Audrey Desvergne

Nicolas Ugarte

Sabrina Radjei

Monique Gareil

Isabelle Petropoulos

Bertrand Friguet
email: bertrand.friguet@upmc.fr

Circadian modulation of proteasome activity and accumulation of oxidized protein in human embryonic kidney

Keywords: Proteasome, circadian rhythmicity, protein oxidation, HEK 293 cells, human dermal fibroblasts, oxidative stress, cellular aging, proteasome activator PA28αβ, Nrf2

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

Introduction:

The circadian clock generates rhythms with a periodicity of 24 hours of various biochemical and physiological processes such as sleep-wake cycles, body temperature, blood pressure, renal activity, and liver metabolism in mammals [START_REF] Bollinger | Circadian rhythms -from genes to physiology and disease[END_REF][START_REF] Dibner | The mammalian circadian timing system: organization and coordination of central and peripheral clocks[END_REF] by regulating the expression of many genes, referred as to clock controlled genes [START_REF] Partch | Molecular architecture of the mammalian circadian clock[END_REF][START_REF] Robinson | Molecular mechanisms of the circadian clockwork in mammals[END_REF]. The molecular mechanisms of the circadian clock involve a transcription/translation feedback loop composed by the activator heterodimer CLOCK/BMAL1 and the repressor heterodimer CRY/PER. In current models of the eukaryotic circadian oscillator, the transcription-translation feedback loop is considered as the prime mechanism sustaining intracellular rhythms. However, proteasome-mediated degradation of proteins, that also includes polyubiquitinated CRY and PER, is critically important for the core cellular circadian clock [START_REF] Van Ooijen | Proteasome function is required for biological timing throughout the twenty-four hour cycle[END_REF][START_REF] Larrondo | Decoupling circadian clock protein turnover from circadian period determination[END_REF][START_REF] Gallego | Post-translational modifications regulate the ticking of the circadian clock. Nature reviews[END_REF]. Furthermore, the peroxiredoxin redox state has been described as an additional non-transcriptional timekeeping mechanism conserved in both eukaryotes and prokaryotes [START_REF] Edgar | Peroxiredoxins are conserved markers of circadian rhythms[END_REF]. This redox oscillation probably reflects an endogenous rhythm in the generation of reactive oxygen species (ROS) [START_REF] O'neill | Circadian redox and metabolic oscillations in mammalian systems[END_REF][START_REF] O'neill | Circadian clocks in human red blood cells[END_REF] and the degradation or repair of hyperoxidized peroxiredoxin [START_REF] Cho | Circadian rhythm of hyperoxidized peroxiredoxin II is determined by hemoglobin autoxidation and the 20S proteasome in red blood cells[END_REF][START_REF] Kil | Circadian Oscillation of Sulfiredoxin in the Mitochondria[END_REF].

ROS can act as important signaling molecules for various cellular functions including circadian rhythms [START_REF] Brown | Nox proteins in signal transduction[END_REF][START_REF] Tamaru | ROS stress resets circadian clocks to coordinate pro-survival signals[END_REF] in many organisms such as Neuropora [START_REF] Gyongyosi | Reactive oxygen species can modulate circadian phase and period in Neurospora crassa[END_REF], Drosophila [START_REF] Grover | Hydrogen peroxide stimulates activity and alters behavior in Drosophila melanogaster[END_REF], zebrafish [START_REF] Hirayama | Circadian control by the reduction/oxidation pathway: catalase represses light-dependent clock gene expression in the zebrafish[END_REF] and humans [START_REF] O'neill | Circadian clocks in human red blood cells[END_REF]. Interestingly in flies with a functional clock, it has been demonstrated daily fluctuations in both the levels of mitochondrial ROS and carbonylated protein, indicative of a circadian rhythm in the production of ROS and removal of protein oxidative damage [START_REF] Krishnan | Circadian regulation of response to oxidative stress in Drosophila melanogaster[END_REF]. Indeed, ROS can attack proteins in different ways and the most frequent irreversible end products are carbonylated proteins [START_REF] Shringarpure | Ubiquitin conjugation is not required for the degradation of oxidized proteins by proteasome[END_REF][START_REF] Baraibar | Oxidative proteome modifications target specific cellular pathways during oxidative stress, cellular senescence and aging[END_REF] that accumulate with age [START_REF] Stadtman | Free radical-mediated oxidation of free amino acids and amino acid residues in proteins[END_REF]. This accumulation is related to a decrease of proteasome activity during aging [START_REF] Conconi | Age-related decline of rat liver multicatalytic proteinase activity and protection from oxidative inactivation by heat-shock protein 90[END_REF][START_REF] Petropoulos | Increase of oxidatively modified protein is associated with a decrease of proteasome activity and content in aging epidermal cells[END_REF][START_REF] Baraibar | Changes of the proteasomal system during the aging process[END_REF][START_REF] Ferrington | Altered proteasome structure, function, and oxidation in aged muscle[END_REF][START_REF] Kapphahn | Age-dependent inhibition of proteasome chymotrypsin-like activity in the retina[END_REF].

Since protein carbonylation cannot be repaired and represents a threat to cell viability, carbonylated proteins are indeed eliminated mainly through degradation by the proteasome [START_REF] Balog | Site-specific methionine oxidation initiates calmodulin degradation by the 20S proteasome[END_REF][START_REF] Friguet | Oxidized protein degradation and repair in ageing and oxidative stress[END_REF][START_REF] Chondrogianni | Protein damage, repair and proteolysis[END_REF].

The proteasomal system, located in the nucleus and the cytosol, plays a crucial role in protein homeostasis and in the regulation of many cellular events since it degrades more than 70-80% of intracellular proteins [START_REF] Groll | 20S Proteasome and Its Inhibitors: Crystallographic Knowledge for Drug Development[END_REF]. The proteasome is able to bind different regulatory proteins. The ATP-dependent association of 19S regulator (PA700, "proteasome activator 700 kDa") to the α-rings of the core particle results in the formation of 26S proteasome that degrades polyubiquitinated proteins. An other important regulator for both the proteasome and immunoproteasome, is the 11S or PA28αβ regulator ("proteasome activator 28 kDa"), the expression of which is induced by both IFN-γ and Nrf2 (nuclear factor erythroid-derived 2like 2). Interestingly, the Nrf2 induced up-regulation of 20S proteasome and PA28αβ has been recently implicated in the oxidative stress response through their efficient contribution to the intracellular removal of oxidized proteins [START_REF] Pickering | Nrf2dependent induction of proteasome and Pa28alphabeta regulator are required for adaptation to oxidative stress[END_REF].

The link between the circadian clock, ROS production, antioxidant defenses and removal of protein oxidative damage [START_REF] Krishnan | Circadian regulation of response to oxidative stress in Drosophila melanogaster[END_REF][START_REF] Patel | Transcriptional control of antioxidant defense by the circadian clock[END_REF] suggests that redox homeostasis elements such as oxidized protein degradation by the proteasome, could be modulated by the circadian system. Interestingly, microarray analysis revealed that several proteasome subunits are regulated by the circadian clock at the transcription level in mouse tissues [START_REF] Panda | Coordinated Transcription of Key Pathways in the Mouse by the Circadian Clock[END_REF][START_REF] Akhtar | Circadian Cycling of the Mouse Liver Transcriptome, as Revealed by cDNA Microarray, Is Driven by the Suprachiasmatic Nucleus[END_REF] and that Nrf2 levels show diurnal variation in mouse livers and Drosophila heads [START_REF] Beaver | Circadian regulation of glutathione levels and biosynthesis in Drosophila melanogaster[END_REF][START_REF] Xu | Diurnal variation of hepatic antioxidant gene expression in mice[END_REF].

