Giridhar Mudduluru

Jonahunnatha Nesson

Santoshi Muppala

Irfan Ahmed Asangani

Kumarswamy Regalla

Laura D Nelson

Heike Allgayer
email: heike.allgayer@umm.de

Prof. Dr. med Heike Allgayer

Curcumin regulates miR-21 expression and inhibits invasion and metastasis in colorectal cancer

Keywords: CAM, Characterization, Curcumin, miR-21, Promoter, Tumor-progression Abbreviations: miRNA, microRNA, pre-miR-21, primary transcript containing miR-21, AP-1, activation protein 1, ChIP, chromatin immunoprecipitation, RT-PCR, Reverse transcription PCR, PMA, phorbol 12-myristate 13-acetate

Introduction

Curcumin (diferuloylmethane), a yellow colored polyphenol, is an active component of the spice turmeric (Curcuma longa) and has been used for many centuries as a food additive and a traditional medicine in Asian countries. Curcumin has chemo-preventive and therapeutic properties against many tumors in in vitro and in vivo models and has been included in clinical trials. [START_REF] Khor | Combined inhibitory effects of curcumin and phenethyl isothiocyanate on the growth of human PC-3 prostate xenografts in immunodeficient mice[END_REF] It suppresses inflammation, cell proliferation and induces apoptosis, and sensitizes tumor cells to cancer therapies. [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Srivastava | Linkage of curcumin-induced cell cycle arrest and apoptosis by cyclin-dependent kinase inhibitor p21(/WAF1/CIP1)[END_REF][START_REF] Thangapazham | Multiple molecular targets in cancer chemoprevention by curcumin[END_REF] It also suppresses invasion and angiogenesis, in cancer. [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF][START_REF] Menon | Anti-metastatic activity of curcumin and catechin[END_REF] Curcumin physically binds to different proteins like thioredoxin reductase, COX2, protein kinase C (PKC), and 5-lipoxygenase (5-LOX) and modulates different molecular target molecules like transcription factors (AP-1, NF-NB, STAT-3 and ȕ-catenin), growth factors and their receptors, cytokines and enzymes. [START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF][START_REF] Beevers | Curcumin inhibits the mammalian target of rapamycin-mediated signaling pathways in cancer cells[END_REF] Curcumin is also known to inhibit Akt/mTOR signalling in different cancer cells. [START_REF] Beevers | Curcumin inhibits the mammalian target of rapamycin-mediated signaling pathways in cancer cells[END_REF][START_REF] Aoki | Evidence that curcumin suppresses the growth of malignant gliomas in vitro and in vivo through induction of autophagy: role of Akt and extracellular signal-regulated kinase signaling pathways[END_REF][START_REF] Chen | Curcumin inhibits lung cancer cell invasion and metastasis through the tumor suppressor HLJ1[END_REF] Curcumin has been administrated up to 10g/day in humans without toxicity, and serum concentrations of 1.77 ± 1.87 mol/L were observed in patients treated with 8g/day. [START_REF] Cheng | Phase I clinical trial of curcumin, a chemopreventive agent, in patients with high-risk or premalignant lesions[END_REF] Many diseases, especially cancer, are the results of deregulation of more than 500 different genes. [START_REF] Vogelstein | Cancer genes and the pathways they control[END_REF] Since curcumin is known for being non-toxic at higher doses, and for its role in inhibiting tumor progression by modulating a vast number of molecules and mechanisms, [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF][START_REF] Menon | Anti-metastatic activity of curcumin and catechin[END_REF] it has been suggested to be used as a potential drug in cancer therapy. MicroRNAs are a class of ~22 nt endogenous, non-coding RNAs generated from a larger stem loop structure, which can be expressed in a cell and tissue specific manner, influencing mRNA stability and translation. They control a wide range of biological functions such as cellular proliferation, differentiation and apoptosis.[12-14] Disruptions of miRNA-target gene regulation, including genomic instability and impaired miRNA processing, have been associated with a growing range of cancers. [START_REF] Kumar | Impaired microRNA processing enhances cellular transformation and tumorigenesis[END_REF][START_REF] Selcuklu | An investigation of microRNAs mapping to breast cancer related genomic gain and loss regions[END_REF] Recent reports show strong evidence that miRNAs are key molecules involved in cancer initiation and progression. [START_REF] Cho | OncomiRs: the discovery and progress of microRNAs in cancers[END_REF]17] miR-21 shows a strong evolutionary conservation across a wide range of vertebrate species in mammalian, avian and fish clades, suggesting a conserved role for miR-21 in gene regulation. [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF] Gene expression studies across tumor samples and cancer cells showed that miR-21 is the only miRNA upregulated in a large-scale profiling of 540 human samples derived from 363 specimens representing six types of solid tumours (breast, colon, lung, pancreas, prostate, and stomach) and 177 respective normal control tissues. [19] Other reports also showed that it is upregulated in other cancer types like glioblastoma, oesophageal cancer, ovarian carcinoma, cholangiocarcinoma, B-cell lymphoma, hepatocellular carcinomas, cervical cancer, uterine leiomyomas, head and neck cancer, chronic lymphocytic leukaemia, squamous cell carcinoma of the tongue and papillary thyroid carcinoma. [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF] This extensive miRNA profiling in different cancers compared with normal tissues/cells identified miR-21 as a key molecule associated with neoplastic transformation and as a biomarker. Functional studies of miR-21 either with sense or antisense transfection experiments in colorectal, [20] breast, [START_REF] Si | miR-21-mediated tumor growth[END_REF][START_REF] Zhu | MicroRNA-21 targets tumor suppressor genes in invasion and metastasis[END_REF] glioblastoma, [START_REF] Chan | MicroRNA-21 is an antiapoptotic factor in human glioblastoma cells[END_REF] hepatocellular, [START_REF] Meng | MicroRNA-21 regulates expression of the PTEN tumor suppressor gene in human hepatocellular cancer[END_REF] and neuroepithelial [START_REF] Sathyan | Competing interactions between micro-RNAs determine neural progenitor survival and proliferation after ethanol exposure: evidence from an ex vivo model of the fetal cerebral cortical neuroepithelium[END_REF] cancer cells determined its role in inducing cell proliferation, anti-apoptosis, migration, invasion and metastasis by differentially regulating molecules like Pdcd4, PTEN, and Bcl-2. These studies strongly suggest its role in oncogenesis/tumor progression. Pri-miR-21 is one of the first human miRNA genes for which the structure was determined as located on chromosome 17 residing within the tenth intron of the gene TMEM-49 (Transmembrane protein-49). [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF][START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] Pri-miR-21 and TMEM-49 are overlapping genes, and in the same direction of transcription are independently transcribed and terminated with their respective poly (A) signal. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] In human promyelotic HL-60 cells, miR-21 expression is induced after phorbol 12-myristate 13-acetate (PMA) stimulation. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] , [START_REF] Kasashima | Altered expression profiles of microRNAs during TPA-induced differentiation of HL-60 cells[END_REF] Two reports in cervical cancer, and leukemia cell lines suggest that the miR-21-gene has two different transcription start sites (TSS): one (CATT) is at intron 10 of TMEM-49 [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] and the second one (ATAAC) is at 891 bp downstream of the TSS reported by [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF], which is in intron 11 of TMEM-40. [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF] Pri-miR-21 promoter regulation is controlled by AP-1, PU.1, the SWI/SNF complex, and įEF1. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF][START_REF] Du | BMP-6 inhibits microRNA-21 expression in breast cancer through repressing deltaEF1 and AP-1[END_REF][START_REF] Talotta | An autoregulatory loop mediated by miR-21 and PDCD4 controls the AP-1 activity in RAS transformation[END_REF] BMP-6 downregulates miR-21 expression by inhibiting the expression and binding of AP-1 and įEF1 to the miR-21 promoter. [START_REF] Du | BMP-6 inhibits microRNA-21 expression in breast cancer through repressing deltaEF1 and AP-1[END_REF] c-Jun and c-Fos are the major regulators of miR-21 among AP-1 family members after PMAstimulation. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] Combining the promising data on curcumin's function as an anti-tumorigenic, and the role of miR-21 in tumorigenesis and progression, we performed this study to determine the pri-miR-21 maximal promoter region and TSS sites in colorectal cancer, and especially to study the effect of curcumin on the transcriptional regulation and expression of miR-21, cell cycle regulation, tumor growth, invasion and in vivo metastasis in this cancer entity. As a result, we show that the traditional medicine compound curcumin inhibits miR-21-transcriptional regulation and expression, tumor growth, invasion, and in vivo metastasis, and stabilizes the miR-21 target Pdcd4 in colorectal cancer. Furthermore, we identified multiple TSS for pri-miR-21, among them two new TSS being the major ones, one at 35 bp and the other at 28 bp upstream to the TSS reported by [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF]. Moreover, we report on a new additional AP-1 site (-663/-659 bp) in the upstream region of pri-miR-21. Finally, we observed that the TSS previously reported by [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF], which is located in the intron 10 of TMEM-49, is spliced from the pri-miR-21 promoter in colorectal cancer cells.

Materials and methods

Cell culture, drug, treatments and Materials

Cells were obtained from the American Type Culture Collection (ATCC; Manassas, VA), and grown at 37°C with ATCC recommended media supplemented with 10% fetal calf serum (FCS). Curcumin was purchased from Sigma Aldrich (Germany) and dissolved in DMSO. Mock-treated control (DMSO) cells were handled identically to curcumin treated cells. Control-miR and pre-miR21 were from Ambion (USA), Taqman primer-probes for the quantification of miR-21 and RNUB6 were from Applied Biosystems (USA), oligonucleotides were obtained from Metabion (Germany).

Preparation of protein extracts and Immunoblotting

Cells were washed with phosphate-buffered saline (PBS) after curcumin treatment and lysed in extraction buffer (Biosource, CA). Protein concentrations were determined by BCA kit (Pierce, Rockford, IL, USA). For immunoblotting, samples (40 µg/lane) were boiled for 5 min, separated via SDS-PAGE, and transferred to PVDF membranes. After transfer, the membranes were blocked with 5% non-fat milk containing Tris-buffered saline with 0.1% Tween (TTBS) for 3 h at room temperature and then probed with the indicated primary antibodies versus Pdcd4 (Abcam, Germany), p-c-Jun (#sc 822x, Santa Cruz) and GAPDH (#sc 1616, Santa Cruz) for 2 h at room temperature. After three washes with TTBS, blots were incubated with appropriate secondary antibodies conjugated with horseradish peroxidase. After final washes with TTBS, the membranes were exposed to film after enhanced chemiluminescence (ECL) (Amersham Biosciences).

