Dieter Enders
email: enders@rwth-aachen.de

Achim Lenzen

Michael Backes

Carsten Janeck

Kelly Catlin

Marie-Isabelle Lannou

Jan Runsink

Gerhard Raabe

Asymmetric Total Synthesis of the 1-epi-Aglycon of the Cripowellins A and B

The unusual [5.3.2]-bicyclic structure of the insecticidal Amaryllidaceae alkaloids cripowellin A (1)a n dB( 2) has been synthesized for the first time via a sequence of Sharpless dihydroxylation, ring-closing metathesis, and intramolecular Heck reaction. The asymmetric synthesis of the 1-epiaglycon 82 proceeds with virtually complete diastereo-and enantioselectivity (de, ee g 98%) in 13 steps and an overall yield of 5.6%. In addition, three alternative approaches toward the aglycon 3 are also described focusing on (1) the alkylation of the 2-benzazepinedithianes 35 and 36 with the electrophile 11, (2) a radical cyclization of the precursor (R/S,S,S)-39, and (3) an intramolecular arylation reaction of the aryl ketone 47. FIGURE 1. Structures of the cripowellins A (1)a n dB( 2). 10538

Introduction

The alkaloids isolated from different species in the Amaryllidaceae plant family certainly represent a unique class among the alkaloids because they have been found to occur only in this family. 1 Conversely, alkaloids of other plant families have not been found in the Amaryllidaceae (with hordenin being the only exception). 2 So far, about 200 alkaloids have been identified, and their often interesting pharmacological properties along with their fascinating molecular structures have rendered them very popular targets for total synthesis.

In 1997, researchers of Bayer AG reported two new Amaryllidaceae alkaloids, cripowellin A (1)a n dB( 2) (Figure 1), which were isolated from bulbs and roots of Crinum powellii, a popular ornamental plant in Europe. 3,4 Their structures were determined by extensive spectroscopic studies, including a combination of MS and 1-D and 2-D NMR techniques. The relative configuration was assigned unambiguously by an X-ray crystallographic analysis of cripowellin A diacetate. Both cripowellins are glycosides whose common aglycon features a [5.3.2]-bicyclic core, an unprecedented structural motif among the Amaryllidaceae alkaloids. Although both sugar entities differ from each other significantly, with an unusual 1,3,5-trioxepane ring in the case of cripowellin A (1), it is reasonable to assume that they are derived biogenetically from β-D-glucose, which accounts for the depicted absolute configuration.

In addition to their unusual structure, both alkaloids exhibit extraordinary insecticidal activity comparable to (1) For representative reviews about the Amaryllidaceae alkaloids, see: (a) Hoshino, O. In The Alkaloids; Cordell, G. A., Ed.; Academic Press: New York, 1998; Vol. 51, pp 324-424. (b) Martin, S. F. In The Alkaloids; Brossi, A., Ed.; Academic Press: New York, 1987; Vol. 30, pp 251-376. (c) Fuganti, C. In The Alkaloids; Manske, R. H. F., Ed.; Academic Press: London, 1975; Vol. 15, pp 83-164. (2) Wildman, W. C. In Chemistry of the Alkaloids; Pelletier, S. W., Ed.; Van Nostrand Reinhold Co.: New York, 1970; pp 151-172. (3) Gehling, M. et al. (Bayer AG), DE 196 10 279 A1, 1997; Chem. Abstr. 1997, 127, 278406. (4) Velten, R.; Erdelen, C.; Gehling, M.; Go ¨hrt, A.; Gondol, D.; Lenz, J.; Lockhoff, O.; Wachendorff, U.; Wendisch, D. Tetrahedron Lett. 1998, 39, 1737-1740. that of natural pyrethroidssnot only with regard to its potency but also its broad activity. In this respect, it is noteworthy that the aglycon seems to be mainly responsible for their biological activity because it shows the same degree of activity as the two glycosides themselves. 4 However, practically nothing is known about the mode of action. 5 To clarify that aspect and to perform investigations on structure-activity relationships, the synthesis of stereoisomers and derivatives of the cripowellins will be necessary.

Due to their unique structures and their high biological activity, Bayer AG has patented them and some of their derivatives. 3 Their exceptional position was also recognized by experts at the Irseer conference about natural products in 1997 where cripowellin A (1) was chosen to be the "second most interesting new natural product". [START_REF]Retrosynthesis Plan II Featuring an Intramolecular Radical Cyclization SCHEME 7[END_REF] Despite this attention, a synthetic approach toward the cripowellins or derivatives had not been reported until very recently when we described the asymmetric synthesis of the 1-epi-aglycon. 7 Similarly, Moon et al. recently demonstrated an alternative approach leading to the racemic bisdeoxy-aglycon of the cripowellins. 8 During the course of our work, originally directed toward the synthesis of the "natural" aglycon, a number of conceptually different approaches were investigated, one of which delivered the 1-epi-aglycon. In the present paper, we report full details of these efforts. 9

Results and Discussion 1. Dithiane-Alkylation Approach. Our initial retrosynthetic analysis of the aglycon 3 of the cripowellins A( 1)a n dB( 2) is outlined in Scheme 1.

In the first step, a retro-lactamization of aglycon 3 was considered, giving the partially protected amino acid 4. We presumed that its synthesis should be possible in a rather straightforward manner by alkylation of the dithiane 5 10 with either one of the electrophiles of type A or B. For the synthesis of the desired dithiane 5, two different routes, a and b, were envisaged utilizing a lactamization-reduction sequence and a Pictet-Spengler reaction, respectively. Synthon 8 may be obtained by simple alkylation or aminoethylation 11 of the (R)-1-amino-2-methoxymethyl pyrrolidine (RAMP) hydrazone 12 of homopiperonal (9). The benzylic stereocenter of 6 could be developed using the RAMP hydrazone methodology. However, its synthesis starting from 6-bromopiperonylic amine 7 was expected to be more laborious.

1.1. Synthesis of Electrophilic A-and B-Type Components. The synthesis of electrophiles of type A and B is summarized in Scheme 2. The iodides 11 and 13 were prepared from their corresponding alcohols 10 13 and 12 14 by simple iodination reactions (PPh 3 , imidazole, I 2 ). The synthesis of 17 began from D-tartaric acid ( 14), which furnished the cyclic anhydride 15 after treatment with pivaloyl chloride. A two-step sequence of reduction and acid-catalyzed lactonization converted 15 to the γ-lactone 16, which was reacted with TMSBr in methanol to afford the bromide 17.

Monobenzylation of the diol 18 15 gave the alcohol 19, which was further transformed into the iodide 20 using conditions similar to those described for 10 and 12 (vide supra).

1.2. Synthesis of 2-Benzazepine Dithianes: Route a. Investigations describing route a are summarized in Scheme 3. With respect to the nitrogen-protecting groups, two different pathways are shown, both commencing with 6-bromopiperonylic amine 7. 16 Two different protecting groups for the nitrogen atom, a p-methoxybenzyl and a benzyl group, were introduced successively to give 21. After bromine-lithium exchange, the lithium species was trapped with DMF to obtain the aromatic aldehyde 22. A sequence consisting of a Wittig reaction with Ph 3 PCHOCH 3 and hydrolysis of the intermediate enol ether furnished the corresponding homologated aldehyde, which was reacted with RAMP to give the hydrazone 23. Disappointingly, the alkylation of 23 with methyl 2-bromoacetate under standard conditions proceeded only in moderate yield and with an unsatisfactory degree of diastereoselectivity.

(5) Researchers at Bayer AG have found out that cripowellin A and B are neither acetylcholin esterase inhibitors nor PP1 inhibitors.

(6) Lindel, T. Nachr. Chem. Technol. Lab. 1997, 45, 775-779. (7) Enders, D.; Lenzen, A.; Raabe, G. Angew. Chem. 2005, 117, 3832-3835; Angew. Chem., Int. Ed. 2005, 44, 3766-3769. (8) (10) A conceptually different route to the racemic dithianes 5 with R 1 ) Cbz, H has already been described: Sa ´nchez, I. H.; Soria, J. J.; Lo ´pez, F. J.; Larraza, M. I.; Flores, H. J. J. Org. Chem. 1984, 49, 157-163. (11) Enders, D.; Janeck, C. F.; Raabe, G. Eur. J. Org. Chem. 2000, 3337-3345. (12) For reviews about the SAMP/RAMP-hydrazone methodology in asymmetric synthesis, see: (a) Enders, D. In Asymmetric Synthesis; Morrison, J. D., Ed.; Academic Press: Orlando, 1984; Vol. 3, pp 275-339. (b) Job, A.; Janeck, C. F.; Bettray, W.; Peters, R.; Enders, D. Tetrahedron 2002, 58, 2253-2329. (c) Enders, D.; Voith, M.; Lenzen, A. Angew. Chem. 2005, 117, 1330-1351; Angew. Chem., Int. Ed. 2005, 44, 1304-1325. (13) Hungerbu ¨hler, E.; Seebach, D. Helv. Chim. Acta 1981, 64, 687-702.

(14) (a) Batsanov, A. S.; Begley, M. J.; Fletcher, R. J.; Murphy, J. A.; Sherburn, M. S. J. Chem. Soc., Perkin Trans. 1 1995, 1281-1294. (b) Musich, J. A.; Rapoport, H. J. Am. Chem. Soc. 1978, 100, 4865-4872. (15) We theorized that the combination of two benzyl protecting groups was probably too bulky, diminishing the energy difference between the two possible diastereomeric transition states leading to a lower asymmetric induction in the alkylation. This argument was supported by the alkylation results from the homopiperonal-RAMPhydrazone 30 bearing no ortho substituent (cf. Scheme 4) and from the corresponding (S)-1-amino-2-methoxymethylpyrrolidine (SAMP)-hydrazone 27 bearing two allyl protecting groups on the nitrogen atom (it is needless to say that we would have replaced SAMP by RAMP as the chiral auxiliary if we had persued with this approach since only the latter induces the right asymmetric induction at the benzylic stereocenter). The synthesis of 27 was carried out according to the preparation of 23sexcept the benzylic protecting groups were both replaced by two allyl groups (cf. 7 f 25). Alkylation of this hydrazone under identical conditions furnished 28, which now gave superior results in terms of both yield (88 vs 53%) and stereoselectivity (de ) 90 vs 82%).

Unfortunately, the removal of the allyl protecting groups proved problematic. Although various standard reaction conditions for their deprotection had been tested (Rh(PPh 3 ) 3 Cl, CH 3 CN/H 2 O (9:1); 17 Pd(PPh 3 ) 4 , DCM, toluenesulfinic acid; 18 Pd(dba) 2 /dppb (1:1), tobenzoic acid 19 ), these blocking groups were not removed in the case of 28.

