Constructing 3-Dimensional Atomic-Resolution Models of Nonsulfated Glycosaminoglycans with Arbitrary Lengths Using Conformations from Molecular Dynamics

International Journal of Molecular Sciences

Article Constructing 3-Dimensional Atomic-Resolution Models of Nonsulfated Glycosaminoglycans with Arbitrary Lengths Using Conformations from Molecular Dynamics

Elizabeth K. Whitmore 1,2 , Devon Martin 1,2 and Olgun Guvench 1,2,*

1 Department of Pharmaceutical Sciences and Administration, University of New England School of Pharmacy, 716 Stevens Avenue, Portland, ME 04103, USA; [email protected] (E.K.W.); [email protected] (D.M.) 2 Graduate School of Biomedical Science and Engineering, University of Maine, 5775 Stodder Hall, Orono, ME 04469, USA * Correspondence: [email protected]; Tel.: +1-207-221-4171

Received: 10 September 2020; Accepted: 15 October 2020; Published: 18 October 2020

Abstract: Glycosaminoglycans (GAGs) are the linear carbohydrate components of proteoglycans (PGs) and are key mediators in the bioactivity of PGs in animal tissue. GAGs are heterogeneous, conformationally complex, and polydisperse, containing up to 200 monosaccharide units. These complexities make studying GAG conformation a challenge for existing experimental and computational methods. We previously described an algorithm we developed that applies conformational parameters (i.e., all bond lengths, bond angles, and dihedral angles) from molecular dynamics (MD) simulations of nonsulfated chondroitin GAG 20-mers to construct 3-D atomic-resolution models of nonsulfated chondroitin GAGs of arbitrary length. In the current study, we applied our algorithm to other GAGs, including hyaluronan and nonsulfated forms of dermatan, keratan, and heparan and expanded our database of MD-generated GAG conformations. Here, we show that individual glycosidic linkages and monosaccharide rings in 10- and 20-mers of hyaluronan and nonsulfated dermatan, keratan, and heparan behave randomly and independently in MD simulation and, therefore, using a database of MD-generated 20-mer conformations, that our algorithm can construct conformational ensembles of 10- and 20-mers of various GAG types that accurately represent the backbone ﬂexibility seen in MD simulations. Furthermore, our algorithm eﬃciently constructs conformational ensembles of GAG 200-mers that we would reasonably expect from MD simulations.

Keywords: molecular dynamics; glycosaminoglycan; proteoglycan; hyaluronan; dermatan; keratan; heparan; carbohydrate conformation; carbohydrate ﬂexibility; glycosidic linkage; ring pucker; force ﬁeld; explicit solvent

1. Introduction Proteoglycans (PGs) are a diverse group of proteins in the extracellular matrix (ECM), as well as on and within cells in animal tissue. PGs play key roles in signal transduction [1,2], tissue morphogenesis [3–7], and matrix assembly [7–10] by binding growth factors [3–7,11–17], enzymes [7,17], membrane receptors [17], and ECM molecules [2,7,17]. Many of these functions are mediated by glycosaminoglycans (GAGs), which are linear, highly negatively-charged, and structurally diverse carbohydrate chains covalently-linked to PGs. Speciﬁcally, GAGs can form covalent and noncovalent complexes with proteins or inhibit complex formation with other biomolecules. All of these functions allow GAGs to modulate disease. For example, hyaluronan can predict disease outcome and is used as

Int. J. Mol. Sci. 2020, 21, 7699; doi:10.3390/ijms21207699 www.mdpi.com/journal/ijms Int. J. Mol. Sci. 2020, 21, 7699 2 of 41 a treatment for osteoarthritis [18,19]; deficiency of dermatan sulfate has been linked to Ehlers-Danlos syndrome, so screening of dermatan sulfate in urine may present a method of diagnosis [20,21]; reduced cerebral cell keratan sulfate levels have been implicated in Alzheimer’s disease [22]; and heparan sulfate has been shown to induce septic shock [23,24]. GAG-protein binding is determined by the sequence, structure, shape, and charge of the GAG and GAG-binding region of the protein [17,25]. Therefore, the three-dimensional structure and conformation of GAGs determine their bioactivity, and even subtle structural differences can change their function. For example, while hyaluronan and chondroitin have many functional differences, the only structural difference is in the chirality of carbon four in the amide monosaccharide derivatives (i.e., N-acetylglucosamine and N-acetylgalactosamine, respectively). The structural and conformational complexities of GAGs make studying GAG conformational thermodynamics at atomic resolution a challenge using existing experimental methods. Structural complexities arise from nontemplate-based synthesis [26] and variable sulfation [27], which means a single GAG type can have variable lengths and sulfation patterns, making it polydisperse and heterogeneous. Conformational complexities result from glycosidic linkage flexibility [28–33] and ring puckering [33]. There are several experimental techniques for studying GAGs, including liquid chromatography-mass spectrometry (LC-MS) [34–36], X-ray crystallography [37–42], and nuclear magnetic resonance (NMR) [43–46], but no single technique is able to account for all of these complexities. While each has its limitations, these experimental techniques provide a critical means to validate molecular dynamics (MD) simulations [46–52]. MD can be used to generate atomic-resolution conformational ensembles of GAGs under physiological conditions, and agreement between MD-generated results and available experimental data builds confidence that MD does indeed generate realistic three-dimensional atomic-resolution GAG models [53–57]. However, all-atom explicit-solvent MD is not a feasible tool for routine simulation of large systems, and GAG biopolymers may consist of up to 200 monosaccharide units [4], which, when fully solvated, would result in a system with over 106 atoms. Coarse-grained (CG) MD is a feasible alternative for simulations of long GAG polymers, but may be limited because it lacks the atomic resolution and the accurate treatment of solvation provided by all-atom explicit-solvent MD [48,58–60]. As an alternative approach to obtaining atomic-resolution, three-dimensional, conformational ensembles of long GAG biopolymers, we developed an algorithm that uses glycosidic linkage and monosaccharide ring conformations from unbiased all-atom explicit-solvent MD simulations [57,61–63] of GAG 20-mers (i.e., 20 monosaccharide units) to rapidly generate GAG polymer conformational ensembles of user-specified length and with a user-specified number of conformations [33]. In our previous work, we examined nonsulfated chondroitin GAGs. Here, we aim to expand the application of our algorithm to hyaluronan and to nonsulfated forms of dermatan, keratan, and heparan. Nonsulfated forms were chosen for their simplicity and homogeneity. The algorithm is expected to produce conformational ensembles that mimic the backbone flexibility observed in simulations only if individual ring and linkage conformations of GAG 20-mers behave randomly and independently in simulation. This means that the algorithm will not produce polymer conformations with higher-order structures. It has been suggested that hyaluronan may take on higher order structures [64], and while it has been shown that helical structures occur in hyaluronan oligosaccharides [65,66], this behavior may not necessarily be extrapolated to long polysaccharides under physiological conditions. Hyaluronan oligosaccharides have been shown to exhibit rigid structures in aqueous solution, possibly resulting from electrostatic effects and hydrogen-bonding between neighboring monosaccharides [65,67–73]. MD studies of hyaluronan di- and trisaccharides in aqueous solution (without ions) revealed that hydrogen-bonds form but do not remain for long periods of time, and do not always occur at the same time in different regions of the oligosaccharide [67,68]. It has been shown that under physiological conditions, the extended conformations and large hydrodynamic radius of hyaluronan can be attributed primarily to hydrogen-bonding between adjacent monoasaccharides (and less so to electrostatic effects) [69]. It is important to note that each of these studies examined short hyaluronan Int. J. Mol. Sci. 2020, 21, 7699 3 of 41 oligosaccharides; thus, atomic-resolution conformational properties of long polysaccharides under physiological conditions have not been reported. We sought to determine (1) if longer polysaccharides of hyaluronan and nonsulfated dermatan, keratan, and heparan took on a higher-order structure during MD simulations in an aqueous solution with physiological ion strength and, consequently, (2) if our algorithm could construct conformational ensembles of GAGs that mimic the backbone flexibility observed in MD simulations. To this end, we ran a microsecond-scale, all-atom, explicit-solvent MD on 20-mers of each GAG type with sequences [-4 glucuronate β1-3 N-acetylglucosamine β1-]10 (hyaluronan), [-4 iduronate α1-3 N-acetylgalactosamine β1-]10 (dermatan), [-3 galactose β1-4 N-acetylglucosamine β1-]10 (keratan), and [-4 iduronate α1-4 N-acetylglucosamine α1-]10 (heparan). Analysis of glycosidic linkage and monosaccharide ring conformations revealed no apparent correlation between individual rings and flanking linkages in any of the 20-mers. Glycosidic linkages took on experimentally-observed helical conformations, and some linkages sampled secondary conformations that caused a kink in the polymer. No patterns of interdependence between adjacent linkage conformations were seen. While ring and linkage conformations did not reach equilibrium in hyaluronan simulations on the microsecond timescale, overall hyaluronan 20-mer appeared to behave randomly. End-to-end distance distributions revealed mostly extended conformations (n.b. we use the term “extended” throughout to describe conformations with high end-to-end distances; this does not necessarily contradict helical structure) 4 with some compact conformations resulting from non- C1 ring puckering, which brought the oxygen atoms in sequential glycosidic linkages closer together, and certain glycosidic linkage conformations that brought neighboring monosaccharides closer together. Thus, these ring and linkage conformations both introduce a kink in the polymer. These conformations are independent and occur rarely on the microsecond timescale. The variability in individual ring and linkage conformations, as well as end-to-end distances and the radii of gyration, demonstrate the flexibility and lack of stable higher-order structures of each of these nonsulfated GAG polymers during simulation in aqueous solution. For each nonsulfated GAG type, monosaccharide ring and glycosidic linkage conformations from MD-generated 20-mers were used as inputs in our algorithm to generate conformational ensembles of 10-, 20-, and 200-mers. For each GAG type, 10- and 20-mer constructed ensembles were compared to 10- and 20-mer MD-generated ensembles. In each case, end-to-end distances in constructed and MD-generated ensembles match, with minimal differences in most probable end-to-end distances. The similarities in backbone conformation of constructed and MD-generated 10- and 20-mer ensembles provide further evidence that there is little correlation between individual glycosidic linkage and ring conformations, and thus, that nonsulfated GAG 10- and 20-mers do not exhibit a higher-order structure. This suggests that our program can be used to construct realistic conformations of long GAG biopolymers (e.g., 200 monosaccharides), and the resulting atomic-resolution models may be used to develop further insights into GAG binding properties, and thus, GAG-protein complex formation. These will be especially useful for studying complexes in which there are multiple biomolecules bound to the same GAG. Other programs exist which are capable of constructing three-dimensional, atomic-resolution GAG polymer models including Glycam GAG Builder [74], POLYS Glycan Builder [75], CarbBuilder [76], MatrixDB GAG Builder [77,78], and CHARMM-GUI [79–82]. These are useful tools for constructing the initial structures of GAGs having user-specified sequences and lengths for MD simulations. Additional features of Glycam and POLYS Glycan Builder include user specification of glycosidic linkage dihedral angle values or construction using conformations from their databases. Glycam, POLYS Glycan Builder, and Carb Builder databases consist of GAG mono- and disaccharide structures sampled in MD and/or determined by molecular mechanics calculations. The MatrixDB databases contain GAG disaccharide conformations from GAG-protein complex crystal structures. CHARMM-GUI uses the CHARMM software [83–85] to construct GAGs with user-specified sequences, using default force field parameters for carbohydrates [57,61–63], adding explicit solvents with user-specified water box size and ion concentrations, and generating inputs for MD equilibration and production simulations. Int. J. Mol. Sci. 2020, 21, 7699 4 of 41

Although the user has the option to choose the GAG length, these tools are best used for short GAG oligosaccharides. Our algorithm diﬀers from these tools in that it draws upon our databases containing full MD-generated unbound GAG 20-mer atomic-resolution conformational ensembles. Furthermore, our algorithm is developed for modeling long GAG biopolymers (e.g., 200-mers), and can eﬃciently produce large conformational ensembles (e.g., 10,000 3-D models) of long GAG biopolymers. Therefore, our algorithm provides an alternative to MD simulation that takes much less time and computational resources.

2. Materials and Methods The following protocol was conducted for each of the hyaluronan and nonsulfated dermatan, keratan, and heparan GAGs.

2.1. Molecular Dynamics: System Construction, Energy Minimization, Heating, and Production Simulations System construction, energy minimization, and heating followed the same protocol we described previously [33]. Briefly, all polymers were constructed with an explicit solvent using the CHARMM software [83–85] v. c41b2 with the CHARMM36 (C36) biomolecular force field for carbohydrates [57,61–63]. The initial conformation of each GAG 10- and 20-mer had glycosidic linkage dihedrals (with IUPAC definitions: φ = O5-C1-O-Cn and ψ = C1-O-Cn-C(n 1)) set to φ = 83.75◦ and ψ = 156.25◦ in all − − − GlcAβ1-3GlcNAc (hyaluronan), IdoAα1-3GalNAc (dermatan), and Galβ1-4GlcNAc (keratan) linkages and φ = 63.75 and ψ = 118.75 in all GlcNAcβ1-4GlcA (hyaluronan), GalNAcβ1-4IdoA (dermatan), − ◦ ◦ and GlcNAcβ1-3Gal (keratan) linkages. These dihedral values were the most energetically stable in nonsulfated chondroitin disaccharide glycosidic linkages during MD simulation [55]. In heparan 10- and 20-mers, all IdoAα1-4GlcNAc glycosidic linkage dihedrals were set to φ = 69 and ψ = 147 − ◦ ◦ and all GlcNAcα1-4IdoA linkage dihedrals were set to φ = 77◦ and ψ = 30◦. These dihedral values were found in an NMR and force field study of heparan disaccharides [30], and gave extended heparan polymer conformations. With these glycosidic linkage conformations, 20-mer end-to-end distances were 99.0 Å, 89.7 Å, 85.8 Å, and 87.5 Å for hyaluronan, dermatan, keratan, and heparan, respectively. The GAG 20-mers were solvated in cubic periodic unit cells with edge lengths of 124.3 Å (63,347 water molecules), 115.0 Å (50,066 water molecules), 111.9 Å (46,103 water molecules), and 111.9 Å (46,122 water molecules) for hyaluronan, dermatan, keratan, and heparan, respectively. Each of these edge lengths is at least 10 Å longer than the maximum dimension of the corresponding 20-mer in a fully-extended (i.e., maximum end-to-end distance) conformation. The TIP3 water model [86,87], as implemented in the CHARMM force field, was used for all simulations, and neutralizing Na+ counterions and 140 mM NaCl [88] were added. The NAMD program [89] v. 2.12 (http://www.ks.uiuc.edu/Research/namd/) was used to minimize the potential energy and heat the system to the target temperature of 310 K under constant pressure at 1 atm. An unbiased constant particle number/constant pressure/constant temperature (NPT) MD run followed, and average periodic cell parameters from the last half of this trajectory were used as cell basis vectors for the quadruplicate canonical (NVT) ensemble MD simulations. NVT MD simulations were preceded by minimization and heating at constant volume with box edge lengths of 123.7 Å, 114.4 Å, 111.3 Å, and 111.3 Å for hyaluronan, dermatan, keratan, and heparan, respectively. Production simulations were performed using a similar protocol as previously described [33] but with a longer timescale and lower frequency for saving snapshots. Briefly, using the CHARMM software, each of four replicates (per GAG system) was equilibrated. Then, unbiased canonical (NVT) ensemble MD simulations were run for 500,000,000 steps (1 µs) and atomic coordinates were saved at 50,000-step (100-ps) intervals for analyses (10,000 snapshots per simulation, 40,000 snapshots per GAG).

2.2. Conformational Analysis GAG conformational parameters include bond length, bond angle, and dihedral angle values. The glycosidic linkage conformational parameters considered were bond lengths for C1-O and O-Cn, Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 5 of 41

2.2.Int. J.Conformational Mol. Sci. 2020, 21 Analysis, 7699 5 of 41 GAG conformational parameters include bond length, bond angle, and dihedral angle values. The glycosidic linkage conformational parameters considered were bond lengths for C1-O and O-Cn, bond angles for O5-C1-O and C1-O-Cn, and dihedral angles φ and ψ (Figure1). To characterize potential bondpatterns angles in glycosidic for O5-C1 linkage-O and conformations,C1-O-Cn, and dihedral dihedral angles angle freeϕ and energies ψ (Figure∆G( φ1)., ψ )To were characterize analyzed. potentialAs φ, ψ dihedralpatterns valuesin glycosidic from MD-generatedlinkage conformations, ensembles dihedral were taken angle to free have energies uniform ΔG probabilities,(ϕ, ψ) were analyzed.∆G(φ, ψ) wasAs ϕ calculated, ψ dihedral by sortingvalues from dihedral MD-generated angle values ensembles into 2.5 were2.5 binstaken and to thenhave usinguniform the ◦ × ◦ probabilities,formula ∆G( φΔG,ψ(ϕ) ,= ψ) RTwasln( calculatedn ) k, where by sortingn is the dihedral bin count angle for values the bin into corresponding 2.5° × 2.5° bins to φand,ψ then, R is i j − ij − ij i j usingthe universal the formula gas constant,ΔG(ϕi,ψj)T =is -RT theln( temperaturenij) – k, where of thenij is MD the simulations, bin count for and thek wasbin corresponding chosen so that theto ϕglobali,ψj, R minimumis the universal was located gas constant, at ∆G = T0 is kcal the/mol. temperature of the MD simulations, and k was chosen so that the global minimum was located at ΔG = 0 kcal/mol.

Figure 1. GAG trisaccharides: (a) hyaluronan [GlcNAcβ1-4GlcAβ1-3GlcNAc], (b) nonsulfated Figure 1. GAG trisaccharides: (a) hyaluronan [GlcNAcβ1-4GlcAβ1-3GlcNAc], (b) nonsulfated dermatan [GalNAcβ1-4IdoAα1-3GalNAc], (c) nonsulfated keratan [GlcNAcβ1-3Galβ1-4GlcNAc], dermatan [GalNAcβ1-4IdoAα1-3GalNAc], (c) nonsulfated keratan [GlcNAcβ1-3Galβ1-4GlcNAc], (d) (d) nonsulfated heparan [GlcNAcα1-4IdoAα1-4GlcNAc]; endocyclic ring atoms and oxygen atoms nonsulfated heparan [GlcNAcα1-4IdoAα1-4GlcNAc]; endocyclic ring atoms and oxygen atoms linking adjacent rings are labeled; arrows indicate rotations about glycosidic linkage bonds C1-O and linking adjacent rings are labeled; arrows indicate rotations about glycosidic linkage bonds C1-O and O-Cn (quantified by φ and ψ dihedral angles, respectively); glycosidic linkage parameters used in O-Cn (quantified by ϕ and ψ dihedral angles, respectively); glycosidic linkage parameters used in the the construction algorithm include C1-O and O-Cn bond lengths, O5-C1-O and C1-O-Cn bond angles, construction algorithm include C1-O and O-Cn bond lengths, O5-C1-O and C1-O-Cn bond angles, and and φ = O5-C1-O-Cn and ψ = C1-O-Cn-C(n 1) dihedral angles. Molecular graphics throughout are ϕ = O5-C1-O-Cn and ψ = C1-O-Cn-C(n−1) dihedral− angles. Molecular graphics throughout are produced produced with the VMD program [90]. with the VMD program [90]. Monosaccharide ring geometries are quantified by all bond lengths, bond angles, and dihedral anglesMonosaccharide within the ring ring and geometries in exocyclic are functional quantified groupsby all bond that arelengths, not part bond of angles, a glycosidic and dihedral linkage. anglesCremer-Pople within the (C-P) ring ring and puckering in exocyclic parameters functional ( φgroups, θ, Q)[ that91] are of eachnot part monosaccharide of a glycosidic ring linkage. in the Cremer-PopleMD-generated (C-P) 20-mer ring ensembles puckering wereparameters computed (ϕ, θ to, Q characterize) [91] of each potential monosaccharide ring puckering ring in the patterns. MD- generatedConformations 20-mer of eachensembles monosaccharide were computed and each to char linkageacterize of the potential 20-mers ring were puckering extracted separatelypatterns. Conformationsfrom each snapshot of each of monosaccharide the MD trajectories. and each First, li tonkage determine of the 20-mers if conformational were extracted data inseparately different fromruns each matched, snapshot and of if therethe MD was trajectories. interdependency First, to determine in the individual if conformational linkage and data ring in conformations, different runs matched,data were and separated if there by was run interdependency and monosaccharide in the/linkage individual number linkage and aggregatedand ring conformations, across all snapshots data werein each separated MD simulation by run and run. monosaccharide/linkage Next, all individual conformations number and were aggregated aggregated across across all snapshots all snapshots in eachin all MD runs simulation (e.g., 10,000 run. snapshots Next, all individual * 4 runs * conformations 10 GlcA monosaccharides were aggregated= 400,000 across samples all snapshots of GlcA in allmonosaccharide runs (e.g., 10,000 conformations snapshots * in 4 hyaluronanruns * 10 GlcA 20-mer) monosaccharides to generate a single= 400,000 dataset samples for each of ofGlcA the monosaccharidetwo monosaccharide conformations types and in two hyaluronan linkage types 20-mer) in each to generate GAG (e.g., a single GlcA dataset monosaccharide, for each of the GlcNAc two monosaccharidemonosaccharide, typesβ1-3 glycosidicand two linkage linkage, types and βin1-4 ea glycosidicch GAG (e.g., linkage GlcA conformations monosaccharide, in hyaluronan GlcNAc 20-mer).

