Lisa Kaminski

Stéphanie Torrino

Maeva Dufies

Zied Djabari

Romain Haider

François-René Roustan

Emilie Jaune

Kathiane Laurent

Nicolas Nottet

Jean-François Michiels

Maeva Gesson

Stéphane Rocchi

Nathalie M Mazure

Matthieu Durand

Jean-François Tanti

Damien Ambrosetti

Stephan Clavel

Issam Ben-Sahra

PhD Frédéric Bost
email: bost@unice.fr

PGC-1α inhibits polyamine synthesis to suppress prostate cancer aggressiveness

Tumorigenesis is dependent on the reprogramming of cellular metabolism, however, the metabolic pathways engaged in the formation of metastasis remain largely unknown. The transcriptional co-activator peroxisome proliferator-activated receptor gamma coactivator 1alpha (PGC-1α) plays a pleiotropic role in the control of cancer cell metabolism and has been associated with a good prognosis in prostate cancer (PCa). Here, we show that PGC-1α represses the migrative and invasive properties of PCa cells through the modulation of the polyamine biosynthesis pathway. Mechanistically, PGC-1α inhibits the expression of c-MYC and ornithine decarboxylase 1 (ODC1), the rate limiting enzyme for polyamine synthesis.

Analysis of in vivo metastasis assays and clinical data from prostate cancer patients supports the proposition that the PGC-1α/c-MYC/ODC1 axis regulates polyamine biosynthesis and prostate cancer aggressiveness. In conclusion, the downregulation of PGC-1α makes PCa cells dependent on polyamine to promote metastasis.

Significance: A major regulator of mitochondrial metabolism controls polyamine synthesis and prostate cancer aggressiveness: potential applications in therapy and identifications of new biomarkers.

INTRODUCTION

Metabolic reprogramming is a hallmark of cancer cells and a consequence of adaptation to a hostile micro-environment with decreased oxygen concentration and nutrients (glucose and glutamine) [START_REF] Hanahan | Hallmarks of cancer: the next generation[END_REF]. These metabolic changes are required for rapid proliferation and invasion and are well characterized for cancer cells from primary tumors but poorly described for metastatic cancer cells. Recent advances in the understanding of cancer cell metabolism has allowed for the emergence of new therapeutic approaches that specifically target these adaptations. For example, in cancer cells that rely on oxidative phosphorylation, we have shown that interfering with the mitochondrial respiration could exhibit repression of tumor growth, cancer cell proliferation and the formation of metastasis [START_REF] Sahra | The antidiabetic drug metformin exerts an antitumoral effect in vitro and in vivo through a decrease of cyclin D1 level[END_REF][START_REF] Bost | Energy disruptors: rising stars in anticancer therapy?[END_REF][START_REF] Dirat | Inhibition of the GTPase Rac1 mediates the antimigratory effects of metformin in prostate cancer cells[END_REF].

One of the main regulators of cellular metabolism is the transcriptional co-activator PGC-1α (Peroxisome proliferator-activated receptor gamma coactivator 1-alpha). PGC-1α controls mitochondrial biogenesis, oxidative phosphorylation and fatty acid oxidation [START_REF] Villena | New insights into PGC-1 coactivators: redefining their role in the regulation of mitochondrial function and beyond[END_REF]. Recently, PGC-1α has been shown to facilitate mitochondrial biogenesis in invasive breast cancer cells and to increase their metastatic potential [START_REF] Lebleu | PGC-1alpha mediates mitochondrial biogenesis and oxidative phosphorylation in cancer cells to promote metastasis[END_REF]. In contrast, overexpression of PGC-1α decreased the formation of metastasis in melanoma and prostate, and was associated with poor prognosis and the formation of metastasis in melanoma and prostate cancer (PCa) [START_REF] Luo | A PGC1α-mediated transcriptional axis suppresses melanoma metastasis[END_REF][START_REF] Torrano | The metabolic co-regulator PGC1alpha suppresses prostate cancer metastasis[END_REF].

However, the metabolic and molecular modifications driving the aggressiveness of PCa cells remain poorly understood.

Oncogenes and tumor suppressors regulate metabolic adaptations of cancer cells. Several studies have demonstrated that the MYC gene copy number is upregulated by 30% in human PCa [START_REF] Jenkins | Detection of c-myc oncogene amplification and chromosomal anomalies in metastatic prostatic carcinoma by fluorescence in situ hybridization[END_REF][START_REF] Qian | Detection of chromosomal anomalies and c-myc gene amplification in the cribriform pattern of prostatic intraepithelial neoplasia and carcinoma by fluorescence in situ hybridization[END_REF]. Furthermore, transgenic mice overexpressing c-MYC in the prostate developed prostatic intraepithelial neoplasia followed by invasive adenocarcinoma, demonstrating that c-MYC drives tumorigenesis in the prostate [START_REF] Ellwood-Yen | Mycdriven murine prostate cancer shares molecular features with human prostate tumors[END_REF]. Expression of the proto-oncogene c-MYC increases glycolysis and glutaminolysis [START_REF] Le | Glucose-independent glutamine metabolism via TCA cycling for proliferation and survival in B cells[END_REF][START_REF] Shim | c-Myc transactivation of LDH-A: implications for tumor metabolism and growth[END_REF], by controlling the expression of genes involved in glucose and glutamine metabolism as well as other metabolic pathways, such as polyamine via the ornithine decarboxylase 1 (ODC1), the rate limiting enzyme of polyamine biosynthesis [START_REF] Bello-Fernandez | The ornithine decarboxylase gene is a transcriptional target of c-Myc[END_REF].

In this study, we demonstrate that PGC-1α is the regulator of a c-MYC-driven onco-metabolic pathway that promotes PCa aggressiveness through the polyamine pathway. The unravelling of this metabolic circuit represents a new therapeutic target in PCa that may help to curb the advanced form of the disease.

MATERIALS AND METHODS

Cell culture

PC3, DU145 and LNCaP cells were purchased from the American Type Culture Collection (ATCC). All cells used in this study were within 20 passages after thawing. PC3 and DU145 cells were cultured in Dulbecco's Modified Eagle's Medium (DMEM, Gibco). LNCaP cells were cultured in Roswell Park Memorial Institute (RPMI) 1640 medium (Gibco). Cell media were supplemented with 10% fetal bovine serum (Gibco) and 1% penicillin/streptomycin (respectively 100 U/mL and 100 µg/mL, Gibco) and incubated at 37°C and 5% CO2. DU145 and LNCaP cells were infected with lentiviral constructs at different MOI (multiplicity of infection; 2, 5 and 10) in the presence of 8 μg/mL hexadimethrine bromide (Sigma). These cells were infected with a pLKO.1 non-target control (NTC) short hairpin RNA (Sigma Mission, shRNA) or individually with five different pLKO.1 Mission shRNA targeting PGC-1α (Sigma) to generate cells lines with stable PGC-1α knockdown. After 24 h of infection, the stably shRNA-expressing cells were selected with 1 μg/mL puromycin (Sigma) for 7 days and maintained in the culture medium with 0.5 μg/mL puromycin. Efficiency of PGC-1α knockdown was determined by qRT-PCR and immunoblots and stably shRNA-expressing cell lines with the best knockdown of PGC-1α, were selected for all the experiments. Lipofectamine RNAiMAX was used for transfection of siRNAs according to the manufacturer's instructions (Invitrogen). Transfections of human prostate cell lines were performed using siRNA pools consisting of four siRNA oligos specifically targeting four different sites of the target mRNAs (On Target Plus; Dharmacon). The purpose of the siRNA pools is to use less of each oligo to minimize any off-target effects. The siRNA sequences are: SMARTpool: ON-TARGETplus PPARGC1A siRNA: L-005111, SMARTpool: ON-TARGETplus MYC siRNA: L-003282, SMARTpool: ON-TARGETplus ESRRA siRNA: L-003403, siGENOME Non-Targeting siRNA Pool #1: D-001206-13. Briefly, cells were seeded at 70%-80% confluence in six-well plates overnight before transfection, and then transfected with 15 nM siRNA sequences or with a nonspecific siRNA using Lipofectamine RNAiMAX. siRNA and Lipofectamine RNAiMAX reagent were diluted in Opti-MEM (Gibco), and the contents were mixed gently. The mixtures were incubated for 10-20 min at room temperature. The incubated mixtures of siRNA and RNAiMAX were added to cells and incubated for 48-72 h.

Lipofectamine 2000 reagent was used for transfections of plasmids according to the manufacturer's instructions (Invitrogen). All the plasmids were purchased from Addgene: pAdTrack Flag-HA-PGC-1 alpha and an empty vector as control pAdTrack-CMV. For plasmid transfection, cells were seeded to be 70-90% confluent at the time of transfection. Plasmids and Lipofectamine 2000 reagent were diluted in Opti-MEM (Gibco). The diluted plasmids were mixed with Lipofectamine 2000 and incubated for 5 min at room temperature. For transient transfection, the transfected cells were collected after 24-48 h for experiments. For the stable PC3 cell line generation overexpressing PGC-1α, cells were selected, after transfection, with 500 µg/mL G418 for 30 days and maintained in the culture medium with 100 µg/mL G418.

Efficiency of PGC-1α overexpression was determined by qRT-PCR and immunoblots.

Steady state metabolomics

To determine the relative levels of intracellular metabolites, extracts were prepared and analyzed by LC/MS/MS. Quadruplicate 10-cm plates (~80% confluent) were incubated in serum-free medium for 15 h. Metabolites were extracted on dry ice with 4 mL 80% methanol (-80°C), as described previously [START_REF] Ben-Sahra | Stimulation of de novo pyrimidine synthesis by growth signaling through mTOR and S6K1[END_REF]. Insoluble material was pelleted by centrifugation at 3000 g for 5 min, followed by two subsequent extractions of the insoluble pellet with 0.5 mL 80% methanol, with centrifugation at 16000 g for 5 min at 4°C. The 5 mL metabolite extract from the pooled supernatants was dried down under nitrogen gas using an N-EVAP (Organomation Associates, Inc). Dried pellets were resuspended using 20 μL HPLC grade water for mass spectrometry. A 7 μL sample was injected and analyzed using a 5500 QTRAP triple quadrupole mass spectrometer (AB/SCIEX) coupled to a Prominence UFLC HPLC system (Shimadzu) via selected reaction monitoring (SRM) of a total of 300 endogenous water soluble metabolites for steady-state analyses of samples [START_REF] Yuan | A positive/negative ion-switching, targeted mass spectrometry-based metabolomics platform for bodily fluids, cells, and fresh and fixed tissue[END_REF]. The normalized areas were used as variables for the univariate statistical data analysis. All univariate analyses and modeling on the normalized data were carried out using Metaboanalyst 4.0 (http://www.metaboanalyst.ca). Univariate statistical differences of the metabolites between two groups were analyzed using two-tailed Student's t-test.