Using two mammalian cellular models, we show in this paper, that both the immortalized HEK 293 cell line and primary human dermal fibroblasts (HDF) synchronized by a serum shock [START_REF] Balsalobre | A Serum Shock Induces Circadian Gene Expression in Mammalian Tissue Culture Cells[END_REF] exhibit a circadian rhythmicity of proteasome activity and accumulation of carbonylated proteins. The circadian regulation of proteasome activity can be explained, at least in part, by the circadian expression of PA28αβ and Nrf2 at the gene and protein levels which is associated with the rhythmic modulation of ROS production and oxidized glutathione content. When challenged with the oxidative agent tert-butyl hydroperoxide (t-BHP), synchronized HEK 293 cells showed differential sensitivity to oxidative stress depending on its timing. Finally, in contrast to young dermal fibroblasts, no circadian activation of the proteasome and rhythmic modulation of ROS levels could be evidenced in senescent fibroblasts.

Materials and Methods

Materials

Dulbecco's Modified Eagle Medium (4.5 mg mL -1 glucose), penicillin, streptomycin, glutamine, trypsin solution for cell culture (0.05% (w/v)) were purchased from Sigma-Aldrich (Saint-Quentin Fallavier, France) and fetal bovine serum from Invitrogen Life technologies (Cergy Pontoise, France). Cell culture plastics were purchased from BD Falcon (Le Pont de Claix, France). Cell proliferation kit II (XTT) was obtained from Roche Diagnostics (Meylan, France). Western blot reagents and membranes were purchased from GE Healthcare (Saclay, France). The bicinchoninic acid (BCA) and Bradford protein assays were purchased from Thermo scientific (Villebon-sur-Yvette, France) and from Expedeon (San Diego, USA), respectively and chemicals for SDS/PAGE from Bio-Rad (Marnes La Coquette, France).

OxyBlot TM protein oxidation detection kit was purchased from Millipore (Molsheim, France).

All other reagents were obtained from Sigma-Aldrich, unless specified.

Cell culture and serum shock treatment

HEK 293 cells were purchased from Sigma-Aldrich and primary HDF were kindly provided by Dr C. Nizard, LVMH-Research (Saint Jean de Braye, France). As previously described by [START_REF] Demirovic | Basal level of autophagy is increased in aging human skin fibroblasts in vitro, but not in old skin[END_REF] for HDF culture studies, skin samples were collected from adult patients, undergoing abdominal plastic surgery performed by independent plastic surgeons and were considered as ""waste", and thus were exempt from any further ethical approval [START_REF] Demirovic | Basal level of autophagy is increased in aging human skin fibroblasts in vitro, but not in old skin[END_REF]. All the waste tissues were completely de-identified prior to being handed over to the researchers. Both HEK 293 cells and HDF were cultivated in Dulbecco"s Modified Eagle"s Medium supplemented with 10 % (v/v) fetal bovine serum, 2 mM L-Glutamine, 100 units/mL penicillin and 100 μg/mL streptomycin at 37 °C and 5 % CO 2 in a humidified incubator. After reaching a sub-confluence (of about 90 % confluence), circadian synchronization of cells was performed by a serum shock treatment [START_REF] Balsalobre | A Serum Shock Induces Circadian Gene Expression in Mammalian Tissue Culture Cells[END_REF] that consists in a two hours exposure to a serum-rich medium (complete DMEM supplemented by 50 % (v/v) of fetal bovine serum). Then cells were replaced in a serum free culture medium. The beginning of the serum shock defined the time 0 (t 0h ). Then every 4 h and during 50 h, cells were collected and RNA or protein extractions were performed.

The senescent HDF were obtained at late passages (passages between 43 and 46) and the replicative senescence of HDF was assessed by monitoring SA-β-galactosidase activity and p16 expression [START_REF] Campisi | Aging, cellular senescence, and cancer[END_REF][START_REF] Munoz-Espin | Cellular senescence: from physiology to pathology. Nature reviews[END_REF].

RNA extraction, reverse transcription and real time qPCR

Total RNA from cultured cells was extracted using a NucleoSpin® RNA II kit (Macherey Nagel, Hoerdt, France). 2 μg of total RNA was used to perform reverse transcription using a SuperScript® III First-Strand Synthesis System (Invitrogen Life Technologies) with random hexamers. Real time qPCR analysis was performed with a LightCycler ® 480 Real-Time PCR System (Roche Diagnostics), using a SYBR Green I dye for product detection. The sequences of the primers used to amplify cDNA are listed in Table 1 and were designed with the Life Invitrogen software (Custom Primers-OligoPerfect TM Designer). The cycling program was set up as followed: 5 min at 95 °C and 43 cycles at 95 °C for 15 sec, 60 °C for 15 sec and 72 °C for 15 sec. Gene expression was normalized with the reference gene gapdh which does not have circadian expression [START_REF] Vandesompele | Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes[END_REF].

Western Blot analyses

For Western Blot analyses, proteins were extracted from cultured cells with a Cell Lytic solution (Sigma-Aldrich) following the manufacturer protocol and protein concentration was then measured by a BCA assay. 20 μg of proteins were separated on SDS-PAGE (Criterion any KD precast gels, BioRad) and electro-transferred onto Hybond nitrocellulose membranes. Membranes were then blocked with the Odyssey blocking buffer (Li-Cor Biosciences, Lincoln, NE, USA) and incubated with Santa Cruz antibodies (Dallas, Texas, USA), p16 (sc-448) and Nrf2 (sc-365949), Enzo Life Sciences antibodies (Villeurbanne, France), either proteasome β1 (BML-PW8140) and β5 (BML-PW8895) and immunoproteasome β1i (BML-PW8205), β2i (BML-PW8150-0100) and β5i (PW8200) catalytic subunits and proteasome regulators PA28αβ (BML-PW185-0100, PW8240) at dilutions of 1/500 for Nrf2, 1/1000 for p16, β1, β2, β5, PA28αβ and β2i, 1/2000 for β1i and 1/5000 for β5i. Then, membranes were washed with PBS and incubated with species infraredconjugated secondary antibodies (Li-Cor Biosciences) at a dilution of 1/15000 and scanned with the Odyssey infrared imaging system (Li-Cor Biosciences). Signal intensities were quantified with the ImageJ software.

Protein carbonyl immunodetection after SDS-PAGE

Immunoblot experiments for carbonyl detection were performed using the OxyBlot Protein Oxidation Detection Kit according to the manufacturer"s instructions. Proteins were extracted from cultured cells with a Cell Lytic solution supplemented with 0.1 M DTT and protein concentration was then measured by a Bradford assay. Carbonyl groups of 10 μg of proteins were derivatized to 2,4-dinitrophenylhydrazone by reaction with 2,4dinitrophenylhydrazine. The derivatized protein samples were separated on SDS-PAGE and electro-transferred onto Hybond nitrocellulose membranes. After Fast Green total proteins coloration (Sigma-Aldrich) and detection with the Odyssey infrared imaging system, the membranes were washed with a washing buffer (PBS 1X, tween 0.1% v/v). Then, they were successively incubated with rabbit anti-dinitrophenol antibodies (Sigma-Aldrich, dilution of 1/5000) and processed following the same procedure as for the western blot analysis.

