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.