when a large number of images are available. It is then possible to reconstruct the real high frequency content of the acquired scene by minimizing only the L 2 -norm data-fit.

Several HDR image generation algorithms have been proposed since the seminal work by Mann and Picard [START_REF] Mann | On being 'undigital' with digital cameras: Extending dynamic range by combining differently exposed pictures[END_REF]. For static scenes, when the input images can be perfectly registered, the irradiance at each pixel is computed as a weighted average of the corresponding samples acquired with different exposure times or gains. Based on this idea, several methods have been proposed following different weighting schemes [START_REF] Aguerrebere | Best algorithms for HDR image generation. a study of performance bounds[END_REF][START_REF] Debevec | Recovering high dynamic range radiance maps from photographs[END_REF][START_REF] Granados | Optimal HDR reconstruction with linear digital cameras[END_REF][START_REF] Hasinoff | Noise-optimal capture for high dynamic range photography[END_REF][START_REF] Kirk | Noise characterization of weighting schemes for combination of multiple exposures[END_REF][START_REF] Mitsunaga | Radiometric self calibration[END_REF][START_REF] Reinhard | High Dynamic Range Imaging -Acquisition, Display, and Image-Based Lighting[END_REF]. However, accurate realignment of aliased images is difficult because it is impossible to correctly apply a geometric transformation to well-sampled details and aliased patterns at the same time. Thus a joint HDR-SR method is needed.

In recent years, some algorithms have been proposed to perform SR and HDR simultaneously. The most conventional approach is to use a weighted least squares scheme, as normally done for SR, but on the irradiance [START_REF] Choi | High dynamic range image reconstruction with spatial resolution enhancement[END_REF][START_REF] Gunturk | High-resolution image reconstruction from multiple differently exposed images[END_REF] or transformed irradiance domain [START_REF] Bengtsson | Regularized optimization for joint super-resolution and high dynamic range image reconstruction in a perceptually uniform (a) (b) Figure 6.8. Detail of HDR-SR with 60 images (a) detail of Figure 6.7(c), ([END_REF]. A different approach [START_REF] Zimmer | Freehand HDR imaging of moving scenes with simultaneous resolution enhancement[END_REF] is to align LR images using optical flow and minimize a regularized energy to achieve the combined HDR-SR reconstruction. Rad et al. [START_REF] Ajdari | Multidimensional image enhancement from a set of unregistered differently exposed images[END_REF] propose to first align the input images and then use a Delaunay triangulation and bi-cubic interpolation to perform the HDR-SR estimation on the irradiance domain. The combined problem has also been studied from a sensor design perspective, with proposed solutions based on specifically adapted sensors [START_REF] Nakai | High resolution and high dynamic range image reconstruction from differently exposed images[END_REF][START_REF] Srinivasa | Enhancing resolution along multiple imaging dimensions using assorted pixels[END_REF].

An aspect common to all these methods is the use of a regularization term, which threatens multi-image super-resolution in terms of high frequency recovery capability. The recovery of the spectrum of the real HR scene cannot be guaranteed. Moreover, the latest results for HDR image generation [START_REF] Aguerrebere | Best algorithms for HDR image generation. a study of performance bounds[END_REF], such as the near optimality of the weighting scheme proposed by Granados et al., are not exploited. To the best of our knowledge, the theoretical background of this problem, necessary to ensure the recovery of HDR and HR content, has not been studied in depth.

1.1. Contributions. In this paper, we study the HDR-SR imaging problem from the following perspective: which image acquisition configuration, i.e. number of acquired images and exposure times, guarantees that the high frequencies and the full dynamic range of a scene will be recovered? We use a realistic camera acquisition model with affine motion hypothesis and propose an image reconstruction method that includes the weighting scheme shown to be nearly optimal for HDR information recovery [START_REF] Aguerrebere | Best algorithms for HDR image generation. a study of performance bounds[END_REF]. We study theoretical bounds for the joint HDR-SR reconstruction error and find that a trade off must be made between the total exposure time and the number of images. This result is illustrated with synthetic and real data experiments. Moreover, we show how exposure times can be selected and that this selection can be decoupled from the SR problem to fulfill our objective. This analysis leads to the proposal of an acquisition strategy which, if the affine motion hypothesis holds and sufficiently long exposure time is available, guarantees the recovery of the full dynamic range and high frequency content of the scene irradiance. Finally, experiments with real data show that our HDR-SR strategy manages to recover this information.

The article is organized as follows. Section 2 introduces the image acquisition model and the reconstruction method. In section 3, the strategy for the choice of exposure times and number of images is presented. Section 4 is devoted to the study of the reconstruction error bounds. In Section 5, we show how exposure times can be selected. An optimal acquisition strategy and its corresponding experimental validation are presented in Section 6. Finally, conclusions are stated in Section 7.

HDR-SR acquisition and reconstruction.

2.1. Acquisition model. We consider a monochromatic irradiance acquisition model with different exposure times for each raw low resolution image w i (we suppose that they are square of size l × l). The acquisition operator A is defined as

A : R M l×M l → R N ×(l×l) u → (w i ) i=1,...,N = (Ω i G i SQ i u) i=1,...,N , (2.1)
where N is the number of LR images, u ∈ R M l×M l is the HR irradiance of size M l × M l, Q i ∈ R (M l×M l)×(M l×M l) are the affine motions associated with each LR image (Q i u is the irradiance reaching the sensor), S ∈ R (l×l)×(M l×M l) is the sub-sampling by a factor M (M can be called the super-resolution zoom or factor) and G i ∈ R (l×l)×(l×l) , G i = gt i is the overall acquisition gain, including the camera gain g (without loss of generality, we take g = 1 to simplify expressions) and the exposure time t i for the i-th LR image. Several images may be acquired with the same exposure time. Ω i ∈ R (l×l)×(l×l) is a diagonal matrix taking value 1 if pixel j does not become saturated or under-exposed for the exposure time t i and 0 otherwise. We suppose Ω = (Ω i ) i=1,...,N to be full rank (every pixel is at least illuminated once). This model is close to the one introduced in [START_REF] Gunturk | High-resolution image reconstruction from multiple differently exposed images[END_REF]. We use a simplified version of it in order to facilitate the study. Unlike [START_REF] Gunturk | High-resolution image reconstruction from multiple differently exposed images[END_REF], the camera response function is here considered to be linear, which is a realistic model for raw images [START_REF] Granados | Optimal HDR reconstruction with linear digital cameras[END_REF]. Our model does not take into account the point spread function of the camera, which can be deconvolved afterward if motion is small [START_REF] Traonmilin | On the amount of regularization for superresolution reconstruction[END_REF]. The quantization error is neglected as, except in very low light conditions, it is small compared to the readout noise variance n R [START_REF] Aguerrebere | Best algorithms for HDR image generation. a study of performance bounds[END_REF]. As we consider a monochromatic acquisition model, the Bayer pattern is ignored. With our model, the production of a demosaicked color HR image without regularization, would take the form of a separate inversion of the 3 color channels. Only the motion due to the shift in the grid would have to be included in Q i . Note that the green channel would have 2 times more LR images than red and blue channels. The digital LR images w = (w i ) i=1,...,N are contaminated by additive noise n:

(2.2) w = Au + n.
A Poisson noise model with Gaussian approximation [START_REF] Aguerrebere | Study of the digital camera acquisition process and statistical modeling of the sensor raw data[END_REF] leads to the spatially varying Gaussian noise

(2.3) n = n u + n R ,
where n u is a Gaussian noise with covariance matrix Σ u proportional to the irradiance (Σ u = diag(Au)) and n R is a Gaussian readout noise with constant variance σ 2 R . Thus the covariance matrix of n is Σ = diag(Au) + σ 2 R I (I = identity matrix). The objective is to recover u from w. [START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF] that M 2 images are necessary to perfectly recover the HR image in the case of constant exposure times. Because we supposed that the HDR acquisition model is a full rank linear map, the composition of the two processes is invertible with M 2 LR images. We minimize the L 2 data-fit to recover an estimate of u

Image reconstruction. It has been shown in

(2.4) ũ = argmin u W 1/2 (Au -w) 2 2 .
Multiplying by W 1/2 = Σ -1/2 normalizes the noise to have constant variance, thus the solution to (2.4) gives the minimum variance linear unbiased estimator of the irradiance. Practically, this problem is solved with a linear conjugate gradient calculation of (W

1/2 A) † W 1/2 w = (A H W A) -1 A H W w.
Since the weights W depend on the irradiance u, an iterative procedure is needed to complete the estimation. The weights can be initialized with a smoothed version of the LR images. In practice, it is found that one iteration yields good results, and the irradiance remains almost unchanged after the first iteration. The iterative computation of this estimator for the HDR image generation in the case of perfectly registered images, is introduced by Granados et al. [START_REF] Granados | Optimal HDR reconstruction with linear digital cameras[END_REF] and shown to be nearly optimal in [START_REF] Aguerrebere | Best algorithms for HDR image generation. a study of performance bounds[END_REF].

If Ω i = I, G i = I and W = I (no HDR in the model), Equation 2.4 is the conventional L 2 super-resolution reconstruction procedure.

An experiment is conducted to evaluate the benefit of using the weights W . For this purpose, synthetic samples are generated from a ground-truth HDR image according to model (2.2), and the reconstruction is performed solving (2.4), with W 1/2 = Σ -1/2 and W = I. The experiment is repeated 100 times, with randomly chosen affine transformations and noise realizations. The signal-to-noise ration (SNR) for each reconstructed pixel is computed from the ground-truth value and the mean square error (MSE) at that pixel (MSE computed from the 100 experiments). Figure 2.1 shows the SNR images in decibels for each weighting type. The results greatly improve when the weights W 1/2 = Σ -1/2 are included. The improvement (gain in SNR) is more remarkable in the darker regions of the scene where the input samples are noisier. An average gain of 3.9 dB (average SNR for all pixels) is found comparing the cases with weights (32.5 dB) and without weights (28.6 dB).