RNA isolation and Reverse Transcriptase-PCR

Total RNA was extracted from tissue culture cells and CAM tumours with TRIZOL (Invitrogen) according to the manufacturer's instructions. The RNA samples were quantified using a spectrophotometer and visualized on a MOPS-formaldehyde gel for quality assurance. 1 µg of total RNA was reverse transcribed by random hexamer primer using SuperScript II reverse transcriptase (Invitrogen), or 100 ng of total RNA was reverse transcribed by gene specific primers (Applied Biosystems (AB)). Expression of pre-miR-21 was determined by Syber green PCR (Primer pairs: pre-miR-21(sense: CAT TGT GGG TTT TGA AAA GGT TA, antisense: CCA CGA CTA GAG GCT GAC TTA GA) and R18 (RN18S1) normalizing control (sense: CGCCGCTAGAGGTGAAATTC, antisense:

CATTCTTGGCAAATGCTTTCG), and mature miRNA was determined by the TaqMan miRNAassay using RNUB6 as the internal normalizing control. All TaqMan-PCRs were performed in triplicates.

MTT assay 3*10 3 cells/well were seeded in a 96-well plate in a total volume of 100 µL medium with 10% FBS. After 24h, cells were treated either with DMSO or curcumin at concentrations between 0-28 µM. After 48h, the growth inhibitory effect was evaluated using 20µL/well of CellTiter96 ® AqueousOneSolution (Promega-USA) according to the manufacturer's instructions.

Cell cycle analysis

Rko and HCT116 cells were treated for 24 hours with DMSO or 2.5 PM and 20 PM of curcumin. After 24 hours cells were washed with PBS twice and harvested by trypsinization. The cells were washed again with PBS and fixed with cold 70% ethanol for 1 hour. The cells were washed with PBS once and then incubated with 4 Pg of ribonuclease A (Roche Applied Science) for 30 min at room temperature. Propidium iodide was added to the cell suspension at a final concentration of 20 Pg/ml and incubated for 30 min. The cells were then analyzed by flow cytometry using FACScan (Becton Dickinson). The results were quantified by using the software Cell Quest (Becton Dickinson).

RACE and generation of luciferase reporter constructs

RACE and luciferase reporter constructs were generated as described previously. [31,[START_REF] Mudduluru | The human receptor tyrosine kinase Axl gene--promoter characterization and regulation of constitutive expression by Sp1, Sp3 and CpG methylation[END_REF] Briefly, the 5' RACE-ready first-strand cDNA was synthesized using 1µg of total RNA from Rko cells and human placenta. The 5' flanking sequence of miR-21 was amplified using a universal primer (UMP, Clontech), and a specific primer: 5'-GTAGGCTCCTGTTGGTCAAAAGAGG -3'. The resulting PCR products were gelpurified, cloned into the pGEM-T easy vector (Promega, WI), and 10 different positive clones of each were sequenced. RT-PCR was performed with a panel of colorectal, cervical (HeLa) and breast (MCF-7) cancer cells to confirm the pre-miR-21 transcription start site and splicing of intron 11 of TMEM-49 from the pre-miR-21 promoter, with sense 5'-GCCATACCAGAGTACAGTATCAGC-3' and antisense 5'-CATCCAGGACAACCAGTTTTCTCC-3'. Approximately 2.0 kb of upstream sequence of the pre-miR-21 promoter was amplified by PCR from human genomic DNA and cloned into the pGL3-basic vector (Promega) using Kpn I and Mlu 1 restriction sites. The 1060 bp construct was generated from the 2 kb construct by Pvu II and Mlu I digestion, backbone blunted using T4 DNA pol I, and ligated. The 448 bp construct was made from the 1060 bp construct by Kpn I and Sac I digestion, backbone blunted using T4 DNA pol I, and ligated. Mutant constructs were generated by the QuikChange XL site-directed mutagenesis kit from Stratagene (La Jolla, CA) using the 1060 bp maximum promoter activity-containing construct as a template. The sequences of oligonucleotides used for cloning and mutation are depicted in Supplementary Table 1. Successful incorporation of the mutations was confirmed by automated sequencing.

Transfection and Luciferase Assays

For luciferase assays, 0.5 × 10 6 Rko or HCT116 cells were plated in 24 well plates, and after 24 hours transfected with Lipofectamin 2000 (Invitrogen). pRL-TK (25 ng, Renilla Luciferase; Promega) was transfected along with Luciferase reporter plasmids (1 µg) to normalize transfection efficiency. After 12 hours of transfection, cells were either mock treated with DMSO or treated with increasing concentrations of curcumin (2.5 µM to 20 µM).

After 24 hours of treatment, cells were washed twice with PBS and lysed with 100 µl passive lysis buffer (Promega) for 20 min. Luciferase activity of 20 µl of cell lysate was measured via the Dual-Luciferase reporter assay system (Promega) according to the manufacturer's instructions. Assays for all samples were performed in triplicate, and the results were averaged.

Chromatin Immunoprecipitation Assay

Chromatin immunoprecipitation (ChIP) assays were performed as described previously, [START_REF] Leupold | Src induces urokinase receptor gene expression and invasion/intravasation via activator protein-1/p-c-Jun in colorectal cancer[END_REF] using either anti-p-c-Jun (sc-822 X), anti-c-Fos (sc-44 X) or anti-IgG (as control, sc-2338 X) antibodies. Rko cells were either mock treated with DMSO or treated with curcumin (10 µM) 1 hour before PMA stimulation. After 24 hours post stimulation cells were processed as described. [START_REF] Mudduluru | The human receptor tyrosine kinase Axl gene--promoter characterization and regulation of constitutive expression by Sp1, Sp3 and CpG methylation[END_REF] P-c-Jun and c-Fos binding to the pri-miR-21 promoter was measured using Syber green PCR with two sets of specific primers. Set 1, sense 5ƍ-GCCTCCCAAGTTTGCTAATG-3ƍ; antisense 5ƍ-TGTACTCTGGTATGGCACAAAGA -3ƍ and Set 2, sense 5ƍ-GAGATCAGGCCATTGCACTC-3ƍ; antisense 5ƍ-GCAACACTGCCTAATGCTTG -3ƍ.

Cell migration and invasion assay

Rko and HCT116 cells were pretreated with curcumin (10M and 16M, respectively). After 24h, cells were trypsinized, and 3x10 5 cells were plated on Boyden chambers either coated with 10µg matrigel/well (for invasion assays) or uncoated (for in vitro migration assays) in serum-free medium containing 0.1% BSA (Bovine serum albumin) and respective curcumin concentrations. 10% FBS medium in the lower chamber served as the chemoattractant. After 13h, non-invading cells were removed with cotton swabs. Invaded cells were trypsinized and counted using the ATP-luminescence-based motility-invasion assay (Promega) as previously described.

[34]

Chorionallantoic membrane (CAM) assay

The CAM assay was performed as described, [START_REF] Leupold | Src induces urokinase receptor gene expression and invasion/intravasation via activator protein-1/p-c-Jun in colorectal cancer[END_REF]34] with a few modifications. Briefly, 2*10 6 cells were inoculated on the CAM of 10-day old chicken embryos. On day 12 and 14, chicken embryos were treated intravenously with curcumin or DMSO, respectively. Untreated embryos served as an additional control. On day 17, the embryos were sacrificed. Metastasis was determined by harvesting lungs and liver, and processing the tissue for genomic human DNA by quantitative alu-PCR.

Statistical analysis

Statistical analyses were performed using the SPSS statistical software (statistical package for social sciences, SPSS, Inc., Chicago, IL). The Student's t-test was performed for data with normal distribution, the Wilcoxon-test for all other analysis. P-values of 0.05 were considered statistically significant.

Results

Race analysis and transcription initiation site of pri-miR-21

Pri-miR-21 is located in intron 10 of the TMEM-49 gene, and both of these genes are transcribed in the same direction. TMEM-49 expression (Supplementary figure 1) did not correlate with miR-21 expression levels published by Asangani et al. 2008 in the screened panel of cancer cell lines, [20,[START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] suggesting that both genes have different promoters. [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF][START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] reported two different TSS for miR-21 and both are located in different introns of the TMEM-49 protein coding genes with a distance between of 891 bp. To define the transcription initiation site(s) for pri-miR-21, 5'-RACE was performed using a TMEM-49 specific primer anchored within exon 12 (Supplementary Fig 2a), with total RNA from Rko cells and human placenta. 5'-RACE amplification from RNA of both samples generated two amplicons with an approximate size of 1200 bp and 500 bp (Fig 1a). Interestingly, no specific amplification of the 500 bp fragment was observed in the normal human placenta. This result was not surprising since miR-21 might not be expressed in human placenta. The 1200 bp fragment size corresponds with the TMEM-49 transcript. Cloning and sequencing of the 500 bp PCR products revealed multiple 5'-start sites, with the majority of clones including a region consisting of 35 bp upstream to the TSS reported by Fujita et al., 2008 (Supplementary Figure 2b,3a). Interestingly, no specific band or sequence corresponding to the TSS reported by Cai et al.

PMA induces pri-miR-21 transcriptional activation and expression

To determine an impact of PMA-stimulation on miR-21 expression, Rko and HCT116 cells were stimulated with 100 nM of PMA in a time-dependent manner. miR-21 was upregulated after 12 hours and reached a maximum upregulation after 24 hours PMA stimulation (Supplementary Fig 4a,b). These results suggest that PMA induces miR-21 expression in colorectal cancer cells. Furthermore, to delineate the miR-21 promoter region required for constitutive and PMA-inducible activity, different luciferase constructs were made either with, or without, the TSS reported by [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF], and our new TSS, and transfected into Rko and HCT116 cells (Fig 1c). Cells were stimulated with DMSO or 100 nM PMA 12 hours post transfection, and after 24 hours of stimulation cells were harvested and analysed. Deletion of 1000 bp downstream of the novel 35 bp TSS determined by us and the TSS reported by Fujita et al., showed a significant increase in the promoter activity either with or without PMA-stimulation, and deletion of 500 bp from the 5' flanking region of these two TSS decreased the promoter activity in both conditions when compared with the 1 kb fragment (Fig 1c). These results suggest that the maximum miR-21 promoter is spanning 1000 bp upstream to the novel TSS determined by our study as well as the TSS reported by Fujita et al., which is 35bp downstream to our novel TSS.

