Preparation of 6,6,1′,1′,6′,6′-hexadeutero sucrose

Article abstract of DOI:10.1016/j.carres.2007.06.024

The preparation of 6,6,1′,1′,6′,6′-hexadeutero sucrose is reported. The synthesis is based on a triple oxidation of a protected sucrose 6,1′,6′-triol to the corresponding 6,1′,6′-tricarboxylic acid or ester, followed by reduction with lithium aluminium de

Full text of DOI:10.1016/j.carres.2007.06.024

Carbohydrate Research 342 (2007) 2303–2308
Note
Preparation of 6,6,10,10,60,60-hexadeutero sucrose
a
a,
Marie-Helene Gouy, Mathieu Danel, Maud Gayral,a Alain Bouchub
´ `
and Yves Queneaua,*
aInstitut de Chimie et de Biochimie Mole´culaires et Supramole´culaires, UMR 5246, CNRS; Universite´ de Lyon;
ˆ
Universite´ Lyon 1; INSA-Lyon; CPE-Lyon; Laboratoire de Chimie Organique, INSA-Lyon, Bat. Jules Verne,
20 Avenue Albert Einstein, Villeurbanne F-69621, France
bTEREOS, Service Innovation rue du petit Versailles, BP 16, 59239 Thumeries, France
Received 22 April 2007; received in revised form 7 June 2007; accepted 22 June 2007
Available online 30 June 2007
Abstract—The preparation of 6,6,10,10,60,60-hexadeutero sucrose is reported. The synthesis is based on a triple oxidation of a pro-
tected sucrose 6,10,60-triol to the corresponding 6,10,60-tricarboxylic acid or ester, followed by reduction with lithium aluminium
deuteride. This triple oxidation could be achieved either using cat. TEMPO–NaOCl (to the acid) or PDC–Ac2O–t-BuOH (to the
t-butyl carboxylic ester).
ꢀ 2007 Elsevier Ltd. All rights reserved.
Keywords: Sucrose; Deuteration; Isotope; Oxidation; Uronic acids; Labelled compounds; TEMPO
Sucrose is a major food ingredient and is therefore the
starting point of many biochemical processes related
to nutrition. Our group being involved in the chemistry
of sucrose, and in physicochemical studies of sucrose
and some of its derivatives,1–4 we became interested in
the synthesis of a simple polydeuterated analogue of
sucrose, which would be very easy to track by classical
analytical methods.5
Indeed, labelled sugars are efficient probes used to elu-
cidate biological mechanisms. For example, commer-
cially available radioactive [3H]- and [14C]-sucroses
have been recently used as tracers for translocation
experiments in plants,6 as a probe for membrane integ-
rity by permeability measurements,7 or in studies di-
rectly related with carbohydrate chemistry such as in
the enzymatic synthesis of labelled fructooligosaccha-
rides.8 Also, [3H]-1-fluorosucrose, used for evidencing
the presence of a sucrose carrier in sugar beet roots,
was prepared by sucrose synthase coupling.9,10 Deute-
rium or carbon 13 labelled sucroses are also interesting
as they can be used for analytical purposes without the
specific requirement associated with handling of radio-
active materials. 13C-Sucrose is known and prepared
by biosynthesis under 13CO2 atmosphere.11,12
Only few deuterated sucroses are described. Two
defined C-monodeutero sucrose analogues, namely,
2- and 3-monodeuterosucroses, have been obtained by
deuteride reduction of 2- and 3-oxo-sucrose.13,14 Also,
the synthesis of a poly-C-deuterated sucrose analogue
has been reported by Raney nickel catalysed deuteration
of sucrose in refluxing deuterium oxide.15–17 This very
direct dehydrogenation–deuteration sequence18–21 pro-
vides deuteration at all carbon atoms bearing a hydroxyl
group. However, significant variations in the rates of
H–D exchange15 at different positions and in the final
deuteration level have been observed (d11 or d5)15–17
and, in the case of a series of monosaccharides, compet-
itive undesired epimerisations have been shown to be
difficult to prevent.22 Using the same method, a d5
sucrose analogue was obtained (instead of the d11
one as in Refs. 15 and 16) when microwave activation
is used.17 Other isotope incorporations in carbohydrate
*
Corresponding author. Fax: +33 04 72 43 88 96; e-mail: yves.
queneau@insa-lyon.fr
`
Present address: Laboratoire de Synthese et Physicochimie de
´
´ ˆ
´
Molecules d’Interet Biologique, CNRS UMR 5068, Universite Paul
Sabatier, Baˆt. 2R1, 118 Route de Narbonne, 31062 Toulouse, France.
