Gwénaël Birot

Amar Kachenoura

Laurent Albera

Christian Bénar

Fabrice Wendling
email: fabrice.wendling@univ-rennes1.fr

Automatic detection of fast ripples

Keywords: EEG, epilepsy, fast ripple, interictal epileptic spike, detection, time-frequency, Fourier transform, wavelet transform, filtering

Highlights

1) We propose a novel method for automatically detecting fast ripples (FRs, 2) The signal energy in low and high frequency bands is used to classify EEG events as FRs, interictal epileptic spikes or artifacts.

3) The sensitivity and the specificity of this method is high enough to avoid "false ripples" caused by sharp transients.

Glossary

High frequency oscillations (HFOs) have been a topic of increasing interest in neuroscience over the past decade. They now constitute a novel trend in neurophysiology [START_REF] Jefferys | Mechanisms of physiological and epileptic HFO generation[END_REF] that has been made possible with the development of digital EEG equipments allowing for high sampling rates and with the identification of oscillations at up to 600 Hz in animals [START_REF] Buzsaki | High frequency oscillations in the intact brain[END_REF].

Among the wide diversity of HFOs which dominant frequency can vary from 30 Hz to 600 Hz, fast ripples (FRs) are particular transient oscillations (a few tens of ms) occurring in the frequency band ranging from 250 Hz to 600 Hz. In the normal brain (monkey), FRs have been associated with cortical spike bursts [START_REF] Baker | EEG oscillations at 600 Hz are macroscopic markers for cortical spike bursts[END_REF]. In the epileptic brain, FRs were shown to be related to abnormal modifications in the excitability of underlying neuronal systems [START_REF] Demont-Guignard | Distinct hyperexcitability mechanisms underlie fast ripples and epileptic spikes[END_REF].

Epileptic FRs have first been observed in animal models (Bragin et al., 1999b) as well as in patients with drug-resistant partial epilepsy (Bragin et al., 1999a). A number of studies then confirmed the existence of interictal HFOs in brain structures involved at the onset of seizures [START_REF] Bragin | Interictal high-frequency oscillations (80-500 Hz) in the human epileptic brain: entorhinal cortex[END_REF][START_REF] Jacobs | Interictal high-frequency oscillations (80-500 Hz) are an indicator of seizure onset areas independent of spikes in the human epileptic brain[END_REF][START_REF] Worrell | High-frequency oscillations and seizure generation in neocortical epilepsy[END_REF] and the potential value of FRs as a marker of the degree of epileptogenicity [START_REF] Engel | High-frequency oscillations: what is normal and what is not?[END_REF][START_REF] Jacobs | High frequency oscillations in intracranial EEGs mark epileptogenicity rather than lesion type[END_REF][START_REF] Worrell | High-frequency oscillations and other electrophysiological biomarkers of epilepsy: clinical studies[END_REF].

In this context, the accurate detection of FRs in depth-EEG signals recorded in patients candidate to surgery could considerably improve the identification and delineation of the epileptogenic zone which is an essential step in planning the best therapeutic strategy [START_REF] Bartolomei | The presurgical evaluation of epilepsies[END_REF]. However, this detection is far from being a trivial problem. In most of aforementioned studies, the detection of FRs was performed visually by inspecting either the raw signals or the filtered signals in the frequency band of interest (beyond 80 Hz). However, on the one hand, the visual inspection of EEG signals remains fastidious. Indeed, the number of events of interest (EOIs) occurring during interictal periods can be potentially high. In addition, the review of EEGs must be performed with an appropriate time scale (strongly magnified w.r.t. those classically used) in order to visually assess the actual presence (or absence) of transient oscillations associated with EOIs. The detection of FRs can also be helped by the use of simple signal processing algorithms like, in particular, the filtering of depth-EEG signals in the frequency band of interest (typically beyond 250 Hz). However, on the other hand, as shown in [START_REF] Benar | Pitfalls of high-pass filtering for detecting epileptic oscillations: a technical note on "false" ripples[END_REF], any high-pass filtering technique has one major pitfall: the lack of specificity due to sharp transients present in depth-EEG signals. Indeed, in this study, authors could verify that some "pulse-like" events (typically, the spike component of interictal epileptic spikes -IES) are associated with an abrupt increase of the signal energy in the higher frequency bands, exactly as in the case of actual FRs. A typical example is provided in Figure 1A. As a consequence, the oscillations generated in the filtered signal that are related to the features of the impulse response of the high-pass filter can be confounded with actual FRs, leading the authors to denote them as "false ripples" (Figure 1B).

In this context, the demand is high for automatic detection procedures with increased specificity, while maintaining a good sensitivity. In this paper, we propose a novel detection method for automatically identifying FRs occurring in depth-EEG signals. To our knowledge, very few methods have been proposed so far to achieve this goal. A few years ago, band-pass filtering techniques were combined with a thresholding procedure of the energy of sub-band signals to automatically detect HFOs [START_REF] Crepon | Mapping interictal oscillations greater than 200 Hz recorded with intracranial macroelectrodes in human epilepsy[END_REF][START_REF] Gardner | Human and automated detection of highfrequency oscillations in clinical intracranial EEG recordings[END_REF][START_REF] Staba | Quantitative analysis of high-frequency oscillations (80-500 Hz) recorded in human epileptic hippocampus and entorhinal cortex[END_REF]. Very recently, Zelman and colleagues [START_REF] Zelmann | A comparison between detectors of high frequency oscillations[END_REF] proposed a new method (referred to as the MNI detector) and compared it to the three aforementioned ones. The initial step of their method was also based on a band-pass filter (80-450 Hz) but included a baseline analysis (based on wavelet entropy) to differentiate channels with transient HFOs from those with continuous HF activity. The decision (presence/absence of a HFO) was based on a threshold. While these methods offer a good sensibility they exhibit poor specificity due to sharp IES or artifacts often present in raw signals. The method proposed in [START_REF] Blanco | Unsupervised classification of high-frequency oscillations in human neocortical epilepsy and control patients[END_REF] makes use of the result of the Staba's method as a first step and then automatically classifies the resulting candidate events using a data mining algorithm. The method could separate actual HFOs (including ripples and FRs) from artifacts in a very large data set but the issue of spurious detections due to IES was not addressed.

In contrast, our detection method was designed to exclusively recognize FRs and to avoid false background activity generated with a realistic computational model of hippocampal activity [START_REF] Wendling | Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG[END_REF]. We also provided how to calculate the optimal threshold that allows the discrimination of FRs from IESs in the method. Results showed that the proposed detection method can achieve good performance with relatively few parameters to adjust. As an important finding, best results were obtained when the energy ratio between oscillations in the FR band vs. gamma band was used as a discriminant factor in the second stage of the detection procedure.

Material and methods

Problem formulation and notations

The depth-EEG signal on which the detection is performed is denoted by {s

Proposed detection methods

Basic principle

Our FR detector involves two stages (figure 2). In the first stage, events of potential of interest (EOIs = events exhibiting significant energy in the frequency band greater than 256 Hz, among which IESs, FRs and artifacts) are detected. This is done using a simple method based on high-pass filtering (HPFM), as depicted in figure 3A. We used here a very simple method but all HFO detectors based on high-pass filtering could work (e.g. method given by [START_REF] Staba | Quantitative analysis of high-frequency oscillations (80-500 Hz) recorded in human epileptic hippocampus and entorhinal cortex[END_REF]). Then, the second stage consists in the recognition of FRs among detected EOIs. This step is the most important and is the main contribution of our work. We tested two methods both based on the ratio between the energy in high frequency band and the energy in low frequency band (see Figures 2B and2C). The first method, called Fourier Transform based Method (FPM) uses a short-term Fourier Transform while the second method, called Wavelet Transform based Method (WTM), uses multi-resolution discrete Wavelet Transform.

Stage 1: detection of EOIs (HPFM)

The detection of EOIs was performed with high-pass filtering of cut-off frequency equal to 256 Hz.

An IIR high-pass filter of order O was used (Butterworth, O=4, 80 dB/decade). The filtered signal at time n is given by: A contribution of the background activity (BKG) may also be present since rest depth-EEG signals have a wide frequency spectrum, including frequencies greater than 256 Hz. Thus, the filtered signal at time n can be expressed as: Et } of the filtered signal can be calculated using a sliding Hanning window of duration N denoted by

[ ] [ ] [ ] hp256 hp256 0 1 0 1 O O i j i j sn b s n i a sn j a = = =
[ ] [ ] ( ) ( ) hp256
[ ] { } N hn. Therefore, we have: [ ] [ ] ( ) [ ] 2 hp256 hp256 N n Et sn h n t = = (1)
Estimated occurrence times of EOIs, ˆp t , are eventually computed as the arguments of the local maxima of

[ ] hp256

Et greater than a threshold :

( ) ( ) { } [ ] ( ) [ ] { } 1P h p 2 5 6 h p 2 5 6 ˆ,..., argmax , t tt E t E t =>
where the arg max function stands for the search of local maxima. In practice, threshold is adjusted from the distribution of E hp256 . Typically, in this study, we chose for any t value such that the probability that E hp256 [t] < is greater than 0.98 (i.e. 98 percentile) for both simulated and real data.

Stage 2: Classification of EOI's (FTM and WTM)

As mentioned, the goal of the EOI classifier is to extract fast ripples from other events detected at the first step, especially IESs. We introduce two methods to achieve this extraction, both based on the ratio between the energy in the high frequency (HF) band and in the low frequency (LF) band.