1.3. Synthesis of 2-Benzazepine Dithianes: Route b. The desired 2-benzazepinedithianes were synthesized in a highly stereoselective fashion by utilizing the Pictet-Spengler reaction as the key step. Scheme 4 outlines the approaches to the 2-benzazepines with a tosyl or a benzyl N-protecting group by employing tosylaziridine and methyl 2-bromoacetate, respectively, as the electrophiles.

The condensation of homopiperonal (9) 20 with RAMP yielded the hydrazone 30, whose alkylation with the aforementioned electrophiles gave the hydrazones 31 and 32, which were obtained with high diastereoselectivity (by 13 C NMR spectroscopy). Both of these hydrazones were transformed to the dithianes 33 and 34 according to Lassaletta's procedure. 21 In the case of 33, the enantiomeric excess was determined to be g98% by HPLC analysis on a chiral stationary phase (the racemate of 33 was prepared accordingly, starting from the dimethylhydrazone 29 of homopiperonal). This evidence implied the absence of racemisation in the transformation of hydrazone to dithiane. Although we were not able to prove this for the dithiane 34, it seems reasonable to make the same assumption.

Dithiane 34 smoothly underwent the Pictet-Spengler cyclization [START_REF][END_REF] to the 2-benzazepine 36. In this respect, it is important to note that the hydrazone 32 could not be cyclized successfully under various conditions, including formaldehyde, NaOH(aq); 11 (CH 2 O) 3 or (CH 2 O) n ,C H 3 -SO 3 H; 23 BF 3 'OEt 2 ,CH 2 (OCH 3 ) 2 ; 24 and (CH 2 O) n , TFA. 25 In the case of 33, the corresponding benzyl amide was initially formed according to the Weinreb protocol. 26 Cyclization was then readily conducted as well. 24 The reduction of the resulting lactam with lithium aluminum hydride yielded the benzyl-protected 2-benzazepine 35.

1.4. Coupling Reactions. With the 2-benzazepinedithianes 35 and 36 and various electrophiles 11, 13, 17, and 20 in hand, model studies with the dithiane 37 were conducted in order to optimize reaction conditions for the coupling process (Scheme 5). [START_REF]For work on 1,3-dithianes[END_REF] We found out, that only the electrophile 11 could be reacted successfully with a metalated species of 37. After screening of different reaction conditions and further optimization we were finally able to isolate the coupling product 38 in a moderate yield of 65%.

However, similar alkylations of dithianes 35 and 36 with the electrophile 11 under these conditions were not feasible. The screening of other electrophiles showed that only very small electrophiles were amenable to this reaction with CH 3 I and D 2 O resulting in yields of 30% and 56%, respectively.

2. Intramolecular Radical Cyclization Approach. The preceding section has shown that a polar, umpolung disconnection adjacent to the dithiane 5 using the A-/Btype electrophiles (cf. Scheme 1) did not prove successful. A radical disconnection adjacent to the carbonyl group was also envisaged (Scheme 6). The key step in this approach was the intramolecular radical cyclization from (S,S,S)-39 to explore addition of the primary carbon radical to the nitrile group. [START_REF] Ziegler | For similar work[END_REF] Breaking of the amide bond in (S,S,S)-39 leads to the secondary amine (S)-40 and the acid 41.

As shown in Scheme 7, saponification of the ester 13 using LiOH gave the desired acid 41 in high yield.

The synthesis of the cyclization precursor is depicted in Scheme 8. Starting from the hydrazone 32 (cf. Scheme 4), magnesium monoperoxyphthalate (MMPP) mediated nitrile formation furnished 42, which readily underwent a Pictet-Spengler cyclization in quantitative yield to 43. Although the toluenesulfonyl protecting group was easily removed at this stage using sodium naphthalide, the benzylic nitrile underwent epimerization. Hence, only racemic (R/S)-40 could be isolated. Despite this fact, we decided to continue with the synthesis, hoping for a possibility to separate diastereomers after a successful cyclization. Among the different conditions tested for amide bond formation with the acid 41 (2-chloro-1methylpyridinium iodide, n-Bu 3 N, DCM (48% yield); 29 Ph 2 P(dO)OC 6 F 5 , Et-i-Pr 2 N, DMF (85% yield) 30 ), a combination of HOBT/EDC 31 worked best to give (R/S,S,S)-39 in 89% yield.

The radical cyclization of (R/S,S,S)-39 using Bu 3 SnH/ AIBN in different solvents did not furnish the desired acetonide aglycon 44, but instead the unreacted starting material was recovered (when using refluxing benzene or toluene) or product 45 (when using refluxing xylene) resulting from a radical dehalogenation was obtained. Iodine-metal exchange using using t-BuLi, n-BuLi, and i-PrMgCl with (R/S,S,S)-39 was attempted hoping for intramolecular nucleophilic addition to the nitrile group.

As one might have anticipated, the presence of the β-oxygen substituent gave rise to olefinic products of β-elimination.

The strategies discussed so far had one thing in common: the characteristic bicycle was planned to be constructed starting from a 2-benzazepine, i.e., a 7-membered ring. Alternatively, because a [5.3.2]-bicycle represents a combination of a 7-, a 9-and a 10-membered ring, one could also think about closing the 10-or the 9-membered ring first. These two concepts have also been followed and will be treated in the following two sections.

3. Intramolecular Ketone-Arylation Approach. If one wants to start with the largest ring, i.e., the 10membered ring, the ethylene bridge has to be broken first retrosynthetically, which is done most easily by a retrointramolecular alkylation reaction (Scheme 9). This leads to the ketone 46, whose synthesis was envisaged to be realized by means of an intramolecular Buchwald-Hartwig arylation (47 f 46). 32 Origins of compound 47 can be easily traced to the secondary amine 48 and the acid 49, and the latter can be obtained by reaction of 50 or 11 with 51 33 or 52.

Extensive investigations were carried out for the synthesis of 49 (Scheme 10). Starting with the electrophiles 50 and 11, utilization of lithiated 1,3-dithiane (52) as the synthetic equivalent of a formyl anion delivered 53 and 54, respectively. The moderate yields obtained in these reactions parallel the observations using the dithianes 35 and 36 (vide supra). The methylation of 53 and 54, on the other hand, proceeded more smoothly to give 55 and 56, respectively. After cleavage of the dithiane moiety, the ketones 57 and 58 were obtained in similar yields.

This reaction sequence was significantly shortened by using the lithiated aminonitrile 51 as an equivalent of an acyl anion. Reaction of 50 and 11 with 51 followed by AgNO 3 -mediated cleavage of the aminonitrile furnished 57 and 58 in only two steps and with improved yields.

So far, both protecting groups did not behave much differently, giving similar yields in each pair of reactions. However, deprotection to the corresponding alcohol 59 proved to be much more efficient with the benzyl derivative 58 (97% vs 27% yield in the case of the TBS protected compound 57). The basicity of TBAF might be responsible for the low yield observed in the reaction with 57: formation of the internal enol followed by elimination of the β-oxygen are a possible side reaction. The synthesis of the desired acid 49 was then completed by oxidation with RuCl 3 /NaIO 4 .

The completion of the synthesis of the precursor for the Buchwald-Hartwig arylation is shown in Scheme 11. Reductive amination of bromopiperonal (60) 34 with 2-benzyloxyethanamine 35 gave the secondary amine 48. Amide formation with the carboxylic acid 49 worked best using 2-fluoro-1-ethylpyridinium tetrafluoroborate (FEP) 36 as the coupling reagent to give the desired precursor 47 in 84% yield.

Unfortunately, bringing about the desired cyclization to 46 using Buchwald's conditions turned out to be an extremely difficult task. 37 With xantphos as the ligand and Pd 2 dba 3 as the Pd 0 source, no conversion of starting material or decomposition were observed under the reaction conditions screened (THF or toluene as solvent, t-BuONa or K 3 PO 4 as base, ϑ ) rt -80 °C).

The Buchwald-Hartwig arylation was not the only possibility that could be envisaged for the cyclization of 47 to 46. The successful synthesis of the corresponding terminal TMS enol ether 61 suggested the possibility for cyclization following the protocol developed by Kuwajima and Urabe, 38 i.e., employing aryl bromides in an arylation of TMS enol ethers using Bu 3 SnF and PdCl 2 (P(o-tol) 3 ) 2 .

A Heck arylation of the corresponding TBS enol ether 62 was also investigated under typical conditions (Pd-(OAc) 2 , PPh 3 ,Et 3 N, DMF, 80 °C; Pd 2 dba 3 ,Ag 2 CO 3 , dppe, toluene, 100 °C). It should be noted that Heck reactions employing alkyl enol ethers have been carried out successfully, 39 although versions using the analogous silyl enol ethers have not been described. Unfortunately, both of these reactions failed to yield 46 (Scheme 12).

The main problem seemed to be the cyclization of the 10-membered cycle and not, e.g., the insertion of Pd 0 into the aryl bromine bond. The occurrence of the latter could be proven by successfully carrying out an intermolecular version of the Kuwajima-Urabe reaction (Scheme 13): the Boc-protected amine 63 and the TMS enol ether 64, obtained by treatment of 57 with TMSOTf and Et 3 N, readily underwent the coupling to give 65 in an unoptimized yield of 52%.

4. Synthesis of the 1-epi-Aglycon via a Sharpless AD-RCM-Heck Sequence. From a topological point of view, the last possibility that remained was to focus on the formation of the 9-membered ring. Taking this into account, our new retrosynthesis is depicted in Scheme 14. After the functional group interconversion ketone f Z-double bond and protection of the free vicinal hydroxy groups as their acetonide, the bicycle 66 was considered. Retrosynthetically, the Heck reaction, 40 starting from 68, was assumed to proceed via intermediate 67 which should furnish 66 upon elimination of L 2 PdHX. Considering Bredt's rule, an elimination toward the aromatic moiety was judged as rather improbable at the beginning of this project (vide infra). Such an intramolecular Heck reaction involving a 9-membered ring had not been reported at the time of this project.