Curcumin inhibits pri-miR-21 promoter activity

Rko and HCT116 cells were treated with curcumin for 48 hours to determine the IC 50 values for cell proliferation (Fig 2a). MTT assay determined the cell lines' IC 50 as 10µM (Rko) and 16 µM (HCT116). To determine the activity of curcumin to regulate pri-miR-21 promoter activity, the maximum promoter activity-giving construct was transfected into Rko and HCT116 cells. 12 hours post transfection, cells were treated for 24 hours with curcumin in different concentrations. Curcumin significantly reduced the promoter activity in both cell lines (Fig 2b). To determine the functional relevance of an upstream new AP-1 binding motif (at -663/-659 bp: AP-1 IV) in the promoter, a mutational construct specifically for this site was generated and luciferase assays performed. Either with or without PMA-stimulation, the promoter activity was decreased. Especially, with PMA-stimulation, the promoter activity of this AP-1 IV mutant construct was significantly reduced, when compared with the PMAstimulated wild type construct. Additionally, combinatorial AP-1 mutation constructs (AP-1 binding motifs -58/-55 bp: AP-1 I; -165/-162 bp: AP-1 II; and -226/-223 bp:AP-1 III, proximal to the TSS reported by [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] were generated along with the new upstream AP-1 binding motif and transfected into Rko and HCT116. Mutation of all four AP-1 motifs reduced the basal promoter activity significantly when compared with the wild type construct, the activity of this mutant being significantly reduced compared with other combinational constructs mutated for different AP-1 motifs. Moreover, PMA-induced promoter activity was most significantly reduced by the construct mutated for all four AP-1 motifs, with an activity comparable to basal promoter activity. The curcumin-inhibited promoter activity was not reduced further when compared with its DMSO control with the four AP-1 mutant construct. However, curcumin pre-treatment inhibited PMA-induced promoter activity in both cell lines (

Curcumin represses miR-21 expression and induces Pdcd4 protein expression

To demonstrate the effect of curcumin on pre-miR-21 and miR-21 expression and function, quantitative PCR and Western blot analysis were performed for pre-miR-21, miR-21, and Pdcd4, which has been shown to be a miR-21 post-transcriptional target,[20] with 24h of curcumin treatment. Rko and HCT116 cells showed a significant reduction in pre-miR and miR-21 expression after curcumin treatment in a dose-dependent manner (Fig 3a,c). Moreover, Curcumin inhibited the PMA-induced miR-21 expression, but not completely (Supplementary Fig 4d). In parallel, Pdcd4 protein amounts were increased significantly (p<0.05) in both cell lines (Fig 3b,d). These results suggest that curcumin is inhibiting miR-21 expression and function in colorectal cancer, as shown by a reduction of its target Pdcd4, an important tumor suppressor in colorectal cancer.

Curcumin arrests tumor cells in the G2/M phase of the cell cycle

Curcumin has been reported to inhibit cell growth and to induce apoptosis in cancer cells. [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF]35] Dose-dependent treatment of curcumin inhibited the growth of Rko and HCT116 cells (Fig 4 a,b). Fluorescence-activated cell sorting (FACS) was carried out to analyze the cell cycle profile of curcumin-treated cells. The proportion of cells with actively replicating DNA, which represents the S-phase, did not change significantly with 24 h of curcumin treatment. However, the proportion of cells containing 2N DNA, which represents the G1-phase, decreased significantly in curcumin-treated Rko (74-36%) and HCT116 cells (67-22%). Similarly, the fraction of cells with 4N DNA, which represents the G2/M-phase, increased in Rko (13-47%) and HCT116 (17-67%) cells in a dose-dependent manner. These results suggest that treatment of Rko and HCT116 cells with curcumin results in the arrest of cells in the G2/M phase of the cell cycle.

Curcumin inhibits migration and invasion

To demonstrate an ability of curcumin to inhibit migration and invasion in colon cancer, Rko and HCT116 cells were pretreated with DMSO or with curcumin (10M and 16M, respectively). After 24 hours, cells were either seeded in Boyden-chambers for migration, or in 10g matrigel-coated chambers for invasion. Curcumin-treated cells showed significantly decreased migration (Rko:p=0.01; HCT116:p=0.04) and invasion (Rko:p=0.05; HCT116:p=0.02) in both cell lines when compared with DMSO-treated cells (Fig 4c,d). These results suggest that curcumin inhibits migration and invasion in colorectal cancer cells.

Curcumin inhibits tumor and metastasis formation in vivo

To study the ability of curcumin to regulate in vivo metastasis, we employed the chorionallantoic membrane (CAM) assay of the chicken embryo, which is able to differentiate primary tumor growth and metastasis, among other phenomena, in a highly sensitive and quantitative in vivo setting. [START_REF] Leupold | Src induces urokinase receptor gene expression and invasion/intravasation via activator protein-1/p-c-Jun in colorectal cancer[END_REF]34] For investigating regulation of primary tumor growth, Rko and HCT116 cells were inoculated on the upper CAM of 10-day old chicken embryos either with, or without, 24 hours pre-treatment of DMSO or curcumin (20M). On day 12, the embryos with pretreated cells were treated on the upper CAM with DMSO or curcumin. The primary tumors on the upper CAM were removed from the experiments performed with the pretreated cells, weighed and quickly frozen in liquid nitrogen. For the metastasis assay, on day 12 and 14 the embryos with plain cells were treated intravenously with 20PM curcumin or DMSO. On day 17, the intravenously treated embryos were sacrificed and their lungs and livers harvested for DNA. The number of cells metastasized into the liver and lungs was measured with a Taq-Man-based PCR amplifying human alu-sequences on the chicken background. [START_REF] Leupold | Src induces urokinase receptor gene expression and invasion/intravasation via activator protein-1/p-c-Jun in colorectal cancer[END_REF]34] We found that curcumin was able to significantly reduce primary tumor growth of Rko (p=0.02) and HCT116 (p=0.016) cells (Fig 5a,c), and also distant metastasis of Rko cells (liver p=0.01, lungs p=0.011). In HCT116 cells, we observed a trend for metastasis inhibition when compared with respective DMSO controls (Fig 5b,d). These data suggest that curcumin inhibits tumor growth and in vivo metastasis of colorectal cancer cell lines.

Curcumin inhibits miR-21 expression in primary tumors in vivo in the CAM assay

To support the in vitro data on curcumin downregulation of miR-21, total RNA was harvested from the frozen resected tumors isolated on the upper CAM from both Rko and HCT116 cells. Quantitative PCR was performed for pre-miR-21 and miR-21 expression, with DMSOor curcumin-treated samples from both cell lines. We observed that all samples/tumors (n=5) treated with curcumin showed reduced pre-miR-21 and miR-21 expression when compared with DMSO treated samples/tumors for both cell lines. Pre-miR-21 expression in individual samples is shown in Supplementary Figure 5. The mean expression of pre-miR-21 was significantly downregulated in curcumin-treated samples in Rko (p=0.0002) and HCT116 (p=0.041). Likewise, mean miR-21 expression in Rko (p=0.00006) and HCT116 (p=0.0035) was significantly downregulated when compared with the mean of DMSO treated samples/tumors (Fig 6 a,b). These results confirm the in vivo relevance of our in vitro findings. Taken together, these data show that curcumin significantly inhibits tumor growth and in vivo metastasis, and that this is, in part, mediated through miR-21.