Method 1: Fourier Transform based Method (FTM)

The first proposed method is based on the digital short-time Fourier transform (with rectangular window) at time t p of the depth-EEG signal {s[n]}:

( ) [ ] 1 2 2 , p p tK n if K p nt K Sft sn e + = =
The energy in a specific frequency band

{ } 1 ,, K ff f =
of the pth EOI is thus given by:

( ) ( ) 2 , f p ff Ep S f t =
The criterion we propose to identify FRs is based on an energy ratio. First, we compute the energy of EOIs in the high frequency band HF (f 256 Hz) and in the low frequency band

( ) { } ( ) { } FR 1 HF/LF 1 ˆ, FTM FTM pp E p => (2)
In practice, it is noteworthy that the LF band was let as a free parameter (optimized from results, see section 3) while the HF band was fixed to 256-512 Hz.

Method 2: Wavelet Transform based Method (WTM)

The second proposed method is based on the ratio between energy in different levels of a dyadic wavelet transform of the EOIs. The dyadic wavelet transform of the depth-EEG signal {s[n]} over the

pth EOI of time support { } ,,,, 1 p p p tK t tK +
can be written as:

( ) [ ] 1 /2 2, 2 2 p p tK j j j p nt K Wt s n n t + = =
where j is the decomposition level and is the mother wavelet. The level j of the dyadic decomposition contains the contribution of the signal including frequencies between f s /2 j and f s /2 j+1 where f s is the sampling frequency. The energy at level j of the wavelet decomposition of the pth EOI is given by the sum over time of the square wavelet transform:

( ) ( ) ( ) ( ) 2 2, j j p t Ep W t =
As for the above-described FTM, the criterion that allows for the classification of the pth EOI is given by the ratio between energy in HF levels and LF levels:

( ) ( ) ( ) ( ) ( ) HF HF/LF LF j j WTM j j Ep Ep Ep =
In practice, the set of levels HF j included only one level (j = 1 at f s =1024 Hz or j = 2 at f s =2048

Hz) corresponding to the 256-512 Hz frequency band while the set LF j corresponding to low frequencies was also let a free parameter (the influence of which is analysed in section 3). Eventually, the occurrence times of EOIs that correspond to FRs are estimated for a given threshold 2 by:

( ) { } ( ) { } HF/LF FR 2 2 ˆ, WTM WTM pp E p => (3)

Real and simulated signals

Human data

Intracerebral stereo-EEG (SEEG or depth-EEG) signals were used for the purpose of this study.

Signals were recorded in patients (n=2) suffering from mesial TLE. The depth-EEG exploration was carried out as part of normal clinical care of both patients. Informed consent was given by patients about the use of data for research purposes. Only signals recorded from electrode contacts located in the hippocampus (Ammon's horn) were used as many FRs as well as IESs could be observed in this brain structure (Figure 2A). Intracerebral electrodes are composed of 10 to 15 cylindrical contacts (length: 2 mm, diameter: 0.8 mm, 1.5 mm apart). Two contacts (more mesial) are usually located in the hippocampus. For the purpose of this study, we chose the electrode contact at which the highest number of EOIs was observed. About 300 EOIs were visually detected in several hours of recording and annotated as FRs (about 150) or IESs (about 150) by the expert (see Table 1). The visual annotation was helped by the use of an EEG review software (Amadeus, developed in the lab -LTSI, University of Rennes -) allowing for strong magnification of the time-scale (1 sec/page). It is worth mentioning that visually detected events were quite representative of those recorded from the hippocampus in mesial TLE according to our experience. Regarding the behavioral state of the two patients, visual analysis of the videos corresponding to analyzed periods of depth-EEG data showed that both patients were lying on the bed. They were awake. Eyes were opened. Both patients were interacting with some other people present in the room. Signals were recorded on a 128-channel Micromed™ system and were sampled at f s =1024 Hz. No hardware filter was present in the acquisition procedure except the high-pass filter (cut-off frequency about 0.1 Hz) classically used to remove the offset on the baseline. The 3D position of the electrode exploring the anterior hippocampus was anatomically checked from the fusion of the telemetric X-ray imaging performed per-operatively (on which the electrode contacts are clearly visible) and the post-operative MRI scan (on which the trajectory of each electrode remains visible).

Animal data

Depth-EEG signals recorded in freely moving mice (n=4) treated with kainic acid (KA) were also used for this study. Readers may refer to [START_REF] Suzuki | Morphogenetic effect of kainate on adult hippocampal neurons associated with a prolonged expression of brain-derived neurotrophic factor[END_REF] for details about this kainate model of TLE.

In brief, it was shown to closely replicate some pathological changes observed in human mTLE. These changes include both histological alterations and interictal/ictal electrophysiological patterns. The model is based on a unilateral injection of a low dose of KA into the dorsal hippocampus of mice.

After injection, mice were implanted with bipolar depth electrodes (consisting of two twisted polyester insulated stainless steel wires, 139 m diameter each and 0.3 mm apart) in both hippocampi (CA1 region). After a latent period of about 2 weeks, spontaneous seizures begin to occur, accompanied by a progressive cell loss in the CA1 and CA3 regions of the hippocampus over a period of 4 to 6 weeks [START_REF] Bouilleret | Early loss of interneurons and delayed subunit-specific changes in GABA(A)-receptor expression in a mouse model of mesial temporal lobe epilepsy[END_REF][START_REF] Suzuki | Morphogenetic effect of kainate on adult hippocampal neurons associated with a prolonged expression of brain-derived neurotrophic factor[END_REF] Depth-EEG signals were recorded on a video-EEG monitoring system (Deltamed TM). They were sampled at f s =2048 Hz. One hardware high-pass filter was present in the acquisition procedure (cut-off frequency: 0.16 Hz). It has no effect on the shape of EOIs. A key point of this experimental model is that during the latent period and the chronic period, both IESs and FRs are frequently observed in depth-EEG signals, as show in Figure 2B. As for human data, the review of depth-EEG signals and the annotation of EOIs (about 400 IESs and 1000 FRs, see Table 1) was assessed by the same expert who used the aforementioned EEG review software allowing for magnification of the time scale.

Simulated signals

In order to assess the detector performance with respect to the level of background activity, simulated long-duration signals in which transient events extracted from the real data (see subsections 2.3.1 and 2.3.2) were mixed up with simulated EEG background activity. This background activity was generated using a realistic model of neuronal population described elsewhere [START_REF] Wendling | Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG[END_REF]. The extracted segments of real data that contained the transient events had a length of 512 ms. In order to avoid any discontinuity in the generated signal (potentially leading to unwanted sharp transients), a weighting function (sigmoid shape) was used to obtain a smooth transition at the junction between the inserted event and the background activity (see Figure 4A). The transient events appeared randomly in the simulated signal following a Poisson's law allowing us to set the mean number of occurrence of each type of transient events per minute. The level of background activity was controlled by a multiplicative coefficient and was quantified by the Fast Ripple to Background Ratio (FRBR). The FRBR quantity was defined as the mean power of FRs relative to the mean power of background activity: gives the cardinal of a range. For each FRBR (-5 dB to +), a 60 min duration signal was simulated with, on average, 8 occurrences of a randomly-chosen EOI per min.

Examples are provided in Figure 3 showing a short segment of simulated signal including a fast ripple (at time t = 0.25 s) and an interictal spike (at time t = 3.75 s). For high FRBR values (Figure 4B and 4C), both EOIs are clearly visible while they can hardly be distinguished from background as the FRBR gets lower (Figure 4D and4E). This is especially true at FRBR = -5 dB (Figure 4E) where both EOIs become impossible to see.

Performance evaluation

Performance criterion

Studied methods were designed to detect the occurrence times of FRs. According to the signal detection theory, receiver operating characteristic (ROC) curves were used to quantitatively analyse the performance of the methods. The ROC curve is a parametric graphical plot representing the True Positive Rate (TPR, also referred to as "sensitivity") as a function of the False Positive Rate (FPR, also referred to as "one minus specificity" or "false alarm rate"). Both values depend on one parameter that is threshold for HPFM, threshold 1 for FTM and threshold 2 for WTM. Each threshold value provides a TPR/FPR couple. The complete ROC curves are obtained by varying the threshold value over a given range. As a complete ROC curve is not handy to show results, we will rather provide the Area under the ROC Curve (AuC), which corresponds to the integral of the ROC curve for FPR ranging from 0 to 1. The AuC value ranges between 0.5 (worst result) and 1 (best results) and provides a compact and direct way of showing method accuracy. Indeed, the perfect detector would exhibit a TPR equal to one for a FPR equal to zero. In such a case the AuC is equal to one. The worst detector would show a line of slope equal to 1, hence the AuC would be 0.5. In practice the AuC could be slightly less than 0.5 due to the variance of the TPF and FPF estimators.

Parameters of evaluated methods

The proposed methods depend on explicit parameters. In this section, we provide some parameters we used. We chose them with preliminary studies not shown in this paper.

For the first step of the procedure (HPFM) we used a fourth order IIR Butterworth high-pass filter (80 dB/decade), which is a good trade-off between performance, stability and complexity. The coefficients of this filter were adjusted such that the cut-off frequency was equal to 256 Hz (i.e. the attenuation at 256 Hz is 3dB). This frequency is in accordance with the FR band. In order to calculate the local energy of the filtered signal (eq. 1), we used a Hanning window of f s /8+1 samples (i.e. 125 ms) which we believe is the very maximum duration of FRs.

For FTM, the duration of EOIs on which the Fourier Transform is calculated was fixed at f s /8 (250 ms). The high frequency band was set to be 256-512 Hz in order to maximize the FR energy while the low frequency band was let as a free parameter. An analysis of the method performance with respect to nine different LF bands was performed (see §2.5.3).

For WTM the time segment of EOIs was also set to f s /8 samples (125 ms). From preliminary analysis in which we tested several mother wavelets (Daubechies 1 to 10), we used a Daubechies 4 mother wavelet. The number of decomposition levels N L depended on the sampling frequency. For signals sampled at 1024 Hz (human data), N L was equal to 8. We retained the first level (j=1) as the HF band (256-512 Hz). For signals sampled at 2048 Hz (animal data), N L was equal to 9. We picked up the second level (j=2) for the HF band (256-512 Hz). As previously, the levels corresponding to the LF band were also let as free parameters for subsequent optimization (see §2.5.3).