Stable Isotopic tracing analysis

To define the relative abundance of polyamine metabolites by LC-MS/MS analysis, a previously described extraction method optimized for polar metabolite was employed [START_REF] Ben-Sahra | Stimulation of de novo pyrimidine synthesis by growth signaling through mTOR and S6K1[END_REF][START_REF] Yuan | A positive/negative ion-switching, targeted mass spectrometry-based metabolomics platform for bodily fluids, cells, and fresh and fixed tissue[END_REF]. Briefly, cells cultured in 10 cm plates to ~90% confluence, were washed with DMEM without arginine prior to addition of labeled [ 13 C6]-arginine (480 µM) for 1 h. Metabolites were extracted on dry ice with 4 ml of 80% Methanol (LC-MS grade). Cells were scraped and placed at -80°C for 20 min before successive centrifugations at 17000g for 5 min. Supernatants were collected and dried under nitrogen gas then resuspended in 50% acetonitrile and 25 µl were injected in a Thermo Q-Exactive (LC-MS) in line with an electrospray source and an Ultimate3000 (Thermo) series HPLC consisting of a binary pump, degasser, and auto-sampler outfitted with a Xbridge Amide column (Waters; dimensions of 4.6 mm × 100 mm and a 3.5 µm particle size). The mobile phase A contained 95% (vol/vol) water, 5% (vol/vol) acetonitrile, 20 mM ammonium hydroxide, 20 mM ammonium acetate, pH 9.0; B was 100% Acetonitrile.

The gradient was as follows: 0 min, 15% A; 2.5 min, 30% A; 7 min, 43% A; 16 min, 62% A; 16-18 min, 75% A; 18-25 min, 15% A with a flow rate of 400 μl/min. The capillary of the ESI source was set to 275°C, with sheath gas at 45 arbitrary units, auxiliary gas at 5 arbitrary units and the spray voltage at 4.0 kV. In positive/negative polarity switching mode, an m/z scan range from 70 to 850 was chosen and MS1 data was collected at a resolution of 70,000. The automatic gain control (AGC) target was set at 1 × 10 6 and the maximum injection time was 200 ms. The top 5 precursor ions were subsequently fragmented, in a data-dependent manner, using the higher energy collisional dissociation (HCD) cell set to 30% normalized collision energy in MS2 at a resolution power of 17,500. The sample volumes of 25 μl were injected. Data acquisition and analysis were carried out by Xcalibur 4.0 software and Tracefinder 2.1 software, respectively (both from Thermo Fisher Scientific).

Immunoblot assays

Cell lines were lysed in RIPA buffer (Tris 50 mM, NaCl 150 mM, SDS 0.1%, Na Deoxycholate 0.5%, NaF 5 mM, NaPY 2.5 mM, NP40 1%, EDTA 10 mM) containing a protease-inhibitor cocktail (Mini-complete, EDTA-free, Roche). Samples were heat denatured with 1X Laemmli buffer. Twenty to fifty micrograms of protein were loaded per well for the 10% sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). After electrophoresis, proteins were transferred to polyvinylidene difluoride (PVDF) membranes (Millipore). Membranes were blocked for 1 h in 2% BSA in Tris-buffered saline and 0.1% Tween20 and were probed overnight at 4 °C with primary antibodies. After washing, blots were probed for 1 h at room temperature with secondary anti-mouse or anti-rabbit immunoglobulin G (IgG) antibodies conjugated to horseradish peroxidase. Immunoreactive bands were visualized by exposing membranes to luminescent signals generated after incubating the membrane with ECL (Millipore) using Syngene PXi. ImageJ software was used to quantify band intensity and the ratios of proteins of interest were normalized to a loading control.

Reagents and antibodies

α-difluoromethylornithine (DFMO) was purchased from Toronto Research. Putrescine, spermine were bought from Sigma. SAM486A was purchased from Medkoo Bioscience Inc.

The c-Myc inhibitor 10058-F4, antibodies for PGC-1α (sc-13067, 1:1000), c-Myc (sc-40, 1:1000), HSP90 (sc-13119, 1:10000) and ERK2 (sc-1647, 1:10000) were purchased from Santa Cruz. ERRα (C15410230, 1:1000) was purchased from Diagenode. ODC1 (O1136, 1:100) and anti-α-Tubulin (T6199, 1:10000) were purchased from Sigma. HRP-conjugated AffiniPure donkey anti-mouse IgG (H+L) (715-035-150, 1:5000) and HRP-conjugated AffiniPure donkey anti-mouse IgG (H+L) (711-035-152, 1:5000) were purchased from Jackson ImmunoResearch Laboratories.

RNA isolation and RT-PCR

Total RNA from cells was extracted using TRIzol reagent according to the manufacturer's instructions (Invitrogen). The quantity and the quality of the isolated RNA were determined using a NanoDrop™ One Spectrophotometer (Thermo Scientific). One microgram of total RNA was reverse transcribed into first strand cDNA using the reverse transcription system (Promega). Real-time quantitative PCR was performed using Fast SYBR Green master mix (Applied Biosystems) on a StepOnePlus System (Applied Biosystems). The gene-specific primer sets were used at a final concentration of 1 μM in a 10 μL final volume. RPLP0 mRNA level was used as an endogenous control to normalize relative expression values of each target gene.

The relative expression was calculated by the comparative Ct method. All real-time RT-PCR assays were performed in triplicate with three independent experiments. For RNA isolation and RT-PCR from paraffin-embedded prostate tumor tissues, total RNA was extracted with PureLink™ FFPE RNA Isolation Kit according to the manufacturer's instructions (Invitrogen).

For each RNA purification, 6 pieces of 10 μm thick sections of paraffin-embedded prostate tissues, with a tissue surface area of 0.5-1 cm 2 , were used. For each patient a sample of both normal prostate and tumor tissue were collected. Briefly, the main steps were: first, deparaffinization in melting buffer at 72°C for 10 min. Then, the tissue was separated from the melted paraffin by centrifugation and digested at 60°C with Proteinase K for 3h. The tissue lysate was further processed by selective binding of RNA to a silica-based membrane in the spin cartridge. Impurities were removed by thorough washing with wash buffer. Total RNA was eluted in RNase-Free Water and the quality and quantity of the purified RNA were determined with a NanoDrop One Spectrophotometer (Thermo Scientific). One microgram of total RNA was reverse transcribed into first strand cDNA using Maxima First Strand cDNA Synthesis Kit (K1671) according to the manufacturer's instructions (Thermo Scientific). Realtime quantitative PCR was performed with TaqMan Fast Universal Master Mix (Applied Biosystems) using the ABI PRISM 7500/Step-One Fast Real Time PCR System following the manufacturer's protocols (Applied Biosystems). TaqMan gene expression assays purchased from Applied Biosystems: PPARGC1 (Hs01016719_m1), MYC (Hs00153408_m1), ODC1 (Hs00159739_m1) and AMACR (Hs00204885_m1). Gene expression values were normalized to the value of the housekeeping gene 18S (Hs99999901_s1) and calculated on the basis of the comparative cycle threshold Ct method (ΔΔCt).

Chromatin Immunoprecipitation

The Chromatin Immunoprecipitation kit was purchased from EMD Millipore, and the assay was performed according to the manufacturer's protocol. Briefly, cells were cross-linked with formaldehyde for 10 min at 37°C and washed in ice-cold PBS, unreacted formaldehyde was quenched with glycine, and then the cells were washed with PBS and resuspended in SDS buffer. Samples were sonicated, diluted in dilution buffer with inhibitors, and precleared with agarose G beads. The supernatant was used directly for immunoprecipitation with anti-ERRα or goat IgG (for a negative control). The immunocomplexes were mixed with DNA-coated agarose G beads and incubated overnight. Pellets were washed in a low-salt wash buffer, highsalt wash buffer, LiCl wash buffer and Tris-EDTA buffer. This was followed by elution of the protein/DNA complex and reversal of cross-linking with 5 M NaCl overnight. The protein was then digested with proteinase K, followed by DNA purification with elution buffer.

Quantification of chromatin immunoprecipitation enrichment by quantitative real-time PCR

(Q-PCR) were carried out using the Step One PCR (Applied Biosystem).

Migration and invasion assays in Boyden chambers.

Migration and invasion assays were performed using cell culture inserts with 8.0 μm pore transparent PET membrane coated with 10 μg/mL fibronectin. For invasion experiments, the inserts were coated with 25 μg/μL of Matrigel and incubated for 3h at 37°C in a CO2 incubator, while for the migration assay, transwells were left uncoated. Briefly, overnight serum-starved cells (12×10 4 cells) were seeded into the top chamber in medium without FBS, while medium with 10% FBS was present in the bottom chamber. The cells were incubated for 3-6 h or 17 h for migration and invasion, respectively. The media and remaining cells were removed from the top chamber with a cotton swab and washed 2 times with PBS. The bottom chamber was aspirated and washed 2 times with PBS. The inserts were fixed with 4% PFA and incubated with a DAPI solution (2 mg/mL) to label cell nuclei. Cell migration and invasion were determined by counting all cells on the total areas at the lower surface of the membrane with a Nikon A1/ A1R Confocal Laser Microscope System. Nuclei were counted and analyzed using Image J software and normalized to area.

Animal experiments

To conduct pulmonary extravasation assays, 1x10 6 DU145, LNCaP or PC3 cells were labeled for 1h with 15 µM CellTracker Green and injected via the tail vein of 6 week-old nude mice.

After 24h, mice were sacrificed, and the lungs were harvested, fixed with 4% PFA, stained with DAPI and analyzed with a Nikon A1 / A1R Confocal Laser Microscope System. Two mice per group were sacrificed after 30 min to confirm that an equal number of cells reached the lung.

Quantification of the lung micrometastasis were performed as follows with Image J. First, the user sets a large threshold based on the DAPI labeling, and the macro measures the tissue area. This value is used at the end of the analysis to normalize cell numbers relative to the imaged tissue area. Secondly, the number of positive cells is counted using the Find Maxima function. This function searches for the local maximum of intensity in a defined area. We adapted this area size depending on the noise in the image, which was different depending on the phenotype.

Bioinformatic analysis

The Cancer Genome Atlas (TCGA) data for Prostate Adenovarcinoma (PRAD) were downloaded from the TCGA data portal (https://portal.gdc.cancer.gov). RNA-seq data were normalized using the Bioconductor package DESeq2. Expression levels of the following genes were evaluated in these patient datasets: PPARGC1A (PGC1α), MYC (c-MYC), AMACR and ODC1. We compared the expression levels of each individual gene in primary tumors and in a reference population (patients without prostate tumors or metastasis). For TCGA data, we compared the PPARGC1A gene expression levels in tumor samples, distinguished by the Gleason grade. P-values were calculated by the Wilcoxon rank sum test.

