Rufine Akue-Gedu

Eric Debiton

Yoan Ferandin

Laurent Meijer

Michelle Prudhomme

Fabrice Anizon

Pascale Moreau

Synthesis and biological activities of aminopyrimidyl-indoles structurally related to meridianins

Keywords: Meridianins, Suzuki cross-coupling, Kinase inhibitors, Dyrk1A inhibitors

The synthesis of new meridianin derivatives substituted at the C-5 position of the 2-aminopyrimidine ring by various aryl groups and substituted or not by a methyl group on the indole nitrogen is described. These compounds were tested for their kinase inhibitory potencies toward five kinases (CDK5/p25, CK1δ/ε, GSK-3α/β, Dyrk1A and Erk2) as well as their in vitro antiproliferative activities toward a human fibroblast primary culture and two human solid cancer cell lines (MCF-7 and PA 1).

Introduction

Meridianins are marine alkaloids isolated and characterized from the south Atlantic tunicate Aplidium meridianum. 1 Meridianins A-G [1], [2] and [3] (Fig. 1), indole derivatives substituted in the C-3 position by a 2-aminopyrimidine ring, were successfully evaluated for their ability to inhibit various protein kinases 3 and to display antitumour activity. 4 The closely related meriolins, a family of 7-azaindole synthetic meridianin analogues, which exhibit potent kinase inhibitory activities and antiproliferative properties were also described. [5] and [6] Figure 1. Meridianins A-G and derivatives A-Q described by our group. Since protein kinases are attractive targets for the discovery of biologically active compounds of potential therapeutic interest, our aim is to identify new ATP-competitive kinase inhibitors. Thus, we were recently interested in meridianin derivatives substituted at the C-5 position of the 2-aminopyrimidine ring. In recent papers, we described the synthesis and biological activities of meridianin G derivatives, substituted or not on the indole nitrogen with a methyl group, and bearing various aryl moieties at the C-5 position of the pyrimidine ring (compounds A-H and J-Q, Fig. 1). [7] and [8] It was shown that the substitution at this C-5 position and the methylation of the indole nitrogen were critical for either kinase inhibitory potencies or in vitro antiproliferative activities. The meridianin derivatives A-H and K-Q were tested toward a panel of 9 protein kinases (KDR, IGF-1R, c-Met, RET, c-Src, c-Abl, PKA, CDK2/cyclin A and HER-1) and their in vitro antiproliferative activities were examined toward a human fibroblast primary culture and two human solid cancer cell lines (MCF-7 and PA 1). Despite weak kinase inhibitory potencies, compounds G, H, L and M exhibited high in vitro antiproliferative activities toward PA 1 cells. It was found that these compounds do not interfere with PA 1 cell-cycle and may be considered as direct cytolysis or apoptosis inducers. Considering these first biological results, it was of interest to pursue the study with new aryl substituents on the pyrimidine ring in order to identify the substitution pattern providing the highest biological potencies. In this paper, we described the synthesis of new meridianin analogues diversely substituted at the C-5 position of the pyrimidine ring and methylated or not on the indole nitrogen. Moreover these compounds were tested for their kinase inhibitory potencies toward five kinases (CDK5/p25, CK1δ/ε, GSK3α/β, Dyrk1A and Erk2) as well as their in vitro antiproliferative activities toward a human fibroblast primary culture and two human solid cancer cell lines (MCF-7 and PA 1).

Chemistry

Compounds 1-9 were synthesized from brominated derivatives A or J, methylated or not on the indole nitrogen. A and J were prepared according to previously described procedure (Scheme 1). 7 Suzuki crosscoupling was performed using various commercially available arylboronic acids, tetrakis(triphenylphosphine)palladium(0) and sodium carbonate in a H 2 O/EtOH/toluene medium. Compounds 1-9 were obtained in 31-60% isolated yields. Due to purification difficulties, the nonmethylated analogues of compounds 7-9 could not be isolated as pure compounds. Results were similar using compounds A or J (compare 1 and 2, 3 and 4, 5 and 6), and yields dropped using aryl boronic acid containing a basic nitrogen atom. Moreover, in order to introduce various amines (aryl or alkylamines) by Buchwald type coupling, in the C-5 position of the pyrimidine ring, compound 10, the iodo analogue of J, was prepared in 77% yield from methylated meridianin G (compound I), using iodine in DMSO. 9 Unfortunately, we never manage to substitute this position by an amine derivative from compound 10 or its brominated analogue J. In summary, the method described here allowed the introduction, in the pyrimidine C-5 position, of heteroaryl moieties or phenyl groups bearing both electron donor or electron acceptor substituents in para or meta positions.

