*3.6. Application to Longer Chondroitin Polymers*

‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ To implement the algorithm in the construction of conformational ensembles of non-sulfated chondroitin polymers of biologically-relevant chain lengths, chondroitin 100-mer and 200-mer ensembles were constructed and the end-to-end distance (Figures 11 and 12), radius of gyration (Figure S2e,f), and bond potential energy distributions (Figure S10c,d) were examined. The skewness of the end-to-end distance distributions shifts toward the right with increasing polymer length. This stands to reason, as there is a greater chance of folding with longer chains. This also explains why there are more frames excluded from these ensembles (i.e., 457 and 1407 frames excluded from the 100-mer and 200-mer ensembles, respectively). Bond potential energy distributions have similarly-shaped curves in all polymer lengths (Figure S10) and energy values increase linearly as a function of atom count (Figure S11). These results suggest that 100-mer and 200-mer conformational ensembles constructed using our algorithm (Figures 11 and 12) are reasonable predictions of biological conformations given their high number of degrees of freedom.

‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ **Figure 11.** (**a**) End-to-end distance probability distribution of constructed 100-mer ensemble; includes four sets of 10,000 conformations; probabilities were calculated for end-to-end distances sorted into 5 Å bins. (**b**,**c**) Snapshots of the non-sulfated chondroitin 100-mer having the most-probable end-to-end distance (225 Å in both snapshots) from constructed ensembles.

‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ **Figure 12.** (**a**) End-to-end distance probability distribution of constructed 200-mer ensemble; includes four sets of 10,000 conformations; probabilities were calculated for end-to-end distances sorted into 10 Å bins. (**b**,**c**) Snapshots of the non-sulfated chondroitin 200-mer having the most-probable end-to-end distance (300 Å in both snapshots) from constructed ensembles.