RESULTS

PGC-1α inhibits aggressiveness and polyamine synthesis in PCa cells.

To understand the metabolic modifications associated with PGC-1α in PCa, we modulated the expression of PGC-1α in human PCa cell lines. Given the tumor suppressor activity of PGC-1α (8), we performed migration and invasion assays in two poorly aggressive PCa cell lines, DU145 and LNCaP, which stably express PGC-1α shRNA (Supplementary Fig. S1A). The same assays were performed in PC3, the most aggressive PCa cells, overexpressing PGC-1α (Supplementary Fig. S1B). The loss of PGC-1α significantly increased the migration and the invasion of the LNCaP and DU145 shPGC-1α cell lines (Fig. 1 A,B) while the overexpression of PGC-1α inhibited the aggressive phenotype of PC3 cells (Supplementary Fig. S1C).

To exclude any off-target effects of the shRNA, we transfected LNCaP and DU145 cells with a pool of siRNA targeting PGC-1α (Supplementary Fig. S1D). As with the shPGC-1α cells, the siRNA knockdown of PGC-1α increased the migration of the cells (Supplementary Fig. S1E). To further validate the role of PGC-1α, we restored its expression in LNCaP and DU145 shPGC-1α cells using a cDNA encoding for a HA-tagged mouse PGC-1α (HA-mPGC-1α) (Supplementary Fig. S1F). The over-expression of PGC-1α hampered the migration and the invasion of the shPGC-1α cell lines, but it also significantly decreased the aggressive phenotype of the shCT cells (Fig. 1C,D). Thus, our results demonstrate that PGC-1α inhibits PCa cells aggressiveness.

To characterize the metabolic changes associated with this phenotype, we performed an unbiased metabolomic profiling of cells knockdown for PGC-1α. Of the 262 small metabolites identified by liquid-chromatography (LC) tandem mass spectrometry (MS/MS), the steady state levels of 32 metabolites were significantly altered in the PGC-1α knock-down cells relative to cells transfected with control shRNA (p<0.02). Eventually, we found 12 metabolites that were significantly upregulated upon PGC-1α silencing, among them, spermine and putrescine, two metabolites that are representative of the polyamine pathway (Fig. 1E,F,G), were among the most up-regulated with a VIP (Variable Importance in Projection) score above 1.85 (Supplementary Fig. S1G). Consistently, the increase of putrescine and spermine was confirmed in another shPGC-1α stable cell line transfected with a shRNA targeting a different region of PGC-1α (Supplementary Figure S1H). In order to confirm the regulation of the polyamine pathway upon PGC-1α loss, we employed a stable isotope-tracing LC-MS/MS experiment with [ 13 C6]-arginine a precursor for polyamine synthesis in cells depleted or not for PGC-1-α. As expected, the downregulation of PGC-1α, although not significant, increased the abundance of 13 C putrescine and 13 C spermidine (Fig. 1H). We also treated the cells with α-difluoromethylornithine (DFMO), a specific and well-characterized inhibitor of the ornithine decarboxylase 1 (ODC1) the rate limiting enzyme of polyamine synthesis (Fig. 1I) [START_REF] Bey | Analogues of ornithine as inhibitors of ornithine decarboxylase. New deductions concerning the topography of the enzyme's active site[END_REF]. As expected, DFMO abolished M+4 labeling of putrescine and spermidine induced by the downregulation of PGC-1α. Addition of exogenous putrescine restored partially the flux of polyamine synthesis as illustrated by the increase of spermidine (Fig. 1H).

These results demonstrate that the increase in polyamine synthesis is one of the major metabolic alteration induced by the downregulation of PGC-1α.

PGC-1α inhibits ODC1 expression via the downregulation of c-MYC.

The rate-limiting enzyme of polyamine synthesis is the ornithine decarboxylase 1 (ODC1). We found, in accordance with the upregulation of polyamine synthesis, that the expression of ODC1 mRNA and protein was significantly increased in shPGC-1α cells (Fig. 2A; Supplementary Fig. S2A). To validate that PGC-1α inhibits the expression of ODC1, we over-expressed PGC-1α in shPGC-1α cells and found that it hampered the expression of ODC1 (Fig. 2A).

ODC1 is one of the first metabolic genes shown to be transcriptionally regulated by the protooncogene c-MYC [START_REF] Dang | c-Myc target genes involved in cell growth, apoptosis, and metabolism[END_REF], and c-MYC increases polyamine synthesis [START_REF] Hogarty | ODC1 is a critical determinant of MYCN oncogenesis and a therapeutic target in neuroblastoma[END_REF]. Thus, we monitored the expression of c-MYC in shPGC-1α cells. We showed that c-MYC mRNA and protein are significantly increased in shPGC-1α cells (Fig. 2B; Supplementary Fig. S2B) suggesting, that like ODC1, PGC-1α represses c-MYC expression. In accordance with this result we found a decrease in the expression of c-MYC mRNA and protein in PC3 cells overexpressing PGC-1α (Supplementary Fig. S2C). To validate that c-MYC upregulates ODC1 expression, we silenced c-MYC with siRNA in shPGC-1α cells and found that the downregulation of c-MYC abrogates the expression of ODC1 (Fig. 2C).

We subsequently studied how PGC-1α regulates c-MYC expression. We took advantage of transcriptomic analyses showing that PGC-1α regulates the Estrogen-Related Receptor Alpha (ERRα) transcriptional program in PCa cells [START_REF] Torrano | The metabolic co-regulator PGC1alpha suppresses prostate cancer metastasis[END_REF]. To determine if ERRα is involved in the regulation of c-MYC expression by PGC-1α, we undertook a silencing approach with a pool of ERRα-targeting siRNA. The silencing of ERRα had no effect on c-MYC expression in shCT cells but it inhibited the expression of c-MYC induced by the knock-down of PGC-1α in LNCaP and DU145 (Fig. 2D). To confirm the involvement of ERRα in the regulation of c-MYC, we performed a chromatin immunoprecipitation (CHIP) with ERRα antibodies and a quantitative PCR with the putative binding site of ERRα in the promoter region of c-MYC and TAPBPL as a control [START_REF] Deblois | Genome-wide identification of direct target genes implicates estrogen-related receptor alpha as a determinant of breast cancer heterogeneity[END_REF]. As expected, ERRα occupied the promoter region of TAPBPL, but the downregulation of PGC-1α did not increase its recruitment (Fig. 2E). On contrary, the downregulation of PGC-1α significantly increased the recruitment of ERRα on the promoter region of c-Myc. In addition, analysis of the publicly available CHIP-seq data revealed that ERRα is one the regulatory transcription factor of c-MYC in several databases (Supplementary Fig. S2D). Altogether, our data provide a molecular mechanism by which PGC-1α represses a c-MYC/ODC1 axis and demonstrate that PGC-1α inhibits c-MYC expression through an ERRαdependent mechanism.

The PGC-1α/c-MYC/ODC1 axis controls the aggressive phenotype of PCa cells via polyamine synthesis.

To determine the contributing role of c-MYC in the aggressive phenotype of the shPGC-1α cells, we inhibited c-MYC with siRNA or the 10058-F4 compound (a specific chemical inhibitor of c-MYC) and performed migration and invasion assays. Under both conditions, the inhibition of c-MYC abolished the pro-migrative and pro-invasive effects of the shPGC-1α PCa cells (Fig. 3A,B,C,D; Supplementary Fig. S3A). This result clearly demonstrates that c-MYC mediates the effects of PGC-1α on PCa cell aggressiveness.

To establish if polyamine synthesis is the metabolic pathway implicated in the aggressive phenotype of shPGC-1α cells, we treated cells with DFMO. DFMO did not inhibit the migration and the invasion of the control cells but it hampered the aggressive phenotype of the shPGC-1α cells (Fig. 3E,F). The contribution of polyamine synthesis to the aggressiveness of shPGC-1α cells was validated by the addition of exogenous putrescine for 24h in the culture media after the DFMO treatment. Indeed, putrescine partially restored the aggressiveness of the shPGC-1α cell lines (Fig. 3E,F). To further confirm the role of ODC1, we used a pool of siRNA.

The decrease of ODC1 inhibited cell migration and invasion induced by the loss of PGC-1α in

LNCaP and DU145 cells. While the addition of putrescine alone had no effect on control cells (siCT in Supplementary Fig. S3C,D), it decreased the invasive properties of shPGC1-α cells (shPGC-1α cells in Supplementary Fig. S3D) but, it rescued partially the aggressiveness (migration and invasion) of ODC1 depleted cells (Supplementary Fig. S3 C,D).

Recently, AMD1 (S-adenosylmethionine decarboxylase 1) that regulates the synthesis of decarboxy S-adenosyl-L-methionine (dcSAM) required for spermine synthesis has been shown to control polyamine synthesis in prostate cancer [START_REF] Zabala-Letona | mTORC1-dependent AMD1 regulation sustains polyamine metabolism in prostate cancer[END_REF]. We thus asked whether this enzyme plays a role in the up-regulation of polyamine synthesis in PGC-1α depleted cells. We treated the cells with an inhibitor of AMD1, SAM486A, validated in preclinical and clinical experiments [START_REF] Eskens | Phase I and pharmacological study of weekly administration of the polyamine synthesis inhibitor SAM 486A (CGP 48 664) in patients with solid tumors. European Organization for Research and Treatment of Cancer Early Clinical Studies Group[END_REF][START_REF] Regenass | CGP 48664, a new Sadenosylmethionine decarboxylase inhibitor with broad spectrum antiproliferative and antitumor activity[END_REF]. SAM486A did not significantly affect the migration and the invasion of the ShCT cells but led to a significant decrease in the aggressiveness of shPGC-1α cells (Fig. 3G,H). All together, these results support the conclusion that the downregulation of PGC-1α reprograms cancer cell metabolism toward polyamine synthesis to promote an aggressive phenotype through an ODC1 and AMD1 dependent pathway.

PGC-1α suppresses the formation of micrometastasis through the downregulation of polyamine synthesis.

To establish the role of PGC-1α in aggressiveness in vivo, we performed an extravasation experiment in mice. DU145 and LNCaP shPGC-1α cells and their respective shCT control cells, treated or not treated with DFMO, were injected into the caudal vein of 6-week-old male athymic nude mice. After twenty-four hours, to allow for the formation of micrometastasis, we analyzed the ability of cells to extravasate through the pulmonary parenchyma and quantified the micrometastasis formation. The downregulation of PGC-1α significantly increased the invasive potential of DU145 and LNCaP cells (Fig. 4A,B; Supplementary Fig. S4A).