Int. J. Mol. Sci. 2020, 21, 7699 6 of 41

2.3. Construction Algorithm to Generate GAG Conformational Ensembles The MD-generated conformational datasets described above made up the database used for the algorithm we developed to generate GAG polymer conformational ensembles of user-specified length and with a user-specified number of conformations (previously described) [33]. Essentially, our algorithm (1) incorporates all bond, bond angle, and dihedral angle conformational parameters from MD simulation of GAG 20-mers, (2) treats monosaccharide rings and glycosidic linkages independently, (3) performs a restrained energy minimization on each constructed conformation to relieve steric overlap while maintaining polymer conformation, and (4) applies a bond potential energy cutoff to exclude conformations that remain nonphysical after minimization. A nonphysical conformation results from either overlapping bonds or a bond that pierces the center of another monosaccharide ring in the initial constructed conformation (Figure S1). As dihedral angles are restrained, minimization addresses these issues by stretching the overlapping or ring-piercing bonds to nonphysical lengths, which increases the post-minimization bond potential energy by more than 132 kcal/mol [33]. The energy cutoff is the sum of a 100 kcal/mol buffer and a polymer-length specific cutoff, which is equal to the post-minimization bond potential energy of the fully-extended conformation. This conformation was constructed by assigning energetically-favorable glycosidic linkage dihedrals from the corresponding MD simulations of each GAG type that give a fully-extended conformation (i.e., with the maximum end-to-end distance observed in simulation). We used the algorithm to construct 20-mer conformational ensembles of each nonsulfated GAG. For internal validation of the algorithm, glycosidic linkage dihedral free energies ∆G(φ,ψ), monosaccharide ring C-P parameters, end-to-end distance distributions, and radii of gyration from MD-generated ensembles and constructed ensembles were compared. Additionally, post-minimization bond potential energy distributions from constructed ensembles were analyzed to validate the calculated bond potential energy cutoff and verify that the ensemble had expected energy distributions for the given polymer length. To evaluate application of MD-generated 20-mer conformations to construct GAG polymers of variable length, we constructed 10-mer ensembles using the algorithm and compared them to 10-mer ensembles generated using the same protocol as 20-mer MD simulations. To assess the efficacy and efficiency of our algorithm to construct conformational ensembles of GAG polymers with biologically-relevant chain lengths, we also constructed 200-mer ensembles.

3. Results and Discussion

3.1. Hyaluronan

3.1.1. Molecular Dynamics Simulations: Glycosidic Linkage and Monosaccharide Ring Geometry Effects on Polymer Backbone Flexibility To examine the backbone flexibility of hyaluronan 20-mers, end-to-end distances and radii of gyration were analyzed in each of the four MD simulation runs. One of the four runs produced more compact conformations, i.e., with lower end-to-end distances and radii of gyration than the other three (Figures2 and S2a and Table1). The system potential energy distributions were identical for all four runs, suggesting that this outlying run was energetically stable (Figure S3). To uncover the conformational factors that contributed to end-to-end distance and explain the differences in backbone flexibility in the different MD runs, the monosaccharide ring and glycosidic linkage conformations were examined. Int. J. Mol. Sci. 2020, 21, 7699 7 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 7 of 41

Figure 2. End-to-endEnd-to-end distance distance probability probability distribution distribution of of MD-generated MD-generated hyaluronan hyaluronan 20-mer 20-mer ensemble; ensemble; each of the fourfour runsruns includesincludes 10,00010,000 conformations;conformations; probabilities were calculated for end-to-end distances sorted into 0.5 Å bins. Table 1. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Hyaluronan Table 1. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Hyaluronan Ensembles 1. Ensembles 1. 20-mer Ensembles 10-mer Ensembles 20-mer Ensembles 10-mer Ensembles MD-GeneratedMD-Generated ConstructedConstructed % MD-GeneratedMD-Generated ConstructedConstructed % % Difference % Difference d (Å)d (Å) d (Å)d (Å) Difference dd (Å)(Å) dd (Å)(Å) Difference RunRun 1 181.5 81.5 80.5 80.5 43.00 43.00 42.2542.25 RunRun 2 281.0 81.0 78.0 78.0 42.50 42.50 41.7541.75 RunRun 3 383.0 83.0 80.5 80.5 44.00 44.00 42.7542.75 RunRun 4 485.0 85.0 78.0 78.0 43.50 43.50 42.7542.75 2 AllAll 2 80.080.0 78.0 78.0 2.53% 2.53% 43.50 43.50 41.7541.75 4.11%4.11% 1 1 Probabilities were were calculated calculated for for end-to-end end-to-end distances distances sorted sorted into 0.5 into Å bins 0.5 forÅ bins the 20-mer for the ensembles 20-mer ensembles and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs. and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs. 4 Analysis of C-P parameters of GlcNAc monosaccharide rings revealed mostly C1 chair conformations,Analysis of as C-P found parameters in crystal structuresof GlcNAc [92 monosaccharide–99] and NMR and rings force revealed field studies mostly [67 ,4100C1 –chair102], 1 1,4 1 withconformations, a minority as of found samples in crystal in boat structures and skew-boat [92–99] conformations,and NMR and force namely field B3,O studies, S3, [67,100–102],B, and S5 4 (Figureswith a minority3a and4 ofa). samples While in non- boat andC1 conformations skew-boat conformations, of GlcNAc namely are rare, B3,O they, 1S3 have, 1,4B, and been 1S5 observed (Figures in3a crystaland 4a). structures While non- of4 proteinC1 conformations co-complexes of GlcNAc [95,103 –are106 ].rare, For they example, have been one GlcNAcobserved ring in crystal in the 1,4 crystalstructures structure of protein of a hyaluronanco-complexes tetramer [95,103–106]. in complex For example, with hyaluronidase one GlcNAc was ring found in the in thecrystalB boatstructure conformation of a hyaluronan [95]. Additionally, tetramer in GlcNAc complex boat with/skew-boat hyaluronidase conformations was found have in been the sampled1,4B boat inconformation biased MD [95]. [107 Additionally,], 1-µs unbiased GlcNAc MD boat/skew-boat [108], and 10- conformationsµs unbiased MD have simulations been sampled of in GlcNAc biased monosaccharidesMD [107], 1-µs unbiased [100]. MD One [108], NMR and and 10-µs force unbiased field study MD suggested simulations that of theseGlcNAc conformations monosaccharides were important[100]. One forNMR GAG-protein and force interactionsfield study suggested [100]. Analysis that these of individual conformations GlcNAc were rings important in each run for revealed GAG- 4 thatprotein these interactions non- C1 conformations [100]. Analysis were of individual not specific GlcNAc to any particularrings in each region run of revealed the 20-mer that and these did non- not occur4C1 conformations simultaneously were in multiple not specific rings to in theany same particular snapshot region (Figure of S4).the 20-mer Furthermore, and did GlcNAc not occur rings 4 4 thatsimultaneously sampled non- in multipleC1 puckers rings returned in the same to C snapshot1 chair conformations (Figure S4). Furthermore, relatively quickly, GlcNAc i.e., rings in under that 25sampled ns (Figure non- S4).4C1 puckers returned to 4C1 chair conformations relatively quickly, i.e., in under 25 ns (Figure S4).

Int. J. Mol. Sci. 2020, 21, 7699 8 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 8 of 41

FigureFigure 3. Cremer–Pople 3. Cremer–Pople data data for for MD-generated MD-generated hyaluronanhyaluronan ensembles: ensembles: (a) (GlcNAca) GlcNAc and and(b) GlcA (b) GlcA in in the 20-merthe 20-mer and and (c) GlcNAc(c) GlcNAc and and (d ()d GlcA) GlcA in in the the 10-mer;10-mer; geometries geometries from from the the four four sets sets of each of each ensemble ensemble are representedare represented by red,by red, green, green, blue, blue, and and magenta magenta dots,dots, respectively respectively and and the the force-field force-ﬁeld geometry geometry is is representedrepresented by aby single a single large large black black dot; dot; Cremer–Pople Cremer–Pople parameters parameters (ϕ (,φ θ,) θfor) for all allrings rings in every in every tenth tenth snapshotsnapshot from from each each ensemble ensemble were were plotted plotted (i.e., (i.e., 1010 rings × 1,0001000 sn snapshotsapshots per per run run × 4 runs4 runs = 40,000= 40,000 × × parameterparameter sets sets for thefor the 20-mer 20-mer and and 20,000 20,000 parameter parameter sets for the the 10-mer). 10-mer).

C-P analysis of GlcA monosaccharide rings in the hyaluronan 20-mer showed that GlcA is 4 found mostly in C1 chair conformations (Figure3b), as seen in crystal structures [ 92–95] and NMR and force field studies [51,67,101,102,107,109,110], with some boat and skew-boat conformations, 3 5 2,5 2 1 1,4 1 including S1,B1,4, S1, B, SO, S3, B, and S5 (Figures3b and4b,c), which were also observed in GlcA rings in unbiased MD simulations of nonsulfated chondroitin 20-mers [33]. Some of these conformations were also sampled rarely in unbiased MD simulations of GlcA monosaccharides [51,107]. The slight differences between boat/skew-boat conformations in our simulations and monosaccharide simulations may have arisen from intramolecular interactions in the hyaluronan 20-mer. As with GlcNAc rings, these conformations did not occur consistently in any one region of the 20-mer, did not 4 occur simultaneously in multiple rings in the same snapshot, and returned to C1 chair conformations 2 quickly, i.e., within 40 ns (Figure S5). Except for SO, each of these GlcA and GlcNAc boat and skew-boat conformations brought the linker oxygen atoms closer together, causing a kink in the polymer chain (Figure4), which may have contributed to more compact polymer conformations. To investigate 4 this, end-to-end distances and radii of gyration of 20-mer conformations with non- C1 ring puckers were analyzed (Figure S6) and both compact and extended conformations were observed. This can be explained by the flexibility in the glycosidic linkages. Of note, MD-generated atomic-resolution 4 snapshots before and after a monosaccharide ring underwent a conformational change between C1 4 + and non- C1 were visualized in VMD to check for ionic interactions (e.g., between Na and carboxylate O− atoms and/or partially-charged hydroxyl O atoms in GlcA, between Cl− and hydroxyl H atoms in GlcA, between Na+ and partially-charged N-acetyl N or O atoms and/or hydroxyl O atoms in GlcNAc, or between Cl− and H atoms of methyl and/or hydroxyl groups in GlcNAc). Specifically, we looked for ions within 5 Å of the exocyclic atoms of the monosaccharide of interest and found that ionic interactions were most often absent during, and thus, did not significantly contribute to, ring puckering in the MD simulation of hyaluronan 20-mer. Int. J. Mol. Sci. 2020, 21, 7699 9 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 9 of 41

1,4 FigureFigure 4. 4.MD-generatedMD-generated hyaluronan hyaluronan conformations: conformations: (a) ( a20-mer) 20-mer with with a a1,4B BGlcNAc GlcNAc conformer conformer (ring (ring atoms in blue; linkage atoms in red) and 4C ,B , 1S , 1,4B, and 1S GlcNAc monosaccharide atoms in blue; linkage atoms in red) and 4C11, B3,O3,O, 1S3, 3 1,4B, and 1S5 5GlcNAc monosaccharide 5 conformations (endocyclic ring atoms and linker oxygen atoms only); (b) 20-mer with a5 S1 GlcA conformations (endocyclic ring atoms and linker oxygen atoms only); (b) 20-mer with a S1 GlcA 3 5 2,5 1 1,4 1 conformer (ring atoms in cyan; linkage atoms in red) and 3S1,B1,4, 5 S1,2,5 B,1 S31,4, B, and1 S5 GlcA conformer (ring atoms in cyan; linkage atoms in red) and S1, B1,4, S1, B, S3, B, and S5 GlcA monosaccharide conformations (endocyclic ring atoms and linker oxygen atoms only); (c) 20-mer with a monosaccharide conformations (endocyclic ring atoms and linker oxygen atoms only); (c) 20-mer with 2 4 2 SO GlcA conformer (ring atoms in cyan; linkage atoms in red) and C1 and SO GlcA monosaccharide a 2SO GlcA conformer (ring atoms in cyan; linkage atoms in red) and 4C1 and 2SO GlcA monosaccharide conformations (endocyclic ring atoms and linker oxygen atoms only); in each 20-mer snapshot, all gray conformations (endocyclic ring atoms and linker oxygen atoms only); in each 20-mer snapshot, all 4 rings are in C1 conformations. gray rings are in 4C1 conformations. To analyze glycosidic linkage conformations, free energies of glycosidic linkage dihedrals ∆G(φ, ψ) C-P analysis of GlcA monosaccharide rings in the hyaluronan 20-mer showed that GlcA is found were calculated (Figure5a,b and Table2). If we assume O 5-C1-O-Cn = H1-C1-O-Cn - 120◦ for φ values mostly in 4C1 chair conformations (Figure 3b), as seen in crystal structures [92–95] and NMR and force and C1-O-C3-C2 = C1-O-C3-H3 - 120◦ and C1-O-C4-C3 = C1-O-C4-H4 + 120◦ for ψ values, our data field studies [51,67,101,102,107,109,110], with some boat and skew-boat conformations, including 3S1, match well with X-ray diﬀraction and force ﬁeld data from hyaluronan tetrasaccharides [49], as well as B1,4, 5S1, 2,5B, 2SO, 1S3, 1,4B, and 1S5 (Figures 3b and 4b,c), which were also observed in GlcA rings in NMR and molecular mechanics data from hyaluronan tetrasaccharides [111], hexasaccharides [112], unbiased MD simulations of nonsulfated chondroitin 20-mers [33]. Some of these conformations were also sampled rarely in unbiased MD simulations of GlcA monosaccharides [51,107]. The slight

Int. J. Mol. Sci. 2020, 21, 7699 10 of 41

and octasaccharides [113]. If we assume C1-O-C3-C2 = C1-O-C3-C4 + 120◦ and C1-O-C4-C3 = C1-O-C4-C5 - 120◦, our data are also in close agreement with X-ray diﬀraction and quantum molecular modeling data [65,114–116], as well as NMR and MD data [102]. This agreement is with conformations sampled about the global minimum in each linkage in our MD simulations. All of these conformations were helical, so it stands to reason that 2-, 3-, and 8-fold helices were observed in hyaluronan oligosaccharides. This does not necessarily mean that adjacent glycosidic linkage conformations were interdependent. In fact, variation in the types of helices observed in the force ﬁeld and experimental studies in only short oligosaccharide units suggests a lack of consistent and uniform helical structures in long hyaluronanInt. J. Mol. Sci. polymers. 2020, 21, x FOR PEER REVIEW 11 of 41

Figure 5. ∆G(φ, ψ) in the MD-generated hyaluronan ensembles for aggregated GlcAβ1-3GlcNAc and GlcNAcFigureβ 1-4GlcA5. ΔG(ϕ, glycosidicψ) in the MD-generated linkage data in hyaluronan the (a,b) 20-mer ensembles and (forc,d aggregated) 10-mer, respectively; GlcAβ1-3GlcNAc contour and linesGlcNAc everyβ 11-4GlcA kcal/mol. glycosidic linkage data in the (a,b) 20-mer and (c,d) 10-mer, respectively; contour Tablelines 2. everyHyaluronan 1 kcal/mol. Glycosidic Linkage Dihedrals (φ,ψ) 1 and Free Energy (∆G(φ,ψ) kcal/mol) Minima.

Table MD-Generated2. Hyaluronan 20-mer Glycosidic LinkageMD-Generated Dihedrals (ϕ 10-mer,ψ) 1 and Free EnergyConstructed (ΔG(ϕ,ψ 20-mer) kcal/mol) Ensemble Ensemble Ensemble Minima. GlcAβ1-3 GlcNAcβ1-4 GlcAβ1-3 GlcNAcβ1-4 GlcAβ1-3 GlcNAcβ1-4 GlcNAcMD-Generated 20-merGlcA GlcNAcMD-GeneratedGlcA 10-mer GlcNAcConstructed GlcA20-mer

Min φ, ψ ∆EnsembleG φ, ψ ∆G φ, ψ ∆GEnsembleφ, ψ ∆G φ, ψ ∆GEnsembleφ, ψ ∆G 71.25GlcA, β1-3 68.75GlcNAc, β1-4 71.25GlcA, β1-3 68.75GlcNAc, β1-4 71.25GlcA, β1-3 71.25GlcNAc, β1-4 I − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 123.75 116.25 123.75 118.75 123.75 116.25 − GlcNAc◦ GlcA◦ − GlcNAc◦ ◦GlcA − GlcNAc◦ ◦ GlcA 53.75 , 83.75 , 58.75 , 81.25 , 56.25 , 83.75 , IIMin −ϕ, ψ◦ 3.06ΔG − ϕ, ψ◦ 1.31ΔG − ϕ, ψ◦ 3.08ΔG − ϕ, ψ◦ 1.16ΔG − ϕ, ◦ψ 3.01ΔG − ϕ,◦ ψ 1.29ΔG 91.25 73.75 86.25 76.25 91.25 73.75 −71.25°,◦ −68.75°,◦ −71.25°,◦ −−68.75°,◦ −71.25°,◦ − −71.25°,◦ I 0.00 58.75 , 0.00 0.00 53.75 , 0.00 0.00 56.25 , 0.00 II’ −123.75° −116.25°◦ 1.42 −123.75° −118.75°◦ 1.27 −123.75° − 116.25°◦ 1.40 33.75 36.25 36.25 − ◦ − ◦ − ◦ −53.75°, −83.75°1, −58.75°, −81.25°, −56.25°, −83.75°, II 3.06 φ, ψ1.31dihedral angles were3.08 sorted into 2.5◦ bins.1.16 3.01 1.29 91.25° −73.75° 86.25° −76.25° 91.25° −73.75° −58.75°, −53.75°, −56.25°, II’Our data alsoshow that a secondary1.42 basin was sampled1.27 in each linkage type in our MD1.40 simulations. In GlcAβ1-3GlcNAc−33.75° linkages, conformations−36.25° in the upper left quadrant−36.25° ( φ , +ψ) − were sampled. A molecular modeling1 ϕ, ψ dihedral study angles that were reportedly sorted into sampled 2.5° bins. the full allowable range of

Our data also show that a secondary basin was sampled in each linkage type in our MD simulations. In GlcAβ1-3GlcNAc linkages, conformations in the upper left quadrant (−ϕ, +ψ) were sampled. A molecular modeling study that reportedly sampled the full allowable range of glycosidic linkage conformations in agreement with experimental data for several disaccharide units also revealed hyaluronan GlcAβ1-3GlcNAc linkage conformations in a secondary basin similar to ours [117]. Furthermore, crystal structures of hyaluronan oligosaccharides in complexes with proteins [92– 95] were examined and we found that most glycosidic linkage conformations were similar to the most energetically-favorable conformations observed in MD simulation, with the exception of one GlcAβ1- 3GlcNAc linkage conformation with −ϕ, +ψ dihedrals, which was seen in a hyaluronan hexasaccharide in complex with hyaluronidase [94]. This suggests that, although rare, this is a

