T Hadi

Bellaye Ps

Messaoudi S 10

Garrido
email: cgarrido@u-bourgogne.fr

Frederic Lirussi
email: frederic.lirussi@u-bourgogne.fr

Carmen Garrido

Lipoproteins LDL versus HDL as nanocarriers to target either cancer cells or macrophages

Keywords: Lipoproteins, vectorization, selective cell targeting, cisplatin, heat shock protein inhibitor, cancer therapy

In this work, we have explored natural unmodified low-and high-density lipoproteins (LDL and HDL) as selective delivery vectors in colorectal cancer therapy. We show in vitro in cultured cells and in vivo (NanoSPECT/CT) in the CT-26 mice colorectal cancer model that LDLs are mainly taken up by cancer cells, while HDLs are preferentially taken up by macrophages. We loaded LDLs with cisplatin and HDLs with the heat shock protein-70 inhibitor AC1LINNC, turning them into a pair of "Trojan horses" delivering drugs selectively to their target cells as demonstrated in vitro in human colorectal cancer cells and macrophages, and in vivo. Coupling of the drugs to lipoproteins and stability was assessed by mass and raman spectrometry analysis. Cisplatin vectorized in LDLs led to better tumor growth suppression with strongly reduced adverse effects such as a renal or liver toxicity. AC1LINNC vectorized into HDLs induced a strong oxidative burst in macrophages and innate anti-cancer immune response. Cumulative anti-tumor effect was observed for both drug-loaded lipoproteins. Altogether, our data show that lipoproteins from patient's blood can be used as natural nanocarriers allowing cell specific targeting, paving the way toward more efficient, safer and personalized use of chemo-and immunotherapeutic drugs in cancer.

Introduction

Among promising immunotherapeutic approaches in cancer are those targeting macrophages.

Macrophages are present in substantial amounts in most solid tumors and influence tumor growth or regression through inflammatory and metabolic switch [START_REF] Mantovani | Tumour-associated macrophages as treatment targets in oncology[END_REF][START_REF] Shapouri-Moghaddam | Macrophage plasticity, polarization, and function in health and disease[END_REF]. Macrophages, depending on their inflammatory status, can have a phenotype either tolerogenic (pro-tumoral) or cytotoxic (anti-tumoral).

Those that infiltrate the tumor are tolerogenic. Switching the polarization of those macrophages so they become cytotoxic is being investigated by many scientists [START_REF] Pathria | Targeting Tumor-Associated Macrophages in Cancer[END_REF]. We recently demonstrated that the stressinducible heat shock protein-70 (HSP70) was abundantly secreted by tumor cells and favored pro-tumor phenotype in macrophages. Accordingly, depletion of HSP70 induced tumor regression via a massive intra-tumor recruitment of cytotoxic macrophages [START_REF] Gobbo | Restoring Anticancer Immune Response by Targeting Tumor-Derived Exosomes With a HSP70 Peptide Aptamer[END_REF].

Concerning cancer chemotherapy, platinum-derived drugs such as cisplatin are major compounds in cancer treatment, particularly in colorectal cancer. However, besides high efficiency, cisplatin cytotoxicity causes cellular damage in healthy tissues, leading to adverse side effects such as renal and liver failure [START_REF] Madias | Platinum nephrotoxicity[END_REF], pulmonary fibrosis or increased cardiovascular events [START_REF] Gietema | Long-term follow-up of cardiovascular risk factors in patients given chemotherapy for disseminated nonseminomatous testicular cancer[END_REF], dramatically limiting the dose of cisplatin that can be used on patients, thereby limiting its efficacy.

More specific cell targeting, toxicity and solubilization issues have prompted the development of nanovectorization approaches. Hence, cisplatin encapsulation into liposomes is considered a promising strategy to reduce the amount of free cisplatin in the plasma and specifically delivering it to target tissues. While most of these attempts did not show significant toxicity reduction, a few studies successfully passed phase II clinical trials but still need phase III validation [START_REF] Oberoi | Nanocarriers for delivery of platinum anticancer drugs[END_REF]. Another approach to improve cisplatin efficacy in colon cancer treatment has been recently proposed through the creation of orally-administered squalenoylated nanoparticles loaded with cisplatin [START_REF] Kotelevets | A Squalene-Based Nanomedicine for Oral Treatment of Colon Cancer[END_REF].

In contrast to these artificial lipid nanovectors, in this work we have explored natural lipoproteins (LDL and HDL) as nanocarriers for colorectal cancer drugs. We studied cisplatin and the potential immunotherapeutic HSP70-targetting drug (AC1LINNC) binding to purified native human lipoproteins, and the influence of such complexation on their selective transport to colorectal cancer cells or macrophages.

Results

Pharmacodynamics parameters of LDL and HDL

We first determined the pharmacodynamics (PK) parameters of lipoproteins in Balb/c mice to choose the optimal time for tissue distribution assessment. Purified HDLs and LDLs were labelled with DOTA-Bodipy-NCS and injected i.v. into mice. Mean concentration time courses are presented in Figure 1A-B. PK parameters were relatively consistent between animals for HDL (Figure 1A, Supplementary table 1). Parameters were more variables between animals for LDL (Figure 1B, Supplementary table 2), due to a rapid decrease in labeled-LDL concentration during the first minutes following i.v. injection. Cmax was rapidly reached after HDL i.v. injection and was about 0.09 mg/mL for a dose of 0.615 mg. Mean exposure between the first and the last measurements (i.e., AUClast) was equal to 45.79 mg/mL.min and represented about 80% of the total exposure. Clearance was low, leading to a median terminal half-life of 14h. After 300 minutes, LDL concentrations were not always quantifiable. Mean exposure between the first and the last measurements (i.e., AUClast) was equal to 4.73 mg/mL.min. Clearance was higher than for HDL, with a median terminal half-life of about 10 h.

The goodness-of-fit plots (Figure 1C-D) shows a good correlation between observed and predicted concentrations, assuming that HDL and LDL followed a bicompartmental model. The major variability was linked to the volume of distribution in the central compartment (i.e., blood) (Supplementary table 3). The developed model enabled us to determine the optimal limited sampling strategy for our further experiments.

Tissue distribution and cancer cell specificity of LDL versus HDL in tumor bearing mice

For in vivo tissue distribution and cellular uptake of LDL and HDL, lipoproteins were labeled with radiolabeled 111 Indium ( 111 In) DOTA-Bodipy-NCS and injected i.v. into colorectal CT26 tumorbearing mice. This was reached 12 days after subcutaneous injection of CT26 cancer cells into the left flank of Balb/c mice. Labeled LDL and HDL in vivo distribution was followed by SPECT-CT and fluorescence microscopy. Lipoproteins uptake in the tumor and different organs (liver, spleen, heart, kidneys, bladder and blood) was visualized over 72h in the whole animal (Figure 2A-B). As expected, the highest levels of both LDLs and HDLs were found in the liver (Figure 2G, Supplemental Data 1A).

However, 24h after systemic injections, lipoproteins could be visualized in the tumors, reaching a peak between 48-72 h (Figure 2A&B). HDL and LDL increase in tumors inversely correlated with their decrease in the heart (Figure 2C-F), indicative of lipoprotein decrease in the bloodstream. Of note, low amounts of both HDL and LDL were observed in the bladder throughout the experiment (Supplemental Data 1B), suggesting that both lipoproteins were not rapidly cleared in the urine. It is worth noting that LDL was more difficult to visualize within the tumor most probably because of its much faster clearance (Figure 1B).

We next aimed to determine LDL and HDL subpopulations fates within the tumor. Twelve hours after injection of bodipy-bound HDL and LDL, the tumors were dissociated and submitted to FACS analysis (Figure 3A&B). Interestingly, we observed that LDL-bodipy was preferentially up taken by CD45 -cells, which are predominantly tumor cells, while HDL-bodipy preferentially accumulated in macrophages (CD45 + /CD11b + /F4/80 + /Ly6G -, Figure 3B). This differential targeting of LDL versus HDL was confirmed in vitro using human cultured cells. Indeed, colorectal cancer HCT116 cells preferentially accumulated LDL-bodipy (Figure 3C) while macrophages (from healthy volunteers' buffy coats) mainly up took HDL-bodipy (Figure 3D) HDL as vectors for potential immunotherapeutic agents such as the HSP70-targetting

AC1LINNC.

With the rational that HDLs abundantly accumulated in macrophages, we decided to complex HDL to a molecule that we screened for its ability to target the heat shock protein-70 (HSP70), a chaperone known for its tumorigenic role involving macrophages differentiation/activity [START_REF] Gobbo | Restoring Anticancer Immune Response by Targeting Tumor-Derived Exosomes With a HSP70 Peptide Aptamer[END_REF][START_REF] Jego | Dual regulation of SPI1/PU.1 transcription factor by heat shock factor 1 (HSF1) during macrophage differentiation of monocytes[END_REF][START_REF] Wang | Exogenous heat shock protein 70 binds macrophage lipid raft microdomain and stimulates phagocytosis, processing, and MHC-II presentation of antigens[END_REF][START_REF] Rerole | Peptides and aptamers targeting HSP70: a novel approach for anticancer chemotherapy[END_REF]. This molecule, designated as AC1LINNC (Supplemental Data 2A), binds to HSP70 with an IC50 of 0.2µM (Supplemental Data 2C) and inhibits HSP70 chaperone activity (Supplemental Data 2B&D).

AC1LINNC is highly hydrophobic and insoluble hampering its use in vivo, thereby increasing the interest for its vectorization. We incubated HDL or LDL (1mM cholesterol each) with AC1LINNC (to a final concentration of 100µM) (Supplemental Data 3A). Mass spectrometry analysis revealed a 30% uptake of AC1LINNC by both LDL and HDL allowing to achieve a final concentration of about 30µM (Figure 4A). To evaluate the stability of AC1LINNC-bound lipoproteins and possible exchange of AC1LINNC between LDL and HDL particles, AC1LINNC-bound LDLs or AC1LINNC-bound HDLs (1mg/ml) were incubated with native HDLs or LDLs (1mg/ml), respectively (Supplemental Data 3B).

AC1LINNC was not detected in the newly added native lipoproteins, indicating that the interaction is stable with no exchange with other lipoproteins (Figure 4B). We found that while the AC1LINNC complexed to LDL had no effect, the same amount of the AC1LINNC vectorized in HDL or solubilized in DMSO induced ROS production in macrophages (Figure 4C).

To confirm the in vivo potential interest of HDL-bound AC1LINNC, we used the rodent CT-26 colorectal cancer model. CT-26 cells were subcutaneously injected into the left flank of Balb/c mice. Day 0 was considered when tumor size reached about 6 mm 3 : at day 10, mice were treated i.p. with PBS, HDL-AC1LINNC (1.5mg/kg), LDL-AC1LINNC or native HDL or LDL. Injections were performed every three days until the end of the experiment (D25, for ethical considerations, Figure 4D&E).