Discussion

Cancer is a complex disease occurring as a result of a progressive accumulation of genetic aberrations and epigenetic changes that enable cells to escape from normal endogenous and environmental controls. [START_REF] Weinberg | The molecular basis of oncogenes and tumor suppressor genes[END_REF] Cancer arises as a localized disease, progresses to an invasive primary tumor and finally becomes metastatic. [37,[START_REF] Min | Urokinase receptor antagonists inhibit angiogenesis and primary tumor growth in syngeneic mice[END_REF] Colon cancer is one of the major causes of cancer related death worldwide, representing the third most common and second leading cause of cancer death. However, still too little is known about the mechanisms of cancer metastasis and especially strategies to inhibit metastasis. miRNAs have been shown to have an important role in tumor biology, including oncogenesis, progression, invasion, metastasis and angiogenesis. miRNAs are now recognized as key players of posttranscriptional control of gene expression. It has been shown that miRNAs are aberrantly expressed or mutated in cancer, suggesting that they may function as a novel class of oncogenes or tumor suppressor genes, and ongoing investigations have been starting to implicate specific miRs in metastasis. [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF][START_REF] Iorio | MicroRNA gene expression deregulation in human breast cancer[END_REF] miRNA-genes were reported to be transcribed by RNA polymerase II to produce pri-miRNAs with a terminal modification of a 5'-7-methyl guanylate (m7G) cap and a 3' poly (A) tail, like traditional protein coding genes. This process has also been reported to be regulated by known transcription factors. miR-21 is one of the first human miRNAs whose structure was determined, [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF][START_REF] Lee | The nuclear RNase III Drosha initiates microRNA processing[END_REF] and gene expression studies on different human tumor samples reported that miR-21 is upregulated especially in lung and colorectal tumor tissues. [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF][19][20] However, the transcriptional regulation of miR-21 is not completely understood and also not clear in terms of TSS. Cai et al., 2004[26] reported a transcriptional start site (TSS) 2445 bp upstream to the pri-miR-21 gene, in the TMEM-49 intron 11, which is constitutively active, in 293 embryonic kidney cells. Loffler et al., 2007[41] reported a different TSS 50 bp upstream to the TSS reported by Cai et al., which is regulated by conserved enhancer binding motifs of signal transducer and activator of transcription 3 (STAT3), in melanoma cells. A third TSS was reported for pri-miR-21 by Fujita S et al., 2008 in cervical cancer (HeLa) and leukemia (HL-60) cell lines [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF], to be located in intron 10 of TMEM-49. However, the previously reported transcriptional start sites were not detected in the study by Fujita et al. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] Moreover, the TSS reported by Fujita et al., minimally overlaps about 60 bases with the TSS of Cai et al., and both are functioning separately, suggesting that each is an independent promoter. [START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF][START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] Our present study with 5' RACE analysis in colorectal cancer with the specific primer in exon 12 of TMEM-49 determined multiple TSS for pri-miR-21, which are either identical to, or even as novel TSS located around, the TSS reported by Fujita S et al. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] No specific bands were observed to support the previously reported TSS by Cai et al., and Loffler et al., in our data. Interestingly, intron 11 of TMEM-49 was observed to be spliced from the pri-miR-21 gene to support RNA polymerase II transcription, which is a common mechanism in the processing of normal protein coding genes, [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF][START_REF] Cai | Human microRNAs are processed from capped, polyadenylated transcripts that can also function as mRNAs[END_REF] Certainly, this TSS is close to the core promoter, with a typical structure for most of the human coding genes, suggesting the general biological importance of this TSS. Still, we think that the most likely explanation for the discrepancies found for diverse TSS in the other studies is that many TSS might in part be cancer entity-specific. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF][START_REF] Cooper | Comprehensive analysis of transcriptional promoter structure and function in 1% of the human genome[END_REF] Subsequently, our promoter analyses on pri-miR-21 revealed that PMA-induced AP-1 binds to the pri-miR-21 promoter and triggers the transcription of the pri-miR-21 gene. Additionally, we found a novel AP-1 binding motif (-663/-659 bp) in the upstream sequence of the pri-miR-21 promoter, which is also important for core promoter activity and PMAstimulated promoter activity in colorectal cancer. Transcriptional regulation of pri-miR-21 has been shown to be controlled by AP-1, PU.1, the SWI/SNF complex, STAT3 and įEF1. [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF][START_REF] Du | BMP-6 inhibits microRNA-21 expression in breast cancer through repressing deltaEF1 and AP-1[END_REF][START_REF] Talotta | An autoregulatory loop mediated by miR-21 and PDCD4 controls the AP-1 activity in RAS transformation[END_REF][START_REF] Loffler | Interleukin-6 dependent survival of multiple myeloma cells involves the Stat3-mediated induction of microRNA-21 through a highly conserved enhancer[END_REF] Enhancement of endogenous activity of AP-1 can be induced through various signalling axes, and is associated with oncogenic transformation. [START_REF] Suzuki | Analysis of AP-1 function in cellular transformation pathways[END_REF][START_REF] Ui | Endogenous AP-1 levels necessary for oncogenic activity are higher than those sufficient to support normal growth[END_REF] It has been shown that enhanced miR-21 expression in several cancers is due to transcriptional regulation by an enhanced activation of AP-1. [START_REF] Cho | OncomiRs: the discovery and progress of microRNAs in cancers[END_REF][START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF][START_REF] Suzuki | Analysis of AP-1 function in cellular transformation pathways[END_REF][START_REF] Ui | Endogenous AP-1 levels necessary for oncogenic activity are higher than those sufficient to support normal growth[END_REF] PMA induces miR-21 expression through AP-1 family transcription factors, mainly c-Jun and c-Fos, [START_REF] Fujita | miR-21 Gene expression triggered by AP-1 is sustained through a double-negative feedback mechanism[END_REF] as we also have shown here. Curcumin physically binds and modulates different target molecules like AP-1, NF-kB. [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF] Correspondingly, we now showed that curcumin reduces miR-21 expression by inhibiting the activation and binding of AP-1 to the pri-miR-21 promoter. Taken together, data suggest that curcumin reduces miR-21 expression by inhibiting AP-1 function. This is the first study to show that curcumin inhibits invasion and in vivo metastasis by reducing miR-21 expression. Pdcd4 is a tumor suppressor shown to inhibit phorbol esterinduced neoplastic transformation,[46] tumor promotion and progression, [START_REF] Jansen | Epidermal expression of the translation inhibitor programmed cell death 4 suppresses tumorigenesis[END_REF] also suppressing tumor progression in human colon carcinoma cells by downregulating MAP4K1 transcription, and inhibiting c-Jun activation and AP-1-dependent transcription. [START_REF] Bitomsky | Transformation suppressor protein Pdcd4 interferes with JNK-mediated phosphorylation of c-Jun and recruitment of the coactivator p300 by c-Jun[END_REF][START_REF] Yang | Tumorigenesis suppressor Pdcd4 down-regulates mitogenactivated protein kinase kinase kinase kinase 1 expression to suppress colon carcinoma cell invasion[END_REF] Recently, we showed that Pdcd4 is post-transcriptionally inhibited by miR-21.

[20] Pdcd4 downregulation in lung and colorectal cancers has been associated with poor patient prognosis. [START_REF] Chen | Loss of PDCD4 expression in human lung cancer correlates with tumour progression and prognosis[END_REF][START_REF] Mudduluru | Loss of programmed cell death 4 expression marks adenoma-carcinoma transition, correlates inversely with[END_REF] Ras-induced AP-1 activity enhanced miR-21 expression and downregulated Pdcd4 by an auto-regulatory loop mechanism. [START_REF] Talotta | An autoregulatory loop mediated by miR-21 and PDCD4 controls the AP-1 activity in RAS transformation[END_REF] Based on these results, we hypothesized that curcumin might inhibit miR-21 expression by downregulating AP-1. Consistent with this, curcumin treatment increased Pdcd4 expression and inhibited AP-1 in our study, leading to a hypothetical model of interactions as depicted in Fig 6c . Our findings suggest that curcumininduced tumor suppression, and inhibition of migration, invasion and in vivo metastasis, might in part be mediated by miR-21-triggered, Pdcd4-dependent mechanisms [20][START_REF] Si | miR-21-mediated tumor growth[END_REF][START_REF] Zhu | MicroRNA-21 targets tumor suppressor genes in invasion and metastasis[END_REF][START_REF] Meng | MicroRNA-21 regulates expression of the PTEN tumor suppressor gene in human hepatocellular cancer[END_REF]. Additionally, we found that curcumin inhibited the cell cycle in G2/M phase, which is in line with earlier findings. [START_REF] Chen | Curcumin inhibits lung cancer cell invasion and metastasis through the tumor suppressor HLJ1[END_REF]52,53] This again could in part be mediated by miR-21-targeted cell cycle regulators. [START_REF] Selcuklu | miR-21 as a key regulator of oncogenic processes[END_REF][START_REF] Chan | MicroRNA-21 is an antiapoptotic factor in human glioblastoma cells[END_REF] However, our present findings certainly cannot exclude other important mechanisms mediated by curcumin in the inhibition of miR-21-regulation andinduced cancer progression (Fig 6c). [START_REF] Kunnumakkara | Curcumin inhibits proliferation, invasion, angiogenesis and metastasis of different cancers through interaction with multiple cell signaling proteins[END_REF][START_REF] Srivastava | Linkage of curcumin-induced cell cycle arrest and apoptosis by cyclin-dependent kinase inhibitor p21(/WAF1/CIP1)[END_REF][START_REF] Thangapazham | Multiple molecular targets in cancer chemoprevention by curcumin[END_REF][START_REF] Kuttan | The molecular targets and therapeutics of curcumin in health and therapeutics of curcumin in health and disease[END_REF][START_REF] Menon | Anti-metastatic activity of curcumin and catechin[END_REF][START_REF] Beevers | Curcumin inhibits the mammalian target of rapamycin-mediated signaling pathways in cancer cells[END_REF][START_REF] Aoki | Evidence that curcumin suppresses the growth of malignant gliomas in vitro and in vivo through induction of autophagy: role of Akt and extracellular signal-regulated kinase signaling pathways[END_REF][START_REF] Chen | Curcumin inhibits lung cancer cell invasion and metastasis through the tumor suppressor HLJ1[END_REF][START_REF] Cheng | Phase I clinical trial of curcumin, a chemopreventive agent, in patients with high-risk or premalignant lesions[END_REF][START_REF] Vogelstein | Cancer genes and the pathways they control[END_REF]35] Taken together, our results suggest that curcumin is an inhibitor of miR-21 and downregulates miR-21 expression by inhibiting AP-1 in colorectal cancer. Curcumin also inhibits in vivo tumor growth, invasion and distant metastasis in colorectal cancer. Additionally, curcumin treatment induces tumor suppressor Pdcd4 expression. Our data add to the understanding of the anti-tumorigenic activities of curcumin and the regulatory mechanisms of miR-21 that function in cancer progression. Our findings also explain a possible mechanism of Pdcd4mediated tumor suppression induced by curcumin treatment. Absorbance was measured at 490 nm, and the percentage of proliferating cells calculated compared to DMSO. b,c) 1 g of the 1.0 kb promoter construct showing maximum activity was transfected along with Renilla into Rko and HCT116 cells. After 12 hours, cells were treated with increasing concentrations of curcumin (5 M to 30 M) for 24 hours. For mutational analysis, 1 g of wild type/mutant construct along with Renilla was transfected into Rko or HCT116 cells. After 12 hours, Rko and HCT116 cells were pretreated in the respective wells for 45 min with curcumin (10 M and 16 M respectively) and stimulated with PMA (100 nM) in the respective wells for 24 hours. The firefly luciferase activity was normalized with Renilla luciferase activity. The data are presented as the mean (±S.D). d) The in vivo association of p-c-Jun and c-Fos with the pri-miR-21 promoter was evaluated with a ChIP assay in Rko cells after 24 hours of DMSO, curcumin, or curcumin with PMA treatment. Immunoprecipitated DNA with the specific antibody was amplified by real time PCR (Syber green) using two sets of primers (First set of primers; region I (-204/+60); Second set of primers; region II (-783/-627)). e, f) Rko and HCT116 cells were plated and pre-treated with curcumin (10 M and 16 M respectively) before PMA stimulation. After 15 min or 24h, cells were lysed and Western blot analysis was performed.

Fig 3 Curcumin inhibits miR-21 expression in vitro

Rko and HCT116 cells were treated with curcumin for 24 hours with increasing concentrations. a, c) pre-miR-21 and mature miR-21 expression was significantly reduced with increasing curcumin concentration. * p 0.05. b, d) PDCD4 protein levels were increased with increasing concentrations of curcumin treatment.