Int. J. Mol. Sci. 2020, 21, 7699 11 of 41 glycosidic linkage conformations in agreement with experimental data for several disaccharide units also revealed hyaluronan GlcAβ1-3GlcNAc linkage conformations in a secondary basin similar to ours [117]. Furthermore, crystal structures of hyaluronan oligosaccharides in complexes with proteins [92–95] were examined and we found that most glycosidic linkage conformations were similar to the most energetically-favorable conformations observed in MD simulation, with the exception of one GlcAβ1-3GlcNAc linkage conformation with φ, +ψ dihedrals, which was seen in a hyaluronan − hexasaccharide in complex with hyaluronidase [94]. This suggests that, although rare, this is a physical conformation. Analysis of individual glycosidic linkages in individual runs (Figure S7) showed that this basin was sampled mostly in two particular GlcAβ1-3GlcNAc linkages in the MD run with the lowest end-to-end distance distribution. Therefore, 20-mer MD snapshots with these glycosidic linkage conformations were analyzed; we found that these linkage conformations were associated with lower end-to-end distances (Figure S8 and Table S1). Visual analysis of these snapshots showed that GlcAβ1-3GlcNAc glycosidic linkages with φ, +ψ dihedrals caused a kink in the polymer, which − explains the more compact polymer conformations in comparison to those containing only linkage conformations at the global free energy minimum (Figure S8). To find out if there was a connection 4 between these glycosidic linkage conformations and non- C1 puckers of adjacent monosaccharide 4 rings, glycosidic linkages flanking non- C1 ring puckers were plotted, and they were all centered about the global minimum, i.e., φ, ψ (Figure S9). In fact, there did not appear to be any correlation − − between GlcAβ1-3GlcNAc linkage φ, +ψ conformations and a non-4C ring pucker in any region of − 1 the polymer. Analysis of GlcNAcβ1-4GlcA glycosidic linkage conformations (Figure5b and Table2) revealed secondary minima in the lower left quadrant ( φ, ψ), which was also seen in a molecular modeling − − study of GAG disaccharides with results validated by experimental data [117]. In hyaluronan 20-mer MD simulations, these conformations were sampled more in the GlcNAcβ1-4GlcA linkages neighboring the GlcAβ1-3GlcNAc linkages with φ, +ψ dihedrals in the MD run with the − lowest end-to-end distances. The same analyses to those performed on 20-mer conformations with GlcAβ1-3GlcNAc linkages with φ, +ψ dihedrals were performed on MD-generated 20-mer − snapshots with GlcNAcβ1-4GlcA linkages with φ, ψ dihedrals. Similarly, these glycosidic linkage − − conformations caused a kink in the polymer chain and were associated with lower end-to-end distances (Figure S10 and Table S1). To determine if there was a correlation between GlcAβ1-3GlcNAc φ, − +ψ linkage dihedrals and GlcNAcβ1-4GlcA φ, ψ linkage dihedrals, snapshots with both of these − − linkage conformations flanking the same monosaccharide ring were examined. It was found that there were very few snapshots in which this was the case. GlcNAcβ1-4GlcA linkage conformations flanking 4 non- C1 monosaccharide rings were also analyzed, and these conformations were centered about the global minimum, i.e., φ, +ψ (Figure S9). Additionally, ionic interactions (e.g., between Na+,O in − − GlcA carboxylate group, and O in C=O of adjacent GlcNAc N-acetyl group, between Cl−, H in GlcNAc + methyl group, and H in GlcA hydroxyl groups, or between Na and O atoms or Cl− and H atoms of hydroxyls in adjacent monosaccharides) did not appear to play a role in the transition of glycosidic linkage conformations between their primary and secondary φ, ψ basins. Hyaluronan 10-mers were also simulated and showed the same conformations as the 20-mer in 4 MD simulation except for GlcNAc monosaccharide rings, which sampled only C1 chair conformations in the 10-mer (Figures3c,d and5c,d and Table2). This was expected, as these conformations occurred very few times in 20-mer MD simulations, and there were half as many samples (i.e., monosaccharide rings) in the 10-mer. Together, these results suggest that (1) realistic helical glycosidic linkage conformations in hyaluronan 10- and 20-mers are seen in MD simulation, (2) non-4C ring puckers, φ, +ψ dihedrals in 1 − GlcAβ1-3GlcNAc linkages, and φ, ψ dihedrals in GlcNAcβ1-4GlcA linkages all contribute to more − − compact conformations, and (3) monosaccharide rings and glycosidic linkages in hyaluronan 10- and 20-mers behave randomly and independently in MD simulation. Int. J. Mol. Sci. 2020, 21, 7699 12 of 41

3.1.2. Construction Algorithm Our construction algorithm was used to construct four sets of hyaluronan 20-mer ensembles with 10,000 conformations each (40,000 conformations total). A comparison of end-to-end distance distributions (Figure6a and Table1) and radii of gyration (Figure S2a,b) showed that our construction algorithm produces ensembles that mimic backbone ﬂexibility observed in MD simulations. Furthermore, the C-P parameters (Figure S11) and glycosidic linkage dihedral free energies ∆G(φ, ψ) (FigureInt. J. Mol. S12) Sci.of 2020 constructed, 21, x FOR PEER conformations REVIEW post-minimization matched those of MD-generated 13 of 41 ensembles (i.e., construction algorithm input data; Figures3a,b and5a,b and Table2), indicating that dihedraldihedral angles angles were were properly properly restrained restrained and and that that minimization minimization did did not not change change the the overall overall ring ring and and linkagelinkage conformation. conformation.

Figure 6. End-to-end distance probability distributions of MD-generated (blue dashed lines) and Figureconstructed 6. End-to-end (red solid distance lines) hyaluronan probability ensembles: distribution (as) 20-merof MD-generated and (b) 10-mer; (blue probabilities dashed lines) were and constructedcalculated (red for end-to-endsolid lines) distanceshyaluronan sorted ensembles: into 0.5 ( Åa) bins20-mer for and the 20-mer(b) 10-mer; and probabilities 0.25 Å bins for were the calculated 10-mer; foreach end-to-end ensemble distances includes sorted four setsinto of0.5 10,000 Å bins conformations. for the 20-mer and 0.25 Å bins for the 10-mer; each ensemble includes four sets of 10,000 conformations. A hyaluronan 10-mer ensemble with 40,000 conformations was also constructed using the algorithm;A hyaluronan similarly, the10-mer end-to-end ensemble distances with 40,000 and radiiconformations of gyration was of also the constructed using 10-mer the algorithm; similarly, the end-to-end distances and radii of gyration of the constructed 10-mer ensemble matched those of the MD-generated 10-mer ensemble (Figures 6b and S2c,d and Table 1). Both ensembles contained mostly extended conformations, as expected for short oligosaccharides with fewer opportunities for kinks or curves. Finally, a hyaluronan 200-mer ensemble containing four sets of 10,000 conformations was constructed using the algorithm. The construction procedure produced end-to-end distances, radii of gyration, and bond potential energies of all conformations, as well as PDB files of conformations with most probable end-to-end distances, bond potential energies above that of the fully-extended conformation, and all excluded conformations (for a total of about 1,000 PDBs for each of the four sets) for visualization and validation of the bond potential energy cutoff. As seen in MD-generated

Int. J. Mol. Sci. 2020, 21, 7699 13 of 41 ensemble matched those of the MD-generated 10-mer ensemble (Figures6b and S2c,d and Table1). Both ensembles contained mostly extended conformations, as expected for short oligosaccharides with fewer opportunities for kinks or curves. Finally, a hyaluronan 200-mer ensemble containing four sets of 10,000 conformations was constructed using the algorithm. The construction procedure produced end-to-end distances, radii of gyration, and bond potential energies of all conformations, as well as PDB files of conformations with most probable end-to-end distances, bond potential energies above that of the fully-extended Int.conformation, J. Mol. Sci. 2020, and 21, x allFOR excluded PEER REVIEW conformations (for a total of about 1000 PDBs for each of the 14 of four 41 sets) for visualization and validation of the bond potential energy cutoff. As seen in MD-generated hyaluronanhyaluronan 10-10- andand 20-mer 20-mer ensembles, ensembles, we expectedwe expect theed end-to-end the end-to-end distance distance distribution distribution curve skewness curve skewnessto shift toward to shift the righttoward (i.e., the lower right end-to-end (i.e., lowe distancesr end-to-end indicating distances more compact indicating conformations) more compact with conformations)increasing polymer with length, increasing as there polymer were morelength, opportunities as there were for kinksmore andopportunities curves resulting for kinks from and ring curvespuckering resulting and the from flexibility ring puckering of the glycosidic and the linkages. flexibility This of patternthe glycosidic was seen linkages. in the end-to-end This pattern distance was seendistributions in the end-to-end of the hyaluronan distance 200-mer distributions constructed of the ensembles hyaluronan (Figure 200-mer7) and constructed in those of nonsulfated ensembles (Figurechondroitin 7) and 100- in those and of 200-mer nonsulfated constructed chondroitin ensembles 100- and [33 ].200-mer The relationship constructed betweenensembles end-to-end [33]. The relationshipdistance and between radius ofend-to-end gyration was distance decreasingly and radius linear of with gyration increasing was decreasingly polymer length. linear In otherwith increasingwords, conformations polymer length. with In the other same words, end-to-end conforma distancetions with have the a same wider end-to-end range of radii distance of gyration have a widerin longer range polymers. of radii of This gyration was evidenced in longer polymers. by comparison This was of R evidenced2 values of by the comparison end-to-end of distance R2 values vs. ofradius the end-to-end of gyration regressiondistance vs. lines radius of hyaluronan of gyration 20- regression and 10-mer lines ensembles, of hyaluronan both MD-generated 20- and 10-mer and ensembles,constructed both (Figure MD-generated S2a–d). As and expected, constructed the end-to-end (Figure S2a–d). distance As and expected, radius the of gyrationend-to-end relationship distance andwas radius decreasingly of gyration linear relationship with increasing was decreasingly polymer length, linear as with shown increasing by comparison polymer of length, hyaluronan as shown 10-, by20-, comparison and 200-mer of constructed hyaluronan ensembles 10-, 20-, and (Figure 200-mer S2b,d,e). constructed This suggests ensembles that our (Figure algorithm S2b,d,e). constructs This suggestshyaluronan that 200-mer our algorithm ensembles co withnstructs the backbonehyaluronan conformations 200-mer ensembles that we would with expectthe backbone to see in conformationsMD simulations. that we would expect to see in MD simulations.

FigureFigure 7. 7. End-to-endEnd-to-end distance probabilityprobability distributiondistribution of of constructed constructed ensemble ensemble of hyaluronanof hyaluronan 200-mer; 200- mer;most most probable probable end-to-end end-to-end distance distance across across all all four four sets sets is is 235 235 Å; Å; probabilitiesprobabilities were calculated for for end-to-endend-to-end distances distances sorted sorted into into 5 5 Å Å bins; bins; the the ensemble ensemble contains contains four four sets sets of of 10,000 10,000 conformations. conformations. 3.2. Nonsulfated Dermatan 3.2. Nonsulfated Dermatan 3.2.1. Molecular Dynamics Simulations: Glycosidic Linkage and Monosaccharide Ring Geometry 3.2.1.Eﬀects Molecular on Polymer Dynamics Backbone Simulations: Flexibility Glycosidic Linkage and Monosaccharide Ring Geometry Effects on Polymer Backbone Flexibility MD simulations of nonsulfated dermatan 20-mer revealed relatively rigid and linear backbone conformations,MD simulations as evidenced of nonsulfated by the narrowdermatan and 20-mer highly revealed left-skewed relatively end-to-end rigid distanceand linear distributions, backbone conformations,which match in as all evidenced four MD runs by the (Figure narrow8 and and Table high3ly), andleft-skewed the linear end-to-end relationship distance between distributions, end-to-end whichdistance match and in radius all four of MD gyration runs (Figure(Figure S13a).8 and Ta Toble understand 3), and the the linear factors relationship contributing between to this end-to- rigid end distance and radius of gyration (Figure S13a). To understand the factors contributing to this rigid behavior of the dermatan 20-mer in simulation, conformations of monosaccharide rings and glycosidic linkages were analyzed.

Int. J. Mol. Sci. 2020, 21, 7699 14 of 41

behavior of the dermatan 20-mer in simulation, conformations of monosaccharide rings and glycosidic Int.linkages J. Mol. Sci. were 2020 analyzed., 21, x FOR PEER REVIEW 15 of 41

Figure 8. End-to-endEnd-to-end distance distance probability probability distribution distribution of of MD-generated MD-generated nonsulfated nonsulfated dermatan dermatan 20-mer ensemble; each each of of the the four four runs runs includes includes 10,000 10,000 conformations; conformations; probabilities probabilities were were calculated calculated for end- for to-endend-to-end distances distances sorted sorted into into0.5 Å 0.5 bins. Å bins. Table 3. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Nonsulfated TableDermatan 3. Most Ensembles Probable1. End-to-End Distances (d) in MD-Generated and Constructed Nonsulfated Dermatan Ensembles 1. 20-mer Ensembles 10-mer Ensembles 20-mer Ensembles 10-mer Ensembles MD-Generated Constructed MD-Generated Constructed MD-Generated Constructed % Difference MD-Generated Constructed % Difference d (Å) d (Å) % Difference d (Å) d (Å) % Difference d (Å) d (Å) d (Å) d (Å) RunRun 1 1 81.581.5 81.581.5 42.25 42.7542.75 Run 2 82.5 83.5 42.50 42.00 Run 2 82.5 83.5 42.50 42.00 Run 3 83.5 84.0 42.00 42.75 RunRun 4 3 81.083.5 81.584.0 42.0042.25 42.7542.75 RunAll 2 4 83.581.0 81.581.5 2.42% 42.25 42.7542.75 1.18% All 2 83.5 81.5 2.42% 42.25 42.75 1.18% 1 Probabilities were calculated for end-to-end distances sorted into 0.5 Å bins for the 20-mer ensembles and 0.25 Å 1bins Probabilities for the 10-mer were ensembles. calculated2 All for= end-to-endend-to-end distancedistances distribution sorted into aggregated 0.5 Å bins across for the all four20-mer runs. ensembles and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs. 4 GalNAc monosaccharide ring C-P parameters (Figure9a) show mostly C1 conformations, as well-established by X-ray diffraction [49,106,118], NMR [47,119], and force field [33,47,49,107] data. GalNAc monosaccharide ring C-P parameters (Figure 9a) show mostly 4C1 conformations, as Biased MD simulations of β-GalNAc monosaccharides showed that nonsulfated β-GalNAc sampled well-established by X-ray diffraction [49,106,118],1 NMR [47,119],1,4 and force field [33,47,49,107] data. boat and skew-boat conformations, namely B3,O, S3, and B, with relatively high free energies [107]. Biased MD simulations of β-GalNAc monosaccharides showed that nonsulfated β-GalNAc sampled1 In line with this study, our simulations showed very few boat and skew-boat puckers, namely S3, 1 1,4 1,4boat 1and skew-boat conformations, namely B3,O, S3, and B, with relatively high free energies [107]. B, S5 (Figure4a; -3GalNAc β1- endocyclic ring and linker oxygen atoms were identical to those of In line with this study, our simulations showed very few boat and skew-boat puckers, namely 1S3, -3GlcNAcβ1-), and B , on the microsecond timescale. These puckers were sampled by different rings 1,4 1 2,5 B, S5 (Figure 4a; -3GalNAcβ1- endocyclic ring and4 linker oxygen atoms were identical to those of - of the 20-mer in different MD runs and returned to C1 within 10 ns (Figure S14), suggesting that this 3GlcNAcβ1-), and B2,5, on the microsecond timescale.4 These puckers were sampled by different rings behavior was random, and confirming that non- C1 GalNAc puckers are not energetically favorable. of the 20-mer in different MD runs and returned to 4C1 within 10 ns (Figure S14), suggesting that this While these boat and skew-boat conformations caused a kink in the polymer chain, there were so few behavior was random, and confirming that non-4C1 GalNAc puckers are not energetically favorable. occurrences of this that they did not impact the overall end-to-end distance distribution. While these boat and skew-boat conformations caused a kink in the polymer chain, there were so few occurrences of this that they did not impact the overall end-to-end distance distribution.

Int. J. Mol. Sci. 2020, 21, 7699 15 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 16 of 41

Figure 9. Cremer–Pople data for MD-generated nonsulfated dermatan ensembles: (a) GalNAc and (b)Figure IdoA in9. Cremer–Pople the 20-mer and data (c) GalNAcfor MD-generated and (d) IdoA nonsulfated in the 10-mer; dermatan geometries ensembles: from (a the) GalNAc four sets and of (b) eachIdoA ensemble in the 20-mer are represented and (c) GalNAc by red, and green, (d) blue,IdoAand in the magenta 10-mer; dots, geometries respectively from andthe four the force-field sets of each geometryensemble is representedare represented bya by single red, largegreen, black blue, dot; an Cremer–Popled magenta dots, parameters respectively (φ, θand) for the all force-field rings in everygeometry tenth snapshotis represented from by each a single ensemble large were black plotted dot; Cremer–Pople (i.e., 10 rings parameters1000 snapshots (ϕ, θ) for per all run rings4 in × × runsevery= 40,000 tenth parametersnapshot from sets foreach the ensemble 20-mer and were 20,000 plotted parameter (i.e., 10 sets rings for × the 1,000 10-mer). snapshots per run × 4 runs = 40,000 parameter sets for the 20-mer and 20,000 parameter sets for the 10-mer). 1 IdoA monosaccharide rings in 20-mer MD sampled a majority of C4 and, to a lesser 2 4 degree,IdoASO monosaccharideand C1 puckers rings (Figure in 20-mer9b and MD Table sampled S2), a as majority observed of 1C in4 and, NMR to anda lesser force degree, field 2SO studiesand 4 [C291 ,45puckers,47,51, 107(Figure,120–125 9b]. and Literature Table reportsS2), as of observed the relative in proportionsNMR and offorce these field three studies ring puckers[29,45,47,51,107,120–125]. in nonsulfated IdoA Literature vary,which reports may of the be re explainedlative proportions by differences of these inthree the ring structure puckers of in neighboringnonsulfated residues IdoA vary, (or lackwhich thereof) may [be45 ,explained120,123,124 by] and differences differences in inthe ion structure concentrations of neighboring [123]. Furthermore,residues (or existinglack thereof) studies [45,120,123,124] were conducted and on differe IdoA monosaccharidesnces in ion concentrations and short [123]. IdoA-containing Furthermore, GAGexisting oligosaccharides studies were (i.e., conducted<20 monosaccharides). on IdoA monosaccharides NMR data and have short shown IdoA-containing that, when at GAG the 1 2 nonreducingoligosaccharides terminal (i.e., in <20 GAG monosaccharides). oligosaccharides, NMR nonsulfated data have IdoA shown is inthat, equilibrium when at the with nonreducingC4, SO, 4 andterminalC1 puckers, in GAG and oligosaccharides, when flanked bynonsulfated nonsulfated IdoA N-acetylated is in equilibrium sugar with derivatives 1C4, 2SO (i.e.,, and GalNAc 4C1 puckers, or 1 2 GlcNAc),and when nonsulfated flanked IdoAby nonsulfated is primarily N-acetylated in C4 and S Osugarconformations derivatives [123 (i.e.,], with GalNAc fewer thanor GlcNAc), 10% of 4 samplesnonsulfated in C1 IdoA[45,124 is ].primarily Indeed, wein 1 foundC4 and this 2SO toconformations be the case in [123], our dermatan with fewer 20-mer than 10% MD simulationsof samples in 1 2 4 (Table4C1 [45,124]. S2). Importantly, Indeed, we none found of thethis toC4 be, S theO, orcaseC 1inpuckers our dermatan introduced 20-mer a kink MD insimulations the polymer (Table chain, S2). soImportantly, we would not none expect of the variations 1C4, 2SO, or in 4C the1 puckers relative introduced proportions a kink of these in the ring polymer puckers chain, to alter so we overall would polymernot expect backbone variations conformations. in the relative IdoA proportion also sampleds of otherthese boatring andpuckers skew-boat to alter conformations overall polymer in 5 2,5 1 1,4 1 20-merbackbone MD conformations. simulations, specifically IdoA also Bsampled1,4, S1, otherB, B boat3,O, andS3, skew-bB, andoatS conformations5 (Figure9b and in Table20-mer S2), MD whichsimulations, is in agreement specifically with resultsB1,4, 5S1 from, 2,5B, MDB3,O simulations, 1S3, 1,4B, and of IdoA1S5 (Figure monosaccharides 9b and Table [107 S2),,126 ].which Another is in 2,5 forceagreement field study with showed results that from MDB and simulations B3,O IdoA of conformers IdoA monosaccharides are also feasible [107,126]. interpretations Another of force existing field NMRstudy data showed [127]. that Furthermore, 2,5B and B3,O a force IdoA field conformers study that are mapped also feasible X-ray interpretations diffraction and of NMR existing data NMR for dermatandata [127]. sulfate Furthermore, [122] and aa molecular force field modeling study that study mapped of IdoA X-ray monosaccharides diffraction and [126 ]NMR showed data that for interconversiondermatan sulfate between [122] and diff erenta molecular boat/skew-boat modeling formsstudy of IdoA monosaccharides is much more common [126] showed than that that betweeninterconversion boat/skew-boat between and different chair forms, boat/skew-boat as it is less forms energetically of IdoA is costly, much which more helpscommon explain than the that samplingbetween of boat/skew-boat multiple different and boat chair/skew-boat forms, as IdoA it is conformations.less energetically As costly, each of which these helps boat/skew-boat explain the 2 puckerssampling (except of multiple for SO different) introduces boat/skew-boat a kink in the IdoA polymer conformations. chain (Figures As each 10 of and these4b,c; boat/skew-boat -4IdoA α1- endocyclicpuckers (except ring and for linker 2SO) oxygenintroduces atoms a kink are identical in the polymer to those chain of -4GlcAc (Figuresβ1-), 10 end-to-end and 4b,c; distances-4IdoAα1- ofendocyclic 20-mer conformations ring and linker with oxygen these atom puckerss arewere identical analyzed to those to determineof -4GlcAcβ if1-), they end-to-end were associated distances of 20-mer conformations with these puckers were analyzed to determine if they were associated with more compact conformations. The end-to-end distance distribution of conformations with boat/skew-

Int. J. Mol. Sci. 2020, 21, 7699 16 of 41

Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 17 of 41 with more compact conformations. The end-to-end distance distribution of conformations with 2 boat/ skew-boatring puckers ring (other puckers than (other 2SO) thanmatchedSO) matchedthat of the that average of the averageof the four of the runs four from runs the from full the MD- full generatedMD-generated 20-mer 20-mer ensemble ensemble (Figure (Figure S15), S15),indicating indicating that these thatthese ring puckers ring puckers do not do necessarily not necessarily give compactgive compact polymer polymer conformations. conformations. Additionally, Additionally, the the end-to-end end-to-end dist distanceance distribution distribution of of 20-mer 2 conformations withwith 2SSOO IdoAIdoA conformationsconformations was was compared compared to to that that of theof the full full MD MD ensemble ensemble (Figure (Figure S15). 2 TheseS15). These distributions distributions were were similar, similar, further further suggesting suggesting that SthatO conformations 2SO conformations are not are associated not associated with withmore more or less or less compact compact 20-mer 20-mer conformations. conformations. To To determine determine if if IdoA IdoA ring ring puckering puckering inin nonsulfated dermatan 20-mer MD was random, an analysis was pe performedrformed of C-P parameters of individual IdoA monosaccharides in each of the four MD runs (Figure S16). This revealed that (1) not all IdoA rings 4 4 overcame the energy barrier to samplesample aa 4C1 pucker, (2) no single IdoA ring sampledsampled 4C1 inin all four MD runs, (3)(3) eacheach IdoAIdoA ringring overcame overcame the the energy energy barrier barrier to to sample sample boat boat/s/skew-boatkew-boat puckers puckers (i.e., (i.e., C-P C-θ ~P 90θ ◦~) 90°) in at in least at least one MD one run, MD and run, (4) and after (4) sampling after sampling boat/skew-boat boat/skew-boat puckers, puckers, some IdoA some rings IdoA returned rings 1 returnedto C4 in asto little1C4 in as as 165 little ns, as while 165 ns, others while remained others remained in boat/skew-boat in boat/skew-boat conformations conformations for the remainder for the remainderof the 1-µs trajectory.of the 1-µs Thesetrajectory. observations These observations support the support idea that the monosaccharide idea that monosaccharide rings in a nonsulfated rings in a nonsulfateddermatan 20-mer dermatan behave 20-mer randomly behave and randomly independently and independently in unbiased MDin unbiased simulation. MD simulation.