Cell-Based Proteasome-Glo β1 and β5 Assay

The proteasome chymotrypsin-like (ChT-L) and post-acid or caspase-like (PA) activities of cells were determined using a chemiluminescent assay (Proteasome Glo cellbased assay, Promega, Madison, U.S.A). The cells were dispensed into white opaque 384well microtiter plates (2500 cells/well, 25 μL of culture medium per well). After one night of equilibration the cells were synchronized as described above. Then, every 4 h, 25 μL of assay buffer containing a recombinant firefly luciferase and the luminogenic proteasome substrates Suc-LLVY-Glo (ChT-L activity) or Z-nLPnLD-Glo (PA activity) were added. After incubation at room temperature for 10 min, chemiluminescence expressed as RLU (relative light unit) was measured on a Fluostar Optima plate reader (BMG Labtech, Champigny sur Marne, France) with a measuring time of 12 sec for each time. The proteasome activity was expressed as RLU/10 4 cells/min.

Cell-Based GSH/GSSG-Glo Assay

The measurements of total glutathione and oxidized glutathione were performed using a chemiluminescent assay (GSH/GSSG-Glo cell-based assay, Promega, Madison, U.S.A). The cells were dispensed into white opaque 384-well microtiter plates (2500 cells/well, 25 μL of culture medium without red phenol per well). After one night of equilibration the cells were synchronized as described above. Every 4 h, 12.5 μL/well of total glutathione lysis reagent or oxidized glutathione lysis reagent was added. After 5 min, 12.5 μL/well of luciferin generation reagent was added to all wells and was incubated during 30 min at room temperature. Then, 50 μL/well of luciferin detection reagent was put. After a further incubation at room temperature for 15 min, chemiluminescence expressed as RLU (relative light unit) was measured on a BMG Labtech Fluostar Optima plate reader with an integration time of 1 sec per well. The level of total glutathione and oxidized glutathione was expressed as RLU/10 4 cells.

Total ROS detection by flow cytometry

Cells were maintained with standard culture conditions as described above. The day before the experiment, 1 million of cells were seeded onto 6 well plates. After the synchronization treatment, the cells were incubated every 4 h during 15 min in the dark at 37 °C with the ROS probe 2,7-dichlorofluorescein diacetate (DCFDA, Sigma-Aldrich) dissolved in DMSO and used at a 10 M final concentration. After incubation with the dye, the cells were washed with PBS and fixed with 10 % of cold methanol. The flow cytometric analysis of fluorescent cells was performed using MACSQuant Analyzer 10 (Miltenyi Biotec, Paris, France). DCFDA signal was detected using a 490 nm bandpass filter behind a 525 nm long-pass with a laser power of 25 mW. The analyses were performed with the MACSQuantify software program. The level of ROS was expressed as FU/10 4 cells.

Mathematical modeling and statistical analyses

Results are presented as mean (or parameter value) of n measurements of separate cultures from different stocks of the same clonal population ± SEM. Data were treated as independent plots. All the fittings were performed by non-linear least squares regression, with the help of the mathematical software Origin 9.1 (OriginLab, RITME informatique, Paris, France). The raw data for each curves were fitted to a sinus-derived damped wave function added to a linear drift term:

y = y 0 + Ae -x/c sin (π ((t-φ)/τ))
with A > 0, τ > 0, t > 0

Where y 0 represent the value before the serum shock, A is the amplitude, c is a constant decay, t is time (h), τ is the endogenous period (h) and φ is the phase (h).

The damping factor e -x/c was applied to sinus-derived wave function to represent cell desynchronization over time. We removed the first two data points at t 0h and t 2h from the parameter estimation procedure as purely circadian variations may be perturbed by the serum shock during the first hours.

The pearson χ 2 test and more particularly the chi-square which is also known as coefficient of determination and the adjusted r-square value that accounts for the degrees of freedom, were the statistical values used to determine the goodness of the fit.

Furthermore, the results were considered acceptable only if the variance (determined by ANOVA) between the raw data was not important (p ≤ 0.01). Statistical differences according to circadian time were tested with multiple-way ANOVA including the Tukey and Fisher tests. Circadian parameters (A, τ and φ) were estimated simultaneously using the Origin 9.1 software.

Results

Circadian rhythmicity of proteasome peptidase activities and protein oxidative damage

To investigate intracellular protein redox homeostasis and its regulation by the circadian clock in human cells, cultivated HEK 293 cells and primary HDF were synchronized by a serum shock [START_REF] Balsalobre | A Serum Shock Induces Circadian Gene Expression in Mammalian Tissue Culture Cells[END_REF] and samples were collected at regular intervals during two days for subsequent analyses. First, expression levels of circadian clock genes were assessed to confirm that both cellular models have been synchronized by the serum treatment.

Circadian oscillations at the transcript levels were observed for bmal1 and per2 genes. As previously described [START_REF] Balsalobre | A Serum Shock Induces Circadian Gene Expression in Mammalian Tissue Culture Cells[END_REF] per2 expression was first induced after the serum shock, then the transcript level goes down and increases at t 10h-12h after the serum treatment to reach a peak of expression at t 22h-26h (Fig. 1A &A"). These clock genes oscillate with a circadian period between 21.3 ± 1.1 h (bmal1) and 24.5 ± 0.9 h (per2) for HEK 293 cells and between 24.6 ± 0.8 h (bmal1) and 26.9 ± 0.8 h (per2) for HDF. As expected, the circadian pattern of the activator bmal1 is in antiphase with the one of per2 (Fig. 1A &A"). Thus, the serum shock treatment successfully synchronized HEK 293 cells and HDF in vitro.

Proteins carrying irreversible oxidative damage such as carbonyls have been reported

to be mainly degraded by the proteasome. Therefore, to find out if the proteasome and protein carbonyl formation follow circadian oscillations, proteasome peptidase activities were monitored within cells (Fig. 1B & To determine the levels of protein carbonyls, synchronized cells were harvested every 4 h for 50 h and proteins were then extracted and their carbonyls derivatized with DNPH to be monitored by immunochemistry as described in Material and Methods. Protein carbonyls content was found to be modulated rhythmically with a period of 21.3 ± 0.5 h for HEK 293 cells and a period of 22.9 ± 0.7 h for HDF. The serum shock treatment results in two maximum peaks, one around t 22h and one around t 46h (Fig. 1C & C"). Interestingly, proteasome activity tracks the circadian oscillations of carbonyls formation since its peptidase activities and protein carbonyl levels oscillate in anti-phase.

Circadian expression of constitutive proteasome and immunoproteasome catalytic subunits and PA28αβ at the mRNA and protein levels

To further investigate how the circadian clock regulates proteasome activities, the mRNA and protein levels of 20S proteasome catalytic β subunits were analyzed (Fig. 1D & D" and 1E & E"). Gene expression analyses show that transcript levels of β1 and β5 catalytic subunits exhibit circadian oscillations with a period of 22.1 ± 1.3 h (β1) and 21.4 ± 1.1 h (β5)

for HEK 293 cells and with a period of 23.4 ± 1.2 h (β1) and 22.4 ± 1.1 h (β5) in HDF.

