Hypersphere and Antiviral Activity of Three Alkyl Chain Iminocyclitols with D and L Ribitol Stereochemistry

: N -Alkyl-C 1 -dialkyl chains iminocyclitols with D or L-ribitol stereochemistry are synthesized with high diastereoselectivity after Grignard reagents addition to N -quaternary pyrrolines salts, and tested for antiviral activity in bovine viral diarrhea virus (BVDV), surrogate for hepatitis C virus (HCV). Dihedral angles are calculated from carbon chemical shift (δ Cn [ppm]) with 3-sphere method without building units. 3-Sphere, a hypersphere in 4D, under Hopf fibration and Lie algebra mathematics theories enable calculation of the dihedral angles from the NMR data (vicinal coupling constant 3 J HnHn+1 [Hz], chemical shift δ Cn [ppm]). Instead of 3D manifold equations on seven sets unit or six sets units are proposed equations between 4D – 2D, in function of the curvature. The relationship between the antiviral activity and the iminocyclitol structure reveals that monoalkyl chain, N -n-C 1 -dodecyl β-L-ribitol trifloroacetate salt 30 (IC 50 1.5 uM) has higher antiviral activity in tangential space, relative to three alkyl chain, N -Methyl-C 1 -butil, nonyl-L-ribitol. HCl 26 (IC 50 < 2 uM) with torus and Dupin cyclide coordinate, both with coordinates in 2D. Three alkyl chain isopropylidene protected pyrrolidine 25 has in 4D with all equations for calculation of the dihedral angles, and in protected pyrroline 19b double bond moves the coordinates in 2D.


Introduction
Five membered ring iminocyclitols possessing alkyl substituents are known to be potent antiviral compounds analog to six membered ring [1][2][3][4]. Recently we published a facile synthesis of five membered N, C 1 -dialkyl iminocyclitols. [5] The antiviral activity of C 1 monoalkyl and N, C 1 dialkyl analogues was evaluated in the bovine viral diarrhea virus assay (BVDV).
Presence of both, N-alkyl group as well as only C 1 -alkyl group enhanced antiviral activity. The key step in our synthesis is the rearrangement exo-imino to endoiminocyclitol via intramolecular 5-exo-tet ring opening of the epoxide with inversion of configuration at C 4 , where the Llyxo sugar (A) is converted to the D-ribo 1-N-pyrroline (B) [5], usefully synthon for synthesis N, C 1 dialkyl or trialkyl analogs ( Figure 1). A second advantage, C 1 alkyl chains installed in an earlier stage overcome secondary reaction, i.e. dimerization and trimerization of C 1 -unsubstituted 1-Npyrrolines. [6] 3-Sphere, a hypersphere in 4 dimensions, enable calculation dihedral angles from vicinal coupling constant [7] and carbon or/and proton chemical shift [8] under unit rule [9,10] or without unit [11]. The sign of the dihedral angle result certainly from vicinal coupling constant and the stereochemistry from unit build from chemical shift. The relationship between the structure of the iminocyclitols and the antiviral activity can be analyzed with hypersphere equations established for calculation of the dihedral angles without building unit [11]. The main question, the tangential D and L Ribitol Stereochemistry

Synthesis of N-Alkyl-C 1 -dialkyl Chains Iminocyclitols with D or L-ribitol Stereochemistry
Melting points were determined using a Fisher Johns apparatus and are uncorrected. 1 H NMR spectra are determinates with Bruker spectrometer of 400 MHz or 500 MHz. 13 C NMR spectra are recorded with a Bruker spectrometer of 75 MHz. Infrared spectra are recorded on Genesis Services FTIR spectrometers.
D-Ribose and D-xylose were purchased from Sigma-Aldrich.

General Procedure for Grignard Addition to 5-O-Mesyloxy-1,4-lactones
The isopropylidene protected 5-O-mesyloxy-1,4-lactone (1 eq) was dissolved in THF anhydrous under Ar, and cooled to -77°C. Maintaining the temperature between -50°C ~ -40°C, the Grignard reagent (1.5 eq) was added and stirred over 30 min. The temperature was allowed to warm to 0°C and the solution was stirred 1 -2 h. After quenching with saturated aqueous NH 4 Cl the mixture was extracted with ethyl acetate. The combined extracts were washed with saturated aqueous NH 4 Cl, dried over Na 2 SO 4 , filtered and evaporated under vacuo. The crude product results as a stereoisomeric mixture at the anomeric position.

Synthesis of Iminium Salts
To a solution of imines (1 eq) in CH 2 Cl 2 anhydrous was added alkyl halides (2 eq). The mixture was allowed to stand 2 -4 days at room temperature in a sealed flask. The reaction was monitoring by TLC (EtOAc:EtOH 7:3). After evaporation of the solvent afforded the iminium salts as an oil used directly in the Grignard reaction.

Hypersphere Approach for Calculation of Dihedral Angles from Carbon Chemical Shift
3D: sin -1 cosϕ = θ HnHn+1 (1) 3D: tan -1 sinϕ = θ HnHn+1 (2) In this paper we proposed the calculation of the dihedral angles θ HnHn+1 [deg] from carbon chemical shift δ Cn [ppm] without building units [11], in attempt to found 1. the best hypersphere equation for every curvature around the iminocyclitol ring with biological activity, 2. to analyzed the implication of the N dimension space on antiviral activity, and 3. the change on shape in function of the structure of the iminocyclitols analyzed. Since in first case the units contain all the manifold circles, in this case are found trigonometric equations between the 4D and 2D (eq. 3, 4, 5, Table 1).