Figure 10. MD-generated nonsulfated dermatan conformations: (a) 20-mer with a B IdoA conformer Figure 10. MD-generated nonsulfated dermatan conformations: (a) 20-mer with a B3,O3,O IdoA conformer (ring atoms in cyan; linkage atoms in red) and B IdoA and 1C IdoA monosaccharide conformations (ring atoms in cyan; linkage atoms in red) and B3,O3,O IdoA and 1C44 IdoA monosaccharide conformations (endocyclic ring atoms and linker oxygen atoms only); (b) 20-mer with a 2S IdoA conformer highlighted (endocyclic ring atoms and linker oxygen atoms only); (b) 20-mer Owith a 2SO IdoA conformer (ring atoms in cyan; linkage atoms in red; 2S α-IdoA is identical to 2S β-GlcA in Figure4c); in both highlighted (ring atoms in cyan; linkage atomsO in red; 2SO α-IdoA is identicalO to 2SO β-GlcA in Figure 20-mer conformations, all IdoA monosaccharides in gray are in 1C and all GalNAc monosaccharides 4c); in both 20-mer conformations, all IdoA monosaccharides in4 gray are in 1C4 and all GalNAc are in 4C . monosaccharides1 are in 4C1. Analysis of dihedral free energies revealed a single ∆G(φ, ψ) minimum for each of IdoAα1-3GalNAc Analysis of dihedral free energies revealed a single ΔG(ϕ, ψ) minimum for each of IdoAα1- and GalNAcβ1-4IdoA glycosidic linkages (Figure 11a,b and Table4). This is consistent across all 3GalNAc and GalNAcβ1-4IdoA glycosidic linkages (Figure 11a,b and Table 4). This is consistent linkages in all runs for each linkage type. The lack of secondary basins in φ, ψ dihedral samples may across all linkages in all runs for each linkage type. The lack of secondary basins in ϕ, ψ dihedral explain the higher degree of rigidity and tendency toward extended backbone conformations of the samples may explain the higher degree of rigidity and tendency toward extended backbone nonsulfated dermatan 20-mer in comparison to hyaluronan and nonsulfated chondroitin [33] 20-mers in conformations of the nonsulfated dermatan 20-mer in comparison to hyaluronan and nonsulfated MD simulation. An X-ray diffraction study of sodium dermatan sulfate observed three different helical chondroitin [33] 20-mers in MD simulation. An X-ray diffraction study of sodium dermatan sulfate forms (i.e., right-handed, left-handed, and achiral) [118] and quantified their dihedral angles, which observed three different helical forms (i.e., right-handed, left-handed, and achiral) [118] and were defined by: φ = O5-C1-O-Cn and ψ = C1-O-Cn-C(n + 1). Assuming C1-O-C3-C2 = C1-O-C3-C4 + quantified their dihedral angles, which were defined by: ϕ = O5-C1-O-Cn and ψ = C1-O-Cn-C(n + 1). 120◦ and C1-O-C4-C3 = C1-O-C4-C5 - 120◦, we see that the right-handed and achiral helical forms Assuming C1-O-C3-C2 = C1-O-C3-C4 + 120° and C1-O-C4-C3 = C1-O-C4-C5 - 120°, we see that the right- corresponded to high ∆G(φ, ψ) values in our nonsulfated dermatan 20-mer MD simulations, and the handed and achiral helical forms corresponded to high ΔG(ϕ, ψ) values in our nonsulfated dermatan left-handed helical form corresponded to glycosidic linkage conformations very close to the ∆G(φ, ψ) 20-mer MD simulations, and the left-handed helical form corresponded to glycosidic linkage global minimum. In line with our results, force field studies that compared MD results to existing conformations very close to the ΔG(ϕ, ψ) global minimum. In line with our results, force field studies that compared MD results to existing NMR and X-ray diffraction data of dermatan sulfate dismissed right-handed and achiral helical forms and confirmed the presence of left-handed helical structure

Int. J. Mol. Sci. 2020, 21, 7699 17 of 41

NMRInt. J. and Mol. X-raySci. 2020 di, ff21raction, x FOR PEER data REVIEW of dermatan sulfate dismissed right-handed and achiral helical forms 18 of 41 and confirmed the presence of left-handed helical structure [49,122]. A quantitative comparison of[49,122]. our MD-generated A quantitative glycosidic comparison linkage of dataour MD-generated to their findings glycosidic and other linkage NMR data data to for their dermatan findings tetrasaccharidesand other NMR [47 data] showed for dermatan close agreement tetrasaccharides if we assume [47] showed O5-C1-O-C closen =agreementH1-C1-O-C if nwe- 120 assume◦ for allO5-Cφ 1- values,O-Cn C= 1H-O-C1-C13-O-C-C2 =n -C 120°1-O-C for3-H all3 -ϕ 120 values,◦ for αC1-31-O-C linkage3-C2 = ψCvalues,1-O-C3-H and3 - 120° C1-O-C for 4α-C1-33 = linkageC1-O-C ψ4 -Hvalues,4 + 120and◦ for C1-O-Cβ1-4 linkage4-C3 = Cψ1-O-Cvalues.4-H4 + 120° for β1-4 linkage ψ values.

Figure 11. ∆G(φ, ψ) in the MD-generated nonsulfated dermatan ensembles for aggregated IdoAFigureα1-3GalNAc 11. ΔG(ϕ and, ψ) GalNAcin the MD-generatedβ1-4IdoA glycosidic nonsulfated linkage dermatan data in theensembles (a,b) 20-mer for aggregated and (c,d) 10-mer, IdoAα1- respectively;3GalNAc contourand GalNAc linesβ every1-4IdoA 1 kcal glycosidic/mol. linkage data in the (a,b) 20-mer and (c,d) 10-mer, respectively; contour lines every 1 kcal/mol. Table 4. Nonsulfated Dermatan Glycosidic Linkage Dihedrals (φ, ψ) 1 and Free Energy (∆G(φ, ψ) kcalTable/mol) 4. Minima. Nonsulfated Dermatan Glycosidic Linkage Dihedrals (ϕ, ψ) 1 and Free Energy (ΔG(ϕ, ψ) kcal/mol) Minima. MD-Generated 20-mer Ensemble MD-Generated 10-mer Ensemble Constructed 20-mer Ensemble MD-GeneratedIdoAβ1-3 GalNAc 20-merβ 1-4 IdoAβ1-3 GalNAcβ1-4 IdoAβConstructed1-3 GalNAc 20-merβ1-4 MD-Generated 10-mer Ensemble GalNAcEnsemble IdoA GalNAc IdoA GalNAc EnsembleIdoA Min , ∆G , ∆G , ∆G , ∆G , ∆G , ∆G IdoAφ ψβ1-3 GalNAcφ ψ β1-4 IdoAφ ψ β1-3 GalNAcφ ψ β1-4 φ IdoAψ β1-3 φGalNAcψ β1-4 66.25 , 61.25 , 68.75 , 58.75 , 68.75 , 61.25 , I −GalNAc◦ 0.00 −IdoA◦ 0.00 −GalNAc◦ 0.00 − IdoA◦ 0.00 − GalNAc◦ 0.00 − ◦IdoA0.00 123.75 106.25 121.25 108.75 121.25 108.75 Min ϕ− , ψ ◦ΔG ϕ, ψ ◦ ΔG −ϕ, ψ ◦ ΔG ϕ, ψ◦ ΔG − ϕ, ψ◦ ΔG ϕ,◦ ψ ΔG 1 φ, ψ dihedral angles were sorted into 2.5◦ bins. −66.25°, −61.25°, −68.75°, −58.75°, −68.75°, −61.25°, I 0.00 0.00 0.00 0.00 0.00 0.00 MD−123.75° simulations of106.25° a nonsulfated dermatan−121.25° 10-mer produced108.75° mostly linear−121.25° backbone conformations108.75° (Figure S13c) and similar monosaccharide1 ϕ, ψ dihedral ring angles (Figure were9) andsorted glycosidic into 2.5° bins. linkage (Figure 11 and Table4) geometries to the nonsulfated dermatan 20-mer. The major diﬀerence was that in 10-mer MD MD simulations of a nonsulfated dermatan 10-mer4 produced mostly linear backbone simulations, 9% of all IdoA rings in all runs were found in C1 form; this was almost exclusively in theconformations nonreducing terminal(Figure S13c) IdoA (i.e.,and ringsimilar #10; monosacch Figure S17aride and Tablering S2),(Figure which 9) isand mostly glycosidic in line linkage with the(Figure aforementioned 11 and Table NMR 4) geometries study of IdoA to the ring nons conformationsulfated dermatan [45]. However,20-mer. Th basede major on difference the ﬁndings was 4 fromthat the in NMR10-mer study MD simulations, and from our 9% dermatan of all IdoA 20-mer rings MD in all simulations, runs were wefound would in C still1 form; expect this the was almost exclusively in the nonreducing terminal IdoA (i.e., ring4 #10; Figure S17 and Table S2), which nonterminal IdoA rings in a GAG polymer to sample some C1 conformations. This supports our positionis mostly that in GAG line 20-merswith the areaforementioned better-suited forNMR predictions study of ofIdoA long-chain ring conformations backbone conformations [45]. However, thanbased short on GAG the findings oligosaccharides. from the NMR study and from our dermatan 20-mer MD simulations, we would still expect the nonterminal IdoA rings in a GAG polymer to sample some 4C1 conformations. This supports our position that GAG 20-mers are better-suited for predictions of long-chain backbone conformations than short GAG oligosaccharides. These findings suggest that (1) monosaccharide rings and glycosidic linkages in nonsulfated dermatan GAG 20-mers behave randomly and independently in MD simulation, (2) nonsulfated

Int. J. Mol. Sci. 2020, 21, 7699 18 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 19 of 41

dermatanThese findings polymers suggest take that on (1)rigid monosaccharide left-handed heli ringscal andstructure glycosidic with linkagesa tendency in nonsulfated toward linear dermatanbackbone GAG conformations 20-mers behave in randomlyunbiased MD and independentlysimulations, and in MD(3) simulation,nonsulfated (2)dermatan nonsulfated 20-mer dermatanconformations polymers in take MD on simulation rigid left-handed provide helical a realistic structure representation with a tendency of longer toward nonsulfated linear backbone dermatan conformationspolymer conformations. in unbiased MD simulations, and (3) nonsulfated dermatan 20-mer conformations in MD simulation provide a realistic representation of longer nonsulfated dermatan polymer conformations. 3.2.2. Construction Algorithm 3.2.2. Construction Algorithm Four sets of 10,000 conformations of a nonsulfated dermatan 20-mer were constructed using our algorithmFour sets and of 10,000 compared conformations to conformations of a nonsulfated seen in nonsulfated dermatan 20-mer dermatan were 20-mer constructed MD. usingAs expected, our algorithmthe C-P and parameter compared plots to conformations (Figure S18) seenand inglycosid nonsulfatedic linkage dermatan free energies 20-merMD. (Figure Asexpected, S19) in the the C-Pconstructed parameter 20-mer plots ensemble (Figure S18) matched and glycosidic those in linkagethe MD-generated free energies 20-mer (Figure ensemble S19) in the (Figures constructed 9a,b and 20-mer11a,b ensemble and Table matched 4). Furthermore, those in the the MD-generated end-to-end distances 20-mer ensemble(Figure 12a) (Figures and radii9a,b of and gyration 11a,b and(Figure TableS13a,b)4). Furthermore, in the constructed the end-to-end ensemble distancesmatched those (Figure in the12a) MD-generated and radii of gyration ensemble, (Figure with only S13a,b) a 2.42% in thedifference constructed in most ensemble probable matched end-to-end those distance in the MD-generated(Table 3). This ensemble,demonstrates with that only our a algorithm 2.42% differenceproduces in mostnonsulfated probable dermatan end-to-end 20-mer distance ensembles (Table th3).at Thismimic demonstrates 20-mer backbone that our flexibility algorithm seen in producesMD simulations. nonsulfated dermatan 20-mer ensembles that mimic 20-mer backbone flexibility seen in MD simulations.

Figure 12. End-to-end distance probability distributions of MD-generated (blue dashed lines) and constructedFigure 12. (red End-to-end solid lines) distance nonsulfated probability dermatan distribution ensembles:s (ofa) MD-generated 20-mer and (b) 10-mer;(blue dashed probabilities lines) and wereconstructed calculated for(red end-to-end solid lines)distances nonsulfated sorted dermatan into 0.5 ensembles: Å bins for ( thea) 20-mer 20-mer and and (b 0.25) 10-mer; Å bins probabilities for the 10-mer;were each calculated ensemble for includesend-to-end four distances sets of 10,000 sorted conformations. into 0.5 Å bins for the 20-mer and 0.25 Å bins for the 10-mer; each ensemble includes four sets of 10,000 conformations.

The nonsulfated dermatan 10-mer ensemble with 40,000 conformations constructed by the algorithm had very similar end-to-end distance and radius of gyration data compared to the MD-

Int. J. Mol. Sci. 2020, 21, 7699 19 of 41

Int. J. Mol.The Sci. nonsulfated 2020, 21, x FOR dermatan PEER REVIEW 10-mer ensemble with 40,000 conformations constructedby 20 of the 41 algorithm had very similar end-to-end distance and radius of gyration data compared to the generatedMD-generated ensemble ensemble (Figures (Figures 12b and 12 bS13c,d and S13c,dand Ta andble 3). Table The3 ).algorithm The algorithm was also was used also to usedcreate to a nonsulfatedcreate a nonsulfated dermatan dermatan 200-mer ensemble. 200-mer ensemble.As expected, As the expected, 200-mer theend-to-end 200-mer distance end-to-end distribution distance (Figuredistribution 13) and (Figure radii 13 of) gyration and radii (Figure of gyration S13e) (Figure showed S13e) that showed conformations that conformations tended to be tended more to compact be more ascompact polymer as polymerlength increased. length increased. The shift The in shiftskewness in skewness of the end-to-end of the end-to-end distance distance distribution distribution with increasingwith increasing polymer polymer length length was wasmore more subtle subtle in nonsulfated in nonsulfated dermatan dermatan than than in in hyaluronan, hyaluronan, as as there there werewere fewer linkage and ring conformations causing kinks in the polymer.

FigureFigure 13. End-to-endEnd-to-end distance distance probability probability distribution distribution of of constructed constructed ensemble ensemble of of nonsulfated dermatan200-mer;dermatan200-mer; most most probable probable end-to-end end-to-end distance distance across across all four all four sets setsis 365 is Å; 365 probabilities Å; probabilities were calculatedwere calculated for end-to-end for end-to-end distances distances sorted sortedinto 5 Å into bins; 5 Å the bins; ensemble the ensemble contains contains four sets four of sets10,000 of conformations.10,000 conformations. 3.3. Nonsulfated Keratan 3.3. Nonsulfated Keratan 3.3.1. Molecular Dynamics Simulations: Glycosidic Linkage and Monosaccharide Ring Geometry 3.3.1.Eﬀects Molecular on Polymer Dynamics Backbone Simulations: Flexibility Glycosidic Linkage and Monosaccharide Ring Geometry Effects on Polymer Backbone Flexibility In MD simulations, nonsulfated keratan 20-mers showed rigid backbone behavior and favored extendedIn MD backbone simulations, conformations, nonsulfated as keratan evidenced 20-mers by end-to-end showed rigid distance backbone distributions behavior (Figure and favored 14 and extendedTable5) which backbone were conformations, identical in all fouras evidenced MD runs, by and end-to-end the high correlationdistance distributions of end-to-end (Figure distance 14 and to Tableradius 5) of which gyration were (Figure identical S20a). in all To four understand MD runs, the and causes the ofhigh this correlation rigid behavior, of end-to-end monosaccharide distance ring to radiusand glycosidic of gyration linkage (Figure conformations S20a). To understand were analyzed. the causes of this rigid behavior, monosaccharide ring and glycosidic linkage conformations were analyzed.

Figure 14. End-to-end distance probability distribution of MD-generated nonsulfated keratan 20-mer ensemble; each of the four runs includes 10,000 conformations; probabilities were calculated for end- to-end distances sorted into 0.5 Å bins.

Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 20 of 41 generated ensemble (Figures 12b and S13c,d and Table 3). The algorithm was also used to create a nonsulfated dermatan 200-mer ensemble. As expected, the 200-mer end-to-end distance distribution (Figure 13) and radii of gyration (Figure S13e) showed that conformations tended to be more compact as polymer length increased. The shift in skewness of the end-to-end distance distribution with increasing polymer length was more subtle in nonsulfated dermatan than in hyaluronan, as there were fewer linkage and ring conformations causing kinks in the polymer.

Figure 13. End-to-end distance probability distribution of constructed ensemble of nonsulfated dermatan200-mer; most probable end-to-end distance across all four sets is 365 Å; probabilities were calculated for end-to-end distances sorted into 5 Å bins; the ensemble contains four sets of 10,000 conformations.

3.3. Nonsulfated Keratan

3.3.1. Molecular Dynamics Simulations: Glycosidic Linkage and Monosaccharide Ring Geometry Effects on Polymer Backbone Flexibility In MD simulations, nonsulfated keratan 20-mers showed rigid backbone behavior and favored extended backbone conformations, as evidenced by end-to-end distance distributions (Figure 14 and Table 5) which were identical in all four MD runs, and the high correlation of end-to-end distance to radius of gyration (Figure S20a). To understand the causes of this rigid behavior, monosaccharide Int. J. Mol. Sci. 2020, 21, 7699 20 of 41 ring and glycosidic linkage conformations were analyzed.

FigureFigure 14. 14. End-to-endEnd-to-end distance distance probability probability distribution distribution of of MD-generated MD-generated nonsulfated nonsulfated keratan keratan 20-mer 20-mer ensemble;ensemble; each each of of the the four four runs runs includes includes 10,000 10,000 conformations; conformations; probabilities probabilities were werecalculated calculated for end- for to-endend-to-end distances distances sorted sorted into 0.5 into Å 0.5bins. Å bins. Table 5. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Nonsulfated Keratan Ensembles 1.

20-mer Ensembles 10-mer Ensembles MD-Generated Constructed MD-Generated Constructed % Diﬀerence % Diﬀerence d (Å) d (Å) d (Å) d (Å) Run 1 88.0 86.0 45.50 45.00 Run 2 90.0 87.5 46.00 45.75 Run 3 90.0 87.0 45.75 45.00 Run 4 89.0 86.0 45.50 45.00 All 2 90.0 87.0 3.39% 45.50 45.00 1.10% 1 Probabilities were calculated for end-to-end distances sorted into 0.5 Å bins for the 20-mer ensembles and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs.