Consistent with data obtained from cultured macrophages, we observed higher macrophages tumor infiltration with a drastic increase in ROS production, along with a mild induction of apoptosis in cancer cells (Figure 4F-J). That was associated with tumor regression (Figure 4 E), thereby bringing proof of concept of a macrophage guided effect of HDL complexes. Interestingly, we did not observe any effect of LDL-AC1LINNC treatment, or of either native HDL or LDL on tumor growth.

Lipoproteins as nano-vectors for the chemotherapeutic drug cisplatin

We next used cisplatin, an efficient drug whose heavy undesirable effects hamper its use.

Lipoproteins were incubated with cisplatin (final concentration of 1mg/ml) for 4 hours at 37°C (Supplemental Data 3A). After dialysis, total cisplatin concentration in lipoproteins was measured by GF-AAS. We observed an integration of 30% and 50% of the initial dose of cisplatin, into LDL and HDL sub-fractions respectively (Figure 5A). As previously described for the AC1LINNC (Supplemental Data 3B) no cisplatin exchange with other lipoproteins was detected (Figure 5B). In sillico (Supplemental Data 4A&B and Supplemental table 4) and raman spectroscopy studies (See Supplemental Data 4C) indicated that cisplatin bound cysteine residues of the ApoB-100 protein.

Antitumor in vivo effect of cisplatin complexed to LDL

The impact of cisplatin-LDL versus -HDL complexes on in vitro tumor cell death was determined by MTT viability test. We observed that LDL-vectorization improved cisplatin-induced cancer cell mortality (Figure 5C), while HDL-vectorization had no effect compared to the control (Supplemental Data 5A). These results were in agreement with our previous data showing that HDLs were not captured by HCT116 tumor cells while LDLs hardly entered macrophages. Consistently, we observed that cisplatin complexed to LDL had no effect on macrophage ROS production (Figure 5D) while HDL-bound cisplatin induced a strong response (Supplemental Data 5B).

This effect of the LDL-cisplatin complexes in tumor cells was further observed in vivo in CT-26 tumor-bearing mice (Figure 5E-K). Mice were treated i.p. ever 3 days with PBS, native HDL or LDL, cisplatin (Cis-Pt, 1.5mg/kg) or cisplatin (1.5mg/kg) complexed to LDL (LDL-Cis) or HDL (HDL-Cis), (Figure 5E). LDL-Cis treatment was associated with a stronger tumor regression than cisplatin alone (Figure 5F), while no significant effects of HDL-Cis or native lipoproteins were observed on tumor growth (Supplemental Data 5C). Consistently, we observed that LDL vectorization of cisplatin was associated with a higher tumor cell death (caspace-3, Figure 5G&I) and a higher proportion of macrophages infiltrating the tumor (F4/80, Figure 5G&J), compared both to control and non-vectorized cisplatin groups. Interestingly, cleaved-caspase-3 staining did not co-localize with F4/80, suggesting a selective pro-apoptotic effect on tumor cells. Additionally, this pro-apoptotic effect was associated with increased ROS production as assessed by DHE/DAPI staining (Figure 5H&K). To summarize, LDL vectorization improves the efficiency of cisplatin, by increasing tumor cell death and, most probably indirectly, favoring cytotoxic macrophage infiltration.

Vectorization of cisplatin by LDL strongly diminishes cisplatin adverse side effects

To investigate the impact of lipoprotein vectorization on cisplatin nephrotoxicity, mice were treated with cisplatin using a standardized kidney injury protocol. Tumor-bearing mice were injected with a single dose of 30 mg/kg cisplatin and euthanized at day 3. Toxicity was assessed by evaluating weight loss and renal dysfunction (Figure 6A). Mice treated with Cis-Pt experienced a 19% weight loss only 3 days following injection. In contrast, mice treated with LDL-bound cisplatin did not experience any weight loss (Figure 6B), while, interestingly, no decrease in cisplatin anti-cancer drug efficiency was observed (Figure 6C). Following cisplatin treatment, mice displayed distortion of the overall renal morphology, dilation of renal tubules, and appearance of protein cast, most of which were significantly attenuated in the cisplatin lipoprotein-vectorized group (Figure 6D&E). In addition to these observations, apoptosis assessed by caspase-3 cleavage was dramatically decreased in the kidney of mice treated with cisplatin complexed to LDL (Figure 6F&G), while the induction of apoptosis in tumor cells was comparable in both groups (Figure 6F&H). Furthermore, since the liver is involved in lipoprotein turnover, we aimed to assess if cisplatin complexed to LDL would induce hepatic toxicity. Interestingly, we found that LDLbound cisplatin did not induce hepatic toxicity, as shown by comparing apoptosis (cleaved caspase-3) in the liver of animals treated with cisplatin versus LDL-cisplatin (Supplemental Data 1B&C).

Altogether, cisplatin complexed to LDL, while preserving cisplatin anti-tumor effect, displays a reduced side effect toxicity.

Combinational effect of AC1LINNC-HDL and cisplatin-LDL complexes

Finally, we tested the impact of the association of cisplatin-LDL complexes together with AC1LINNC-HDL complexes. Tumor-bearing mice were treated with LDL-Cisplatin, HDL-AC1LINNC or the combination of both. While we did not observed a stronger decrease in tumor growth when using the combinational therapy (Figure 7A&B), immunofluorescent staining revealed i) a strong induction of cancer cell apoptosis (Figure 7C&E), comparable to that observed in the animals treated with LDL-Cisplatin alone ii) a strong burst in macrophage infiltration (Figure 7C&F) comparable to HDL-AC1LINNC alone. This suggests that this combined strategy aiming to simultaneously target cancer cells with one drug (cisplatin-LDL) and tumor-infiltrating macrophages with the other (AC1LINNC-HDL) allows a complementary additive effect that could prove more efficient during prolonged treatment.

Discussion

In the field of cancer treatment, liposomal encapsulation of lipophilic drugs such as doxorubicin (Doxil, AmBisome) or vincristine (Marquibo) led to improved efficacy and safety. These new formulations were approved by the US Food and Drug Administration [START_REF] Barenholz | Doxil(R)--the first FDA-approved nano-drug: lessons learned[END_REF][START_REF] Allen | Liposomal drug delivery systems: from concept to clinical applications[END_REF]. However, the use of liposomal carriers for hydrophilic cisplatin has not achieved these goals so far. Among the few liposomal formulations of cisplatin that reached clinical trials, encapsulation of cisplatin in SPI-77® liposomes did not produce significant clinical efficacy in phase II studies despite its safer toxicity profile [START_REF] Seetharamu | Phase II study of liposomal cisplatin (SPI-77) in platinum-sensitive recurrences of ovarian cancer[END_REF], due to inefficient release of the drug from the carrier [START_REF] Veal | A phase I study in paediatric patients to evaluate the safety and pharmacokinetics of SPI-77, a liposome encapsulated formulation of cisplatin[END_REF]. Although Lipoplatin® (active encapsulation of cisplatin into PEGylated liposomes) showed enhanced antitumor efficacy compared to free cisplatin in some patients along with reduced renal toxicity, phase II and III studies demonstrated inconsistent effects on survival rates [START_REF] Stathopoulos | Lipoplatin formulation review article[END_REF]. Finally, LiPlaCis®, a phospholipase A2-sensitive liposomal cisplatin carrier have shown a poor safety profile, leading to the discontinuation of phase I studies [START_REF] De Jonge | Early cessation of the clinical development of LiPlaCis, a liposomal cisplatin formulation[END_REF].

In the present study, we considered native human LDL and HDL as carriers for several reasons: 1) lipoproteins are endogenous, physiological and stable molecular complexes that can carry a wide variety of molecules in the bloodstream; 2) they bear specific apolipoproteins that allow targeting to specific receptors; 3) certain chemotherapeutic drugs such as cisplatin display affinity for plasma proteins and therefore are likely to bind to apolipoproteins [START_REF] Boulikas | Cisplatin and platinum drugs at the molecular level. (Review)[END_REF]. This latter hypothesis was supported in the present work by in silico studies showing that hydrophobic cisplatin interacts with the protein moiety, and not the lipid moiety of lipoproteins. Further, we demonstrate in vitro that cisplatin association to LDL and HDL is highly efficient and stable in aqueous solution, with no subsequent release of bound cisplatin into the buffer or towards other non-loaded lipoproteins. These results, together with our in vivo kinetics experiments suggest that cisplatin binding to lipoproteins can significantly prolong its half-life in the blood (only 0.24 hours for free cisplatin [START_REF] Newman | Comparative pharmacokinetics, tissue distribution, and therapeutic effectiveness of cisplatin encapsulated in long-circulating, pegylated liposomes (SPI-077) in tumor-bearing mice[END_REF]). This may allow the molecule to reach its target tissue instead of being quickly cleared in an unspecific manner.

Accordingly, we were able to show that substantial amounts of labeled lipoproteins could be found within CT-26 tumors after their systemic administration in mice.

Interestingly, LDL and HDL targeted different cells within the tumor. While labeled HDL preferentially accumulated in tumor macrophages, LDL were mainly found within CT-26 cancer cells. A possible explanation is that LDL receptor (LDL-R) expression is abnormally elevated in cancer cells [START_REF] Firestone | Low-density lipoprotein as a vehicle for targeting antitumor compounds to cancer cells[END_REF][START_REF] Goldstein | The LDL receptor[END_REF]. In contrast, HDL, which uptake cholesterol excess from peripheral cells back to the liver, have been shown to interact with immune cells via specific membrane transporters and scavenger receptors, particularly present in macrophages. The specific tropism of the LDL for tumor cells may explain the practically lack of cisplatin's side effects such as renal and hepatic toxicity, when conjugated to LDL.

Since HDL particles are abundantly taken up by macrophages, we believe that loading of HDL with immunotherapeutic compounds may be more promising than with chemotherapeutic drugs. Thus, HDL might have a strong therapeutic interest to vectorise molecules that influence macrophages polarization toward an anti-tumor phenotype, and proof of the concept is shown in this work with an HSP70 inhibitor affecting macrophages differentiation/activation [START_REF] Jego | Dual regulation of SPI1/PU.1 transcription factor by heat shock factor 1 (HSF1) during macrophage differentiation of monocytes[END_REF][START_REF] Wang | Exogenous heat shock protein 70 binds macrophage lipid raft microdomain and stimulates phagocytosis, processing, and MHC-II presentation of antigens[END_REF]. Overall, we conclude that the usage of HDL might allow in the future a more targeted/safer administration into the patient of immunotherapeutic agents alone or in combination with LDL-vectorized chemotherapeutic agents, such as cisplatin.