Results and discussion

In vitro antiproliferative activities of compounds 1-10 were evaluated toward a human fibroblasts primary culture and two human solid cancer cell lines (MCF-7 and PA 1). The antiproliferative effect (IC 50 ) of the tested drug was assessed by the resazurin reduction test. 10 Under the conditions used, none of the newly synthesised compounds showed any significant cytotoxic activity (IC 50 < 50 µM) on fibroblasts or MCF-7 cell lines. Only mild activities (IC 50 around 30 µM) were observed on PA 1 cells with compounds 1, 2, 5 and 10 (Table 1). These results indicate that the substituents introduced at the C-5′ position are detrimental to the cytotoxic effect of these series on PA 1 cells. The kinase inhibitory potencies of compounds 1-10 and that of previously synthesised derivatives G, H, L and M which have shown interesting antiproliferative activities toward PA1 cells were evaluated as IC 50 values toward five protein kinases (CDK5/p25, CK1δ/ε, GSK-3α/β, Dyrk1A and Erk2). Only two compounds were mildly active toward CDK5/p25 with IC 50 values in the micromolar range. These derivatives are both methylated on the indole nitrogen and substituted either by a pyridyl group (compound 9, IC 50 = 5.3 µM) or by an iodine atom (compound 10, IC 50 = 2.6 µM) in the C-5 position of the aminopyrimidine moiety. Considering the other kinases, the best inhibitory potencies were sub-micromolar inhibition of CK1δ/ε (compound 1, IC 50 = 0.49 µM), GSK-3α/β (compound 6, IC 50 = 0.63 µM), Dyrk1A (compounds 1, IC 50 = 0.6 µM; 3, IC 50 = 0.64 µM; 5, IC 50 = 0.58 µM; 7, IC 50 = 0.9 µM; 10, IC 50 = 0.4 µM) and Erk2 (compound G, IC 50 = 0.58 µM). Regarding these results, this series of compounds could be particularly interesting in the development of new inhibitors of Dyrk1A kinase. Comparison of the activity of nonmethylated compounds (1, 3, 5) toward Dyrk1A with that of their N-CH 3 analogues (2, 4, 6) indicate that the non-methylated analogues are more active than their methylated counterparts. Nevertheless, two methylated derivatives bearing either a p-carboxyphenyl moiety (7) or an iodine atom (10) at the C-5 position of the pyrimidine ring exhibited Dyrk1A sub-micromolar inhibition as well.

Conclusion

Encouraging preliminary biological evaluation of diversely substituted meridianins led us to synthesize new derivatives. Suzuki cross-coupling could be applied to compounds A or J, for coupling with either aromatic boronic acids bearing both electron donor and electron acceptor substituents or heteroaromatic boronic acids. Surprisingly, the cytotoxic activity of newly synthesised derivatives 1-10 toward PA 1 cells is significantly smaller than that of the previously described compounds G, H, L, M. This could be due to a lower cellular penetration of compounds 1-10 or lower interaction, due to the modification of the aryl moiety, with the cellular target(s) involved in their antiproliferative activity. Compounds G, 1, 3, 5-7 and 10 have shown sub-micromolar inhibition potencies toward some of the kinases tested. The interesting inhibition of Dyrk1A kinase, which is known to be involved in Alzheimer's disease 11 and Down syndrome, 12 leads us to expand our effort in the synthesis of diversely substituted meridianin derivatives as new potential inhibitors of this kinase.

Kinase preparations and assays

Kinase activities were assayed in Buffer A or C, at 30 °C, at a final ATP concentration of 15 µM. Blank values were subtracted and activities expressed in % of the maximal activity, i.e. in the absence of inhibitors. Controls were performed with appropriate dilutions of DMSO. CDK5/p25 (human, recombinant) was prepared as previously described. [13] and [14] Its kinase activity was assayed in buffer C, with 1 mg histone H1 /ml, in the presence of 15 µM [γ-33 P] ATP (3,000 Ci/mmol; 10 mCi/ml) in a final volume of 30 µl. After 30 min incubation at 30 °C, 25 µl aliquots of supernatant were spotted onto 2.5 × 3 cm pieces of Whatman P81 phosphocellulose paper, and, 20 s later, the filters were washed five times (for at least 5 min each time) in a solution of 10 ml phosphoric acid/liter of water. The wet filters were counted in the presence of 1 ml ACS (Amersham) scintillation fluid. GSK-3αβ (porcine brain, native) was assayed, as described for CDK5/p25 but in Buffer A and using a GSK-3 specific substrate (GS-1: YRRAAVPPSPSLSRHSSPHQSpEDEEE) (pS stands for phosphorylated serine). 15 GS-1 was synthesized by Millegen (Labege, France). CK1δ/ε (porcine brain, native) was assayed as described for CDK5/p25 but using the CK1-specific peptide substrate RRKHAAIGpSAYSITA, 16 obtained from Millegen (Labege, France). Erk2 (rat, recombinant) was assayed as described for CDK5/p25 but using the specific substrate Ets1 (amino acids 1-138) in buffer A. DYRK1A (rat, recombinant, expressed in Escherichia coli as a GST fusion protein) was purified by affinity chromatography on glutathione-agarose and assayed as described for CDK5/p25 using myelin basic protein (1 mg/ml) as a substrate.

In vitro antiproliferative assays 5.2.1. Cell cultures

Stock cell cultures were maintained as monolayers in 75 cm 2 culture flasks in Glutamax Eagle's minimum essential medium (MEM) with Earle's salts supplemented with 10% fetal calf serum, 5 ml 100 mmol/l sodium pyruvate, 5 ml of 100× non-essential amino acids and 2 mg gentamicin base. Cells were grown at 37 °C in a humidified incubator under an atmosphere containing 5% CO 2 .

Survival assays

Cells were plated at a density of 5 × 10 3 cells in 150 µl culture medium in each well of 96-well microplates and were allowed to adhere for 16 h before treatment with tested drug. A stock solution 20 mmol/l of each tested drug was prepared in DMSO and kept at -20 °C until use. Then 50 µl of each tested solution were added to the cultures. A 48 h continuous drug exposure protocol was used. The antiproliferative effect of the tested drug was assessed by the resazurin reduction test.

Resazurin reduction test

Plates were rinsed with 200 µl PBS at 37 °C and emptied by overturning on absorbent toweling. Then 150 µl of a 25 µg/ml solution of resazurin in MEM without phenol red was added to each well. Plates were incubated for 1 h at 37 °C in a humidified atmosphere containing 5% CO 2 . Fluorescence was then measured on an automated 96-well plate reader (Fluoroscan Ascent FL, Labsystem) using an excitation wavelength of 530 nm and an emission wavelength of 590 nm. Under the conditions used, fluorescence was proportional to the number of living cells in the well. The IC 50 , defined as the drug concentration required to inhibit cell proliferation by 50%, was calculated from the curve of concentration-dependent survival percentage, defined as fluorescence in experimental wells compared with fluorescence in control wells, after subtraction of the blank values.