C-P parameters of GlcNAc monosaccharides in keratan 20-mer MD (Figure 15a) showed similar 4 conformations to GlcNAc in hyaluronan 20-mer. There were predominantly C1 chair conformations, which are also found in a keratan sulfate tetrasaccharide crystal structure [128], with very few transitions 2 1 1,4 (i.e., no more than one per ring or two per run) to boat/skew-boat conformations (i.e., SO, S3, B, 1 4 and S5), which were sampled for no more than 20 ns before returning to C1 chair (Figure S21). 4 Analysis of end-to-end distance and radius of gyration of 20-mer conformations containing non- C1 ring puckers showed that these ring puckers were not associated with compact 20-mer conformations (Figure S22). C-P analysis of Gal monosaccharides showed that for the duration of the keratan 20-mer 4 MD simulations, Gal remained in C1 chair (Figure 15b), which was the predominant conformation found in NMR [119,129–131] and force ﬁeld data [107] for Gal in general, and in a keratan sulfate tetrasaccharide crystal structure [128]. Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 21 of 41

Table 5. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Nonsulfated Keratan Ensembles 1.

20-mer Ensembles 10-mer Ensembles MD-Generated Constructed MD-Generated Constructed % Difference % Difference d (Å) d (Å) d (Å) d (Å) Run 1 88.0 86.0 45.50 45.00 Run 2 90.0 87.5 46.00 45.75 Run 3 90.0 87.0 45.75 45.00 Run 4 89.0 86.0 45.50 45.00 All 2 90.0 87.0 3.39% 45.50 45.00 1.10% 1 Probabilities were calculated for end-to-end distances sorted into 0.5 Å bins for the 20-mer ensembles and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs.

C-P parameters of GlcNAc monosaccharides in keratan 20-mer MD (Figure 15a) showed similar conformations to GlcNAc in hyaluronan 20-mer. There were predominantly 4C1 chair conformations, which are also found in a keratan sulfate tetrasaccharide crystal structure [128], with very few transitions (i.e., no more than one per ring or two per run) to boat/skew-boat conformations (i.e., 2SO, 1S3, 1,4B, and 1S5), which were sampled for no more than 20 ns before returning to 4C1 chair (Figure S21). Analysis of end-to-end distance and radius of gyration of 20-mer conformations containing non- 4C1 ring puckers showed that these ring puckers were not associated with compact 20-mer conformations (Figure S22). C-P analysis of Gal monosaccharides showed that for the duration of the keratan 20-mer MD simulations, Gal remained in 4C1 chair (Figure 15b), which was the predominant conformation found in NMR [119,129–131] and force field data [107] for Gal in general, and in a Int.keratan J. Mol. Sci. sulfate2020, 21 tetrasaccharide, 7699 crystal structure [128]. 21 of 41

Figure 15. Cremer–Pople data for MD-generated nonsulfated keratan ensembles: (a) GlcNAc and (b)Figure Gal in 15. the Cremer–Pople 20-mer and (c data) GlcNAc for MD-generated and (d) Gal innonsulfated the 10-mer; keratan geometries ensembles: from ( thea) GlcNAc four sets and of (b) eachGal ensemble in the 20-mer are represented and (c) GlcNAc by red, and green, (d) blue, Gal in and the magenta 10-mer; dots, geometries respectively from andthe four the force-field sets of each geometryensemble is representedare represented by a by single red, largegreen, black blue, dot; and Cremer–Pople magenta dots, parameters respectively (φ ,andθ) forthe allforce-field rings in everygeometry tenth is snapshotrepresented from by each a single ensemble large black were dot; plotted Cremer–Pople (i.e., 10 rings parameters1000 snapshots (ϕ, θ) for per all run rings in × × 4 runsevery= 40,000tenth snapshot parameter from sets each for the ensemble 20-mer andwere 20,000 plotted parameter (i.e., 10 setsrings for × the1,000 10-mer). snapshots per run × 4 runs = 40,000 parameter sets for the 20-mer and 20,000 parameter sets for the 10-mer). Glycosidic linkage free energy ∆G(φ, ψ) analysis of Galβ1-4GlcNAc linkages revealed a global minimum in the basin with φ, +ψ and a secondary minimum in the basin with φ, ψ (Figure 16a − − − and Table6), similar to hyaluronan GlcNAc β1-4GlcA linkages (Figure5b,d and Table2), but with additional rare conformations in +φ, +ψ. A molecular modeling study, which was shown to agree with experimental data, showed that β1-4 linkages in keratan sulfate disaccharides took on the same conformations as β1-4 linkages in hyaluronan disaccharides [117], confirming the primary and secondary basins sampled in our 20-mer MD simulations. Keratan 20-mer conformations with glycosidic linkage conformations in the tertiary basin (i.e., +φ, +ψ) were visualized and end-to-end distances were analyzed (Figure S23). These conformations formed a slight bend in the polymer chain and were associated with more compact polymer backbone conformations. However, there did not appear to be any close contacts between atoms of adjacent monosaccharides in this conformation or in previous snapshots that could explain these linkage bond rotations. Furthermore, this conformation was not specific to any particular region of the polymer. Therefore, this behavior was likely random. As φ, ψ β1-4 linkage conformations are associated with compact hyaluronan polymer conformations, − − and nonsulfated keratan 20-mer is relatively rigid and favors extended conformations in contrast to hyaluronan, we sought to determine the effects of Galβ1-4GlcNAc linkage conformations in the secondary (i.e., φ, ψ) basin on keratan 20-mer backbone flexibility in MD simulations. As in − − hyaluronan, these conformations caused a kink in the keratan 20-mer chain and were associated with more compact conformations (Figure S23 and Table S1). However, these conformations were slightly less stable in keratan 20-mer MD (Table6) than in hyaluronan MD (Table2), and were, therefore, less common. Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 22 of 41

Glycosidic linkage free energy ΔG(ϕ, ψ) analysis of Galβ1-4GlcNAc linkages revealed a global minimum in the basin with −ϕ, +ψ and a secondary minimum in the basin with −ϕ, −ψ (Figure 16a and Table 6), similar to hyaluronan GlcNAcβ1-4GlcA linkages (Figure 5b,d and Table 2), but with additional rare conformations in +ϕ, +ψ. A molecular modeling study, which was shown to agree with experimental data, showed that β1-4 linkages in keratan sulfate disaccharides took on the same conformations as β1-4 linkages in hyaluronan disaccharides [117], confirming the primary and secondary basins sampled in our 20-mer MD simulations. Keratan 20-mer conformations with glycosidic linkage conformations in the tertiary basin (i.e., +ϕ, +ψ) were visualized and end-to-end distances were analyzed (Figure S23). These conformations formed a slight bend in the polymer chain and were associated with more compact polymer backbone conformations. However, there did not appear to be any close contacts between atoms of adjacent monosaccharides in this conformation or in previous snapshots that could explain these linkage bond rotations. Furthermore, this conformation was not specific to any particular region of the polymer. Therefore, this behavior was likely random. As −ϕ, −ψ β1-4 linkage conformations are associated with compact hyaluronan polymer conformations, and nonsulfated keratan 20-mer is relatively rigid and favors extended conformations in contrast to hyaluronan, we sought to determine the effects of Galβ1-4GlcNAc linkage conformations in the secondary (i.e., −ϕ, −ψ) basin on keratan 20-mer backbone flexibility in MD simulations. As in hyaluronan, these conformations caused a kink in the keratan 20-mer chain and were associated with more compact conformations (Figure S23 and Table S1). However, these conformations were slightly less stable in keratan 20-mer MD (Table 6) than in hyaluronan MD (Table Int. J. Mol. Sci. 2020, 21, 7699 22 of 41 2), and were, therefore, less common.

Figure 16. ∆G(φ, ψ) in the MD-generated nonsulfated keratan ensembles for aggregated Galβ1-4GlcNAc andFigure GlcNAc 16.β1-3Gal ΔG(ϕ glycosidic, ψ) in the linkage MD-generated data in the nonsulfated (a,b) 20-mer ke andratan (c, densembles) 10-mer, respectively; for aggregated contour Galβ1- lines4GlcNAc every 1 kcaland/mol. GlcNAcβ1-3Gal glycosidic linkage data in the (a,b) 20-mer and (c,d) 10-mer, respectively; contour lines every 1 kcal/mol. Table 6. Nonsulfated Keratan Glycosidic Linkage Dihedrals (φ, ψ) 1 and Free Energy (∆G(φ, ψ) kcal/mol) Minima. Table 6. Nonsulfated Keratan Glycosidic Linkage Dihedrals (ϕ, ψ) 1 and Free Energy (ΔG(ϕ, ψ) kcal/mol)MD-Generated Minima. 20-mer Ensemble MD-Generated 10-mer Ensemble Constructed 20-mer Ensemble

GalMD-Generatedβ1-4 GlcNAc 20-merβ1-3 GalβMD-Generated1-4 GlcNAc 10-merβ1-3 Galβ1-4ConstructedGlcNAc 20-merβ1-3 GlcNAc Gal GlcNAc Gal GlcNAc Gal Ensemble Ensemble Ensemble Min φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G

73.75 , 81.25 , 71.25 , 81.25 , 71.25 , 81.25 , I − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 − ◦ 0.00 116.25 156.25 116.25 156.25 118.75 158.75 ◦ − ◦ ◦ − ◦ ◦ − ◦ 56.25 , 56.25 , 53.75 , II − ◦ 1.75 − ◦ 1.67 − ◦ 1.75 31.25 36.25 33.75 − ◦ − ◦ − ◦ 1 φ, ψ dihedral angles were sorted into 2.5◦ bins.

Analysis of GlcNAcβ1-3Gal glycosidic linkages showed a global free energy minimum in the φ, ψ basin (Table6) similar to that of IdoA β1-3GalNAc linkages in nonsulfated dermatan MD − − (Figure 11a,c and Table4), but with additional rare occurrences in a secondary basin in φ, +ψ, − conﬁrmed by the aforementioned molecular modeling study [117], and a small tertiary basin in +φ, ψ (Figure 16b). To determine the eﬀects of GlcNAcβ1-3Gal linkage conformations in these secondary − and tertiary basins on backbone conformation, we visualized 20-mer conformations containing these glycosidic linkage conformations and analyzed end-to-end distances (Figure S24). Glycosidic linkage conformations in the tertiary basin caused a kink and were associated with more compact 20-mer conformations. In contrast to hyaluronan, nonsulfated keratan β1-3 glycosidic linkage conformations in the secondary basin (i.e., φ, +ψ) caused only a slight bend in the polymer chain, but were still − associated with compact 20-mer conformations (Table S1). Both secondary and tertiary GlcNAcβ1-3Gal linkage conformations were rare in keratan 20-mer MD, which helps explain why the keratan 20-mer chain was relatively rigid and favored extended conformations in MD simulation. Int. J. Mol. Sci. 2020, 21, 7699 23 of 41

Backbone conformational analysis of nonsulfated keratan 10-mer MD revealed that the 10-mer chain was rigid and favored extended conformations (Figure S20c and Table5), which is similar behavior to that of nonsulfated keratan 20-mer in MD simulation. This stands to reason, as conformations of monosaccharide rings (Figure 15) and glycosidic linkages (Figure 16 and Table6) in keratan 10-mer MD matched those in keratan 20-mer MD, with the only differences being that (1) Gal briefly (i.e., for <5 ns) 1 sampled a S5 skew-boat conformation once in each of two of the 10-mer MD runs (Figure S25), and (2) GlcNAcβ1-3Gal linkages in the 10-mer did not sample conformations in the tertiary basin (i.e., +φ, ψ) sampled in the 20-mer. Boat/skew-boat conformations including 1S were shown to − 5 have a high secondary free energy minimum (i.e., > 4 kcal/mol) in biased MD simulations of Gal monosaccharides [107], indicating that while possible, these conformations are not very stable in Gal monosaccharides. In both biased and unbiased MD simulations of a tetrasaccharide with a central Gal-GlcNAc disaccharide unit, the free energy minimum of Gal boat/skew-boat conformations 4 was much higher (i.e., ~7 kcal/mol) [108], suggesting that non- C1 conformations are less stable 4 in Gal linked to other monosaccharides. This could explain why Gal does not sample non- C1 conformations in keratan 20-mer MD, and suggests that these conformations would not be seen in long polymers. Although +φ, ψ conformations in GlcNAcβ1-3Gal linkages are rare, they are physical − conformations [117] that minorly contribute to polymer backbone flexibility. This further supports our belief that conformational landscapes from 20-mer MD are better-suited to construct conformational ensembles of GAGs with biologically-relevant chain lengths than those of short GAG oligosaccharides. The higher degree of rigidity and probability of extended conformations in nonsulfated keratan MD compared to hyaluronan MD can be explained by the facts that: (1) for each glycosidic linkage type, the conformations that caused a kink in the polymer chain were less stable and, thus, rarer 4 in nonsulfated keratan MD than in hyaluronan MD; and (2) GlcNAc and Gal are mostly rigid C1 chair conformers in nonsulfated keratan whereas GlcNAc and GlcA took on more boat/skew-boat conformations that caused kinks in hyaluronan. Importantly, nonsulfated keratan 10- and 20-mers behaved randomly, and glycosidic linkages and monosaccharide rings behaved independently in MD simulations.

3.3.2. Construction Algorithm Nonsulfated keratan 20-mer conformational ensembles (four sets of 10,000 conformations) were constructed using our algorithm and compared to MD-generated keratan 20-mer ensembles. The monosaccharide ring (Figure S26) and glycosidic linkage (Figure S27) conformations in the constructed keratan 20-mer ensemble were identical to the input data (i.e., MD-generated keratan 20-mer conformations; Figures 15a,b and 16a,b and Table6), as expected. The end-to-end distances (Figure 17a and Table5) and radii of gyration (Figure S20a,b) were similar in constructed and MD-generated ensembles, demonstrating that nonsulfated keratan 20-mer conformational ensembles provide an accurate representation of backbone flexibility in nonsulfated keratan 20-mer MD simulations. Four sets of nonsulfated keratan 10-mer ensembles with 10,000 conformations each were constructed, and the results were compared to those of nonsulfated keratan 10-mer MD. The end-to-end distances (Figure 17b and Table5) and radii of gyration (Figure S20c,d) in constructed 10-mer ensembles matched those of MD-generated 10-mer ensembles, demonstrating that MD-generated 20-mer conformations can be applied to construct ensembles of keratan polymers of different lengths that mimic backbone flexibility seen in MD simulation. A nonsulfated keratan 200-mer ensemble was constructed and, as expected, the end-to-end distance distribution (Figure 18) and radii of gyration (Figure S20e) showed that as the polymer length increased, conformations tended to be more compact. Notably, this shift in the end-to-end distance distribution curve was more subtle in keratan than in hyaluronan, which stands to reason, as monosaccharide rings and glycosidic linkages are more rigid and tend to be more extended in keratan 20-mer MD than in hyaluronan 20-mer MD. Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 24 of 41

Nonsulfated keratan 20-mer conformational ensembles (four sets of 10,000 conformations) were constructed using our algorithm and compared to MD-generated keratan 20-mer ensembles. The monosaccharide ring (Figure S26) and glycosidic linkage (Figure S27) conformations in the constructed keratan 20-mer ensemble were identical to the input data (i.e., MD-generated keratan 20- mer conformations; Figures 15a,b and 16a,b and Table 6), as expected. The end-to-end distances (Figure 17a and Table 5) and radii of gyration (Figure S20a,b) were similar in constructed and MD- generated ensembles, demonstrating that nonsulfated keratan 20-mer conformational ensembles Int. J. Mol.provide Sci. 2020 an, 21 accurate, 7699 representation of backbone flexibility in nonsulfated keratan 20-mer24 ofMD 41 simulations.

Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 25 of 41

constructed and, as expected, the end-to-end distance distribution (Figure 18) and radii of gyration (FigureFigure 17.S20e)End-to-end showed that distance as the probability polymer distributionslength increased, of MD-generated conformations (blue tended dashed to lines)be more and compact.constructedFigure Notably, (red17. End-to-end solid this lines)shift indistance nonsulfated the end-to-end probability keratan dist distributionance ensembles: distributions (ofa) MD-generated 20-mer curve and was ( bmore )(blue 10-mer; subtle dashed probabilities in lines)keratan and thanwere in calculatedconstructed hyaluronan, for (red end-to-end which solid lines)stands distances no tonsulfated reason, sorted keratanas intomonosaccharide 0.5ensembles: Å bins for (a )rings the20-mer 20-mer and and glycosidic and(b) 10-mer; 0.25 Ålinkages binsprobabilities for are the more10-mer; rigidwere each andcalculated ensemble tend to for be includes end-to-end more extended four distances sets ofin 10,000ke sortedratan conformations. into20-mer 0.5 ÅMD bins than for inthe hyaluronan 20-mer and 20-mer0.25 Å bins MD. for the 10-mer; each ensemble includes four sets of 10,000 conformations.

Four sets of nonsulfated keratan 10-mer ensembles with 10,000 conformations each were constructed, and the results were compared to those of nonsulfated keratan 10-mer MD. The end-to- end distances (Figure 17b and Table 5) and radii of gyration (Figure S20c,d) in constructed 10-mer ensembles matched those of MD-generated 10-mer ensembles, demonstrating that MD-generated 20- mer conformations can be applied to construct ensembles of keratan polymers of different lengths that mimic backbone flexibility seen in MD simulation. A nonsulfated keratan 200-mer ensemble was

FigureFigure 18. End-to-end18. End-to-end distance distance probability probability distribution distribution of constructedof constructed ensemble ensemble of nonsulfatedof nonsulfated keratan 200-mer;keratan most 200-mer; probable most end-to-end probable end-to-end distance acrossdistance all across four setsall four is 305sets Å; is probabilities305 Å; probabilities were were calculated for end-to-endcalculated for distances end-to-end sorted distances into 5 sorted Å bins; into the 5 ensemble Å bins; the contains ensemble four contains sets of four 10,000 sets conformations. of 10,000 conformations.

3.4. Nonsulfated Heparan

3.4.1. Molecular Dynamics Simulations: Glycosidic Linkage and Monosaccharide Ring Geometry Effects on Polymer Backbone Flexibility The backbone flexibility of nonsulfated heparan 20-mer, quantified by the end-to-end distances (Figure 19 and Table 7) and radii of gyration (Figure S28a) in MD simulations was analyzed. The wide end-to-end distance distribution curves and tendency toward lower end-to-end distances, relative to those of the extended 20-mer conformation, indicated that nonsulfated heparan 20-mer was highly flexible and tended toward compact conformations in MD simulations. To determine factors contributing to this conformational flexibility, monosaccharide ring and glycosidic linkage conformations were examined for patterns.

Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 25 of 41 constructed and, as expected, the end-to-end distance distribution (Figure 18) and radii of gyration (Figure S20e) showed that as the polymer length increased, conformations tended to be more compact. Notably, this shift in the end-to-end distance distribution curve was more subtle in keratan than in hyaluronan, which stands to reason, as monosaccharide rings and glycosidic linkages are more rigid and tend to be more extended in keratan 20-mer MD than in hyaluronan 20-mer MD.

Figure 18. End-to-end distance probability distribution of constructed ensemble of nonsulfated keratan 200-mer; most probable end-to-end distance across all four sets is 305 Å; probabilities were calculated for end-to-end distances sorted into 5 Å bins; the ensemble contains four sets of 10,000 Int. J.conformations. Mol. Sci. 2020, 21 , 7699 25 of 41

3.4. Nonsulfated Heparan 3.4. Nonsulfated Heparan

3.4.1.3.4.1. Molecular Molecular Dynamics Dynamics Simulations: Simulations: Glycosidic Glycosidic Linkage Linkage and and Monosaccharide Monosaccharide Ring Ring Geometry Geometry EffectsEffects on on Polymer Polymer Backbone Backbone Flexibility Flexibility TheThe backbone backbone flexibility flexibility of of nonsulfated nonsulfated heparan heparan 20-mer, 20-mer, quantified quantified by by the the end-to-end end-to-end distances distances (Figure(Figure 1919 and and Table Table 7)7) and and radii radii of of gyration gyration (Figure (Figure S28a) S28a) in MD in MD simulations simulations was wasanalyzed. analyzed. The wideThe wideend-to-end end-to-end distance distance distribution distribution curves curves and and tendency tendency toward toward lower lower end-to-end end-to-end distances, distances, relativerelative to to those those of of the the extended extended 20-mer 20-mer conforma conformation,tion, indicated indicated that that nonsulfated nonsulfated heparan heparan 20-mer 20-mer waswas highly highly flexible flexible and and tended toward compact co conformationsnformations in MD simulations. To To determine determine factorsfactors contributing contributing to to this this conformational conformational flexibility, flexibility, monosaccharide monosaccharide ring ring and and glycosidic glycosidic linkage linkage conformationsconformations were were examined examined for for patterns. patterns.

Figure 19. End-to-end distance probability distribution of MD-generated nonsulfated heparan 20-mer ensemble; each of the four runs includes 10,000 conformations; probabilities were calculated for end-to-end distances sorted into 0.5 Å bins.