Medium-sized rings, as described for the conversion of 68 to 69, are sometimes very difficult to access by ringclosing metathesis. 41 We tried to advance our strategy by choosing the acetonide as protecting group because it represents a conformational constraint that should favor the RCM process. 42,43 Similarly, the tertiary amide functionality should have the same effect. 44 The synthesis of the acid 71 was straightforward and is summarized in Scheme 15. It commenced with the esterification of the known alcohol 72 45 to give 73, 46 which was subjected to a slightly modified Sharpless AD. 47 This reaction furnished the diol 74 in good yield (72%) with A. H. Angew. Chem. 2003, 115, 4740-4782; Angew. Chem., Int. Ed. 2003, 42, 4592-4633. (c) Fu ¨rstner, A. Angew. Chem. 2000, 112, 3140-3172; Angew. Chem., Int. Ed. 2000, 39, 3012-3043. (d) Maier, M. E. Angew. Chem. 2000, 112, 2153-2157; Angew. Chem., Int. Ed. 2000, 39, 2073-2077 Chem. 1997, 109, 2124-2145; Angew. Chem., Int. Ed. Engl. 1997, 36, 2036-2055. (i) Schmalz, H.-G. Angew. Chem. 1995, 107, 1981-1984; Angew. Chem., Int. Ed. Engl. 1995, 34, 1833-1836. (j) Acetonide formation and saponification of the ester functionality afforded the primary alcohol 75 in nearly quantitative yield.

This alcohol was oxidized to the corresponding acid 71 over two steps, which was then used in the amide coupling reaction without further purification. The other coupling partner, amine 70, was synthesized by reductive amination of bromopiperonal (60) with 3-buten-1-amine (Scheme 16).

The amide 69 was obtained upon coupling with FEP in a high yield of 66% over three steps. The RCM reaction was first carried out with Grubbs's first-generation catalyst, yielding a mixture of the desired lactam 68 and oligomers. In this reaction, Grubbs's second-generation catalyst led to a significant improvement as no oligomers were detected by TLC analysis, and the lactam 68 was isolated in 77% yield.

4.1. Heck Reactions. With the precursor for the intramolecular Heck reaction in hand, we explored conditions which had been described mainly by Overman et al. in the general synthesis of bicyclic structures. 48 Under these conditions, only starting material could be isolated. As the insertion of Pd 0 into the aryl-bromine bond was to be expected under these conditions (cf. to Scheme 13), the reason for the failure may have been a high activation energy necessary for the Heck reaction. In fact, by changing the reaction solvent to DMF to allow higher reaction temperatures, the formation of the bicyclic compound 76 was observed (Scheme 17).

Surprisingly, the bicyclic compound that is epimeric at C1 in comparison to the natural products (see the observed NOE) was exclusively obtained. Other phosphine ligands were also tested under these reaction conditions (dppe, dppp, P(o-tol) 3 , P(2-furyl) 3 , PMePh 2 ), but all of them gave the same stereochemical outcome.

The following investigations revealed that it was very hard to selectively functionalize the bicyclic compound 76. Neither hydroborations (BH 3 'THF, THF; 9-BBN, THF, reflux; 49 CB, N,N-dimethylacetamide, DCM; 50 CB, SmI 3 , THF 51 ), oxymercurations (Hg(OAc) 2 , THF/H 2 O; 52 Hg(OAc) 2 , THF/H 2 O,))); 53 Hg(OAc) 2 , THF/H 2 O, PTSA), bromohydrin formation (NBS, DMSO/H 2 O), 54 oxidation with molecular oxygen (Co(tfa) 2 ,O 2 , i-PrOH, MS 4 Å, reflux), 55 Wacker oxidations (PdCl 2 , CuCl, O 2 , DMF/H 2 O, 60-70 °C; 56 PdCl 2 , EtOH, reflux 57 ), oxidation with chromyl chloride (CrO 2 Cl 2 , acetone, -78 °C f rt), 58 nor oxidations using Ag I salts (Ag 2 CrO 4 ,I 2 , pyr, DCM, 0 °C f rt; 59 AgNO 2 ,I 2 ,E t 2 O 60 ) proved successful in any way.

(44) For secondary and tertiary amides in ring closing metatheses, see: (a) Brouwer, A. J.; Liskamp, R. M. J. J. Org. Chem. 2004, 69, 3662-3668. (b) Banfi, L.; Basso, A.; Guanti, G.; Riva, R. Tetrahedron Lett. 2003, 44, 7655-7658. (45) Rao, J. A.; Cava, M. P. J. Org. Chem. 1989, 54, 2751-2753. (46) The asymmetric dihydroxylation of allylic alcohols normally proceeds with only moderate enantioselectivitysin contrast to their corresponding p-methoxybenzoic acid esters: Corey, E. J.; Guzman-Perez, A.; Noe, M. C. J. Am. Chem. Soc. 1995, 117, 10805- Epoxidation of the olefin 76 was feasible. Nevertheless, the reaction had to be carefully optimized. Dimethyldioxirane (DMDO) gave the best results because it permitted the use of an excess of the reagent at lower temperature (Scheme 18), avoiding decomposition which predominated at higher temperatures. The epoxide 77 could be obtained in a moderate yield of 55% after 9 days. The low yield along with the long reaction time did not make this approach very attractive.

Fortunately, screening other reaction conditions for the Heck reaction was continued. Under conditions that are generally regarded as cationic, the outcome of the Heck reaction was completely changed (Scheme 19).

The trisubstituted olefin 78 was isolated in 59% yield as a mixture of E-and Z-isomers. Along with 78, minor amounts of 76 were also formed (78/76 ) 8.2:1, according to GC), which could be separated easily due to the higher polarity of 76. The formation of this bridgehead alkene 78, which can also be considered to be an anti-Bredt alkene, was really astonishing because the additional ring strain in this bicyclic compound could not be compensated by stability from the conjugation with the aromatic moiety. The double bond of this bridgehead alkene was not configurationally stable under the reaction conditions employed since the E/Z-ratio was observed to be time dependent (after 4 h (complete conversion): E/Z ) 1:1.7, after 24 h E/Z ) 1:1, according to GC). Both isomers could be separated by preparative HPLC, and the major isomer was shown to possess the Z-configuration (see the observed NOEs). Once again, the Heck reaction was completely diastereoselective, and only the isomer with the opposite orientation of the ethylene bridge, when compared to the natural products, was formed. To the best of our knowledge, this represents the first successful example of a (highly diastereoselective) intramolecular Heck reaction at a highly functionalized (aza)cyclononene derivative.

With 78 in hand, the synthesis of the 1-epi-aglycon was within reach because a regiochemical differentiation between olefinic carbons was assumed to be easier than in the case of 76.

Our first attempt toward this goal is illustrated in Scheme 20. After hydroboration with an excess of borane (5 equiv) and quenching with water, the mixture of ( 60) Cardillo, G.; Shimizu, M. J. Org. Chem. 1977, 42, 4268-4270. The spectroscopic data of the isolated compound 79 clearly revealed that the amide group in 78 had undergone an undesired reduction to the corresponding amine. The chemoselectivity problem could not be overcome by performing the same reaction sequence with an equimolar amount of borane.

Completion of the Synthesis of the 1-epi-Aglycon.

An alternative sequence proved to be more successful (Scheme 21). The mixture of olefins 78 was initially transformed into the R-hydroxy ketone 80 via a two-step sequence of dihydroxylation and Swern oxida-tion. With an excess of SmI 2 in the presence of t-BuOH, the deoxygenation of 80 proceeded smoothly to give 81. 61 The high yield of 99% in this reaction was astonishing because R-hydroxy ketones are normally not regarded as good reduction substrates for SmI 2 . 62 Likewise, the stability of the acetonide is noteworthy since the reductive cleavage of the R-C-O bond is commonly observed (in the case of carboxylic acid esters). 63 The final cleavage of the acetonide protecting group to give the 1-epi-aglycon 82 of the cripowellins A and B was most easily conducted in the presence of the acidic ion-exchange resin Dowex-50 64 because it made further purification of the 1-epi-aglycon 82 unnecessarysin contrast to the cleavage using PdCl 2 (CH 3 CN) 2 in refluxing CH 3 CN/H 2 O (1:1). 65 With regard to the known structure of the bisacetate of cripowellin A and the biological activity of the cripowellins, we were interested in the conformation of 82.In the search for derivatives of the 1-epi-aglycon 82, our efforts were rewarded by bisacetate 83, which provided crystals suitable for an X-ray structure analysis. 66 A comparison of its crystal structure with the one obtained from the bisacetate of cripowellin A clearly shows the same spatial orientation of the keto and the lactam carbonyl groups. Both are syn to each other and in the same spatial proximity. This substructure had been identified as the probable pharmacophor by researchers of Bayer AG after extensive investigations on structureactivity relationships. 5 Therefore, it seems reasonable to expect the 1-epi-aglycon 82 to be biologically active, too. Yet, this still needs to be proven by biological tests.

Apart from confirming the relative stereochemistry of 83 and its predecessors, the X-ray structure also clarified the fact that both the 1-epi-aglycon 82 and its bisacetate 83 seemed to have undetected carbonyl carbon signals according to 13 C NMR spectroscopy. The matter became J. Am. Chem. Soc. 1994, 116, 9927-9934. (66) CCDC 263133 ( 83) contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/ data_request/cif. clear after performing a high-temperature NMR experiment on the bisacetate 83 which revealed its carbonyl carbon signal again. One has to conclude that the bicyclic system of both 82 and 83 adopts at least two conformational minima. On the NMR time scale, the exchange between these minima is rather slow at room temperature, which causes significant line broadening (also visible in their 1 H NMR spectra, see the Supporting Information). By heating the sample, this interconversion is faster, the line broadening is reduced, and the signal of the carbonyl carbon is easier to observe.

Conclusions. In this paper, we have described attempts to achieve the asymmetric total synthesis of the aglycon 3 of the cripowellins A (1)andB(2). Our efforts were finally rewarded by featuring a sequence of a highly enantioselective Sharpless dihydroxylation, a ring-closing metathesis and a highly diastereoselective intramolecular Heck reaction. This strategy allowed the construction of the unusual [5.3.2]-bicyclic structure of the aglycon for the first timesin the form of its 1-epi-analogue. The synthesis is efficient (13 steps in the longest linear sequence, 15 steps altogether; 5.6% overall yield), and diastereo-and enantioselectivity are virtually complete (de, ee g 98%). The crystal structure of the bisacetate of the 1-epi-aglycon, 83, reveals the same spatial orientation of the ketone and the lactam carbonyl groups as in the case of the cripowellins. Therefore, it is reasonable to assume that the 1-epi derivatives may exhibit the same biological activity as the cripowellins and their aglycon themselves. The 1-epi-aglycon 82 might clarify the hitherto unknown mode of action of the cripowellins.