0008-6215/$ - see front matter ꢀ 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.carres.2007.06.024

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M.-H. Gouy et al. / Carbohydrate Research 342 (2007) 2303–2308
chemistry such as 12C- or 13C-cyanide addition followed
by deuterium reduction,23 molybdate catalysed C-1–
C-2 rearrangement24 or radical reduction of halides
by Bu3SnD25 are unlikely to fit with the sucrose
target.
detritylation, which is also convenient, provided that
strictly controlled acid conditions are used for the
deprotection step in order to prevent concomitant cleav-
age of the very labile glycosidic bond.27,28
Two methods were compared for the oxidation of
triol 2 (Scheme 2). The oxidation by the NaOCl–KBr–
cat. TEMPO system29,30 under the conditions of Davis
and Flitsch31 in basic heterogeneous medium (using here
THF as the organic phase) led to a tricarboxylic acid salt
(sodium or potassium form), which was not isolated.
The crude tricarboxylate was treated with CH3I in
DMF leading to the methyl triester 3. Alternatively,
the PDC–t-BuOH–Ac2O method for the oxidation of
primary alcohols to their corresponding t-butyl carbox-
ylic esters was evaluated. This method first described by
Corey et al.32 involves the oxidation of intermediate tert-
butylic hemiketals and was shown to be efficient in the
case of a glucidic substrate for the preparation of
uronates. Some variations in the order of addition of
the reagents and the work-up procedure have been
reported,33–35 notably a slow addition of the alcohol in
the oxidising system, which proved to be more efficient
in our case. Triester 4 was thus obtained. The best yields
were obtained when a solution of triol 2 in CH2Cl2 was
added dropwise to the mixture of reagents, using 2 equiv
of PDC per CH2OH group. Careful precipitation of the
chromium salts in ether on a silica gel column allowed
an easy cleaning and purification of tri t-butyl tricarbox-
ylic ester 4, which was obtained in 51% yield. The use of
PDC in DMF, which normally provides the correspond-
ing carboxylic acid, failed to produce the triacid from 2
but provided a complex mixture of degradation prod-
ucts among which monosaccharidic derivatives were
identified.
Among possible deuteration levels and positions,
6,6,10,10,60,60-hexadeutero sucrose was chosen for
several reasons. First, the difference in mass units for
hexadeutero sucrose (M = 348) compared to sucrose
(M = 342) provides a clear signature in mass spectro-
scopy. Second, as soon as sucrose is cleaved into a mix-
ture of glucose and fructose, a mass difference persists
for each of these two monosaccharides allowing further
tracking of their chemical outcome, moreover being dif-
ferent (+2 for glucose and +4 for fructose). Third, trans-
formation of CH2OH groups into CD2OH groups by
the oxidation–reduction sequence described in this
paper does not provide any epimer or regioisomer mix-
ture. Finally, the selection of all three primary hydroxyl
groups of sucrose as a starting point of the synthesis is
an easy sequence.
The starting triol 2 (2,3,4,30,40-pentabenzyl sucrose)
was prepared from sucrose in a three-step sequence
(Scheme 1) based on the selective protection (TBDMS)26
of the three primary hydroxyl groups followed by the
benzylation (BnBr, NaH, DMF) of all secondary hydr-
oxyl groups and TBAF desilylation in THF. The silyl-
ation–benzylation–TBAF desilylation sequence used
here is an alternative to the tritylation–benzylation–
OH
OH
O
O
HO
HO
BnO
BnO
3 steps
a.
OH
OH
OH
OBn
O
OH
OBn
O
Trimethyl ester 3 was then submitted to the reduction
by LiAlD4 in THF leading to triol 5 in 63% yield,
following a procedure described for the synthesis of
labelled ribonucleosides.36 A similar approach and using
the bulkier t-butyl ester 4 proved to be less reactive, pro-
viding 5 in 46% yield (Scheme 3). The best yields were
O
O
OH
OH
OBn
OH
2
sucrose (1)
Scheme 1. Preparation of sucrose triol 2. Reagents and conditions: (a)
Refs. 27 and 28 (1) TBDMSCl, pyridine, cat. DMAP, 70 ꢁC, 64%; (2)
NaH, BnBr, DMF, 0 ꢁC then rt, 53%; (3) TBAF, THF, 60 ꢁC, 77%.