Methods

Cell culture and mice

HCT116 cells (CCL-247 TM ) were from the American Type Culture Collection (ATCC). Human macrophages were isolated from healthy donor Buffy Coats (EFS Besançon, France) and differentiated as described [START_REF] Hadi | Beta3 adrenergic receptor stimulation in human macrophages inhibits NADPHoxidase activity and induces catalase expression via PPARgamma activation[END_REF]. 6-8-week-old female Balb/c mice were from Charles River. Mouse colon carcinoma cells CT26 (CRL-2638 TM ATCC) were injected subcutaneously in the left flank. Time 0 was considered when tumor size reached 6 mm 3 . Mice were treated with cisplatin (1.5 mg/kg), or LDL-Cis (100µM cholesterol, 1.5mg/kg cisplatin). For toxicity experiments, mice were injected i.p. at day 10 with PBS, Cisplatin (20 mg/kg), or LDL-Cis (100µM cholesterol, 20mg/kg cisplatin). Tumors were measured every three days. Experiments were approved by the ethical comity of the Université de Bourgogne (protocol N3613).

Lipoprotein purification

LDL and HDL were purified from plasma (EFS Besançon, France) as described [START_REF] Redgrave | Separation of plasma lipoproteins by density-gradient ultracentrifugation[END_REF]. For biodistribution experiments, lipoproteins were labelled with DOTA-Bodipy [START_REF] Duheron | Dual labeling of lipopolysaccharides for SPECT-CT imaging and fluorescence microscopy[END_REF], a fluorescent probe (excitation/emission spectra (522/529 nm maxima) combined to a radioactive trap. Briefly, LDL or HDL (2mg of protein) were incubated 4 hours at 37°C in bicarbonate buffer containing 565µg DOTA-Bodipy [START_REF] Bernhard | First bodipy-DOTA derivatives as probes for bimodal imaging[END_REF]. Bicarbonate buffer and unbound label were removed and lipoproteins recovered in sterile PBS by filtration in centrifugal concentration tubes (30kDa cutoff Centricon, Merck-Millipore).

Cisplatin and AC1LINNC incorporation in lipoproteins:

Cisplatin (Sigma Aldrich, 479306-1G) was dissolved in 0.9%NaCl to a 10mg/ml concentration.

AC1LINNC was diluted DMSO to a 100µM concentration. Cisplatin or AC1LINNC solutions were diluted 10 times in 1mM LDL or HDL fractions and incubated 4 hours at 37°C. Unbound Cisplatin, AC1LINNC and DMSO were removed by successive dialyses using Spectrum™ Spectra/Por™ 1 RC Dialysis Membrane Tubing (6000-8000Da cutoff, Fisher Scientific, 08-670C). For LDL/HDL Cisplatin exchange assays, Cisplatin-bound LDL or Cisplatin-bound HDL (1µM) were incubated 24 hours at 37°C with native HDL or LDL (1µM). Cisplatin incorporation in LDL and HDL was then assessed by GF-AAS (graphite furnace coupled to atomic absorption spectrophotometry) and AC1LINNC incorporation by mass spectrometry.

Bio-distribution and pharmacokinetics imaging

Tumor bearing Balb/c mice (~300mm 3 ) received 5µg 111 In-DOTAGA-HDL or 111 In-DOTAGA-LDL (8-10MBq) i.v.. SPECT/CT dual imaging was performed 1h, 24h and 72h after injections using a NanoSPECT/CT small animal imaging tomographic γ-camera (Bioscan Inc., Washington, DC). Mice were anaesthetized with isoflurane (1.5-3% in air) and positioned in a cradle. CT (55 kVp, 34 mAs) and helical SPECT acquisitions were performed in immediate sequence. Both indium-111 photopeaks (171 and 245keV) were used with 10% wide energy windows. Radioactivity was measured (from blood, tumor, and organs) with a scintillation γ-counter. Data were then converted to percentage of injected dose per gram of tissue (%ID/g). SPECT/CT fusion image was obtained using the InVivoScope software (Bioscan Inc.). Radioactivity contents from image analysis were expressed in Bq/g, converted to percentage of injected dose, and compared to those determined by ex vivo counting.

Statistical analysis

Differences among two groups were determined using two-tailed unpaired Fisher's t-test, and ANOVA followed by Bonferroni's multiple comparison test for more than two groups, using SigmaStat version 3 (GraphPad Software). Differences were considered significant when p < 0.05.

FiguresFigure 1 :

 1 Figures

Figure 2 .

 2 Figure 2. LDL-and HDL-Bodipy biodistribution in tumor bearing mice. A, B: Female Balb/c mice (n=3) were grafted by subcutaneous injection of 1.10 6 CT26 colorectal tumor cells. When tumor reached

Figure 3 :

 3 Figure 3: LDL-bodipy accumulates in cancer cells while HLD-bodipy preferentially target

Figure 4 :

 4 Figure 4: HSP70 inhibitor vectorization in HDL prevents tumor growth by targeting

Figure 5 :

 5 Figure 5: In vivo effects of cisplatin vectorization in LDL. A: LDL and HDL were purified by density

F:

  Tumor volume was measured every 3 days, and represented as mean value +/-SEM, *: p<0.05, **: p<0.01, arrow indicates first injection. G: Apoptosis and macrophage infiltration were determined in histological slides labeled with a cleaved caspase-3 antibody (Green) and a F4/80 antibody (Red), and with DAPI. Images were chosen in random fields and are representative of five images taken for each condition. n=5, scale bar = 50µm. H: ROS production in tumors was measured in histological slides by DAPI/DHE staining. Images, taken in random fields, are representative of five different ones taken for each condition. n=5, scale bar = 50µm. I, J & K: Quantifications of the immune-fluorescence intensity of Cleaved Caspase-3 (I), F4/80 (J) and DHE (K). Data are represented as mean increase vs. PBS +/-SEM. n=4, *: p<0.05, ****: p<0.0001. P values were calculated using one-way ANOVA (A, F, I, J, K) or two-tailed unpaired t-tests (C, D).

Figure 6 :

 6 Figure 6: LDL vectorization of cisplatin diminish cisplatin adverse effects. A: Balb-c mice were injected with CT-26 colorectal cancer cells (10 6 cells/mice, s.c.). When tumors reached approximately 300 mm 3 (by day 10), mice were i.p. injected with either LDL-PBS (100µM cholesterol, n=4), cisplatin

Figure 7 :

 7 Figure 7: In vivo additive effect of cisplatin loaded LDL and AC1LINNC loaded HDL. A: Balb-c mice were injected with CT-26 colorectal cancer cells (10 6 cells/mice, s.c.). At the indicated times mice

Acknowledgments

We thank the Platforms Cellimap for their technical support. S.Y, S.F and C.R. were supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 690853. The computational studies work was performed using HPC resources from GENCI-[TGCC/CINES/IDRIS] (Grant 2015-[c2016077586]) and Mésocentre de calcul de Franche-Comté.

Funding

The work was supported by a French Government grant managed by the French National Research Agency under the program "Investissements d'Avenir" with reference ANR-11-LABX-0021 (LabEX LipSTIC). We also thank the Conseil Regional de Bourgogne-Franche Comté, the European Union program FEDER, and the "Ligue National contre le Cancer" for their financial support.


Virgile Trannoy

Nathalie Guillou

Carine Livage

Catherine Roch-Marchal

Mohamed Haouas

Anne Léaustic

Clémence Allain

Gilles Clavier

Pei Yu

Thomas Devic

Fluorescent Zr(IV) Metal Organic Frameworks based on an Excited state intramolecular proton transfer (ESIPT)-type ligand

Keywords: Metal-Organic Frameworks, Fluorescence, ESIPT, Zirconium, Structure analysis, Stability

We report here the preparation of a series of Zr(IV) Metal Organic Frameworks of the MIL-140 structure type incorporating a ligand exhibiting an intense Excited State Intramolecular Proton Transfer (ESIPT) fluorescence. These solids were obtained by systematically varying the substitution rate of 4,4'-biphenyldicarboxylate by 2,2'-bipyridine-3,3'-diol-5,5'-dicarboxylate, and thoroughly characterized by complementary techniques, including high resolution powder X-ray diffraction, solid state NMR spectroscopy, nitrogen sorption experiments and time-resolved fluorescence. We showed that the incorporation of the ESIPT-type ligand induces an increase of the hydrophilicity, leading ultimately to a higher sensitivity toward hydrolysis, a phenomenon rarely observed in this structure type considered as one of the most stable among the Zr carboxylate MOFs. Eventually, the optimization of the amount of fluorescent ligand within the structure allowed combining a decent microposity (SBET > 750 m 2 .g -1 ) and a high stability even in boiling water, together with a high fluorescence quantum yield (> 30%). E* (S 1 ) E (S 0 ) Enol form Enol emission Keto emission K* (S 1 ) K (S 0 ) Keto form hν enol form cis-keto form