Experimental Section

This section comprises all compounds belonging to the AD-RCM-Heck approach (Chapter 4). A general procedure for an aqueous workup, which is summarized in the form (quenching agent; solvent used for extraction; drying agent), can be found in the Supporting Information. [1,3]dioxol-5-ylmethyl)-2,2-dimethyl-3a,5,6,7,10,10a-hexahydro-1,3-dioxa-5-azacyclopentacyclononen-4-one (68). A flask containing a solution of the bisolefin 69 (0.868 g, 1.9 mmol) in DCM (1.9 L) was evacuated and filled with argon (4×). It was heated to reflux, and a solution of Grubbs' second-generation catalyst (0.163 g, 0.2 mmol) in DCM (10 mL) was added portionwise (2.5 mL each 30 min). After the last addition, reflux was continued for 1 h. The solution was allowed to reach rt, and DMSO (0.68 mL, 9.6 mmol) was added. After stirring overnight and removal of the solvent under reduced pressure, the residue was purified by column chromatography (pentane/ether 1:1) to give 0.629 g (1.5 mmol, 77%) of the olefin 68 as a colorless foam. HPLC: tR 12.3 min (LiChrosorb Si 60 (pentane/ether 4:6, 0.5 mL/min)); Rf 0.24 (pentane/ether 1:1); [R] 25 D +48.3 (c 0.4, CHCl3); 1 H NMR (300 MHz, CDCl3) δ 1.48 (s, 3H), 1.58 (s, 3H), 2.32-2.44 (m, 1H), 2.50-2.66 (m, 3H), 3.33 (m, 1H), 3.70 (m, 1H), 4.03 (m, 1H), 4.08 (d, J ) 14.8, 1H), 4.50 (d, J ) 8.4, 1H), 5.05 (d, J ) 14.8, 1H), 5.56 (m, 1H), 5.79 (m, 1H), 5.95 (s, 2H), 6.92 (s, 1H), 6.96 (s, 1H); 13 C NMR (75 MHz, CDCl3) δ 26.2, 26.3, 27.2, 28.5, 44.5, 50.4, 76.8, 79.9, 101.9, 110.1, 110.2, 112.3, 114.2, 128.1, 128.3, 129.2, 147.9, 170.4; MS (CI, 100 eV) m/z 345 (17), 344 (100), 215 (15), 213 (17); IR (CHCl3) 2990, 2938, 1657, 1480, 1377, 1238, 1167, 1091, 1039, 931, 886, 849, 802, 755, 665, 515 in DCM (15 mL) was added dropwise. Stirring was continued for 30 min, after which Et3N (15.1 mL, 107 mmol) was added slowly. Ten minutes later, the cold bath was removed, and stirring was continued at room temperature for 10 min. An aqueous workup (H2O; DCM; MgSO4) yielded the corresponding aldehyde, which was purified by column chromatography (pentane/ether 2:1). It was directly used for the next step: it was dissolved in a mixture of water (60 mL) and acetone (60 mL), and the solution was cooled to 0 °C. 2-Methyl-2-butene (42.0 mL, 395 mmol), NaH2PO4'2H2O (6.705 g, 43.0 mmol), and NaClO2 (80%, 6.074 g, 53.7 mmol) were added successively (vigorous stirring!). The ice bath was removed, and the reaction was stirred at room temperature for 30 min. It was extracted with EtOAc several times. The organic extracts were combined, dried over MgSO4, and concentrated. All volatiles were removed under high vacuum to yield the crude acid 71 (3.027 g, 16.3 mmol), which was dissolved in DCM (60 mL). The solution was cooled to 0 °C, and the amine 70 (5.108 g, 18.0 mmol) and FEP (4.233 g, 19.9 mmol) were added. Eti-Pr2N (8.6 mL, 52.0 mmol) was added dropwise, and the reaction was allowed to warm to room temperature overnight. The reaction mixture was concentrated to a small volume, which was subjected to column chromatography (pentane/ether 4:1) to yield 6.398 g (14.1 mmol, 66% over three steps) of the amide 69 as a colorless oil. f 0.30 (pentane/ether 4:1); [R] 25 D +18.0 (c 0.7,CHCl3). The NMR spectra clearly show the presence of two rotamers (ratio about 1:1). For the interpretation of their 1 H NMR spectra they are treated as two different compounds: 1 H NMR (400 MHz, CDCl3) δ 1.39 (s, 6H), 1.43 (s, 3H), 1.46 (s, 3H), 2. 28-2.51 (m, 8H), 3.22 (m, 1H), 3.33 (m, 1H), 3.40-3.61 (m, 2H) 1, 27.0, 31.6, 33.2, 37.1, 45.4, 46.3, 48.0, 50.6, 76.8, 76.9, 77.0, 101.6, 101.8, 107.9, 108.5, 110.0, 112.4, 112.7, 113.0, 113.6, 116.8, 117.5, 117.6, 129.0, 129.3, 133.35, 133.44, 134.1, 134.8, 147.4, 147.6, 168.9, 169.0; MS (EI, 70 eV) m/z 453 (M +• , 1), 451 (1), 373 (21), 372 (100), 215 (33), 213 (33), 141 (14), 83 (32), 55 (13); IR (CHCl3) 3077, 2985, 2934, 1652, 1480, 1374, 1239, 1163, 1111, 1040, 996, 925, 855, 803, 756, 672, 516. Anal. Calcd for C21H26BrNO5: C, 55.76; H, 5.79; N, 3.10. Found: C, 55.79; H, 5.80; N, 3.35.

5-(6-Bromobenzo

(6-Bromobenzo[1,3]dioxol-5-ylmethyl)but-3-enylamine (70). Molecular sieves 4 Å (17 g) and 3-buten-1-amine (3.690 g, 51.9 mmol) were added to a solution of bromopiperonal (60) (9.836 g, 43.0 mmol) in DCM (80 mL). After being stirred overnight, the molecular sieves were removed by filtration, and the solvent was evaporated under reduced pressure. The crude imine was dissolved in methanol (130 mL) and NaBH 4 (1.626 g, 43.0 mmol) was added portionwise. After the evolution of hydrogen had ceased, stirring was continued for 1 h. All volatiles were evaporated under reduced pressure, and the residue was subjected to an aqueous workup (H2O; DCM; Na2SO4). Purification by column chromatography (pentane/ether 3:1 f 2:1 f 1:1 f ether) gave 11.432 g (40.2 mmol, 94%) of the amine 70 as a colorless oil: Rf 0.24 (pentane/ether 1:1); 1 H NMR (300 MHz, CDCl3) δ 1.50 (s, 1H), 2.28 (m, 2H), 2.68 (t, J ) 6.8, 2H), 3.76 (s, 2H), 5. 01-5.13 (m, 2H), 5.79 (m, 1H), 5.95 (s, 2H), 6.89 (s, 1H), 6.99 (s, 1H); 13 C NMR (75 MHz,CDCl3) δ 34.3,48.0,53.5,101.6,110.1,112.7,114.0,116.4,132.7,136.4,147.3,147.4; MS (EI, 70 eV) m/z 285 (M +• , 2), 283 (2), 244 (35), 242 (36), 215 (100), 213 (94); IR (CHCl3) 3075, 2976, 2899, 2829, 1640, 1501, 1477, 1411, 1356, 1238, 1115, 1040, 995, 932, 866, 833, 780, 722, 657, 559. Anal. Calcd for C12H14BrNO2: C, 50.72; H, 4.97; N, 4.93. Found: C, 50.29; H, 5.06; N, 5.25. (2E)-4-Methoxybenzoic Acid hexa-2,5-dienyl Ester (73). Et3N (20 mL, 142 mmol) and a catalytic amount of DMAP were added to a solution of (E)-2,5-hexadien- 1-ol (4.549 g, 46.4 mmol) in DCM (120 mL) at 0 °C. A solution of p-methoxybenzoyl chloride (9.500 g, 55. 7 mmol) in DCM (20 mL) was added, and the reaction was allowed to warm to room temperature overnight. An aqueous workup (1 M HCl; DCM; MgSO4) and column chromatography (pentane/ether 10:1) gave 9.389 g (40.4 mmol, 87%) of the ester 73 as a clear oil: Rf 0.58 (pentane/ether 4:1); 1 H NMR (300 MHz, CDCl3) δ 2.84 (m, 2H), 3.85 (s, 3H), 4.76 (m, 2H), 5.01-5.11 (m, 2H), 5.66-5.92 (m, 3H), 6.91 (m, 2H), 8.00 (m, 2H); 13 C NMR (75 MHz,CDCl3) δ 36.3,55.4,65.1,113.6,115.9,122.8,125.3,131.6,133.3,135.9,163.3,166.1;MS (EI,70 eV) m/z 232 (M +• , 7), 135 (100), 80 (28), 79 (16); IR (film) 3077, 3006, 2938, 2840, 1713, 1607, 1511, 1460, 1422, 1378, 1316, 1260, 1169, 1104, 1031, 976, 944, 919, 849, 771, 697, 614, 512. Anal. Calcd for C14H16O3: C, 72.39; H, 6.94. Found: C, 72.13; H, 6.87.

(2R,3R)-4-Methoxybenzoic Acid 2,3-Dihydroxyhex-5enyl Ester (74). The olefin 73 (6.965 g, 30.0 mmol), MeSO2-NH2 (2.854 g, 30.0 mmol), K2OsO4'2H2O (66.3 mg, 0.18 mmol, 0.6 mol %), and AD-mix β (42 g, 1.4 g/mmol olefin) were added successively to a mixture of water (150 mL) and t-BuOH (150 mL) at 0 °C. This suspension was stirred vigorously for 2. 25 h, after which it was quenched by the addition of Na2SO3 (45 g, 1.5 g/mmol olefin). After the mixture was stirred for 5 min, an aqueous workup (H2O; EtOAc; MgSO4) and column chromatography (pentane/EtOAc 1:2) gave 5.737 g (21.5 mmol, 72%) of the diol 74 as an amorphous solid. Note: The column chromatography has to be conducted carefully in order to separate the byproduct bearing the benzoyl group at one of the secondary hydroxy groups (resulting from a migration of the benzoyl protecting group under the basic conditions of the Sharpless-AD). It is more polar than 74: Rf 0.80 (EtOAc); ee g 98% (Chiralpak AD (n-heptane/i-PrOH 8:2, tR 14.5 min, 0.7 mL/min)); [R] 23 D +8.9 (c 1.9, CHCl3); 1 H NMR (300 MHz, CDCl3) δ 2.31-2.48 (m, 3H), 2.75 (s, 1H), 3.73 (m, 1H), 3.86 (m, 1H), 3.87 (s, 3H), 4.38 (dd, J ) 11.6, 6.4, 1H), 4.47 (dd, J ) 11.6, 4.7, 1H), 5. 13-5.22 (m, 2H), 5.87 (m, 1H), 6.93 (m, 2H), 8.00 (m, 2H); 13 C NMR (75 MHz, CDCl3) δ 38. 1, 55.5, 66.2, 70.4, 71.8, 113.7, 118.5, 122.0, 131.8, 134.1, 163.7, 166.8; MS (EI, 70 eV) m/z 266 (M +• , 2), 195 (11), 153 (28), 152 (25), 136 (10), 135 (100); IR (KBr) 3297, 2976, 2937, 2844, 1716, 1608, 1513, 1472, 1423, 1385, 1318, 1261, 1170, 1127, 1065, 1031, 995, 918, 848, 769, 696, 615, 542, 509. Anal. Calcd for C 14H18O5: C, 63.15; H, 6.81. Found: C, 62.93; H, 7.10.