Nevertheless, protein expression of the 20S proteasome catalytic β subunits did not show circadian oscillations, suggesting that the cyclic proteasome activity may result from its activation rather than de novo synthesis of its subunits. Indeed, it has been described that both the 20S immunoproteasome and the proteasome activator PA28αβ (11S) are implicated in the degradation of oxidized proteins [START_REF] Pickering | Nrf2dependent induction of proteasome and Pa28alphabeta regulator are required for adaptation to oxidative stress[END_REF]. The mRNA (Fig. 2A &A") and protein (Fig. 2B &B") expression analyses of 20S immunoproteasome β1i and β5i catalytic subunits revealed that only β5i exhibits circadian oscillations at both mRNA and protein levels in the two cellular models with a periodicity around 22.6 ± 1.3 h (mRNA) and 22.2 ± 1.5 (protein) for HEK 293 cells (Fig. 2A and 2B) and 25.5 ± 0.9 h (mRNA) 23.2 ± 0.5 h (protein) for HDF (Fig. 2A" and 2B").

Besides 20S proteasome catalytic β1 and β5 and immunoproteasome catalytic β5i subunits, gene expression analyses also revealed that PA28αβ is under the clock control. Both

PA28α and PA28β components are rhythmically produced at the mRNA and protein levels in the two cellular models. In HEK 293 cells, PA28αβ shows, an oscillating period of 21.1 ± 1.1 h for PA28α and 21.7 ± 1.4 h for PA28β at the transcript level (Fig. 2C). The PA28α and β proteins also display circadian rhythmicity with periods of 25.2 ± 0.9 h and 20.8 ± 1.3 h respectively with peaks of expression around t 25h and t 50h (Fig. 2D). In HDF, the circadian period of PA28α is 26.2 ± 0.8 h and 27.2 ± 0.5 h for PA28β at the transcript level (Fig. 2C").

The PA28α and β proteins oscillate with maximum peaks around t 27h and t 51h and display circadian periods of 25.6 ± 1.2 h and 23.4 ± 0.7 h respectively (Fig. 2D"). Interestingly, in both cellular models the oscillation of PA28αβ protein levels precedes the one of proteasome activities.

Circadian rhythmicity of Nrf2 gene and protein expression, ROS production and oxidized glutathione content

To further elucidate the circadian modulation of proteasome peptidase activities and oxidized protein content, we have analyzed Nrf2 expression and monitored ROS production and the intracellular redox status by measuring oxidized glutathione. Indeed, Pickering et al.

(2012) have shown that adaptation to oxidative stress includes Nrf2-dependent increase in cellular capacity to degrade oxidized proteins that are attributable to increased expression of 20S proteasome and immunoproteasome subunits and of PA28αβ [START_REF] Pickering | Nrf2dependent induction of proteasome and Pa28alphabeta regulator are required for adaptation to oxidative stress[END_REF]. Moreover, transcript levels of Nrf2, as well as several of its target genes, have been recently reported to show diurnal variation in mouse livers and Drosophila heads [START_REF] Beaver | Circadian regulation of glutathione levels and biosynthesis in Drosophila melanogaster[END_REF][START_REF] Xu | Diurnal variation of hepatic antioxidant gene expression in mice[END_REF]. To investigate whether Nrf2 expression is subjected to circadian modulation that would explain, at least in part, the circadian up-regulation of PA28αβ and proteasome catalytic β subunits, Nrf2 mRNA and protein levels were determined in synchronized HEK 293 cells and HDF. As shown in Fig. 3A & A" and 3B & B", both Nrf2 gene and protein expression followed circadian oscillations with a period of 24.4 ± 0.8 h and 27.6 ± 1.9 h respectively in HEK 293 cells (Fig. 3A &B) and of 20.7 ± 0.9 h and 23.1 ± 1.2 h in HDF (Fig. 3A" & B"). Interestingly, the circadian protein pattern of Nrf2 precedes the pattern of β1, β2, β5, β5i and PA28αβ mRNA levels.

Since Nrf2 is one of the main sensor of oxidative stress, we measured the ROS level using the fluorescent probe DCFDA by flow cytometry as described in Materials and Methods. As shown in Fig. 3C & C", ROS are produced rhythmically with a period of 22.6 ± 0.8 h in HEK 293 cells and of 22.1 ± 0.7 h in HDF. Interestingly, their oscillation pattern slightly precedes, in HEK 293 cells, or matches, in HDF, the protein carbonyls pattern and is in anti-phase with proteasome activities. The intracellular redox status was also monitored by assessing an antioxidant defense system known to be controlled by the Nrf2 pathway, namely the glutathione system. The levels of oxidized glutathione was measured and exhibited circadian fluctuations with a period of 24.6 ± 0.4 h for HEK 293 cells and 22.1 ± 2.5 h for HDF (Fig.

3D & D").

Differential sensitivity of synchronized HEK 293 cells to oxidative stress depending of its timing

Since the proteasome, PA28αβ and Nrf2 are under circadian control, the sensitivity of synchronized HEK 293 cells to external oxidative stress applied at different times was tested.

Synchronized HEK 293 cells were exposed during 1 h to 200 μM of oxidative agent tert-butyl hydroperoxide (t-BHP) at t 6h , t 18h , t 30h and t 42h . It appears that cells are significantly more resistant to oxidative stress at t 6h and t 30h as compared to t 18h and t 42h (Fig. 4). The former times correspond to the high range of proteasome peptidase activities and PA28αβ protein expression while the latter match the nadir of both parameters. Interestingly, the high survival rates also match the lower levels of oxidized glutathione. Hence, HEK 293 cells are more resistant to external oxidative stress when the proteasome peptidase activities are high, which also corresponds to the lower range of oxidized protein and glutathione (Fig. 1C) and endogenous ROS levels (Fig. 3C).

Lack of circadian rhythmicity of proteasome peptidase activities, protein oxidative damage, ROS production and oxidized glutathione content in synchronized senescent

HDF

Cellular replicative senescence represents a model for studying cellular aging while senescent cells have also been implicated both in organismal aging and the occurrence of several age-related diseases [START_REF] Bollinger | Circadian rhythms -from genes to physiology and disease[END_REF][START_REF] Kelleher | Circadian molecular clocks and cancer[END_REF][START_REF] Arellanes-Licea | The circadian timing system: a recent addition in the physiological mechanisms underlying pathological and aging processes[END_REF]. Since senescent cells have been previously reported to exhibit increased oxidized protein levels, impaired proteasome function and expression of genes involved in the circadian clock [START_REF] Kunieda | Cellular senescence impairs circadian expression of clock genes in vitro and in vivo[END_REF][START_REF] Khapre | Circadian clock protein BMAL1 regulates cellular senescence in vivo[END_REF], HDF were grown until they reached senescence (passage between 43 and 46), monitored by SA-β-galactosidase activity and p16, and then synchronized by a serum shock. Expression levels of bmal1 and per2 genes were analyzed and a circadian oscillation at the transcript level was observed for these two genes.

Thus, the serum shock treatment successfully synchronized HDF in culture with members of the positive and negative hands of the core loop, bmal1 and per2 oscillating with periods of about 32.9 ± 4.7 h and 31.4 ± 3.9 h respectively (Fig. 5A), which is significantly longer than the period between 24.6 ± 0.8 h and 26.9 ± 0.8 h observed in young fibroblasts. As expected, proteasome peptidase activities were significantly lower by 4.5 fold in senescent cells (82.4 ± 23.4 RLU/10 4 cells/min; n=3) as compared to young ones (371.6 ± 25.4 RLU/10 4 cells/min; n=3) while oxidized protein content was higher by about 2 fold. Their levels of ROS and GSSG were also found higher by about 3 (10680 ± 1044 vs 3604 ± 585 FU/10 4 cells) and 6 (118x10 4 ± 17x10 4 vs 20x10 4 ± 5x10 4 RLU/10 4 cells) fold respectively in senescent cells as compared to young fibroblasts. In contrast to the synchronized young fibroblasts, proteasome activities (Fig. 5B) and protein carbonyl levels (Fig. 5C) did not exhibit circadian rhythmicity.