Chemistry

IR spectra were recorded on a Perkin-Elmer Paragon 500 spectrometer in cm -1 ). NMR spectra were performed on a Bruker AVANCE 400 ( 1 H: 400 MHz, 13 C: 100 MHz), chemical shifts δ are noted in ppm and the following abbreviations are used: singlet (s), doublet (d), triplet (t), doublet of doublet (dd), doublet of doublet of doublet (ddd), doublet of triplet (dt), multiplet (m), broad signal (br s). Mass spectra (ESI+) were determined on a high resolution Waters Micro Q-Toff apparatus. Chromatographic purifications were performed on flash silica gel Geduran SI 60 (Merck) 0.040-0.063 mm column chromatography. TLC were performed on fluorescent silica gel plates (60 F254 from Merck).

General procedure for the preparation of compounds 1-9

A solution of Na 2 CO 3 (2.5 equiv) in H 2 O (2 ml/mmol) was added to a suspension of bromide A (288 mg, 1.0 mmol) or J (302 mg, 1.0 mmol), the required boronic acid (1.1 equiv), Pd(PPh 3 ) 4 (57.8 mg, 5 mol %) in EtOH (3 ml/mmol) and toluene (3 ml/mmol). The reaction mixture was refluxed overnight under argon and the cooled resulting mixture was evaporated onto silica gel. Purification as indicated provided the desired compounds.

4-(1H-Indol-3-yl)-5-(3-methoxyphenyl)pyrimidin-2-amine (1)

Purification of the residue by flash chromatography (cyclohexane/EtOAc 7:3) provided 1 (185 mg, 58%) as a yellow powder. Mp 98-100 °C; HRMS (ESI+) calcd for C 19 H 17 N 4 O (M+H) + 317.1402, found 317.1385; IR (KBr): 3650-3150, 1605 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 3.71 (3H, s, CH 3 ), 6.52-6.58 (2H, br s, NH 2 ), 6.69 (1H, d, J = 3.0 Hz), 6.83-6.86 (2H, m), 6.91-6.95 (1H, m), 7.06 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz; J 3 = 1.0 Hz), 7.12 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.31 (1H, t, J = 8.0 Hz), 7.34 (1H, d, J = 8.0 Hz), 8.00 (1H, s), 8.46 (1H, d, J = 8.0 Hz), 11.23-11.33 (1H, br s, NH); 13 C NMR (100 MHz, DMSO-d 6 ): 55.0 (OCH 3 ), 111.4, 112.6, 114.9, 120.0, 121.8, 121.9, 122.9, 128.9, 129.8, 157.8 (CH), 112.7, 120.9, 126.2, 135.8, 140.3, 159.5, 159.8, 162.5 (C).

4-(1-Methyl-1H-indol-3-yl)-5-(3-methoxyphenyl)pyrimidin-2-amine (2)

Purification of the residue by flash chromatography (cyclohexane/EtOAc 7:3) provided 2 (198 mg, 60%) as a yellow powder. Mp = 82-84 °C; HRMS (ESI+) calcd for C 20 H 19 N 4 O (M+H) + 331.1559, found 331.1546; IR (KBr): 3650-3150, 1604 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 3.61 (3H, s, NCH 3 ), 3.72 (3H, s, OCH 3 ), 6.56-6.59 (2H, br s, NH 2 ), 6.73 (1H, s), 6.83 (1H, ddd, J 1 = 7.5 Hz, J 2 = 1.5 Hz, J 3 = 1.0 Hz), 6.86 (1H, dd, J 1 = 2.5 Hz, J 2 = 1.5 Hz), 6.93 (1H, ddd, J 1 = 8.5 Hz, J 2 = 2.5 Hz, J 3 = 1.0 Hz), 7.08 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.18 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J Mp >250 °C, decomposition; HRMS (ESI+) calcd for C 18 H 16 N 5 (M+H) + 302.1406, found 302.1397; IR (KBr): 3550-3100, 1614 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 5.09-5.16 (2H, br s, NH 2 ), 6.42 (1H, ddd, J 1 = 7.5 Hz, J 2 = 1.5 Hz, J 3 = 1.0 Hz), 6.45-6.51 (3H, br s, 1CH+NH 2 ), 6.57 (1H, ddd, J 1 = 8.0 Hz, J 2 = 2.5 Hz, J 3 = 1.0 Hz), 6.75 (1H, d, J = 3.0 Hz), 7.05-7. 16

Scheme 1 .

 1 Scheme 1. Synthesis of compounds 1-10.

  Buffer A: 10 mM MgCl 2 , 1 mM EGTA, 1 mM DTT, 25 mM Tris-HCl pH 7.5, 50 µg heparin/ml. Buffer C: 60 mM β-glycerophosphate, 15 mM p-nitrophenylphosphate, 25 mM Mops (pH 7.2), 5 mM EGTA, 15 mM MgCl 2 , 1 mM DTT, 1 mM sodium vanadate, 1 mM phenylphosphate.

  3 = 1.0 Hz), 7.29 (1H, t, J = 8.0 Hz), 7.40 (1H, d, J = 8.0 Hz), 8.03 (1H, s), 8.35 (1H, d, J = 8.0 Hz); 13 C NMR (100 MHz, DMSOd 6 ): 32.8 (CH 3 ), 55.0 (OCH 3 ), 109.8, 112.7, 114.8, 120.2, 121.7, 121.9, 122.8, 129.7, 132.6, 158.1 (CH), 112.0, 120.8, 126.5, 136.4, 140.0, 159.4, 159.5, 162.4 (C).

5. 3 . 4 . 4 -

 344 (1H-Indol-3-yl)-5-(3-aminophenyl)pyrimidin-2-amine (3) Purification of the residue by flash chromatography (cyclohexane/EtOAc 4:6) provided 3 (125 mg, 41%) as a yellow powder.

