*3.5. Definition of 4C1, 1C4, 2SO, OS2, and Other Ring Puckering Conformations*

C-P parameters (*θ*, *φ*) were used to define ring puckering conformations as follows (note: analogous puckers for Neu5Ac compounds have all superscripted/subscripted numbers in puckering conformations incremented by 1 to reflect the different atom numbering in Neu5Ac, as shown in Figure 2):

	- -3,OB: 0◦ ≤ *φ* < 15◦ or 345◦ ≤ *φ* < 360◦
	- -3S1: 15◦ ≤ *φ* < 45◦
	- -B1,4: 45◦ ≤ *φ* < 75◦
	- -5S1: 75◦ ≤ *φ* < 105◦
	- -2,5B: 105◦ ≤ *φ* < 135◦
	- -2SO: 135◦ ≤ *φ* < 165◦

#### **4. Conclusions**

The data presented here provide a thorough accounting of the ring puckering free energies for the ten common vertebrate monosaccharides and idose, as represented by the CHARMM force field. In addition to demonstrating that the CHARMM force field reliably models ring puckering across this set diverse of molecules, the results show that doing so is possible with a single set of self-consistent force-field parameters developed using a standardized force field parametrization protocol [36,38]. This, in combination with examples of CHARMM force field studies on glycosidic linkages [91–96], lends confidence to the application of these parameters in the modeling of carbohydrate-containing protein systems, such as glycoproteins and proteoglycans as well as transmembrane proteins in glycolipid-containing bilayers. Accurate simulations for these types of systems can help expand the frontiers of protein structural biology by bridging gaps in experimental approaches for characterizing carbohydrate-containing protein systems.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/ijms23010473/s1.

**Author Contributions:** Conceptualization, O.G.; methodology, O.G. and D.M.; software, O.G. and D.M.; validation, O.G. and D.M.; formal analysis, O.G. and D.M.; resources, O.G.; data curation, O.G.; writing—original draft preparation, O.G.; writing—review and editing, O.G., D.M. and M.G.; visualization, O.G. and M.G.; supervision, O.G.; project administration, O.G.; funding acquisition, O.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Foundation, grant number MCB-1453529 to O.G. The APC was funded by the University of New England School of Pharmacy.

**Acknowledgments:** O.G. gratefully acknowledges communications with Jérôme Hénin and Anthony Serianni.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **Appendix A**

During the course of the present work, we discovered a set of typos in the jul20 parameter file that affect Neu5Ac puckering energetics. These typos affect only Neu5Ac in the present work and will be corrected in a future official update to the CHARMM force field (A. D. MacKerell, Jr., personal communication). For the time being, the jul20 "par\_all36\_carb.prm" CHARMM parameter file can be manually corrected by adding the following lines to that file and deleting all other lines that refer to these same parameters:


The typos affect two dihedrals in the Neu5Ac ring, with the first parameter affecting rotation about the C4-C5 bond and the second two rotation about the C5-C6 bond. The above three lines revert the parameters to the original values in the publication describing parametrization for Neu5Ac [38]. Figure A1 demonstrates the large qualitative difference between the eABF Δ*G*(α1, α2) results using the incorrect force field dihedral parameters resulting from the typos and the correct force field dihedral parameters that are the original values from that publication. In Figure A1, (α1, α2) values from all instances of Neu5Ac in the PDB are overlaid on top of the Δ*G*(α1, α2) contour plots, and clearly show the superiority of the correct force field parameters as judged by the overlap of the PDB data with the global minima in the Δ*G*(α1, α2) contour plots (data were extracted from the PDB on 30 July 2021 by searching with the SMILES string "CC(=O)NC1C(CC(OC1C(C(CO)O)O)(C(=O)O)O)O" and separating hits into either α anomers or *β* anomers, of which there were 439 and 52, respectively found across a total of 170 PDB entries). In the case of the incorrect parameters, there is poor overlap, while with the correct parameters there is excellent overlap.

For αNeu5Ac and MeαNeu5Ac simulated using the incorrect parameters (Figure A1a and Figure A1c, respectively), the global minimum is in a boat/skew-boat region of (α1, α2) space whereas the vast majority of crystallographic structures in the α anomeric form are in the 2C5 chair pucker conformation. However, with the correct force field parameters, the global minimum is in the 2C5 region of (α1, α2) space for both αNeu5Ac (Figure A1b) and MeαNeu5Ac (Figure A1d), and the small proportion of α anomeric crystallographic structures outside of this region are located in or near a secondary minimum with favorable free energy (i.e., < 3 kcal/mol).

**Figure A1.** *Cont.*

**Figure A1.** Δ*G*(α1, α2) from eABF simulations using incorrect versus correct dihedral force field parameters for Neu5Ac along with (α1, α2) data from all Neu5Ac structures in the PDB (searched 30 July 2021). Δ*G*(α1, α2) contour data are for αNeu5Ac with incorrect parameters (**a**), αNeu5Ac with correct parameters (**b**), MeαNeu5Ac with incorrect parameters (**c**), MeαNeu5Ac with correct parameters (**d**), *β*Neu5Ac with incorrect parameters (**e**), *β*Neu5Ac with correct parameters (**f**), Me*β*Neu5Ac with incorrect parameters (**g**), and Me*β*Neu5Ac with correct parameters (**h**). α<sup>1</sup> and α<sup>2</sup> are in degrees. Δ*G*(α1, α2) is from the first simulation in the triplicate and is in kcal/mol, with contours drawn every 1 kcal/mol and colored from 0–3 kcal/mol. PDB data were divided into two groups: those from α anomers and those from *β* anomers. Crystallographic data from the α anomers are displayed as small +'s in (**a**–**d**) and crystallographic data from the *β* anomers are displayed as small +'s in (**e**–**h**).

For the *β* anomers simulated using the incorrect parameters (*β*Neu5Ac (Figure A1e) and Me*β*Neu5Ac (Figure A1g)), there are no crystallographic Neu5Ac structures in the *β* anomeric form that coincide with the global minimum. In contrast, with the correct parameters, nearly all of these crystallographic structures in the *β* anomeric form, which are in the 2C5 chair pucker conformation, coincide with the global Δ*G*(α1, α2) minimum for both *β*Neu5Ac (Figure A1f) and Me*β*Neu5Ac (Figure A1h).

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