(2S,3S)-4-Methoxybenzoic Acid 2,3-Dihydroxyhex-5enyl Ester (ent-74). Analogous to the synthesis of 74, the olefin 73 (0.232 g, 1.0 mmol) was reacted with AD-mix R to give 0.176 g (0.66 mmol, 66%) of the diol ent-74 as an amorphous solid (no additional K2OsO4'2H2O was added in this case, which accounts for the slightly lower yield): ee g 98% (Chiralpak AD (n-heptane/i-PrOH 8:2, Rt 16.3 min, 0.7 mL/min)); [R] 23 D -8.2 (c 0.8, CHCl3). The other analytical data correspond to those of its enantiomer 74.

(4R,5R)-(5-Allyl-2,2-dimethyl[1,3]dioxolan-4-yl)methanol (75). PTSA (0.205 g, 1.1 mmol) was added to a solution of the diol 74 (5.737 g, 21.5 mmol) in 2,2-DMP (150 mL). After 1 h, the reaction was worked up (satd NaHCO 3 solution/H2O 1:1; Et2O; MgSO4). The crude product was dissolved in methanol (150 mL), and K2CO3 (4.466 g, 32.3 mmol) was added. Two hours later, the reaction mixture was concentrated to a small volume and subjected to an aqueous workup (H2O; DCM; MgSO4). Purification by column chromatography (pentane/ ether 4:1 f 1:1) yielded 3.594 g of the alcohol 75 (20.9 mmol, 97% over two steps) as a colorless liquid: Rf 0.50 (pentane/ ether 1:1); [R] 23 D +25.2 (c 0.9, CHCl3); 1 H NMR (300 MHz, CDCl3) δ 1.42 (s, 3H), 1,43 (s, 3H), 2.05 (t, J ) 5.9, 1H), 2.40 (m, 2H), 3.60 (m, 1H), 3.77-3.85 (m, 2H), 3.98 (dt, J ) 8.2, 6.0, 1H), 5.10-5.20 (m, 2H), 5.85 (m, 1H); 13 C NMR (75 MHz, CDCl3) δ 27.0, 27.3, 37.3, 61.9, 75.8, 81.0, 108.8, 117.9, 133.5; MS (EI, 70 eV) m/z 157 (72), 141 (15), 131 (49), 83 (28), 79 (23), 69 (15), 67 (13), 59 (100), 55 (23), 54 (11); IR (film) 3432, 3079, 2986, 2932, 2878, 1643, 1455, 1435, 1376, 1246, 1168, 1062, 998, 917, 842, 694, 615, 515; HRMS calcd for C9H16O3 -CH3 157.0865, found 157.0865.

(1S,14S,16Z,18R)-16,16-Dimethyl-5,7,15,17-tetraoxa-12azapentacyclo[10.8.2.0 2,10 .0 4,8 .0 14,18 ]docosa-2,4(8),9,19-tetraen-13-one (76). A Schlenk tube with a screw cap and Teflon seal was charged with Pd(OAc)2 (0.064 g, 0.29 mmol) and PPh3 (0.223 g, 0.85 mmol). Et3N (0.70 mL, 5.0 mmol) and a solution of the olefin 68 (0.600 g, 1.4 mmol) in DMF (17 mL) were added in a counterflow of Ar. After the tube had been sealed, it was evacuated and filled with Ar (3×). It was placed in an oil bath at 110 °C. Shortly afterward, a deep red color appeared, and stirring was continued for 6 h. The mixture was allowed to cool to room temperature. It was worked up (H 2O; Et2O; MgSO4) yielding a crude product that is dried under high 1-epi-Aglycon of the Cripowellins A and B Org. Chem, Vol. 70, No. 25, 2005 10549 vacuum (to remove residual DMF). Column chromatography (pentane/EtOAc 1:1 f 1/2) gave 0.286 g (0.83 mmol, 59%) of the bicyclic olefin 76 as a beige-brown foam (performing the reaction on a smaller scale yields an almost colorless product): Rf 0.29 (pentane/EtOAc 1:2); de g 98% (GC, 1 H NMR); [R] CHCl3); 1 H NMR (400 MHz, CDCl3) δ 1.33 (s, 3H), 1.44 (s, 3H), 1.88 (dt, J ) 15.4, 4.5, 1H), 2.66 (m, 1H), 3.46 (dd, J ) 13.7, 5.5, 1H), 3.75 (dd, J ) 8.4, 4.0, 1H), 3.95 (dt, J ) 4.8, 13.1, 1H), 4.02 (m, 1H), 4.14 (d, J ) 15.1, 1H), 4.80 (d, J ) 8.5, 1H), 4.99 (d, J ) 15.1, 1H), 5.90 (m, 4H), 6.60 (s, 1H), 6.70 (s, 1H); 13 C NMR (100 MHz, CDCl3) δ 25.6, 27.1, 29.6, 43.6, 44.0, 47.7, 76.5, 77.0, 101.0, 110.4, 111.2, 111.6, 130.5, 131.5, 132.5, 133.1, 145.3, 146.6, 169.8; MS (EI, 70 eV) m/z 344 (M +• , 24), 343 (100), 286 (16), 285 (22), 257 (11), 256 (29), 229 (18), 228 (39), 215 (24), 199 (12), 187 (15), 185 (18), 174 (31), 173 (24), 172 (14), 161 (14), 135 (50), 115 (15); IR (CHCl3) 3009, 2938, 2884, 1659, 1486, 1427, 1377, 1347, 1240, 1214, 1163, 1101, 1041, 998, 936, 870, 825, 756, 669, 476; HRMS calcd for C19H21NO5 343.1420, found 343.1420.

(1R,14S,18R,19S,21S)-16,16-Dimethyl-5,7,15,17,20-pentaoxa-12-azahexacyclo[10.9.2.0 2,10 .0 4,8 .0 14,18 .0 19,21 ]tricosa-2,4(8),9-trien-13-one (77). The Heck product 76 (0.173 g, 0.50 mmol) was dissolved in a precooled (-24 °C) solution of DMDO in acetone (13 mL of a 0.086 M solution, 1.1 mmol) and stored in a freezer for 9 days at -24 °C. It was warmed to room temperature and concentrated under reduced pressure. Purification by column chromatography (pentane/EtOAc 1:4) gave 0.100 g (0.28 mmol, 55%) of the epoxide 77 as a colorless foam: R f 0.23 (pentane/EtOAc 1:3); de 85% (GC, 13 C NMR). The following NMR data refer to the excess diastereomer: 1 H NMR (500 MHz, CDCl3) δ 1.35 (s, 3H), 1.47 (s, 3H), 2.14 (dt, J ) 15.6, 4.4, 1H), 2.78 (m, 1H), 2.94 (dd, J ) 8.5, 7.6, 1H), 3.17 (dd, J ) 7.6, 4.3, 1H), 3.23 (t, J ) 4.7, 1H), 3.59 (dd, J ) 14.0, 6.1, 1H), 3.98 (m, 2H), 4.11 (d, J ) 15.3, 1H), 4.98 (d, J ) 15.6, 1H), 5.02 (d, J ) 8.6, 1H), 5.91 (m, 2H), 6.67 (s, 1H), 6.74 (s, 1H); 13 C NMR (75 MHz, CDCl3) δ 25.7, 26.1, 27.3, 40.0, 44.6, 47.8, 57.9, 58.3, 73.6, 79.0, 101.2, 110.4, 113.3, 113.9, 127.5, 132.2, 145.8, 146.2, 169.6; MS (EI, 70 eV) m/z 360 (M +• , 16), 359 (77), 344 (15), 302 (36), 301 (100), 244 (16), 227 (11), 215 (14), 199 (17), 176 (10), 175 (55), 174 (18), 173 (35), 172 (11), 161 (15), 131 (15), 115 (10), 103 (14); IR (CHCl3) 2992, 2937, 2889, 1661, 1486, 1427, 1378, 1336, 1290, 1249, 1214, 1156, 1104, 1060, 1037, 932, 888, 854, 832, 794, 755, 696, 667, 634, 603, 508, 480; HRMS calcd for C19H21NO6 359.1369, found 359.1369.

(14S,18R,20E/Z)-16,16-Dimethyl-5,7,15,17-tetraoxa-12azapentacyclo[10.8.2.0 2,10 .0 4,8 .0 14,18 ]docosa-1(20),2,4(8),9tetraen-13-one (78). A two-necked flask was charged with the olefin 68 (0.560 g, 1.3 mmol), Pd(OAc)2 (0.045 g, 0.020 mmol), Ag2CO3 (1.092 g, 4.0 mmol), and dppp (0.109 g, 0.26 mmol). One neck was sealed with a septum, and the other one was connected to a reflux condenser. A three-way stopcock equipped with a ballon was used to seal the condenser. The apparatus was evacuated and filled with Ar (3×). The ballon was used to maintain a slight overpressure of Ar. Toluene (18 mL) was added through the septum, and the flask was placed in an oil bath at 124 °C. After 4 h, the reaction was cooled to room temperature and filtered through a short plug of silica gel (eluting with EtOAc). The solvent was evaporated and the residue purified by column chromatography (pentane/EtOAc ) 2:1 f 1:1 f 1:2) yielding 0.268 g (0.78 mmol, 59%) of the bicyclic olefin 78 as a colorless foam: HPLC t R 19.9 min (LiChrosorb Si 60 (Et2O/pentane 8:2), 0.6 mL/min; tR 15.7 min for the minor diastereomer); Rf 0.50 (pentane/EtOAc 1:2); de ) 25% (referring to the double bond isomers); [R] 24 D -51.0 (c 0.3, CHCl3; Z-isomer).

Major diastereomer (Z-78): 1 H NMR (400 MHz, CDCl3) δ 1.44 (s, 3H), 1.45 (s, 3H), 2.22 (ddd, J ) 14.4, 7.8, 4.5, 1H), 2.43 (ddd, J ) 12.8, 11.2, 6.8, 1H), 2.71 (dd, J ) 12.9, 7.1, 1H), 3.04 (dt, J ) 14.3, 10.0, 1H), 3.54 (dd, J ) 13.3, 6.7, 1H), 3.81 (m, 1H), 3.92 (d, J ) 15.9, 1H), 4.20 (ddd, J ) 9.5, 8.5, 4.5, 1H), 4.78 (d, J ) 8.2, 1H), 5.25 (d, J ) 15.7, 1H), 5.87 (dd, J

  Moon, B.; Han, S.; Yoon, Y.; Kwon, H. Org. Lett. 2005, 7, 1031-1034. (9) (a) Catlin, K. RWTH Aachen, unpublished results. (b) Janeck, C. F., Ph.D. Thesis, RWTH Aachen, 2000. (c) Backes, M., Ph.D. Thesis, RWTH Aachen, 2004. (d) Lenzen, A., Ph.D. Thesis, RWTH Aachen, 2005.