Optimization of parameter LF in FTM and WTM

In order to determine the optimal LF bands for both FTM and WTM (see eq. 2 and eq. 3), we analysed the method performance for nine different values of the LF band: [0,512], [0,256], [0,128], [0,64],

[0,32], [128,256], [64,128], [32,64] and [32,128] Hz. The optimization was performed using the classification rate for two different situations: i) the FR rate is known, i.e. we calculated the good classification rate using optimal threshold computed at appropriate FR rate, ii) the FR rate is unknown, i.e. we calculated the good classification rate using optimal threshold computed for an arbitrary FR rate equal to 0.5. The second technique allowed us to know the supplementary errors committed when FR rate is not known and set to an arbitrary value.

Results

Choice of the LF band in methods FTM & WTM. We performed a sensitivity analysis with respect to the choice of the LF band for FTM and WTM (2 nd stage of the proposed detection method). For both algorithms, the objective was to find which LF band maximizes the separation between FRs and IESs in EOIs manually selected by the expert. The study was performed both on human and animal data (data described in § 2.3.1 and 2.3.2). The results for the nine selected frequency bands are reported in table 3 for human data and in table 4 for animal data. First, for both types of data, results revealed that both methods showed dependency on this parameter. This was particularly true for FTM. For instance, in human data (table 3), the TPR at fixed FPR = 0.05 was found to vary from 0.238 (LF = ]128, 256] Hz) to 0.968 (LF = ]32, 128] Hz). The same result also held for mouse data. Second, the performance of FTM was found to be comparable to that WTM w.r.t. the choice of LF when parameter AuC was considered. Stronger differences were observed when one considers the second criterion (TPR at fixed FPR = 0.05). Interestingly, the performance of WTM was found to dramatically decrease when the LF band included very low frequencies (lowest performance obtained for LF = ]0, 32] Hz for human and animal data). Finally, both methods exhibited best results for ]32-64] Hz and ]32-128] Hz bands with an AuC almost equal to 0.99 (see grey boxes in tables 3 and 4). WTM had similar performance than FTM in term of AuC but slightly lower performance (0.94 vs. 0.96 for both human and animal data) in term of TPR for a FPR fixed at 0.05. This result could be explained by a detailed analysis of the ROC curves which showed that, for FTM, the TPR increased in a steep manner at low FPR (2 to 5 %) but reached the value of 1 for higher values.

Threshold analysis of FTM and WTM

We give in table 2 the mean and variance of FTM and WTM criteria as well as the result of the Kolmogarov test. We divided results between human and animal data. We found that all the distributions were Gaussian and that the mean value of FRs was always greater than the mean values of IES. Moreover, these mean values of the criteria do not differ so much from human to animal data (0.07 and 0.09 for FTM, and 0.04 and 0.09 for WTM). From these estimated Gaussian distributions the optimal threshold and the related good detection rate as a function of the FR rate are given in figure 5. We found that the optimal threshold did not vary significantly for FR rate ranged from 0.1 to 0.9. The related good classification rates was high (>0.93) when the optimal threshold was computed from a known FR rate. This good classification rates remained high (>0.9) when the optimal threshold was computed from FR rate arbitrarily set to 0.5. product.

FRBR

Simulated signals.

We compared the performance of the three methods (HPFM, FTM and WTM) using signals simulated as described in section 2.3.3. The interesting aspect of such simulations is that the level of background activity, characterized by the FRBR, could be varied. Results are given in Table 5. First, they revealed that the HPFM exhibited very low performance whatever the level of background activity relative to that of EOIs to be detected. This means that a simple high-pass filtering procedure could not discriminate FRs from IESs. In other word, this result showed that the signal energy beyond 256 Hz could not be used alone as a criterion to detect FRs. Second, results also showed that FTM and WTM exhibited comparable results for a FRBR equal to 15 dB (which corresponded to the value estimated from real data): in both cases, the AuC was found to be high (>0.98) as was TPR (> 0.93) for a fixed FPR equal to 0.05. As expected, when the amplitude of EOIs to be detected became low w.r.t. the amplitude of background activity (FRBR = 5 dB and FRBR = -5 dB), the performance of both methods decreased. Interestingly, WTM showed higher robustness w.r.t.

this parameter (AuC = 0.889 and TPR = 0.458) compared to FTM (AuC = 0.679 and TPR = 0.129) in a situation where EOIs were (almost) impossible to detect visually (FRBR = -5dB). This result can be explained by the use of a mother wavelet in WTM which shape is close to that of actual FRs in the 256-512Hz band. This "shape fitting" allows for changes that can still be detected in the convolution appeared at the time instants where EOIs (defined as events exhibiting energy in the HF band) were present in the depth-EEG signal. This segment was chosen for the presence of three types of EOIs (see FR, IES and ART labels in Figure 6A). In the first stage of the detection procedure, HPFM makes use of a threshold = 1.5 (corresponding to 0.98 percentile) to extract EOIs (marked on the signal by a vertical line). For the second stage, the behaviour of FTM is displayed in Figure 6C where we represented the criterion value (i.e.

( )

HF/LF

FTM Ep

) for each EOI detected by HPFM at the first stage.

Detection results were obtained for a threshold value equal to 1 = 0.030. In this example, FTM detected both FRs (marked as True Positive (TP)) and did not exhibit false detection (FP) since the two IESs and the two artifacts were rejected. Finally, results obtained with WTM are displayed in figure 5C. In this example, using a threshold value equal to 2 = 0.025, the method could detect both FRs (as wanted) but also exhibited a false positive.

Quasi-simultaneous FRs and IESs. We implemented both methods in a user-friendly software that allows for direct visual assessment of the detector performance on real data. The graphical user interface is illustrated in figure 7A. It includes two plots showing the raw signal (upper plot, black color) and the same signal (lower plot, red color) on top of which automatically detected EOIs are marked by vertical bars (FRs: green color, IES: blue color). This GUI offers strong magnification on EOIs for careful visual inspection of detection results, as illustrated in figure 7B. In this example, one can observe the behaviour of the proposed detection method (here FTM) in the case where both the IES and the FR occur quasi-simultaneously (a few tens of ms delay). Interestingly, the detector is able to automatically mark both events when the duration N of the sliding Hanning window used in the first stage of the detection procedure is short enough (32 ms in this case).

Discussion and perspectives

The detection of transient events in EEG signals has long been a topic of large interest in clinical neurophysiology. This problem has been -and is still -considered as a difficult problem in signal processing. During the past decades, many methods were proposed to automatically detect interictal epileptic spikes (IESs), starting from pioneering works of Gotman [START_REF] Gotman | Automatic recognition and quantification of interictal epileptic activity in the human scalp EEG[END_REF].

Proposed algorithms were based on Fourier or wavelet transforms, on mimetic and rule-based approaches, on neural networks, on adaptive filtering (template matching), on principal or independent component analysis. Readers may refer to [START_REF] Gotman | Automatic detection of seizures and spikes[END_REF] and to (Fleureau et al., 2011a;[START_REF] Tzallas | Epileptic spike detection using a kalman filter based approach[END_REF] for partial reviews.

Recently, fast ripples (FRs) have attracted a lot of attention since they could constitute an interictal electrophysiological marker for epilepsy [START_REF] Engel | High-frequency oscillations: what is normal and what is not?[END_REF][START_REF] Jefferys | Mechanisms of physiological and epileptic HFO generation[END_REF]. Indeed, FRs might prove more specific than IESs with respect to the underlying epileptogenicity [START_REF] Demont-Guignard | Distinct hyperexcitability mechanisms underlie fast ripples and epileptic spikes[END_REF] and might be more specifically generated in brain structures involved at the onset of seizures [START_REF] Zijlmans | High-frequency oscillations mirror disease activity in patients with epilepsy[END_REF]. In this context, the reliable detection of fast ripples (FRs) can provide The main findings of this study are summarized hereafter, first from a methodological viewpoint, and then from a clinical viewpoint.

The use of simulated signals. We decided to start from realistic simulations of depth-EEG signals.

Simulated signals were obtained from the insertion of real EOIs (namely FRs and IESs) into background EEG activity generated from a neural mass model published elsewhere [START_REF] Wendling | Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition[END_REF]. This approach provided a "ground truth" on both the occurrence time and the type of EOIs that is crucial in the objective assessment of any detection procedure. In addition, this approach also allowed us to test an important factor that was not tested in previous reports [START_REF] Gardner | Human and automated detection of highfrequency oscillations in clinical intracranial EEG recordings[END_REF][START_REF] Staba | Quantitative analysis of high-frequency oscillations (80-500 Hz) recorded in human epileptic hippocampus and entorhinal cortex[END_REF][START_REF] Zelmann | A comparison between detectors of high frequency oscillations[END_REF]: the detection robustness when the amplitude of background EEG becomes predominant w.r.t. the amplitude of EOIs to be detected.

transients (IES) [START_REF] Benar | Pitfalls of high-pass filtering for detecting epileptic oscillations: a technical note on "false" ripples[END_REF]. In addition, our method is conceptually simple. In practice, it is easy to implement and use.

Specificity and sensitivity. The method was found to show slightly improved performance when the WT is used for the second stage. In all studied situations, results showed that the use of the FT or the WT for the second stage lead to a much higher performance compared to the use of a simple high-pass filter. Using the WT, the method could achieve the detection of FRs with sensitivity greater to 0.93 when the specificity was set to 0.95. In other words, in a situation where 95% of detected EOIs are actually FRs, only 7% of these EOIs are missed (either undetected or wrongly labeled) by the proposed method. As expected, we also found that the method performance depends on the amplitude of FRs respective to the level of background activity. As the "fast ripple to background" ratio (FRBR) decreased, the method sensitivity rapidly dropped when high specificity was maintained. However, it should be noted that the poorer performance (45.8% sensitivity) was obtained in a situation where the FRBR was so low (-5 dB) that FRs became undetectable by visual inspection.