5. 3 . 5 . 4 -( 1 -

 3541 Methyl-1H-indol-3-yl)-5-(3-aminophenyl)pyrimidin-2-amine (4) Purification of the residue by flash chromatography (cyclohexane/EtOAc 4:6) provided 4 (110 mg, 35%) as a yellow powder. Mp = 183-185 °C; HRMS (ESI+) calcd for C 19 H 18 N 5 (M+H) + 316.1562, found 316.1548; IR (KBr): 3600-3100, 1651, 1602 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 3.60 (3H, s, CH 3 ), 5.08-5.16 (2H, br s, NH 2 ), 6.41 (1H, d, J = 7.5 Hz), 6.48 (1H, t, J = 1.5 Hz), 6.48-6.52 (2H, br s, NH 2 ), 6.58 (1H, dd, J 1 = 8.0 Hz, J 2 = 1.5 Hz), 6.73 (1H, s), 7.06 (1H, t, J = 7.5 Hz), 7.11 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.19 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.40 (1H, J = 8.0 Hz), 7.93 (1H, s), 8.53 (1H, d, J = 8.0 Hz); 13 C NMR (100 MHz, DMSO-d 6 ): 32.9 (CH 3 ), 109.

5. 3 . 6 . 4 -[ 2 - 5 . 3 . 7 . 4 -[ 2 - 5 . 3 . 8 . 4 -[ 2 -

 36425374253842 Amino-4-(1H-indol-3-yl)pyrimidin-5-yl]benzamide (5)Purification of the residue by flash chromatography (cyclohexane/EtOAc 4:6) provided 5 (160 mg, 49%) as a yellow powder. Mp >250 °C; HRMS (ESI+) calcd for C 19 H 16 N 5 O (M+H) + 330.1355, found 330.1344; IR (KBr): 3600-3100, 1665, 1610 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 6.62-6.68 (2H, br s, NH 2 ), 6.67 (1H, d, J = 3.0 Hz), 7.05 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.12 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.5 Hz), 7.33-7.40 (4H, m), 7.89 (2H, d, J = 8.5 Hz), 7.98-8.02 (1H, br s, NH), 8.05 (1H, s), 8.37 (1H, d, J = 8.0 Hz), 11.26-11.32 (1H, br s, NH);13 C NMR (100 MHz, DMSO-d 6 ): 111.5, 120.1, 121.9, 122.6, 127.9 (2C), 128.9, 129.2 (2C), 158.0 (CH), 112.7, 120.4, 126.1, 132.6, 135.9, 142.0, 159.9, 162.6 (C), 167.5 (C O). Amino-4-(1-methyl-1H-indol-3-yl)pyrimidin-5-yl]benzamide (6) Purification of the residue by flash chromatography (cyclohexane/EtOAc 4:6) provided 6 (184 mg, 54%) as a yellow powder. Mp >250 °C; HRMS (ESI+) calcd for C 20 H 18 N 5 O (M+H) + 344.1511, found 344.1494; IR (KBr): 3600-3100, 1681, 1594 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 3.62 (3H, s, CH 3 ), 6.62-6.70 (2H, br s, NH 2 ), 6.80 (1H, s), 7.06 (1H, t, J = 7.5 Hz), 7.18 (1H, t, J = 7.5 Hz), 7.36 (2H, d, J = 8.0 Hz), 7.35-7.41 (1H, br s, NH), 7.41 (1H, d, J = 8.0 Hz), 7.87 (2H, d, J = 8.0 Hz), 7.97-8.02 (1H, br s, NH), 8.07 (1H, s), 8.20 (1H, d, J = 8.0 Hz); 13 C NMR (100 MHz, DMSO-d 6 ): 32.8 (CH 3 ), 109.9, 120.2, 121.9, 122.5, 127.9 (2C), 129.0 (2C), 132.6, 158.4 (CH), 112.0, 120.3, 126.3, 132.5, 136.5, 141.7, 159.4, 162.6 (C), 167.5 (C O). Amino-4-(1-methyl-1H-indol-3-yl)pyrimidin-5-yl]benzoic acid (7) Purification of the residue by flash chromatography (EtOAc/MeOH 9:1) provided 7 (207 mg, 60%) as a yellow powder. Mp >250 °C; HRMS (ESI+) calcd for C 20 H 17 N 4 O 2 (M+H) + 345.1352, found 345.1342; IR (KBr): 3250-2800, 1608 cm -1 ; 1 H NMR (400 MHz, DMSO-d 6 ): 3.63 (3H, s, CH 3 ), 6.66-6.72 (2H, br s, NH 2 ), 6.83 (1H, s), 7.05 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.17 (1H, ddd, J 1 = 8.0 Hz, J 2 = 7.0 Hz, J 3 = 1.0 Hz), 7.38-7.42 (3H, m), 7.91 (2H, d, J = 8.5 Hz), 8.08 (1H, s), 8.16 (1H, d, J = 8.0 Hz), 12.73-13.09 (1H, br s, COOH); 13 C NMR (100 MHz, DMSO-d 6 ): 32.8 (CH 3 ), 109.9, 120.2, 121.9, 122.4, 129.3 (2C), 129.7 (2C), 132.7, 158.4 (CH), 111.9, 120.1, 126.3, 129.1, 136.5, 143.3, 159.4, 162.6 (C), 167.2 (C O). 5.3.9. 4-(1-Methyl-1H-indol-3-yl)-5,5′-bipyrimidin-2-amine (8) Purification of the residue by flash chromatography (cyclohexane/EtOAc 2:8) provided 8 (95 mg, 31%) as a yellow powder.

Table 1 .