Table 7. Most Probable End-to-End Distances (d) in MD-Generated and Constructed Nonsulfated Heparan Ensembles 1.

20-mer Ensembles 10-mer Ensembles MD-Generated Constructed MD-Generated Constructed % Diﬀerence % Diﬀerence d (Å) d (Å) d (Å) d (Å) Run 1 68.5 70.0 37.00 37.25 Run 2 68.5 72.0 36.25 38.25 Run 3 67.5 67.5 37.50 37.25 Run 4 66.5 71.5 36.75 36.75 All 2 68.5 72.0 4.98% 37.00 37.25 0.67% 1 Probabilities were calculated for end-to-end distances sorted into 0.5 Å bins for the 20-mer ensembles and 0.25 Å bins for the 10-mer ensembles. 2 All = end-to-end distance distribution aggregated across all four runs.

4 C-P parameters of GlcNAc rings (Figure 20a) revealed all C1 chair conformations, in line with NMR and force field data for α-GlcNAc [119]. This stands to reason, as we would not expect much difference in ring conformation between α- and β-GlcNAc, because the only structural difference is the orientation of the exocyclic oxygen atom on C1 (i.e., the linker oxygen on nonterminal GlcNAc monosaccharides in GAG polysaccharides). This structural difference will impact glycosidic linkage conformation but is less likely to impact GlcNAc ring conformation. The IdoA monosaccharide C-P parameters (Figure 20b) from nonsulfated heparan 20-mer MD were similar to those of IdoA in 1 2 4 nonsulfated dermatan 20-mer MD (Figure9b): predominantly C4, SO, and some C1, which is also in Int. J. Mol. Sci. 2020, 21, 7699 26 of 41 line with NMR and force field data for nonsulfated IdoA in heparan sulfate oligosaccharides [120,123] and nonsulfated heparan trisaccharides [126], and occasional boat and skew-boat conformations (Figure4b,c; -4IdoA α1- endocyclic ring and linker oxygen atoms in heparan are identical to those of -4GlcAβ1- in hyaluronan). As with GalNAc in dermatan, the presence of neighboring GlcNAc 4 monosaccharides substantially decreased sampling of C1 conformations [123], which is in line with 2 our results. One NMR and force field study reported 19–49% SO conformations of nonsulfated IdoA in heparan sulfate hexasaccharides, and found that as the degree of GlcNAc sulfation increased, 2 the percentage of SO conformations in adjacent nonsulfated IdoA decreased [120]. As we studied 2 only nonsulfated heparan, we would expect to see a higher proportion of IdoA SO conformations (i.e., close to 49%) if simulated under the same conditions. However, the aforementioned study performed MD in aqueous solution with only neutralizing Na+ ions, whereas our systems contained an additional 140 mM NaCl. Another NMR and molecular modeling study showed that increasing 1 2 1 NaCl salt concentrations caused a shift in equilibrium of C4 and SO toward C4 conformations of 2-O-sulfated IdoA flanked by sulfated glucosamine [123]. This may explain the tendency toward 1 1 C4 IdoA conformations, with ~54% of IdoA rings across all four 20-mer MD runs in C4, ~25% in 2 4 4 SO, and ~4% in C1 (Table S3). Furthermore, very few IdoA rings sampled C1 chair conformations, 4 and one run contained no IdoA C1 chair conformations (Figure S29), which is in contrast to the 4 more random distribution of IdoA C1 chair conformations in nonsulfated dermatan 20-mer MD (Figure S16). This is likely the result of random kinetic trapping during nonsulfated heparan 20-mer MD simulations, which means IdoA only rarely overcame energy barriers between boat/skew-boat and 4 C1 conformations. Importantly, it appears that all relevant IdoA conformations (i.e., those in line with the literature) were sampled in nonsulfated heparan 20-mer MD simulations. Therefore, we believe our database of MD-generated 20-mer conformations contains a full conformational landscape of IdoA ringsInt. in J. Mol. nonsulfated Sci. 2020, 21 heparan., x FOR PEER REVIEW 27 of 41

Figure 20. Cremer–Pople data for MD-generated nonsulfated heparan ensembles: (a) GlcNAc and (b) IdoAFigure in 20. the Cremer–Pople 20-mer and (c data) GlcNAc for MD-generated and (d) IdoA nonsulfated in the 10-mer; heparan geometries ensembles: from ( thea) GlcNAc four sets and of (b) eachIdoA ensemble in the are20-mer represented and (c) GlcNAc by red, green, and (d blue,) IdoA and in magentathe 10-mer; dots, geometries respectively from and the the four force-ﬁeld sets of each geometryensemble is represented are represented by a singleby red, large green, black blue, dot; an Cremer–Popled magenta dots, parameters respectively (φ, andθ) for the all force-field rings in everygeometry tenth is snapshot represented from by each a single ensemble large wereblack plotteddot; Cremer–Pople (i.e., 10 rings parameters1000 snapshots (ϕ, θ) for per all run rings in × × 4 runsevery= 40,000 tenth parametersnapshot from sets foreach the ensemble 20-mer and were 20,000 plotted parameter (i.e., 10 sets rings for × the 1,000 10-mer). snapshots per run × 4 runs = 40,000 parameter sets for the 20-mer and 20,000 parameter sets for the 10-mer).

The primary goal of our algorithm is to predict backbone conformations of long GAG chains, which requires that (1) monosaccharide rings in GAG 20-mers behave independently in MD simulation and (2) contributions of ring puckers to backbone flexibility match those expected in nonsulfated heparan polymers in aqueous solution. There did not appear to be any interdependency between adjacent rings, suggesting that monosaccharide rings behave independently in nonsulfated heparan 20-mer MD simulations. To determine the effects of IdoA ring puckering on polymer backbone conformations, end-to-end distances of 20-mer conformations containing monosaccharides in (1) boat and skew-boat conformations that caused a kink in the polymer chain and (2) 2SO conformations, were analyzed (Figure S30). The end-to-end distance distribution of 20-mer conformations with the ring puckers that caused a kink was similar to that of the average of the four MD runs and the most probable end-to-end distance was only 1 Å lower in conformations with ring puckers that caused a kink, suggesting that boat and skew-boat conformations that introduce a kink do not necessarily give less compact 20-mer conformations, and thus are not major factors contributing to backbone flexibility. The distribution curve of 20-mer conformations with 2SO IdoA ring puckers and that of 20-mer conformations with non-2SO boat/skew-boat puckers that caused a kink were qualitatively similar to that of the full 20-mer MD ensemble, but had additional peaks in probability of higher end-to-end distances. These findings suggest that IdoA boat/skew-boat conformations are associated with the full range of 20-mer backbone conformations in MD simulations with only a slight tendency toward extended 20-mer conformations. Therefore, the proportion of IdoA 2SO conformations likely does not have a major effect on nonsulfated heparan 20- mer backbone flexibility. Next, glycosidic linkage dihedral free energies ΔG(ϕ, ψ) were examined (Figure 21 and Table 8). IdoAα1-4GlcNAc glycosidic linkages sampled primarily −ϕ, +ψ with secondary basins in −ϕ, −ψ and GlcNAcα1-4IdoA glycosidic linkages sampled conformations in a single basin (+ϕ, +ψ). We compared our results to those of an NMR and force field study that performed two sets of MD on each of

Int. J. Mol. Sci. 2020, 21, 7699 27 of 41

The primary goal of our algorithm is to predict backbone conformations of long GAG chains, which requires that (1) monosaccharide rings in GAG 20-mers behave independently in MD simulation and (2) contributions of ring puckers to backbone flexibility match those expected in nonsulfated heparan polymers in aqueous solution. There did not appear to be any interdependency between adjacent rings, suggesting that monosaccharide rings behave independently in nonsulfated heparan 20-mer MD simulations. To determine the effects of IdoA ring puckering on polymer backbone conformations, end-to-end distances of 20-mer conformations containing monosaccharides in (1) boat 2 and skew-boat conformations that caused a kink in the polymer chain and (2) SO conformations, were analyzed (Figure S30). The end-to-end distance distribution of 20-mer conformations with the ring puckers that caused a kink was similar to that of the average of the four MD runs and the most probable end-to-end distance was only 1 Å lower in conformations with ring puckers that caused a kink, suggesting that boat and skew-boat conformations that introduce a kink do not necessarily give less compact 20-mer conformations, and thus are not major factors contributing to backbone 2 flexibility. The distribution curve of 20-mer conformations with SO IdoA ring puckers and that of 2 20-mer conformations with non- SO boat/skew-boat puckers that caused a kink were qualitatively similar to that of the full 20-mer MD ensemble, but had additional peaks in probability of higher end-to-end distances. These findings suggest that IdoA boat/skew-boat conformations are associated with the full range of 20-mer backbone conformations in MD simulations with only a slight tendency 2 toward extended 20-mer conformations. Therefore, the proportion of IdoA SO conformations likely does not have a major effect on nonsulfated heparan 20-mer backbone flexibility. Next, glycosidic linkage dihedral free energies ∆G(φ, ψ) were examined (Figure 21 and Table8). IdoAα1-4GlcNAc glycosidic linkages sampled primarily φ, +ψ with secondary basins in φ, ψ and − − − GlcNAcα1-4IdoA glycosidic linkages sampled conformations in a single basin (+φ, +ψ). We compared our results to those of an NMR and force field study that performed two sets of MD on each of 1 nonsulfated IdoAα1-4GlcNAc and GlcNAcα1-4IdoA disaccharides, one with IdoA restrained to C4 2 and the other with IdoA restrained to SO, each with a biasing potential on glycosidic linkage dihedrals defined by φ = H1-C1-O-C4 and ψ = C1-O-C4-H4 [30]. If we assume O5-C1-O-C4 = H1-C1-O-C4 - 120◦ in IdoAα1-4GlcNAc linkages, O5-C1-O-C4 = H1-C1-O-C4 + 120◦ in GlcNAcα1-4IdoA linkages, and C1-O-C4-C3 = C1-O-C4-H4 + 120◦ in both linkage types, our data are in close agreement with theirs. Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 28 of 41

nonsulfated IdoAα1-4GlcNAc and GlcNAcα1-4IdoA disaccharides, one with IdoA restrained to 1C4 and the other with IdoA restrained to 2SO, each with a biasing potential on glycosidic linkage dihedrals defined by ϕ = H1-C1-O-C4 and ψ = C1-O-C4-H4 [30]. If we assume O5-C1-O-C4 = H1-C1-O-C4

Int.- J. 120° Mol. Sci.in 2020IdoA, 21α,1-4GlcNAc 7699 linkages, O5-C1-O-C4 = H1-C1-O-C4 + 120° in GlcNAcα1-4IdoA 28linkages, of 41 and C1-O-C4-C3 = C1-O-C4-H4 + 120° in both linkage types, our data are in close agreement with theirs.

Figure 21. ∆G(φ, ψ) in the MD-generated nonsulfated heparan ensembles for aggregated IdoAFigureα1-4GlcNAc 21. ΔG( andϕ, ψ GlcNAc) in the αMD-generated1-4IdoA glycosidic nonsulfated linkage heparan data in the ensembles (a,b) 20-mer for aggregated and (c,d) 10-mer, IdoAα1- respectively;4GlcNAc contourand GlcNAc lines everyα1-4IdoA 1 kcal glycosidic/mol. linkage data in the (a,b) 20-mer and (c,d) 10-mer, respectively; contour lines every 1 kcal/mol. Table 8. Nonsulfated Heparan Glycosidic Linkage Dihedrals (φ, ψ) 1 and Free Energy (∆G(φ, ψ) kcalTable/mol) Minima.8. Nonsulfated Heparan Glycosidic Linkage Dihedrals (ϕ, ψ) 1 and Free Energy (ΔG(ϕ, ψ) kcal/mol) Minima. MD-Generated 20-mer MD-Generated 10-mer Constructed 20-mer Ensemble Ensemble Ensemble MD-Generated 20-mer MD-Generated 10-mer Constructed 20-mer

IdoAα1-4 EnsembleGlcNAcα1-4 IdoAα1-4 EnsembleGlcNAc α1-4 IdoAα1-4EnsembleGlcNAc α1-4 GlcNAc IdoA GlcNAc IdoA GlcNAc IdoA IdoAα1-4 GlcNAcα1-4 IdoAα1-4 GlcNAcα1-4 IdoAα1-4 GlcNAcα1-4 Min φ , ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G φ, ψ ∆G GlcNAc IdoA GlcNAc IdoA GlcNAc IdoA 73.75 , 76.25 , 76.25 , 73.75 , 76.25 , 71.25 , I −Min ◦ ϕ0.00, ψ ΔG ◦ ϕ, 0.00ψ Δ−G ◦ ϕ, ψ0.00 ΔG ϕ◦ , ψ 0.00ΔG − ϕ,◦ ψ 0.00ΔG − ϕ, ψ◦ Δ0.00G 128.75◦ 88.75◦ 128.75◦ 88.75◦ 128.75◦ 116.25◦ 103.75 ,−73.75°, 76.25°, 103.75−76.25°,, 73.75°, 98.75−76.25°,, −71.25°, II − I ◦ 3.13 0.00 0.00− ◦ 2.66 0.00 0.00 − ◦ 3.230.00 0.00 68.75 128.75° 88.75° 63.75128.75° 88.75° 68.75128.75° 116.25° − ◦ − ◦ − ◦ 66.25 ,−103.75°, 66.25−103.75°, , 61.25−98.75°,, II’ − II ◦ 3.38 3.13 − ◦ 2.99 2.66 − ◦ 3.343.23 31.25 −68.75° 33.75−63.75° 36.25−68.75° − ◦ − ◦ − ◦ −66.25°, 1 φ, ψ dihedral angles−66.25°, were sorted into 2.5 bins. −61.25°, II’ 3.38 2.99 ◦ 3.34 −31.25° −33.75° −36.25° GlcNAcα1-4IdoA glycosidic1 ϕ linkage, ψ dihedral conformations angles weredi sortedffer from into 2.5° any bins. other GAG glycosidic linkage conformation because of the orientation of the linker oxygen atom with respect to GlcNAc. Specifically, the oxygenGlcNAc atomα1-4IdoA on C1 of glycosidicα-GlcNAc islinkage in the conformations opposite orientation differ asfrom that any on C other1 of any GAG other glycosidic GAG monosaccharidelinkage conformation (Figure1 because). The GlcNAc of the orientationα1-4IdoA linkages of the linker have oxygen a coiled atom conformation with respect (Figure to GlcNAc. S31), whichSpecifically, helps explain the oxygen the high atom tendency on C1 of towardα-GlcNAc compact is in the conformations opposite orientation in nonsulfated as that on heparan C1 of any comparedother GAG to other monosaccharide GAGs. (Figure 1). The GlcNAcα1-4IdoA linkages have a coiled conformation (FigureAs IdoA S31),α1-4GlcNAc which helps linkages explain have the high secondary tenden conformations,cy toward compact we sought conformations to determine in nonsulfated if their behaviorheparan was compared random to and other independent. GAGs. ∆G(φ, ψ) was plotted for each individual IdoAα1-4GlcNAc linkageAs in IdoA eachα1-4GlcNAc MD run and linkages there have did secondary not appear conforma to be anytions, connection we sought betweento determine adjacent if their IdoAbehaviorα1-4GlcNAc was random linkages and or independent. any patterns ΔG across(ϕ, ψ) diwasfferent plotted MD for runs. each individual To determine IdoA theα1-4GlcNAc effects of IdoAα1-4GlcNAc linkages with φ, ψ dihedrals on 20-mer backbone flexibility, end-to-end − − distances of 20-mer conformations with these glycosidic linkage conformations were analyzed. Although these linkage conformations caused a kink in the polymer chain (as with hyaluronan GlcNAcβ1-4GlcA linkages), they were not associated with more compact conformations (Figure S32). Int. J. Mol. Sci. 2020, 21, 7699 29 of 41

In fact, the end-to-end distance distribution of heparan 20-mer conformations with IdoAα1-4GlcNAc linkage φ, ψ dihedrals was similar to that of the full MD-generated 20-mer ensemble. This was − − likely because these linkage conformations occurred infrequently in nonsulfated heparan 20-mer MD, meaning a single heparan 20-mer conformation was not likely to have many kinks resulting from these φ, ψ linkage dihedrals. These findings are in line with the literature, which suggests that IdoA − − ring conformational flexibility in heparin/heparan sulfate oligo- and polysaccharides does not affect glycosidic linkage conformation or overall backbone shape [132]. To determine if there was any interdependency between different IdoA ring puckers and flanking IdoAα1-4GlcNAc linkage geometries in 20-mer MD simulations, conformations of all IdoAα1-4GlcNAc 1 2 4 2 linkages flanking each of C4, SO, C1, and boat/skew-boat (non- SO) conformations were analyzed separately (Figure S33). There did not appear to be strong associations between any particular IdoA ring conformation and flanking IdoAα1-4GlcNAc linkage conformation, which is in line with 1 2 IdoAα1-4GlcNAc disaccharide data from NMR and MD with restrained C4 and SO IdoA ring conformations and a biasing potential on glycosidic linkage dihedrals [30]. This supports our hypothesis that glycosidic linkages and monosaccharide rings behave independently in MD simulation of nonsulfated heparan 20-mer. Backbone conformational analysis of nonsulfated heparan 10-mer in MD simulation revealed flexible, compact conformations (Figure S28c and Table7), as seen in nonsulfated heparan 20-mer MD. Monosaccharide ring and glycosidic linkage conformations in nonsulfated heparan 10-mer MD were similar to those of nonsulfated heparan 20-mer MD. These findings indicate that in MD simulations of nonsulfated heparan 10- and 20-mers, (1) IdoAα1-4GlcNAc glycosidic linkages with φ, − ψ dihedrals cause a kink in the polymer chain but are rare and thus do not contribute to compact − polymer conformations and (2) monosaccharide rings and glycosidic linkages behave randomly and independently.

3.4.2. Construction Algorithm A nonsulfated heparan 20-mer ensemble with 40,000 conformations was constructed by the algorithm. Monosaccharide ring C-P parameters (Figure S34) and glycosidic linkage conformations (Figure S35) post-minimization in the constructed ensemble matched the input data (Figures 20a,b and 21a,b), as expected. Additionally, the end-to-end distance distribution and radii of gyration of the constructed ensemble closely resembled those of the MD-generated 20-mer ensemble (Figures 22a and S28a,b and Table7), demonstrating that our algorithm generates nonsulfated heparan 20-mer ensembles with backbone conformations that mimic backbone ﬂexibility seen in 20-mer MD. Int. J. Mol. Sci. 2020, 21, 7699 30 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 30 of 41

Figure 22. End-to-end distance probability distributions of MD-generated (blue dashed lines) and constructedFigure 22. (red End-to-end solid lines) distance nonsulfated probability heparan distribution ensembles:s (ofa) MD-generated 20-mer and (b) (blue 10-mer; dashed probabilities lines) and wereconstructed calculated (red forend-to-end solid lines) distancesnonsulfated sorted heparan into 0.5ensembles: Å bins for (a the) 20-mer 20-mer and and (b) 0.25 10-mer; Å bins probabilities for the 10-mer;were each calculated ensemble for includesend-to-end four distances sets of 10,000 sorted conformations. into 0.5 Å bins for the 20-mer and 0.25 Å bins for the 10-mer; each ensemble includes four sets of 10,000 conformations. A nonsulfated heparan 10-mer ensemble with 40,000 conformations was also constructed by the algorithmA nonsulfated and had end-to-end heparan distances10-mer ense andmble radii with of gyration40,000 conformations that matched was those also of constructed MD-generated by the nonsulfatedalgorithm heparan and had 10-mer end-to-end ensembles distances (Figures and 22radiib and of gyration S28c,d and that Table matched7). This those demonstrates of MD-generated that nonsulfatednonsulfated heparan heparan 20-mer 10-mer conformations ensembles (Figures from MD 22b can and be S28c,d used to and construct Table 7). 10-mer This demonstrates ensembles that that mimicnonsulfated the backbone heparan ﬂexibility 20-mer seen conformations in nonsulfated from heparan MD can 10-mer be used MD. to construct 10-mer ensembles that mimicThe constructedthe backbone nonsulfated flexibility seen heparan in nonsulfated 200-mer ensemble heparan 10-mer had reasonably MD. expected end-to-end distanceThe probability constructed distributions nonsulfated (Figure heparan 23), 200-mer i.e., the ensemble skewness had of the reasonably curves shifted expected toward end-to-end the right,distance indicating probability more compact distributions conformations (Figure 23), with i.e., increasing the skewness polymer of the length. curves Theshifted heparan toward 200-mer the right, end-to-endindicating distance more compact distribution conformations curve was with qualitatively increasing similar polymer to that length. of hyaluronan The heparan 200-mer 200-mer (i.e., end- theto-end probability distance peak distribution was of similar curve magnitude was qualitatively and most probablesimilar to end-to-end that of hyaluronan distances 200-mer were similar), (i.e., the whichprobability stands to peak reason, was as of ring similar and linkagemagnitude conformations and most probable in nonsulfated end-to-end heparan distances 20-mer were MD causesimilar), morewhich compact stands backbone to reason, conformations, as ring and linkage as in hyaluronan conformations 20-mer in nonsulfated MD. heparan 20-mer MD cause more compact backbone conformations, as in hyaluronan 20-mer MD.