Parameters to be adjusted. An interesting feature of the proposed method is that the number of parameters to be adjusted is rather limited. For the first stage, any band pass filter (250-600 Hz) can be used to compute the signal energy in the FR frequency band and then to obtain EOIs by thresholding (parameter ). For the purpose of this study, we used a 4 th order Butterworth filter with cut-off frequencies equal to 256 Hz and 512 Hz to have a correspondence with the FTM and the WTM. An IIR implementation (recursive filter) was preferred for its rapidity. Parameter can be easily adjusted from the empirical histogram of the filtered signal energy values (see §2.2.2). For the second stage of the detection procedure, the essential parameter to distinguish FRs from IESs was found to be the energy ratio between high and low frequency bands (HF and LF, respectively). The HF band must be adjusted to best match the frequency band of FRs (typically, 250-600 Hz). In this study, we used a HF band ranging from 256 Hz to 512 Hz, constrained by the dyadic discrete wavelet transform. We let the LF band as a free parameter and obtained the best results (in term of separation of FRs from IESs) for a LF band equal to [32-128 Hz] which coincided with the gamma frequency band on the EEG. This result also indicates that our method is likely to not be affected by slow waves (typically in the delta frequency band) which can be present in EEG signals during sleep, in particular.

Finally, for the WTM, the mother wavelet and the number of levels must also be adjusted. We tested several configurations (data not shown). Best results were obtained for a Daubechies 4 wavelet decomposition on eight or nine levels depending on the sampling frequency (1024 and 2048 Hz, respectively). The classification of FRs and IESs is done by thresholding the energy ratio between high and low frequency bands. Interestingly, one can notice that these values do not differ so much from one recording to another (same order of magnitude). This result indicates that the energy distribution in proposed sub-bands (gamma and FR) is robust with respect to the type of recording (performed in humans and in mice) and suggests that the algorithm can be used in some other situations (like other experimental models of epilepsy) characterized by the occurrence of HFOs in the FR frequency band (HF subband).

Potential clinical value.

Both methods are relatively easy to implement. Besides the performance study (in term of recognition of FRs and IESs), we could also analyse more difficult situations where genuine FRs occur quasi-simultaneously with, or are part of, IESs. Indeed, the co-occurence of spikes and fast ripples (denoting different pathological condition of underlying neuronal systems) can be encountered and consequently is also relevant to detect. . Interestingly, for appropriate setting of the time window used in the first stage, and given that both types of events do not occur strictly at the same time, our method can still separate them. More generally, in most of epilepsy surgery units, recordings are performed in patients candidate to surgery using long-term video-EEG monitoring (8-24 hours a day, 5-10 days). Huge data sets are generated by the acquisition systems since signals are generally recorded on 128 to 256 channels at 1 kHz. We think that the proposed detection method can dramatically decrease the workload in assessing the presence of FRs in these intracranial EEGs. In addition, it may allow for systematic identification of FRs during interictal periods which represent large amounts of data compared to seizure episodes. To us, it is clear that the therapeutic strategy cannot depend only of the presence/absence of high frequency oscillations (HFOs) in explored brain structures. However, the objective quantification of HFOs over interictal periods can efficiently complement the classical often qualitative way of analyzing depth-EEG data recorded in patients with drug-resistant epilepsy.

Perspectives. The online implementation of the proposed method is a topic of interest for future work.

In addition, some other time-frequency methods (empirical mode decomposition (Fleureau et al., 2011a;Fleureau et al., 2011b) and matching pursuit [START_REF] Jmail | A comparison of methods for separation of transient and oscillatory signals in EEG[END_REF][START_REF] Mallat | Matching pursuit in a time-frequency dictionary[END_REF] in particular) could also be tested in the second stage of the detection procedure to check whether the overall performance could still be increased. Finally, these detection methods (based on timefrequency features of the signal) will also be compared with that recently proposed methods by Blanco et al. [START_REF] Blanco | Unsupervised classification of high-frequency oscillations in human neocortical epilepsy and control patients[END_REF] and Zelmann and collaborators [START_REF] Zelmann | A comparison between detectors of high frequency oscillations[END_REF], although not designed to specifically detect FRs but HFOs in a more general way. This comparative study should be doable since time-frequency based methods can be adapted quite straightforwardly to the detection of ripples (128-256 Hz) in addition to fast ripples. Such a comparison will be performed through the use of different performance metrics as suggested by Casson et al. (Casson et al., 2009).

Thus we have to maximize P ne with respect to , i.e. to find the roots of the derivative of P ne with respect to . The derivative is given by: ( ) ( ) ( ) ( ) Thus the optimal , denoted by opt is one of the two roots of a second order polynomial function in which the coefficients are know if m0, m1, 0, 1, P(H0) and P(H1) = 1 -P(H0) are known. In practice, the root which maximizes P ne has to be chosen. The corresponding rate of good classification is given by: ( )

ne

Figure 1 :

 1 Figure 1: Typical FRs and IESs recorded from hippocampus in human (TLE) and in an animal model of epilepsy (mouse, kainate model). (A) Human FRs and IESs (depth-EEG signals) with corresponding spectrograms. Note that both EOIs (the FR and the IES) exhibit energy in the 250-600 Hz. (B) FRs and IESs recorded from hippocampus using macro-electrodes (human: depth-EEG, mouse: LFPs). Upper plots: raw signals. Lower plots:

Figure 2 :

 2 Figure 2: Overview of the method for automatic detection of FRs. The human depth-EEG signal (A) and animal depth-EEG signal (B) exhibits FRs and IESs. With a simple high-pass filter, very sharp components of the IESs could be interpreted as a FRs. In the proposed methodology (C), stage 1 (HPFM) allows for the detection of events (FRs, IESs and some artifacts) exhibiting significant energy in the FR band (256-512 Hz). The second stage acts as a classifier and separates FRs from the other EOIs. This classification is achieved using the energy ratio between the HF (256-512 Hz) band and lower frequency band. The energy ratio is computed using either a short-time Fourier Transform (FTM) or a dyadic wavelet transform (WTM). See glossary for abbreviations.

  of{EONI[n]} is vanished while a significant contribution of EOIs is preserved.

Figure 3 :

 3 Figure 3: Step-by-step pipeline of studied methods (HPFM, FTM and WTM). (A) HPFM consists in i) high-pass filtering the signal (cut-off frequency = 256 Hz), ii) calculating the short-time energy of the filtered signal and iii) finding the local maxima of the short-time energy greater than a threshold in order to estimate the occurrence times of EOIs. (B) FTM consists in computing the short-time Fourier transform at the instant of detected EOIs, ii)calculating the ratio between the EOI energy in the HF band vs. in the LF band, and iii) thresholding this ratio in order to separate FRs from IESs and artifacts. (C) WTM consists in i) computing the dyadic wavelet transform of the EOI, ii) calculating the ratio between energy of the decomposition level corresponding to the 256-512 Hz and decomposition levels of lower frequencies and iii) thresholding this ratio in order to identify FRs. See glossary for abbreviations.

Figure 4 :

 4 Figure 4: Generation of simulated depth-EEG signals. (A) EOIs extracted from real data were inserted in simulated background activity. The background level was controlled and quantified by the fast ripple to background ratio (FRBR). Examples of simulated depth-EEG including one FR and one IES for FRBR = (B), FRBR = 15 dB (C) , FRBR = 5 dB (D), FRBR = -5 dB (E). See glossary for abbreviations.

  range where fast ripples occur while BKG is the time range of background activity. The function ( ) card .

FTM

  and WTM. Both methods show best performance for the 32-128 Hz and 32-64 Hz bands. Gray boxes indicate best performance. See glossary for abbreviations.

Figure 5 :

 5 Figure 5: Optimal threshold and good classification rate of the methods as a function of the occurrence rate of fast ripples. For each graph, on top is the optimal threshold as a function the fast ripple rate. On the bottom is the

Figure 6 :

 6 Figure 6: Behavior of proposed methods on real human data (A). The short-time energy in the 256-512 Hz band (B) shows peaks at occurrence times of EOIs, which can be either FRs, IESs or artifacts. (C) Fourier Transform based method. Top: ratio between energies in the 256-512 Hz band and in the 32-128 Hz band. Bottom: detection

Figure 7 :

 7 Figure 7: Implementation of the proposed detector (FTM) in a user-friendly software specifically designed to directly inspect detection results. (A) The user selected in the EEG reviewing software (not shown) a segment of about 224 s of data (upper plot). Detection results appear directly on the signal (lower plot, red trace) as green bars (FRs) or blue bars (IESs). (B) A zoom on a 3 s segment of signal (upper plot). In this segment, FRs (green arrows) and mixed IESs/FRs (bleu/green arrows) occur. As seen in detection results (lower plot), all FRs are detected. In addition, two bars (blue and green) are automatically positioned by the detector in the presence of quasi-simultaneous IESs and FRs.

  additional and quantified arguments to epileptologists to assess the epileptogenic nature of some brain structures explored with intracranial electrodes. Conversely to IESs, very few methods have been proposed so far to automatically and specifically detect FRs in EEG signals. This is the issue we addressed in this study. To proceed, we proposed a novel detection procedure based on two stages (global detection of EOIs and local classification). The evaluation methodology was based on the simulation of long-duration depth-EEG signals and on ROC curves. Finally, tests were performed on real data recorded either in a patient with TLE or in an animal model of TLE.