 1 Inhibitory potencies toward five protein kinases (IC 50 in µM) and antiproliferative activity of compounds G, H, L, M and 1-10 (IC 50 in µM)

	Compounds Kinase inhibition-IC 50 in µM			Antiproliferative activity toward
		CDK5/p25 CK1δ/ε GSK3α/β Dyrk1A Erk2
	G	11.0	8.3	1.9	2.3	0.58 0.09
	H	>10	>10	3.0	2.9	3.2	0.08
	L	>10	>10	1.4	5.0	>10 0.05
	M	>10	>10	>10	>10	>10 0.08
	1	>10	0.49	3.0	0.60	3.10 28
	2	>10	2.2	3.8	3.1	>10 34
	3	>10	3.3	6.0	0.64	6.9	>50
	4	>10	3.1	5.0	1.9	>10 >50
	5	>10	3.4	2.0	0.58	1.90 38
	6	>10	4.1	0.63	2.0	7.00 >50
	7	>10	>10	>10	0.9	>10 >50
	8	>10	12.0	6.1	3.2	>10 >50
	9	5.3	4.2	1.2	2.4	1.30 >50
	10	2.6	1.1	4.2	0.4	4.0	31

  (3H, m), 7.34 (1H, d, J = 8.0 Hz), 7.91 (1H, s), 8.62 (1H, d, J = 8.0 Hz), 11.25-11.35 (1H, br s, NH); 13 C NMR (100 MHz, DMSO-d 6 ): 111.3, 112.9, 114.7, 116.8, 120.0, 121.8, 123.2, 129.2, 129.3, 157.4 (CH), 112.7, 121.7, 126.4, 135.8, 139.6, 149.1, 159.8, 162.3 (C).

  8, 112.8, 114.6, 116.8, 120.3, 121.9, 123.2, 129.3, 132.9, 157.6 (CH), 112.0, 121.7, 126.7, 136.4, 139.3, 149.0, 159.3, 162.3 (C).

Acknowledgments

The authors thank the European Union Prokinase Research Consortium for financial support and Bertrand Légeret for mass spectrometry analysis. This research was also supported by grants from "Association France-Alzheimer Finistère" (LM), CRITT Santé Bretagne (LM) and "Fondation Jérôme Lejeune" (LM).


Harry H Hilton
email: h-hilton@illinois.edu

La conception analytique des propriétés viscoélastiques optimales des materiaux pour les sandwichs et les composites Analytical Formulation of Optimal Viscoelastic Designer Material Properties for Sandwich / Composites

Keywords: aero-servo-viscoelasticity, designer viscoelastic materials, functionally graded materials, failure probability, servo controls, structural control, survival times, torsional creep divergence, viscoelasticity

. For the same structural weight, the optimized designer viscoelastic sandwich composite plate clearly shows substantial longer survival times and orders of magnitude smaller probabilities of delamination. Extensions of these analyses to multi-element structures, i. e. entire structures, are also presented.

INTRODUCTION

Viscoelastic mechanical properties of existing materials, such as metals, concrete, polymers, cheeses and human and animal tissue, are extensively described in [6 -10] while relations between their chemistry and such properties are only now starting to be understood [START_REF] Van Krevelen | Properties of Polymers -Their Correlation with Chemical Structure[END_REF]. Current conventional wisdom and practice in structural analysis of air, space, 1 hal-00392800, version 1 -9 Jun 2009 Manuscrit auteur, publié dans "JNC 16, Toulouse : France (2009)" naval and land vehicles call for use of the best "off the shelf" available materials. Novel and unconventional analytical direct and inverse protocols have been previously successfully formulated [START_REF] Hilton | General analysis of viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances[END_REF], [12 -14] through computer simulations in a number of pilot studies seeking to determine the best designer viscoelastic material properties and their spatial nonhomogeneous distributions (viscoelastic functionally graded materials, i.e. VFGM) throughout structural members tailored and engineered to specific tasks, such as beam bending, column and plate buckling, thermal stresses, structural survival times, aero-viscoelastic flutter and aero-acoustics, to mention a few.

The term "composites" is generically used to denote any substance made of two or more materials with distinct properties. Notable examples are textiles, reinforced concrete, polymer or ceramic matrices with polymer or metal fibers [15 -27] . Another example is a plasma sprayed five-layer functionally graded ZrO2 / Ni Co Cr AlY thermal barrier coating of a µ-meter scale thickness described in [START_REF] Aik | Plasma sprayed functionally graded ZrO2/NiCoCrAlY thermal barrier coating[END_REF] and shown in Fig. 2 .

ANALYSIS Viscoelastic Constitutive Relations

Consider an anisotropic, isothermal, composite, rectangular plate with dimensions a⊗b⊗h in a Cartesian coordinate system x = {xi} with i = 1, 2, 3, with x3 normal to the plane of the plate. All materials, i.e. fibers and matrix, obey linear viscoelastic constitutive relations of the type [29 -31]

σij(x, t) = t Z -∞ E ijkl 2 6 4t -t, = Ξ 1 (x) z }| { x, F(x) | {z } = Ξ(x,t-t ) 3 7 5 kl (x, t ) dt (1)
where F(x) represents the relation describing the distribution of fiber orientation θor(x), number of plies N pl (x), number of fibers per ply N f p (x), volume fractions v f r (x) and stacking sequences st(x), or

F(x) = F [θor(x), N pl (x), N f p (x), v f r (x), st(x)] (2)
This function may also be thought of as defining functionally graded material (FGM) properties. The various roles of these functions in relation to optimum material performance (designer materials) will be analyzed in subsequent sections. Due to the complexity and number of variables some a priori specifications of these functions may be necessary and practical. For instance, some variables may not be independent of each other. If the stacking sequence is to be optimized or prescribed because of manufacturing dictates, then only one of the θors can be an independent variable. The N pl and N f p determine the v f r . As a simple example one can consider a configuration where the the number of fibers is constant and the stacking sequence is repeated such that ply angles are θn = θ1 + (n -1)∆θ for n = 1, 2, . . . , N pl and