Int. J. Mol. Sci. 2020, 21, 7699 31 of 41 Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 31 of 41

Figure 23. End-to-end distance probability distribution of constructed ensemble of nonsulfated heparan Figure 23. End-to-end distance probability distribution of constructed ensemble of nonsulfated 200-mer; most probable end-to-end distance across all four sets is 260 Å; probabilities were calculated heparan 200-mer; most probable end-to-end distance across all four sets is 260 Å; probabilities were for end-to-end distances sorted into 5 Å bins; the ensemble contains four sets of 10,000 conformations. calculated for end-to-end distances sorted into 5 Å bins; the ensemble contains four sets of 10,000 4. Conclusionsconformations.

4. ConclusionsCollectively, our findings support our hypotheses that (1) glycosidic linkages and monosaccharide rings in hyaluronan and nonsulfated dermatan, keratan, and heparan GAG 20-mers behave randomly andCollectively, independently our in MDfindings simulation support and (2)our using hypotheses a database ofthat conformations (1) glycosidic from correspondinglinkages and monosaccharideGAG 20-mer MD rings simulations in hyaluronan and treating and glycosidicnonsulfated linkages dermatan, and monosaccharidekeratan, and heparan rings independently,GAG 20-mers behaveour algorithm randomly can and effi cientlyindependently construct in conformationalMD simulation ensemblesand (2) using of hyaluronana database of and conformations nonsulfated fromdermatan, corresponding keratan, and GAG heparan 20-mer GAG MD 10- andsimulations 20-mers that and mimic treating backbone glycosidic flexibility linkages observed and in monosaccharidecorresponding MD rings simulations. independently, Additionally, our algorith our algorithmm can efficiently constructed cons setstruct of 10,000conformational molecular ensemblesconformations of hyaluronan of nonsulfated and nonsulfated GAG 200-mers dermatan, with backbone keratan, conformations and heparan GAG that we10- wouldand 20-mers reasonably that mimicexpect backbone to see in MD flexibility simulation observed and didin corresponding so within 12 h. MD This simulations. suggests that Additionally, the algorithm our can algorithm generate constructedconformational sets ensembles of 10,000 ofmolecular nonsulfated conformati heterogeneousons of nonsulfated GAG polymers GAG of arbitrary200-mers length with inbackbone under a conformationsday. For perspective, that we 1- wouldµs MD reasonably simulations, expect each producing to see in MD 10,000 simulation snapshots and (i.e., did 3-D so atomicwithin coordinate12 h. This suggestssets), of GAGthat the 10- algorithm and 20-mers can weregenerate completed conformational in about ensembles 1–2 weeks of and nonsulfated 1–2 months, heterogeneous respectively, GAGand using polymers modern of GPU-acceleratedarbitrary length in hardware under a and day. software. For perspective, Furthermore, 1-µs the MD algorithm’s simulations, potential each producingenergy minimization 10,000 snapshots and bond (i.e., potential 3-D atomic energy c cutooordinateff criterion sets), exclude of GAG nonphysical 10- and conformations20-mers were completedfrom constructed in about ensembles, 1–2 weeks leaving and 1–2 only months, conformations respectively, with and reasonably using modern expected GPU-accelerated bond energies hardware(Figures S36–S39). and software. Furthermore, the algorithm’s potential energy minimization and bond potentialA comparison energy cutoff of the criterion different exclude GAG 20-mernonphysical MD simulations conformations provided from furtherconstructed insights ensembles, into the leavingrelationship only betweenconformations GAG structure with reasonably and conformation. expected bond For example,energies no(Figures associations S36, S37, between S38, and adjacent S39). monosaccharideA comparison conformations of the different were GAG seen 20-mer in any of MD the si GAGmulations 20-mer provided MD simulations, further insights but differences into the in relationshipconformations between of the same GAG monosaccharide structure and ringconforma type intion. diff erentFor example, GAGs were no observed. associations This between indicates adjacentthat the structuremonosaccharide of adjacent conformations monosaccharides were seen contributes in any of to the ring GAG conformation. 20-mer MD Furthermore, simulations, IdoA but differencesmonosaccharides in conformations were much of more the same conformationally monosaccharide flexible ring than type GlcAin different monosaccharides GAGs were in observed. GAG 10- Thisand 20-merindicates MD that simulations, the structure even thoughof adjacent the structural monosaccharides difference contributes between these to tworing monosaccharide conformation. Furthermore, IdoA monosaccharides were much more conformationally flexible than GlcA types (specifically, the orientation of the carboxylate group on C5) is subtle. Interestingly, dermatan and monosaccharidesheparan are the only in GAGsGAG 10- with and IdoA 20-mer monosaccharides, MD simulations, yet hyaluronan even though and the heparan structural showed difference the most betweenconformational these two flexibility, monosaccharide and heparan types showed (specificall the greatesty, the tendencyorientation toward of the compact carboxylate conformations group on Ccompared5) is subtle. to Interestingly, other GAGs. Thisdermatan was likely and heparan because are of variability the only GAGs in glycosidic with IdoA linkage monosaccharides, conformation, yetwhich hyaluronan is independent and heparan of monosaccharide showed the most ring conformational conformation. Independenceflexibility, and ofheparan glycosidic showed linkages the greatestand monosaccharide tendency toward rings compact was further conformations evidenced compared by the fact to other that GAGs. despite This diff erenceswas likely in flankingbecause ofmonosaccharide variability in glycosidic structure inlinkage different conformation, GAG types, which there wereis independent similarities of between monosaccharide all 1–3 linkage ring conformation.conformations Independence and between of all glycosidic 1–4 linkage linkages conformations, and monosaccharide with the exception rings was of further GlcNAc evidencedα1–4IdoA bylinkages the fact in that heparan. despite differences in flanking monosaccharide structure in different GAG types, there were similarities between all 1–3 linkage conformations and between all 1–4 linkage conformations, with the exception of GlcNAcα1–4IdoA linkages in heparan.

Int. J. Mol. Sci. 2020, 21, 7699 32 of 41

A comparison of MD-generated GAG 20-mer conformations to those of GAG 10-mers and to existing experimentally-determined conformations of monosaccharides and GAG oligosaccharides supported the use of 20-mer data for the construction of longer GAG polymers. For example, certain 4 IdoA conformations (namely C1 chair) were found more in unbound monosaccharide rings and terminal rings of GAG oligosaccharides than in central rings. Similarly, galactose occasionally sampled 4 non- C1 conformations in monosaccharide rings and short oligosaccharides, including nonsulfated keratan 10-mer in MD simulation, but boat/skew-boat conformations of galactose were decreasingly common in central rings of polymers of increasing length. This is in line with our observation that 4 only C1 conformations of galactose were sampled in nonsulfated keratan 20-mer MD. Additionally, some nonhelical glycosidic linkage conformations that caused a kink in the polymer chain, and thus contributed to compact GAG backbone conformations, were found more in GAG 20-mers than in short GAG oligosaccharides. Therefore, conformational landscapes from GAG 20-mer MD simulations likely provide a better representation of conformations of long GAG polymers than existing conformational landscapes of monosaccharides and GAG oligosaccharides. A comparison of backbone conformational analyses of 200-mers of different GAG types provided insights into structural features and conformational behaviors contributing to GAG polymer backbone flexibility. For example, 200-mer end-to-end distance distribution curves were qualitatively similar in nonsulfated dermatan (Figure 13), keratan (Figure 18), and chondroitin [33], whereas hyaluronan and nonsulfated heparan polymer end-to-end distance distributions (Figures7 and 23, respectively) showed an even higher tendency toward compact conformations with increasing polymer length than other nonsulfated GAGs. To find possible explanations for this, we compared observations from MD analyses of all GAG types. In hyaluronan 10- and 20-mer MD simulations, (1) GlcNAc conformations were similar to those in nonsulfated keratan and heparan MD, and (2) GlcA conformations were similar to those in nonsulfated chondroitin MD [33]. Furthermore, IdoA rings showed more flexibility in MD simulation of nonsulfated dermatan and heparan than GlcA rings in hyaluronan and chondroitin 2 MD [33]. However, boat/skew-boat conformations (except for SO) in IdoA did not appear to 1 2 4 cause more compact polymer backbone conformations than C4, SO, and C1 IdoA conformations, while boat/skew-boat GlcA ring conformations were more highly associated with more compact polymer backbone conformations in hyaluronan and chondroitin [33]. Additionally, in hyaluronan 10- and 20-mer MD simulations, (1) GlcNAcβ1-4GlcA linkages took on the same conformations as Galβ1-4GlcNAc linkages in nonsulfated keratan MD, IdoAα1-4GlcNAc linkages in nonsulfated heparan MD, and GalNAcβ1-4GlcA in nonsulfated chondroitin MD [33] (i.e., primarily φ, +ψ with − a secondary basin at φ, ψ) and (2) GlcAβ1-3GlcNAc linkages took on the same conformations − − as IdoAα1-3GalNAc in nonsulfated dermatan MD, GlcNAcβ1-3Gal in nonsulfated keratan MD, and GlcAβ1-3GalNAc linkages in nonsulfated chondroitin MD [33] (i.e., primarily φ, ψ), but with − − more conformations at φ, +ψ. All secondary and tertiary conformations (i.e., φ, ψ in 1–4 linkages − − − and φ, +ψ in 1–3 linkages) were nonhelical and caused a kink or slight bend in the polymer chain, − and were, therefore, associated with more compact conformations. The differences in energetic stability of secondary and tertiary linkage conformations between different GAG types can be explained by the adjacent monosaccharide structure. The major observation that is unique to hyaluronan is that both glycosidic linkage types take on more of these nonhelical secondary conformations in 10- and 20-mer MD simulations than any of nonsulfated dermatan, keratan, or chondroitin [33] in 10- and 20-mer MD simulations. Heparan is unique, in that it has all 1–4 linkages, while all other GAGs have alternating 1–3 and 1–4 linkages, and it contains α-GlcNAc, which gives unique conformations in GlcNAcα1-4IdoA linkages. These characteristics give nonsulfated heparan a tendency toward more coiled structures than other GAGs. Based on these observations and the fact that nonsulfated dermatan, keratan, and chondroitin showed more extended polymer backbone conformations than hyaluronan and nonsulfated heparan in MD simulations, it is likely that: (1) monosaccharide structure and conformational flexibility determine adjacent monosaccharide conformational flexibility; (2) although there is a much higher degree of ring Int. J. Mol. Sci. 2020, 21, 7699 33 of 41

Int. J. Mol. Sci. 2020, 21, x FOR PEER REVIEW 33 of 41 flexibility in IdoA than in GlcA, the flexibility of GlcA rings is more highly associated with GAG polymer with GAG polymer backbone flexibility than that of IdoA rings; and (3) nonhelical glycosidic linkage backbone flexibility than that of IdoA rings; and (3) nonhelical glycosidic linkage conformations, conformations, which cause kinks in GAG polymer chains, contribute to more compact GAG polymer which cause kinks in GAG polymer chains, contribute to more compact GAG polymer backbone backbone conformations and, thus, a higher degree of GAG polymer backbone flexibility. These are conformations and, thus, a higher degree of GAG polymer backbone flexibility. These are valuable valuable insights that would be difficult to obtain from conformational analyses of only solid-state insights that would be difficult to obtain from conformational analyses of only solid-state structures structures and MD-generated conformational ensembles of short GAG oligosaccharides. Other and MD-generated conformational ensembles of short GAG oligosaccharides. Other important insights important insights that can be gained from 3-D atomic-resolution conformational ensembles of GAG that can be gained from 3-D atomic-resolution conformational ensembles of GAG polymers include polymers include potential binding properties, and thus, predictions of binding poses with other potential binding properties, and thus, predictions of binding poses with other biomolecules of biomolecules of interest. Models of long-chain GAG polymers (Figure 24 and [33]) can help interest. Models of long-chain GAG polymers (Figure 24 and [33]) can help characterize complete characterize complete PGs and GAG-mediated complexes between multiple biomolecules, and PGs and GAG-mediated complexes between multiple biomolecules, and consequently, improve our consequently, improve our understanding of the bioactivity and function of GAG biopolymers in understanding of the bioactivity and function of GAG biopolymers in animal tissue. animal tissue.

Figure 24. Constructed 200-mer conformations with probable end-to-end distances for each GAG type: Figure 24. Constructed 200-mer conformations with probable end-to-end distances for each GAG (a) hyaluronan, (b) nonsulfated dermatan, (c) nonsulfated keratan, (d) nonsulfated heparan; n.b. depth type: (a) hyaluronan, (b) nonsulfated dermatan, (c) nonsulfated keratan, (d) nonsulfated heparan; n.b. is not shown, so some conformations appear to have overlap. depth is not shown, so some conformations appear to have overlap.

Int. J. Mol. Sci. 2020, 21, 7699 34 of 41

Supplementary Materials: The following are available online http://www.mdpi.com/1422-0067/21/20/7699/s1, Table S1: Most Probable End-to-End Distances (d) in MD-Generated 20-mer Conformations with Glycosidic Linkage Conformations in Secondary Basins, Table S2: Percent of Occurrences of Different IdoA Ring Puckers in Nonsulfated Dermatan MD Simulations, Table S3: Percent of Occurrences of Different IdoA Ring Puckers in Nonsulfated Heparan MD Simulations, Figure S1: Constructed hyaluronan 20-mer conformation with a pierced ring, Figure S2: Scatterplots of radius of gyration as a function of end-to-end distance in MD-generated and constructed hyaluronan ensembles, Figure S3: System potential energy probability distribution of the MD-generated hyaluronan 20-mer ensemble, Figure S4: C-P plots and C-P parameter θ timeseries for each GlcNAc monosaccharide ring in the MD-generated hyaluronan 20-mer ensemble, Figure S5: C-P plots and C-P parameter θ timeseries for each GlcA monosaccharide ring in the MD-generated hyaluronan 20-mer ensemble, Figure S6: Scatterplot of radius of 4 gyration as a function of end-to-end distance in MD-generated hyaluronan 20-mer conformations with non- C1 ring puckers, Figure S7: ∆G(φ,ψ) plots for each glycosidic linkage in the MD-generated hyaluronan 20-mer ensemble, Figure S8: MD snapshots of hyaluronan 20-mer GlcAβ1-3GlcNAc glycosidic linkages with dihedrals in different basins and end-to-end distance distributions of 20-mer conformations with linkages in secondary basin, 4 Figure S9: ∆G(φ,ψ) plots for glycosidic linkages flanking non- C1 ring puckers in the MD-generated hyaluronan 20-mer ensemble, Figure S10: MD snapshots of hyaluronan 20-mer GlcNAcβ1-4GlcA glycosidic linkages with dihedrals in different basins and end-to-end distance distributions of 20-mer conformations with linkages in secondary basin, Figure S11: C-P plots for GlcNAc and GlcA in the constructed hyaluronan 20-mer ensemble, Figure S12: ∆G(φ, ψ) for aggregated glycosidic linkage data from the constructed hyaluronan 20-mer ensemble, Figure S13: Scatterplots of radius of gyration as a function of end-to-end distance in MD-generated and constructed nonsulfated dermatan ensembles, Figure S14: C-P parameter θ timeseries for each GalNAc monosaccharide ring in the MD-generated nonsulfated dermatan 20-mer ensemble, Figure S15: End-to-end distance distributions of MD-generated nonsulfated dermatan 20-mer conformations with boat/skew-boat ring puckers that cause a kink in 2 the polymer chain and SO conformations, Figure S16: C-P plots and C-P parameter θ timeseries for each IdoA monosaccharide ring in the MD-generated nonsulfated dermatan 20-mer ensemble, Figure S17: C-P plots and C-P parameter θ timeseries for each IdoA monosaccharide ring in the MD-generated nonsulfated dermatan 10-mer ensemble, Figure S18: C-P plots for GalNAc and IdoA in the constructed nonsulfated dermatan 20-mer ensemble, Figure S19: ∆G(φ, ψ) for aggregated glycosidic linkage data from the constructed nonsulfated dermatan 20-mer ensemble, Figure S20: Scatterplots of radius of gyration as a function of end-to-end distance in MD-generated and constructed nonsulfated keratan ensembles, Figure S21: C-P plots and C-P parameter θ timeseries for each GlcNAc monosaccharide ring in the MD-generated nonsulfated keratan 20-mer ensemble, Figure S22: Scatterplot of radius of gyration as a function of end-to-end distance in MD-generated nonsulfated keratan 20-mer conformations with 4 non- C1 ring puckers, Figure S23: MD snapshots of nonsulfated keratan 20-mer Galβ1-4GlcNAc glycosidic linkages with dihedrals in different basins and end-to-end distance distributions of 20-mer conformations with linkages in secondary and tertiary basins, Figure S24: MD snapshots of nonsulfated keratan 20-mer GlcNAcβ1-3Gal glycosidic linkages with dihedrals in different basins and end-to-end distance distributions of 20-mer conformations with linkages in secondary and tertiary basins, Figure S25: C-P plots and C-P parameter θ timeseries for each Gal monosaccharide ring in the MD-generated nonsulfated keratan 10-mer ensemble, Figure S26: C-P plots for GlcNAc and Gal in the constructed nonsulfated keratan 20-mer ensemble, Figure S27: ∆G(φ, ψ) for aggregated glycosidic linkage data from the constructed nonsulfated keratan 20-mer ensemble, Figure S28: Scatterplots of radius of gyration as a function of end-to-end distance in MD-generated and constructed nonsulfated heparan ensembles, Figure S29: C-P parameter θ timeseries for each IdoA monosaccharide ring in the MD-generated nonsulfated heparan 20-mer ensemble, Figure S30: End-to-end distance distributions of MD-generated nonsulfated heparan 20-mer conformations with boat/skew-boat ring puckers that cause a kink in the polymer chain and 2 SO conformations, Figure S31: Snapshot of nonsulfated heparan 20-mer MD-generated ensemble highlighting GlcNAcα1-4IdoA linkages, Figure S32: End-to-end distance distributions of MD-generated nonsulfated heparan 20-mer conformations with linkage dihedrals in secondary basins, Figure S33: ∆G(φ,ψ) plots for IdoAα1-4GlcNAc linkages flanking different IdoA conformations in the MD-generated nonsulfated heparan 20-mer ensemble, Figure S34: C-P plots for GlcNAc and IdoA in the constructed nonsulfated heparan 20-mer ensemble, Figure S35: ∆G(φ, ψ) for aggregated glycosidic linkage data from the constructed nonsulfated heparan 20-mer ensemble, Figure S36: Bond potential energy probability distributions from constructed hyaluronan ensembles, Figure S37: Bond potential energy probability distributions from constructed nonsulfated dermatan ensembles, Figure S38: Bond potential energy probability distributions from constructed nonsulfated keratan ensembles, Figure S39: Bond potential energy probability distributions from constructed nonsulfated heparan ensembles. Author Contributions: Conceptualization, E.K.W. and O.G.; methodology, E.K.W. and O.G.; software, E.K.W. and O.G.; validation E.K.W. and O.G.; formal analysis, E.K.W.; investigation E.K.W. and O.G.; resources, O.G.; data curation, E.K.W., D.M., and O.G.; writing—original draft preparation, E.K.W.; writing—review and editing, E.K.W., D.M., and O.G.; visualization, E.K.W.; supervision, O.G.; project administration, O.G.; funding acquisition, O.G. All authors have read and agree to the published version of the manuscript. Funding: This research and the APC were funded by the National Science Foundation, grant number MCB-1453529 to O.G. Acknowledgments: We would like to thank Richard Venable of the National Institutes of Health for sharing the Cremer-Pople parameter calculation code, modified from the original version by Tell Tuttle of the University of Strathclyde. Int. J. Mol. Sci. 2020, 21, 7699 35 of 41

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.