  Consequently we have to solve the following equation in order to find the optimal threshold:

  EOI p n } denotes the time course of the pth EOI, t p is the time instant where it occurs, P is the number of EOIs and {EONI[n]} is the time course of other transient events (of non-interest). The

	by t p . Each EOI is assumed to have a finite time support of length less than 2K (values used in practice are discussed in section 2.5). Thus the pth EOI's time support in {s[n]} is delimited by { } ,,,, 1 p p p tK t tK + . Consequently the depth-EEG signal at time n can be written as [ ] [ ] [ ] BKG EOI EONI P p p sn n n t n = + [ ] EOIs are classified in three types: fast ripples (FRs), interictal epileptic spikes (IESs) and artifacts. Accordingly, the depth-EEG signal can be expressed as [ ] [ ] [ ] IES FR ART FR IES ART 11 1 BKG FR IES ART EONI P P P pp pp pp pp p sn n n t n t n t n == = =+ + + + where [ ] FR p n , [ ] IES p n and [ ] ART p n are the time course of the pth FR, IES and artifact, respectively, FR p t , IES p t and ART p t are the times where they occur, respectively, and FR P , IES P and ART P are the number of FRs, IESs and artifacts, respectively. + where { The proposed methods aim at detecting the occurrence times of FR, i.e. FR p t for p varying from one to
	p	1 =

[n]}. This signal mainly contains background (denoted by {BKG[n]}) activity in which some transient events may appear randomly. These transient events include i) events of interest (EOIs) characterized by significant energy (compared to BKG) in the frequency band of interest, typically ranging from 250-600 Hz (rounded to 256-512 Hz in our case for methodological reason) and ii) some other events of noninterest (EONI) exhibiting energy at lower frequencies. The occurrence time of the pth EOI is denoted FR P .

  where hp(.) is the high pass filter function. Assuming that the level of BKG in the 256-512 Hz band is not higher than the level of EOIs in the 256-512 Hz band, the local maxima of the local energy of

						P
			sn h p =	BKG	n	+	h p	EOI	p	n t	p
						p	1 =
	[ ] sn correspond to the occurrence times of EOIs. hp256
	The local energy {	hp256	[ ]

Table 1 :

 1 . Upon completion of the experiments, histological analyses were performed to verify the location of the KA injection, the location of the hippocampal electrode and the pattern of neuronal loss/dispersion of dentate gyrus granule cells. All animal procedures were conducted in accordance with the European Communities Council Directive of 24 November 1986 (86/609/EEC). The experimental design was made to minimize animal suffering. Details about the recordings used in this study.

	Data set	Duration (s)	Recorded brain	Number of	Number of IES
			structure	FRs
	human #1	4000	Anterior	62	95
			hippocampus
	human #2	2000	Posterior	80	61
			hippocampus
	mouse #1	7200	Hippocampus (CA1),	318	50
			ipsilateral to KA
			injection
	mouse #2	1500	Hippocampus (CA1)	75	161
			contralateral to KA
			injection
	mouse #3	7200	Hippocampus (CA1)	0	182
			contralateral to KA
			injection
	mouse #4	914	Hippocampus (CA1),	680	0
			ipsilateral to KA
			injection

Table 2 :

 2 Estimated mean and variance of the FTM and WTM criteria, and results of the Kolmogorov test.

					Closest Gaussian		Kolmogorov test (Normal
	Data	Method	Class	distribution Mean Variance	Significance	law)	Result
								level
	Human	FTM WTM	FR IES FR IES	0.06897 0.00707 0.04047 0.01048	0.00083 0.00010 0.00009 0.00005	0.05 0.05 0.05 0.05	Positive Positive Positive Positive
	Animal	FTM WTM	FR IES FR IES	0.08900 0.00638 0.09333 0.02374	0.00225 0.00010 0.00058 0.00021	0.05 0.05 0.05 0.05	Positive Positive Positive Positive
			]0,512] ]0,256] ]0,128] ]0,64] ]0,32] ]128,256] ]64,128] ]32,64] ]32,128]
	AuC		0.955	0.955 0.955 0.952 0.945	0.883	0.973	0.983	0.982
	TPR for a	0.503	0.503 0.503 0.483 0.440	0.238	0.822	0.965	0.968
	FTM
	FPR value
	of 0.05
	AuC		0.912	0.912 0.912 0.909 0.918	0.960	0.975	0.986	0.986
	TPR for a	0.355	0.355 0.355 0.355 0.276	0.766	0.897	0.945	0.943
	WTM
	FPR value
	of 0.05

These results led us to choose the band ]32, 128] Hz as the LF band to estimate the occurrence times of FRs (see eq. 2 and eq. 3) in simulated and real signals, as reported hereafter.

Table 3 :

 3 Human data(TLE, hippocampus). Influence of the choice of the LF band in FTM and WTM. Both methods show best performance for the 32-128 Hz and 32-64 Hz bands. Gray boxes indicate best performance.

	See glossary for abbreviations.

Table 4 :

 4 Animal

			]0,512] ]0,256] ]0,128] ]0,64] ]0,32] ]128,256] ]64,128] ]32,64] ]32,128]
		AuC	0.835 0.835 0.836 0.832 0.818	0.956	0.987 0.990	0.991
	FTM	TPR for a
		FPR value of 0.05	0.588 0.592 0.592 0.579 0.542	0.693	0.920 0.935	0.964
		AuC	0.896 0.896 0.896 0.898 0.899	0.988	0.990 0.994	0.995
	WTM	TPR for a
		FPR value of 0.05	0.788 0.788 0.791 0.798 0.740	0.939	0.977 0.941	0.945

data (mouse, kainate model of TLE, hippocampus). Influence of the choice of the LF band in

Table 5 :

 5 Influence of the FRBR on the performance of HPFM, FTM and WTM. HPFM exhibits low AuC for all values of FRBR indicating a conceptual inability of the method for distinguishing FRs from IES. For FTM and WTM, the AuC decreases with the FRBR. WTM is more robust for low FRBR. Gray boxes indicate best performance. See glossary for abbreviation.

  Assuming that probability density functions are Gaussian, then we have:

						1 P = -P H d d	p	R	1 / H	+	P H	0	p	R	/ H	0
	where	R p	(	/H	)	is the conditional probability density function of R given H. Thus we have:
						R R p p	( (	) ) 10 ( ) /H P H = ( ) 01 /H P H

Acknowledgement

This work was supported by "Region Bretagne" (CRITT Santé Bretagne, « RIPPLE » project, 2012).

database of FRs and IES extracted from human and animal data. We determined which low frequency band (for FTM) and which levels (for WTM) of the wavelet decomposition maximized the Area under the ROC curve (note that parameter LF does not intervene in HPFM).

Parameters of simulated signals

Simulated signal are determined by three parameters: the occurrence frequency of FRs, the occurrence frequency of IESs and the level of the background activity. We expected that the occurrence frequency of transient events has no influence on the performance of the proposed methods. We arbitrarily fixed this parameter to 4 occurrences per minute for each type of events. Conversely, the level of background activity was expected to have a significant influence on the algorithm performance, hence a study of performance with respect to the Fast Ripple to Background Ration (FRBR) was also performed. To proceed, we used simulated signals when the FRBR was respectively set to infinity (no background activity), 15dB, 5 dB and -5dB. In addition to FTM and WTM, we also included HPFM in this study.

Analysis of FTM ( 1 ) and WTM ( 2 ) thresholds

In order to determine the optimal thresholds that best separates FRs from IESs at the second stage of the algorithm ( 1 for FTM or 2 for WTM) and the resulting good classification rate, we assumed that the probability density function of the FTM and WTM criteria for FRs and IESs were Gaussian. Note that this hypothesis was validated using the Kolmogorov test [START_REF] Papoulis | Probability, Random Variables and Stochastic Processes[END_REF]. Knowing the analytical expression of these Gaussian probability density functions, we were able to determine the theoretical thresholds 1 and 2 that maximize the probability of good classification of the EOIs (see details in appendix A). These optimal thresholds as well as the resulting classification rates depend on the estimated probability density functions (i.e. the mean and standard deviation of the HF/LF ratio) but also on the occurrence rate of FRs in the EOIs (i.e. the percentage rate of FRs among the EOIs selected at first stage). While we believe that the estimated mean and standard deviation are consistent and reproducible, the occurrence rate of FRs in the EOIs is strongly data dependent. Therefore we first estimated the optimal threshold as a function of FR rate. Then we calculated the corresponding good A two-stage detection procedure. The basic principle of the proposed method is to first perform a global detection of EOIs (defined as transient events leading to an increase of signal energy within the 256-512 Hz frequency band) and then perform a local analysis to assign each EOI to a specific class (FR vs. IES or artifacts). We found that the combination of the two stages could bring an appropriate solution to the problem of automatically identifying FRs in depth-EEG signals. The first stage consists of a classical high-pass filtering (cut-off frequency: 256 Hz). It could be achieved using any filter (either infinite or finite impulse response) as we found that detection results were independent from the filter design procedure. It is worth mentioning that this first stage is also inspired from a current practice in EEG analysis. Indeed, high-pass filtering of EEG signals (available on most EEG reviewing softwares) is classically used by epileptologists to get rid of the background activity and to better reveal some signal oscillations occurring in the frequency band of interest, typically the highfrequency band. However, it should be also reminded that both FRs and sharp transients (like IESs) both lead to such oscillations in the 250-500 Hz ("fast ripples" vs. "false ripples"), as demonstrated in [START_REF] Benar | Pitfalls of high-pass filtering for detecting epileptic oscillations: a technical note on "false" ripples[END_REF]. In our method, the first stage is complemented by a second stage which makes use of the energy distribution (in the frequency domain) of the signal to classify EOIs. Two variants were proposed for this second stage, either based on the Fourier (FT) or the Wavelet (WT) Transform.