Image registration.

Image registration is a critical part of SR as the quality of the result will be directly linked to the precision of motion estimation. With low resolution images, registration can be inaccurate [START_REF] Robinson | Fundamental performance limits in image registration, Image Processing[END_REF]. For super-resolution, high resolution motion estimation is often performed with the variable projection method [START_REF] Golub | Separable nonlinear least squares: the variable projection method and its applications[END_REF][START_REF] Robinson | Optimal Registration Of Aliased Images Using Variable Projection With Applications To Super-Resolution[END_REF][START_REF] Rochefort | An Improved Observation Model for Super-Resolution Under Affine Motion[END_REF][START_REF] Zhang | Commutability of Blur and Affine Warping in Super-Resolution With Application to Joint Estimation of Triple-Coupled Variables[END_REF]. It has been shown that this method gives good results when enough images are available [START_REF] Traonmilin | On the amount of regularization for superresolution reconstruction[END_REF]. We adapt this method to our joint HDR-SR reconstruction problem. For a given HDR setting (Ω i and G i known), let A(θ) be a SR operator parametrized by the affine motion parameter θ ∈ R 6N and ũ(θ) the solution of (2.4) with operator A(θ). The variable projection aims at finding the minimizer

(2.5) θ = argmin θ W 1/2 (A(θ)ũ(θ) -w) 2 2 .
It is a non-linear non convex functional having local minima. From an initial solution, we perform a conjugate gradient descent of functional (2.5).

The initial solution is calculated as follows. We calculate the cross-correlation of each LR images pair for different translations and find the translation maximizing the cross-correlation. We remark that the translation τ ij between images i and j should be the sum of the translation Result of optimal reconstruction for HDR-SR. SNR for each pixel obtained from 100 experiments with randomly chosen affine transformations and noise realizations. Left: Ground-truth image from [START_REF] Hasinoff | Noise-optimal capture for high dynamic range photography[END_REF]. Center: SNR obtained without weights (W = I). Right: SNR obtained using W 1/2 = Σ -1/2 . The improvement is more remarkable in the darker regions of the scene where the input samples are noisier. An average gain of 3.9 dB (average SNR for all pixels) is found comparing the cases with weights (32.5 dB) and without weights (28.6 dB).

τ ik between images i and k and translation τ kj between k and j. Then, to obtain the final translation to the reference image, we average all the available τ 1k + τ kj . We then scan for initial rotation and zoom to avoid local minima.

Strategy for the choice of acquisition parameters.

In order to establish an HDR-SR reconstruction strategy, we must define the set of exposure times and the number of images (per exposure time) to acquire. Given a set of exposure times t 1 , . . . , t N , the reconstruction error can be arbitrarily large because the condition number of the acquisition operator A cannot be bounded. For instance, it is infinite if the camera does not move (Q i = I). Therefore, it is not possible to find the exposure times minimizing the reconstruction error for the HDR-SR combined problem without knowledge of the camera motion. In practice, the motion is seldom known. In particular, it is unknown for images acquired with a hand-held camera.

Performing a joint optimization of exposure times and number of images for HDR-SR would require a precise statistical model describing camera motion. Even with this information, calculating precise estimates of the reconstruction error would be difficult because we would have to estimate the interaction between the local conditioning of super-resolution [START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF] and the spatial variations of the SNR. Moreover, this joint problem is a highly dimensional non-convex problem, which would be hard to embed in a camera.

Hence, we propose to define a reconstruction strategy combining the optimality results for each separate problem, HDR and SR, so as to minimize the worst case reconstruction error of the combined problem. With HDR processing, we know that parts of the images are illuminated by few images. From SR theory, these parts must be covered by enough images to enable a reconstruction without regularization. Consequently, we proceed as follows.

Proposed strategy. For the HDR reconstruction problem, an optimal HR HDR image is obtained if p HR images with exposures t 1 , . . . , t p are combined, these exposures being chosen to minimize the HDR reconstruction error (c.f. Section 5). Hence, we propose to consider the SR conditions which best estimate each of these p HR images. This will guarantee that the joint HDR-SR reconstruction performs well.

Suppose that, for each t 1 , . . . , t p , we find a set of motions for the N images acquired with that exposure that lead to a good SR reconstruction of the p HR images. Then a naive linear HDR-SR method would be to perform a classical HDR technique, with these p reconstructed HR images, thus limiting the final reconstruction noise. But we know that our joint method (minimization (2.4)) leads to the optimal L 2 reconstruction error, given this dataset. Consequently, by minimizing the reconstruction error of the separate HDR and SR problems, we guarantee a good reconstruction error for the joint HDR-SR problem. Given a set of exposure times t 1 , . . . , t p that minimize the HR HDR reconstruction error, two cases are to be considered. First, if the total exposure time and the total number of images are not limited, the best strategy for each exposure (t i ) i=1,...,p is to take as many LR images as possible with this exposure in order to improve the SR reconstruction. With equal exposure times, the problem becomes a pure super-resolution problem where more images improve the quality of the reconstruction [START_REF] Champagnat | Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework[END_REF][START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF]. Longer exposures are not desirable since they increase the number of saturated pixels thus increasing the reconstruction error. Secondly, a more realistic case, is that of a limited total exposure time (e.g. because of scene motion). In order to ensure a correct HR reconstruction with a super-resolution factor (or zoom) M , the minimum total exposure time for frames acquired with time t i is M 2 t i . However, as it will be shown in the following section, there is an optimal number of LR images N > M 2 for a fixed total exposure time.

Reconstruction error bound for HDR-SR.

In the following section we study the reconstruction error bounds for the HDR-SR estimation problem for a fixed total exposure time T and N images acquired with equal exposure T /N , i.e. the reconstruction of the HR irradiance frame.

4.1. Optimal number of images for a fixed total exposure time. In a HDR context, when neglecting motion blur, the longer the exposure time without saturation, the better. We show here that when we must perform SR at the same time (i.e. compute the pseudoinverse of A), taking more images with a shorter exposure can be better. We study the case of HDR-SR for a given total exposure time T without saturation, i.e. Ω i = I. N images are acquired with a total exposure time T , each with equal exposure time t = T /N . Because the overall acquisition gain is linear, the problem is equivalent to the acquisition of N LR irradiances v with A ′ = G -1 A, with a noise n ′ with covariance matrix:

(4.1) Σ ′ = diag(A ′ u/t + σ 2 R /t 2 ).
Then,

(4.2) v = A ′ u + n ′ .
A ′ is the conventional super-resolution modeling operator, i.e. a super-resolution operator where acquisition gain is not considered. Thanks to this normalization, we will be able to use results from the super-resolution literature directly. The super-resolution of N images with exposure T /N can be done solving the problem

(4.3) ũ = argmin v W ′1/2 (A ′ u -v) 2 2 , with W ′ = Σ ′-1 .
Reconstruction error bound. The noise in the reconstructed image n rec is thus bounded by (c.f. Appendix A)

(4.4) n rec 2 2 ≤ κ(N ) 2 σ 2 max (A ′ ) m 2 l 2 m (1 + rN )N 2 ,
where κ(N ) is the conditioning of A ′H A ′ (ratio of extremal eigenvalues of

A ′H A ′ ), σ max (A ′ ) is the maximum singular value of A ′ , m = sup(u) ⋍ sup(A ′ u), m = inf(u) ⋍ inf(A ′ u), r = σ 2 R /(T m), r = σ 2 R /(T m
) and l is the size of the input images. Hence, the optimal number of images for a fixed total time T is the one that minimizes n rec 2 . In [START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF], it was shown that κ(N ) can be bounded in probability by a decreasing function of the number of images N . Moreover, it can be shown [START_REF] Traonmilin | Outlier Removal Power of the L1-Norm Super-Resolution[END_REF] that

N/M 2 ≤ A ′ 2 2 = σ 2 max (A ′ ) ≤ N .
Hence, to optimize the reconstruction error bound, we minimize the function

(4.5) f (N ) = κ(N ) 2 (1 + rN )N,
with respect to N . When N is close to the critical case M 2 , κ(N ) can be large but decreases to 1 with N [START_REF] Traonmilin | On the amount of regularization for Super-Resolution interpolation[END_REF]. The conditioning of the SR operator has been also studied extensively in [START_REF] Champagnat | Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework[END_REF][START_REF]Statistical performance analysis of super-resolution, Image Processing[END_REF]. Consequently, f will have a minimum. Notice that the r factor is proportional to σ 2 R and cannot be neglected in low light conditions. If we added saturation for a particular time T /N 0 with N 0 ≥ M 2 , the bound would still be valid for N > N 0 . For N ≤ N 0 , matrix A ′ is not invertible, thus the error is not bounded.

Experimental study of f (N ).

Synthetic data. To illustrate the behavior of f (N ), we compute the curve for the case of 2D translational super-resolution. For each number of images N , we randomly simulate 100 translation parameters and compute the corresponding f (N ) by explicitly calculating κ(N ) (which can be done because the SR is then a 2D Vandermonde system in the frequency domain [START_REF] Ahuja | Multidimensional Generalized Sampling Theorem for wavelet Based Image Superresolution[END_REF][START_REF] Papoulis | Generalized sampling expansion, Circuits and Systems[END_REF]). With the same procedure, we generate the f (N ) curve for the affine superresolution case. Here κ(N ) is approximated by the ratio n rec 2 / n in 2 . Figure 4.1 shows the results obtained with M = 2 and r = 0.03 (chosen with realistic values: σ 2 R = 30, T = 1/10, m = 10 4 ).

It can be verified that the minimum of f is not reached at the critical case (N = M 2 = 4), meaning that it is better to take more than M 2 images with shorter exposure times. This fact shows that a compromise must be made between the number of images needed to perform super-resolution (more than M 2 ) and the noise level on those images. Given the total exposure time T , a degradation of the performance can be observed for large N . This can be explained by the fact that each image has a shorter exposure time. For short enough exposures, the variance σ 2 R of the readout noise becomes prominent. The amount of noise in LR images becomes too big to be compensated by the averaging effect of super-resolution, thus increasing the reconstruction error.