The treatment with DFMO did not affect the aggressiveness of the shCT cells, but it significantly hampered the invasive properties of the shPGC-1α cells demonstrating that inhibition of polyamine synthesis reduces micrometastasis in cells with elevated polyamine anabolism. To validate the anti-invasive activity of PGC-1α , we tested the aggressiveness of PC3 cells overexpressing PGC-1α. The expression of PGC-1α strongly inhibited extravasation and the treatment with exogenous putrescine restored the ability to form micrometastases (Fig. 4C). We showed previously that the addition of putrescine on control cells did not affect the migration and invasion (Supplementary Fig. S3C,D). In order to determine if putrescine affects the formation of micrometastasis, we treated DU145 shCT with putrescine prior to their injection into mice. Putrescine led to a slight but significant decrease of micrometastasis (Supplementary Fig. S4B).

Taken together, our data show that putrescine alone does not increase metastasis but PGC-1α suppresses the formation of micrometastasis and polyamines are required for this process.

The downregulation of PGC-1α is associated with increased c-MYC and ODC1 in human tumor biopsies

To determine if the PGC-1α/c-MYC/ODC1 axis has a clinical relevance, we analyzed mRNA expression of these genes in normal and tumor matched tissues from 73 patients with advanced PCa (Table 1). We extracted mRNA from paraffin embedded tissues and performed a RT-qPCR analysis on paired tumor and normal adjacent tissue. The expression of AMACR (a well characterized biomarker of PCa), PGC-1α, c-MYC and ODC1 are presented in Fig. 5A. As expected, the expression of AMACR was significantly higher in tumors compared to the healthy gland. Importantly, we found that the expression of PGC-1α mRNA was significantly lower in tumors compared to the adjacent normal tissue and in the same tumor tissue, the expression of c-MYC and ODC1 was increased.

Based on the TCGA-PRAD database (healthy tissue: n= 52 and primary tumors: n= 498), we constructed a heatmap to visualize the co-expression pattern of the PGC-1α/c-MYC/ODC1 axis genes in normal and tumoral tissues with increasing Gleason grades. PGC-1α expression is high in normal tissues and gradually decreases with elevated Gleason scores. In contrast, the expression of ODC1 and c-MYC is low in normal tissue and increased with Gleason grade (Fig. 5B). To confirm this observation, we performed a correlative analysis using the same database.

We observed a weak but significant correlation between PGC-1α and ODC1 expression as well as PGC-1α and c-MYC in PCa tumors and normal tissue with r=0.30 (p=2.9x10 -13 ) and r= 0.24 (p= 6.48x10 -9 ), respectively (Fig. 5C).

We then analyzed the Taylor et al. dataset that includes healthy tissues (n=29), primary tumors (n=131) and metastasis (n=19) [START_REF] Taylor | Integrative genomic profiling of human prostate cancer[END_REF]. ODC1 and C-MYC are significantly increased in metastasis and the primary tumor compared to the healthy tissue and PGC-1α is dowregulated in the tumor and the metastasis (supplementary Figure S5A).

Finally, in accordance with our results and other studies, high expression of ODC1 (p=0.0146) (Figure 5D) and low expression or PGC-1α (8) are significantly correlated with progressionfree survival.

Taken together, our data demonstrate that the low expression of PGC-1α is associated with high expression of c-MYC and ODC1 in PCa patients. It provides evidence that the PGC-1α/c-MYC/ODC1 axis defines a gene signature that may have a prognostic value for aggressive PCa and may also be the target of future therapies.

DISCUSSION

We demonstrate here that the transcriptional co-activator, PGC-1α, is one of the regulator of an onco-metabolic program regulating prostate cancer cell aggressiveness. The downregulation of PGC-1α makes PCa cells dependent on the polyamine pathway to promote metastasis. Indeed, the decrease of PGC-1α induces the upregulation of c-MYC and ODC1, the rate-limiting enzyme of polyamine synthesis. Both the bioinformatic analysis of a PCa dataset and our results on human biopsies demonstrate that low expression of PGC-1α correlates with higher levels of c-MYC and ODC1 in tumors. In addition, we demonstrate, based on the analysis of public databases, that high expression of ODC1 is associated with a lower PFS. Thus, our results highlight the importance of the PGC-1α/c-MYC/ODC1 axis as a potential prognostic marker of PCa aggressiveness.

Recent studies have demonstrated that the downregulation of PGC-1α promotes cancer cell aggressiveness and metastasis in PCa, melanoma and hepatocarcinoma [START_REF] Torrano | The metabolic co-regulator PGC1alpha suppresses prostate cancer metastasis[END_REF][START_REF] Luo | PGC-1 Coactivators: Shepherding the Mitochondrial Biogenesis of Tumors[END_REF][START_REF] Liu | Peroxisome proliferator-activated receptor gamma coactivator-1 alpha acts as a tumor suppressor in hepatocellular carcinoma[END_REF]. However, the role of PGC-1α is different in breast cancer, where the expression of PGC-1α promotes breast cancer metastasis [START_REF] Andrzejewski | PGC-1alpha Promotes Breast Cancer Metastasis and Confers Bioenergetic Flexibility against Metabolic Drugs[END_REF] and circulating (metastatic) breast cancer cells express high levels of PGC-1α [START_REF] Lebleu | PGC-1alpha mediates mitochondrial biogenesis and oxidative phosphorylation in cancer cells to promote metastasis[END_REF]. The elevated expression of PGC-1α correlates with increased mitochondrial respiration and glucose consumption as well as greater fuel flexibility in breast cancer cells. This opposite role of PGC-1α in different cancer is puzzling. PGC-1α interacts with a wide variety of transcription factors and it is regulated by several signaling pathways [START_REF] Deblois | The PGC-1/ERR signaling axis in cancer[END_REF], thus, depending on the organs the target genes may differ. Hormones may also interfere with PGC-1α normal function especially in prostate and breast. Indeed, PGC-1α interacts with the androgen receptor [START_REF] Shiota | Peroxisome proliferator-activated receptor gamma coactivator-1alpha interacts with the androgen receptor (AR) and promotes prostate cancer cell growth by activating the AR[END_REF] and the estrogen receptor [START_REF] Tcherepanova | Modulation of estrogen receptor-alpha transcriptional activity by the coactivator PGC-1[END_REF]. Finally, because of the different metabolic status of tumors (glycolytic vs oxidative phosphorylation), modifications of PGC-1α expression may induce different biological responses.

Even though PGC-1α plays a central role in mitochondrial biogenesis, we did not observe significant differences in the energetic status of the cell lines with modified expression of PGC-1α. The ATP concentration as well as the mitochondrial mass were not altered. This not surprising since PGC-1β (another member of the PGC-1 family) has overlapping and cooperative actions in vivo, and may therefore compensate the dowregulation of PGC-1α [START_REF] Zechner | Total skeletal muscle PGC-1 deficiency uncouples mitochondrial derangements from fiber type determination and insulin sensitivity[END_REF][START_REF] Lai | Transcriptional coactivators PGC-1alpha and PGC-lbeta control overlapping programs required for perinatal maturation of the heart[END_REF].

The importance of polyamines in PCa proliferation is well established [START_REF] Bettuzzi | Tumor progression is accompanied by significant changes in the levels of expression of polyamine metabolism regulatory genes and clusterin (sulfated glycoprotein 2) in human prostate cancer specimens[END_REF][START_REF] Gupta | Chemoprevention of prostate carcinogenesis by alpha-difluoromethylornithine in TRAMP mice[END_REF]. It was recently demonstrated that this pathway drives PCa aggressiveness through the activation of the prooncogenic complex mTORC1. mTORC1 controls the stability of S-adenosylmethionine decarboxylase 1 (AMD1), the enzyme that regulates the production of decarboxylated Sadenosylmethionine (dcSAM), a substrate for polyamine synthesis [START_REF] Zabala-Letona | mTORC1-dependent AMD1 regulation sustains polyamine metabolism in prostate cancer[END_REF]. In our study, the inhibition of AMD1 reversed the aggressiveness of shPGC-1α cells, reinforcing the role of polyamine metabolism in the formation of metastasis induced by PGC-1α loss. Thus, we have characterized a new regulatory pathway orchestrated by PGC-1α, which drives PCa cancer aggressiveness through polyamine synthesis. Our data demonstrate that addition of exogenous putrescine alone does not increase aggressiveness of PCa cells, suggesting that the phenotype observed is solely linked to the loss of PGC-1α. Indeed, we demonstrate that the downregulation of PGC-1α triggers a metabolic switch that makes PCa cells depend on polyamine synthesis to promote aggressiveness. This conclusion is strengthened by the fact that putrescine rescues the inhibitory effects of DFMO.Targeting polyamine synthesis may be interesting for cancer therapy in PCa with low PGC-1α levels. Many studies have shown that DFMO (the inhibitor of ODC1) inhibits the proliferation and the aggressiveness of gastric, prostate, nonmelanoma skin cancer and neuroblastoma cell lines. DFMO is also an inhibitor of tumor growth in animal models, where it reduced pancreatic intraepithelial neoplasm by 40% [START_REF] Mohammed | Eflornithine (DFMO) prevents progression of pancreatic cancer by modulating ornithine decarboxylase signaling[END_REF]. Similarly, addition of DFMO in drinking water decreased significantly tumor growth in TRAMP mice, a transgenic model of PCa [START_REF] Gupta | Chemoprevention of prostate carcinogenesis by alpha-difluoromethylornithine in TRAMP mice[END_REF]. Preclinical evidence strongly supports the use of DFMO in cancer therapy and many clinical trials have already been performed, while others are ongoing for the treatment of different cancers such as gliomas, prostate and gastric cancer [START_REF] Alexiou | Difluoromethylornithine in cancer: new advances[END_REF]. So far, the results of these clinical trials have shown moderate effects [START_REF] Horn | Phase I-II clinical trial with alpha-difluoromethylornithine-an inhibitor of polyamine biosynthesis[END_REF][START_REF] Levin | Phase III randomized study of postradiotherapy chemotherapy with combination alpha-difluoromethylornithine-PCV versus PCV for anaplastic gliomas[END_REF][START_REF] Lynch | An international randomised trial of celecoxib versus celecoxib plus difluoromethylornithine in patients with familial adenomatous polyposis[END_REF]. Even though DFMO very efficiently inhibits polyamine synthesis in patients [START_REF] Simoneau | The effect of difluoromethylornithine on decreasing prostate size and polyamines in men: results of a year-long phase IIb randomized placebo-controlled chemoprevention trial[END_REF], dietary sources of polyamines compensate for the inhibitory effects of DFMO on endogenous polyamine synthesis. Thus, strategies combining a low polyamine diet and DFMO may be potentially interesting. A recent study that combines DFMO and the inhibitor of the solute carrier family 3 member 2 (AMXT 1501), a transporter of polyamines, demonstrated the efficiency of this strategy in neuroblastoma [START_REF] Gamble | Inhibition of polyamine synthesis and uptake reduces tumor progression and prolongs survival in mouse models of neuroblastoma[END_REF].