Concerning the Nrf2 protein (Fig. 5D) and ROS levels (Fig. 5E), their rhythmicity are also completely lost. However, oxidized glutathione levels showed rhythmicity with a period of 48 h (Fig. 5F), which is longer than those of the clock genes in senescent cells (Fig. 5A) and about twice as much as the period observed for the young cells (Fig. 3D").

Discussion

The adaptation of organisms at different temporal niches is governed by the circadian clock. The daily variation of some stressors on ancient earth, especially oxidative atmosphere and strong solar radiation, can generate damages and promote various pathologies, forcing the circadian system to evolve as a protective system. Many studies describe ROS as one of the main inducers of biological disorders. Indeed, if the production and the elimination of ROS are not properly managed, the cells can undergo oxidative stress due to an imbalanced cellular redox state, leading to genomic and protein deterioration and ultimately to cell death. Protein carbonylation is the most widely used biomarker for oxidative damage to proteins, and reflects cellular damage induced by multiple forms of ROS. Carbonylated proteins cannot be repaired [START_REF] Ferrington | Altered proteasome structure, function, and oxidation in aged muscle[END_REF][START_REF] Nystrom | Role of oxidative carbonylation in protein quality control and senescence[END_REF] and are eliminated by the proteasome which represents the main proteolytic system implicated in many cellular pathways including oxidized protein degradation in the nucleus and the cytosol [START_REF] Kapphahn | Age-dependent inhibition of proteasome chymotrypsin-like activity in the retina[END_REF][START_REF] Friguet | Oxidized protein degradation and repair in ageing and oxidative stress[END_REF][START_REF] Chondrogianni | Protein damage, repair and proteolysis[END_REF]. Age-associated impairment of proteasomal function has been reported to contribute to the accumulation of oxidized protein with age [START_REF] Baraibar | Changes of the proteasomal system during the aging process[END_REF][START_REF] Ferrington | Altered proteasome structure, function, and oxidation in aged muscle[END_REF][START_REF] Kapphahn | Age-dependent inhibition of proteasome chymotrypsin-like activity in the retina[END_REF][START_REF] Ethen | Transformation of the proteasome with age-related macular degeneration[END_REF]. ROS can also serve as second messengers to control physiological and pathological processes [START_REF] Thannickal | Reactive oxygen species in cell signaling[END_REF].

Thus, redox homeostasis appears to be critical for cellular function. A direct link between redox homeostasis and the circadian clock has been recently established since oscillations of the redox state of peroxiredoxin have been described as an additional timekeeping mechanism [START_REF] Edgar | Peroxiredoxins are conserved markers of circadian rhythms[END_REF][START_REF] O'neill | Circadian clocks in human red blood cells[END_REF][START_REF] O'neill | Circadian rhythms persist without transcription in a eukaryote[END_REF]. Interestingly, hyperoxidized peroxiredoxins have also been shown to be degraded by the proteasome, hence contributing to the peroxiredoxin redox state-dependent timekeeping mechanism. Moreover, circadian rhythmicity of anti-oxidative defenses and its aged-associated impairment has also been reported [START_REF] Patel | Transcriptional control of antioxidant defense by the circadian clock[END_REF][START_REF] Khapre | Circadian clock protein BMAL1 regulates cellular senescence in vivo[END_REF] suggesting that other important elements of redox homeostasis such as oxidized protein degradation by the proteasome could be modulated by the circadian clock.

In this study, HEK 293 cells, as well as HDF, that represent a more physiologically relevant cellular model [START_REF] Sandu | Human skin keratinocytes, melanocytes, and fibroblasts contain distinct circadian clock machineries[END_REF], were synchronized by a serum shock [START_REF] Balsalobre | A Serum Shock Induces Circadian Gene Expression in Mammalian Tissue Culture Cells[END_REF]. As expected, both mammalian cellular models showed oscillations of the circadian clock genes bmal1 and per2 (Fig. 1A &A"). In both cellular models, the proteasome peptidase activities exhibited circadian rhythmicity (Fig. 1B &B"). This finding may have important implications for the rhythmic regulation of the abundance of proteins that are degraded by the proteasome and might also explain previously reported discrepancies between transcriptome and proteome circadian rhythmicity [START_REF] Yang | Cutting through complexity: the proteolytic properties of alternate immunoproteasome complexes[END_REF][START_REF] Luck | Rhythmic degradation explains and unifies circadian transcriptome and proteome data[END_REF]. Interestingly, oxidatively damaged protein content, monitored by measuring levels of protein carbonylation as a function of time (Fig. 1C & C"), also showed a circadian modulation, which was in anti-phase with the one observed for proteasome peptidase activities (Fig. 1B &B"). A direct circadian regulation of many antioxidant enzymes with an E-Box present in their promoter sequence, as well as some proteasome subunits, has been previously evidenced at the transcript level by microarray analyses [START_REF] Yan | Analysis of gene regulatory networks in the mammalian circadian rhythm[END_REF]. However, the rhythmic pattern that we observed for the catalytic β subunits transcript levels (Fig. 1D &D") was not found at the protein level (Fig. 1E &E"), which indicates that the circadian modulation of proteasome peptidase activities may originate from other mechanisms than circadian de novo synthesis of proteasome subunits. Indeed, the constitutive 20S proteasome has a long half-life of 133 h versus 27 h for the 20S immunoproteasome [START_REF] Heink | IFN-gamma-induced immune adaptation of the proteasome system is an accelerated and transient response[END_REF]. Moreover, it has been shown that the 20S immunoproteasome and PA28αβ also play a key role in oxidized protein degradation [START_REF] Pickering | Nrf2dependent induction of proteasome and Pa28alphabeta regulator are required for adaptation to oxidative stress[END_REF]. Our results show that, in both synchronized HEK 293 cells and HDF, only one immunoproteasome catalytic subunit β5i (Fig. 2A & A" and Fig. 2B &B") but the two isoforms of the activator PA28αβ exhibited circadian oscillations both at the transcript and protein levels (Fig. 2C & C" and Fig. 2D & D") that were matching those observed for proteasome peptidase activities (Fig. 1B &B").

Furthermore, [START_REF] Pickering | Nrf2dependent induction of proteasome and Pa28alphabeta regulator are required for adaptation to oxidative stress[END_REF] have also reported a common regulation of constitutive proteasome and immunoproteasome catalytic subunits and their regulators. Indeed, due to the presence of an ARE (antioxidant response element) motif in the promoter sequence of β1, β2, β5, β5i and PA28αβ, they proposed that the Nrf2 pathway, which has been recently shown to be under circadian control [START_REF] Pekovic-Vaughan | The circadian clock regulates rhythmic activation of the NRF2/glutathione-mediated antioxidant defense pathway to modulate pulmonary fibrosis[END_REF], could be the master oxidative regulator of the proteasome.