These two transforms were used to compute a crucial parameter for distinguishing FRs from other EOIs: the energy ratio between high frequency (HF, 250-500 Hz) and low frequency (LF) bands. The choice for the LF band is discussed below (see § Parameters to be adjusted). A comparable procedure was proposed in [START_REF] Blanco | Unsupervised classification of high-frequency oscillations in human neocortical epilepsy and control patients[END_REF] where a data mining procedure is used on candidate HFO events detected by a high-pass filtering procedure [START_REF] Staba | Quantitative analysis of high-frequency oscillations (80-500 Hz) recorded in human epileptic hippocampus and entorhinal cortex[END_REF]. This unsupervised data mining provides several classes that allow for the discrimination of different kinds of HFOs and artifacts.

While the method is very effective to achieve this goal, it looks like it requires more effort for implementation compared to our method and is probably more demanding in term of computing time.

In addition, although unsupervised, training sets are necessary which is not the case in our method.

Besides, the issue of IES and IES superimposed with FRs was not addressed by the authors. In this respect, our intent was different as we specifically addressed the "false ripples" issue due to sharp Appendix A. Optimal threshold For an Event Of Interest (EOI), we have two hypothesis. H 1 : the EOI is a Fast Ripple (FR) and H 0 : the EOI is not a FR. Let R be the high frequency to low frequency ratio given in section 2.2 and the threshold that discriminates EOIs that are FR from the ones that are not. To be optimal, this threshold has to maximize the probability to take the good decision, i.e. to detect a FR when the EOI is actually an FR and to not detect an FR when the EOI is not an FR. This probability, also called one minus classification error rate, is given by ne 1 0 P = P ( n e H) + P ( n e H)

where ne stands for "no error". This can be written with conditional probabilities as:


Benjamin Erable

Isabelle Goubet
email: igoubet@univ-lr.fr

Sylvain Lamare

Marie-Dominique Legoy

Thierry Maugard
email: tmaugard@univ-lr.fr

Bioremediation of halogenated compounds: Comparison of dehalogenating bacteria and improvement of catalyst stability

Keywords: Haloalkane dehalogenase, Rhodococcus erythropolis NCIMB13064, Sphingomonas paucimobilis UT26, Xanthobacter autotrophicus

Five bacterial strains were compared for halogenated compounds conversion in aqueous media. Depending on the strain, the optimal temperature for dehalogenase activity of resting cells varied from 30 to 45 °C, while optimal pH raised from 8.4 to 9.0. The most effective dehalogenase activity for 1-chlorobutane conversion was detected with Rhodococcus erythropolis NCIMB13064 and Escherichia coli BL21 (DE3) (DhaA). The presence of 2-chlorobutane or propanal in the aqueous media could inhibit the 1-chlorobutane transformation.

Introduction

Halogenated compounds are an important class of environmental pollutants [START_REF] Mohamed | Volatile organic compounds in some urban locations in United States[END_REF]. Because of their toxicity, the bioremediation of these compounds has been widely studied and the biotechnological approach is now a promising field which could in the future supply reliable, simple and cheap technologies to treat halogenated pollutants contamination [START_REF] Hardman | Biotransformation of halogenated compounds[END_REF].

Several articles have dealt with strains capable of hydrolytic dehalogenation of halohaliphatic compounds. The physiology, biochemistry and genetics of dehalogenating bacteria and substrates specificity of their enzymes are currently being studied [START_REF] Janssen | Degradation of halogenated aliphatic compounds by Xanthobacter autotrophicus GJ10[END_REF][START_REF] Keuning | Purification and characterization of hydrolytic haloalkane dehalogenase from Xanthobacter autotrophicus GJ10[END_REF][START_REF] Hardman | Biotransformation of halogenated compounds[END_REF][START_REF] Nagata | Purification and characterization of haloalkane dehalogenase of a new substrate class from a hexachlorohexane degrading bacterium, sphingomonas paucimobilis UT26[END_REF][START_REF] Janssen | Microbial dehalogenation[END_REF][START_REF] Damborsky | Structure-specificity relationships for haloalkane dehalogenases[END_REF][START_REF] Janssen | Evolving haloalkane dehalogenases[END_REF].

Xanthobacter autotrophicus GJ10 was one of the first isolated. This bacterium is able to use a number of halogenated short chain hydrocarbons as sole carbon source for growth [START_REF] Janssen | Degradation of halogenated aliphatic compounds by Xanthobacter autotrophicus GJ10[END_REF]. Indeed it constitutively produces a haloalkane dehalogenase (DhlA) which catalyzes the hydrolytic dehalogenation of halogenated C 2 -C 4 alkanes, including chlorinated, brominated and iodinated compounds [START_REF] Keuning | Purification and characterization of hydrolytic haloalkane dehalogenase from Xanthobacter autotrophicus GJ10[END_REF][START_REF] Schanstra | Specificity and kinetics of haloalkane dehalogenase[END_REF].

Other strains producing hydrolytic haloalkane dehalogenases belonging to the same family have been identified. R. erythropolis NCIMB13064 and Sphingomonas paucimobilis UT26 express respectively the DhaA (dehalogenase from R. erythropolis) and LinB (dehalogenase from S. paucimobilis) [START_REF] Nagata | Cloning and sequencing of a dehalogenase gene encoding an enzyme with hydrolase activity involved in the degradation of gammahexachlorocyclohexane in Pseudomonas paucimobilis[END_REF][START_REF] Curragh | Haloalkane degradation and assimilation by Rhodococcus rhodochrous NCIMB13064[END_REF]. The structure of these enzymes are very similar to the one of DhlA with some differences in the geometry and size of the active site cavity [START_REF] Janssen | Evolving haloalkane dehalogenases[END_REF]. Nevertheless these three haloalkane dehalogenases differ by their substrate specificity and the bacteria producing these enzymes also differ in their range of growth substrate. Short chain 1-haloalkanes (C 3 -C 10 ) appear to be metabolized by R. erythropolis NCIMB13064 [START_REF] Curragh | Haloalkane degradation and assimilation by Rhodococcus rhodochrous NCIMB13064[END_REF] while [START_REF] Nagata | Cloning and sequencing of a dehalogenase gene encoding an enzyme with hydrolase activity involved in the degradation of gammahexachlorocyclohexane in Pseudomonas paucimobilis[END_REF] showed that not only short haloalkanes but also 1-chlorodecane and 2-chlorobutane, which are poor substrates for DhlA and DhaA, were good substrates for resting E. coli cells overproducing LinB dehalogenase. These strains could also be used for complementary degradation of mixture of halogenated pollutants.

The aim of this article is to compare the ability of these different strains and two recombinant E. coli strains to convert halogenated pollutants in a continuous gas/liquid reactor. Moreover, gaseous effluents can sometimes contain several halogenated compounds and very few studies have been dedicated to the study of competition of these different substrates for the catalyst. We also studied the influence of a secondary halogenated pollutant on the depollution efficiency of such reactor.

Materials and methods

2.1. Microorganisms, culture conditions and chemicals R. erythropolis NCIMB13064, S. paucimobilis UT26, X. autotrophicus GJ10 and two recombinant strains of E. coli BL21 (DE3) the first containing the gene coding for the dehalogenase from R. erythropolis NCIMB13064 (E. coli BL21 (DE3) (DhaA)) and the second containing the gene coding for the dehalogenase from X. autotrophicus GJ10 (E. coli BL21 (DE3) (DhlA)) were used for this study.

R. erythropolis NCIMB13064 was obtained from the National Collection of Industrial and Marine Bacteria LTD, Aberdeen, Scotland. The organism was grown in 1 l Erlenmeyer flasks sealed with Teflon line screw caps; the flasks contained 200 ml of a minimal medium described by [START_REF] Sorkhoh | Growth of Candida albicans on hydrocarbons: influence on lipids and sterols[END_REF] adjusted at pH 7.0. The medium was sterilized by autoclaving for 15 min at 121 °C. After cooling, 100 ll of filtered sterilized 1-chlorobutane (0.22 lm Minisart sartorius filters) was added twice as sole carbon source at 24 h interval. This method was chosen since it has been shown that adding twice 100 ll of 1-chlorobutane at 24 h interval, provide both a good growth and an interesting specific dehalogenase activity [START_REF] Erable | Haloalkane hydrolysis by Rhodococcus erythropolis cells: A comparison of conventional aqueous phase dehalogenation and non-conventional gas phase dehalogenation[END_REF].

S. paucimobilis UT26 and X. autotrophicus GJ10 were grown in 1 l aerobic flasks containing 200 ml of Luria Bertani (LB) medium at pH 7.0. The LB medium had the following composition (gl À1 ): 10.0 Tryptone, 5.0 Yeast extract, and 5.0 NaCl. The medium was sterilized by autoclaving for 15 min at 121 °C.

E. coli BL21 (DE3) (DhlA) and E. coli BL21(DE3)(D-haA) were grown in 1 l aerobic flasks containing 200 ml of LB medium adjusted at pH 7.0 and supplemented with 100 lg ml À1 ampicillin. The culture was incubated at 30 °C until it reached an OD 690 of 0.7 after which it was induced with 0.4 mM isopropyl-b-D-thiogalactopyranoside (IPTG).

All the bacterial cultures were incubated at 30 °C on an orbital shaker (160 rpm). Cell growth was monitored by measuring the optical density at 690 nm.

All substrates for culture media were purchased from Sigma Company (USA) except Tryptone and Yeast extract, which were obtained from Fluka (USA). All halogenated compounds: 1-chloropropane, 1-chlorobutane, 1-chloropentane, 1-chlorohexane, 1-chloroheptane, 1-chlorohexane, 1-chloroheptane, 1-chlorooctane, 1.2-dichloroethane, 1.2dibromoethane, 1-bromobutane, 1-bromopentane, 1-bromohexane, 1-iodobutane, 2-chlorobutane, 2-bromobutane and 1-propanol, propanal and propionic acid were purchased from Flucka (USA). Their purity was 99%. Deionised water was obtained via a Milli-Q system (Millipore, France).