SCHEME 1 .

 1 SCHEME 1. Retrosynthesis I with the Alkylation of the 2-Benzazepine Dithiane 5 as the Key Step

SCHEME 2 .

 2 SCHEME 2. Synthesis of A-and B-Type Electrophiles

SCHEME 8 .

 8 SCHEME 8. Radical Cyclization Approach

( 41 )

 41 Representative reviews about the RCM: (a) Deiters, A.; Martin, S. F. Chem.Rev. 2004, 104, 2199-2238. (b) Schrock, R. R.; Hoveyda,

  Felpin, F.-X.; Lebreton, J. Eur. J.Org. Chem. 2003, 3693-3712. (42) For the metathetic synthesis of 9-membered rings using similar conformational constraints to the dioxolane ring, see: (a) Harris, P. W. R.; Brimble, M. A.; Gluckman, P. D. Org. Lett. 2003, 5, 1847-1850. (b) Clark, J. S.; Marlin, F.; Nay, B.; Wilson, C. Org. Lett. 2003, 5,89-92. (c) Kaliappan, K. P.; Kumar, N. Tetrahedron Lett. 2003, 44, 379-381. (d) Hirama, M.; Oishi, T.; Uehara, H.; Inoue, M.; Maruyama, M.; Oguri, H.; Satake, M. Science 2001, 294, 1904-1907. (e) Clark, J. S.; Hamelin, O. Angew. Chem. 2000, 112, 380-382; Angew. Chem., Int. Ed. 2000, 39, 372-374. (f) Bamford, S. J.; Goubitz, K.; van Lingen, H. L.; Luker, T.; Schenk, H.; Hiemstra, H. J. Chem. Soc., Perkin Trans. 1 2000, 345-351. (g) Oishi, T.; Nagumo, Y.; Hirama, M. Chem. Commun. 1998, 1041-1042. (h) Delgado, M.; Martı ´n,J.D.Tetrahedron Lett. 1997, 38, 6299-6300. (43) There are only very few examples for the metathetic synthesis of 9-membered rings without conformational constraints. They are limited almost exclusively to those 9-membered cyclic ethers for whose synthesis the gauche effect can be exploited: (a) Crimmins, M. T.; Powell, M. T. J. Am. Chem. Soc. 2003, 125, 7592-7595. (b) Crimmins, M. T.; Emmitte, K. A.; Choy, A. L. Tetrahedron 2002, 58, 1817-1834. (c) Baba, Y.; Saha, G.; Nakao, S.; Iwata, C.; Tanaka, T.; Ibuka, T.; Ohishi, H.; Takemoto, Y. J. Org. Chem. 2001, 66,81-88. (d) Crimmins, M. T.; Choy, A. L. J. Org. Chem. 1997, 62, 7548-7549.

  SCHEME 10. Studies Leading to the Keto Acid 49

  SCHEME 15. Synthesis of the Acid 71

(

  61) White, J. D.; Somers, T. C. J. Am. Chem. Soc. 1994, 116, 9912-9920. (62) Molander, G. A.; Hahn, G. J. Org. Chem. 1986, 51, 1135-1138. (63) Molander, G. A. Org. React. 1994, 46, 211-367. (64) Ho, P.-T. Tetrahedron Lett. 1978, 19, 1623-1626. (65) (a) Lipshutz, B. H.; Pollart, D.; Monforte, J.; Kotsuki, H. Tetrahedron Lett. 1985, 26, 705-708. (b) Schmeck, C.; Hegedus, L. S.

  SCHEME 18. Synthesis of the Epoxide 77

  . Anal. Calcd for C19H22BrNO5: C, 53.79; H, 5.23; N, 3.30. Found: C, 53.53; H, 5.14; N, 2.99. . A solution of DMSO (3.51 mL, 49.4 mmol) in DCM (15 mL) was slowly added to a solution of oxalyl chloride (2.03 mL, 23.7 mmol) in DCM (100 mL) at -78 °C. After 15 min, a solution of the alcohol 75 (3.701 g, 21.5 mmol)

SCHEME 21 .

 21 SCHEME 21. Completion of the Synthesis of the 1-epi-Aglycon 82 of the Cripowellins A and B

  , 4.13 (d, J ) 7.4, 1H), 4.27 (d, J ) 7.4, 1H), 4.51 (d, J ) 4.1, 1H), 4.55 (d, J ) 2.2, 1H), 4.68-4.80 (m, 4H), 5.00-5.19 (m, 8H), 5.70-5.93 (m, 4H), 5.95 (m, 2H), 5.98 (m, 2H), 6.66 (s, 1H), 6.70 (s, 1H), 6.98 (s, 1H), 7.02 (s, 1H); 13 C NMR (100 MHz, CDCl3) δ 26.

J.Org. Chem, Vol. 70, No. 25, 2005 10539

J.Org. Chem, Vol. 70, No. 25, 2005 10541

J.Org. Chem, Vol. 70, No. 25, 2005 10545

J.Org. Chem, Vol. 70, No. 25, 2005 10547

Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 380) and the Fonds der Chemischen Industrie. We thank Prof. Rosenkranz, Prof. Stetter, and Dr. Lieb and co-workers of the Bayer AG for valuable discussions at the beginning of this project. Supporting Information Available: Experimental procedures and characterization data for compounds 11, 13, 15-17, 19-43, 45, 47-50, 53-59, and 62-65 and NMR spectra of compounds 80-83. This material is available free of charge via the Internet at http://pubs.acs.org. JO0518093 1-epi-Aglycon of the Cripowellins A and B Org. Chem, Vol. 70, No. 25, 2005 10551 Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org) Powered by TCPDF (www.tcpdf.org)


D Frey

J Royan

R Piegay

A.-M Kermarrec
email: marie.kermarrec@irisa.fr

E Anceaume

Solipsis: A Decentralized Architecture for Virtual Environments

Keywords: Peer-to-peer System, Metaverse, Shared Virtual Worlds, Massively Decentralized System, Adaptative 3D Streaming K.6.1 [Management of Computing and Information Systems]: Project and People Management-Life Cycle; K.7.m [The Computing Profession]: Miscellaneous-Ethics

Lack of scalability is a key issue for virtual-environment technology, and more generally for any large-scale online experience because it prevents the emergence of a truly massive virtual-world infrastructure (Metaverse). The Solipsis project tackles this issue through the use of peer-to-peer technology, and makes it possible to build and manage a world-scale Metaverse in a truly distributed manner. Following a peer-to-peer scheme, entities collaborate to build up a common set of virtual worlds. In this paper, we present a first draft of the Solipsis architecture as well as the communication protocol used to share data between peers. The protocol is based on Raynet, an n-dimensional Voronoi-based overlay network. Its data-dissemination policy takes advantage of the view-depedent representation of 3D contents. Moreover, the protocol effectively distributes the execution of computationally intensive tasks that are usually executed on the server-side, such as collision detection and physics computation. Finally, we also present our web component, a 3D navigator that can easily run on terminals with scarce resources, and that provides solutions for smooth transitions between 3D Web and Web 2.0.

INTRODUCTION

The Metaverse concept, first described by Neal Stephenson in his science fiction novel 'Snow Crash' published in 1992, and more generally depicted in the whole cyberpunk writing movement, has deeply influenced generations of virtual reality pioneers, artists, game designers and nowadays virtual worlds enthusiasts. Over the last sixteen years, the notion has evolved toward a synonym for virtual world, loosing progressively the 'Universe' part of the concatenation and the huge and infiniteness feeling emanating from it.

However, for us the Metaverse is a system of numerous, interconnected virtual and typically user-generated worlds (or Metaworlds) all accessible through a single-user interface. According to this strict definition, the only Metaverse existing today is a prehistoric one: the World Wide Web itself. Plenty of virtual worlds flourish these days claiming they are the Metaverse, but they only are a part of it, as websites are the leaves of the worldwide web tree. We need three things to reach this cyberpunk authors' dream. First, a way to sustain the incredible amount of data and MIPS involved, then a set of protocols to provide interoperability and finally new tools to build virtual worlds as easily as a traditional HTML page. These requirements are the cornerstones of our project.

The paper is structured as follows. We first present a synthetic overview of the Solipsis research project in Section 2, and an analysis of related work in Section 3. Then we describe how we envision to manage decentralized virtual worlds, describing in details our peer-to-peer architecture, how we manage 3D-model sharing and physics computation, and how to stream 3D contents in an adaptative way. Finally, in Section 5, we present our navigator, which is the user interface used to interact with the Solipsis Metaverse, while in Section 6, we conclude the paper and outline our future directions.

PROJECT OVERVIEW

In a word, Solipsis is a platform for massively multi-participant and user-generated virtual worlds. It relies on a peer-to-peer architecture that makes scalability its main characteristic: the universe may thus be inhabited by an unlimited number of participants. As there is no central authority, the virtual universe is by definition public and the inhabitants' freedom, as well as the world builders and developers' imagination, are boundless.

Expected results

We seek to spark off the emergence of an unbounded public virtual universe that is designed, created, run, but also potentially hosted, by people throughout the world. Freedom can be spotted as the main characteristic of this opensourced system (license GNU/GPL v2+) because the virtual universe does not belong to any organization; it belongs to all the users.

The major deliverable is a new network communication protocol adapted to the strong constraints of self-produced environments, to massively multi-user applications and to virtual reality, which make the system more scalable as the resources its uses are those provided by its users.

We also work on creating an ergonomic and user-friendly interface to allow non-professional agents to easily create 3D scenes and contents (declarative or automatic modeling, tagging..). Nevertheless, we do not want to mark a break with the actual flat 2D web; rather, we aim to start a smooth transition towards an immersive Internet making the most of both 2D and 3D. As we will see in part V, our navigator can be embedded in a regular webpage -in-web world -or map regular webpages as an interactive texture on any 3D surface -in-world web.

The last major expected result is a deep analysis on the behavior (virtual social life, game, education, services..) of metaverse users to give directions for future developments.

RELATED WORK

The Web3D consortium originally had the ambition to create a freely navigable online world [START_REF] Pesce | Cyberspace[END_REF]. Unfortunately, due to technical constraints, such as bandwidth limitations, the VRML standard was only used to encode simple 3D contents in order to visualize them on web sites. Only related research and bandwidth increase have now made it possible to draft the architecture of a Web3D, metaverse or cyberspace.