Interestingly, we did observe circadian oscillations only for β1, β2, β5, β5i and PA28αβ mRNA levels and not for β1i that has no ARE motif in its promoter sequence. Therefore, we have investigated the circadian regulation of Nrf2 pathway as an endogenous modulator of proteasome function in synchronized HEK 293 cells and HDF. As shown in Fig. 3, Nrf2 gene and protein expression, ROS production and oxidized glutathione were found to oscillate in a circadian manner. As summarized in Fig. 6, these findings suggest that the circadian controlled Nrf2 pathway stimulates oxidized protein degradation by the proteasome mainly through the circadian induction of de novo synthesis of the proteasome activator PA28αβ.

ROS oscillations matched the protein carbonylation ones and they were both in anti-phase with proteasome activities. Since the circadian transcription factor CLOCK/BMAL1 positively regulate Nrf2 transcription through temporal control of the E-box motif in the Nrf2 gene promoter, Nrf2 protein oscillates in a circadian manner and drive circadian transcription of the proteasome catalytic subunits and PA28αβ as well as a key set of antioxidant genes including those involved in glutathione metabolism as previously described [START_REF] Xu | Diurnal variation of hepatic antioxidant gene expression in mice[END_REF][START_REF] Pekovic-Vaughan | The circadian clock regulates rhythmic activation of the NRF2/glutathione-mediated antioxidant defense pathway to modulate pulmonary fibrosis[END_REF]56].

We next investigated whether the circadian modulation of protein redox homeostasis and degradation of oxidized protein by the proteasome would impact on cellular resistance to an external oxidative stress applied with equal strength at different times of the day. As shown in Fig. 4, HEK 293 cells exposed for 1 h to sub-lethal doses of t-BHP showed differential sensitivity to oxidative stress induced cell death depending on its timing. Interestingly, the highest sensitivity to oxidative stress was observed at t 18h and t 42h , that both correspond to the lower proteasome peptidase activities and the higher levels of oxidized proteins and glutathione (Fig. 1C & Fig. 3D). The importance of such circadian timing has been demonstrated in various biological areas. Indeed, previous studies strongly support the administration of drugs at certain times of day as a valuable method for improving anticancer above, a hallmark of cellular aging is the accumulation of oxidatively damaged proteins that has been associated with both increased ROS production and alteration of protein maintenance systems such as the proteasome [START_REF] Friguet | Oxidized protein degradation and repair in ageing and oxidative stress[END_REF]64]. The link between the biological clock and protein redox homeostasis, including proteasome mediated oxidized protein degradation, could thus explain, at least in part, such changes observed during the aging process.

Interestingly, the premature aging phenotype observed in bmal1 deficient mice has been linked to an increased of ROS levels compared to wild type mice that was suggested to originate as a consequence of the loss of the transcription activation by CLOCK/BMAL1 of the antioxidant enzymes [65]. In the light of our results, defects in protein redox homeostasis and alteration of proteasome function may also have contributed to this accelerated aging.

Taken together, our results support a critical link between the circadian clock, the redox homeostasis and the accumulation of oxidized protein during cellular aging.

Genes & Development Primers for the reference gene gapdh were designed according to previously published sequences [START_REF] O'neill | Circadian rhythms persist without transcription in a eukaryote[END_REF] while the remaining sequences were designed with the AmplifX software. subunits was analyzed at the protein level in cellular extracts by western blotting as described in Material and Methods. Quantification of proteasome subunit content was achieved using the ImageJ software. In the both cellular models no circadian rhythmicity were detected at the protein level for the catalytic subunits.

Gene

Forward primer Reverse primer

Gapd

Expression values of all genes were first normalized to the gapdh gene expression while expression values of all proteins were first normalized to the total protein load obtained upon Fast Green gel staining. A second normalization to the mean value of the time course experiment was performed for gene and protein expression levels, carbonylated protein content and proteasome activities.

Results are expressed as means +/-SEM, n = 5. All the curves and the periods were obtained using the Origin 9.1 software (OriginLab). Expression values of all genes were first normalized to the gapdh gene expression while expression values of all proteins were first normalized to the total protein load obtained upon Fast Green gel staining. A second normalization to the mean value of the time course experiment was performed for gene and protein expression levels.

Results are expressed as means +/-SEM, n = 4. All the curves and the periods were obtained using the Origin 9.1 software (OriginLab). Sub-confluent HEK 293 cells were synchronized with a serum shock treatment (t 0h ) and then at t 2h , t 6h , t 18h , t 30h or t 42h cells were exposed to an oxidative stress using 200 μM of t-BHP for 1 h. Cell viability was then measured using a XTT viability test and normalized to the value obtained t 0h . Values represent the mean +/-SEM of three independent experiments. Asterisks indicate statistical difference according to the ANOVA test (* P < 0.01).

  B") and protein carbonyl levels were analysed in cellular extracts (Fig. 1C & C") in serum shock synchronized cells. Both ChT-L and PA proteasome activities display similar circadian patterns (Fig 1B & B"). The serum shock treatment generates a peak of activity followed by a decrease until t 18h-20h , then both activities increase again to reach a peak at t 30h-34h , in the two cellular models, following a periodicity of 24.3 ± 0.3 h (ChT-L) and 24.2 ± 0.4 h (PA) for HEK 293 cells and 23.1 ± 0.6 h (ChT-L) and 22.6 ± 0.7 h (PA) for HDF (Fig. 1B & B").

  treatment. Cancer chronotherapy can change by several fold the efficiency and tolerability of anticancer medications in experimental models and cancer patient[57]. Since the proteasome is a recognized target for anticancer treatment, it would be important to assess whether proteasome inhibition and hence anticancer treatment efficacy can be optimized depending on the timing of proteasome inhibitors addition. Indeed, several inhibitors are approved by the FDA as bortezomib and carfilzomib in the treatment of multiple myeloma[58, 59]. However, several studies have demonstrated that these inhibitors also induce resistance to cell death due to the activation of cell survival pathways[60, 61]. In this context, administration of proteasome inhibitors at appropriate timing could increase their efficacy by reducing cancer cell resistance and decrease their toxicity-related side effects by using lower doses.Finally, to analyze the effects of the circadian disturbance observed during aging and age-associated pathologies on redox homeostasis and degradation of oxidized proteins by the proteasome, we have measured proteasome activities, ROS, oxidized protein and glutathione levels in synchronized senescent HDF as a function of time. Indeed, age-related impairments of circadian rhythmicity have been reported in model organisms as well as in humans[62] while alterations of the circadian clock gene expression was observed in senescent smooth muscle cells in vitro and in vivo[START_REF] Kunieda | Cellular senescence impairs circadian expression of clock genes in vitro and in vivo[END_REF]. Although senescent HDF could be synchronized by the serum shock treatment (Fig.5A), the bmal1 and per2 gene expression was oscillating with smaller amplitudes and longer periods observed with young HDF. In contrast with the synchronized young fibroblasts, neither proteasome activities, protein carbonyls, Nrf2, ROS, and oxidized glutathione levels showed circadian rhythmicity (Fig.5B, C, D, E& F). These findings are consistent with those reported by Stratford et al. (2006) who have shown a striking difference in the interferon induced regulation of immunoproteasome levels in replicative senescence as compared with constitutive proteasome [63]. As already stated

Figure 1 :

 1 Figure 1: Proteasome peptidase activities and protein oxidative damage display circadian rhythmicity in synchronized HEK 293 cells and HDF Sub-confluent HEK 293 cells and HDF were synchronized using a serum shock as described in Materials and Methods. Cells were harvested after a 2 h exposure to a medium containing 50% (v/v) of serum and then every 4 h for 50 h in a serum free medium. (A)(A') Total RNA was extracted and mRNA levels of clock circadian genes were determined by Real Time qPCR. The expression of both per2 (closed squares) and bmal1 (open squares) exhibited a circadian periodicity of 21.3 ± 1.1 h and 24.5 ± 0.9 h respectively in the HEK 293 cells (A) and 24.6 ± 0.8 h and 26.9 ± 0.8 h in HDF (A'), hence validating serum shock synchronized HEK 293 cells and HDF as circadian cellular models. As expected, the expression of per2 (closed circles) did not show circadian rhythmicity in non synchronized HEK 293 cells and HDF. (B)(B') Intracellular proteasome peptidase activities were monitored using a Cell-Based Proteasome-Glo β5 and β1 Assay as described in Material and Methods. ChT-L (closed

Figure 2 :

 2 Figure 2: Proteasome catalytic subunits gene expression and proteasome activator PA28αβ gene and protein expressions display circadian rhythmicity in synchronized HEK 293 cells and HDF Sub-confluent HEK 293 cells and HDF were synchronized using a serum shock as described in Materials and Methods. Cells were harvested after a 2 h exposure to a medium containing 50% (v/v) of serum and then every 4 h for 50 h in a serum free medium.