ONa
O
OMe
O
O
O
BnO
BnO
BnO
BnO
O
O
ONa
O
OMe
O
OBn
O
OBn
O
OBn
OBn
a.
b.
O
O
ONa
OMe
BnO
BnO
3
2
t
t
H
O Bu
O Bu
HO
O
O
O
O
O
HO
t
t
BnO
BnO
BnO
BnO
BnO
BnO
O
O
H
O Bu
O Bu
OBn
OBn
OBn
O
OBn
OBn
OBn
O
O
O
O
O
O
t
t
H
O Bu
O Bu
BnO
BnO
BnO
O
HO
4
Scheme 2. Oxidation of sucrose triol 2. Reagents and conditions: (a) (1) cat. TEMPO–NaOCl–KBr, NaHCO3, THF–H2O, 0 ꢁC; (2) CH3I, DMF, rt,
37%. (b) PDC, CH2Cl2, Ac2O, t-BuOH, 51%.

M.-H. Gouy et al. / Carbohydrate Research 342 (2007) 2303–2308
2305
D
D
OH
D
OH
D
O
O
BnO
BnO
HO
HO
a.
b.
D
D
D
OH
O
D
OH
O
3 or 4
OBn
OH
OBn
OH
O
O
D
D
D
D
OBn
OBn
OH
OH
6
5
Scheme 3. Deuteration and deprotection. Reagents and conditions: (a) LiAlD4, THF, ꢀ78 ꢁC to rt, 63% from 3 and 46% from 4; (b) H2, 10% Pd/C,
EtOH–H2O, rt, quant.
Table 1. Selected C NMR chemical shift values for non-deuterated and deuterated sucrose and 2,3,4,30,40-pentabenzyl sucrosea
13
Compound
C-1
C-2
C-3
C-4
C-5
C-20
C-30
C-40
C-50
Sucrose (1)
Sucrose-d6 (6)
Pentabenzyl sucrose (2)
Pentabenzyl sucrose-d6 (5)
92.54
92.58
91.57
91.65
71.43
71.46
79.41
79.32
72.91
72.96
82.43
82.52
69.56
69.59
78.22
78.25
72.76
72.67
74.20
74.29
104.04
104.03
106.56
106.56
76.71
76.76
86.75
86.80
74.32
74.36
82.90
82.76
81.73
81.66
82.90
82.76
a At 75 MHz in D2O for 1 and 6 and in CDCl3 for 2 and 5.
obtained using 2.5 equiv of LiAlD4 and work-up proce-
dures using classical acidic treatment or precipitation of
aluminium salts under basic conditions gave similar
results. Good yields were also obtained using the alter-
native ‘basic’ work-up: for n g of LiAlH4 (or LiAlD4),
addition of n mL of water, then n mL of 15% NaOH,
then 3n mL of water in order to produce a granular
precipitate, which can be easily filtered.37,38 The final
deprotection was achieved by palladium catalysed
hydrogenolysis in EtOH providing 6,6,10,10,60,60-hexa-
deutero sucrose (6) in quantitative yield. Dilution with
water during the reaction, maintaining pH > 5, pre-
vented the acid catalysed glycosidic bond cleavage.
When the acidity of the medium was not controlled,
hydrolysis of the disaccharidic backbone was observed
leading to mixtures of hexadeuterosucrose, dideutero-
glucose and tetradeuterofructose, these two latter being
mixtures of anomers.
and 5). Finally, the conservation of the conformation
of hexadeuterosucrose (6) in aqueous solution is
confirmed by the rotatory power (+64), very close to
that of sucrose (+66). The lower value for 6 is consistent
with the molecular mass variation (+1.7%).
In conclusion, the preparation of 6,6,10,10,60,60-hexa-
deutero sucrose, a defined polydeuterated sucrose ana-
logue, has been achieved in 6 steps (or 7 depending on
the oxidation method) from sucrose. Starting from the
known pentabenzyl sucrose having all three primary
hydroxyl groups available, the oxidation–reduction
sequence was performed using either the Corey procedure
for the uronate synthesis by direct oxidation of primary
alcohols to their corresponding t-butyl ester, or the
TEMPO–NaOCl method. Deuteride reduction and
deprotection provided the hexadeutero analogue,
which proved to behave in a very similar manner com-
pared to sucrose. Further studies of the physicochemi-
cal and biological behaviour of this analogue are
programmed.