This can be verified with the results obtained for various r values in Figure 4.1. The r factor can be thought of as the inverse of the dynamic range of the acquired scene, since it is equal to the ratio between the constant noise variance σ 2 R and the maximum acquired irradiance mT (up to the factor N ). As the value of r decreases, the minimum of f (N ) is reached at a larger N . This is due to the fact that both, decreasing σ 2 R or increasing T , improves image quality and thus allows the use of shorter exposure times. Moreover, notice that the error bound increases quite slowly after its minimum. Hence, whether we choose a number of images at the minimum or slightly above will have little impact on the results. Curves of similar shape are obtained for larger M values, with the minimum reached for a larger N . This is caused by the larger conditioning of the SR problem for larger M [START_REF] Baker | Limits on super-resolution and how to break them, Pattern Analysis and Machine Intelligence[END_REF].

Real data. In order to experimentally verify the previous results, we take pictures of a planar surface using a hand held camera (c.f Figure 4.2). The small hand motion gives the sampling diversity needed for HDR-SR and guarantee that motion blur is not too large. The goal is to compare the HDR-SR reconstruction error (M = 2) obtained with a constant total exposure time T , but with two different exposure times, t 1 = 1/41 and t 2 = 1/64, i.e. with a different number of images, N 1 = T /t 1 and N 2 = T /t 2 . In the same way, the HDR-SR results are compared for the two different exposure times when fixing the total number of images N , i.e. for a different total exposure time N t 1 and N t 2 in each case. The reconstruction error (estimated from the variance of gray parts) with respect to the total exposure time and the number of images, for the two different exposure times, is shown in figures 4.2 (a) and (d) respectively. In this example, for a fixed number of images, it is better to take pictures at 1/41 seconds. However, for a fixed total exposure time, it is better to combine more images with the shorter exposure 1/64 seconds. The same behavior can be observed in the extracts of the reconstructed images shown in figures 4.2 (b) and (c). Hence, we verify that the longest exposure time is not necessarily optimal.

4.2. Discussion and practical consequences. In this section, we explain the trade off that must be made when performing HDR and SR simultaneously: in an HDR setting, we look for the biggest exposure times which do not saturate (or saturate for the fewest images possible) while with SR, more images are generally better. This leads to the following remarks depending on the acquisition setup:

• With a fixed total exposure time, the number of images must be above the critical case for SR (M 2 ), thus with a shorter exposure. However, it must not exceed by much the critical case since for very short exposures the reconstruction noise increases with N . • With a fixed number of images, the more images with the longest possible exposure time the best. However, the previous remark give us the knowledge that if this number of images is the optimal one from the previous section, then it is not possible to do better with the same total exposure time. • With any exposure time / number of images, the best strategy is taking as much images as possible of the longest exposure time. Taking a lot of images with very short times is not a good strategy.

5. Exposure times selection for HDR reconstruction. The selection of the exposure times is a key aspect of the HDR imaging problem. Several approaches can be found in the literature that tackle this problem from different perspectives. Some of the proposed methods look for the optimal times set that ensures that a predefined dynamic range will be captured [START_REF] Grossberg | High Dynamic Range from Multiple Images: Which Exposures to Combine?[END_REF][START_REF] Hone | Minimal-bracketing sets for high-dynamic-range image capture[END_REF]. Another group of methods focuses on the quality of the reconstructed HDR image and optimizes a risk function that depends on the mean squared error [START_REF] Hirakawa | Optimal exposure control for high dynamic range imaging[END_REF] or the signal to noise ratio of the reconstruction [START_REF] Granados | Optimal HDR reconstruction with linear digital cameras[END_REF][START_REF] Hasinoff | Noise-optimal capture for high dynamic range photography[END_REF]. These methods need a prior estimation of the scene irradiance, which is assumed to be available for instance through the irradiance histogram.

In this work, we focus on the minimization of the HDR-SR reconstruction error, and we seek for the exposure times set that minimizes the HDR reconstruction error for a given number of exposures N ′ . The determination of the number of different exposure times N ′ is an important problem in HDR imaging, since it has a major impact on the quality of the results and on the practical constraints of the acquisition. Given that it is not the goal of this work to study this problem, we consider instead the value N ′ as a given parameter, which might eventually be set from the known irradiance histogram. An histogram of the scene irradiance is assumed known. In this section we concentrate on the extension of the dynamic range of the image (M = 1, Q i = I, S = I) and propose an algorithm to find this exposure times set.

In this case, the solution to equation (2.4) gives the following estimator of the irradiance at position j:

(5.1) ũj = N ′ i=1 t i Ω ij w ij u j t i +σ 2 R N ′ h=1 t 2 h Ω hj u j t h +σ 2 R .
Thus the irradiance estimator variance in this case is given by

(5.2) n rec 2 2 = l 2 M 2 j=1 1 N ′ h=1 t 2 h Ω hj u j t h +σ 2 R .
Then, we consider the optimal set of times as the one that minimizes (5.2).

If we neglect the readout noise variance σ 2 R , the irradiance estimator variance expressed in (5.2) depends on the square root of the signal √ u j . Thus, the minimization of (5.2) prioritizes noise reduction in bright regions. We opt to normalize the estimator variance by the signal as a way to counter this dependence and prioritize noise reduction in low light pixels, since noise is generally amplified in those pixels by post-processing tone mapping techniques used to display HDR images. Several tone mapping techniques perform a contrast reduction of the irradiance image that magnifies the noise visibility mainly in dark regions [START_REF] Reinhard | High Dynamic Range Imaging -Acquisition, Display, and Image-Based Lighting[END_REF]. Nevertheless, this is clearly one possible option among multiple valid options. Other approaches are also valid (e.g. normalization by the squared signal u 2 j so as to minimize the squared signal to noise ratio) and may be incorporated into the proposed HDR-SR acquisition strategy by modifying (5.2) accordingly. Therefore, we consider the normalized irradiance estimator variance

(5.3) n ′ rec 2 2 = l 2 M 2 j=1 1 u j N ′ h=1 t 2 h Ω hj u j t h +σ 2 R = l 2 M 2 j=1 1 N ′ h=1 t 2 h Ω hj t h +σ 2 R /u j ,
and the set of exposure times (5.4) t1 , . . . , tN ′ = arg min

t 1 ,...,t N ′ n ′ rec 2 2 .
To minimize the non-convex function (5.3), we propose to use an exhaustive evaluation method. First, the shorter exposure time is determined by the fact that all irradiance values must be correctly acquired for at least one exposure time (matrix A is full rank). For the same reason, a lower bound is determined for the longer exposure. Then, given the number N ′ of exposure times to acquire (which might be automatically extracted from the scene histogram), we need to minimize function (5.3) with respect to the remaining N ′ -1 times. We find this minimum by evaluating all combinations of available times. This methodology is feasible and fast in practice since N ′ is usually in the order of 2 to 4 and the number of available exposures in the camera is about 50 (e.g. 55 for the Canon 7D). Figure 5.1 shows the inverse of function (5.3) for the example scene presented on the first experiment of Section 6 with N ′ = 2. The large flat region for the longer exposure times represents the large error caused by the saturation of most (or all) pixels in the image. A large error is also found for very short exposure times, since the readout noise becomes important for all irradiance values. The maximum of the function (minimum of (5.3)) is reached between these two extremes, as a compromise between saturation and noise level. This compromise is determined from the proportion of pixels belonging to each irradiance range, which is derived from the irradiance histogram of the scene.

6. Acquisition strategy. From the results presented in previous sections we derive the following strategy for the a regularized HDR-SR reconstruction that guarantees the recovery of the amplitude and frequency content of the scene irradiance. The exposure times are first selected following the procedure introduced in section 5. For this purpose, two images are taken to compute the histogram of the scene irradiance and find the optimal exposure times for the HDR reconstruction. One image must capture bright regions (no saturated pixels) and the other must capture dark regions (no under-exposed pixels). From the concatenated histograms of the two exposures, the high dynamic range histogram of the irradiance is built. With this histogram, the minimization from equation (5.4) is performed for the given number of exposure times.

The number of images to take for each exposure time is thus defined from the study presented in section 4. It should be taken as the minimum of function f according to the second remark in section 4.2. The function f , thus the optimal N , depends on the scene irradiance. However, for M = 2, we find in practice that it is reached at about N = 20 for a large range of irradiances. It can be larger for smaller r values, but in those cases the function is quite flat and the result is not greatly affected by this choice. Because N = 20 is a feasible number of shots for burst acquisition with a hand-held camera, it can be taken as the reference number of images needed for each exposure time. Hence, 20 hand-held pictures are taken for each of the selected exposures and the joint HDR-SR is performed solving (2.4) with all images. As stated in Section 3, the joint HDR-SR reconstruction gives the minimum L 2 reconstruction error and is thus preferable over the separate reconstruction (super-resolution for each HDR exposure and then HDR imaging to combine the HR frames). Moreover, separate registration for times which saturate a large part of the image can fail (e.g. the series of images from 6.4 (c) (f)).

6.1. Experiments. The following experiments were conducted in order to test the capacity of the proposed strategy to recover the dynamic and frequency information lost by a single image acquisition without the need of regularization hypothesis on the scene. To be as close as possible to our model we used the raw images from a high end commercial camera for real data experiments (second and third experiments) Synthetic data. In the experiment of Figures 6.2 and 6.3, we illustrate how taking the advocated number of images yields a better reconstruction than a total variation (TV) regularization [START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF] with less images. We generate synthetic LR images, according to Model (2.2), from an HR irradiance map (extracted from a real scene). For TV regularization, we generate 2 LR images at the three exposure times 1 64 , 1 41 and 1 32 seconds. We add a total variation regularization term to minimization (2.4) and choose the regularization parameter giving the best PSNR. For the unregularized case, we generate 20 images for each of these times, and perform minimization (2.4). The difference in reconstruction quality can be noticed both qualitatively, and in terms of PSNR. The unregularized version has a 6dB PSNR improvement, and the content of the image is not altered (frequencies are not distorted). The TV High dynamic range planar surface. We use a planar surface half illuminated by a strong source, thus generating two levels of irradiance. The scene is shown in Figure 6.1. Acquiring a plane matches the hypothesis of affine motion (small homography). In a more complex scene, segmenting the image in parts where the affine motion hypothesis is valid might be necessary.