We found that PGC-1α knockdown led to the increase of c-MYC expression in PCa cells and, conversely, that the over-expression of PGC-1α decreases c-MYC protein levels. The c-MYC/PGC-1α balance has been shown to control not only the metabolic phenotype of pancreatic cancer stem cells (CSC), but also their sensitivity to metabolic drugs targeting the mitochondria, such as metformin. Low expression of c-MYC allows high expression of PGC-1α resulting in higher bioenergetic capacities in CSC [START_REF] Sancho | MYC/PGC-1alpha Balance Determines the Metabolic Phenotype and Plasticity of Pancreatic Cancer Stem Cells[END_REF]. Here, we found that low expression of PGC-1α allows for high expression of c-MYC in PCa cells, thus triggering the increase of polyamine synthesis and making PCa more aggressive. The link between c-MYC and polyamine synthesis is not new since ODC1 expression is known to be regulated by c-MYC, and glutaminolysis has been shown to be directly linked to polyamine synthesis in a c-MYCdependent manner during T lymphocyte activation [START_REF] Wang | The transcription factor Myc controls metabolic reprogramming upon T lymphocyte activation[END_REF]. Our findings demonstrate that PGC-1α regulates a pathway integrating c-MYC and ODC1. Mechanistically, we also show that PGC-1α and ERRα act together to regulate c-MYC expression. When PGC-1α is downregulated, ERRα is required for the increase of c-MYC. These results are in agreement with recent studies demonstrating that ERRα is involved in PCa progression and the formation of bone metastasis (44 , 45).

In summary, our study reinforces the central role of the polyamine pathway in PCa progression, but it also reveals a link between PGC-1α and an onco-metabolic pathway. Our findings not only describe new signatures of cancer progression but also provide tools to identify new therapeutic options.

Figure 1 :

 1 Figure 1: PGC1-α silencing results in cellular polyamine build-up and increased cell migration

Figure 2 :

 2 Figure 2: PGC-1α represses c-MYC and ODC1 expression. A, Expression of ODC1 in LNCaP and

Figure 3 :

 3 Figure 3: The PGC-1α/c-MYC/ODC1 axis controls the aggressive phenotype in PCa cells via

Figure 4 :

 4 Figure 4: PGC-1α inhibits the formation of micrometastasis and putrescine restores the

Figure 5 :

 5 Figure 5: The downregulation of PGC-1α is associated with increased c-MYC and ODC1 in

Acknowledgements: Metabolomics services were performed by the Beth Israel Deaconess Medical Center Mass spectrometry Facility of Harvard Medical School. We thank Charlotte Hinault for carefully reading the manuscript. This work was supported by a grant from the Fondation ARC pour la recherche sur le Cancer, l'Association pour la Recherche sur les Tumeurs de la Prostate (ARTP), ITMO-Cancer. This work has been supported by the French government, through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01. L.K. is supported by the French Ministry of Research. S.T. has a grant from the Fondation de France, R.H. and E.J. were supported by the foundation ARC and FRR by the CHU of Nice. I.B.S is supported by the NIH R00-CA194192 and LAM foundation grants. F.B., N.M.M. and J.F.T. are CNRS investigators. Metabolomics services were performed by the Metabolomics Core Facility at Robert H. Lurie Comprehensive Cancer Center of Northwestern University.

A


Adil Guo

W Benaarbia

A Sun

A Becker

M Morris

P Pavier

M Flewitt

C Tierney

Wales

X F Guo

A Benaarbia

W Sun

A Morris

M Pavier

P Flewitt

M Tierney

C Wales

Optimisation and thermo-mechanical analysis of a coated steam dual pipe system for use in advanced ultra-supercritical power plant

Keywords: Thermal barrier coating, Dual pipe system, System optimisation, Cyclic viscoplasticity

Optimisation and thermo-mechanical analysis of a coated steam dual pipe system for use in advanced ultra-supercritical power plant X.F.

Introduction

Currently, there is an increasing demand to improve the thermal efficiency of power plant by increasing steam-operating temperatures [START_REF] Ou | Effect of carbon on the microstructure and stress rupture properties of a new Ni-Cr-W-Fe alloy for advanced ultra-supercritical power plants[END_REF][START_REF] Sun | Phenomenological and microstructural analysis of intermediate temperatures creep in a Ni-Fe-based alloy for advanced ultra-supercritical fossil power plants[END_REF][START_REF] Abe | Progress in creep-resistant steels for high efficiency coal-fired power plants[END_REF]. Several advanced ultrasupercritical power plants with target steam temperature up to 700 °C have been proposed to achieve cycle efficiencies in the order of 55% [START_REF] Viswanathan | US program on materials technology for ultra-supercritical coal power plants[END_REF][START_REF] Gibbons | Recent advances in steels for coal fired power plant: a review[END_REF]. Using conventional steam cycle design, such high operation temperatures require the use of nickel-based alloys such as Inconel 740, Haynes 230 and CCA 617, to replace the traditional 9-12%Cr ferritic heat resistant steels. These high temperature materials are of great importance for power plant components (superheaters, reheaters, steam transfer pipes, etc.) due to their resistance to creep damage and steam oxidation [START_REF] Jablonski | Processing of advanced cast alloys for A-USC steam turbine applications[END_REF][START_REF] Speicher | Microstructure evolution in Alloy 617B after a long-term creep and thermal aging at 700 °C[END_REF]. However, nickel-based alloys are significantly more costly than 9-12%Cr steels and are in relatively scarce supply. An alternative plant design is therefore required to achieve higher steam operating temperatures at an acceptable cost.

Thermal barrier coatings (TBCs), especially partially stabilized zirconia-yttria (YSZ), have been widely used in aircraft and industrial gas-turbine engines to provide thermal insulation and oxidation protection for superalloy components [START_REF] Padture | Thermal barrier coatings for gas-turbine engine applications[END_REF][START_REF] Boissonnet | Thermal transport properties of new coatings on steels for supercritical steam power plants[END_REF][START_REF] Evans | Mechanisms controlling the durability of thermal barrier coatings[END_REF]. Inspired by this approach, a steam transfer piping system operating at steam temperatures of up to 700°C has been designed to improve the energy efficiency of advanced ultrasupercritical power plants without the use of nickel-based alloys [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF]. Fig. 1 exhibits a schematic illustration of the coated pipe system where an internal (primary) steam pipe conveys steam from the boiler outlet to the high-pressure steam turbine with an external (secondary) steam pipe conveying the counter-cooling steam [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF]. Due to the use of low-thermal conductivity thermal insulation coating and a counter-cooled pipe system, the coated primary steam pipe has a significant thermal gradient through the wall thickness, and therefore large thermal stresses will be generated during start-up, shut down and steady-state operations. The geometry and material properties of the TBC system, particularly those of the top coat layer, greatly affect the thermal insulation capacity and also the generation of thermal-expansion mismatch stresses. These stresses may be large enough to influence the structural integrity of the system.

In order to analyse the thermal and mechanical response of the dual pipe system, preliminary analyses have been carried out by Guo et al [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF] based on analytical solutions and finite element analyses. The effects of several factors, for example the top coat thickness, thermal expansion coefficients and the temperature of the cooling steam on the temperature and stress distributions of the system, have been identified.

Although these factors were found to have a significant effect, no attempt was made to optimise the material properties or the dimensions of the system. Due to fluctuating energy demand and market competition, more frequent cyclic operation is witnessed in current power plant operation. This has led to the prevalence of high temperature damage mechanisms, such as creep and creep-fatigue. In past decades, the modelling of both fatigue and creep behaviours of high temperature materials has achieved significant progress, especially within a cyclic viscoplasticity framework [START_REF] Chaboche | On the plastic and viscoplastic constitutive equationspart i: Rules developed with internal variable concept[END_REF][START_REF] Tong | Modelling of cyclic plasticity and viscoplasticity of a nickel-based alloy using chaboche constitutive equations[END_REF][START_REF] Ahmed | Unified viscoplasticity modeling for isothermal low-cycle fatigue and fatigue-creep stress-strain responses of Haynes 230[END_REF][START_REF] Wu | Uniaxial mean stress relaxation of 9-12% Cr steel at high temperature: Experiments and viscoplastic constitutive modelling[END_REF][START_REF] Kyaw | Determination of material parameters for a unified viscoplasticity-damage model for a P91 power plant steel[END_REF][START_REF] Chaboche | Viscoplastic constitutive equations of combustion chamber materials including cyclic hardening and dynamic strain aging[END_REF][START_REF] Barrett | An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue[END_REF][START_REF] Zhang | Interaction of cyclic softening and stress relaxation of 9 -12% Cr steel under strain-controlled fatigue-creep condition: experimental and modeling[END_REF][START_REF] Wang | A unified viscoplastic constitutive model with damage for multi-axial creep-fatigue loading[END_REF][START_REF] Zienkiewicz | Visco-plasticity -plasticity and creep in elastic solids -a unified numerical solution approach[END_REF][START_REF] Xie | Cyclic hardening/softening behavior of 316L stainless steel at elevated temperature including strain-rate and strain-range dependence: Experimental and damage-coupled constitutive modeling[END_REF]. Generally speaking, this framework can be split into two broad groups: unified and non-unified viscoplasticity. In unified viscoplasticity, viscous creep and plastic strains are represented by a single inelastic measure and considered as ratedependent [START_REF] Chaboche | On the plastic and viscoplastic constitutive equationspart i: Rules developed with internal variable concept[END_REF][START_REF] Barrett | An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue[END_REF][START_REF] Xie | Cyclic hardening/softening behavior of 316L stainless steel at elevated temperature including strain-rate and strain-range dependence: Experimental and damage-coupled constitutive modeling[END_REF]. In non-unified viscoplasticity, both strains are considered as separate measures, where the creep strain is taken to be rate-dependent and the plastic strain to be rate-independent [START_REF] Cailletaud | Study of plastic/viscoplastic models with various inelastic mechanisms[END_REF][START_REF] Velay | Cyclic behavior modeling of a tempered martensitic hot work tool steel[END_REF]. Constitutive models with specific isotropic and kinematic hardening rules have been developed for different materials [START_REF] Prager | Recent developments in the mathematical theory of plasticity[END_REF][START_REF] Armstrong | A mathematical representation of the multiaxial bauschinger effect, Central Electricity Generating Board[END_REF][START_REF] Ohno | Kinematic hardening rules with critical state of dynamic recovery, part i: formulation and basic features for ratchetting behaviour[END_REF][START_REF] Freed | A viscoplastic theory with thermodynamic considerations[END_REF].