F(x) = F(θ1, ∆θ, N pl , N f p ) (3)
The integrals always reduce to convolution ones with E = E(x, t -t ) whenever the F is time independent and and no transient temperatures are present to modify viscoelastic material properties. The spatially non-homogeneous anisotropic relaxation modulus functions are definable in terms of Prony series [START_REF] Baron De Prony | Essai experimental et analytique[END_REF], such that

E ijkl (x, t) = E ∞ ijkl [Ξ1(x)] + N ijkl X n=1 E ijkln [Ξ1(x)] exp - t τ ijkln [Ξ1(x)] ! = ( 4
)
where the instantaneous elastic modulus E 0 ijkl is given by

E 0 ijkl (x) = E ijkl (x, 0) = E ∞ ijkl [Ξ1(x)] + N ijkl X n=1 E ijkln [Ξ1(x)] (5)
The underscored indices indicate no summations.

Governing Relations, Constraints and Designer Composite Materials

In general terms the problem can be stated in the following manner. The viscoelastic composite plate obeys depending on loading conditions (tractions, moments, etc.) one or up to LL number of differential-integral relations, which can be expressed in general terms as

L " x, t, F(x), E ijkln [Ξ1(x)] , τ ijkln [Ξ1(x)] | {z } = Ξ L (x) " = 0 = 1, 2, . . . , LL (6)
subject to P℘ number of boundary conditions (BC)

BC℘ " x, t, ΞL(x) " = 0 ℘ = 1, 2, . . . , P℘ (7)
with a pre-determined constraint function C based on weight ρ, maximum deflections wmax, structural lifetime tLF , failure probability PF , cost COST , etc., given by

C " x, t, F(x), E ijkln [Ξ1(x)] , τ ijkln [Ξ1(x)] , ρ, wmax, COST , tLF , PF , . . . | {z } = Ξ C (x) " = 0 (8)
A number of protocols for determining the various parameters are presented and analyzed in [START_REF] Hilton | General analysis of viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances[END_REF]. Let Sp be the general designation for each individual parameter in Eqs. ( 6) to ( 8) with a total number κ. Selecting, for instance, a

Lagrangian multiplier (λ ) approach one obtains after applying Galerkin's method to eliminate all x-dependencies

∂ ∂Sp n L (t, Ξ * L ) + λ C (t, Ξ * C ) o = 0 (9)
= 1, 2, . . . , LL and p = 1, 2, . . . , κ + LL

The time dependence in ( 9) is removed through the use of the least squares method with at least 25(κ + LL) time values.

Specifically, a plate under aerodynamic loading has a governing relation for the mid-plane deflection w(x, t) which reads

L1 n w(x1, x2, t) o = t Z -∞ ∂ 2 ∂x 2 1 " D1(x, t -t ) ∂ 2 w(x, t ) ∂x 2 1 « dt | {z } viscoelastic bending resistance (T 1 ) + t Z -∞ » 2 ∂ 2 ∂x1∂x2 " D2(x, t -t ) ∂ 2 w(x, t ) ∂x1∂x2 « + ∂ 2 ∂x 2 2 " D3(x, t -t ) ∂ 2 w(x, t ) ∂x 2 2 «- dt | {z } viscoelastic bending resistance (T 1 ) - 2 6
where the plate w = w(x, t) = w(x1, x2, t) and the wing W = W (x2, t) unless otherwise indicated. In the absence of chordwise bending the panel effective angle of attack due to wing contributions is

AW (α, θ, W ) = fα(x 2 )=built
For elastic plates based on Eqs. ( 10) similar relations can be derived without the time integrals and with

D E m (x) ≡ Dm(x, t, t ) (12)
If the elastic or viscoelastic material is isotropic then in terms T1, the bending rigidities become

D1 = D2 = D3 ≡ D ( 13
)
and the T1 terms reduce to

Term T1 viscoelastic =⇒ t Z -∞ D(x, t -t ) ∇ w(x, t ) dt or t Z -∞ D(x, t, t ) ∇ w(x, t ) dt (14) Term T1 elastic =⇒ D E (x) ∇ w E (x, t) (15)
with

∇ = ∂ 4 ∂x 4 1 + 2 ∂ 4 ∂x 2 1 ∂x 2 2 + ∂ 4 ∂x 4 2 (16)
It is to be noted that in corresponding elastic isotropic cases, the modulus D E is defined as

D E = E E h 3 12 [1 -(ν E ) 2 ] ( 17
)
whereas for equivalent isotropic viscoelastic materials the use of Poisson's ratio is inappropriate and counter-indicated [START_REF] Hilton | The significance of anisotropic viscoelastic Poisson ratio stress and time dependencies[END_REF][START_REF] Hilton | Implications and constraints of time independent Poisson ratios in linear isotropic and anisotropic viscoelasticity[END_REF], since there is no viscoelastic counterpart for the elastic expression [START_REF] Whitney | Structural Analysis of Laminated Anisotropic Plates[END_REF], except under severely restricted conditions.

In all other more general cases, viscoelastic Poisson ratios are time, loading history and stress dependent [START_REF] Hilton | The significance of anisotropic viscoelastic Poisson ratio stress and time dependencies[END_REF], [START_REF] Hilton | Implications and constraints of time independent Poisson ratios in linear isotropic and anisotropic viscoelasticity[END_REF]. For viscoelastic materials, therefore, only relaxation moduli or functions can be used to define bending rigidities, i. e.

D ijkl (t) = E ijkl (t) h 3 12 ( 18
)
The linearity or nonlinearity of terms in the governing relation of Eq. ( 10) is independently influenced by geometry (size of deflections), material property characterizations. boundary conditions and failure conditions. It should be noted that if a single term of the governing relations exhibits nonlinear properties, then integral transforms, such as Laplace and Fourier, are inapplicable and solutions to the governing DEs or integral-differential relations must be obtained by other means.