The strategy introduced in section 6 is used first to find the 3 optimal exposure times (which are enough to capture the two different illumination levels of the scene) for the scene:

1 100 , 1 80 and 1 32 seconds. Then, 20 hand-held pictures are taken for each of the three selected exposures (total exposure time is approximately 1.1 second). Finally, the joint HDR-SR is performed solving (2.4) for all images. Figure 6.4 shows example images for each exposure time in the irradiance domain (i.e. at the same scale) along with the corresponding saturation masks. We observe the increasing saturation for increasing exposure time. In Figure 6.5, the result of the HDR-SR reconstruction with factor M = 2 is displayed along with the result of a bi-cubic interpolation of the reference image for comparison purposes. All images are at the appropriate scale for a fair comparison. As expected, the HR image resulting from HDR-SR reconstruction is sharper and less noisy than the bi-cubic interpolation. In this practical case, the intrinsic frequency content of the scene is not very rich because the camera has a physical anti-aliasing filter that cuts much of the high frequencies. However, the recovery of higher frequency information (which does not rely on any regularity model of the scene) is visible, especially on the plot of frequency spectra.

Complex scene. An HDR-SR experiment was conducted in the scene shown in Figure 6.6. The strategy introduced in section 6 is used to find 3 optimal exposure times for the scene: exposures. The total exposure time is approximately 1.4 seconds. In order to apply (2.4), the HDR-SR reconstruction must be performed in sub-regions of the images verifying the affine motion hypothesis. The joint HDR-SR for each region is performed solving (2.4) from the corresponding regions of all input images. Figure 6.7 shows the HDR-SR reconstruction for a bright and a dark region of the scene. The recovery of high resolution content is particularly 7. Conclusions. In this work, we exposed how the HDR-SR problem can be set-up as a minimization problem including state of the art techniques from both sides of the problem. We showed that particular care is necessary when choosing acquisition parameters for high dynamic range super-resolution. A balance between noise generation due to the conditioning of super-resolution and the noise intensity corresponding to the length of exposure times should be found. We also showed how exposure times for HDR-SR can be chosen. The main conclusion of this work is the suggested strategy which ensures that, if the affine motion hypothesis holds and sufficiently long exposure time is available then all the information contained in the irradiance scene (both in amplitude and in frequency) is recovered.

A. Reconstruction error bound. Computation of the reconstruction error bound for the weighted least squares solution of (2.4). First, using operator norm inequalities:

n rec 2 2 = (A ′H W ′ A ′ ) -1 A ′H W ′ n in 2 2 (A.1) ≤ (A ′H W ′ A ′ ) -1 2 2 A ′H W ′1/2 2 2 W ′1/2 n in

  Figure 2.1.Result of optimal reconstruction for HDR-SR. SNR for each pixel obtained from 100 experiments with randomly chosen affine transformations and noise realizations. Left: Ground-truth image from[START_REF] Hasinoff | Noise-optimal capture for high dynamic range photography[END_REF]. Center: SNR obtained without weights (W = I). Right: SNR obtained using W 1/2 = Σ -1/2 . The improvement is more remarkable in the darker regions of the scene where the input samples are noisier. An average gain of 3.9 dB (average SNR for all pixels) is found comparing the cases with weights (32.5 dB) and without weights (28.6 dB).

Figure 4 . 1 .

 41 Figure 4.1. Plot of log(f (N )) versus N (M = 2). (a) Result for 100 experiments (blue) and average (red) of 2D translational SR for each N with r = 0.03 . The minimum is reached at N = 12 . (b) Plot of the average log(f ) for different values of r for translational SR. Minimum at 12 (r=0.3), 13 (r=0.03) and 30 (r=0.003). (c) Affine super-resolution, 20 experiments for each N . The minimum is reached at N = 19, (d) Plot of average log(f (N )) versus N for different values of r for affine SR. Minimum at 14 (r=0.3), 19 (r=0.03) and 34 (r=0.003).

Figure 4 . 2 .

 42 Figure 4.2. Reconstruction error with respect to total exposure time and number of images (M = 2). (a) Reconstruction error with respect to total time. (b) Reconstruction error with respect to number of images. (c) SR result with 7 images at 1/41s. (d) One LR image with exposure 1/41s. (e) SR result with 10 images at 1/64s. (f ) one LR image at with exposure 1/64s.

1 Figure 5 . 1 .

 151 Figure 5.1. Inverse of the normalized reconstruction error (inverse of Equation (5.3)) for the first example scene of Section 6.

Figure 6 . 1 .

 61 Figure 6.1. A picture of the practical set-up of our first experiment

Figure 6 . 2 .

 62 Figure 6.2. Comparison between regularization with few 6 images and without regularization with 60 images, (a) One of the LR images, (b) HR image, (c) optimal TV regularization with 6 images, (d) SR without regularization and 60 images. See details in Figure 6.3.

Figure 6 . 3 .

 63 Figure 6.3. Detail of Figure 6.3. (a) One of the LR images, (b) HR image, (c) optimal TV regularization with 6 images, PSNR=43.48dB, (d) SR without regularization and 60 images, PSNR=49.92dB.

Figure 6 . 4 .

 64 Figure 6.4. Acquired LR irradiance images with different exposure times with their respective saturation masks (saturated parts are in black) (a) reference image at 1 100 , (b) image at 1 80 , (c) image at 1 30 , (d) saturation mask for image (a), (e) saturation mask for image (b), (f ) saturation mask for image (c).

Figure 6 . 5 .Figure 6 . 6 . 2 /T 2 l 2 N 1 +

 6566221 Figure 6.5. Result of HDR-SR with 60 images (a) bi-cubic interpolation of the first LR image, (b) our result of HDR-SR, (c) scaled and zoomed version of (a), (d) scaled and zoomed version of (b), (e) 2D frequency spectrum of (a), (f ) 2D frequency spectrum of our result (b)


Alexia Comte

Pierre Christen
email: pierre.christen@univ-amu.fr.

Sylvain Davidson

Matthieu Pophillat

Jean Lorquin

Richard Auria

Gwenola Simon

Laurence Casalot

Biochemical, Transcriptional and Translational Evidences of the Phenol-meta-Degradation Pathway by the Hyperthermophilic Sulfolobus solfataricus 98/2

Phenol is a widespread pollutant and a model molecule to study the biodegradation of monoaromatic compounds. After a first oxidation step leading to catechol in mesophilic and thermophilic microorganisms, two main routes have been identified depending on the cleavage of the aromatic ring: ortho involving a catechol 1,2 dioxygenase (C12D) and meta involving a catechol 2,3 dioxygenase (C23D). Our work aimed at elucidating the phenol-degradation pathway in the hyperthermophilic archaea Sulfolobus solfataricus 98/2. For this purpose, the strain was cultivated in a fermentor under different substrate and oxygenation conditions. Indeed, reducing dissolved-oxygen concentration allowed slowing down phenol catabolism (specific growth and phenol-consumption rates dropped 55% and 39%, respectively) and thus, evidencing intermediate accumulations in the broth. HPLC/Diode Array Detector and LC-MS analyses on culture samples at low dissolved-oxygen concentration (DOC = 0.06 mg.L 21 ) suggested, apart for catechol, the presence of 2-hydroxymuconic acid, 4-oxalocrotonate and 4-hydroxy-2-oxovalerate, three intermediates of the meta route. RT-PCR analysis on oxygenasecoding genes of S. solfataricus 98/2 showed that the gene coding for the C23D was expressed only on phenol. In 2D-DIGE/ MALDI-TOF analysis, the C23D was found and identified only on phenol. This set of results allowed us concluding that S. solfataricus 98/2 degrade phenol through the meta route.