Chaboche [START_REF] Chaboche | A review of some plasticity and viscoplasticity constitutive theories[END_REF] has presented a review of many of these models. However, only few models available in literature are able to predict the anisothermal fatigue behaviour of the investigated material [START_REF] Barrett | An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue[END_REF][START_REF] Zhang | Anisothermal cyclic plasticity modelling of martensitic steels[END_REF][START_REF] Benaarbia | Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor[END_REF]. In this work, a unified viscoplastic model with non-linear anisothermal isotropic and kinematic hardening formulations is used to carry out the thermo-mechanical analyses.

This study describes an optimised design methodology based on a thermomechanical analysis of a novel coated dual pipe system for use in advanced ultrasupercritical power plant. The optimisation procedure is presented in section 2, where the theoretical formulations of model are introduced. In section 3, the finite element approach is presented, including a description of the viscoplastic model and the associated model parameters for the coating system. Section 4 discusses the system parameter optimisation and the significance of the results by comparing the stress evolutions in the baseline simulation and optimised models. Finally, a FE analysis of the dual pipe system under cyclic loading is performed using the viscoplastic model to evaluate the developed optimisation model.

Optimisation of the dual pipe system

In order to discuss the thermal and stress distributions of the coated dual pipe system generated during steady-state operation, a one-dimensional model of the coating-pipe structure has been built up in previous work [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF]. There are 3 layers, the top coat (TC), bond coat (BC) and the substrate pipe in the model. The sectional diagram of the system is shown in Fig. 2.

Optimisation model

In this work, the thermal-expansion mismatch stresses at the TC and BC interfaces are taken to be the critical factor leading to failure of the TBC system [START_REF] Padture | Thermal barrier coatings for gas-turbine engine applications[END_REF][START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF].

The optimisation model is therefore

= - → min, (1)
∈ , (2)
≤ ≤ , = 1, 4 (3)
where is the objective function, is the optimisation variable set (a vector in the n-dimensional space, ). In terms of the key governing parameters which have been identified [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF], the optimisation variable set is

= # $ % , $ & , ' ( , ) * + , (4)
where $ % is the thickness of the TC, $ & is the thickness of primary pipe, ' ( is the thermal conductivity of the TC, ) * is the hydraulic mean diameter in the cooling jacket [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF]. and are the hoop stresses on the outer surface of the TC and on the inner surface of the BC. and are the lower and upper bounds of .

No lower limit is imposed on the value of $ % since the TC layer needs to be as thick as necessary to reduce the temperature of the primary pipe to the required level.

At present, the maximum thickness of the coating tested in open literature is 4 mm [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF][START_REF] Jadhav | Thick ceramic thermal barrier coatings with high durability deposited using solution-precursor plasma spray[END_REF]. However, if the TC layer is too thick, it will lead to accelerated failure [START_REF] Padture | Thermal barrier coatings for gas-turbine engine applications[END_REF]. Thus, the upper boundary for $ % is chosen to be 3 mm. Some practical engineering dimension constraints have been imposed during the optimisation analysis, so the boundaries for $ & can be selected to be between 30 mm and 60 mm, and ) * between 100 mm and 200 mm. Changes to the value of ) * will affect the flow of steam in the cooling jacket and therefore the heat transfer coefficient between the primary pipe and the steam. These additional effects have not been considered in this work. Additionally, in order to cover a wide range of possible coating materials, the boundaries for ' ( can be chosen to be between 1.0 and 1.5 W/m°C [START_REF] Bose | High Temperature Coatings[END_REF][START_REF] Taylor | Creep properties of a Pt-aluminide coating[END_REF][START_REF] Pan | Evolution of a diffusion aluminide bond coat for thermal barrier coatings during thermal cycling[END_REF].

The thermal efficiency of the dual pipe system is considered as a constraint in the optimisation model. The thermal efficiency is calculated following the work of Wales et al [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF]. The thermal efficiency constraint inequality is defined as , -, -≥ 0,

where , is the thermal efficiency constraint function while , -stands for the threshold value of thermal efficiency. Here, considering the operating costs and profitability of power plants, , -is set as 51.40% [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF].

In the current coated dual pipe system, superheated steam at 700°C is transported using the coated P91 pipe so that the temperature experienced by the primary P91 pipe does not exceed 580°C. This temperature constraint of the primary pipe is set in the optimisation model. The temperature constraint equation is expressed

as 0 -0 -≤ 0, 6
where 0 is the temperature constraint function, 0 -is the maximum temperature of the primary temperature (580°C), as described in Fig. 2.

Arbitrary values of $ % , $ & , ' ( 234 ) * are used as initial values and the proposed algorithm is used to find optimised values of $ % , $ & , ' ( 234 ) * .

Optimisation procedure

In order to determine the optimum dimensions and material properties of the dual pipe, a combined FE simulation and optimisation approach is used. The optimisation is implemented using Matlab. The function for solving the minimum of constrained nonlinear multi-variable functions, fmincon, is provided within the Matlab optimisation toolbox.

A detailed description of the FE simulation is given in section 3.1. Since the initial guess values for $ % , $ & , ' ( 234 ) * are provided, these parameters are passed into the Abaqus input file by using a Matlab programme, and then a sequentially coupled thermo-mechanical analysis is carried out to obtain the initial hoop stress data within the system for each iteration. Additionally, a series of iterative calculations are also performed with different optimised parameters which are determined from the Matlab optimisation programme. During each iteration, all the system parameters in the Abaqus input file are updated by the new ones based on the FE analysis pre-processing.

In the FE post-processing, a python script is used to extract the hoop stresses at the TC and BC interfaces from the Abaqus output file. All the optimisation procedures run automatically until convergence is reached. The optimisation algorithms used in this study are illustrated in Fig. 3, where the thermal efficiency calculation module is also included [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF].

3. Finite element models of the coated dual pipe system under thermo-mechanical loading

Thermal and stress analysis models under steady-state operation

Assuming closed end conditions with no system loading (i.e. the stresses present are owing to internal pressure and external pressure only) [START_REF] Sun | Steady-state creep reference rupture stresses for internally pressurised pipes for use in life prediction[END_REF], a coated straight pipe of constant section may be greatly simplified to the 2-D axisymmetric finite element model, as shown in Fig. 4. The uncoupled thermal simulation is first performed in a heat transfer procedure, followed by the stress analysis which closely depends on the temperature field of the system.

Geometry and meshing

In section 4, the results corresponding to the optimised parameters will be compared with the values of those parameters used in previous work [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF]. These parameters are referred to here as the baseline parameters and are as follows: the thickness of the TC is 2.5 mm, the inner radius of the primary P91 steam pipe is 120 mm and the wall thickness is 60 mm (Fig. 4). To generate a compatible oxide to enable the ceramic to adhere to the underlying steel pipe, a thin BC layer of 0.5 mm in thickness is assumed. 8-node isoparametric quadratic axisymmetric temperature and continuum elements with reduced 2×2 integration (Abaqus element types DCAX8 and CAX8R) are used for the thermal and stress analyses. The model consists of 63,500 elements with 191,755 nodes to guarantee adequate computational accuracy.

Material properties

The materials of the TC, BC and internal steam pipe used in this study are assumed to be isotropic and homogeneous, and all layers in TBCs are assumed to be elastic and viscous as proposed in literature [START_REF] Dong | The influence of temperature gradient across YSZ on thermal cyclic lifetime of plasma-sprayed thermal barrier coatings[END_REF]. Here, 8YSZ, NiCoCrAlY, and P91 steel are chosen as the candidate TC, BC and the substrate, respectively. Some temperature dependent material properties of the TC, BC and the substrate required for the FE models, such as Young's modulus (E), yield strength, density, coefficient of thermal expansion (CTE), conductivity and specific heat, are taken from literature [START_REF] Dong | The influence of temperature gradient across YSZ on thermal cyclic lifetime of plasma-sprayed thermal barrier coatings[END_REF][START_REF] Gadag | Thermo-elastic properties of dense YSZ and porous Ni-ZrO2 monolithic and isotropic materials[END_REF][START_REF]A335 P91 -Special alloy steel for high temperature application in power plants[END_REF][START_REF] Hawa | Modeling of thermal and lattice misfit stresses within a thermal barrier coating[END_REF]. Other properties over a wider range of temperatures can be estimated based on linear interpolation of the existing data. These are given in Table 1.

Boundary conditions

In the baseline simulation conditions, the internal primary steam pipe is set to operate at a temperature up to 700°C, with the second outer cooling steam pipe at a temperature of 450°C. To maintain accurate boundary conditions, a mean axial stress ( 5) is applied to represent the closed end with a constant displacement constraint.

Symmetric boundary conditions are used as indicated in Fig. 4. The internal steady state pressure of the primary steam pipe is set at 35 MPa, with the steam pressure of the counter-flow at 7.5 MPa [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF][START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF].

Anisothermal FE model under cyclic loading

Compared with a constant and relatively uniform wall thickness temperature in a conventional steam circuit operating under steady-state conditions with well lagged piping, the coated dual pipe system has a significant thermal gradient through the wall thickness. Also, the effect of temperature on the material properties should be considered. Operating conditions for future ultra-supercritical power plants, such as expected cyclic mechanical loadings to accommodate increasing levels of renewable energy on the grid, will give rise to creep-fatigue damage of the system. Therefore, analysis of the TBC system is carried out using an anisothermal unified viscoplastic model. To demonstrate the effectiveness of the optimisation method, anisothermal FE analyses of the system before and after optimisation are also performed.

The constitutive model

In this study, an improved unified Chaboche-Lemaitre constitutive model presented in [START_REF] Benaarbia | Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor[END_REF] is employed to describe the anisothermal creep-fatigue response of the material under investigation. The main constitutive equations can be described as below

6 7 = 6 7 8 + 6 7 :& , (7)
6 7 8 = ) 7;< => ;< , (8) 6? 7 :
& = @? A 7 = B 〈 D E 〉 G HI = HI G HI = HI , (9)
JK , 7 , ; 0M = N K 7 , 7 M -K0, @ 0 M -' 0 , [START_REF] Evans | Mechanisms controlling the durability of thermal barrier coatings[END_REF] where 6 7 , 6 7 8 and 6 7

:& are the total strain, elastic strain and viscoplastic strain tensors.

