2.1.4. Conformational Analysis

Chondroitin conformational properties were quantified by bond length, bond angle, and dihedral angle values. Glycosidic linkage conformational values considered were bond lengths for C1-O and O-C*n*, bond angles defined by O5-C1-O and C1-O-C*n*, and φ and ψ dihedral angles with IUPAC definitions: φ = O5-C1-O-C*<sup>n</sup>* and ψ = C1-O-C*n*-C(*n*−1) (Figure 2). Glycosidic linkage dihedral free energies ∆*G*(φ, ψ) were analyzed to characterize potential conformational patterns. φ, ψ dihedral values from the MD-generated 20-mer ensemble are taken to have uniform probabilities. ∆*G*(φ, ψ) is therefore computed by binning these values into 2.5◦ × 2.5◦ bins and then using the relationship ∆*G*(φ*<sup>i</sup>* ,ψ*<sup>j</sup>* ) = -*RT*ln(*nij*) – *k*, where *nij* is the bin count for the bin corresponding to φ*<sup>i</sup>* , ψ*<sup>j</sup>* , *R* is the universal gas constant, *T* is the temperature of the MD simulations, and *k* is chosen so that the global minimum is located at ∆*G* = 0 kcal/mol. ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ *<sup>−</sup>* ‐ ‐ ‐ 

‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ <sup>−</sup> **Figure 2.** Non-sulfated chondroitin trisaccharide with glycosidic linkage dihedral angles, monosaccharide ring atoms, and linker oxygen atoms labeled; glycosidic linkage parameters used in the construction algorithm include C<sup>1</sup> -O and O-C*<sup>n</sup>* bond lengths, O<sup>5</sup> -C<sup>1</sup> -O and C<sup>1</sup> -O-C*<sup>n</sup>* bond angles, and φ = O<sup>5</sup> -C<sup>1</sup> -O-C*<sup>n</sup>* and ψ = C<sup>1</sup> -O-C*n*-C(*n*−1) dihedral angles.

‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ Geometric values defining monosaccharide ring conformations included all bond lengths, bond angles, and dihedral angles within the ring and in exocyclic functional groups that are not part of a glycosidic linkage. To characterize potential conformational patterns in monosaccharide rings, Cremer-Pople (C-P) ring-puckering parameters (φ, θ, *Q*) of each monosaccharide ring in the MD-simulated 20-mer ensemble were computed. Conformations of each element (i.e., each GlcA monosaccharide, GalNAc monosaccharide, β1-3 linkage, and β1-4 linkage) were extracted separately from each saved snapshot of the 20-mer MD trajectories. Initially, data were separated out by run and residue/linkage number and aggregated across all snapshots in each run to determine if conformational data were the same in different runs and if individual linkage and ring conformations are dependent upon one another. Subsequently, all individual conformations were aggregated across all snapshots in all runs (e.g., 10,000 snapshots \* 4 runs \* 10 GlcA monosaccharides = 400,000 samples of GlcA monosaccharide conformations) to yield one set of data for each of: (1) GlcA monosaccharide

conformation, (2) GalNAc monosaccharide conformation, (3) β1-3 linkage conformation, and (4) β1-4 linkage conformation.
