*3.3. GAG Structures in the Solid-State*

The solid-state features of chondroitin sulfate, dermatan sulfate, hyaluronan, and keratan sulfate have been established by X-ray fiber diffraction [71] (Table 2) and are available in GAG-DB. They encompass several allomorphs that occur in different experimental conditions, including the nature of the counterions (Na <sup>+</sup>, Ca ++, and K <sup>+</sup>). More structural features such as the polarity of the polysaccharide chains, their interactions with the counterions and packing features can be deduced.

β β α β α α

**s ccharides y** 

β β – β β –


**Table 2.** Characterization of the helix symmetry of GAGs polysaccharides in the solid-state.

The organization of all these polysaccharide chains in the form of helices seems recurrent. Two parameters, *n* and *h*, characterize helical structures, where *n* is the number of repeat units (disaccharide unit) per turn of the helix and *h* is the projection of one repeat unit on the helical axis. The sign attributed to *n* indicates the chirality of the helix. The positive value of *n* corresponds to the right-handed helix and a negative value to a left-handed helix. Such helical descriptors provide a simple way to classify the secondary structures and their potential allomorphs. β α β β

As with the disaccharide segments of GAGs, the values of the Φ and Ψ torsional angles found in all the conformations of GAGs fall in the low energy regions of the corresponding potential energy surfaces. It is therefore relevant to question whether secondary structures other than those derived from crystallographic characterization do occur. The sets of (Φ, Ψ) values corresponding to the low energy conformations can be propagated regularly, to generate structures, which can be further optimized to form integral helices. When applied to hyaluronan structures, the analysis indicates that this polysaccharide display a wide range of energetically stable helices (Figure 8). They span the left-handed 4-fold symmetry to the right-handed five-fold symmetry with a rise per disaccharide between 9.51 and 10.13 Å [81]. Φ Ψ torsional Φ, Ψ

The Φ and Ψ **Figure 8.** Stable regular helical conformation of single-stranded hyaluronic acid projected parallel and orthogonal to their axes (drawn with SweetUnityMol [82]). The Φ and Ψ conformations are shown on the corresponding potential energy surfaces.

The results indicate that small variations in the glycosidic torsion angles might have a significant influence on the symmetry and pitch of the resulting helices without any noticeable energetic cost. This illustrates the capacity of hyaluronic acid to display different sites available for interactions

–

with proteins and would occur, at no cost in energy, without altering the directionality of the polysaccharide chain.