The viscoplastic strain rate 6? 7 :& is expressed by a power flow law where @? is the viscoplastic multiplier rate, defined as @? = O 7 denotes the back stress tensor while the von Mises yield function J is dependent on the drag stress, 0, @ 0 , with the viscoplastic multiplier, @, the yield stress, ' 0 , and the second invariant N . The N -term is expressed by

N K , 7 M = O B KR 7 -7 MKR 7 -7 M, (11)
In this constitutive model, the anisothermal evolution of the kinematic hardening parameter 7 using the Chaboche decomposition [START_REF] Chaboche | A review of some plasticity and viscoplasticity constitutive theories[END_REF] is given as

7 = ∑ 7 ; ; >, , (12) ? 7
where U ; 0 and Y ; 0 are the temperature dependent material parameters. The terms U , ; 0 and Y , ; 0 represent the partial derivative of U ; 0 and Y ; 0 with respect to the temperature. The anisothermal evolution of the drag stress R can be expressed by ? K0, @ 0 M = #_ 0 -K0, @ 0 M + `=> 0 a 0 +` 0 @? 0 +b@ 0 a , 0 + K0, @ 0 M -a 0 @ 0 #`= > 0 `, 0 + _ => 0 _ , 0 +c0, ?

where _ 0 and ` 0 are temperature dependent material properties and a 0 represents the linear drag stress evolution. The terms a , 0 , `, 0 and _ , 0 are the partial derivatives of a 0 , ` 0 and _ 0 with respect to temperature. The detailed theoretical derivation of 7 and K0, @ 0 M can be found in [START_REF] Benaarbia | Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor[END_REF].

Material model parameters

A bespoke user material subroutine (UMAT) for the unified viscoplastic model described here has been generated in previous work [START_REF] Benaarbia | Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor[END_REF][START_REF] Benaarbia | A thermodynamically-based viscoelasticviscoplastic model for the high temperature cyclic behaviour of 9-12% Cr steels[END_REF]. The associated temperature dependent material properties of the P91 steel are given in Table 2. The UMAT used in this study was calibrated and validated using a series of isotropic holdtime cycle tests conducted at different temperatures as reported in several papers [START_REF] Kyaw | Determination of material parameters for a unified viscoplasticity-damage model for a P91 power plant steel[END_REF][START_REF] Saad | Characterization of viscoplasticity behaviour of P91 and P92 power plant steels[END_REF][START_REF] Hyde | Thermo-mechanical fatigue testing and simulation using a viscoplasticity model for a P91 steel[END_REF]. For the TC and BC layers, the temperature-dependent Young's modulus and yield stress are taken from literature [START_REF] Dong | The influence of temperature gradient across YSZ on thermal cyclic lifetime of plasma-sprayed thermal barrier coatings[END_REF][START_REF] Gadag | Thermo-elastic properties of dense YSZ and porous Ni-ZrO2 monolithic and isotropic materials[END_REF][START_REF]A335 P91 -Special alloy steel for high temperature application in power plants[END_REF][START_REF] Hawa | Modeling of thermal and lattice misfit stresses within a thermal barrier coating[END_REF]. Other temperature-dependent material properties are taken to be equal to those of the P91 steel.

Cyclic thermo-mechanical loading

In this work, a simplified cyclic thermal and mechanical loading for the dual pipe system has been used, as shown in Fig. 5. The loading starts from a stress-free state at hour dwell period at 20°C. In addition to the thermal loading, the internal and external pressures varying with time are imposed on the inner and outer surfaces of the coated primary pipe system. The mechanical loading cycle also consists of a 6h period of startup and a 5h shutdown with a 72h dwell period at full power in between, followed by a 7h dwell period at rest. It represents the typical high energy demand in the market, when the main steam pipeline is turned on; when the demand falls and they are turned off. The peak magnitude of the internal and external pressures described in section 3.1.3 are achieved during the 72 hour period.

Results

System optimisation analysis

Optimisation of the system parameters

The procedures described in Sections 2 and 3 will now be used to determine the optimised system parameters of the dual pipe system. To avoid affecting optimisation results caused by the differences in the magnitude of optimisation variables, the values of the variables have been normalised to the same order of magnitude during optimisation. The procedure starts from initial guessed values for $ % , $ & , ' ( 234 ) *

(the baseline values defined in section 3.1.1) and continues by performing iterations to find the minimum value of the hoop stress mismatch at the TC/BC interface. The convergence history of the optimised results is shown in Fig. 6. The results show that the values converge after 23 iterations. Additionally, it can be seen that the optimisation variables of $ % , $ & , ' ( 234 ) * converge rapidly after 5 iterations and the hoop stress mismatch at the TC/BC interface caused by the thermal and mechanical stresses reaches a minimum (see. Fig. 7). However, at this point the thermal efficiency of the system is less than the constrained value of 51.40% which is set as a constraint in the optimisation model. In order to increase the thermal efficiency, the thickness of the primary pipe $ & must be increased to recover the thermal efficiency to the constrained value, since this increase of $ & can reduce the significant influence of the cooling system on the thermal efficiency. Thus, it can be observed from Fig. 6 that $ & starts to increase after 13 iterations, whereas the values of $ % , ' ( 234 ) * are almost unchanged during iteration. Table 3 compares the set of optimised values with the initial guessed values.

Comparisons of temperature and stress distributions in the baseline and optimised models

Fig. 8 presents the temperature and stress distributions through the wall thickness of the coated primary pipe for the baseline geometry. The use of the thermal insulation coating reduces the inner surface temperature of the substrate pipe to about 560°C. The resulting temperature gradient through the wall thickness seen in Fig. 8(a)

inevitably gives rise to large thermal stresses within the system.

The stress distribution of the coated primary steam pipe system through the wall thickness is shown in Fig. 8(b). The radial stress is continuous through the wall thickness, whereas the hoop stress is discontinuous across the interfaces at the TC/BC and BC/substrate. The magnitude of the radial stress is quite small compared to that of the hoop stress which therefore plays a dominant role in determining the structural integrity of the system. This hoop stress is composed of a part generated by the thermal loading and a part generated by the mechanical pressure loading. The thermal part is much larger than the mechanical part, so the regulation of thermal stresses presents the key technical challenge. As observed in Fig. 8(b), in addition to the maximum hoop stress distributed on the external surface of the primary pipe, the positive hoop stress at the TC/BC interface is about 185 MPa due to the thermal expansion mismatch at the interface. Also, the variation of von Mises stress through the wall thickness can be seen in Fig. 8(b). Note from Fig. 8(b) that a peak value of von Mises stress can be observed at the TC/BC interface, but the stress decreases significantly on both sides of the peak.

Fig. 9 shows the temperature and stress distributions in the optimised primary steam pipe system. It can be seen in Fig. 9(a) that the inner surface temperature of the primary pipe reaches 518°C under the steady-state operation, as the TC thickness increases to 3 mm. The temperature difference between the inner and outer walls of the primary pipe changes from 110°C in the baseline model to 68°C in the optimised model.

This can be attributed to the increase in TC thickness ($ % ) and the decrease of the and the optimised model, the decrease in the stresses is mainly due to the decrease of thermal stresses in the coated dual pipe system. In the optimised system, the decrease of the primary pipe thickness as well as the temperature difference between the inner and outer walls of the primary pipe contributes to the reduction of thermal stresses.

Anisothermal FE analyses under cyclic loading

It is likely that the coated dual pipe system will experience cyclic mechanical loadings in service and this may lead to creep-fatigue. As described in section 4.1.2, there is a significant stress mismatch at the TBC interfaces, especially around the interface between the TC and BC, under steady-state operating conditions. Moreover, during start-up and shut-down operations, several cycle-dependent phenomena often take place within the TBC system, which may ultimately give rise to the premature failure by interfacial delamination. Therefore, preliminary thermo-mechanical analyses have been carried out using the anisothermal viscoplastic model, as described in section 3.2.1.

The hoop stress and von Mises stress distributions through the wall thickness in the optimised model generated during the first cycle at the end of steady-state and shut down operations are shown in Fig. 11, which can be compared with distributions for the baseline model in Fig. 10. During the first cycle at the end of steady-state operation, Fig. 10 shows that the maximum von Mises stress is located on the external surface of the P91 pipe. In the optimised model, the position of the maximum von Mises stress changes from the external surface of the P91 pipe to the TC/BC interface (Fig. 11).

During the first cycle at the end of shut-down, the maximum von Mises stress for both the baseline and optimised conditions is located on the internal surface of the TC, as shown in Fig. 10 and Fig. 11. Moreover, comparing Fig. 10 and Fig. 11, it is clear that the value of the maximum von Mises stress for the baseline model is much larger than for the optimised model. Since the maximum von Mises stress located on the internal surface of the TC in the coated dual pipe system during shut-down is much larger than during steady-state operation in the model, TBC failure may be caused by spallation of the TC. This result is consistent with the experiment observation reported by Padture et al. [START_REF] Padture | Thermal barrier coatings for gas-turbine engine applications[END_REF].

Discussion

An analytical optimisation method

In this work, a procedure has been developed to optimise the design of the dual pipe system. However, since the procedure involves an interaction between Abaqus and Matlab, it is complicated and time consuming.

Alternatively, an analytical optimisation method can be developed using the same objective function, based on the analytical solution of the thermal stresses presented in previous work [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF]. Using this method, the temperature profile within the dual pipe system during steady-state operation can be expressed as

0 r = -e f H ; H 4g + H > ≤ g ≤ h> , = 1,2,3 , (15)
where Ti(r) and ki(r) are the temperature and conductivity coefficients at the i-th layer, Ai and Bi are the integral constants.

The axial stress, H g , and hoop stress, H g , at the i-th layer caused by the thermal stress are given by

H g = - i H >=j H k H e ∆0 m g g4g + i H n H >hj H >= j H - i H o H >hj H , (16)
H g = i H >=j H k H e ∆0 m g g4g + i H n H >hj H >= j H + i H o H >hj H - i H k H >=j H 0 , (17)
where Ei is the modulus of elasticity, ν q is Poisson's ratio, αi is the coefficient of linear thermal expansion, ∆T q r is the change in the temperature at the i-th layer. Ci and Di are the constants of integration.

In the previous work, it has been proven that the analytical model above is capable to calculate the temperature profiles and thermal stress fields of the coated steam dual pipe system during steady state operation [START_REF] Guo | Thermal and stress analyses of a novel coated steam dual pipe system for use in advanced ultra-supercritical power plant[END_REF]. Here, the initial hoop stresses at the TC and BC interfaces can be obtained by Eq. ( 17) followed by calculations of the optimised hoop stresses using updated system parameters determined from the Matlab optimisation processes. The entire optimisation process is executed continuously until convergence is reached. The optimisation algorithm is shown in Fig. 12, where the thermal efficiency calculation is also included. Using this method, FE analysis can be avoided, although it would be diffiucult to extend the calculations to include non-steady state conditions.