INTRODUCTION

Porous coordination polymers or Metal-Organic Frameworks (MOFs), with their wide variety of chemical composition and structural diversity are now considered promising candidates not only for purely sorption-related applications, but also in other areas where their tunable optical or electronic properties are definite advantages. Specifically, light emitting MOFs have been proposed for optical sensing, lighting, imaging, or luminescence thermometry. [START_REF] Allendorf | Luminescent metal-organic frameworks[END_REF][START_REF] Lustig | Metal-organic frameworks: functional luminescent and photonic materials for sensing applications[END_REF][START_REF] Zhang | Luminescent sensors based on metal-organic frameworks[END_REF][START_REF] Cui | Luminescent Functional Metal-Organic Frameworks[END_REF][START_REF] Liu | Metal-Organic Frameworks as Sensory Materials and Imaging Agents[END_REF][START_REF] Mahata | Luminescent rare-earth-based MOFs as optical sensors[END_REF][START_REF] Müller-Buschbaum | MOF based luminescence tuning and chemical/physical sensing[END_REF] Although lanthanide-based emitters have been widely studied, organic luminophores are also appealing, especially because of their greater sensitivity to guest molecules. Nevertheless, this sensitivity is often affected by low quantum yields of fluorescence, a consequence of short luminophore-luminophore contacts leading to intra-framework quenching phenomena. [START_REF] Monguzzi | Highly Fluorescent Metal-Organic-Framework Nanocomposites for Photonic Applications[END_REF][START_REF] Liu | A new luminescent metalorganic framework based on dicarboxyl-substituted tetraphenylethene for efficient detection of nitro-containing explosives and antibiotics in aqueous media[END_REF][START_REF] Li | AIE-active tetraphenylethene functionalized metal-organic framework for selective detection of nitroaromatic explosives and organic photocatalysis[END_REF][START_REF] Deng | Highly Fluorescent Metal-Organic Frameworks Based on a Benzene-Cored Tetraphenylethene Derivative with the Ability To Detect 2,4,6-Trinitrophenol in Water[END_REF] In order to create highly emissive MOFs, we have focused our attention on the use of ligands presenting an ESIPT-type fluorescence (Excited State Intramolecular Proton Transfer). [START_REF] Eon | Advanced Organic Optoelectronic Materials: Harnessing Excited-State Intramolecular Proton Transfer (ESIPT) Process[END_REF][START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] ESIPT is an ultrafast photochemical process and its resulting emission characterized by an "abnormally" large Stokes shift and a very environment-specific sensitivity induced by the intramolecular hydrogen bond. A four-level photo-cycle (E  E*  K*  K) diagram is shown in Figure 1 to illustrate the main photochemical and photophysical processes involved in the case of an archetypal molecule of this family, the 2-(2-hydroxyphenyl)-benzothiazole (HBT). Unlike many organic emitters, self-quenching in ESIPT-type fluorophores is minimized due to the absence of spectral overlapping between absorption and emission. This unique feature of ESIPT emission is appealing for the design of efficient fluorescent materials. [START_REF] Eon | Advanced Organic Optoelectronic Materials: Harnessing Excited-State Intramolecular Proton Transfer (ESIPT) Process[END_REF][START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] ESIPT chromophores-based MOFs are thus prime candidates for potential applications in a wide variety of fields such as chemical sensors, fluorescence imaging or light emitting diodes. To date, only a very limited number of porous materials with ESIPT-type fluorescence have been reported, showing far above average fluorescent quantum yields. [START_REF] Lustig | Metal-organic frameworks: functional luminescent and photonic materials for sensing applications[END_REF][START_REF] Jayaramulu | Tunable emission from a porous metal-organic framework by employing an excited-state intramolecular proton transfer responsive ligand[END_REF][START_REF] Jayaramulu | Luminescent Microporous Metal-Organic Framework with Functional Lewis Basic Sites on the Pore Surface: Specific Sensing and Removal of Metal Ions[END_REF][START_REF] Shustova | Selective Turn-On Ammonia Sensing Enabled by High-Temperature Fluorescence in Metal-Organic Frameworks with Open Metal Sites[END_REF][START_REF] Douvali | Turn-On Luminescence Sensing and Real-Time Detection of Traces of Water in Organic Solvents by a Flexible Metal-Organic Framework[END_REF][START_REF] Douvali | Alkaline Earth Metal Ion/Dihydroxy-Terephthalate MOFs: Structural Diversity and Unusual Luminescent Properties[END_REF][START_REF] Chen | Ultrafast water sensing and thermal imaging by a metal-organic framework with switchable luminescence[END_REF][START_REF] Pournara | A new Cd 2+ -dihydroxyterephthalate MOF: Synthesis, crystal structure and detailed photophysical studies[END_REF][START_REF] Bhattacharya | Eye-Catching Dual-Fluorescent Dynamic Metal-Organic Framework Senses Traces of Water: Experimental Findings and Theoretical Correlation[END_REF][START_REF] Chen | An Efficient Visible and Near-Infrared (NIR) Emitting SmIII Metal-Organic Framework (Sm-MOF) Sensitized by Excited-State Intramolecular Proton Transfer (ESIPT) Ligand[END_REF][START_REF] Li | A semiconductor and fluorescence dual-mode room-temperature ammonia sensor achieved by decorating hydroquinone into a metalorganic framework[END_REF] Most of these solids are based on divalent cations (Mg, Zn, Ca, Sr, Ba) and carboxylate linkers, and are therefore prone to hydrolysis. [START_REF] Low | Virtual High Throughput Screening Confirmed Experimentally: Porous Coordination Polymer Hydration[END_REF] Figure 1. Diagram of the ESIPT process. Adapted from ref [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] . Copyright 2016 The Royal Society of Chemistry.

Group IV metal ions are well known for their strong affinity with oxygenated complexing groups, resulting in high metalligand bond stability toward hydrolysis. [START_REF] Kim | Discovery, development, and functionalization of Zr(iv)-based metal-organic frameworks[END_REF][START_REF] Devic | High valence 3p and transition metal based MOFs[END_REF][START_REF] Bai | Zr-based metal-organic frameworks: design, synthesis, structure, and applications[END_REF] Based on this consideration, we focused our attention on Zr(IV)-dicarboxylate MOFs. While the UiO-6n series exhibits the well-known fcc structure type with twelve organically linked Zr6 oxo-clusters leading to octahedral and tetrahedral cages, the pseudo-polymorphs MIL-140s are built up from chains of edge sharing ZrO7 polyhedra connected through the ligands to define triangular channels. [START_REF] Cavka | A New Zirconium Inorganic Building Brick Forming Metal Organic Frameworks with Exceptional Stability[END_REF][START_REF] Guillerm | A Series of Isoreticular, Highly Stable, Porous Zirconium Oxide Based Metal-Organic Frameworks[END_REF] In this structure type, the organic moieties are located on two independent crystallographic sites in a 1 to 1 ratio (Figure 2). MIL-140s present lower porosities than their UiO-6n analogues, but higher chemical and mechanical stabilities. [START_REF] Guillerm | A Series of Isoreticular, Highly Stable, Porous Zirconium Oxide Based Metal-Organic Frameworks[END_REF] Although MIL-140 type solids are less numerous than the UiO-6n ones, the incorporation of functionalized linear ligands was already successfully achieved. [START_REF] Liang | Microwave-assisted solvothermal synthesis of zirconium oxide based metal-organic frameworks[END_REF][START_REF] Liang | Tuning the cavities of zirconium-based MIL-140 frameworks to modulate CO2 adsorption[END_REF][START_REF] Liang | Microwave-Assisted Solvothermal Synthesis and Optical Properties of Tagged MIL-140A Metal-Organic Frameworks[END_REF] Among the MIL-140s, the one built up from the 4,4'-biphenyldicarboxylate (BPDC) and quoted MIL-140C appears as a suitable platform. In order to synthesize MIL-140C-type emitting MOFs, we focused our attention on the 2,2'-bipyridine-3,3'-diol-5,5'-dicarboxylic acid (H2BP(OH)2DC, see Scheme 1), which exhibits an intense ESIPT fluorescence in the solid state, and is analogous in size and shape to the H2BPDC. In this article, we report the synthesis of an ESIPT fluorescent MIL-140C series with different BP(OH)2DC/BPDC ratios. Their in-depth structural characterization by combining high resolution X-ray powder diffraction (XRPD) and solid-state NMR is presented, as well as the study of their chemical stability and optical properties, with a special focus on the maximization of the quantum yield.

MATERIALS AND METHODS

Reagents and Chemicals. ZrCl4 (anhydrous, 99.5%), acetic acid (99.7%), and N,N'-dimethylformamide (DMF, 99.8 %) were purchased from Sigma-Aldrich while 4,4'-biphenyldicarboxylic acid (H2BPDC, 97 %) was purchased from ABCR. All chemicals were used without further purification. The synthesis of the ESIPT fluorophore H2BP(OH)2DC is described in supporting information. Synthesis of MIL-140C_n. The protocol is derived from the procedure reported by De Vos et al. for the preparation of MIL-140C. [START_REF] Van De Voorde | Isolation of Renewable Phenolics by Adsorption on Ultrastable Hydrophobic MIL-140 Metal-Organic Frameworks[END_REF] A solution 1 of ZrCl4 (233 mg, 1 mmol) in DMF (4 mL) and a solution 2 containing 1.5 mmol of dicarboxylic acid with the proper H2BP(OH)2DC/H2BPDC ratio (see Table S1) and glacial acetic acid (367 µL, 6.4 mmol) in DMF (6 mL) were heated at the boiling point. Solution 1 was then added to solution 2 and the mixture heated to reflux for 16 h. The white to yellow powders were recovered by centrifugation and washed with DMF. In order to remove all traces of free organic ligand from the pores, the solids were transferred to autoclaves and heated at 100°C for 14 h first in DMF, then in MeOH. The powder was recovered by centrifugation and then dried under vacuum at 80°C overnight.

CHARACTERIZATIONS

Routine X-Ray powder diffraction (XRPD) patterns were collected at room temperature on a Siemens D5000 Diffractometer working in Bragg-Brentano geometry [(θ-2θ) mode] by using CuKα radiation. The high resolution XRPD data used for the structural analysis were measured at room temperature on a Bruker D8 Advance diffractometer with a Debye-Scherrer geometry, equipped with a Ge(111) monochromator selecting Cu Kα1 radiation (λ = 1.540598 Å) and a LynxEye detector. Powders were loaded in 0.5 mm diameter glass capillaries and dried at 100 °C overnight prior to the measurements. Data were collected in the 2θ range 4-90°. Extractions from the peak positions, pattern indexing, whole powder pattern decomposition, difference Fourier calculations and Rietveld refinements were carried out with the TOPAS program. [START_REF]Topas V5: General Profile and Structure Analysis Software for Powder Diffraction Data[END_REF] Prior to the sorption measurements, the solids were activated under vacuum at 220 °C overnight using a BELPREP apparatus. N2 sorption isotherms at 77 K were measured with a BELSORP Max porosimeter, and surface areas were estimated by applying the Brunauer-Emmett-Teller (BET) model. For solid-state NMR measurements, the solids were packed in 3.2 mm zirconia rotors and the MAS spectra were recorded on a Bruker Avance 500 spectrometer at a resonance frequency of 500.1 MHz for 1 H, and 125.8 MHz for [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C. The samples were spun at 20 kHz for the 1 H detection measurements and at 10 kHz for the [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C detection experiments. For the 1 H MAS NMR spectra 8 scans were recorded with a recycle delay of 9 s and a 90° pulse of 2 µs. The 1 H 13 C cross-polarization (CP) MAS NMR spectra were recorded using a 3 ms contact time, 1.5 s recycle delay and 1 H SPINAL-64 decoupling. 1024 transients were accumulated. The 1 H-1 H single quantum-double quantum (SQDQ) MAS NMR spectra used the back-to-back (BABA) sequence with recoupling time ranging from 0.2 to 0.4 ms. 256 t 1 slices with 16 transients each were recorded with a recycle delay of 1 s. For the 1 H- [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C HETCOR MAS NMR spectrum, the contact time was set to 2 ms, 32 t 1 slices with 256 transients each were recorded, with recycle delay of 1 s. 2-D NMR data were recorded using the States procedure to obtain phase sensitive spectra. Tetramethylsilane was used as an external chemical shift reference for both 1 H and [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C. Thermogravimetric analyses (TGA) were performed on a Mettler-Toledo TGA/DSC 1 apparatus. Solids were heated up to 600 °C with a heating rate of 5°C.min -1 in an oxygen flow (50 mL.min -1 ). Fourier transform infrared (FT-IR) spectra were recorded using a Nicolet 6700 FT-IR spectrometer with a diamond attenuated total reflectance unit. The spectra were recorded from 4000 to 400 cm -1 with a resolution of 2 cm -1 at 32 scans. Absolute fluorescent quantum yields were measured using a Fluorolog-3 from Horiba Jobin-Yvon equipped with an integrating sphere. Fluorescence decay curves were obtained by the time-correlated single-photon counting (TCSPC) method with a femtosecond laser excitation composed of a Titanium Sapphire laser (Tsunami, Spectra-Physics) pumped by a doubled Nd:YVO4 laser (Millennia Xs, Spectra-Physics). Light pulses at 800 nm from the oscillator, were selected by an acousto-optic crystal at a repetition rate of 4 MHz, and then doubled at 400 nm by a non-linear crystal. Fluorescence photons were detected at 90° through a monochromator and a polarizer at magic angle by means of a Hamamatsu MCP R3809U photomultiplier, connected to a SPC-630 TCSPC module from Becker & Hickl. The instrumental response function was recorded before each decay measurement with a fwhm (full width at half-maximum) of ~25 ps. The fluorescence data were analyzed using the Globals software package developed at the Laboratory for Fluorescence Dynamics at the University of Illinois at Urbana-Champaign, which includes reconvolution analysis and global non-linear least-squares minimization method.