Preparation of cells

Cells grown for 24 h (E. coli BL21) or 48 h (R. erythropolis, S. paucimobilis, X. autotrophicus) were harvested by centrifugation (8000 rpm for 10 min), washed with 50 mM Tris/HCl buffer at pH 8.4 (S. paucimobilis) pH 8.5 (X. autotrophicus and the corresponding E. coli BL21 (DE3) (DhlA)) or at pH 9.0 (R. erythropolis and the corresponding E. coli BL21 (DE3) (DhaA)) and resuspended in 50 mM Tris/HCl buffer at the same pH and at an approximate OD 690 of 15.

Dehalogenation in a batch system

The haloalkane dehalogenase activity of resting cells was assayed at 30 °C in 50 mM Tris HCl buffer (pH 8.4, 8.5 or 9.0). Tests were performed with 50 ml of diluted cell suspension (approximate OD 690 of 3) (in Tris/HCl buffer) in 100 ml bottles. Kinetics were started by the addition of 100 ll of 1-chlorobutane (1.8 g l À1 ). 2 ml was periodically sampled and cells were removed by centrifugation at 1000 rpm for 2 min. 1 ml of the supernatant was assayed for butan-1-ol concentration by gas chromatography analysis using 1-hexanol as an internal standard and the same analytical conditions as for the analysis of the gas phase exiting the reactor.

Dehalogenation in a continuous system

The gas/liquid bioreactor consisted of a 1 l flask Erlenmeyer containing 200 ml of bacterial suspension at 5 g l À1 . Substrate feeding was obtained by passing nitrogen, used as a carrier gas, through substrate saturation flasks. Substrates were continuously passed through the bioreactor and reacted with the suspended resting cells. The gas leaving the bioreactor was analysed by gas chromatography. The acquisition and control of the operating parameters (substrate concentration, temperature, and pressure) were monitored on line as shown in Fig. 1. The vapour phase leaving the reactor was sampled using a 250 ll loop on a six-way valve (Valco) maintained at 190 °C. Samples were automatically injected into the split injector of a gas chromatograph. Calibration for 1-chlorobutane and 1-butanol leaving the reactor were performed by sampling vapours generated with one of the saturation flask filled with 1-chlorobutane or 1-butanol and by programming increasing the vapour concentration of this substrate through an empty reactor.

A typical test was carried out at 30 °C, with 200 ml of bacterial suspension at 5 g l À1 . The total flow passing into the Erlenmeyer flask was 500 lmol min À1 and the 1-chlorobutane flow was fixed at 17 lmol min À1 (1.5 mg min À1 ). The dehalogenase activity was expressed in lmol of alcohol per min and per g of cells.

Chromatographic analysis

Analysis were performed on a gas chromatograph (Hewlett Packard model 5890 A), equipped with a Flame Ionisation Detector (FID). The column used was an OV 1701 fused silica capillary column (25 m • 0.25 mm i.d. • 0.25 lm film thickness; Chrompack, France). The split ratio was 43.2/2.7. The injector was kept at 200 °C, and the detector was kept at 250 °C. The column temperature was held at 60 °C for 2 min, then programmed to increase at 10 °C min À1 to 140 °C. Nitrogen was used as a carrier gas and the flow rate in the column was 2.1 ml min À1 . Hydrogen and air were supplied to the FID at 40 and 400 ml min À1 respectively. Quantitative data were obtained after integration on a HP 3396A integrator.

Results and discussion

Comparison of dehalogenating bacteria

DhlA and LinB were constitutively produced by X. autotrophicus GJ10 and S. paucimobilis UT26 respectively. The expression of DhaA was induced by 1-chlorobutane addition for R. erythropolis NCIMB13064 cells. DhlA and DhaA produced by the recombinant E. coli BL21 were induced by IPTG (Table 1).

The generation time depended on the strain considered (Table 1). R. erythropolis NCIMB13064 possessed the highest generation time (310 min). However, this was also the only strain cultivated on mineral medium supplemented with 1-chlorobutane. After growth, the cells were recovered and tested for the degradation of 1-chlorobutane. The effects of several parameters such as temperature, pH or substrate concentration were first observed on the dehalogenase activities of resting cells (Table 2).

The optimal temperature for the dehalogenase activity of R. erythropolis NCIMB13064 resting cells was 45 °C. [START_REF] Stafford | The microbial degradation of chloroalkanes[END_REF] determined an optimal temperature of 45 °C for the free DhaA. The optimal temperature for dehalogenating activity of these resting cells corresponds to the optimal temperature of the free enzyme rather than to the optimal temperature for the growth of this microorganism (28 °C). The dehalogenase activity from E. coli BL21 (DE3) (DhaA) is more sensitive to the temperature than that observed in the strain of origin since 40 °C was its optimal temperature. In the case of X. autotrophicus GJ10, E. coli BL21 (DE3) (DhlA) and S. paucimobilis UT26, optimal temperatures of whole cells dehalogenase activities corresponded to those generally published for the purified enzyme [START_REF] Janssen | Degradation of halogenated aliphatic compounds by Xanthobacter autotrophicus GJ10[END_REF][START_REF] Nagata | Purification and characterization of haloalkane dehalogenase of a new substrate class from a hexachlorohexane degrading bacterium, sphingomonas paucimobilis UT26[END_REF]. It should be noted that an increase of 5 °C above the optimal temperature involved a 50% loss of the activity for the resting cells.

The optimum pH varied from 8.4 to 9.0 depending on the strain (Table 2). Various studies with free dehalogenases report similar data [START_REF] Keuning | Purification and characterization of hydrolytic haloalkane dehalogenase from Xanthobacter autotrophicus GJ10[END_REF][START_REF] Nagata | Purification and characterization of haloalkane dehalogenase of a new substrate class from a hexachlorohexane degrading bacterium, sphingomonas paucimobilis UT26[END_REF][START_REF] Dravis | Enzymatic dehalogenation of gas substrates with haloalkane dehalogenase[END_REF]. Under these optimal conditions (temperature and pH), all the studied strains could transform 1-chlorobutane but maximal rates of conversion were different. Indeed, the more efficient dehalogenating bacteria were E. coli BL21 (DE3) (DhaA) and S. paucimobilis UT26 with a maximal transformation velocity of 23 lmol min À1 g À1 (Table 2).

However, E. coli BL21 (DE3) (DhaA) had higher affinity for 1-chlorobutane than S. paucimobilis UT26 (Km = 5 and 23 mM respectively). In contrast, X. autotrophicus GJ10 was less effective with a 6 lmol min À1 g À1 rate of 1-chlorobutane conversion. The 1-chlorobutane is not the best substrate for all the studied strains but it is often used as a reference substrate. DhlA from X. autotrophicus GJ10 is better known for its affinity for short dihalogenated substrates such as 1.2-dichloroethane or 1.2-dibromoethane whereas LinB from S. paucimobilis is known for its affinity for mono-halogenated substrates (C 4 -C 10 ) [START_REF] Damborsky | Analysis of the reaction mechanism and substrate specificity of haloalkane dehalogenases by sequential and structural comparisons[END_REF].

Since the behavior of the free dehalogenases varies with respect to the substrates, the dehalogenating activity of resting cells was also tested with different substrates. All strains tested were active on the brominated, chlorinated and iodinated compounds selected. Except for 1-chloropropane, the short chain compounds were better transformed in aqueous medium than those with long carbon chain. For almost all strain, 1-chlorobutane was better transformed than 1-chloropentane which was better degraded than 1-chlorohexane. The same trend was noticed for brominated compounds. This observation can be directly connected to the aqueous solubility of the compounds. However S. paucimobilis UT26 is more active than the other strains for the long chain compounds (C 6 -C 10 ). Except for S. paucimobilis resting cells, rate of conversion of 1-bromohexane was always higher than that of 1-chlorohexane. These data observed with whole cells are in agreement with those reported for the purified enzymes [START_REF] Janssen | Degradation of halogenated aliphatic compounds by Xanthobacter autotrophicus GJ10[END_REF][START_REF] Stafford | The microbial degradation of chloroalkanes[END_REF][START_REF] Damborsky | A mechanistic approach to deriving quantitative structure-activity relationship models for microbial degradation of organic compounds[END_REF]. But the reverse trend can be observed when comparing rates of conversion of 1-bromobutane and 1-chlorobutane or 1-bromopentane and 1chloropentane. Only S. paucimobilis UT26 was able to transform secondary mono-halogenated compounds such as 2-chlorobutane with rates comparable to those of 1-chlorobutane degradation. X. autotrophicus GJ10 clearly showed a specificity for short dihalogenated compounds such as 1.2-dichloroethane or 1.2-dibromoethane.

Continuous dehalogenation in a gas/liquid bioreactor

We observed in the preceding study that the cells of E. coli BL21 (DE3) (DhaA) could be useful in the bioremediation of the 1-chlorobutane. Indeed, the kinetic parameters obtained in batch reaction for resting cells (dehalogenating activity = 23 lmol min À1 g À1 and Km = 5 mM) and the low generation time of this strain (40 min) could be interesting for the transformation of 1-chlorobutane. Consequently, fresh harvested E. coli BL21 (DE3) (DhaA) cells were tested in a continuous gas/liquid bioreactor for the transformation of 1-chlorobutane (Fig. 1). We observed that it is not possible to preserve a stable dehalogenase activity when resting cells were placed in a standard Tris/HCl 50 mM, pH 9.0 buffer (Fig. 2). Maximal dehalogenase activity was detected after only 50 h of reaction. Rate of conversion then decreased and no activity was detected after 400 h of reaction. The rate of deactivation was found to be 0.3% maximal activity per hour.