Fig 4 Curcumin inhibits the cell cycle, migration and invasion

a,b) Curcumin arrests cells in the G2/M phase. Rko and HCT116 were pretreated for 24 hours and cell cycle analysis was performed. c, d) Migration and invasion assays with curcumin treatment in Rko and HCT116 cells. After 24 hours of curcumin treatment, cells were plated on Boyden chambers with matrigel (10g/well) for invasion and without matrigel for migration assays. Cells were collected after 13h from the top, and migrated/invaded cells were collected from the bottom of the chambers, and counted using the ATP-luminescence-based motility-invasion assay. Mock treated cells served as a control. The experiment was performed three times independently, with triplicates each time. Data represents the average (±S.D.) of one of the three independent experiments.* Statistically significant changes. p<0.05. 6 6 Rko or HCT116 cells were inoculated on the upper chorioallantoic membrane (CAM) of chicken eggs (n=5). Cells were pretreated with DMSO or curcumin for primary tumor growth, and on the second day treated again with the respective concentration on the upper CAM. For metastasis assays, embryos were intravenously injected with DMSO, or curcumin, on 12 th and 14 th day. On the 17 th day, the embryos were sacrificed and either tumor weights were measured, or DNA of the liver and lungs was extracted a, c) Average of tumor weights from DMSO or curcumin-treated cells grown in chicken embryos. b, d) Genomic DNA was analysed by Real-Time Alu-PCR to determine the number of metastasized Rko and HCT116 cells in liver and lungs after DMSO or curcumin treatment. The individual cell number per egg is given in the box. p values were calculated against the average of curcumin-and DMSO-treated/injected samples. * p0.05.

Fig 5 Curcumin reduces tumor growth and metastasis in vivo 2x10

Fig 6 Curcumin inhibits miR-21 expression in vivo (CAM tumors)

Curcumin inhibits miR-21 expression in resected tumors from chicken embryos. a, b) Relative miR-21 expression is represented in a box plot. miR-21 expression was significantly reduced in the resected curcumin-treated tumors in both cell lines (Rko: p=0.00006; HCT116: p=0.0035). c) Scheme of functional interactions between curcumin, AP-1 and miR-21 regulated genes.

  , 2004 was observed (data not shown). Furthermore, RT-PCR performed with the specific primers binding to TMEM-49 intron 10 (pri-miR-21 promoter) and exon 12 in a panel of cancer cells (Supplementary Fig 2a) resulted in a 477 bp fragment (Fig 1b). These observations suggest a splicing mechanism of intron 11 of TMEM-49 from the pri-miR-21 promoter, which is a common mechanism of classical genes (Supplementary Fig 3b), and two novel major TSS at 35 bp and at 28 bp upstream to the previously reported TSS by Fujita et al., 2008, for the pri-miR-21 promoter.

  Fig 2c). ChIP analysis was performed to determine the in vivo relevance of AP-1 transcription factor binding to the promoter for curcumin treatment, PMA-stimulation, and the combination of both. PMA-stimulation increased the binding of pc-Jun/AP-1 and c-Fos/AP-1 to the pri-miR-21 promoter (Fig 1d). Under similar conditions, curcumin decreased the binding of p-c-Jun and c-Fos. Additionally, 1 hour pre-treatment with curcumin followed with PMA stimulation could not increase the binding of p-c-Jun and c-Fos to the promoter (Fig 2d). Similar results were observed in Western blot analysis; curcumin inhibited c-Jun activation in terms of phosphorylation (Fig 2e,f; Supplementary Fig 4c). These results suggest that curcumin inhibits pri-miR-21 transcriptional regulation, and also its PMA induction, through AP-1 family members.

  and correspondingly, the TSS reported by Cai et al., and Loffler et al., were located within TMEM-49 intron 11. In our study, the construct which included the Cai-TSS was not able to induce promoter activity as opposed to the TSS by Fujita el al., and the novel TSS presented by us, suggesting that the TSS by Cai et al. is not essential for the pri-miR-21 promoter in colorectal cancer cells. Our findings of the pri-miR-21 TSS within intron 10 support the findings of Fujita S et al. in colorectal cancer.

  Ozsolak et al., 2008[43] identified and assayed the transcriptional activity of 4 regions upstream of pri-miR-21. Two of them are very similar to the promoters reported by Cai et al., and Fujita et al. They observed a superior induction of promoter activity with the region identified by Fujita et al, and also found that the promoter reported by Cai et al., is more active in HeLa cells, however not active in melanoma cells. These observations support the notion that there may be cell lineage and/or tumor type specificity for the usage of the respective TSS and the transcriptional regulation of pri-miR-21.

  Figure legendsFig 1 RACE analysis to determine the miR-21 transcription start sites, and promoter characterization a) Total RNA from Rko and normal human placenta was used for 5´ RACE PCR analysis. Two major bands, one at a1200 bp (TMEM-49) and a second one at a500 bp (pri-miR-21) were detected. b) RT-PCR was performed with a panel of cancer cells to confirm the splicing of introns between TMEM-19 Exon 11 and 12 and the transcription start site. c) Schematic representation of a series of deletion constructs of the promoter and reporter assay showing pri-miR-21 promoter activity. 1 Pg of pri-miR-21-luciferase constructs, or pGL3-basic vector together with 25 ng of Renilla luciferase plasmid were transiently transfected into Rko cells. After 12 hours of transfection, cells were stimulated with 100 nM PMA for 24 hours. The firefly luciferase activity was normalized with Renilla luciferase activity. The data are presented as the mean (±S.D.) of three independent experiments performed in quadruplicates. d) The in vivo association of p-c-Jun and c-Fos activating the pri-miR-21 promoter was evaluated with ChIP assay in Rko cells with and without PMA stimulation. Immunoprecipitated DNA with the specific antibody was amplified by real time PCR (Syber green) using two sets of primers (First set of primers; region I (-204/+60); Second set of primers; region II (-783/-627)).

Fig 2

 2 Fig 2 Curcumin inhibits AP-1 binding to miR-21 and pri-miR-21 promoter activity a) MTT assays were performed with increasing concentrations of curcumin for 48 hours.Absorbance was measured at 490 nm, and the percentage of proliferating cells calculated compared to DMSO. b,c) 1 g of the 1.0 kb promoter construct showing maximum activity was transfected along with Renilla into Rko and HCT116 cells. After 12 hours, cells were treated with increasing concentrations of curcumin (5 M to 30 M) for 24 hours. For mutational analysis, 1 g of wild type/mutant construct along with Renilla was transfected into Rko or HCT116 cells. After 12 hours, Rko and HCT116 cells were pretreated in the respective wells for 45 min with curcumin (10 M and 16 M respectively) and stimulated with PMA (100 nM) in the respective wells for 24 hours. The firefly luciferase activity was normalized with Renilla luciferase activity. The data are presented as the mean (±S.D). d) The in vivo association of p-c-Jun and c-Fos with the pri-miR-21 promoter was evaluated with a ChIP assay in Rko cells after 24 hours of DMSO, curcumin, or curcumin with PMA treatment. Immunoprecipitated DNA with the specific antibody was amplified by real time PCR (Syber green) using two sets of primers (First set of primers; region I (-204/+60); Second set of primers; region II (-783/-627)). e, f) Rko and HCT116 cells were plated and pre-treated with curcumin (10 M and 16 M respectively) before PMA stimulation. After 15 min or 24h, cells were lysed and Western blot analysis was performed.

1 : 7 ~2 49 : 49 :

 174949 Fig 1 b) a)

  Fig 3

  Fig 4

  Fig 5

  Fig 6 b) a)

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.© 2010 The Authors Journal compilation © 2010 Portland Press Limited

Acknowledgements

HA was supported by the Alfried Krupp von Bohlen und Halbach Foundation (Award for Young Full Professors), Essen, Hella-Bühler-Foundation, Heidelberg, Dr. Ingrid zu Solms Foundation, Frankfurt/Main, the Hector Foundation, Weinheim, Germany, the FRONTIER Excellence Initiative of the University of Heidelberg, the BMBF, Germany, and the Walter Schulz Foundation, Munich, Germany. The authors thank Erika Hillerich and Paolo Ceppi for excellent help and critical appraisal of the manuscript.

Authors contributions

GM, JNG, SM, IAA, KR carried out experiments; collection and/or assembly of data by GM, JNG; data analysis and interpretation by GM, JNG, SM; Manuscript writing by GM, LDN, HA; Financial support by HA; Final approval of manuscript by all authors.


Prof. Dr Norbert F Schrage
email: schrage@acto.de

Markus Frentz

Martin Reim

Changing the composition of buffered eye drops prevents undesired side effects

Keywords: Cornea, calcification, phosphate, side effects, citrate buffer, hyaluronic acid, healing

Purpose:

The Ex Vivo Eye Irritation Test (EVEIT) is used to analyse the clinical observations of corneal calcification attributed to the presence of phosphate within applied eye drops used in treating glaucoma, Still-Chauffard syndrome, ocular burns and dry eyes.

Method:

Live corneas from abattoir rabbit eyes were cultured in order to study epithelial healing following mechanical abrasion of the corneal surface combined with repeated exposure to various eye drops.

Results:

Obvious corneal calcification of the wound area along with a complete epithelial healing covering the calcified area was observed following exposure to phosphate hyaluronate eye drops. Epithelial healing without calcification was achieved using citrate hyaluronate eye drops.

Conclusion:

Clinical observations show that topical use of artificial tears containing phosphate on injured eyes may lead to sight-threatening corneal complications. Simulation of such treatment conditions by the EVEIT convincingly demonstrate that changes in the composition of the pharmaceutically used treatments can prevent this undesired side effect.

Although considerable healing was achieved during the repeated application of eye drops, using either phosphate or citrate buffered, only the drops containing citrate did not develop corneal calcification on the eye. We therefore recommend discontinuing the use of phosphate buffered eye drops, or other topically applied solutions, to avoid further injury to the patient.

Introduction:

It is well known that the phosphate concentration is very low in the stroma of human corneas [START_REF] Langefeld | The corneal stroma, an inhomogenous structure[END_REF]. This is also true for the stroma of rabbit corneas [START_REF] Von Fischern | Changes in the mineral composition of the rabbit cornea after alkali burns[END_REF], making them an excellent animal model for analysing the effects of ophthalmologic treatments on corneas

The development of calcified patches on corneas is usually slow under physiological conditions, sometimes lasting months or years as been reported by Huige et al. for phosphate containing steroids [START_REF] Huige | Deposits in the superficial corneal stroma after combined topical corticosteroid and betablocking medication[END_REF]. Nevertheless, Bernauer et al. [START_REF] Bernauer | Corneal calcification following intensified treatment with sodium hyaluronate artificial tears[END_REF] described the development of calcification in conjunction with corneal wounds which have been treated with phosphate buffered artificial tears in conjunction with corneal wounds. The same effects were observed previously [START_REF] Schrage | Phosphate buffer in alkali eye burns as an inducer of experimental corneal calcification[END_REF] during the treatment of corneal burns with phosphate containing drugs [START_REF] Schrage | Relationship of eye burns with calcifications of the cornea? Graefe's Archive for[END_REF] and in an experimental eye burn model on rabbit corneas treated with phosphate buffer rinsing. Recent reports [START_REF] Bernauer | Corneal calcification following intensified treatment with sodium hyaluronate artificial tears[END_REF][START_REF] Bernauer | Phosphate concentration in artificial tears[END_REF] from clinical practice concerning calcified human corneas has finally led to considerable changes in the formulation of artificial tears [START_REF] Hylo-Comod | citrate buffered hyaluronate artificial tears. Medical information[END_REF] by replacing phosphate with citrate in treatment buffers.