Figure 3 :

 3 Figure 3: Nrf2 expression, ROS level and oxidized glutathione display circadian rhythmicity in synchronized HEK 293 cells and HDF Sub-confluent HEK 293 cells and HDF were synchronized using a serum shock as described in Materials and Methods. Cells were harvested after a 2 h exposure to a medium containing 50% (v/v) of serum and then every 4 h for 50 h in a serum free medium.

Figure 4 :

 4 Figure 4: Resistance of synchronized HEK 293 cells to t-BHP oxidative agent varies according to the timing of the stress.

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	Table

Table 1 : Sequences of primers used for the Real-Time qPCR analyses.

 1

Acknowledgments

The authors wish to acknowledge the support of FP6 EU Project Proteomage (N° 518230) and FP7 COST Action CM1001. In addition, they are very thankful to M. Moreau and C. Nizard from LVMH-Research for providing us the HDF, A. Munier, J.F. Gilles, and R. Schwartzmann from the Cell Imaging and Flow Cytometry Facility of the IBPS (Paris, France) for precious help in microscopy/cytometry/ image analysis and to A. Chaffotte from the Pasteur Institute (Paris, France) for his advice on mathematical modeling using Origin 9.1.

Oxidative stress dependent Nrf2-activation has been previously associated with an increase in the cellular capacity to degrade oxidized proteins that is attributable to the Nrf2-dependent increased expression of the 20S proteasome subunits and its activator PA28αβ that contain an ARE motif in their promoter sequence. Hence, the oscillating expression and activation of Nrf2 is inducing a rhythmic transcriptional synthesis of its target genes, especially the proteasome catalytic subunits β1, β2 and β5 and immunoproteasome β5i as well as the proteasome activator PA28αβ subunits. The cyclic protein expression of the PA28αβ proteins unlike β1, β2, β5 argues for PA28αβ being the main circadian mediated regulator of the rhythmic proteasome activity and rhythmic variation intracellular protein carbonyl levels.

List of figures:


Ge Xin
email: ge.xin@insa-lyon.fr

Jerome Antoni

Nacer Hamzaoui

An Exploring Study of Hidden Markov Model in Rolling Element Bearing Diagnostis

Rolling element bearing is a crucial component in rotating machinery, so the diagnosis of bearing fault has attracted a lot of attention in both scientific and application areas. The objective of fault diagnosis can be viewed as a separation of informative events concerning different types of fault in noisy measurements. Therefore, it is appealing to model the raw signal as a linear combination of few components with the prior knowledge and assumption. Hidden Markov model (HMM) is a probabilistic model of joint probability of a collection of random variables which represent the hidden states as state variables given the observation sequence. In this paper, an exploring study in rolling element bearing diagnostics based on HMM is investigated and a new fault separation scheme is proposed. We analyse the performance of the proposed scheme through numerical experiments and demonstrate its potentiality in industrial applications.

Introduction

As crucial components in rotating machinery, rolling element bearing have received constant research attention, in particular for their diagnostis [START_REF] Randall | Rolling element bearing diagnostics-a tutorial[END_REF]- [START_REF] Antoni | Cyclostationary modelling of rotating machine vibration signals[END_REF]. Typically when a defect occurs during operation, it excites some resonances at a specific rate called 'bearing characteristic frequencies'. The excitation, which is generally amplitude modulated, embodies all the information concerning different types of faults. In industrial applications, however, such transient signals are usually embedded in heavy background noise which jeopardizes their detection. For the sake of separating the fault signature from noisy measurements, a reasonable transformation should be devised to represent the fault signal and the noise, respectively.

A proper transformation is used to extract the fault property from the acquired raw signal, which enables the following step to achieve the diagnostic identification. In terms of transform domain, there exists several feature extraction techniques which can be divided into three main categories: time domain, frequency domain and time-frequency domain. Intuitively speaking, in terms of statistical signal processing, time domain and frequency domain analyses are both directly based on the stationary assumption, thus leading to scalar indicators (RMS value, crest factor, kurtosis factor, or some complex combination of them) or vectorial indicators (signal spectrum, cepstrum or envelope spectrum) [START_REF] Antoni | Cyclic spectral analysis of rolling-element bearing signals: Facts and fictions[END_REF][START_REF] Tang | Sparse representation based latent components analysis for machinery weak fault detection[END_REF]. To the contrary, time-frequency domain reveals the instantaneous features jointly in time and frequency which is appealing for non-stationary signal analysis, e.g. Wigner-Ville distribution, wavelet transform, and high-order spectral analysis [START_REF] Meng | Rotating machinery fault diagnosis using Wigner distribution[END_REF]- [START_REF] Rai | Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform[END_REF]. However, as it is proved by Antoni in [START_REF] Antoni | Cyclic spectral analysis of rolling-element bearing signals: Facts and fictions[END_REF][START_REF] Antoni | Cyclostationary modelling of rotating machine vibration signals[END_REF], rolling element bearing vibrations are random cyclostationary.

In our present work, a general algorithm is proposed to implement the decomposition of a vibration signal into two states: 1) a stationary component with a Gaussian probability density function and 2) a transient signal with a different Gaussian probability density function. The algorithm is inspired by the Gaussian mixture problem which has been well addressed in the Data Mining community: it uses the EM algorithm in each frequency band of a Short-Time Fourier Transform (STFT). The purpose is to capture the maximum-likelihood estimate of the parameters of an underlying distribution from a given data set and therefore better discriminate informative signals from noise. It provides a proper classification result for diagnostic identification. This algorithm is evaluated through simulations which validates the efficiency of the proposed classification scheme in detecting the transient signals without pre-selected parameters.

The rest of the paper is organized as follows. Section 2 introduces the mathematical description of the problem, the basic theory of HMM and its solving method, the EM algorithm. In section 3, a classification scheme based on HMM is proposed. Then, the performance of the proposed algorithm is evaluated through numerical experiments in section 4. The conclusion is made in section 5.

Mathematical model and HMM

Mathematical description

Our target is to extract the informative signal x(t) embedded in noisy measurement y(t). This simple model is described by the following equation:

y(t) = x(t) + n(t) (1)
where n(t) denotes an additive zero-mean stationary Gaussian noise with standard deviation σ .