This low stability of the dehalogenase activity was already observed in batch system with free dehalogenases. The hydrolysis of 1-chlorobutane produces both butan-1-ol and HCl. This acid is known to have two effects: acidifying the medium (by H + ) and inhibiting dehalogenase (by Cl À ) [START_REF] Oakley | Exploring the structure and activity of haloalkane dehalogenase from Sphingomonas paucimobilis UT26: evidence for product-and water-mediated inhibition[END_REF]. The presence of an alcohol produced by the hydrolysis of halogenated compounds or the products of its metabolism (alcohol ! aldehyde ! carboxylic acid) could also have an effect on the dehalogenase activity of resting cells. The tests of transformation of the 1-chlorobutane were carried out in Tris/HCl 50 mM buffer at the optimal pH for each strain. The concentration of 1-chlorobutane varied from 0 to 20 mM. The production of butan-1-ol was measured by GC.

Effect of the addition of an alcohol, an aldehyde or an acid on conversion of 1-chlorobutane by resting cells

Consequently, we examined the effect of secondary products resulting from the hydrolysis of 1-chloropropane (propanol, propanal, propionic acid) on the dehalogenase activity of whole cells (Fig. 3). Propanol, propanal and pro-pionic acid were used as effectors for reasons of separation and solubility. Propanol, propanal or propionic acid were added in the reaction medium at a concentration of 2 ml l À1 and butan-1-ol production was determined, using 1-chlorobutane as a substrate.

First of all, the presence of propanol in the reaction medium had no significant effect on the velocity of 1-chlorobutane transformation in butan-1-ol. The propanal had a more important effect on the dehalogenase activity. This could be due the toxicity of the aldehyde. Cells of R. erythropolis NCIMB13064 were the most sensitive to the presence of propanal in the medium. Indeed 95% of the dehalogenase activity of R. erythropolis was inhibited in the presence of propanal at a concentration of 2 ml l À1 . A similar effect was noticed in the presence of propanoic acid except in the case of R. erythropolis cells.

Effect of 2-chlorobutane on conversion of 1-chlorobutane by resting cells

Gaseous effluents can contain a mixture of pollutants and the treatment of several halogenated compounds by biological method is even more difficult than the degradation of a single halogenated pollutant. 2-chlorobutane is a recalcitrant substrate for the majority of the strains stud- 3. The effect of propanol, propanal and propionic acid on resting cells dehalogenase activity. The tests of transformation of the 1-chlorobutane were carried out in Tris/HCl 50 mM buffer. The temperature and pH were those determined as optimal for each strain. The concentration of 1-chlorobutane was 14 mM and the concentration of secondary product was 2/1000 (v/v). The production of butan-1-ol was measured by GC. ied (Table 3), only S. paucimobilis UT26 has a good affinity for this compound. We studied the influence of 2-chlorobutane on the transformation of the 1-chlorobutane by resting cells (Table 4).

The dehalogenase activity of the various strains with exception of S. paucimobilis UT26 was measured for increasing concentrations of 2-chlorobutane. The dehalogenase activity of resting cells was inversely proportional to the concentration of 2-chlorobutane. E. coli BL21 was the most sensitive strain to 2-chlorobutane. Half of the initial dehalogenase activity of these cells was inhibited by the presence of 19 mM of 2-chlorobutane.

Conclusions

The study in aqueous phase made it possible to define the optimal temperature and pH conditions for dehalogenase activity of resting cells. For the transformation of the 1chlorobutane, two strains have a strong effectiveness: R. erythropolis NCIMB13064 and E. coli BL21 (DE3) (DhaA). Production of the cells of E. coli BL21 (DE3) (DhaA) is eight times faster than that of R. erythropolis NCIMB13064 and should also be preferred for remediation. However the use of E. coli BL21 (DE3) (DhaA) for the continuous conversion of 1-chlorobutane is limited by the low stability of its dehalogenase activity. The studied strains have different specificities for halogenated substrates and thus the association of these strains could be interesting to treat a broad range of halogenated compounds. Since the optimal pH and temperature differ depending on the strain, they should be used in successive batch reactor rather than in association. The tests were carried out in Tris/HCl 50 mM buffer. The temperature and pH are those determined as optimal for each strain. The concentration of substrates in the reaction medium is 10 mM. The production of corresponding alcohol is evaluated in the course of time by GC. Rate of degradation of 1-chlorobutane is taken as the reference (100%).

The values between brackets are reported from the literature and represent values already observed with the purified dehalogenase [START_REF] Janssen | Degradation of halogenated aliphatic compounds by Xanthobacter autotrophicus GJ10[END_REF][START_REF] Stafford | The microbial degradation of chloroalkanes[END_REF][START_REF] Damborsky | A mechanistic approach to deriving quantitative structure-activity relationship models for microbial degradation of organic compounds[END_REF]. ND: Not determined. The tests of transformation of the 1-chlorobutane were carried out in Tris/HCl 50 mM buffer. The temperature and pH were those determined as optimal for each strain. The concentration of 1-chlorobutane was 14 mM. The production of butan-1-ol was measured by GC.

Fig. 1 .

 1 Fig. 1. Representation of the continuous gas/liquid bioreactor.

  Fig.3. The effect of propanol, propanal and propionic acid on resting cells dehalogenase activity. The tests of transformation of the 1-chlorobutane were carried out in Tris/HCl 50 mM buffer. The temperature and pH were those determined as optimal for each strain. The concentration of 1-chlorobutane was 14 mM and the concentration of secondary product was 2/1000 (v/v). The production of butan-1-ol was measured by GC.

Fig. 2 .

 2 Fig. 2. Continuous 1-chlorobutane transformation by resting cells of E. coli BL21 (DE3) (DhaA) at 40 °C. Dehalogenase activity is expressed as the 1-chlorobutane transformation (lmol min À1 g À1 of bacteria).

Table 1

 1 List of selected bacteria and media used to produce the different dehalogenases

	Bacterial strain	Dehalogenase	Growth medium	Added substrate	Mean generation
					time (min)
	R. erythropolis NCIMB13064	DhaA	Mineral	1-Chlorobutane	310
	E. coli BL21 (DE3) (DhaA)	DhaA	Luria Bertani	IPTG	40
	X. autotrophicus GJ10	DhlA	Luria Bertani	/	48
	E. coli BL21 (DE3) (DhaA)	DhlA	Luria Bertani	IPTG	38
	S. paucimobilis UT26	LinB	Luria Bertani	/

Table 2

 2 Optimal physicochemical parameters for the dehalogenase activity of resting cells

	Bacterial strain	Optimal temperature	Optimal pH for	K m (mM)	Maximal rate
		for dehalogenase	dehalogenase activity		of 1-chlorobutane
		activity (°C)			transformation
					(lmol min À1 g À1 )
	R. erythropolis NCIMB13064	45	9.0	3	16
	E. coli BL21 (DE3) (DhaA)	40	9.0	5	23
	X. autotrophicus GJ10	30	8.5	15	6
	E. coli BL21 (DE3) (DhlA)	30	8.5	19	9
	S. paucimobilis UT26	35	8.4	23	23

Table 3

 3 Relative dehalogenase activity of the different resting cells

		R. erythropolis	E. coli BL21	X. autotrophicus	E. coli BL21	S. paucimobilis
		NCIMB13064	(DE3) (DhaA)	GJ10	(DE3) (DhlA)	UT26
	Experimental conditions	30 °C, pH 9.0	30 °C, pH 9.0	30 °C, pH 8.5	30 °C, pH 8.5	30 °C, pH 8.4
	1-Chloropropane	50 (48)	44	75 (165)	116	30 (135)
	1-Chlorobutane	100 (100)	100	100 (100)	100	100 (100)
	1-Chloropentane	82 (78)	56	18 (16)	4	56 (120)
	1-Chlorohexane	25 (75)	19	5 (10)	1	60 (145)
	1-Chloroheptane	ND (59)	7	0 (0)	0	70 (161)
	1-Chlorooctane	5 (33)	2	0 (0)	0	76 (139)
	1-Chlorode ´cane	ND (10)	0	0 (ND)	0	8 (27)
	1-Bromobutane	99 (106)	144	82 (87)	102	56 (234)
	1-Bromopentane	58 (51)	35	67 (ND)	145	28 (355)
	1-Bromohexane	45 (32)	20	37 (ND)	114	13 (ND)
	1-Iodobutane	47 (58)	137	34 (ND)	30	67 (ND)
	2-Chlorobutane	8 (8)	2	0 (ND)	0	73 (ND)
	2-Bromobutane	34 (52)	47	0 (ND)	18	99 (ND)
	1,2-Dichloroe ´thane	ND (ND)	66	159 (323)	223	10 (ND)
	1,2-Dibromoe ´thane	ND (ND)	211	116 (303)	200	201 (ND)

Table 4

 4 The effect of inhibitor (2-chlorobutane) on resting cells dehalogenase activity for 1-chlorobutane

	2-chlorobutane	R. erythropolis	E. coli BL21	X. autotrophicus	E. coli BL21
	concentration (mM)	NCIMB13064	(DE3) (DhaA)	GJ10	(DE3) (DhlA)
	0	100	100	100	100
	6	95	82	90	85
	14	91	71	81	77
	19	84	51	77	63

Acknowledgements

We thank Prof. D.B. Janssen (Department of Biochemistry, Groningen Biotechnology Center, University of Groningen) for providing us X. autotrophicus GJ10 and the two E. coli BL21 strains and are grateful to Pr. Damborsky (Protein Engineering Group, Faculty of Science, Masaryk University) for providing us the S. paucimobilis UT26 strain. This work was supported by an ADEME/Re ´gion Poitou Charentes grant.