In this study we aimed to evaluate the presence or absence of corneal calcification after clinical use of such eye drops by taking advantage of the EVEIT approach. In studying the morphological changes in the cornea during the wound healing process, determining residual clarity and the appearance of calcification or other types of turbidity is a simple but convincing approach in the evaluation and development of new ophthalmologic treatments. By exposing ex vivo cultured corneas to pharmaceutical preparations we have shown that removing phosphate from these solutions prevents the calcification found with use of phosphate containing solutions.

Materials and Methods:

EVEIT

The Ex Vivo Eye Irritation Test (EVEIT) is a non-animal-consuming, self-healing system that uses living corneal tissue. This procedure uses corneas taken from animals which are otherwise slaughtered for food preparation. The heads are decapitated and the eyes are treated with Polyspectran ® drops (Alcon Pharma, Freiburg, Germany) and sealed with plaster. The heads are immediately transported at 4°C and prepared for experimentation within no more than 8 hours.

After re-opening the eye lids for preparation, the corneas were excised with a 12 mm trephine and adhering tissues were gently removed. The corneas were placed in special culture chambers (ACTO e.V., Aachen, Germany). The chambers were gently filled with serum-free minimal essential medium (MEM) (Cat. No. T031-05, Biochrom AG, Berlin, Germany, containing 200 mg CaCl 2 and 140 mg NaH 2 PO 4 •2H 2 O in its Earle's salt composition), supplemented with Piperacillin (2 mg/ml; Ratiopharm GmbH, Ulm, Germany), Amikacin (0.2 mg/ml; Fresenius Kabi Deutschland GmbH, Bad Homburg vor der Höhe, Germany), and Nystatin (400 U/ml; Valeant Pharmaceuticals Germany GmbH, Eschborn, Germany). The medium was continuously replenished by a micropump with an entrance pH of 7.4 ± 0.2 and a flow rate of 6μl/min. The culture chambers were held at 32°C in normal air without supplementary CO 2 and 100% relative humidity for 24 hours before the explanted corneas were used for further experiments.

Examination techniques

The epithelial surface was microscopically examined daily for the duration of the experiment. Surface staining was performed with fluoresceine solution (1.7 mg/ml fluoresceine; Sigma-Aldrich, St. Louis, MO, USA in 0.9 % saline). The corneas were briefly flushed with isotonic Ringer's solution (DeltaSelect GmbH, Pfullingen, Germany) to remove excess fluoresceine prior to being photographed. Samples of MEM from the artificial anterior chamber outflow were taken according to our protocol and analysed for glucose, lactate and pH (Bayer Automatic Analyser; Rapid Lab 860; Siemens Diagnostics, Fernwald, Germany) to monitor the corneal metabolism.

Healing measurements and corneal calcification

After one day of stabilization in the EVEIT culturing system and establishment of the epithelial integrity by fluoresceine staining of the surface, we applied four small abrasions (3-6 mm 2 ) with a small dental drill (Arkansasschleifer 638XF, Meisinger, Stuttgart, Germany). All corneas were then cultured and treated with either eye drops or MEM (serving as control) for the following 3 days and all defects were monitored daily with fluoresceine staining. The green fluorescence (Fig. 1) indicates the areas of epithelial defects. The areas were photographed and measured by means of Diskus ® software (Hilgers, Königswinter, Germany). Corneal calcifications were visually defined as distinct white, opaque structures and interpreted as either present or absent. To substantiate the asserted calcification by histological examination, all corneas were snap frozen at the end of the experimental time (4 days). Cryosections were prepared and stained according to von Kossa to detect calcium deposits within the exposed corneas. Here, a grading scheme to quantify the calcium deposits within the cornea was applied ranging from 0 (no staining) to 4 (complete staining of epithelium and upper stroma).

Application of test substances

We used an artificial tear replacement solution adjusted to this citrate content of 14.581mmol/l Ca 2+ in 0.9% saline solution (Delta Select, Germany). This solution was applied once per hour onto the corneas, providing 11.7µg Ca 2+ .

During the experiment we compared HYLO-COMOD ® and HYLO-CARE ® both of which contain a phosphate buffer and are longer commercially available, with HYLO-LASOP ® , which now contains citrate buffer (all Ursapharm GmbH, Saarbruecken, Germany).

Each one of these unpreserved hyaluronate drops were applied, along with the artificial tear replacement by using two separate dropping devices, exactly over the apex of the cornea. Controls were represented by corneas treated with MEM and artificial tear replacement in the same manner.

A 20 μl drop of each solution was applied hourly for 3 days, with a time difference of 30 minutes between applications of the test substance and the artificial tears. A soft-tipped cannula, applying continuous suction, was placed on the lower side of the cornea in culture to remove excess fluid.

Osmometry

Osmolarities of all eye drops were measured with the Osmomat® 030 (Gonotec, Berlin, Germany). The applied substances were in the range of 260-390 mOsmol/kg (hyaluronate phosphate eye drops 262 ± 1.9 mOsmol/kg; hyaluronate citrate 272 ± 1.5 mOsmol/kg; MEM 383 ± 3.3 mOsmol/kg; artificial tears containing CaCl 2 317 ± 1.3 mOsmol/kg).

Results:

All 10 corneas which were treated with hyaluronate phosphate and artificial tears showed distinct white opaque spots at all 40 abraded areas, suggesting strong corneal calcifications. Coincidently, as shown in figure 2a, the calcified corneas showed significant closure of the epithelial defects after 3 days (as determined by negative fluoresceine staining; Fig. 2a). Histological analysis of these corneas via von Kossa staining confirmed the visual appearances and highlighted the dense calcifications especially at the location of epithelial scrapings (Fig. 2b).

However, the five corneas treated with hyaluronate citrate and artificial tears showed a completely clear, smooth surface devoid of any visual calcification after 3 days of treatment. A slight positive fluorescein staining of the surface was still detectable at the end of the experiment, which indicates that some epithelial damage remained (Fig. 2 c).

None of the corneas exposed to these drops showed a positive result for the von Kossa stain (Fig. 2 d).

Throughout the 3 days of culture, all 6 controls (24 drops MEM/day) showed considerable healing down to approximately half of the surface area of the initial abrasions (Fig. 2 e) and no calcification was visually apparent.

Although the MEM contains a small amount of phosphate (0.9mmol/l), calcification is therefore possible however was not detectable in our experimental conditions. No calcium deposits in the corneal stroma were visually observed, as compared to that seen in the cases of phosphate buffered eye drop (50.9mmol/l [START_REF] Bernauer | Corneal calcification following intensified treatment with sodium hyaluronate artificial tears[END_REF]) treatment, only the histological analysis showed trace evidence of calcium deposits or calcium salts (Fig. 2 f). The Fisher's test revealed a highly significant correlation of the achieved corneal calcification to the presence of phosphate in the used eye drops (p<0.001).

However, histological analysis of the MEM treated corneas demonstrated very slight amounts of surplus calcium.

During the experimental time the measured pH values in all groups always stayed in the defined range of 7.4 ± 0.2. Monitoring the corneal metabolism according to our protocol by measuring the lactate production in the outflow medium of chamber showed that all corneas in each group exceeded the determined lowest value of 1.0 mMol/l.

Discussion:

There is no doubt that mixtures of phosphate and calcium ions immediately form calcium phosphate or calcium apatite. Both compounds have a very low water solubility which decreases with increasing pH or temperature. Stanley [START_REF] Stanley | Water permeability of the human cornea[END_REF], Leopold [START_REF] Leopold | Chemical injuries of the cornea[END_REF] and Caldeira [START_REF] Caldeira | Conjunctival and corneal changes in renal failure. Influence of renal transplantation[END_REF] published the calcium content in tears to be in the order of 0.0211 to 0.041µg/µl with a basic secretion rate of 120 to 240µl/h [START_REF] Maurice | The tonicity of an eye drop and its dilution by tears[END_REF]: this results in a calcium introduction onto the corneal surface in the range of 2.53 to 9.84µg/h for the healthy eye. As the tear secretion rate is upregulated during eye injury as simulated here, values above this range are expected.

A limitation to the EVEIT experimental system is an obvious absence of natural tear production which provides the corneal surface with calcium. This absence would undermine the natural emergence of possible calcified spots while using phosphate buffered eye drops. Additionally, the citrate buffer in the new formulated hyaluronate drops can withdraw calcium ions from the corneal surface thereby affecting epithelial healing. To overcome these obstacles we introduced artificial tears containing a physiological amount of calcium.