RESULTS AND DISCUSSION

Synthesis and basic characterization H2BP(OH)2DC (Scheme 1) was prepared from the corresponding ester at the gram scale. As expected, after excitation at 390 nm, this molecule exhibits an ESIPT-type fluorescence with an emission band centered at 562 nm and a quantum yield of 29% in the solid state (see Table 1). Scheme 1. 2,2'-bipyridine-3,3'-diol-5,5'-dicarboxylic acid (H2BP(OH)2DC)

MOFs

were prepared from various ratios H2BP(OH)2DC/H2BPDC (0/100, 10/90, 50/50 and 100/0). The resulting products, labelled MIL-140C_0, MIL-140C_0.1, MIL-140C_0.5 and MIL-140C_1 respectively, were first characterized by X-ray powder diffraction (XRPD). All solids present diagrams similar to that of the pristine MIL-140C_0, indicating that they all belong to the intended structure type (Figure 3).

Figure 3. XRPD of MIL-140C_0, _0.1, _0.5 and _1.

A slight shift of the Bragg peaks toward higher angles upon increasing the amount of fluorophore is observed, indicating a decrease of the unit cell volume of the solids (see Figure S6 and Table S4). As discussed later, this effect arises not only from the partial substitution of BPDC by BP(OH)2DC, but also from a variable amount of water adsorbed in the pores. Elemental analyses confirm the successful incorporation of BP(OH)2DC within the framework (see Table S2). Analysis of MIL-140C_0.5 suggests a preferential incorporation of BP(OH)2DC over BPDC (65% of BP(OH)2DC in the final product instead of 50% in the initial reaction mixture), in agreement with the solid-state NMR analyses (see Table S3 and below). Infrared spectroscopy also corroborates the presence of the fluorophore within MIL-140C_0.1, MIL-140C_0.5 and MIL-140C_1. Few specific bands of the BP(OH)2DC ligand, notably at 1233 and 1330 cm -1 (C-O elongation and O-H stretching, respectively), 1476 and 1129 cm -1 (elongation and deformation of the C-N bond, respectively), and at 916 and 975 cm -1 (aromatic γC-H bands) clearly increase with the amount of BP(OH)2DC (Figure S1). It should also be noted that almost no signal is visible in the 1700 cm -1 region, confirming the absence of free carboxylic acid, and hence the incorporation of BP(OH)2DC within the framework and not as a guest within the pores.

In depth structural analysis

Structural insights and quantitative information about the arrangement of the ligands within the solids were obtained from solid-state NMR analysis. [START_REF] Allendorf | Luminescent metal-organic frameworks[END_REF] H MAS NMR was first used to follow specifically the proton involved in the ESIPT process (Figure 4). The spectrum of MIL-140C_0 exhibits non-resolved resonances in the range 5-8 ppm assigned to the aromatic protons of the linker. The 1 H NMR of MIL-140C_1 shows a more complex spectrum where beside resonances of water (4 ppm) and of OH defects in the ZrO7 chain (1-3 ppm), [START_REF] Salomon | Immobilization of polyoxometalates in the Zr-based metal organic framework UiO-67[END_REF][START_REF] Lawrence | Determining the structural stability of UiO-67 with respect to time: a solid-state NMR investigation[END_REF] four signals are now visible for aromatic protons at 6.1, 6.7, 7.6, and 8.5 ppm in addition to two new low-field resonances at 11.8 and 13.4 ppm. Detailed decomposition of the spectra can be found in Figure S2 in Supporting Information. These particular lowfield signals, between 11 and 15 ppm, are signature of deshielded protons involved in strong H-bonding and correspond to the phenol groups of the ligands engaged in the ESIPT process. The splitting of the signals of these protons and those of the aromatics with the expected 1:1 ratio is an indication of the existence of two crystallographic nonequivalent BP(OH)2DC ligands, in line with the reported structure of MIL-140s (see Figure 2). The partially substituted solids MIL-140C_0.1 and MIL-140C_0.5 were then studied. First, upon deconvolution of the 1 H spectra (Figure S3), the amount of BP(OH)DC was quantified. In line with the chemical analyses, a preferential incorporation of the fluorescent ligand was found both in MIL-140C_0.1 (16%) and MIL-140C_0.5 (65%) (see Table S3). Interestingly, the distribution of the signals characteristics of the phenol groups is no longer statistical in these solids. Indeed, at a low substitution rate (10%), a single signal is observed at 11.8 ppm. This indicates that for MIL-140C_0.1, the BP(OH)2DC are positioned in a preferential site. This preferential occupancy is also observed with MIL-140C_0.5, showing a ca 65:35 ratio between the signals at 11.8 and 13.4 ppm. The solids were further analyzed by [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C MAS NMR (Figures S3 and S4). For MIL-140C_0, the spectrum presents two sets of resonances in the ranges 120-150 and 170-180 ppm, corresponding to aromatic and carboxylate carbons respectively. [START_REF] Bennett | Connecting defects and amorphization in UiO-66 and MIL-140 metal-organic frameworks: a combined experimental and computational study[END_REF] Signals in the same ranges are observed for MIL-140C_1, but two additional resonances are also visible at 156.0 and 157.4 ppm, and attributed to the carbons bearing OH groups. As in the 1 H NMR spectra, their relative proportion evolves depending on the level of substitution, with a preferential occupancy of the site associated with the signal at 156.0 ppm.

This experiment confirms the existence of two distinct chemical environments for the ligands and short contacts between them through the Hb and Hc protons. b) 1 H-13 C NMR HETCOR CPMAS spectrum of MIL-140C_1, allowing the assignment of all 1 H and 13 C NMR lines with respect to two distinct ligands (A and A' corresponding to site 2 and site 1, respectively).

To gain further structural insights, MIL-140C_1 was finally subjected to 2-D correlation experiments. [START_REF] Allendorf | Luminescent metal-organic frameworks[END_REF] H-1 H SQ-DQ and 1 H-13 C HETCOR-CPMAS experiments confirmed the existence of two separate sets of resonances for phenolic OH groups and aromatic protons, associated with two distinct crystallographic sites occupied by the BP(OH)2DC ligand within the same solid, and allowed the full assignment of proton and carbon signals, as shown in Figure 5. Therefore, the two crystallographic sites are differentiated by NMR on the base of their preferential occupancy with respect to the nature of the framework ligand, and denoted as ligand A and A' in Figure 5. In order to properly identify the sites associated with this preferential occupancy, all MIL-140C_n structures were refined from high resolution XRPD data (see Figures S6 and Table S4 for the final Rietveld plots and refinement parameters respectively). Indeed, whereas the structure of the smaller analogue MIL-140A (based on terephthalate) was experimentally solved and refined, the ones of MIL-140s obtained from longer linkers, and notably MIL-140C, were simply simulated based on experimental unit cell parameters. [START_REF] Guillerm | A Series of Isoreticular, Highly Stable, Porous Zirconium Oxide Based Metal-Organic Frameworks[END_REF] Therefore, the structure of MIL-140C_0 was first re-investigated. The whole powder pattern fitting without structural model showed that the previously reported unit cell parameters do not agree with the current pattern. Hence, the LP-Search indexing procedure was used to determine the correct unit cell in the C2/c space group. The structural model of the MIL-140A was then used as the starting point in the Rietveld refinement by replacing the terephthalate by the BPDC, which was treated as rigid body. As for MIL-140A, the BPDC ligands are located on two nonequivalent crystallographic sites in a 1 to 1 ratio. As shown in Figure 2, ligands in site 1 are stacked parallel to each other with a distance between the aromatic rings of ca. 3.9 Å, while ligands in site 2 are sideby-side with the shortest interatomic C•••C distance of 5.4 Å (C•••C distance between the carboxylic group equal to 7.8 Å). A 20° torsion angle is obtained between the benzene rings of the BPDC of site 1 whereas the flatness of site 2 is imposed by the inversion center. Attempts to lower the symmetry to the Cc space group were undertaken but did not significantly improve the refinement. Although phenyl rings are expected to be tilted in biphenyl moieties, the precise value of the torsion angle cannot be determined from our laboratory XRPD data (see discussion below). Rietveld refinements of modified MIL-140C series were then undertaken in the Cc space group due to the lower symmetry of the organic linker. Moreover, tilt angle between phenyl rings was arbitrary fixed to 0 for both sites in the three compounds, knowing that no tilt was observed in the structure of the parent 2,2'-bipyridine-3,3'-diol-5,5'-diethyl dicarboxylic ester solved from single crystal X-ray diffraction. 38 Figure 6 presents the comparison of crystal structures obtained for the whole series. For MIL-140C_0.1, the refinement revealed that the BP(OH)2DC ligands are all located in a single site, namely site 1 (see Figure 2). This full agrees with the NMR experiments, which indicate the occurrence of a preferential site of occupancy for the BP(OH)2DC ligand (ligand A' on Figure 5), which ultimately corresponds to site 1. Such a preference is also found in the structure of MIL-140C_0.5, where ca. 3/4 of the BP(OH)2DC ligands are localized in the site 1, in rather good agreement with the value extracted from the NMR analysis (2/3). As mentioned above, the value of the angle between the aromatic rings of the ligands cannot be accurately determined by XRPD. Moreover, rotation of these rings likely occurs in the solid state. Nevertheless, the presence of two strong OH•••N intramolecular hydrogen bonds is expected to favor a planar conformation for the BP(OH)2 motif, whereas short intramolecular CH•••HC contacts favor the stabilization of a tilted geometry for the BPDC motif, as commonly observed in molecular compounds. This could explain why the BP(OH)2DC ligands are more easily accommodated in site 1, which is associated with shorter inter-ligand distances.