Results and Discussion
The imino double bond is a site for nucleophilic additions of organometalic reagents, severely limited by the low electrophilicity [12][13][14] of azometin carbon or by competition between α-deprotonation (enamine or azaallyl anion formation) or intramolecular addition of hydroxyl group to the imine group [15]. The electrophilicity of the imine carbon C=N can be increased by: N-alkylation, N-oxidation, N-acylation, Nsulfonylation to give, respectively, reactive iminium salts, reactive nitrones, acylimines, and sulfonimines. [12] For example phenyl magnesium bromide addition to benzyl protected nitrone with D-xylose stereochemistry has high stereoselectivity through a Felkin-Anh transition state model, resulting after deprotection the natural product Nhydroxylpyrrolidine, namely Radicanine B. [16] The standard methods for activation at the imine carbon involve coordination of a Lewis acid with the nitrogen lone pair [17] or by addition of external promoters. Additions to polyhydroxylated cyclic imines with C 1 unsubstituted have been reported. [18][19][20][21] Allylmagnesium reagent has lower diastereoselectivity relative to other Grignard reagents. [22] Grignard reagents are prepared in dry organic solvents and inert atmosphere [23], or in air using ball milling technique [24].
Low diastereoselectivity of Grignard addition to anomeric position of isopropylidene protected 5-O-mesyloxy-1,4lactone 1b can be explained (Scheme 1) in case of α anomer 2 with Cram chelation model or for β anomer 3 with Felkin-Anh model with preferred si attach. The chelating effect of the oxygen atom is increased by the presence of isopropylidene group. The isopropylidene group is likely to enforce a rigid butterfly conformation that favors nucleophile approach from the convex face.
The α, β anomeric mixture of hemiacetals 2, 3 upon treatment with NH 3 in aq EtOH yielded imines 4. Methansulfonyl chloride react by a direct displacement mechanism so is expected solvent nucleophilicity to have the major effect. The isopropylidene group forces the molecule into a rigid cis-bicyclo [3.3.0] ring system which may be optimal for the intramolecular cyclization (Thoape-Ingold effect). Wasserman et al claim that δ,ε epoxyimines undergo intramolecular cyclization, in consequence 6,7-epoxy-2heptanone upon treatment with benzylamine yielded N-benzyl-6-oxa-8-azabicyclo [3.2.1]octane. In contrast to imine formation (Figure 1), in the epoxy heptanone system, intramolecular addition of the hydroxymethyl groups to imino double bond yield oxatropane [25][26][27]. The highly diastereoselectivity of the Grignard reagents additions the imino double bond (Figure 1) can be understood on the base of the nonchelation control (Cram selectivity) supported by the Yamamoto [28] model. The addition is governed by steric effect, the isopropylidene group reduces the degree of freedom of a molecule and that favors nucleophile approach from the less-hindered β-face of the C=N bond. [12] Metal coordination to oxygen enhanced the steric effect. [29] The reactivity of the C=N was increased by addition of Grignard reagent to the N-quaternary salts 5, synthetized with iodomethane in methylen chloride. The presence of the C=N + Xbond was confirmed by characteristic 13 C NMR (C 1 ~ 191 -185 ppm) relative to imines C=N bond C 1 ~ 179 ppm. The nucleophilic addition of organometallic reagent to the Nquaternary salts (Figure 3) was performed in ether, THF, toluene, or preferably methylene chloride. The 13   The pyrrolidine (6) ring system is conformationally more flexible than the pyrroline (4, 5) ring system, NMR data assigned based on COSY and HMQC show a switch between H 2 and H 3 in imine 4 relative to N-quaternary salts 5 (Table 1), slightly unexpected. Isopropylidene deprotection decreased steric bulkiness and the vicinal coupling constants becomes: 7a 3 J H3H4 of 5.9 [Hz] and 3 J H3H2 of 4.7 [Hz], 9b,c 3 J H3H4 of 9.2 [Hz] and 3 J H3H2 of 4.0 [Hz], 11c 3 J H3H4 of 8.8 [Hz] and 3 J H3H2 of 5.0 [Hz].
These results demonstrate the potential of these compounds as antivirals for flaviviruses [32]. The missing inhibitory activity of pyrolines with D-ribose stereochemistry without substituent at C 1 , as result from QASAR study [33], increased once the alkyl chain are introduced at C 1 .

Conclusion
Iminocyclitols bearing three alkyl chains synthesized by Grignard reagents addition to N-quaternary pyrrolines salts with high diastereoselectivity are evaluated in bovine viral diarrhea virus assay (BVDV) surrogate for hepatitis C. Dihedral angles are calculated from carbon chemical shift without building unit with 3-sphere theory for pyroline 19b, isopropylidene protected pyrrolidine 25 and deprotected pyrrolidine 26. The sign of the dihedral angles results only from the vicinal angle ϕ and its trigonometric equations. Attempts to found explication between antiviral activity and structure of iminocyclitols based on tangential space or 2D coordinate of torus -Dupin ciclide.