Compression and adaptive 3D Streaming

A lot of research work has focused on the compression of 3D models, as well as on adaptive streaming methods that allow a progressive and fast transmission over networks of the required 3D contents visualized from the current viewpoint.

First, existing 3D compression algorithms use both techniques adapted from the 1D and 2D cases (like wavelets, entropy coding, and predictive coding), and completely different approaches that take advantage of the properties of 3D surfaces (like Edgebreaker, Subdivision Surfaces, and triangle strips) [START_REF] Gioia | Real-time reconstruction of wavelet-encoded meshes for view-dependent transmission and visualization[END_REF] [START_REF] Isenburg | Compressing polygon mesh geometry with parallelogram prediction[END_REF]. Also, parametric solutions, that provide intuitive modeling tools, are widely used to create avatars, complex creatures, or vehicles in games. More complex 3D contents can be created using procedural modeling solutions that have the drawback of requiring a reconstruction process executed on the fly on the client side. Parametric and procedural modeling provide very good compression rate compared to usual mesh compression algorithms, but no generic solutions exist to model a great variety of objects.

The second solution consists in filtering the 3D contents required to visualize the scene from a given viewpoint. Indeed, a complete download of a huge 3D scene is not necessary to render with optimal details the virtual environment from a given viewpoint. First, the area of a 3D model projected on the screen depends not only on its size, but especially on its distance from the viewpoint. Many solutions have therefore been proposed to adapt the resolution of 3D models to the current viewpoint [START_REF] Funkhouser | Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments[END_REF]. Continuous levels of detail allow to transmit refinements progressively as the viewpoint comes closer to 3D objects [START_REF] Hoppe | Progressive meshes[END_REF][START_REF] Luebke | A developer's survey of polygonal simplification algorithms[END_REF]. Second, most of 3D objects in huge and complex 3D scenes are occulted by other ones during the navigation. Thanks to an offline computation of 3D objects visible from regions resulting from a partitioning of the navigation area, servers can signifanctly reduce the amount of data that has to be sent to the client, without affecting the visual quality [START_REF] Teller | Visibility preprocessing for interactive walkthroughs[END_REF][START_REF] Wonka | Instant visibility[END_REF]. Unfortunately, visibility filtering methods have to be disabled during flying-over navigation, since occultations are clearly limited. In fact, these filtering methods provide multi-resolution functionalities allowing an adaptive 3D streaming of the virtual environments.

Centralized architectures

Several architectures take advantage of filtering methods presented previously [START_REF] Macedonia | Npsnet: A network software architecture for large-scale virtual environment[END_REF][START_REF] Greenhalgh | MASSIVE: A distributed virtual reality system incorporating spatial trading[END_REF][START_REF] Funkhouser | RING: A client-server system for multi-user virtual environments[END_REF][START_REF] Frécon | Dive -a scalable network architecture for distributed virtual environments[END_REF]. Commercial platforms such as Google Earth [1] and Second Life [2] have recently known a tremendous craze from the public. The first allows navigation into and over a well-detailed model of the earth, with terrain and buildings. In doing this, it takes advantage of an adaptive streaming of terrain textures [START_REF] Tanner | The clipmap: a virtual mipmap[END_REF], associated with a multi-resolution wavelet-based representation for terrain, and static levels of detail for buildings. The second provides an advanced social-network service combined with general aspects of a metaverse. The Second Life client integrates modeling tools that allow users to create new components of the virtual environment.

In addition to the above, more than fifty online virtual worlds have appeared over the last few years, and are usually based on centralized architectures. Huge environments are generally partitioned, according to a grid, in regions that are managed by dedicated servers, called region servers. Unfortunately, in order to synchronize the game states of the world for all connected clients, most processes such as collision detection, physics computation, and animation, are executed on the server side. Moreover, the region server is the only source that can provide clients with the 3D models of the scene for its visualization. Thus, the number of clients that can navigate into a region managed by only one server is clearly limited.

Peer to Peer Architectures for Virtual Worlds

A centralized architecture cannot lead to a truly self-scalable solution, even with the use of multiple servers. Indeed, client-server architectures lead to prohibitive deployment and maintenance costs when it comes to very large scale applications with thousands of connected clients. On the other hand, thanks to their self-adaptation features, P2P network overlays have clearly proved to be an effective alternative to powerful servers.

Based on the fact that if peers have nearly the same viewpoint, they are likely to need the same data, geometric proximity is obviously the main criterion for setting up peer connectivity within virtual environments. However, finding and maintaining the appropriate peer connectivity is a very difficult problem in a dynamic environment and in the presence of churn, that is where peer viewpoints are allowed to move freely and when peers can disconnect or appear at any time. Solipsis [START_REF] Keller | Toward a peer-to-peer shared virtual reality[END_REF][START_REF] Keller | Solipsis: A massively multi-participant virtual world[END_REF] and VON [START_REF] Hu | Scalable peer-to-peer networked virtual environment[END_REF] are the first P2P layers providing a solution for 2D environments. In these P2P architectures, peers are connected to each other according to their current 2D position. Dedicated algorithms are used to achieve the global stability of the P2P network while fulfilling a global connectivity constraint (i.e. there must exist at least one path between each pair of peers).

Maintaining real-time peer connectivity in a n-dimensionnal space is much more complex. For this reason, Douglas et al. [START_REF] Douglas | Enabling massively multiplayer online gaming applications on a p2p architecture[END_REF] have proposed a region-based approach using a distributed spatial data index in a multidimensional space to find nearby objects with which direct connections can be established. Finally, Cavagna et al. [START_REF] Cavagna | P2p network for very large virtual environment[END_REF] show that server-less P2P networks can efficiently deal with very large environments, first by using well-suited descriptors to specify areas of interest for continuous levels of detail (for on-demand streaming), and second by having peers exchange information about their own serving capabilities (for self-regulating peer-upload bandwidth).

DECENTRALIZED VIRTUAL WORLDS MANAGEMENT

Our response to the demand for an efficient metaverse platform capable of 3D interactions among entities is the new version of Solipsis. Its key characteristic is the ability to distribute the cost associated with the management of its metaverse among the hosts participating in it. This is made possible through the decentralization of heavy processes like collision detection, computation of physics, as well as communication among the large number of nodes that participate in the metaverse. In the following, we present the main characteristics of the architecture and of the protocol enabling such decentralization.

Definitions

The Solipsis metaverse consists of a set of entities, each belonging to one of three categories: avatars, objects, and sites. Avatars are the main actors of the metaverse as they are the only entities that are capable of autonomous movement. In most cases they are virtual representations of the users of the metaverse and are directly controlled by them using the navigator platform described in Section 5. Objects, on the other hand, are virtual representation of entities from the real world such as furniture, books and whatever object may be moved or picked up by an avatar. Avatar and objects may also be robotic-like entities controlled by user-defined software components. Finally, sites constitute the basic building blocks of the metaverse and represents portions of the virtual space that may be occupied by objects or in which avatars can roam.

Avatars, objects, and sites are all associated with 3Ddescriptions, each consisting of a mesh-or prims-based model, a set of textures, and, in the case of avatars or objects, also of an animation. Such 3D-descriptions constitute the basis for the rendering of entities in the navigator platform.

The state of an entity in the metaverse is determined by an entity descriptor, from now on referred to simply as descriptor. An entity's descriptor can contain information regarding its position, its physical properties, and whatever is needed to display the entity and compute its interaction with the rest of the metaverse. For example, a descriptor containing a key frame can be used to synchronize animations, videos, and so on. Moreover, filtering descriptors defining areas (concentric spheres, hierarchical partitioning, cells) associated with a level of detail or a set of visible objects may be used to achieve efficient on-demand streaming while satisfying view-dependency criteria. Finally, descriptors may contain load-balancing information regarding, for example, the available resources or serving capabilities of a host [START_REF] Cavagna | P2p network for very large virtual environment[END_REF]. Table 1 shows a sample descriptor containing the most relevant information. Although the descriptor is shown as a single object, the Solipsis implementation may split it into several descriptors regarding, for example, physical properties, location, or level of details in order to reduce communication cost.

Solipsis Hosts and Nodes

From a practical viewpoint, the Solipsis platform is distributed over a set of hosts that maintain information about every entity that is currently present in the metaverse. Each host is associated with a single instance of the Solipsis platform, and throughout its lifetime, it may create new entities or destroy previously created ones according to the requests of the navigator component. Also, similar to an entity, each host is associated with a unique identifier (UID).

Because each host may be responsible for several entities at the same time, we define a (Solipsis) node as the set of resources dedicated to the management of a given entity. Each node encapsulates information about the corresponding entity's descriptors as well as the threads of control responsible for managing all the interactions of the node with the rest of the Solipsis metaverse as well as with the navigator platform.

P2P Architecture

A fundamental aspect of Solipsis is its completely decentralized architecture designed to accommodate large numbers of entities, accessed by large numbers of users distributed over the Internet. The core of this decentralized architecture is a peer-to-peer overlay network, which is essentially a graph where nodes are connected by virtual logical links, each of which may consist of several physical links in the underlying IP network. These logical links may be laid out according to some proximity metric so as to enable efficient storage and retrieval of information. Recent years have seen the emergence of a large number of peerto-peer overlay networks, with different structures and capabilities. In the context of Solipsis, we leverage the potentialities of peerto-peer overlays by building our metaverse on top of RayNet [START_REF] Beaumont | Peer to peer multidimensional overlays: Approximating complex structures[END_REF]. Raynet is a multi-dimensional overlay network based on the concept of Voronoi tessellation. As shown in Figure 1, each node in the overlay is associated with a position in a multi-dimensional space. Neighborhood relationships between peers are then determined by the distance between the corresponding points in this space. Specifically, two Raynet nodes are neighbors in the overlay if the two corresponding points are neighbors in the Delaunay graph comprising all the points associated with Raynet nodes.

Given a set of generator points{p ∈ ℜ d }, the Delaunay graph is obtained as the adjacency graph of the corresponding Voronoi diagram, which in turn is a tessellation of the d-dimensional space ℜ d . Specifically, the cell in the tessellation associated with a point p x is such that it contains all the points that are closer to p x than to any other generator point in the set. This property enables Raynet to route to any node in the overlay by means of a simple greedy approach. Moreover, the addition of Kleinberg-like [START_REF] Kleinberg | The Small-World Phenomenon: An Algorithmic Perspective[END_REF] long-range links allows this routing process to converge to its destination node in a polylogarithmic number of hops on average.