Spectroscopic data of sucrose (1) and hexadeutero-
1
sucrose (6) were compared. In the H NMR spectra of
6, H-6, H-10 and H-60 are absent, and the very small
deuterium-hydrogen coupling constants39 only widen
the peaks for H-5 and H-50. H-5 exhibits a doublet
(J4,5 = 10.1 Hz) proving the trans diaxial relationship
between H-4 and H-5, and the coupling constant of
8.4 Hz between H-40 and H-50 is also very close of the
natural value (8.2 Hz) for sucrose, therefore confirming
that no epimerisation took place during the oxidation–
reduction sequence. Chemical shifts are also conserved.
In the 13C NMR spectrum, longer relaxation time for
C-6, C-10 and C-60 gave as expected signals, which did
not reach more than the noise level.13,14,40 Extremely
close chemical shifts values for all other carbon atoms
suggest that the conformation is not affected by the deu-
teration (Table 1). This conservation is observed for
sucrose (1 and 6) and the pentabenzylated sucroses (2
1. Experimental
1.1. General methods
´
Sucrose was obtained from Beghin-Say. Chromatogra-
phy solvents were purchased from SDS and Carlo Erba.
HPLC solvents were purchased from SDS. Reactions
were monitored by TLC using glass silica gel plates
(Merck 60 F254). The plates were developed using UV
light and vapourisation with a solution of 10% H2SO4
in EtOH (v/v). Flash chromatography separations were
performed using Merck Gerudan Silica Gel Si 60 (40–
63 lm). NMR spectra were recorded on Bruker AC
spectrometers at 75.47 MHz for 13C NMR and

2306
M.-H. Gouy et al. / Carbohydrate Research 342 (2007) 2303–2308
300.13 MHz (or 500.13 MHz) for 1H NMR. Assignment
of carbon resonances is based on C–H correlations.
Mass spectra were recorded by the Centre de Spec-
883.3530. IR m (cmꢀ1): 736, 697, 1027, 1091, 1147,
1743. 1H NMR (CDCl3, 500 MHz) d 3.61 (dd, 1H,
J2–3 = 9.5 Hz, H-2); 3.64 (s, 3H, CO2Me); 3.68 (s, 3H,
CO2Me); 3.72 (t, 1H, H-4); 3.74 (s, 3H, CO2Me); 3.97
´
´
trometrie de Masse of the Universite Claude Bernard
(Villeurbanne). Microanalyses were performed by the
Service Central d’Analyse of the CNRS (Vernaison).
Optical rotations were measured with a Perkin–Elmer
241 polarimeter. Known triol 2 was obtained from
sucrose in 3 steps: a solution of sucrose in pyridine
(7 mL per mmol) was treated with TMDPSCl
(3.8 equiv) and DMAP (cat. 10 mg per mmol) for 10 h
at 70 ꢁC. The mixture is concentrated, diluted with
AcOEt and water (10 mL per mmol each). After extrac-
tion of the aqueous layer with AcOEt, the combined
organic layers are washed with 1 M HCl (5 mL/mmol),
dried and purified by flash chromatography, giving
2,3,4,30,40-penta-O-benzyl-tri-O-(tert-butyldiphenylsilyl)-
sucrose (Ref. 26). To a solution of this latter in DMF
(25 mL/mmol) cooled at 0 ꢁC was added NaH (2.1 equiv
per OH). After 15 min, benzyl bromide (2.1 equiv Per
OH) was added and the mixture was stirred at rt during
15 h, then poured in iced water (same volume) and
neutralised by addition of 1 M HCl. The products were
extracted with ether and the organic phase was dried
over MgSO4, concentrated and purified by flash chro-
matography (CH2Cl2/hexanes, 1:1 v/v). Treatment of
the fully protected derivative with TBAF (1.1 equiv
per OH) in THF (5 mL per mmol) at 60 ꢁC overnight
led to triol 2 after extraction with CH2Cl2 (3 times), dry-
ing over MgSO4, concentration and flash chromato-
graphy of the residue (CH2Cl2/MeOH, 4:1 v/v) in 26%
overall yield from sucrose.