Porosity, hydrophilicity and stability

The porosity of the MIL-140C_n series was probed by nitrogen adsorption measurements at 77 K. As shown in Figure 7, all solids present a reversible type I isotherm, characteristic of microporous materials. The Brunauer-Emmett-Teller (BET) surface areas reached 790, 750 and 700 m 2 .g -1 for MIL-140C_0.1, _0.5 and _1, respectively, compared to the expected value of 840 m 2 .g -1 for MIL-140C_0. [START_REF] Guillerm | A Series of Isoreticular, Highly Stable, Porous Zirconium Oxide Based Metal-Organic Frameworks[END_REF] The pore volume followed the same trend (0.31, 0.27 and 0.25 cm 3 .g -1 for MIL-140C_0.1, _0.5 and _1, respectively). The surface area and pore volume thus slightly decrease when the amount of BP(OH)2DC increases, as a consequence of the bulkier character of BP(OH)2DC compared to BPDC and the slight contraction of the unit-cell. The examination of the crystal structures with the Platon software indeed confirmed this trend (accessible void estimated to 42, 40 and 39 % for MIL-140C_0.1, _0.5 and _1, respectively).

Figure 7. N2 adsorption measurements at 77 K of MIL-140C_0.1, MIL-140C_0.5 and MIL-140C_1.

Thermogravimetric analyses (TGA) were performed on all solids, both fresh and after two weeks of air exposure (Figures S7 and S8 respectively). For fresh MIL-140C_0.5 and MIL-140C_1, the TG curves present a slight (~2.5 %) continuous loss of mass between 25 and ca. 250 °C, attributed to the removal of water from the pores, followed by a major weight loss starting at ca. 350 °C and associated with the combustion of the ligand. For MIL-140C_0 and MIL-140C_0.1, the first weight loss is almost undetected (< 1%), in agreement with the hydrophobicity of the MIL-140s structures. After two weeks in air, no change is observed for MIL-140C_0.1 (Figure S9). On the contrary, the TG curves of MIL-140C_0.5 and MIL-140C_1, exhibit a more pronounced weight loss at low temperature of respectively 7.6 and 9.6%, corresponding to 1.7 and 2.2 water per Zr. This indicates that by increasing the amount of BP(OH)2DC ligand, the structure becomes more hydrophilic. Furthermore, in the case of MIL-140C_0.5 and MIL-140C_1, the water removal occurred on a wide temperature range (20-170 °C), suggesting strong interactions between the water molecules and the framework. Indeed, it was possible to propose a plausible location of the water molecules from the structure determination. As shown in Figure 6, the refinement of the residual electronic density within the pores suggests the presence of 0.2 water molecule per Zr for MIL-140_0.1, while no water at all was observed for MIL-140_0. These values reached 1. Knowing that MIL-140C is among the most stable Zr-based MOFs, the stability of the series towards water was evaluated.

First, for both hydrophobic (MIL-140C_0.1) and hydrophilic (MIL-140C_1) solids, no loss of crystallinity was observed after exposure to air for one month (Figure 8 and S9-S10). After ca. 4 months, while no change was still detected for MIL-140C_0.1, an obvious variation of the diffraction pattern occurred for MIL-140C_1 (Figure S11). Note here that a similar behavior was already observed by D'Alessandro et al. when introducing large amount of 2,2'-bipyridine-5,5'-dicarboxylate within this structure type. [START_REF] Liang | Tuning the cavities of zirconium-based MIL-140 frameworks to modulate CO2 adsorption[END_REF] This effect is clearly related to the presence of water, since MIL-140C_1 stored in dry atmosphere remains unaffected (see Figure S12). The stability was finally evaluated after suspending the solids in water (1 mg.mL -1 ) for one week. Even under boiling conditions, no change was noticed on the powder XRD pattern of MIL-140C_0.1 (Figure 8d), confirming the high stability of the BP(OH)2DC-poor solids. Concerning MIL-140C_1, it was found to be unaltered at room temperature (Figure S13), whereas under refluxing conditions, an almost complete transformation to a new crystalline phase is observed (Figure 8g). A closer look indicates that this new phase does not contain crystallized ZrO2 (Figure S15) and is the one which started to form after a long exposure to ambient air (Figure S11). Moreover, the infrared spectra of MIL-140C_1 before and after the transformation are almost identical (Figures S15), and do not present vibration bands characteristics of the formation of free carboxylic acid (~1700 cm -1 ) as often observed upon degradation of MOFs. Hence, the resulting product is likely a new coordination compound. Previously, Bennett et al. followed the degradation of MIL-140C upon ball milling, and noticed a complete amorphization together with the formation of free carboxylic acid groups. [START_REF] Bennett | Connecting defects and amorphization in UiO-66 and MIL-140 metal-organic frameworks: a combined experimental and computational study[END_REF] Here, the transformation pathway is markedly different. The indexation of the XRPD pattern of the final product converged to a triclinic unit cell [a = 4.012 (8), b = 14.061 (7), c = 15.376(5) Å,  = 111.06(3),  = 91.4(3) and  = 94.0(4)°, V = 806(2) Å 3 ], with a satisfactory figure of merit (M20 = 27), confirmed by its full pattern matching (Rwp = 0.087, see Figure S15). The poor quality of the dataset precluded any deeper structural analysis. Nevertheless, nitrogen sorption measurements carried out at 77 K suggests that this solid presents a very limited accessible porosity (see Figure S17).

To summarize, while the chemical stability of MIL-140C is maintained in BP(OH)2DC-poor solids (MIL-140_0.1), the BP(OH)2DC rich samples are less stable, and this instability is associated with the easier adsorption of water. Hence, one may conclude that the high stability of most MIL-140 solids then derives from their strong hydrophobic character rather than from the unique nature of the constitutive inorganic building unit. [START_REF] Guillerm | A Series of Isoreticular, Highly Stable, Porous Zirconium Oxide Based Metal-Organic Frameworks[END_REF][START_REF] Liang | Tuning the cavities of zirconium-based MIL-140 frameworks to modulate CO2 adsorption[END_REF] This is moreover in line with previous studies on less water stable M(II) carboxylate MOFs, which evidenced the interplay between hydrophobicity and water stability. 39-40

Photophysical properties

The optical properties of MIL-140C_0.1, MIL-140C_0.5 and MIL-140C_1 were investigated in the solid state and compared with the one of free H2BP(OH)2DC. As expected, upon excitation at 390 nm, all MIL-140C-n solids present a yellow emission characteristic to the ESIPT fluorescence of the ligand, while the MIL140C_0 only shows a weak blue fluorescence emission (Figure 9). A slight blueshift is observed when moving from the free ligand to MIL-140C_1 (emission centered at 562 and 550 nm respectively). The fluorescent quantum yield of the whole series was also evaluated, and the resulting values are summarized in Table 1. All these compounds exhibit a high quantum yield (> 15%), of the same order of magnitude as the free ligand. The maximum value (35%) is obtained for MIL-140C_0.1, likely because the high level of dilution of the BP(OH)2DC emitter in the framework prevents the intermolecular quenching (see below). S5). For all MIL-140C_n derivatives, the resulting decays could be satisfactorily fitted using a three-exponential model with three decay times (0.88, 3.16 and 4.79 ns). By comparison, the decays of the H2BP(OH)2DC precursor could be fitted with a three exponentials model with decay times of 0.60, 2.60 and 5.11 ns (Table S6). While these decay times cannot be directly attributed to distinct crystallographic environments for the BP(OH)2DC ligand, we can note that in all cases, the long decay time is very close to the fluorescence lifetime measured for the diester precursor BP(OH)2(COOEt)2 in dichloromethane (4.64 ns). [START_REF] Yu | Adjusting the Stability of Metal-Organic Frameworks under Humid Conditions by Ligand Functionalization[END_REF] For a given solid, the relative contributions of the three decay times to the overall fluorescence only slightly vary with the emission wavelength. This indicates that there are no excited-state processes such as excimers formation or resonance energy transfer occurring in these solids. The comparison of the three MIL-140C_n derivatives at a given emission wavelength shows that the higher the substitution rate the shorter the average fluorescence decay time (see Table S5). At high doping rates, there is apparition of some Aggregation Caused Quenching (ACQ), that could be due to stacking interactions between BP(OH)2DC ligands, while at low doping rate BP(OH)2DC ligands are diluted with BPDC ligands which limits the quenching. As a consequence, using low doping rate appears as an efficient strategy to limit ACQ. Further experiments were conducted to evaluate the sensitivity of the emission of the most stable solids (MIL-140C_0.1 and MIL-140C_0.5) towards pH variation. All experiments were carried out in very dilute conditions (5.10 -6 mol.L-1, corresponding to ca. 2 mg of MOF per liter of water) to prevent reabsorption of the emitted fluorescence. The emission properties of a solution of ligand were first investigated (Figure S19). Upon increasing the pH from 4 to 8, the emission peak centered at ca. 500-510 nm is only slightly blue shifted, whereas as soon as pH 8-9 is reached, this peak vanishes and a new peak centered at 450-460 nm appears. While the first emission peak is attributed to the ESIPT process (see Figure 1), the second one, considering the pKa of the phenol group (~9) is associated to a partially deprotonated form of the dienol motif and thus a different electronic transition. For the MOFs in suspension (Figure S20), similar behaviors occur: a first emission peak centered at ~550 nm is visible in acidic medium, while a new band centered at 460 nm, this time of higher intensity, appears above pH 9.

Nevertheless the increase of the pH above ~7 is also accompanied with a dissolution of the MOFs, in line with previous stability studies, which showed that under very dilute conditions, MOFs are usually unstable once pH reaches a higher value than the pKa of the binding group (here carboxylate). [START_REF] Cunha | Rationale of Drug Encapsulation and Release from Biocompatible Porous Metal-Organic Frameworks[END_REF][START_REF] Bellido | Understanding the Colloidal Stability of the Mesoporous MIL-100(Fe) Nanoparticles in Physiological Media[END_REF] Hence, while the sensitivity of the emission properties of the ligand makes it appealing for the detection of slight modifications of the pH in the 8-10 range, this range does not match with the stability range of the MOFs.

CONCLUSION

We reported here a series of Zr(IV)-based MOF series built up from an ESIPT-type fluorescent ligand. All these solids belong to the MIL-140 structure-type, and were found to combine a significant microporosity (SBET > 700 m 2 .g -1 ) together with a high luminescent quantum yield (> 15%). These solids were found to be more hydrophilic than the pristine MIL-140C, and, as a consequence, less stable towards water. Nevertheless, by playing with the rate of ligand substitution, as exemplified with MIL-140C_0.1, it was possible to combine a good chemical stability with an optimized quantum yield (35%). Such solids thus appear of potential interest e.g. as emitters in light emitting devices or for optical detection in aqueous medium under proper pH conditions.