As discussed before, time-frequency representation is apt to reveal the symptomatic property of the energy distribution to vary with pseudo-periodic intervals in the case of a fault (the mathematical model is demonstrated in Eq.5). The STFT is a common time-frequency representation that adds a time variable to the conventional Fourier spectrum in order to study the time-varying characteristics of signal. Therefore, the decomposition of vibration signal for damage detection is done by applying the STFT in order to capture the fault signature. Let {w[n]} N w -1 n=0 be a positive and smooth N w -long data-window which shift R samples (from 1 to N) to truncate a segment of x[n] at times kR, ..., kR+N w -1, and let f b denote the frequency bin index. Then it is defined as:

ST FT x (k, f b ) = kR+N w -1 ∑ n=kR w k [n] • x[n] • e -j2π f b n/N w (2)

Hidden Markov model

A hidden Markov model is a probabilistic model of joint probability of a collection of random variables which represent the hidden states as state variables given the observation sequence. As a dual random process, a hidden Markov model has two kinds of stochastic variable, namely the hidden state and the observation vector. The state sequence is unobservable, but can be estimated by the observation sequence [START_REF] Rabiner | A tutorial on hidden Markov models and selected applications in speech recognition[END_REF]- [START_REF] Miao | Condition monitoring and classification of rotating machinery using wavelets and hidden Markov models[END_REF].

As mentioned before, vibration signals can be described as a linear combination of a random cyclostationary component and a Gaussian stationary noise. In the time-frequency domain, stationary noise is spread over the whole picture and the informative part is embodied in it. Hence Gaussian mixed model (GMM) can be employed to model the probability distribution of the observation. We assume that data Y is observed(assume it is i.i.d.) and X is latent random variables, meaning that it is hidden/unobserved. We assume that a complete data set exists C = (X,Y) and also specify a joint density function:

p(c | Θ) = p(x, y | Θ) = p(x | y, Θ)p(y | Θ) (3)
where Θ embodies the mean µ and covariance σ which belongs to the different states x(latent random variable). Suppose that we are given a training set {y (1) , ..., y (m) }, z (i) ∼ Multinomial(φ ) (where φ j ≥ 0, ∑ k j=1 φ j = 1, and the parameter φ j gives p(z (i) = j)), and x (i) | z (i) = j ∼ N(µ j , Σ j ). Let k denote the number of values that the z (i) 's can take on. The parameters of GMM are thus φ , µ and σ . To estimate them, the total likelihood of the measurement is evaluated:

l(φ , µ, Σ) = m ∑ i=1 logp(x (i) ; φ , µ, Σ) = m ∑ i=1 log k ∑ z (i) =1 p(x (i) | z (i) ; µ, Σ)p(z (i) ; φ ) (4)

EM algorithm

Any probability distribution could be described as a mixture of a few Gaussian distributions. To estimate these parameters of Gaussian densities, maximum-likelihood parameter estimation is employed. However, there exist latent variables which denote the probability of state. This is what will make the estimation problem difficult.

The EM algorithm is an efficient iterative procedure to estimate the maximum-likelihood parameter in the presence of missing or hidden data. It consists of two steps: the E-step and the M-step which are presented below [START_REF] Bilmes | A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models[END_REF]. In the E-step, the missing data are estimated given the observed data and current estimate of the model parameters. In the M-step, the likelihood function is maximized under the assumption that the missing data are known. Convergence is assured since the algorithm is guaranteed to increase the likelihood at each iteration. Here are the EM iteration steps:

Repeat until convergence: (E-step) For each i, j, set

w (i) j := p(z (i) = j | x (i) ; φ , µ, Σ) (M-step)
Update the parameters:

φ j : = 1 m m ∑ i=1 w (i) j µ j : = ∑ m i=1 w (i) j x (i) ∑ m i=1 w (i) j Σ j : = ∑ m i=1 w (i) j (x (i) -µ j )(x (i) -µ j ) T ∑ m i=1 w (i) j

Bearing fault separation based on GMM

In this study, we propose an informative signal separation scheme based on GMM. It provides a proper classification result for diagnostic identification. The details of the separation process are as follows:

1. Transform the raw signal into time-frequency domain using STFT (see Eq.2), so that the stationary component is taken in each segment corresponding to frequency axis and the non-stationary component is carried by the time axis.

2. Assume the measurement is a mixture of Gaussian distributions (see Eq.3). For each frequency bin, it consists of two states: a stationary component with a Gaussian probability density function on the one hand and a transient signal with a different Gaussian probability density function on the other hand.

3. The EM algorithm is employed to estimate the power spectrum of the two states and the probability of being in any state given the data.

4. Based on the estimated parameters and probability of states, the underlying information can be extracted (as shown in following section). An indicator of state is calculated and therefore the state decision is made. Hereafter, a vibration signal is decomposed into two components. Finally, the informative signal is extracted.

Verification on Numerical experiments

The following discussion is based on numerical simulations. First of all, a synthetic signal is generated which simulates the vibrations (m/s 2 ) excited by an outer-race fault as shown in Figure 1. To see this more clearly, let us recall the more realistic model for the vibration signal produced by a faulty bearing [START_REF] Antoni | Cyclic spectral analysis of rolling-element bearing signals: Facts and fictions[END_REF]:

y(t) = +∞ ∑ i=-∞ h(t -iT -τ i )A i + n(t) (5)
where τ i ∼ (µ τ = 0, σ τ ) and A i ∼ (µ A = 0, σ A ) account for the uncertainties on the arrival time (jitters) and on the magnitude of the ith transient, respectively. Therefore a noisy signal y[n] (time duration is 1s, sampling frequency is 10 4 Hz) with length N = 10 4 is produced by Eq.5 as shown in Figure 1(c). The excitation with averaged interval (T = 0.03s) and response of the system are presented in Figure 1(a)∼(b), respectively. For the random part, σ τ = 0.01T and σ A = 0.1 are set as shown in Eq.5.

Figure 2: (a) Spectrum (b) P(state 2|data)

Figure 2 shows the spectrum with Nw = 2 6 length hanning-window and estimated probability of being in state 2 given the data, respectively. P(state 2|data) is w (i) 2 = p(z (i) = 2 | x (i) ; φ , µ, Σ) normalized by differences between final likelihood at convergence of 1 and 2-component model along frequency-axis. As we can see in Figure 2, the probability of being in state 2 reveals the spectrum distribution of informative signal which corresponds to the estimated spectrum of state 2 denoted in red dash line of Figure 3. The estimated spectrum is normalized between 0 and 1. There are two states which have a constant power spectrum conrresponding to noise component and a non-flat power spectrum corresponding to transient signal.

Conclusion

In this paper, an exploring study in rolling element bearing diagnostis based on HMM is investigated and a new fault separation scheme is proposed. Though in numerical experiments, the validity of the estimated parameters and probability of states is demonstrated. The indicator of state results in a state decision which decomposes the noisy measurement into two components based on different Gaussian distributions. Therefore the informative signal is discriminated from noise. It provides a proper classification result for diagnostic identification. What's more, it reveals the underlying information from a given data set without pre-selected parameter and has a potentiality in industrial applications.

Figure 1 :

 1 Figure 1: Synthesised vibration signal: (a) excitation, (b) response, (c) noisy signal with the NSR = 2.

Figure 3 :

 3 Figure 3: Estimated spectra in state 1 and 2

Figure 4 :

 4 Figure 4: (a) State indicator with statistical threshold in red dash line and (b) State decision

Figure 5 :

 5 Figure 5: Re-estimated spectra state 1 and 2

Figure 6 :

 6 Figure 6: Noisy measurement, reference and separated signal