Introduction

Phenol is an aromatic-ring-containing compound largely used in organic chemical industry mostly for the production of bisphenol A, or as intermediate in resins, fibers, paints or pharmaceutical syntheses [START_REF] Busca | Technologies for the removal of phenol from fluid streams: a short review of recent developments[END_REF]. It also has applications in the perfumery, molecular-biology or medicine fields. Besides, it is considered as relatively dangerous for health, classified in the European Union as a mutagenic agent, with a threshold-value exposure for man set at 5 ppm in France. It is all the more harmful because of its high volatility and/or diffusivity providing a rapid propagation in the environment. Some authors have reviewed technologies used for phenol removal from wastewaters and gaseous streams [START_REF] Busca | Technologies for the removal of phenol from fluid streams: a short review of recent developments[END_REF]. A great number of microorganisms are able to degrade phenol and use it as sole energy or carbon source [START_REF] Agarry | Microbial degradation of phenols: a review[END_REF][START_REF] Sridevi | Metabolic pathways for the biodegradation of phenol[END_REF]. The aerobic biodegradation has received an increasing interest in the last few decades. Phenol has been chosen as a model molecule to study the aromatic-ring fission [START_REF] Van Schie | Biodegradation of phenol: Mechanisms and applications[END_REF]. For monoaromatic compounds, such as phenol, benzoate, salicylate, benzene, etc., the first key degradation step involves its oxidation to catechol by a monooxygenase [START_REF] Tao | Oxidation of benzene to phenol, catechol, and 1,2,3-trihydroxybenzene by toluene 4-monooxygenase of Pseudomonas mendocina KR1 and toluene 3-monooxygenase of Ralstonia pickettii PKO1[END_REF][START_REF] Viggor | Evaluation of different phenol hydroxylase-possessing phenol-degrading pseudomonads by kinetic parameters[END_REF]. Then, catechol is degraded via two alternative pathways, depending on the microorganism [START_REF] Van Schie | Biodegradation of phenol: Mechanisms and applications[END_REF]. In the ortho route, aromatic ring is cleaved between the hydroxyl groups by the catechol 1,2 dioxygenase (C12D), leading to the cis,cis muconic acid. In the meta route, the ring cleavage occurs next to the two hydroxyl groups (Figure S1). It is catalyzed by the catechol 2,3 dioxygenase (C23D), and leads to the 2-hydroxymuconic semialdehyde (2-HMS) [START_REF] Tsirogianni | Mass spectrometric mapping of the enzymes involved in the phenol degradation of an indigenous soil pseudomonad[END_REF][START_REF] Banerjee | Phenol degradation by Bacillus cereus: Pathway and kinetic modelling[END_REF]. Then, the 2-HMS can be degraded either through the hydrolytic route or the 4-oxalocrotonate (4-OC) route [START_REF] Powlowski | Genetic and biochemistry of phenol degradation by Pseudomonas sp. CF600[END_REF][START_REF] Cao | Induction of ortho-and meta-cleavage pathways in biodegradation of high benzoate concentration: MS identification of catabolic enzymes[END_REF][START_REF] Omokoko | Isolation of the phe-operon from G. stearothermophilus comprising the phenol degradative meta-pathway genes and a novel transcriptional regulator[END_REF]. Both ortho and meta routes can be active for the same microorganism depending on the substrate. For example, only the ortho route was involved on salicylate while both routes were activated on benzoate in Pseudomonas cepacia [START_REF] Hamzah | Catechol ring-cleavage in Pseudomonas cepacia: the simultaneous induction of ortho and meta pathways[END_REF]. It can also depend on the aromatic concentration as demonstrated, in Pseudomonas putida grown on benzoate. At low concentrations (, 200-300 mg.L 21 ), only the ortho pathway is involved, while both degradation routes are activated at higher concentrations [START_REF] Cao | Induction of ortho-and meta-cleavage pathways in biodegradation of high benzoate concentration: MS identification of catabolic enzymes[END_REF][START_REF] Loh | Ortho pathway of benzoate degradation in Pseudomonas putida: induction of meta pathway at high substrate concentrations[END_REF]. In the latter case, a proteomic study showed the simultaneous presence of 8 catabolic enzymes: 3 corresponding to the ortho-cleavage route and 5 involved in the meta-cleavage one [START_REF] Cao | Induction of ortho-and meta-cleavage pathways in biodegradation of high benzoate concentration: MS identification of catabolic enzymes[END_REF].

If most phenol biodegradation studies concerned mesophilic microorganisms, some involved thermophilic bacteria from the Bacillus genus [START_REF] Mutzel | Isolation and characterization of a thermophilic bacillus strain, that degrades phenol and cresols as sole carbon source at 70uC[END_REF][START_REF] Feitkenhauer | Determination of the kinetic parameters of the phenol-degrading thermophile Bacillus thermoleovorans sp. A2[END_REF] or hyperthermophilic archaea [START_REF] Izzo | The thermophilic archaeon Sulfolobus solfataricus is able to grow on phenol[END_REF][START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF][START_REF] Christen | Kinetics of aerobic phenol biodegradation by the acidophilic and hyperthermophilic archaeon Sulfolobus solfataricus 98/2[END_REF]. In the past two decades, some reviews have dealt with the promising future of thermophile and hyperthermophile enzymes for industrial applications: thermo-stable amylases, xylanases, proteases or DNA polymerases for potential use in food, chemical or pharmaceutical industries [START_REF] Niehaus | Extremophiles as a source of novel enzymes for industrial application[END_REF][START_REF] Bouzas | Industrial applications of hyperthermophilic enzymes: A review[END_REF][START_REF] Turner | Potential and utilization of thermophiles and thermostable enzymes in biorefining[END_REF]. Besides their stability at high temperature, these enzymes are also known to withstand denaturant or acidic/alkaline conditions. Moreover, they are highly specific, robust and can be produced through either fermentation by the thermophilic microorganism or by cloning in fast-growing mesophiles by DNA recombinant technology [START_REF] Haki | Developments in industrially important thermostable enzymes: a review[END_REF]. Most of the thermophilic microorganisms belong to the Archaea group, grow at low pH and usually live in extreme environments such as solfataric fields or submarine hydrothermal areas [START_REF] Stetter | A brief history of the discovery of hyperthermophilic life[END_REF]. Their physiological characteristics and the general features of their genome sequences have been reviewed elsewhere [START_REF] Bertoldo | Thermophilic microorganisms and their novel biocatalysts[END_REF].

Oxygen availability is an important parameter in phenol aerobic biodegradation [START_REF] Nikakhtari | Modelling oxygen transfer and aerobic growth in shake flasks and well-mixed bioreactors[END_REF][START_REF] Contreras | Modelling phenol biodegradation by activated sludges evaluated through respirometric techniques[END_REF][START_REF] Kapley | Role of oxygen in the utilization of phenol by Pseudomonas CF600 in continuous culture[END_REF] especially at high temperature (80uC), for which its solubility in water is only 3 mg.L 21 . Viggor et al. [START_REF] Viggor | Evaluation of different phenol hydroxylase-possessing phenol-degrading pseudomonads by kinetic parameters[END_REF] showed that oxygen was a co-substrate of the monooxygenase, responsible for the oxidation of phenol to catechol. In thermophilic Bacilli, it has been shown that maximal degradation was reached at an O 2 delivery of 1 vvm, while inactivation of the C23D was observed at high O 2 levels [START_REF] Ali | Meta-pathway degradation of phenolics by thermophilic Bacilli[END_REF]. This limiting effect at low O 2 levels was also observed with Pseudomonas CF600 together with the accumulation in the medium of 2-HMS, an intermediate of the meta pathway [START_REF] Kapley | Role of oxygen in the utilization of phenol by Pseudomonas CF600 in continuous culture[END_REF].

Amongst high-temperature tolerant Archaea, our interest has focused on Sulfolobus solfataricus 98/2, which genome has been sequenced [START_REF] Lucas | Sulfolobus solfataricus 98/2, complete genome[END_REF]. Its ability to grow on phenol was recently discussed [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF][START_REF] Ulas | Genome-scale reconstruction and analysis of the metabolic network in the hyperthermophilic archaeon Sulfolobus solfataricus[END_REF], and kinetic parameters of phenol biodegradation were established [START_REF] Christen | Kinetics of aerobic phenol biodegradation by the acidophilic and hyperthermophilic archaeon Sulfolobus solfataricus 98/2[END_REF]. Moreover, a C23D gene was identified in the 98/2 strain [START_REF] Chae | Comparative analysis of the catechol 2,3-dioxygenase gene locus in thermoacidophilic archaeon Sulfolobus solfataricus strain 98/2[END_REF].

In this work, experiments were designed to study phenoldegradation route in S. solfataricus 98/2 cultivated in a fed-batch bioreactor. Growth, substrate and oxygen consumptions as well as product accumulated in the broth and CO 2 production are monitored. Transcriptomic and proteomic studies are also carried out in order to determine the metabolic pathway used for phenol degradation.

Materials and Methods

Strain and medium

S. solfataricus 98/2 was used in this study [START_REF] Rolfsmeier | Purification and characterization of a maltase from the extremely thermophilic crenarchaeote Sulfolobus solfataricus[END_REF]. Cells were maintained at -80uC and reactivated on the mineral medium reported elsewhere [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. The strain was previously adapted to phenol by repeated batches at concentrations up to 400 mg.L 21 , shown to be well tolerated by the strain [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF][START_REF] Christen | Kinetics of aerobic phenol biodegradation by the acidophilic and hyperthermophilic archaeon Sulfolobus solfataricus 98/2[END_REF].

Experimental set up

S. solfataricus was batch-cultivated in a 2.7 L reactor described in a previous paper [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. Working volume was 1.8 L. The fermentor was equipped with pH, redox, dissolved-oxygen and temperature probes connected to an automat (Wago, France). The automat was connected to a computer for process monitoring and data capture (BatchPro Software, Decobecq Automatismes, France).

Experimental conditions

S. solfataricus was cultivated at 80uC by repeated additions of phenol at concentrations up to 400 mg.L 21 , this level being shown to be under the inhibition threshold [START_REF] Christen | Kinetics of aerobic phenol biodegradation by the acidophilic and hyperthermophilic archaeon Sulfolobus solfataricus 98/2[END_REF]. Flask cultures (500 mL) of phenol-adapted S. solfataricus 98/2 were used to inoculate the fermentor filled with standard mineral medium with phenol (initial optical density (OD) in a range of 0.15-0.20). Oxygen was first fed to maintain a dissolved-O 2 concentration (DOC) of 1.5 mg.L 21 . When biomass reached about 0.35 g.L 21 , the oxygen set up was decreased to a DOC of 0.06 mg.L 21 . In all experiments, stirring was adjusted to 300 rpm and total aeration-flow rate to 100 mL.min 21 . Under these conditions, the K L a value for oxygen was 82.8 h 21 [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. DOC was regulated through the O 2 /N 2 ratio in the inlet gas. The pH was maintained at 3.2 with NaOH 0.5 mM. The exit gas was efficiently cooled to avoid phenol loss by evaporation as described elsewhere [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. For proteomic and transcriptomic studies, experiments were also carried out on glucose (1.8 g.L 21 ).

Analytical methods

Cell density was determined by OD measurement at 600 nm. Cell dry weight was calculated from OD data by using the relation of 1 OD unit = 320 mg.L 21 [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF].