ASSOCIATED CONTENT

Supporting Information. Detailed synthetic conditions, elemental analyses, XRPD data, TG analyses, IR spectra, [START_REF] Padalkar | Excited-state intramolecular proton-transfer (ESIPT)-inspired solid state emitters[END_REF] C NMR spectra, fluorescence decay analysis. This material is available free of charge via the Internet at http://pubs.acs.org. Crystallographic data are available through the Cambridge Structural Database (CCDC 1895855-1895858).

Figure 2 .

 2 Figure 2. Crystal structure of MIL-140C_0. Top: view along the c axis; bottom: details of the arrangement of the ligands in site 1 along the a axis (blue), and in the site 2 along the b axis (green).

Figure 4 .

 4 Figure 4. 1 H solid state NMR spectra of the MIL-140C_n series.

Figure 5 .

 5 Figure 5. a) 1 H-1 H NMR SQDQ Baba spectrum of MIL-140C_1. This experiment confirms the existence of two distinct chemical environments for the ligands and short contacts between them through the Hb and Hc protons. b) 1 H-13 C NMR HETCOR CPMAS spectrum of MIL-140C_1, allowing the assignment of all 1 H and 13 C NMR lines with respect to two distinct ligands (A and A' corresponding to site 2 and site 1, respectively).

Figure 6 .

 6 Figure 6. Crystal structures of the MIL-140C_n series, view along the c axis.Figure6presents the comparison of crystal structures obtained for the whole series. For MIL-140C_0.1, the refinement revealed that the BP(OH)2DC ligands are all located in a single site, namely site 1 (see Figure2). This full agrees with the NMR experiments, which indicate the occurrence of a preferential site of occupancy for the BP(OH)2DC ligand (ligand A' on Figure5), which ultimately corresponds to site 1. Such a preference is also found in the structure of MIL-140C_0.5, where ca. 3/4 of the BP(OH)2DC ligands are localized in the site 1, in rather good agreement with the value extracted from the NMR analysis (2/3). As mentioned above, the value of the angle between the aromatic rings of the ligands cannot be accurately determined by XRPD. Moreover, rotation of these rings likely occurs in the solid state. Nevertheless, the presence of two strong OH•••N intramolecular hydrogen bonds is expected to favor a planar conformation for the BP(OH)2 motif, whereas short intramolecular CH•••HC contacts favor the stabilization of a tilted geometry for the BPDC motif, as commonly observed in molecular compounds. This could explain why the BP(OH)2DC ligands are more easily accommodated in site 1, which is associated with shorter inter-ligand distances.

  4 and 1.8 for MIL-140_0.5 and MIL-140_1 respectively, with short intermolecular COH•••H2O and H2O•••H2O distances, confirming the hydrophilic character of the BP(OH)2DC rich solids.

Figure 8 .

 8 Figure 8. Powder X-ray diffraction patterns of a) MIL-140C_1 simulated from the crystal structure, b) MIL-140C_0.1 as synthesized, c) MIL-140C_0.1 after 1 month in air, d) MIL-140C_0.1 after 1 week in boiling water, e) MIL-140C_1 as synthesized, f) MIL-140C_1 after 1 month in air, and g) MIL-140C_1 after 1 week in boiling water.

Figure 9 .

 9 Figure 9. a) Pictures of MIL-140C_0, _0.1, _0.5 and _1 under UV light at 365 nm and b) emission spectra of H2BP(OH)2DC (green), MIL-140C_0.1 (red), _0.5 (blue) and _1 (purple) after excitation at 390 nm. Time-resolved fluorescence emission was also studied for MIL-140C_0.1, MIL-140C_0.5 and MIL-140C_1 and compared with the solid molecular precursor H2BP(OH)2DC. Fluorescence decays were recorded at three emissions wavelengths (510, 530 and 580 nm, see TableS5). For all MIL-140C_n derivatives, the resulting decays could be satisfactorily fitted using a three-exponential model with three decay times (0.88, 3.16 and 4.79 ns). By comparison, the decays of the H2BP(OH)2DC precursor could be fitted with a three exponentials model with decay times of 0.60, 2.60 and 5.11 ns (TableS6). While these decay times cannot be directly attributed to distinct crystallographic environments for the BP(OH)2DC ligand, we can note that in all cases, the long decay time is very close to the fluorescence lifetime measured for the diester precursor BP(OH)2(COOEt)2 in dichloromethane (4.64 ns).[START_REF] Yu | Adjusting the Stability of Metal-Organic Frameworks under Humid Conditions by Ligand Functionalization[END_REF] For a given solid, the relative contributions of the three decay times to the overall fluorescence only slightly vary with the emission wavelength. This indicates that there are no excited-state processes such as excimers formation or resonance energy transfer occurring in these solids. The comparison of the three MIL-140C_n derivatives at a given emission wavelength shows that the higher the substitution rate the shorter the average fluorescence decay time (see TableS5). At high doping rates, there is apparition of some Aggregation Caused Quenching (ACQ), that could be due to stacking interactions between BP(OH)2DC ligands, while at low doping rate BP(OH)2DC ligands are diluted with BPDC ligands which limits the quenching. As a consequence, using low doping rate appears as an efficient strategy to limit ACQ. Further experiments were conducted to evaluate the sensitivity of the emission of the most stable solids (MIL-140C_0.1 and

Table 1 .

 1 Fluorescent quantum yield of the title solids.

		ex / nm	em /nm	Φ
	BP(OH)2DC	390	562	0.29
	MIL-140c_0.1	390	539	0.35
	MIL-140c_0.5	390	547	0.27
	MIL-140c_1	390	550	0.17

ACKNOWLEDGMENT

We acknowledge the labex CHARMMMAT (ANR-11-LABEX-0039) for the postdoctoral fellowships of Virgile Trannoy. Arnaud Brosseau (PPSM) is gratefully acknowledged for his help with the time-resolved fluorescence measurements.

Funding Sources

This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Inves-tissements d'Avenir" Program no. CHARMMMAT ANR-11-LABX-0039.

AUTHOR INFORMATION

Corresponding Author * E-mail address: virgile.trannoy@cnrs-imn.fr, pei.yu@u-psud.fr, thomas.devic@cnrs-imn.fr.

Author Contributions

V.T., A.L. and P.Y. took care of the synthesis and characterization of the fluorescent ligand; V.T., C.L., C.R.M. and T.D. were involved in the synthesis and characterization of the MOFs, N.G. conducted the PXRD analysis, M.H. conducted the NMR experiments; V.T., C.A. and G.C. were in charge of the optical studies. The manuscript was written through contributions of all authors.


F R Éd

Éric Chapoton

Christian Krattenthaler

Jiang Zeng

MOMENTS OF q-JACOBI POLYNOMIALS AND q-ZETA VALUES

We explore some connections between moments of rescaled little q-Jacobi polynomials, q-analogues of values at negative integers for some Dirichlet series, and the q-Eulerian polynomials of wreath products of symmetric groups.

Introduction

This article is about a connection between three kinds of objects, namely (A) q-analogues of Dirichlet series and their values at negative integers, (B) basic hypergeometric polynomials and their sequences of moments, (C) weighted enumeration of elements in coloured symmetric groups. Let us give more details on these three points in order. The point (A) is about a q-analogue of the Dirichlet series

L(s, c, r) = m≥1 m≡c (mod r) 1 m s , (0.1)
where c, r are fixed integers. This is the Riemann zeta function when (c, r) = (1, 1). For general c and r, the summands do not form a multiplicative sequence, so there is no Euler product. One defines as in [START_REF] Chapoton | Fractions de Bernoulli-Carlitz et opérateurs q-zeta[END_REF] a q-analogue of this Dirichlet series as an operator

L q (s, c, r) = m≥1 m≡c (mod r) 1 [m] s q F m , (0.2)
where [m] q = (q m -1)/(q-1) is the usual q-integer and F m is the formal Frobenius operator, acting on formal power series in z with no constant term and coefficients in Q(q), defined by F m (f )(q, z) = f (q m , z m ). Whenever the Dirichlet series L(s, c, r) factorizes as an Euler product, then so does the operator L q (s, c, r) as a product of commuting operators.

One then introduces some q-analogues of the values of L(s, c, r) at non-positive integers, namely L q (-n, c, r)(z) for n ≥ 0. As images of the formal power series f (z) = z, these are formal power series in the variable z with coefficients in Q(q). As we will see, these are in fact rational functions in q and z.

The point (B) is about the little q-Jacobi polynomials, a system of orthogonal polynomials in one variable. This is one of the families in the Askey-Wilson scheme of basic hypergeometric orthogonal polynomials (cf. [START_REF] Koekoek | Hypergeometric orthogonal polynomials and their q-analogues[END_REF]). The little q-Jacobi polynomials, orthogonal with respect to the variable x, depend on the variable q and two further parameters. For each choice of integers (c, r), by an appropriate choice of these parameters and some affine change in the variable x, one obtains a system of orthogonal polynomials involving the variables q and z. Their sequence of moments, which are evaluations of the associated linear functional at the monomials x n , are therefore rational functions in q and z.

The point (C) is about the complex reflection groups G(r, n) defined as the wreath product of a symmetric group S n by a cyclic group Z r . The elements of these groups can be seen as coloured permutation matrices, where non-zero entries contain a root of unity of order dividing r. By using two combinatorial statistics on these elements, one can refine the number r n n! of elements of G(r, n) into a polynomial in two variables q and z, with positive integer coefficients. In this context, the parameter c is absent.

The aim of this article is to show that (A), (B) and (C) all give essentially the same rational function in q and z. More precisely, the rational functions from (A) and (B) are essentially the quotients of the polynomial from (C) by simple denominators. The part (C) is involved only when the parameter c equals 1.

The relationship between (C) and (A) is merely a reformulation of the results by Biagioli and the third author in [START_REF] Biagioli | Enumerating wreath products via Garsia-Gessel bijections[END_REF]. The relationship between (A) and (B) is a (q, z)-analogue of well-known results about Bernoulli numbers and Euler numbers, for which we refer to [START_REF] Dilcher | Hankel determinants of sequences related to Bernoulli and Euler Polynomials[END_REF].

1. Preliminaries 1.1. Orthogonal polynomials. In this subsection we recall some fundamental results of the theory of orthogonal polynomials [START_REF] Seio | An introduction to orthogonal polynomials[END_REF]10]. Let K be a field.

Definition 1.1. Let ϕ : K[x] → K be a linear functional. A sequence of polynomials {p n (x)} n≥0 in K[x]
is said to be orthogonal with respect to the linear functional ϕ if:

(i) p n (x) is of degree n, for n = 0, 1, . . . ; (ii) ϕ(p n (x) p n ′ (x)) = K n δ n,n ′ , K n = 0, for n = 0, 1, . . . . The sequence {µ n } n≥0 with µ n = ϕ(x n ) for n ≥ 0 is called the moment sequence associated with ϕ.
Sometimes the polynomials {p n (x)} are also said to be orthogonal with respect to the sequence of moments {µ n } n≥0 .