Alternative objective functions

As described, the optimisation procedure attempts to reduce the hoop stress mismatch at the TC/BC interface. For such a complex system, other objective functions to represent typical failure mechanisms can also be used to optimise the system, such as the maximum temperature experienced by the primary P91 pipe and the thermal efficiency of the complete system. Another potential parameter that could be considered is the strain range in the TBC, since larger strain excursions associated with larger temperature excursions are more damaging.

Significant progress has been made in understanding the physical damage and failure mechanisms of the TBC system [START_REF] Padture | Thermal barrier coatings for gas-turbine engine applications[END_REF]. During start-up, shut-down and steady state operations, several interrelated time and cycle-dependent phenomena, such as the Fig. 13 shows effect of $ & on cycle thermal efficiency. The value for $ & needs to be a compromise between improving efficiency and reducing the stresses in the TBC.

Conclusions and future work

In this work, an optimised design methodology has been developed based on a thermo-mechanical analysis of a novel coated dual pipe system for use in advanced ultra-supercritical power plant. In addition, a FE analysis of the system under cyclic loading has been performed using the viscoplastic model to evaluate the developed optimisation model. The main conclusions are as follows: 3. An analytical optimisation method, which includes both heat transfer and thermal stress calculations, is also developed to determine the dimensions and material properties of the coated dual pipe system, although it would be difficult to extend the calculations to include non-steady conditions.

This study demonstrates the feasibility of using high temperature materials in current widespread use, for significantly higher temperature application in ultrasupercritical plant designs. This higher temperature application necessarily requires novel design options to be considered. This study has demonstrated how modelling and optimisation techniques can be used to explore the design feasibility of the proposed coated dual pipe system. The integrity of the interface between the TBC and primary steam transfer pipe presents a key technical challenge. Further development of coating systems and testing is required to demonstrate the successful operation of the proposed dual pipe system. Several time-and cycle-dependent phenomena, such as the formation of a thermally-grown oxide layer, the interdiffusion of high concentration elements between different interfaces as well as premature spallation failure require further investigation.

Table 1 Temperature dependent material properties of the top coat (TC), bond coat (BC) and the substrate for a range of temperatures [38-41] . Table 2 Temperature dependent material properties in the extended Chaboche-Lemaitre viscoplasticity constitutive model [38-44] . 1.9 1.9 1.9 Fig. 1 Schematic diagram of the coated steam dual pipe system for use in advanced ultra-supercritical power plant [11] . by FE [12] .

TC BC P91 E (MPa) -3.22×10 1 T + 2.05×10 5 -7.05×10 1 T + 2.01×10 5 -1.88×10 2 T + 2.47×10 5 k (MPa) -4.34×10 -1 T + 4.43×10 2 -4.34×10 -1 T + 4.43×10 2 -4.48×10 -1 T + 4.43×10 2 -2.24×10 -1 T + 6.07×10 2 -2.24×10 -1 T + 6.07×10 2 -2.24×10 -1 T + 6.07×10 2 (MPa) -4.30×10 -1 T + 3.05×10 2 -4.30×10 -1 T + 3.05×10 2 -4.30×10 -1 T + 3.

Highlights:

► A combination of an optimisation algorithm and FE simulation is developed to determine the optimum dimensions and material properties of the coated dual pipe system. ► An analytical optimisation Algorithm is introduced. ► A unified viscoplastic model is used for the thermo-mechanical analysis of the system under the cyclic loading. ► The integrity of the interface between the TBC and primary steam transfer pipe presents a key technical challenge.

  and A 7 the viscoplastic flow direction. Q 0 and 3 0 are the temperature dependent material parameters which represent the viscoplastic resistance and hardening exponent functions. R 7 is the deviatoric stress tensor of the Cauchy stress tensor, 7 , defined as R 7 = 7 -> B ;; S 7 .

20°C, and consists

  of a number of repeating cycles with thermal and mechanical loadings. For the thermal loading, each cycle of the inner surface of the TC is composed of a 6 hour heat-up period from 20°C to 700°C, a 72 hour dwell period at 700°C, a 5 hour cool-down period from 700°C to 20°C and a 7 hour dwell period at 20°C. The external surface of the primary pipe is exposed to a 6 hour heat-up period from 20°C to 450°C, a 72 hour dwell period at 450°C, a 5 hour cool-down period from 450°C to 20°C and a 7

  primary pipe thickness ($ & ). The value of the hoop stress mismatch at the TC/BC interface reduces from 522 MPa in the baseline model to 472 MPa in the optimised model. The maximum von Mises stress is located at the TC/BC interface during steadystate operation, and its value decreases from 326 MPa in the baseline model to 253 MPa in the optimised model. As the mechanical loadings are the same in the baseline model

1 . 2 .

 12 A combined FE simulation and optimisation algorithm is developed which is capable of determining the optimised dimensions and material properties by calculating the hoop stress mismatch at the TC/BC interface generated by the thermal and mechanical loadings. FE analyses are carried out to calculate the temperature profiles and stress distributions of the system in the baseline and optimised models. The results show that the value of hoop stress mismatch at TC/BC interface decreases from 522 MPa in the baseline model to 472 MPa in the optimised model, and the value of the maximum von Mises stress reduces from 326 MPa to 253 MPa. The current study has demonstrated the methods of performing thermomechanical analysis under cyclic loading for the coated dual pipe system using a unified viscoplastic model with non-linear anisothermal isotropic and kinematic hardening rules. The comparison results before and after optimisation show that the value of the maximum von Mises stress of 1360 MPa in the baseline model during shut down is much larger than that in the optimised model of 453.7 MPa.

05×10 2 - 7 3 T + 4 .00×10 - 1 (

 27341 MPa.s / ) 5.26×10 4 exp[-1.8× 10 4 /(8.314(T+273.15))] 5.26×10 4 exp[-1.8× 10 4 /(8.314(T+273.15))] 5.26×10 4 exp[-1.8× 10 4 /(8.314(T+273.15))]

  n

Fig. 2

 2 Fig. 2 Sectional diagram of the coating-pipe structure. Point 1 is the inner edge of the TC layer, point 2 is the TC-BC interface, point 3 is the BC-pipe interface, point 4 is the outer edge of the pipe.

Fig. 3

 3 Fig. 3 Flow chart of the combined FE simulation and optimisation algorithm.

Fig. 4

 4 Fig. 4 The geometry and boundary conditions for the axisymmetric FE model (D0=120 mm, dp =60 mm, dc=2.5 mm, db=0.5 mm, L =500 mm, Pi=35 MPa, P0=7.5 MPa).

Fig. 5 Fig. 6

 56 Fig. 5 Schematic diagram for intermittent operation showing the variation of the temperature and mechanical loadings on the internal and external surfaces of the coated dual pipe system.

Fig. 7 Fig. 8 (

 78 Fig. 7 Optimised values of stress mismatch at TC/BC interface values versus iterations using the combined FE simulation and optimisation approach.

Fig. 9 (

 9 Fig. 9 (a) Temperature field and (b) stress distributions in the optimised model calculated by FE.

Fig. 10

 10 Fig. 10 Hoop stress and von Mises stress in the baseline model generated during the first cycle at the end of the steady-state and shut-down operations.

Fig. 11

 11 Fig. 11 Hoop stress and von Mises stress in the optimised model generated during the first cycle at the end of the steady-state and shut-down operations.

Fig. 12

 12 Fig. 12 Flow chart of the analytical optimisation algorithm

Table 3

 3 Optimised results with initial guess values.

		Initial guess values	Final optimised values
	wc (m)	0.002	0.003
	wp (m)	0.060	0.038
	kw (W/m°C)	1.5	1.0
	(m)	0.1	0.2

Acknowledgements

This work is supported by Engineering and Physical Sciences Research Council (EPSRC), United Kingdom, through the project "Novel High Temperature Steam Transfer Pipes" [Grant number: EP-R000859-1] and the National Natural Science Foundation of China (51805274). The authors would also like to thank EDF UK for technical support.

formation of thermally grown oxides (TGO), may take place in the coated dual pipe system. In general, the large thermal-expansion mismatch among the TC, TGO and BC can create a significant stress field in the TBCs system [START_REF] Li | A semi-analytical model for predicting stress evolution in multilayer coating systems during thermal cycling[END_REF][START_REF] Chen | Influence of inhomogeneous thermally grown oxide thickness on residual stress distribution in thermal barrier coating system[END_REF]. With the growth of the TGO during service condition, the stress at the BC and TGO interface can ultimately result in interface cracking and system failure by spallation of the top-coat. The thickness of the TGO could be used as the objective function to optimise the dual pipe system since it is one of the most important factors controlling the integrity of the TBC system. In addition, thermal mechanical fatigue may also be a typical failure mechanism of the system. Because the fatigue failure depends more on the stress amplitudes, which may be considered as an alternative objective function to optimize the system.

Based on the analysis above, many factors can be used as the objective function to optimise the structure of the dual pipe system. For the current complex optimisation problem, different objectives under consideration may conflict with each other, and optimising a particular solution with respective to a single objective can result in unacceptable results with regard to the other objective. To solve this problem, a reasonable solution is to use multi-objective optimisation method which weights the importance of all the key factors (for example the maximum temperature experienced by the primary P91 pipe, the thermal efficiency of the system and the thickness of the TGO) in the same optimisation function [START_REF] Konak | Multi-objective optimization using genetic algorithms: A tutorial[END_REF].

Thermal efficiency

In the proposed dual pipe system, the use of a counter-cooled pipe system will inevitably result in a loss of heat from the supercritical steam and therefore contribute to the loss of thermal efficiency of the system. This will partly offset the higher efficiency achieved from the initially much higher superheated steam temperature. The calculation of thermal efficiency [START_REF] Wales | Reducing steam transport pipe temperatures in power plant[END_REF] for an ideal system with no zero heat and pressure losses gives a figure of 51.8%. This compares with 52.4% for a conventional design using materials that can withstand the temperature of the supercritical steam.

The parameters used in the optimisation procedure, $ % , $ & , ' ( , and ) * , have a significant impact on the thermal efficiency of the system. To improve the efficiency, values for $ % , $ & , 234 ) * should be as high as possible, while ' ( should be low. Of the 4 parameters, $ & , the thickness of primary pipe was found to be the most important parameter: a lower value for $ & gives a reduced stress mismatch at the TC/BC interface.