Phenol consumption and intermediate-metabolite production were followed, after centrifugation of the sample (5 min, 14000 rpm), by HPLC equipped with a Diode Array Detector (DAD), as previously described [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. Intermediary-metabolite concentrations are expressed as mg eq.phenol .L 21 . Chemical structures of intermediates were explored by Liquid Chromatography Mass Spectrometry (LC-MS) using a Hitachi Elite LaChrom L-2130 liquid chromatograph coupled to a Bruker Esquire 6000 MS. The MS detector is equipped with an electro spray ionization in positive and negative mode and a quadrupole analyzer. Separation was achieved with a Varian Polaris C18 column eluted by a gradient of acetonitrile in water containing acetic acid (0.1% v/v), from 0 to 40% acetonitrile during 20 min, at a flow rate of 200 mL.min 21 . The cone and capillary voltages were maintained at 30 and 3500 V, respectively. To determine those chemical structures, 10 mL of culture were centrifuged; the supernatant extracted with ethyl acetate and analyzed by GC-MS as already described [START_REF] Liebgott | Bioconversion of tyrosol into hydroxytyrosol and 3,4-dihydroxyphenylacetic acid under hypersaline conditions by a new Halomonas sp. strain HTB24[END_REF].

Both biomass and phenolic-compound analyses were made by triplicate and the average value was reported. Specific growth rate (m,h 21 ) and specific degradation rate (q P , mg.g 21 .h 21 ) were calculated from biomass and phenol concentration data.

Oxygen consumption was calculated through the O 2 mass flow needed to maintain the DOC set point in the broth. Carbon dioxide production was measured online in the exit gas by infrared analyzer. The oxygen yield factor (Y X/O2 , g.g 21 ), the respiratory quotient (Q resp , mol.mol 21 ), the biomass yield on phenol (Y X/P , g.g 21 ) and the carbon balance were calculated as previously described [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF].

RNA extraction

Cells of S. solfataricus (50 mL), grown in different conditions, were harvested by centrifugation 10 min at 7400 rpm at 4uC. Pellets were snap-frozen in liquid N 2 . RNA was extracted from the cell pellets using the High Pure RNA Isolation Kit (Roche Applied Science, USA). The purified nucleic acids were then treated with Turbo DNase (Ambion, USA) and RNA were purified again with the same kit. The quantity and quality of the obtained RNA were evaluated spectrophotometrically on a BioSpec-nano spectrophotometer (Shimadzu, Kyoto, Japan) and samples were diluted to 20 ng. mL 21 before conservation at -80uC.

Semi-quantitative reverse-transcription PCR (RT-PCR) analyses

For RT-PCR analysis, total RNA (0.2 mg) was used to synthesize cDNA by triplicate in 20-mL reactions using the SuperScriptH III Reverse Transcriptase and random primers (InVitrogen, USA). PCR was performed for 15, 20, 25 or 30 cycles using a step-cycle program of 98uC for 30 s, 50uC for 30 s, and 72uC for 20 s. Primers were designed using the Primer3 software. Primer pairs are listed Table 1. The amplification products were separated on a 1% agarose gel by electrophoresis, and the gel images were acquired using a Gel Doc Imager (Biorad, USA). DNA controls were carried out to exclude any DNA contamination.

2D-DIGE

The cells were harvested by centrifugation at 7000 g at 4uC for 15 minutes and washed with ice-cold phosphate buffered saline. The cells were broken by sonication in urea lysis buffer (8 M urea, 2 M thiourea, 4% (w/v) 3-[(3-Cholamidopropyl) dimethyl ammonio]-1-propane sulfonate (CHAPS), pH 8.5). The samples were then clarified by ultracentrifugation at 35000 g at 4uC for 1 h. Soluble proteins were purified and concentrated by precipitation with 4 volumes of ice-cold acetone, and solubilized for 1 h in 100 mL urea lysis buffer. The protein concentration was estimated using Bradford assay (Biorad, Hercules, CA, USA) according to the manufacturer's instructions. All samples were then washed with the 2D-Clean-up kit (GE Healthcare, USA) and solubilized in urea lysis buffer to a final concentration of 2.5 mg. mL 21 . The soluble S. solfataricus-protein fractions were labeled with cyanine dyes: Cy3, Cy5, Cy2 (CyDyes, GE Healthcare, USA). 25 mgo f each protein extract was labeled separately at 4uC in the dark for 30 min with 200 pmol. mL 21 of the N-hydroxysuccinimide esters of cyanine dyes (Cy3 or Cy5). The internal standard, corresponding to a pool of the samples (12.5 mg of each individual extract), was prepared in parallel and labeled with Cy2. Total protein labeled with Cy2, Cy3 and Cy5 were combined and mixed with an equal volume of 2x urea lysis buffer containing 1% carrier ampholytes pH 4-7 according to the manufacturer's instructions. For the first dimension (IsoElectric Focusing, IEF), precasted IPG (Immobilized pH Gradient) strips were used (pH 4-7, non linear (NL), 11 cm length; Immobiline DryStrips, GE Healthcare, USA). Typically, 75 mg of protein (25 mg for each dye) was loaded onto each IPG strip and the IEF was carried out (IPGPhor III, GE Healthcare, USA). The IEF protocol was as follows: 0-300 V gradient for 1h; 300-1000V gradient for 1.5 h; 1000-6000 V gradient for 2 h; 6000 V for 2 h. Temperature was set up at 20uC. Prior to SDS PAGE, IPG strips were equilibrated during 20 min in an equilibration buffer (6 M urea, 50 mM Tris pH 8.8, 2% SDS, 38.5% glycerol) added with 65 mM DTT for the first 10 min and 2% iodoacetamide for the further 10 min. The second dimension was performed using a Criterion Dodeca Cell separation unit (Biorad, Hercules, CA, USA) and precast 10% SDS-PAGE gels (Biorad, Hercules, CA, USA). IPG strips were placed on the top of the precast gels, overlaid with 0.5% agarose in 2x running buffer containing bromophenol blue. Gels were run at 206C using the following XT-MES running buffer (Biorad, Hercules, CA, USA): 1X for the cathode and 2X running buffer for the anode part. Electrophoresis was conducted overnight at 15 V and stopped when the bromophenol-blue-dye front has reached the bottom of the gel. After SDS PAGE, cyanine-dye-labeled-protein gels were scanned directly using the Typhoon FLA9000 scanner (GE Healthcare, USA). All gels were scanned with a resolution of 50 mm. Determination of protein abundance and statistics based on 2D DIGE were carried out with the Decyder Software (version 6.5, GE Healthcare, USA). First step for the spot detection is the creation of crop images of the region of interest. Cropped images were imported onto Decyder. Spot detection was set as 10000 with a filter volume set at 30000. Spot selection was performed for a ratio up to 2 and a t-test p-value , 1%.

Gel digestion and MALDI-TOF MS

MALDI-TOF MS is based on the Decyder analysis. Spots of interest were excised using Shimadzu Biotech Xcise System (Champs sur Marne, France). The proteins were subjected to ingel digestion with trypsin, (Sequencing-grade modified porcine trypsin; Promega, Madison, WI, USA). Tryptic peptides were then extracted from the gel by successive treatment with 5% formic acid and 60% acetonitrile/5% formic acid. Each treatment is followed by sonication (5 min). Extracts were pooled and dried in a Speedvac evaporator. Peptides, resuspended in an a-cyano-4hydroxycinnamic-acid-matrix solution (prepared by diluting 6 times a saturated solution in 50% acetonitrile/0.3% trifluoroacetic acid), were then spotted on the metal target. Mass analyses were performed on a MALDI-TOF Bruker Ultraflex III spectrometer (Bruker Daltonics, Wissembourg, France) controlled by the Flexcontrol 2.0 package (Build 51). This instrument was used at a maximum accelerating potential of 25 kV and was operated in reflector mode and the m/z ranges from 600 to 3500. Six external standards (Peptide Calibration Standard II, Bruker Daltonics, Wissembourg, France) were used to calibrate each spectrum to a mass accuracy within 10 ppm with a minimal resolution of 10000 the angiotensin II peak (Monoisotopic mass = 1046.542 Da).

Peak picking was performed with Flexanalysis 2.0 software (Bruker Daltonics, Wissembourg, France) with an adapted-analysis method. Parameters used were as follows: SNAP peak detection algorithm, S/N threshold fixed to 6 and a quality factor threshold of 30. A list of contaminations was constituted from a blank sample (blank piece of gel treated and analyzed exactly as a true sample).

The trypsin peaks of this blank sample were excluded of the database search.

Protein identification

Database searches for MS spectra were conducted using MASCOT software 2.2 (Matrix Science), available online, against the S. solfataricus P2-complete-proteome NCBI database for known proteins. Peptide-mass tolerance was set to 100 ppm. Criteria used for protein identification are given by Mascot as a Probability Based Mowse Score. Ion score is -10*Log (P), where P is the probability that the observed match is a random event. Protein scores greater than X (X is a number between 55 and 74, from one search to the other) are significant (p,0.05). The matching of theoretical pI and PM of the identified protein with those observed in the 2D-gel experiments was also used as another criterion of confidence.

Results

Growth kinetics and yields, degradation products and carbon balance

As suggested previously, modifying the operating conditions for culture, such as DOC, can be a way to identify the phenol degradation pathway through the apparition of intermediary metabolites [START_REF] Kapley | Role of oxygen in the utilization of phenol by Pseudomonas CF600 in continuous culture[END_REF]. When S. solfataricus was grown with a DOC of 1.5 mg.L 21 after two sequential phenol batches (phenol initial concentration , 400 mg.L 21 ), biomass reached a concentration of 0.35 g.L 21 within 4 days (data not shown). At the third phenol addition (350 mg.L 21 ), the DOC was drastically decreased to 0.06 mg.L 21 . Kinetic and respirometric yields and rates are presented in Table 2. Although cells were repeatedly grown on phenol (no lag phase was observed at 1.5 mg.L 21 ), at the lower O 2 level, a short adaptation period was needed for growth and phenol consumption (Figure 1A). Then, biological activity started again and was characterized by am of 0.0106 h 21 and a q p of 29.0 mg.g 21 .h 21 . These parameters were lower than those observed at 1.5 mg.L 21 (m = 0.0235 h 21 and q p = 47.5 mg.g 21 .h 21 , respectively (Table 2)). In the same way, when the O 2 concentration decreased, so did the Y X/P (from 0.539 to 0.426 g.g 21 ).