0
0
(t, 1H, J3–4 = 9.5 Hz, H-3); 4.46 (d, 1H, J3 –4 ¼ 5:7 Hz,
H-30); 4.52 (t, 1H, H-40); 4.54–4.59 (m, 3H, CH2Ph);
4.59 (d, 1H, J4 –5 ¼ 5:0 Hz, H-50); 4.61–4.65 (m, 3H,
CH2Ph); 4.72–4.82 (m, 3H, CH2Ph); 4.76 (d, 1H,
J4–5 = 10.4 Hz, H-5); 4.95 (d, 1H, J = 11.7 Hz, CH2Ph);
5.77 (d, 1H, J1–2 = 3.5 Hz, H-1); 7.22–7.35 (m, 25H, Ph).
13C NMR (CDCl3, 75 MHz) d 52.89, 53.11, 53.52
(3CO2Me); 71.69 (C-5); 72.97, 73.40, 73.83, 75.53,
76.26 (5CH2Ph); 79.64 (C-2); 80.27 (C-4); 80.64 (C-50);
81.45 (C-3); 84.06 (C-40); 85.70 (C-30); 93.30 (C-1);
104.29 (C-20); 128.19–139.24 (5Ph); 168.51, 170.46,
170.95 (3CO2Me).
0
0
1.3. Tri-tert-butyl 2,3,4,30,40-penta-O-benzyl sucrose
tricarboxylate (4)
tert-Butanol (3.5 mL, 37.40 mmol) and Ac2O (1.8 mL,
18.90 mmol) were added to a solution of PDC (1.37 g,
3.65 mmol) in CH2Cl2 (15 mL) under N2 atmosphere
and the mixture was stirred at rt. Then a solution of triol
2 in CH2Cl2 (21.8 mL) was added (500 mg, 0.63 mmol)
and stirring was continued for 4 h. The reaction mixture
was then poured into a column of ether containing a
short pad of silica gel. After 15 min, time for all chro-
mium salts to precipitate, the column was eluted with
ether. After concentration and flash chromatography
of the residue (hexane/AcOEt: 9:1 v/v), pure ester 4
was obtained as a colourless oil (322 mg, 51%). Com-
20
pound 4: ½aꢁD +27 (c 0.9, CH2Cl2). HRMS-FAB+:
1.2. Trimethyl 2,3,4,30,40-penta-O-benzyl sucrose
tricarboxylate (3)
[M+Na]+ 1025.4674; found, 1025.4663. IR m (cmꢀ1):
736, 697, 1095, 1156, 1737, 2931, 2978. 1H NMR
(CDCl3, 500 MHz) d 1.42, 1.45, 1.47 (3s, 27H, CMe3);
3.64 (dd, 1H, J2–3 = 9.5 Hz, H-2); 3.75 (t, 1H,
J3–4 = 9.6 Hz, H-4); 4.08 (t, 1H, H-3); 3.35–4.43 (m,
3H, H-30, H-40, H-50); 4.53–4.70 (m, 6H, CH2Ph);
4.71 (d, 1H, J4–5 = 10.2 Hz, H-5); 4.80–5.00 (m, 4H,
CH2Ph); 6.04 (d, 1H, J1–2 = 3.4 Hz, H-1); 7.22–7.39
(m, 25H, Ph). 13C NMR (CDCl3, 75 MHz) d 28.48,
28.56, 28.67 (3CMe3); 72.57 (CH2Ph); 72.63 (C-5);
73.65, 75.10, 76.17 (4CH2Ph); 80.01 (C-50); 80.08 (C-
2); 80.59 (C-4); 81.40 (C-3); 82.14, 82.85, 83.54
(3CMe3); 84.59 (C-40); 85.79 (C-30); 92.36 (C-1); 103.55
(C-20); 127.96–139.50 (5Ph); 167.67, 169.14, 170.02
(3CO2CMe3).