Let us write OPS as a shorthand for orthogonal polynomial system.

Theorem 1.1 (Favard's theorem). A sequence of polynomials {p n (x)} n≥0 in K[x] is a monic OPS if and only if there is a sequence {b n } n≥0 and a non-zero sequence {λ n } n≥0 such that p 0 (x) = 1, p 1 (x) = x -b 0 and

p n+1 (x) = (x -b n )p n (x) -λ n p n-1 (x) for n ≥ 1. (1.1)
Theorem 1.2. Let the polynomials (p n (x)) n≥0 satisfy (1.1). Then, if we fix µ 0 := λ 0 = 0, the functional ϕ with respect to which this OPS is orthogonal is unique. Furthermore, for Q n (x) = α -n p n (αx + β), α = 0, we have

Q n+1 (x) = x - b n -β α Q n (x) - λ n α 2 Q n-1 (x), for n ≥ 1, (1.2)
and, if (p n (x)) n≥0 is the OPS with respect to the moments (µ n ), then (Q n (x)) is the OPS with respect to the moments ν n given by

ν n = ϕ x -β α n = α -n n j=0 n j (-β) n-j µ j , for n ≥ 0. (1.3)
Theorem 1.3. The generating function of the moments {ϕ(x n )} has the continued fraction expansion

n≥0 ϕ(x n ) t n = λ 0 1 -b 0 t - λ 1 t 2 1 -b 1 t - λ 2 t 2 . . . . (1.4)
There is also an associated formula for Hankel determinants of the sequence of moments, see [10, 8, 9] 1.2. Wreath product of a symmetric group by a cyclic group. Let r ≥ 1 and n ≥ 1 be integers. Let S n be the symmetric group on {1, . . . , n}. A permutation σ ∈ S n will be denoted by σ = σ(1) • • • σ(n). The wreath product Z r ≀ S n of Z r by S n is the set

G(r, n) := {(c 1 , . . . , c n ; σ) | c i ∈ {0, . . . , r -1}, σ ∈ S n }.
(1.5)

Using a fixed primitive r-th root of unity ξ, one can see the elements in this set as square matrices, starting from the permutation matrix for σ and replacing the non-zero entry in column i by ξ c i . This group is therefore also called the group of r-coloured permutations. We will represent its elements as

γ = [γ(1), . . . , γ(n)] = [σ(1) c 1 , . . . , σ(n) cn ]. We denote by col(γ) := n i=1 c i , the colour weight of any γ ∈ G(r, n). For example, if γ = [4 1 , 3 0 , 2 4 , 1 2 ] ∈ G(5, 4) then col(γ) = 7.
We endow the set of possible values for the γ(i) with the following total order:

n r-1 < • • • < n 1 < • • • < 1 r-1 < • • • < 1 1 < 0 < 1 0 < • • • < n 0 .
The 0 is inserted here to separate the "positive" values i 0 from the "negative" values i c with c ≥ 1. It will also be used in the statistics that we are going to define now.

The descent set of γ ∈ G(r, n) is defined by

Des G (γ) := {i ∈ {0, . . . , n -1} | γ(i) > γ(i + 1)}, (1.6)
where γ(0) := 0, and its cardinality is denoted by des G (γ).

The major index is defined to be the sum of descent positions:

maj(γ) = i∈Des G (γ) i,
and the flag-major index is defined by fmaj(γ) := r • maj(γ) + col(γ).

For example, for γ = [4 1 , 3 0 , 2 4 , 1 2 ] ∈ G(5, 4) we have Des G (γ) = {0, 2}, des G (γ) = 2, maj(γ) = 2, and fmaj(γ) = 17. Biagioli and the third author [START_REF] Biagioli | Enumerating wreath products via Garsia-Gessel bijections[END_REF] defined the generating polynomials for G(r, n) with respect to the bi-statistic (des, fmaj):

G r,n (Z, q) = γ∈G(r,n) Z des G (γ) q fmaj(γ) , (1.7)
and they proved the following identity. We refer the reader to Subsection 1.3 for the meaning of the q-notations.

Theorem 1.2 (Carlitz-MacMahon identity for G(r, n)). Let r and n be positive integers. Then G r,n (Z, q)

(Z; q r ) n+1 = k≥0 Z k [rk + 1] n q .
(1.8)

The above formula gives a nice generalization of identities of Carlitz [START_REF] Carlitz | A combinatorial property of q-Eulerian numbers[END_REF] for the symmetric group (corresponding to the case where r = 1), and of Chow and Gessel [START_REF] Chow | On the descent numbers and major indices for the hyperoctahedral group[END_REF] for the hyperoctahedral group (corresponding to the case where r = 2). 1.3. Little q-Jacobi polynomials. We use the standard q-notations from [START_REF] Koekoek | Hypergeometric orthogonal polynomials and their q-analogues[END_REF], among which

[x] q = 1 -q x 1 -q , the q-Pochhammer symbol

(a; q) n = (1 -a)(1 -aq) . . . (1 -aq n-1 ),
and the convenient shorthand (a, b; q) n = (a; q) n (b; q) n .

We furthermore need the q-binomial theorem [7, p. 16]

1 Φ 0 (a; -; q, z) = ∞ k=0 (a; q) k (q; q) k z k = (az; q) ∞ (z; q) ∞ (1.9)
and the q-Chu-Vandermonde formula [7, p. 17]

2 Φ 1 (q -n , b; c; q, q) = ∞ k=0 (q -n ; q) k (b; q) k (c; q) k (q; q) k q k = (c/b; q) n (c; q) n b n .
(1.10)

The little q-Jacobi polynomials [7, p. 482] have the explicit representation

p n (x; a, b | q) = 2 Φ 1 q -n , abq n+1 aq ; q, qx = ∞ k=0 (q -n ; q) k (abq n+1 ; q) k (aq; q) k (q; q) k (qx) k , (1.11)
and are orthogonal with respect to the inner product defined by

1 0 f (x)g(x)d q w(x) = ∞ k=0 f (q k )g(q k )w(q k ),
where

w(x) = (aq, bq; q) ∞ (abq 2 , q; q) ∞ • (qx; q) ∞ (bqx; q) ∞ x α+1
with a = q α . Let p n (x) be the monic little q-Jacobi polynomials, i.e.,

p n (x; a, b | q) = (-1) n q -( n 2 ) (abq n+1 ; q) n (aq; q) n p n (x).
Then the normalized recurrence relation [7, p. 483] reads

xp n (x) = p n+1 (x) + (A n + C n )p n (x) + A n-1 C n p n-1 (x), (1.12)
where

A n = q n (1 -aq n+1 )(1 -abq n+1 ) (1 -abq 2n+1 )(1 -abq 2n+2 ) , C n = aq n (1 -q n )(1 -bq n ) (1 -abq 2n )(1 -abq 2n+1 )
.

By the q-binomial theorem (1.9), the nth moment is

µ n = 1 0
x n d q w(x) = (aq; q) n (abq 2 ; q) n , for n = 0, 1, 2, . . . . (1.13) We can also verify (1.13) by using the explicit formula (1.11) and the q-Chu-Vandermonde formula (1.10): namely, for n ≥ 1, we have We can now prove the connection between (B) and (A).

Theorem 1.4. For integers r ≥ 1, the nth moment µ n of the shifted little q-Jacobi polynomials p n (q -c (1 + (q -1)x); Zq -r , 1 | q r ) is

µ n = (1 -Z) k≥0 ([rk + c] q ) n Z k .
(1.15)

For c = 1, we have

µ n = G r,n (Z, q) (Zq r ; q r ) n .
(1.16)

Proof. By (1.3), the nth moment of p n (q -c (1 + (q -1)x); a, b | q r ) is

ν n = q nc (q -1) -n n j=0
n j (-q c ) j-n (aq r ; q r ) j (abq 2r ; q r ) j .

Substituting a by Zq -r and b by 1, we get

ν n = q nc (q -1) -n n j=0 n j (-q c ) j-n 1 -Z 1 -Zq rj = (1 -Z)(q -1) -n k≥0 Z k n j=0 n j (-1) n-j q (rk+c)j = (1 -Z) k≥0 ([rk + c] q ) n Z k .
The last statement follows from (1.8).

Theorem 1.5. The generating function for the moments µ n in (1.15) has the continued fraction expansion n≥0 .17) where the coefficients b n and λ n are given by

µ n t n = 1 1 -b 0 t - λ 1 t 2 1 -b 1 t - λ 2 t 2 . . . . ( 1
λ n = Zq 2r(n-1)+2c [rn] 2 q (1 -Zq r(n-1) ) 2 (1 -Zq 2rn )(1 -Zq r(2n-1) ) 2 (1 -Zq r(2n-2) ) (1.18) and b n = q c q -1 q rn (1 -Zq rn ) 2 (1 -Zq 2rn )(1 -Zq r(2n+1) ) + Zq r(n-1) (1 -q rn ) 2 (1 -Zq r(2n-1) )(1 -Zq 2rn ) -q -c . (1.19)
Proof. This follows by combining (1.12) and Theorems 1.4, 1.2 and 1.3 with α = (q -1)/q c and β = q -c .

Zeta operators at negative integers

We define the q-difference operator on the formal power series f in z by ∆ z (f ) = f (qz) -f (z) q -1 .

(2.1)

Note that ∆ z (z m ) = [m] q z m . This implies that repeated application of the operator ∆ z creates the sequence of values at negative integers for the q-analogues of Dirichlet series. Indeed, for n ≥ 0, we have L q (-n, c, r)(z) = m≥1 m≡ c(mod r)

[m] n q z m .

(2.2) and therefore ∆ z (L q (-n, c, r)(z)) = L q (-n -1, c, r)(z).

(2.3) Computing the initial value for n = 0, one finds L q (0, c, r)(z) = z c 1 -z r .

(2.4)

By induction using (2.3), the expression L q (-n, c, r)(z) is a rational function in q and z with denominator (z r , q r ) n+1 .

The general relation between (A) and (B) is therefore, by comparison of (2.2) with (1.15), using (2.4), that L q (-n, c, r)(z)/L q (0, c, r)(z) = µ n Z=z r .

(2.5)

For c = 1, comparison with (1.8) reveals the combinatorial expression L q (-n, c, r)(z) = z G r,n (z r , q) (z r , q r ) n+1 ,

which makes the precise connection between (A) and (C).

1 0p

 1 n (x; a, b | q)d q w(x) = 0. (1.14)

1 Research partially supported by the Austrian Science Foundation FWF (grant S50-N15) in the framework of the Special Research Program "Algorithmic and Enumerative Combinatorics" Date: December 2, 2020.

[9] Christian Krattenthaler. Advanced determinant calculus: a complement. Email address: zeng@math.univ-lyon1.fr