At DOC of 0.06 mg.L 21 , carbon dioxide production and redox potential profiles were similar to those observed at 1.5 mg.L 21 , i.e. O 2 consumption and CO 2 production increased and redox potential decreased with growth (data not shown). This has already been described [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. However, the yield coefficient for oxygen (Y X/O2 ) was 0.415 g.g 21 for a DOC of 1.5 mg.L 21 and decreased significantly to 0.265 g.g 21 for a DOC of 0.06 mg.L 21 . The respiratory quotient (Q resp ) was closed to the theoretical value of 0.87 mol.mol 21 and was not affected by the oxygen level (Table 2).

At 0.06 mg.L 21 , during phenol consumption, catecholidentified with a standard solution by its absorption spectrum (l max = 275 nm) and its retention time (7.20 min) in HPLC/DAD analysis -appeared in the broth after 20 h (Figure 1). Catechol reached a maximum concentration of 90 mg eq.phenol .L 21 at 32 h and then decreased (Figure 1A). Its dissimilation is correlated with the appearance of various, but minor, compounds, also evidenced by HPLC/DAD. Only three of the peaks corresponded to compounds with a defined l max . They are characterized by retention times of 2.55, 3.2 and 3.6 min, respectively, with the analysis conditions given in the Material and Methods section. They displayed a l max of 290, 254 and 265 nm, respectively (Figure 1B). Trace amounts of them appeared after 28 h (Figure 1A) and their concentration increased strongly when catechol concentration decreased (36 h). At the end of the run (40 h), they reached a maximum concentration of 6.4, 47.4 and 12.3 mg eq. phenol .L 21 , respectively.

LC/MS analysis formally confirmed the presence of catechol in all the samples withdrawn after 20 h of run, but not the cis,cis muconic acid (l max = 260). In the same way, 4-OC, belonging to the meta pathway, was also identified. Moreover, at the same time that the intermediate metabolites are detected (28 h), a yellow color appeared instantaneously in the samples in contact with air. Its intensity grew with time. In contrast, none of the samples at 1.5 mg.L 21 displayed this phenomenon.

At both DOC, carbon balances are closed to 100% (Table 2). However, at 1.5 mg.L 21 , carbon from phenol is exclusively directed toward CO 2 (63.1%) and biomass (34.3%), while at 0.06 mg.L 21 , carbon distribution is different. In this case, the CO 2 proportion is maintained relatively constant (60.2%) while the biomass part decreased (27.2%) and a significant intermediary metabolite amount was observed (15.7%).

Genomic analyses

Few studies concerned the enzymes involved in phenol degradation through the meta or ortho pathways in Sulfolobales. Chae et al. [START_REF] Chae | Comparative analysis of the catechol 2,3-dioxygenase gene locus in thermoacidophilic archaeon Sulfolobus solfataricus strain 98/2[END_REF] have clearly identified the presence of a C23Dcoding gene in S. solfataricus 98/2 through PCR amplification, sequencing and heterologous production in E. coli (Accession number EF494887). This enzyme showed the highest activity against catechol and 4-chlorocatechol. The corresponding orf was not identified in the genome annotation (Accession number NC_017274.1). Using a primer pair designed on the S. solfataricus P2 C23D genomic sequence (sso1223), we were able to amplify a fragment which sequence perfectly matched the one amplified by Chae et al. [START_REF] Chae | Comparative analysis of the catechol 2,3-dioxygenase gene locus in thermoacidophilic archaeon Sulfolobus solfataricus strain 98/2[END_REF]. We decided to name this orf, according to the S. solfataricus 98/2-genome annotation, ssol_2912 (KF701465). No other gene coding for protein potentially involved in the meta pathway were identified in the genome of S. solfataricus 98/2. However, 4 genes coding for putative C12D, involved in the ortho degradation pathway, were found in the genome: ssol_0230 (4hydroxyphenyl pyruvate dioxygenase), ssol_1707 (gentisate 1,2 dioxygenase), ssol_2369 (homogentisate 1,2 dioxygenase) and ssol_2712 (extra diol ring clivage dioxygenase).

Transcriptional analysis

To investigate which nutrient conditions induce the transcription of these different oxygenases in S. solfataricus, the transcription levels of these genes were examined by semi-quantitative RT-PCR analysis. For this analysis, mRNA were isolated from samples of S. solfataricus grown in liquid media with glucose or phenol as the sole carbon source and different oxygen concentrations. RT-PCR controls, using primer pairs designed to amplify 16S rRNA gene, showed the same expression level in each culture condition (Figure 2A). Using the primer pair designed to amplify ssol_0230, ssol_1707, ssol_2369, ssol_2712 and ssol_2912 genes, a unique band of the expected size was obtained (Figure 2B-F). The mRNA transcription levels of ssol_0230 were equivalent when the strain was harvested from the medium with glucose or phenol and with a DOC of 1.5 mg.L 21 (Figure 2B, lanes 2-3), but decreased when the strain was cultivated with phenol at a DOC of 0.06 mg.L 21 (Figure 2B, lane 1). The mRNA transcription levels of ssol_1707 were equivalent with low and high oxygen concentrations in presence of phenol (Figure 2C, lanes 1-2) and slightly lower when the strain was harvested from the medium with glucose as substrate (Figure 2C, lane 3). The mRNA transcription levels of ssol_2369 were equivalent in the strain cultivated with glucose and phenol (Figure 2D, lanes 2-3). However, it increased when the strain was harvested from the medium with phenol at a DOC of 0.06 mg.L 21 (Figure 2D, lane 1). The mRNA transcription level of ssol_2712 was slightly lower when the strain was harvested from the medium with glucose compared to phenol (Figure 2E, lanes 2-3). Yet, the transcriptional level of the extra-diol-ring-clivagedioxygenase gene was higher in the media with high oxygen concentration (Figure 2E, lanes 1-2). The mRNA transcription level of ssol_2912 was undetectable when the strain was harvested from the medium with glucose as the sole carbon source (Figure 2F, lane 3). Nevertheless, it greatly increased when the strain was harvested from the media with phenol (Figure 2F, lanes 1-2). This differential expression of the C23D gene was detected in the medium whatever the DOC.

Proteomic analysis

To investigate the influence of phenol on protein production in S. solfataricus 98/2, a 2D-DIGE experiment was performed. We compared the whole protein content of the cells grown on phenol or glucose. The representative 2D-DIGE gel is shown in Figure 3A. Interestingly, among the proteins more abundant on phenol only, spot 181 (Figure 3A) was identified as the C23D by MALDI-TOF MS. This enzyme is only detected on phenol (Figure 3B). Besides, no other dioxygenase could be identified as produced more abundantly on phenol. In particular, no differential production was observed for the putative C12D (Ssol_0230, Ssol_1707, Ssol_2369 and Ssol_2712).

Discussion

Phenol and its derivatives are widely distributed environmental pollutants that are responsible for many unhealthy effects on humans. Degradation of such compounds has become of increasing interest for many years. As pointed out by Cao et al. [START_REF] Cao | Induction of ortho-and meta-cleavage pathways in biodegradation of high benzoate concentration: MS identification of catabolic enzymes[END_REF], the most effective and economical way to remove them from the environment is the microbiological way. The catabolism of phenol involves the action of a monooxygenase responsible for the oxygenation of phenol to catechol. The latter is then subjected to either a meta or an ortho cleavage of the aromatic ring yielding 2-HMS or cis-cis muconic acid, respectively [START_REF] Agarry | Microbial degradation of phenols: a review[END_REF][START_REF] Van Schie | Biodegradation of phenol: Mechanisms and applications[END_REF][START_REF] Banerjee | Phenol degradation by Bacillus cereus: Pathway and kinetic modelling[END_REF].

In this paper, we designed experiments to understand which pathway is involved in phenol degradation in S. solfataricus 98/2. One of the easiest ways to define the degradation pathway is to identify the reaction products. However, in S. solfataricus 98/2 cultivated in standard conditions, phenol is completely metabolized into CO 2 ,H 2 O and biomass [START_REF] Christen | Phenol biodegradation by the thermoacidophilic archaeon Sulfolobus solfataricus 98/2 in a fed batch bioreactor[END_REF]. In their paper, Kapley et al. [START_REF] Kapley | Role of oxygen in the utilization of phenol by Pseudomonas CF600 in continuous culture[END_REF] observed that 2-HMS accumulated at low DOC (2 mg.L 21 ), probably because of a slower metabolism, which, in turn, allowed observing transitory accumulation of intermediary compounds. In our first experiment, performed at 1.5 mg.L 21 , the growth parameters were determined. Nevertheless, in this condition and in contrary to what was expected, we were unable to detect any intermediate for the phenol degradation. Our experimental set up enables to work at a regulated and constant DOC. The problem of reducing the DOC to a very low level is that, is this case, the oxygen might become the limiting factor for the growth. Previous experiments showed that, with our experimental set up, for DOC as low as 0.06 mg.L 21 , the carbon source still remains the limiting factor (data not shown). With such operating conditions, the behavior of the strain was notably modified. At this level, in comparison to the parameters measured at 1.5 mg.L 21 , growth (m) and phenol-biodegradation rates (q p ) were slowed down (55% and 39%, respectively). These results can be compared to those reported by Ali et al. [START_REF] Ali | Meta-pathway degradation of phenolics by thermophilic Bacilli[END_REF] who demonstrated that phenol specific degradation decreased with the oxygen concentration. Biomass yields on phenol (Y X/P ) and on oxygen (Y X/O2 ) at 1.5 mg.L 21 are in the range of those reported in the literature (Table 2). For example, for two different P. putida strains cultivated on phenol in a continuous fed stirred-tank reactor, Seker et al. [START_REF] Seker | Multi-substrate growth kinetics of Pseudomonas putida for phenol removal[END_REF] and Nikakhtari and Hill [START_REF] Nikakhtari | Modelling oxygen transfer and aerobic growth in shake flasks and well-mixed bioreactors[END_REF] reported values of Y X/P of 0.521 g.g 21 and 0.73 g.g 21 , respectively and of Y X/O2 of 0.338 g.g 21 and 0.360 g.g 21 , respectively. Feitkenhauer et al. [START_REF] Feitkenhauer | Kinetic parameters of continuous cultures of Bacillus thermoleovorans sp. A2 degrading phenol at 65uC[END_REF] reported, with a Bacillus thermooleovorans strain, an Y X/O2 of 0.48 g.g 21 . At 0.06 mg.L 21 , we found that both parameters dropped 21% and 36%, respectively, indicating a less effective use of phenol or oxygen for biomass build up. Moreover, these coefficients (Y X/S and Y X/O2 ) have already been shown to be sensitive to O 2 levels for S. solfataricus as demonstrated by Simon et al. [START_REF] Simon | Effect of O 2 concentrations on Sulfolobus solfataricus P2[END_REF].