The capability of the EVEIT in effectively and reproducibly predicting the potential toxic effects of topical application on the eye has been demonstrated in earlier experiments [START_REF] Frentz | Repeated exposure to benzalkonium chloride in the Ex Vivo Eye Irritation Test (EVEIT): observation of isolated corneal damage and healing[END_REF][START_REF] Spöler | Analysis of hydrofluoric acid penetration and decontamination of the eye by means of time-resolved optical coherence tomography[END_REF][START_REF] Spöler | Dynamic analysis of chemical eye burns using high-resolution optical coherence tomography[END_REF] and we here could exemplify the practicability of the EVEIT in the evaluation of pharmaceutical products. This study identified that the addition of phosphate in eye drops is an important factor in inducing calcification of the corneal surface following injury. We were able to support experimentally the clinical findings of Bernauer et al. [START_REF] Bernauer | Corneal calcification following intensified treatment with sodium hyaluronate artificial tears[END_REF][START_REF] Bernauer | Phosphate concentration in artificial tears[END_REF] who observed this in cases of keratoconus [START_REF] Lema | Inflammatory molecules in the tears of patients with keratoconus[END_REF], dry eye [START_REF] Luo | Experimental dry eye stimulates production of inflammatory cytokines and MMP-9 and activates MAPK signaling pathways on the ocular surface[END_REF] and vernal conjunctivitis [START_REF] Ebihara | Tear chymase in vernal keratoconjunctivitis[END_REF] and demonstrate that excessive use of phosphate containing drugs is associated with corneal calcification. These results also confirm that calcified deep stromal tissue is related to early changes in the mineral composition of the cornea. This has similarly been shown for eye burns [START_REF] Von Fischern | Changes in the mineral composition of the rabbit cornea after alkali burns[END_REF][START_REF] Schrage | Relationship of eye burns with calcifications of the cornea? Graefe's Archive for[END_REF] due elevated phosphate concentrations in combination with the normal tear calcium content [START_REF] Leopold | Chemical injuries of the cornea[END_REF] leading to undesired side effects. We have demonstrated that using a citrate based buffer instead of phosphate based in eye drop formulations to be a better and safe choice of therapy. Even with high dropping rates it is unlikely that the citrate buffer chelating capacity will exceed the calcium supply by normal [START_REF] Caldeira | Conjunctival and corneal changes in renal failure. Influence of renal transplantation[END_REF][START_REF] Maurice | The tonicity of an eye drop and its dilution by tears[END_REF] or elevated tear secretion especially in dry eye syndromes or superficial corneal damages the artificial tears most likely will be used.

Additionally we observed distinct stages of corneal healing following the various types of repeated applications. These results led us to the assumption that hyaluronate eye drops improved epithelial healing after deliberate damages, even in large areas of corneal damages such as used in these particular experiments.

With these available ophthalmologic lubricants relevant epithelial defects such as those caused by severe dry eyes, mechanical scraping, photorefractive and phototherapeutic excimer ablations, corneal ulcers and eye burns can also be treated successfully without any risk of calcification.

Figures:

Fig. showed slightly elevated levels of the targeted ion at the site of injury.

Tables:

Tab.1: Summary of all performed experiments

1 :Fig. 2 :

 12 Fig.1: Fluoresceine stained cornea with measurements of injured area [mm 2 ]

Acknowledgements:

This work was partially supported by Ursapharm Arzneimittel GmbH & Co. KG, Saarbrücken, Germany, who supplied the hyaluronate eye drops containing citrate. Staff costs, equipment, and other materials were financed by ACTO e.V., and by the Department of Ophthalmology, University Hospital, Aachen, Germany. Ursapharm GmbH had no influence on the proposed working programme, or on the results, data interpretation or text presented here.

We also thank Sara D. Sackett and Felix Spöler for their selfless help in revising this manuscript.

Licence for Publication:

The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for Government employees) on a worldwide basis to the BMJ Publishing Group Ltd and its Licensees to permit this article (if accepted) to be published in BJO editions and any other BMJPGL products to exploit all subsidiary rights, as set out in our licence (http://group.bmj.com/products/journals/instructions-for-authors/licence-forms/).

Competing Interest:

None to declare


François Dubois

Abdelkader Saïdi

Unconditionnally stable scheme for Riccati equation

Keywords: control problems, ordinary differential equations, stability AMS classification: 34H05, 49K15, 65L20, 93C15

In this contribution we present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.

1) Introduction

We study the optimal control of a differential linear system

(1)

dy dt = A y + B v ,
where the state variable y(t) belongs to IR n and the control function v(•) takes its values in IR m , with n and m beeing given integers. Matrix A is composed by n lines and n columns and matrix B contains n lines and m columns. Both matrices A and B are independent of time. With the ordinary differential equation ( 1) is associated an initial condition

(2) y(0) = y 0 with y 0 given in IR n and the solution of system (1)(2) is parametrized by the function v(•):

The control problem consists of finding the minimum u(•) of some quadratic functional J(•):

(3)

J(u(•)) ≤ J(v(•)), ∀ v(•) .
The functional J(•) depends on the control variable function v(•), is defined by the horizon T > 0, the symmetric semi-definite positive n by n constant matrix Q and the symmetric definite positive m by m constant matrix R. We set classically :

(4)

J(v(•)) = 1 2 T 0
(Qy(t), y(t)) dt + 1 2 T 0 (Rv(t), v(t)) dt .

• Problem (1)(2)(3)(4) is a classical linear quadratic mathematical modelling of dynamical systems in automatics (see e.g. Lewis [Le86]). When the control function v(•) is supposed to be square integrable (v(•)

∈ L 2 (]0; T [, IR m )) then the control problem (1)(2)(3)(4) has a unique solution u(•) ∈ L 2 (]0; T [, IR m ) (see for instance Lions [Li68]).
When there is no constraint on the control variable the minimum u(•) of the functional J(v) is characterized by the condition:

(5) dJ(u)

• w = 0 , ∀ w ∈ L 2 (]0, T [, IR m ) ,
which is not obvious to compute directly.

• When we introduce the differential equation (1) as a constraint between y(•) and v(•), the associated Lagrange multiplyer p(•) is a function of time and is classically named the adjoint variable. Research of a minimum for J(•) (condition (5)) can be rewritten in the form of research of a saddle point and the evolution equation for the adjoint variable is classical (see e.g. Lewis [START_REF] Lewis | Optimal Control[END_REF]):

(6) dp dt + A t p + Q y = 0 ,
with a final condition at t = T , (7) p(T ) = 0 and the optimal control in terms of the adjoint state p(•) takes the form:

(8) R u(t) + B t p(t) = 0 .
• We observe that the differential system (1)(6) together with the initial condition (2) and the final condition (7) is coupled through the optimality condition (8). In practice, we need a linear feedback function of the state variable y(t) instead of the adjoint variable p(t). Because adjoint state p(•) depends linearily on state variable y(•) we can set:

p(t) = X(T -t) • y(t) , 0 ≤ t ≤ T ,
with a symmetric n by n matrix X(•) which is positive definite. The final condition (7) is realized for each value y(T ), then we have the following condition:

(9) X(0) = 0 .

We set K = BR -1 B t ; we remark that matrix K is symmetric positive definite, we replace the control u(t) by its value obtained in relation (8) and we deduce after elementary algebra the evolution equation for the transition matrix X(•):

(10) dX dt -XA + A t X + X K X -Q = 0 ,
which defines the Riccati equation associated with the control problem (1)(2)(3)(4).

• In this paper we study the numerical approximation of differential system (9)(10).

Recall that the given matrices Q and K are n × n symmetric matrices, with Q semidefinite positive and K positive definite; the matrix A is an n by n matrix without any other condition and the unknown matrix X(t) is symmetric. We have the following property (see e.g. Lewis [Le86]).

Proposition 1. The solution of Riccati equation is positive definite. Let K, Q, A be given n × n matrices with K, Q symmetric, Q positive and K definite positive. Let X(•) be the solution of the Riccati differential equation (10) with initial condition (9). Then X(t) is well defined for any t ≥ 0, is symmetric and for each t > 0, X(t) is definite positive and tends to a definite positive matrix X ∞ as t tends to infinity:

X(t) -→ X ∞ if t -→ ∞. Matrix X ∞
is the unique positive symmetric matrix which is solution of the so-called algebraic Riccati equation:

-(XA + A t X) + XKX -Q = 0 .
• As a consequence of this proposition it is usefull to simplify the feedback command law (8) by the associated limit command obtained by taking t -→ ∞, that is:

(11) v(t) = -R -1 B t X ∞ y(t) ,
and the differential system (1) (11) is stable (see e.g. [START_REF] Lewis | Optimal Control[END_REF]). The practical computation of matrix X ∞ by direct methods is not obvious and we refer e.g. to Laub [START_REF] Laub | A Schur Method for Solving Algebraic Riccati Equations[END_REF]. If we wish to compute directly a numerical solution of instationnary Riccati equation (10) classical methods for ordinary differential equations like e.g. the forward Euler method

1 ∆t (X j+1 -X j ) + X j K X j -(A t X j + X j A) -Q = 0 ,
or Runge Kutta method fail to maintain positivity of the iterate X j+1 at the order (j + 1):

(12) (X j+1 x , x) > 0, ∀ x ∈ IR n , x = 0 ,
if X j is positive definite and if time step ∆t > 0 is not small enough (see e.g. Dieci and Eirola [START_REF] Dieci | Preserving monotonicity in the numerical solution of Riccati differential equations[END_REF]). Morever, there is to our best knowledge no simple way to determine a priori if time step ∆t > 0 is compatible or not with condition (12).

• In the following, we propose a method for numerical integration of Riccati equation (10) which maintains condition (12) for each time step ∆t > 0. We present in second section the simple case of scalar Riccati equation and present the numerical scheme and its principal properties of the general case in section 3. We describe several numerical experiments in section 4.

2) Scalar Riccati equation

• When the unknown is a scalar variable, we write Riccati equation in the following form:

(13) dx dt + k x 2 -2 a x -q = 0 , with (14) k > 0, q ≥ 0 ,
and an initial condition:

(15)

x(0) = d, d ≥ 0 .
We approach the ordinary differential equation (13) with a finite difference scheme of the type proposed by Baraille [Ba91] for hypersonic chemical kinetics and independently with the "family method" proposed by Cariolle [START_REF] Cariolle | Modèle unidimentionnel de chimie de l'ozone, Internal note[END_REF] and studied by Miellou [START_REF] Miellou | Existence globale pour une classe de systèmes paraboliques semilinéaires modélisant le problème de la stratosphère : la méthode de la fonction agrégée[END_REF]. We suppose that time step ∆t is strictly positive. The idea is to write the approximation x j+1 at time step (j + 1)∆t as a rational fraction of x j with positive coefficients. We decompose first the real number a into positive and negative parts : a = a +a -; a + = max(0; a) ≥ 0, a -= max(0; -a) ≥ 0, a + a -= 0 and factorize the product x 2 into the very simple form:

x 2 j+1/2 = x j x j+1 . Definition 1.
Numerical scheme in the scalar case. For resolution of the scalar differential equation (13), we define our numerical scheme by the following relation:

(16)

x j+1x j ∆t + k x j x j+1 -2 a + x j + 2 a -x j+1q = 0 .