For nonhomogeneous materials Eqs. ( 18) must be returned to their fundamental roots and become

D ijkl (x1, x2, t) = h/2 Z -h/2 E ijkl (x1, x2, x3, t) x 2 3 dx3 ( 19
)
rather than the simple moment and product of inertia expressions associated with homogeneous elastic and/or viscoelastic material plates. For auxetic materials, quantities associated with shear, such as D2, D6.D 7 , can be orders of magnitude larger than the corresponding bending stiffnesses, i.e. D2 D1 D3, etc., [START_REF] Hilton | General analysis of viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances[END_REF], [START_REF] Hilton | Designer auxetic viscoelastic sandwich columns tailored to minimize creep buckling failure probabilities and prolong survival times[END_REF].

Stability and Failure Considerations

Viscoelastic plates are subject to two separate and unrelated failure modes : (1) creep buckling -stability criteria in bending and/or twisting and (2) failures due to de-bonding and/or internal core cracks -material property induced failures due to combined bending, compressive and shear stresses. In addition if they are subjected to aerodynamic loading such as lift and/or aerodynamic noise they will subject to further modes of instability, such as panel flutter.

The classical elastic and creep buckling definitions are elastic =⇒ lim

σ 11 →σ cr 11 n w E (x, q) o → ∞ or lim σ 11 →σ cr 11  ∂w E (x, q) ∂σ11 ff → ∞ σ cr 11 = π 2 kc E 0 12(1 -ν 2 E ) " h b « 2 (20)
viscoelastic =⇒ lim

t→tcr {w(x, t)} → ∞ or lim t→t * cr  ∂w(x, t) ∂t ff → ∞ σ11 < σ cr 11 (21)
However, in [35 -37] it has been shown that small deflection linear viscoelastic analysis without any twisting results in finite deflections for 0 < tcr and t * cr < ∞. This proof can be readily extended to the present coupled deformations. Consequently, alternate creep buckling definitions must be formulated. Two distinct types based on (1) strain reversal in time and on [START_REF] Hilton | Analytical formulation of optimum material properties for viscoelastic damping[END_REF] time dependent material failure criteria have been offered.

In [START_REF] Hoff | The development of a technique for testing stiff panels in edgewise compression[END_REF] it has been proposed and successfully experimentally demonstrated that for elastic plates the buckling load can be established by analyzing graphs of outer plate fiber strains where compressive strains due loads and tensile strains due to bending take place. The elastic in-plane buckling load Ncr is then defined as

lim N →Ncr ∂ ˆ E c (N ) + E t (N ) ∂N → 0 t = 0 (22)
This definition has been modified in [START_REF] Hilton | Viscoelastic column dynamic creep buckling -failure probabilities and survival times[END_REF] for creep buckling of columns and can now be applied to plates in the form

lim t→t # cr ∂ [ c(t) + t(t)] ∂t → 0 0 ≤ N11 < N cr 11 and 0 < t # cr < ∞ ( 23
)
If thermal loads are present, then one needs to change the domain to 0 ≤ N11(t) + N T 11 (t) < N cr 11 in order to incorporate in-plane thermal load N T αβ effects. Viscoelastic failure criteria, such as ultimate stresses, degrade in time independently of relaxation moduli and failures may occur before or after any creep buckling instabilities manifest themselves. These are material failures which are independent of creep buckling and define the life time of the structure designated as tLF . Consequently, tcr or t * cr or t # cr may be greater, smaller or equal than tLF [START_REF] Hilton | Dynamic creep buckling of linear viscoelastic columns including failure probabilities and survival times[END_REF], [START_REF] Hilton | Viscoelastic column dynamic creep buckling -failure probabilities and survival times[END_REF]. Indeed, in Refs. [START_REF] Hilton | Creep collapse of viscoelastic columns with initial curvature[END_REF], [START_REF] Gerard | Introduction to Structural Stability Theory[END_REF] and [START_REF] Steinbacker | Aircraft Structural Mechanics[END_REF] the Shanley & Ryder [START_REF] Shanley | Stress ratios : The answer to the combined loading problem[END_REF] interaction or stress ratio curve approach has been used to estimate plate failures under combined inelastic deterministic stresses. Some failure mechanisms observed in composites are substantially different from those seen in metals as for example delamination which is a phenomenon unique to composites [START_REF] Dillard | A numerical procedure for predicting creep and delayed failures in laminated composites[END_REF], [44] [45]. From an aerospace design analysis point of view, one needs only to consider delamination onset because at that stage a structure has for all practical purposes failed, particularly if it is a light weight flight structure. In [START_REF] Dillard | A numerical procedure for predicting creep and delayed failures in laminated composites[END_REF] an expression has been formulated for the temperature, moisture and time dependency of uniaxial composite failure stresses. An extensive review of available experimental composite failure data is presented in [START_REF] Hilton | Stochastic viscoelastic delamination onset failure analysis of composites[END_REF] where such data is used to formulated deterministic and stochastic delamination failure analyses.

Experimental results indicate that uniaxial deterministic delamination onset stresses in tension and shear obey laws of the type

σ F ij (t) = 8 > > > > < > > > > : σ F ij0 -∞ ≤ t ≤ t F 2 σ F ij0 " 1 - ˛log `t/t F 4 ĺog (t F 3 /t F 4 ) ˛# 0 < t F 2 ≤ t ≤ t F 3 0 t ≥ t F 3 ( 24
)
where all parameters are material, temperature, moisture and uni-axial load (compression, shear, bending, etc.) dependent (Fig. 3 ).