The slower growth of the strain (characterized by the 55% reduction of the growth rate), at a DOC of 0.06 mg.L 21 , gave suitable conditions for the accumulation of some of the intermediates (15.7%), as confirmed by the carbon balance (Table 2). After 20 h of culture, catechol, resulting from the oxidation of the aromatic ring, appeared in the culture. It accumulated up to 90 mg.L 21 and decreased (Figure 1). Its consumption is correlated to the appearance of, at least, three other compounds. The l max of two of these compounds are characteristic of two intermediates of the meta-degradation pathway: the 2-hydroxymuconic acid (2- HMA, l max = 290 nm) from the 4-OC route and the 4-hydroxy-2-oxovalerate (HOV, l max = 265 nm) (Figure S1). Concomitantly, a yellow coloration is be detected in the sample after contact with air. As soon as the early seventies, Buswell and Twoney [START_REF] Buswell | Utilization of phenol and cresols by Bacillus stearothermophilus, strain PH24[END_REF] reported the presence of this color during the degradation of phenol and cresol by a Bacillus stearothermophilus strain. This color has been reported as typical of the meta pathway biodegradation of monoaromatic compounds and associated with the presence of 2-HMS in thermophilic Bacilli strains [START_REF] Mutzel | Isolation and characterization of a thermophilic bacillus strain, that degrades phenol and cresols as sole carbon source at 70uC[END_REF][START_REF] Adams | The metabolism of aromatic ring fission products by Bacillus stearothermophilus strain IC3[END_REF]. This has also been extensively reported in mesophilic strains (Alcaligenes, Ralstonia, Pseudomonas) [START_REF] Kapley | Role of oxygen in the utilization of phenol by Pseudomonas CF600 in continuous culture[END_REF][START_REF] Leonard | Carbon and energy flux constraints in continuous cultures of Alcaligenes eutrophus grown on phenol[END_REF][START_REF] Leonard | Phenol degradation by Ralstonia eutropha: colorimetric determination of 2hydroxymuconate semialdehyde accumulation to control feed strategy in fedbatch fermentations[END_REF]. The analysis of the last sample, using a more sensitive MS detector, strongly suggested the presence of 2-HMS. Moreover, the cis,cis muconic acid, characteristic of the ortho route, was not detected neither by UV 260nm nor by MS.

Dioxygenases are responsible for the opening of the ring. C12D open the ring between the C1 and C2 carbons of the catechol (ortho cleavage), while C23D open between C2 and C3 (meta cleavage). In the genome of S. solfataricus 98/2, four open reading frames putatively coding for 1,2 dioxygenases have been identified: ssol_0230 (4-hydroxyphenyl pyruvate dioxygenase gene), ssol_1707 (gentisate 1,2 dioxygenase gene), ssol_2369 (homogentisate 1,2 dioxygenase gene), and ssol_2712 (extra diol ring clivage dioxygenase gene). The expression of these genes has been semiquantitatively followed depending on the growth conditions. Even if the expression of some of these genes seems to be oxygen dependant (ssol_0230 and ssol_2369), it is worth noting that all of the genes were expressed whether the carbon source was glucose or phenol. One open reading frame putatively coding for a C23D was identified in S. solfataricus 98/2 genome: ssol_2912 (C23D gene). The semi-quantitative analysis of its expression showed that, in presence of glucose, the transcript was not detectable indicating a regulation of the expression depending on the carbon source. No difference observed in the expression of the gene coding for 16S rRNA validated the approach.

To confirm the presence or the absence of the protein depending on the growth condition, a comparative analysis of the proteome between cells harvested on glucose or on phenol was performed. The only detectable difference among the dioxy-genases is on the production of the C23D. The four C12D were not identified in this experiment. However, their theoretical pI being within the tested range (Ssol_1707: 6.11, Ssol_2369: 6.24, Ssol_0230: 6.37 and Ssol_2712: 5.06, respectively), their absence means that the four proteins are equally produced on glucose and phenol.

In conclusion, our set of results (transcriptomic and proteomic) seems to indicate that both degradation pathways are functional in presence of phenol. However, the activation of the C23D, only when phenol is present, and the accumulation of only intermediary compounds related to this pathway lead us to the conclusion that the aromatic ring is preferentially opened through the meta pathway.

Figure 1 .

 1 Figure 1. Analysis of S. solfataricus 98/2 cultures grown on phenol at a DOC of 0.06 mg.L 21 . (A) biomass, catechol and other intermediate productions and phenol consumption. The intermediate curve corresponds to the sum of all the detected compounds. (B) HPLC chromatograms (l = 270 nm) obtained at three different time course of the run (P: phenol, C: catechol, I: intermediates). doi:10.1371/journal.pone.0082397.g001

Figure 2 .Figure 3 .

 23 Figure 2. RT-PCR analyses. (A) 16S rRNA, (B) ssol_0230 (4hydroxyphenyl pyruvate dioxygenase), (C) ssol_1707 (gentisate 1,2 dioxygenase), (D) ssol_2369 (homogentisate 1,2 dioxygenase), (E) ssol_2712 (extra diol ring cleavage dioxygenase), and (F) ssol_2912 (C23D) genes from S. solfataricus. Amplified fragments are 200-bp long. Lane 1: cells of S. solfataricus cultivated with phenol and a DOC of 0.06 mg.L 21 . Lane 2: cells of S. solfataricus cultivated with phenol and a DOC of 1.5 mg.L 21 . Lane 3: cells of S. solfataricus cultivated in glucose and a DOC of 1.5 mg.L 21 . Lane 4: positive control, PCR amplification on genomic DNA as template. Lane 5: negative control experiment performed omitting reverse transcriptase during RT-PCR reaction and showing complete absence of DNA in the RNA samples. La: 1 kb Ladder (Fermentas, France). doi:10.1371/journal.pone.0082397.g002

Table 1 .

 1 Primers used in gene-expression analyses in S. solfataricus 98/2.

	Genes	Proteins	Primers
	ssol_0230	4-hydroxyphenyl pyruvate dioxygenase	59-CACTGTGGCCAAGTTTCTGA-39
			59-CCATAACGCTTTTGGGATGT-39
	ssol_1707	Gentisate 1,2 dioxygenase	59-AGGGGACTAACGCCTACGAT-39
			59-AAACATCACCTGCCTTCCAC-39
	ssol_2369	Homogentisate 1,2 dioxygenase	59-TACGCATCCTTTTGACGTTG-39
			59-GGAACAGACTGGGGGTGATA-39
	ssol_2712	Extradiol cleavage dioxygenase	59-CGGTTTCCCAGAAGAGACCT-39
			59-GGGCTATTGTCGGTAATGGA-39
	ssol_2912	Catechol 2,3 dioxygenase	59-TGCGCCTAATTTCTGTCTGA-39
			59-ATTGGGAGCCAATAGTGTGG-39

doi:10.1371/journal.pone.0082397.t001

Table 2 .

 2 Kinetic and respirometric rates and yields of phenol degradation by phenol-grown S. solfataricus 98/2 cells at two dissolved-oxygen concentrations (DOC).

	Parameters	DOC
		1.5 mg.L 21	0.06 mg.L 21
	m (h 21 )	0.0235 (R 2 = 0.996) 0.0106 (R 2 = 0.995)
	q p (mg.g 21 .h 21 )	47.5 (61.4)	29.0 (61.1)
	Y X/P (g.g 21 )	0.539 (60.023)	0.426 (60.057)
	Q resp (mol.mol 21 )	0.828 (60.008)	0.805 (60.005)
	Y X/O2 (g.g 21 )	0.415 (60.005)	0.265 (60.035)
	Carbon balance (%)	97.4 (65.5)	103.1 (60.7)
	-biomass* (%)	34.3 (61.5)	27.2 (63.7)
	-carbon dioxide	63.1 (64.0)	60.2 (62.9)
	(%)
	-metabolites (%) 0	15.7 (60.2)

*on the basis of a phenol-grown biomass empirical formulae of CH 1.8 O 0.5 N 0.2 and a molecular weight of 24.6 g.mol 21

[START_REF] Feitkenhauer | Determination of the kinetic parameters of the phenol-degrading thermophile Bacillus thermoleovorans sp. A2[END_REF]

. doi:10.1371/journal.pone.0082397.t002

PLOS ONE | www.plosone.org 1 December 2013 | Volume 8 | Issue 12 | e82397

PLOS ONE | www.plosone.org

December 2013 | Volume 8 | Issue 12 | e82397

Acknowledgments

The authors thank Corinne Valette for technical help. We also would like to thank Dr B. Omokoko and Dr. W. Hartmeier for allowing the use of their figure to inspire Figure S1.

Alexia Comte was the recipient of a CIFRE fellowship (Kemesys/ANRT). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Supporting Information