• The scheme ( 16) is implicit because some linear equation has to be solved to compute x j+1 when x j is supposed to be given. In the case of our scheme this equation is linear and the solution x j+1 is obtained from scheme (16) by the homographic relation:

(17)

x j+1 = 1 + 2a + ∆t x j + q ∆t k ∆t x j + (1 + 2a -∆t) .
Proposition 2. Algebraic properties of the scalar homographic scheme. Let (x j ) j∈IN be the sequence defined by initial condition : x 0 = x(0) = d and recurrence relation (17). Then sequence (x j ) j∈IN is globally defined and remains positive for each time step: x j > 0, ∀j ∈ IN, ∀∆t > 0. If ∆t > 0 is chosen such that:

(18) 1 + 2|a|∆tk q ∆t 2 = 0 , then (x j ) j∈IN converges towards the positive solution x * of the "algebraic Riccati equation" k x 2 -2 a xq = 0 and (19)

x * = 1 k a + a 2 + kq .

• In the exceptional case where ∆t > 0 is chosen such that (18) is not satisfied, then the sequence (x j ) j∈IN is equal to the constant 1 + 2 a + ∆t k ∆t for j ≥ 1 and the scheme (17) cannot be used for the approximation of Riccati equation (13).

Theorem 1.

Convergence of the scalar scheme. We suppose that the data k, a, q of Riccati equation satisfy ( 14) and ( 18) and that the datum d of condition ( 15) is relatively closed to x * , i.e.:

(20) - 1 k τ + η ≤ d -x * ≤ C ,
where C is some given strictly positive constant (C > 0) , x * calculated according to relation (19) is the limit in time of the Riccati equation, τ is defined from data k, a, q by: τ = 1 2 a 2 + kq , and η is some constant chosen such that (21) 0 < η < 1 k τ .

• We denote by x(t; d) the solution of differential equation (13) with initial condition (15). Let (x j (∆t ; d ∆ )) (j∈IN) be the solution of the numerical scheme defined at the relation (17) and let d ∆ be the initial condition:

x 0 (∆t ; d ∆ ) = d ∆ .
We suppose that the numerical initial condition d ∆ > 0 satisfies a condition analogous to (20):

- 1 k τ + η ≤ d ∆ -x * ≤ C ,
with C and η > 0 equal to the constant introduced in (20) and satisfying (21).

• Then the approximated value (x j (∆t ; d ∆ )) j∈IN is arbitrarily closed to the exact value x(j∆t ; d) for each j as ∆t -→ 0 and d ∆ -→ d . More precisely, if a = 0 we have the following estimate for the error at time equal to j∆t :

| x(j∆t ; d) -x j (∆t ; d ∆ ) |≤ A (∆t + | d -d ∆ |), ∀ j ∈ IN , 0 < ∆t ≤ B
with constants A > 0, B > 0 , depending on data k, a, q, η but independent on time step ∆t > 0 and iteration j .

• If a = 0 , the scheme is second order accurate in the following sense:

|x(j∆t; d) -x j (∆t; d ∆ )| ≤ A (∆t 2 + | d -d ∆ |), ∀ j ∈ IN , 0 < ∆t ≤ B
with constants A et B independent on time step ∆t and iteration j.

A direct application of the Lax theorem for numerical scheme associated to ordinary differential equations is not straightforward because both Riccati equation and the numerical scheme are nonlinear. Our proof is detailed in [START_REF] Dubois | Homographic scheme for Riccati equation[END_REF].

3) Matrix Riccati equation

In order to define a numerical scheme to solve the Riccati differential equation ( 10) with initial condition (9) we first introduce a strictly positive real number, which is chosen positive in such a way that the real matrix [µ I -(A + A t )] is definite positive:

(22) 1 2 (µ x , x) -(A x , x) > 0 , ∀ x = 0 .
Then we introduce the definite positive matrix M wich depends on µ and matrix A:

M = 1 2 µ I -A .
The numerical scheme is then defined by analogy with relation (16). We have the following decomposition :

(23)

A = A + -A - with A + = 1 2 µ I, A -= M, µ > 0, M positive definite.
Taking as an explicit part the positive contribution A + of the decomposition (23) of matrix A and in the implicit part the negative contribution A -= M of the decomposition (23), we get (24)

   1 ∆t (X j+1 -X j ) + 1 2 (X j KX j+1 + X j+1 KX j ) + + (M t X j+1 + X j+1 M) = µX j + Q .
The numerical solution given by the scheme X j+1 at time step j + 1 is then defined as a solution of Lyapunov matrix equation with matrix X as unknown:

S t j X + X S j = Y j with (25) S j = 1 2 I + ∆t 2 KX j + ∆t M and (26) Y j = X j + µ ∆t X j + ∆t Q .
We notice that S j is a (non necessarily symmetric) positive matrix and that Y j is a symmetric definite positive matrix if it is the case for X j .

4)

First numerical experiments 4-1 Square root function

• The first example studied is the resolution of the equation :

(29) dX dt + X 2 -Q = 0, X(0) = 0 with n = 2, A = 0, K = I and matrix Q equal to (30) Q = 1 2 1 -1 1 1 1 0 0 100 1 1 -1 1 .
• We have tested our numerical scheme for fixed value ∆t = 1/100 and different values of parameter µ : µ = 0.1, 10 -6 , 10 +6 . For small values of parameter µ, the behaviour of the scheme does not change between µ = 0.1 and µ = 10 -6 . Figures 1 to 4 show the evolution with time of the eigenvalues of matrix X j and the convergence is achieved to the square root of matrix Q. For large value of parameter µ (µ = 10 +6 ), we loose completely consistency of the scheme (see figures 5 and 6).

Figures 1 and2. Square root function test. Two first eigenvalues of numerical solution (µ = 0.1).

Figures 3 and4.

Square root function test. Two first eigenvalues of numerical solution (µ = 10 -6 ).

Figures 5 and6.

Square root function test. Two first eigenvalues of numerical solution (µ = 10 +6 ).

4-2

Harmonic oscillator

• The second exemple is the classical harmonic oscillator. Dynamical system y(t) is governed by the second order differential equation with command v(t) :

(31) d 2 y(t) dt 2 + 2 δ dy(t) dt + ω 2 y(t) = b v(t) .
This equation is written as a first order system of differential equations :

(32) Y = y(t) dy(t) dt , dY dt = 0 1 -ω 2 -2 δ Y (t) + 0 b v(t)
.

In this case, we have tested the stability of the scheme for fixed value of parameter µ (µ = 0.1) and different values of time step ∆t and coefficients of matrix R inside the cost function of relation (4): R = α 0 0 α .

• We have chosen three sets of parameters : α = ∆t = 1/100 (reference experiment, figures 7 and 8), α = 10 -6 , ∆t = 1/100 (very small value for α, figures 9 and 10) and α = 1/100 , ∆t = 100 (too large value for time step, figures 11 and 12). Note that for the last set of parameters, classical explicit schemes fail to give any answer. As in previous test case, we have represented the two eigenvalues of discrete matrix solution X j as time is increasing. On reference experiment (figures 7 and 8), we have convergence of the solution to the solution of algebraic Riccati equation. If control parameter α is chosen too small, the first eigenvalue of Riccati matrix oscillates during the first time steps but reach finally the correct values of limit matrix, the solution of algebraic Riccati equation. If time step is too large, we still have stability but we loose also monotonicity. Nevertheless, convergence is achieved as in previous case. Harmonic oscillator. Two first eigenvalues of numerical solution (µ = 0.1, α = 0.01, ∆t = 100).

5) Conclusion

We have proposed a numerical scheme for the resolution of the matrix Riccati equation. The scheme is implicit, unconditionnaly stable, needs to use only one scalar parameter and to solve a linear system of equations for each time step. This scheme is convergent in the scalar case and has good monotonicity properties in the matrix case. Our first numerical experiments show stability and robustness when various parameters have large variations. Situations where classical explicit schemes fail to give a solution compatible with the property that solution of Riccati equation is a definite positive matrix have been computed. We expect to prove convergence in the matrix case and we will present in [START_REF] Dubois | Homographic scheme for Riccati equation[END_REF] experiments on realistic test models such as a string of vehicles and the discretized wave equation.

Figures 7 and 8 .

 8 Figures 7 and 8. Harmonic oscillator. Two first eigenvalues of numerical solution (µ = 0.1, α = 0.01, ∆t = 0.01).

Figures 9

 9 Figures 9 and 10. Harmonic oscillator. Two first eigenvalues of numerical solution (µ = 0.1, α = 10 -6 , ∆t = 0.01).

Figures 11 and 12

 12 Figures 11 and 12. Harmonic oscillator. Two first eigenvalues of numerical solution (µ = 0.1, α = 0.01, ∆t = 100).

  Figures 11 and 12. Harmonic oscillator. Two first eigenvalues of numerical solution (µ = 0.1, α = 0.01, ∆t = 100).

Acknowledgments

The authors thank Marius Tucsnak for helpfull comments on the first draft of this paper.

Definition 2. Symmetric matrices. Let n be an integer greater or equal to 1. We define by S n (IR), (respectively S + n (IR), S + * n (IR)) the linear space (respectively the closed cone, the open cone) of symmetricmatrices (respectively symmetric positive and symmetric definite positive matrices). The following inclusions S + * n (IR) ⊂ S + n (IR) ⊂ S n (IR) are natural.

Proposition 3. Property of the Lyapunov equation. Let S be a matrix which is not necessary symmetric, such that the associated quadratic form:

S + S t ∈ S + * n (IR) . Then the application ϕ defined by :

is a one to one bijective application on the space S n (IR) of real symmetric matrices of order n. Morever, if matrix ϕ(X) is positive (respectively definite positive) then the matrix X is also positive (respectively definite positive):

if ϕ(X) ∈ S + n (IR) , then X ∈ S + n (IR) .

• The numerical scheme has been written as an equation with unknown X = X j+1 which takes the form: ϕ j (X) = Y j with ϕ j given by a relation of the type (27) with the help of matrix S j defined in (25) and a datum matrix Y j defined by relation (26). Then we have the following propositions.

Proposition 4. Homographic scheme computes a definite positive matrix. The matrix X j defined by numerical scheme (24) with the initial condition X 0 = 0 is positive for each time step ∆t > 0 :

If there exists some integer m such that X m belongs to the open cone S + * n (IR) , then matrix X m+j belongs to the open cone S + * n (IR) for each j.

Proposition 5. Monotonicity. Under the condition 1 2 KX ∞ + X ∞ K < µ + 1 ∆t I , the scheme (24) is monotone and we have more precisely :

(28) 0 ≤ X j ≤ X ∞ =⇒ 0 ≤ X j ≤ X j+1 ≤ X ∞ .