To a solution of triol 2 (2.8 g, 3.5 mmol) in THF
(100 mL) were added saturated aqueous NaHCO3
(60 mL), TEMPO (120 mg, 0.768 mmol), KBr (660 mg,
5.546 mmol) and NBu4Cl (660 mg, 2.375 mmol). To this
mixture cooled to 0 ꢁC was added dropwise over 3 h a
mixture of aqueous NaOCl (13% w/w, 260 mL) and sat-
urated aqueous NaHCO3 (100 mL). The reaction mix-
ture was then warmed to rt and isopropanol (35 mL)
was added. After 30 min of stirring at rt, the mixture
was evaporated to dryness and the crude residue was
suspended in anhydrous DMF (135 mL). CH3I
(5.7 mL) was added and the mixture was stirred vigor-
ously during 15 h. After dilution with diethyl ether
(20 mL), the salts were filtrated and washed with ether
(3 · 20 mL) and the etheral solutions were combined
and concentrated. Flash chromatography of the residue
(hexane/AcOEt: 3:1 v/v) led to pure 3 (1.1 g, 37%) as a
1.4. 6,6,10,10,6,60-Hexadeutero-2,3,4,30,40-penta-
O-benzyl sucrose (5)
To a 1 M solution of LiAlD4 in THF (0.5 mL,
0.50 mmol) cooled at ꢀ78 ꢁC under nitrogen atmo-
sphere was added a solution of triester 3 (176 mg,
0.201 mmol) in THF (0.5 mL). After 10 min of stirring
20
colourless oil. Compound 3: ½aꢁD +31 (c 0.9, CH2Cl2).
Anal. Calcd for C50H52O14: C, 68.5; H, 6.0. Found: C,
68.6; H, 6.0. HRMS-FAB+: [M+Li]+ 883.3517; found,

M.-H. Gouy et al. / Carbohydrate Research 342 (2007) 2303–2308
2307
at ꢀ78 ꢁC, the mixture was warmed to rt and stirred fur-
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63%) as a colourless oil. The same procedure applied
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pound 5: ½aꢁD +10 (c 1.2, CH2Cl2). HRMS-FAB+:
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1
H + D, 7.0. H NMR (CDCl3, 500 MHz) d 1.90, 2.79,
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J4–5 = 9.8 Hz, H-4); 3.64 (dd, 1H, J2–3 = 9.8 Hz, H-2);
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82.52 (C-3); 82.76 (C-40, C-50); 86.80 (C-30); 91.65 (C-
1); 106.56 (C-20); 128.27–138.90 (Ph).
0
0
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1.5. 6,6,10,10,6,60-Hexadeuterosucrose (6)
To a solution of triol 5 (124 mg, 0.155 mmol) in EtOH
(2.2 mL) was added 10% Pd/C (80 mg) and the mixture
was stirred under H2 (1 atm) at rt for 2 h while water
was added regularly (total 2.2 mL) in order to maintain
the pH > 5. After centrifugation and filtration, the solu-
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sucrose 6 white solid was freeze dried (54 mg, quant.).
20
½aꢁD +64 (c 0.9, H2O). HRMS-FAB+: [M+Na]+
(C12H16D6O11Na) 371.1436; found, 371.1442. Anal.
Calcd for C47H46D6O11: C, 70.7; H + D, 7.3. Found:
C, 70.5; H + D, 7.0. 1H NMR (CDCl3, 300 MHz) d
3.45 (t, 1H, H-4); 3.55 (dd, 1H, J2–3 = 9.9 Hz, H-2);
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3.75 (t, 1H, J3–4 = 9.3 Hz, H-3); 3.82 (d, 1H, J4–5
=
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10.1 Hz, H-5); 3.87 (d, 1H, J4 –5 ¼ 8:4 Hz, H-50); 4.04
0
0
(t, 1H, H-40); 4.20 (d, 1H, J3 –4 ¼ 8:8 Hz, H-30); 5.40
(d, 1H, J1–2 = 3.8 Hz, H-1). 13C NMR (D2O, 75 MHz)
d 69.59 (C-4); 71.46 (C-2); 72.67 (C-5); 72.96 (C-3);
74.36 (C-40); 76.76 (C-30); 81.66 (C-50); 92.58 (C-1);
104.03 (C-20).
0
0
Acknowledgements
This work was achieved in part in the former CNRS-
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´
Beghin-Say joint research facility in Villeurbanne.
Financial support from CNRS and MENESR is grate-
fully acknowledged as well as a grant to MD from
CNRS and Beghin-Say (TEREOS). Also, the authors
´
thank Professeur A. Doutheau for fruitful discussions.

2308
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