Within the context of Solipsis, we use the Raynet structure to organize site nodes into a 3-dimensional overlay in which the positions of nodes mimic those of the corresponding sites in the metaverse.1 This allows our architecture to exploit very simple protocols to manage the interaction between avatars, objects and the sites they are currently located in as we describe in the following.

Decentralized physics computation

The choice of a peer-to-peer overlay such as Raynet is motivated by our goal to scale to metaverses containing very large numbers of entities, possibly gathered within the same site or within an otherwise small region of space. Organizing sites nodes into such an overlay, however, is only half of the picture. Solipsis also incorporates a fully decentralized protocol that distributes the cost associated with heavy computations such as those regarding collision detection, physics, or animation.

Each avatar node is responsible for computing its own position based on physical criteria like its mass, momentum, and forces applied by the entities in its surroundings. Our decentralized approach allows it to achieve this result by taking into account only a small set of 3D models: those associated with the current site and with the entities that are in the avatar's immediate surroundings. For example, in the case of collisions, each avatar may immediately rule out the entities that are at a distance that is greater than the radii, R b , of the spheres enclosing its and their own bounding boxes plus a configurable safety distance.

The basis for this decentralized computation of physics is a communication protocol that allows nodes to exchange information about entities' positions with three levels of heartbeat messages. Critical information that is required for the computation of collision detection is exchanged directly in a peer-to-peer fashion between the avatars that may potentially collide with each other, based on the size of their bounding boxes. Less critical information that is nonetheless necessary to provide the navigator with a clear snapshot of the current scene state is instead propagated indirectly, in a multi-hop fashion. Finally, information about distant objects or objects that have just joined the metaverse is propagated by site nodes to the avatars within their cells at a significantly lower frequency.

An avatar joining Solipsis contacts the site node responsible for its joining -or latest -location. Although the avatar is not part of the overlay, it can easily do this by using the Raynet to route a message containing its descriptor to the site node that is closest to its own position. This node then reacts by providing the avatar with the descriptors of the entities that are potentially visible from its location. From this point on, the avatar and site nodes exchange this information periodically to implement the low frequency updates described above. An analogous mechanism is used to manage the positions of object nodes. The use of the Raynet always allows avatars and objects to contact the right node as they move from site to site.

In addition, avatar and object nodes interact with the avatars and objects around them in order to exchange the critical up-to-date information about the entities that may collide with them. Also, while sending an update to a nearby node, avatar and object nodes also include information received from other nearby nodes that are not within collision distance of the destination node; thus implementing the second level of peer-to-peer updates.

Dynamic Object Management

While avatars are the main actors in the Solipsis environment, objects also play an important part as they can interact with avatars, be picked up, be moved from one location to another, or even move freely through space subject to gravity or other forces, or according to a script of animation. This requires our protocol to determine the current position of objects in addition to that of avatars. This is achieved through a combination of three mechanisms that depend on the state the object is currently in.

Let us consider an object that is currently stationary within a site S's cell. The position of the object is maintained by S's site node, which also maintains the main copy of the object's descriptor. As soon as an avatar tries to interact with the object, by moving it or picking it up, its avatar node sends a request to the site node to take over responsibility for the object. The site node grants such responsibility to the first avatar requesting it, according to the order in which requests reach the site node.

When permission to take over the object is granted, the object is dynamically detached from the site and attached to the avatar. The corresponding descriptors are updated, and the avatar nodes starts computing physics and maintaining the descriptor for the object. Note that physics computation need not be performed by site nodes, in that an object can only be attached to a site when it is in static equilibrium.

After interacting with the object, the avatar may pass the object on to another avatar, or leave it in the current or in a different site. In the former case, the recipient of the object takes over its management, and starts computing its physics, and animation, and updating its descriptor. In the latter, on the other hand, the object may be left in a stationary or in a dynamic state. If the object is stationary, then the site may take control of its descriptor and manage it without computing any physics. If, on the other hand, the object is moving, or subject to forces that are not in equilibrium, then a new object node with a corresponding thread is instantiated on the host associated with the avatar to which the object was attached. This new object node takes responsibility for managing the object's movements and updating its descriptor until it is picked up by a new avatar or until it reaches an equilibrium state at some site. It should be noted that a host may keep managing an object, even if the associated avatar is at a distant location. This allows hosts to manage robotic-like entities that are controlled by user-defined software components, e.g. by associating streaming video to objects.

Decentralized 3D-Model Sharing

The architecture we have described so far assumes that nodes are able to retrieve the 3D-description of entities in order to compute collisions and display the entities after filtering them based on the information in their descriptors. In the following, we describe our mechanism for maintaining and retrieving these 3D-descriptions. As with the rest of the protocol, our goal is to distribute the cost of managing 3D-descriptions among Solipsis participants.

3D-descriptions are managed by the nodes responsible for the corresponding entities, and may be downloaded by any node that needs to display the object or perform collision detection. However, having all hosts download a given 3D-description from the node responsible for its entity would place an unnecessary load on the corresponding host. We address this issue, by having Solipsis nodes cache previously downloaded descriptions. This allows them to offer them for download to other Solipsis nodes running on the same or remote hosts.

All the nodes residing on a host, store their own 3D-descriptions as well as those of other visible objects in a shared repository (depicted in Figure 2) that is accessible by all the nodes running on the same host. Moreover, each node records in its entity's descriptor a list of the hosts that currently hold a copy of any of the files that constitute the associated 3D description. Whenever a node caches a 3D-description, it informs the node responsible for the entity, which then updates the corresponding descriptor to include a reference to the new copy and then propagates it with its subsequent heartbeat messages. Similarly, when a node detects that a host listed in the descriptor does not have the current copy of an entity's description, it sends a message to the corresponding node, which updates the descriptor accordingly.

Managing Disconnections

The architecture of Solipsis is designed to tolerate unexpected disconnections of hosts throughout its operation. First, site nodes always cache the 3D-descriptions, in addition to the descriptors, of neighboring site nodes. This allows the RayNet to manage the disconnection of a site node by automatically assigning its management to any of the neighboring site nodes. The disconnection of an avatar or object node, on the other hand, is treated by attaching the object or avatar to its current site and by leaving it in a stationary state until the corresponding user reconnects.

THE NAVIGATOR

A navigator must be able to create a huge metaverse and democratize its use. For this reason, we base our navigator on the Ogre 3D rendering engine. Its robustness, efficiency, upgradability and openness are, in fact, essential features for a durable system. Moreover, Ogre 3D can be easily embedded in web pages thanks to a Mozilla or ActiveX plugin. Conversely, web pages can be mapped on 3D models as interactive textures thanks to the Navi library based on Gecko. Thus, the navigator allows a Web 2.0 navigation inside the Web 3D, as well as a Web 3D navigation inside the Web 2.0. Our view is, in fact, that Web 3D and Web 2.0 should integrate each other (see figure 3). Since the vitual universe belongs to all users, modeling tools are embedded within the navigator in order to create, modify or delete contents. At the moment, we focus on intuitive tools, but procedural, declarative, parametric and sketchbased modeling tools are obviously considered. Finally, to provide access to the virtual universe on mobile devices, nodes can be hosted by proxy servers, to reduce the amount of computation that has to be performed on terminals with scarce resources. Thus, hosts can compute collision detection, physics animation, data-exchange management, and viewpoint-based filtering, and then communicate with the navigator that only needs to render the virtual environment and interact with it (see figure 2).

CONCLUSIONS AND PERSPECTIVES

We presented our vision for a decentralized architecture for virtual environments. Our solution is based on an n-dimensional Voronoibased peer-to-peer network, called RayNet. This allows it to distribute communication and computational cost among the various nodes present in the virtual space. Our architecture enables the decentralization of complex tasks related to physic-realistic modeling. To achieve this, nodes preliminarily filter the set of avatars and objects that may collide with their own and then evaluate collisions and physics for a small set of entities. Our solution also supports dynamic objects that may be picked up and dropped by avatars or controlled by means of user-defined software. Moreover, it enables adaptive streaming of 3D models in a completely decentralized fashion while adapting streamed data to avatars' viewpoints. Also, the use of an n-dimensional overlay allows us to extend the metaverse to support social or semantic proximity between object or avatar nodes. Access to the metaverse is made possible by a navigator that may run as a stand-alone platform or embedded within a web page. The navigator exploits interactive texturing to enable the visualization of Web 2.0 components in the virtual world and it integrates tools for modeling new 3D contents. Moreover, it supports operation on resource-scarce devices such as mobile phones. Our project team is currently working on a fully open-source implementation of the Solipsis architecture, and we hope that the community of users will help us improve Solipsis and enable us to evaluate its effectiveness in a world-wide testbed.

Figure 1 :

 1 Figure 1: The p2p architecture showing the mapping of the Raynet layer on the virtual world layer according to the proximity of nodes in the virtual space. The host layer shows clients connected into a peer to peer scheme. Note that while the positions of avatars and objects are also shown, for clarity, on the Raynet layer, only site nodes actively join the RayNet and form the corresponding Voronoi diagram.

Figure 2 :

 2 Figure 2: Nodes hosted on a proxy server to allow accesses to the metaverse on terminals with low resources such as mobiles.

Figure 3 :

 3 Figure 3: Web based navigator embedding modeling tools, and providing a mapping of web pages as interactive textures.

Table 1 :

 1 Example of a simple descriptor

	UID	universal identifier of the entity
	seqNum sequence number
	owner	identifier of the node managing the entity
	type	site, avatar or object
	loc	location in the 3D space
	ori	orientation in the 3D space
	shape	shape from a predefined set
	box	bounding box of the object
	R p	perceptibility radius: distance from which the object
		is visible in the absence of obstacles
	R b	radius of smallest sphere enclosing the entity
	objs a	list of entities attached to the current one
	f 1	first file of 3d-description
	v 1	version number for first file
	c 1	list of hosts that have cached v 1 of f 1
	...	...
	f n	n-th file of 3d-description
	v n	version number for n-th file
	c n	list of hosts that have cached v n of f n
	...	additional fields for progressive levels of details

Extensions of the metaverse architecture to higher dimensions are naturally supported by the Raynet overlay.

ACKNOWLEDGEMENTS

First, the authors wish to thank all people who contributes to the Solipsis project as well as all pioneers of the decentralization of virtual environments whithout who this project would not be also advanced: M. Keller, M. Simon, M. Cavagna, M. Bouville and M. Beaumont. This work was supported in part by a French collaborative R&D project (ANR-RIAM) leaded by Orange Labs, funded by ANR and Media & Networks cluster of Brittany, involving IRISA, Rennes 2 University, Archivideo and Artefacto.


Dahlborg

Effect of Heat Treatment of a Melt on the Structure and Properties of the Corresponding Crystalline Ingots or Castings