DISCUSSION and CONCLUSIONS

In Eq. ( 10) the input forces are Terms T11 (lift) and T20 (aerodynamic noise). Each force in its own right creates a self-excited system and can result in time dependent viscoelastic panel instabilities, such as creep buckling and creep flutter. Additionally and independently failures due to delamination, aging, cracks, etc., can take place. These failure modes are illustrated in Figs. 4 and5. The first plots indicate the importance of aerodynamic noise at lower flight velocities, while flutter generally predominates at higher values. Fig. 5 shows the relative contributions to maximum panel deflections due to aerodynamic noise, creep buckling and creep flutter. Each instability mode in turn provides limits on panel lifetimes or survival times, unless preceded by delamination or other material failures, which have their own survival times.

As can be seen from the results displayed in the above Analysis Section, the number of candidate optimization variables defining the designer material can be large. In Ref. [START_REF] Van Krevelen | Properties of Polymers -Their Correlation with Chemical Structure[END_REF], protocols for manufacturing polymers to order, i.e. to

Fig. 1 .

 1 Fig. 1 -MASTER RELAXATION MODULUS

Fig. 2 .Fig. 3 .University of Illinois a 28 Fig. 4 . 28 Fig. 5 . 1 )Fig. 6 .

 2328428516 Fig. 2. Five-layer functionally gradedZrO 2 /Ni Co Cr AlY coating[START_REF] Aik | Plasma sprayed functionally graded ZrO2/NiCoCrAlY thermal barrier coating[END_REF]

  in plane force due to angle change between x 1 & x 2 directions (T 7 )

		2												3
	-	6 6 6 6 6 6 4 -∞ t Z |	Z a 0	D6(x1, x2, t -t )	∂w(x1, x2, t ) ∂x1 {z	∂w(x1, x2, t ) ∂x2	dx1 dt }	+ N EX 12 (t) | {z } (T 8 ) external force	5 7 7 7 7 7 7	∂ 2 w ∂x1∂x2
		2												3
	-	6 6 6 6 6 6 4 -∞ t Z | in plane force due to angle change between x 1 & x 2 directions (T 9 ) Z a 0 D 7 (x1, x2, t -t ) ∂w(x1, x2, t ) ∂x1 ∂w(x1, x2, t ) ∂x2 dx2 dt {z }	+ N EX 12 (t) | {z } (T 10 ) external force	5 7 7 7 7 7 7	∂ 2 w ∂x1∂x2
								8				2	wing contribution	panel contribution	3	9
		+ a0 q sin	> > > < > > > :	π 2 αST	6 6 6 4	Eq. (11) }| AW (α, θ, W ) + z { | combined angle due to attack of deformed wing and panel z }| arctan " 1 U∞ ∂w(x, t) ∂t + ∂w(x, t) ∂x1 {z	{ « } 7 7 7 5	> > > = > > > ;
			|											{z lift forces (T 11 )	}
	+ N P 11 (x, t)	∂ 2 w ∂x 2 1	+ N P 22 (x, t)	∂ 2 w ∂x 2 2	+	N T 11 (x, t)	∂ 2 w ∂x 2 1	+ N T 22 (x, t)	∂ 2 w ∂x1∂x2
		| x 1 piezo force (T 12 ) {z }			| x 2 piezo force (T 13 ) {z }	| x 1 thermal force (T 14 ) {z }	| x 2 thermal force (T 15 ) {z }
				+ 2 N T 12 (x, t)	∂ 2 w ∂x1∂x2	+	∂M T 11 ∂x 2 2	+	∂M T 22 ∂x 2 1	+ 2	∂M T 12 ∂x1∂x2	=
					|		{z thermal shear force (T 16 )	}	| {z } x 3 load due to M T 11 (T 17 )	| {z } x 3 load due to M T 22 (T 18 )	| {z } x 3 load due to M T 12 (T 19 )
												0	panel contributions	wing contributions	1
										∆p	B B B @ x, t, α,	z w,	∂w ∂x	,	}| ∂w ∂t	,	{ ∂ 2 w ∂t 2 ,	z θ, W,	}| ∂W ∂t	,	{ ∂ 2 W ∂t 2	C C C A
										|				{z aerodynamic noise pressure (T 20 )	}
														3
	6 6 6 6 6 4 -∞ t Z | in plane force due to length change in x 1 direction (T 2 ) Z a 0 D 4 (x1, x2, t -t ) " ∂w(x1, x2, t ) ∂x1 « 2 dx1 dt {z }	+ N EX 11 (x2, t) | {z } external force (T 3 )	7 7 7 7 7 7 5	∂ 2 w ∂x 2 1	∂ 2 w(x, t) ∂t 2 {z } inertia effects + mp | (T 4 )
				2										3
		+	6 6 6 6 6 6 4 -∞ t Z |	Z b 0	D5(x1, x2, t -t ) {z "	∂w(x1, x2, t ) ∂x2	« 2	dx2 dt }	+ N EX 22 (x1, t) | {z } (T 6 ) external force	5 7 7 7 7 7 7	∂ 2 w ∂x 2

in plane force due to length change in x 2 direction (T 5 )

JNC 16 -Toulouse 2009 produce prescribed relaxation moduli, failure conditions, weight, cost, etc., are presented and it is shown that they still are in their early development phase. Consequently, at this stage designer material properties serve as a guide for manufacturers to plan for what material properties are needed to be engineered now and in the near future. In the meantime, results obtained for designer materials serve to improve the design selection by helping to identify, based on their properties, the "best" currently available materials to be used for particular service conditions. Fig. 6 presents a typical example of the merits of the viscoelastic composite designer material protocols by selecting proper values for the variables that produce lower delamination probabilities and longer life times than conventional procedures based on catalogue available materials. charts can be generated for optimal designer lifetimes governing creep buckling and flutter conditions. Weibull failure probability distribution functions [START_REF] Weibull | A statistical distribution function of wide applicability[END_REF] were used in the analysis.

ACKNOWLEDGEMENT

Support by grants from the Technology Research, Education an Commercialization Center (TRECC) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) are gratefully acknowledged.