Abbreviations

PG Proteoglycan GAG Glycosaminoglycan MD Molecular dynamics GlcA Glucuronate IdoA Iduronate Gal Galactose GlcNAc N-acetylglucosamine GalNAc N-acetylgalactosamine

References

1. Yoneda, A.; Couchman, J.R. Regulation of cytoskeletal organization by syndecan transmembrane proteoglycans. Matrix Biol. 2003, 22, 25–33. [CrossRef] 2. Kolset, S.O.; Prydz, K.; Pejler, G. Intracellular proteoglycans. Biochem. J. 2004, 379, 217–227. [CrossRef] [PubMed] 3. Mizumoto, S.; Fongmoon, D.; Sugahara, K. Interaction of chondroitin sulfate and dermatan sulfate from various biological sources with heparin-binding growth factors and cytokines. Glycoconj. J. 2012, 30, 619–632. [CrossRef][PubMed] 4. Sugahara, K.; Mikami, T.; Uyama, T.; Mizuguchi, S.; Nomura, K.; Kitagawa, H. Recent advances in the structural biology of chondroitin sulfate and dermatan sulfate. Curr. Opin. Struct. Biol. 2003, 13, 612–620. [CrossRef][PubMed] 5. Sugahara, K.; Mikami, T. Chondroitin/dermatan sulfate in the central nervous system. Curr. Opin. Struct. Biol. 2007, 17, 536–545. [CrossRef] 6. Kawashima, H.; Atarashi, K.; Hirose, M.; Hirose, J.; Yamada, S.; Sugahara, K.; Miyasaka, M. Oversulfated chondroitin/dermatan sulfates containing GlcAβ1/IdoAα1-3GalNAc(4,6-O-disulfate) interact with L- and P-selectin and chemokines. J. Biol. Chem. 2002, 277, 12921–12930. [CrossRef] 7. Lander, A.D.; Selleck, S.B. The elusive functions of proteoglycans: In vivo veritas. J. Cell Biol. 2000, 148, 227–232. [CrossRef] 8. Stallcup, W.B.; Dahlin, K.; Healy, P. Interaction of the NG2 chondroitin sulfate proteoglycan with type VI collagen. J. Cell Biol. 1990, 111, 3177–3188. [CrossRef] 9. Van Susante, J.L.C.; Pieper, J.; Buma, P.; van Kuppevelt, T.H.; van Beuningen, H.; van Der Kraan, P.M.; Veerkamp, J.H.; van den Berg, W.B.; Veth, R.P.H. Linkage of chondroitin-sulfate to type I collagen scaﬀolds stimulates the bioactivity of seeded chondrocytes in vitro. Biomaterials 2001, 22, 2359–2369. [CrossRef] 10. Streit, A.; Nolte, C.; Rásony, T.; Schachner, M. Interaction of astrochondrin with extracellular matrix components and its involvement in astrocyte process formation and cerebellar granule cell migration. J. Cell Biol. 1993, 120, 799–814. [CrossRef] 11. Djerbal, L.; Lortat-Jacob, H.; Kwok, J. Chondroitin sulfates and their binding molecules in the central nervous system. Glycoconj. J. 2017, 34, 363–376. [CrossRef][PubMed] 12. Forsten-Williams, K.; Chu, C.L.; Fannon, M.; Buczek-Thomas, J.A.; Nugent, M.A. Control of growth factor networks by heparan sulfate proteoglycans. Ann. Biomed. Eng. 2008, 36, 2134–2148. [CrossRef][PubMed] 13. Bhavanandan, V.P.; Davidson, E.A. Mucopolysaccharides associated with nuclei of cultured mammalian cells. Proc. Natl. Acad. Sci. USA 1975, 72, 2032–2036. [CrossRef] 14. Fedarko, N.S.; Conrad, H.E. A unique heparan sulfate in the nuclei of hepatocytes: Strucural changes with the growth state of the cells. J. Cell Biol. 1986, 102, 587–599. [CrossRef][PubMed] 15. Ishihara, M.; Fedarko, N.S.; Conrad, H.E. Transport of heparan sulfate into the nuclei of hepatocytes. J. Biol. Chem. 1986, 261, 13575–13580. Int. J. Mol. Sci. 2020, 21, 7699 36 of 41

16. Tumova, S.; Hatch, B.A.; Law, D.J.; Bame, K.J. Basic fibroblast growth factor does not prevent heparan sulphate proteoglycan catabolism in intact cells, but it alters the distribution of the glycosaminoglycan degradation products. Biochem. J. 1999, 337, 471–481. [CrossRef][PubMed] 17. Kjellén, L.; Lindahl, U. Specificity of glycosaminoglycan-protein interactions. Curr. Opin. Struct. Biol. 2018, 50, 101–108. [CrossRef][PubMed] 18. Sharif, M.; George, E.; Shepstone, L.; Knudson, W.; Thonar, E.J.M.; Cushnaghan, J.; Dieppe, P. Serum hyaluronic acid level as a predictor of disease progression in osteoarthritis of the knee. Arthritis Rheum. 1995, 38, 760–767. [CrossRef] 19. Ghosh, P. The role of hyaluronic acid (hyaluronan) in health and disease: Interactions with cells, cartilage and components of synovial fluid. Clin. Exp. Rheum. 1994, 12, 75–82. 20. Mizumoto, S.; Kosho, T.; Hatamochi, A.; Honda, T.; Yamaguchi, T.; Okamoto, N.; Miyake, N.; Yamada, S.; Sugahara, K. Defect in dermatan sulfate in urine of patients with Ehlers-Danlos syndrome caused by a CHST14/D4ST1 deficiency. Clin. Biochem. 2017, 50, 670–677. [CrossRef] 21. Kosho, T. CHST14/D4ST1 deficiency: New form of Ehlers–Danlos syndrome. Pediatr. Int. 2016, 58, 88–99. [CrossRef] 22. Lindahl, B.; Eriksson, L.; Spillmann, D.; Caterson, B.; Lindahl, U. Selective loss of cerebral keratan sulfate in Alzheimer’s disease. J. Biol. Chem. 1996, 271, 16991–16994. [CrossRef][PubMed] 23. Martin, L.; Schmitz, S.; De Santis, R.; Doemming, S.; Haase, H.; Hoeger, J.; Heinbockel, L.; Brandenburg, K.; Marx, G.; Schuerholz, T. Peptide 19-2.5 inhibits heparan sulfate-triggered inflammation in murine cardiomyocytes stimulated with human sepsis serum. PLoS ONE 2015, 10, e0127584. [CrossRef][PubMed] 24. Schmidt, E.P.; Overdier, K.H.; Sun, X.; Lin, L.; Liu, X.; Yang, Y.; Ammons, L.A.; Hiller, T.D.; Suflita, M.A.; Yu, Y. Urinary glycosaminoglycans predict outcomes in septic shock and acute respiratory distress syndrome. Am. J. Resp. Crit. Care 2016, 194, 439–449. [CrossRef][PubMed] 25. Gallagher, J. Fell-Muir Lecture: Heparan sulphate and the art of cell regulation: A polymer chain conducts the protein orchestra. Int. J. Exp. Pathol. 2015, 96, 203–231. [CrossRef][PubMed] 26. Shriver, Z.; Raguram, S.; Sasisekharan, R. Glycomics: A pathway to a class of new and improved therapeutics. Nat. Rev. Drug Discov. 2004, 3, 863–873. [CrossRef][PubMed] 27. Trottein, F.; Schaffer, L.; Ivanov, S.; Paget, C.; Vendeville, C.; Cazet, A.; Groux-Degroote, S.; Lee, S.; Krzewinski-Recchi, M.-A.; Faveeuw, C.; et al. Glycosyltransferase and sulfotransferase gene expression profiles in human monocytes, dendritic cells and macrophages. Glycoconj. J. 2009, 26, 1259–1274. [CrossRef] 28. Gandhi, N.S.; Mancera, R.L. The Structure of glycosaminoglycans and their interactions with proteins. Chem. Biol. Drug Des. 2008, 72, 455–482. [CrossRef] 29. Casu, B.; Petitou, M.; Provasoli, M.; Sinay, P. Conformational flexibility: A new concept for explaining binding and biological properties of iduronic acid-containing glycosaminoglycans. Trends Biochem. Sci. 1988, 13, 221–225. [CrossRef] 30. Mulloy, B.; Forster, M.J.; Jones, C.; Drake, A.F.; Johnson, E.A.; Davies, D.B. The effect of variation of substitution on the solution conformation of heparin: A spectroscopic and molecular modelling study. Carbohydr. Res. 1994, 255, 1–26. [CrossRef] 31. Zamparo, O.; Comper, W.D. The hydrodynamic frictional coefficient of polysaccharides: The role of the glycosidic linkage. Carbohydr. Res. 1991, 212, 193–200. [CrossRef] 32. Samsonov, S.A.; Gehrcke, J.-P.; Pisabarro, M.T. Flexibility and explicit solvent in molecular-dynamics-based docking of protein–glycosaminoglycan systems. J. Chem. Inf. Model. 2014, 54, 582–592. [CrossRef][PubMed] 33. Whitmore, E.K.; Vesenka, G.; Sihler, H.; Guvench, O. Efficient Construction of Atomic-Resolution Models of Non-Sulfated Chondroitin Glycosaminoglycan Using Molecular Dynamics Data. Biomolecules 2020, 10, 537. [CrossRef][PubMed] 34. Toyoda, H.; Kinoshita-Toyoda, A.; Selleck, S.B. Structural analysis of glycosaminoglycans in Drosophila and Caenorhabditis elegans and demonstration that tout-velu, a drosophila gene related to EXT tumor suppressors, affects heparan sulfate in vivo. J. Biol. Chem. 2000, 275, 2269–2275. [CrossRef][PubMed] 35. Yang, H.O.; Gunay, N.S.; Toida, T.; Kuberan, B.; Yu, G.; Kim, Y.S.; Linhardt, R.J. Preparation and structural determination of dermatan sulfate-derived oligosaccharides. Glycobiology 2000, 10, 1033–1039. [CrossRef] [PubMed] 36. Zaia, J.; Costello, C.E. Compositional analysis of glycosaminoglycans by electrospray mass spectrometry. Anal. Chem. 2001, 73, 233–239. [CrossRef][PubMed] Int. J. Mol. Sci. 2020, 21, 7699 37 of 41

37. Shao, C.; Zhang, F.; Kemp, M.M.; Linhardt, R.J.; Waisman, D.M.; Head, J.F.; Seaton, B.A. Crystallographic analysis of calcium-dependent heparin binding to annexin A2. J. Biol. Chem. 2006, 281, 31689–31695. [CrossRef] 38. Capila, I.; Hernáiz, M.a.J.; Mo, Y.D.; Mealy, T.R.; Campos, B.; Dedman, J.R.; Linhardt, R.J.; Seaton, B.A. Annexin V–heparin oligosaccharide complex suggests heparan sulfate–mediated assembly on cell surfaces. Structure 2001, 9, 57–64. [CrossRef] 39. Dementiev, A.; Petitou, M.; Herbert, J.-M.; Gettins, P.G.W. The ternary complex of antithrombin–anhydrothrombin–heparin reveals the basis of inhibitor specificity. Nat. Struct. Mol. Biol. 2004, 11, 863–867. [CrossRef][PubMed] 40. Li, W.; Johnson, D.J.D.; Esmon, C.T.; Huntington, J.A. Structure of the antithrombin–thrombin–heparin ternary complex reveals the antithrombotic mechanism of heparin. Nat. Struct. Mol. Biol. 2004, 11, 857–862. [CrossRef][PubMed] 41. Li, Z.; Kienetz, M.; Cherney, M.M.; James, M.N.G.; Brömme, D. The crystal and molecular structures of a cathepsin K:chondroitin sulfate complex. J. Mol. Biol. 2008, 383, 78–91. [CrossRef] 42. Imberty, A.; Lortat-Jacob, H.; Pérez, S. Structural view of glycosaminoglycan–protein interactions. Carbohydr. Res. 2007, 342, 430–439. [CrossRef][PubMed] 43. Ferro, D.R.; Provasoli, A.; Ragazzi, M.; Torri, G.; Casu, B.; Gatti, G.; Jacquinet, J.C.; Sinay, P.; Petitou, M.; Choay, J. Evidence for conformational equilibrium of the sulfated L-iduronate residue in heparin and in synthetic heparin mono- and oligo-saccharides: NMR and force-field studies. J. Am. Chem. Soc. 1986, 108, 6773–6778. [CrossRef] 44. Bossennec, V.; Petitou, M.; Perly, B. 1H-n.m.r. investigation of naturally occurring and chemically oversulphated dermatan sulphates. Identification of minor monosaccharide residues. Biochem. J. 1990, 267, 625–630. [CrossRef][PubMed] 45. Ferro, D.R.; Provasoli, A.; Ragazzi, M.; Casu, B.; Torri, G.; Bossennec, V.; Perly, B.; Sinaÿ, P.; Petitou, M.; Choay, J. Conformer populations of l-iduronic acid residues in glycosaminoglycan sequences. Carbohydr. Res. 1990, 195, 157–167. [CrossRef] 46. Yamada, S.; Yamane, Y.; Sakamoto, K.; Tsuda, H.; Sugahara, K. Structural determination of sulfated tetrasaccharides and hexasaccharides containing a rare disaccharide sequence, -3GalNAc(4,6-disulfate)beta1-4IdoAalpha1-, isolated from porcine intestinal dermatan sulfate. Eur. J. Biochem. 1998, 258, 775–783. [CrossRef] 47. Silipo, A.; Zhang, Z.; Cañada, F.J.; Molinaro, A.; Linhardt, R.J.; Jiménez-Barbero, J. Conformational analysis of a dermatan sulfate-derived tetrasaccharide by NMR, molecular modeling, and residual dipolar couplings. Chembiochem 2008, 9, 240–252. [CrossRef] 48. Sattelle, B.M.; Shakeri, J.; Cliff, M.J.; Almond, A. Proteoglycans and their heterogeneous glycosaminoglycans at the atomic scale. Biomacromolecules 2015, 16, 951–961. [CrossRef] 49. Almond, A.; Sheehan, J.K. Glycosaminoglycan conformation: Do aqueous molecular dynamics simulations agree with x-ray fiber diffraction? Glycobiology 2000, 10, 329–338. [CrossRef] 50. Gandhi, N.S.; Mancera, R.L. Can current force fields reproduce ring puckering in 2-O-sulfo-α-l-iduronic acid? A molecular dynamics simulation study. Carbohydr. Res. 2010, 345, 689–695. [CrossRef] 51. Sattelle, B.M.; Hansen, S.U.; Gardiner, J.; Almond, A. Free energy landscapes of iduronic acid and related monosaccharides. J. Am. Chem. Soc. 2010, 132, 13132–13134. [CrossRef] 52. Balogh, G.; Gyöngyö;si, T.S.; Timári, I.; Herczeg, M.; Borbás, A.; Fehér, K.; Kövér, K.E. Comparison of carbohydrate force fields using Gaussian Accelerated Molecular Dynamics simulations and development of force field parameters for heparin-analogue pentasaccharides. J. Chem. Inf. Model. 2019, 59, 4855–4867. [CrossRef][PubMed] 53. Ng, C.; Nandha Premnath, P.;Guvench, O. Rigidity and flexibility in the tetrasaccharide linker of proteoglycans from atomic-resolution molecular simulation. J. Comput. Chem. 2017, 38, 1438–1446. [CrossRef][PubMed] 54. Guvench, O. Revealing the mechanisms of protein disorder and N-glycosylation in CD44-hyaluronan binding using molecular simulation. Front. Immunol. 2015, 6, 305. [CrossRef][PubMed] 55. Faller, C.E.; Guvench, O. Sulfation and cation effects on the conformational properties of the glycan backbone of chondroitin sulfate disaccharides. J. Phys. Chem. B 2015, 119, 6063–6073. [CrossRef][PubMed] 56. Favreau, A.J.; Faller, C.E.; Guvench, O. CD44 receptor unfolding enhances binding by freeing basic amino acids to contact carbohydrate ligand. Biophys. J. 2013, 105, 1217–1226. [CrossRef][PubMed] Int. J. Mol. Sci. 2020, 21, 7699 38 of 41

57. Guvench, O.; Mallajosyula, S.S.; Raman, E.P.; Hatcher, E.; Vanommeslaeghe, K.; Foster, T.J.; Jamison, F.W., II; Mackerell, A.D., Jr. CHARMM additive all-atom force field for carbohydrate derivatives and its utility in polysaccharide and carbohydrate-protein modeling. J. Chem. Theory Comput. 2011, 7, 3162–3180. [CrossRef] 58. Brannigan, G.; Lin, L.C.; Brown, F.L. Implicit solvent simulation models for biomembranes. Eur. Biophys. J. 2006, 35, 104–124. [CrossRef] 59. Srinivas, G.; Cheng, X.; Smith, J.C. A solvent-free coarse grain model for crystalline and amorphous cellulose fibrils. J. Chem. Theory Comput. 2011, 7, 2539–2548. [CrossRef] 60. Ingólfsson, H.I.; Lopez, C.A.; Uusitalo, J.J.; de Jong, D.H.; Gopal, S.M.; Periole, X.; Marrink, S.J. The power of coarse graining in biomolecular simulations. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4, 225–248. [CrossRef] 61. Guvench, O.; Greene, S.N.; Kamath, G.; Brady, J.W.; Venable, R.M.; Pastor, R.W.; Mackerell, A.D., Jr. Additive empirical force field for hexopyranose monosaccharides. J. Comput. Chem. 2008, 29, 2543–2564. [CrossRef] [PubMed] 62. Guvench, O.; Hatcher, E.R.; Venable, R.M.; Pastor, R.W.; Mackerell, A.D. CHARMM additive all-atom force field for glycosidic linkages between hexopyranoses. J. Chem. Theory Comput. 2009, 5, 2353–2370. [CrossRef] [PubMed] 63. Mallajosyula, S.S.; Guvench, O.; Hatcher, E.; Mackerell, A.D., Jr. CHARMM additive all-atom force field for phosphate and sulfate linked to carbohydrates. J. Chem. Theory Comput. 2012, 8, 759–776. [CrossRef] [PubMed] 64. Hascall, V.C.; Heinegård, D. Aggregation of cartilage proteoglycans II. Oligosaccharide competitors of the proteoglycan-hyaluronic acid interaction. J. Biol. Chem. 1974, 249, 4242–4249. [PubMed] 65. Winter, W.; Smith, P.; Arnott, S. Hyaluronic acid: Structure of a fully extended 3-fold helical sodium salt and comparison with the less extended 4-fold helical forms. J. Mol. Biol. 1975, 99, 219–235. [CrossRef] 66. Sheehan, J.; Gardner, K.; Atkins, E. Hyaluronic acid: A double-helical structure in the presence of potassium at low pH and found also with the cations ammonium, rubidium and caesium. J. Mol. Biol. 1977, 117, 113–135. [CrossRef] 67. Almond, A.; Brass, A.; Sheehan, J.K. Dynamic exchange between stabilized conformations predicted for hyaluronan tetrasaccharides: Comparison of molecular dynamics simulations with available NMR data. Glycobiology 1998, 8, 973–980. [CrossRef] 68. Almond, A.; Sheehan, J.K.; Brass, A. Molecular dynamics simulations of the two disaccharides of hyaluronan in aqueous solution. Glycobiology 1997, 7, 597–604. [CrossRef] 69. Gribbon, P.; Heng, B.C.; Hardingham, T.E. The molecular basis of the solution properties of hyaluronan investigated by confocal fluorescence recovery after photobleaching. Biophys. J. 1999, 77, 2210–2216. [CrossRef] 70. Atkins, E.; Meader, D.; Scott, J. Model for hyaluronic acid incorporating four intramolecular hydrogen bonds. Int. J. Biol. Macromol. 1980, 2, 318–319. [CrossRef] 71. Scott, J.E. Supramolecular organization of extracellular matrix glycosaminoglycans, in vitro and in the tissues. FASEB J. 1992, 6, 2639–2645. [CrossRef] 72. Scott, J.E.; Cummings, C.; Brass, A.; Chen, Y. Secondary and tertiary structures of hyaluronan in aqueous solution, investigated by rotary shadowing-electron microscopy and computer simulation. Biochem. J. 1991, 274, 699–705. [CrossRef][PubMed] 73. Scott, J.; Heatley, F.; Moorcroft, D.; Olavesen, A. Secondary structures of hyaluronate and chondroitin sulphates. A 1H nmr study of NH signals in dimethyl sulphoxide solution. Biochem. J. 1981, 199, 829. [CrossRef][PubMed] 74. Singh, A.; Montgomery, D.; Xue, X.; Foley, B.L.; Woods, R.J. GAG Builder: A web-tool for modeling 3D structures of glycosaminoglycans. Glycobiology 2019, 29, 515–518. [CrossRef][PubMed] 75. Engelsen, S.B.; Hansen, P.I.; Perez, S. POLYS 2.0: An open source software package for building three-dimensional structures of polysaccharides. Biopolymers 2014, 101, 733–743. [CrossRef] 76. Kuttel, M.M.; Ståhle, J.; Widmalm, G. CarbBuilder: Software for building molecular models of complex oligo-and polysaccharide structures. J. Comput. Chem. 2016, 37, 2098–2105. [CrossRef] 77. Clerc, O.; Deniaud, M.; Vallet, S.D.; Naba, A.; Rivet, A.; Perez, S.; Thierry-Mieg, N.; Ricard-Blum, S. MatrixDB: Integration of new data with a focus on glycosaminoglycan interactions. Nucleic Acids Res. 2018, 47, D376–D381. [CrossRef][PubMed] Int. J. Mol. Sci. 2020, 21, 7699 39 of 41

78. Clerc, O.; Mariethoz, J.; Rivet, A.; Lisacek, F.; Pérez, S.; Ricard-Blum, S. A pipeline to translate glycosaminoglycan sequences into 3D models. Application to the exploration of glycosaminoglycan conformational space. Glycobiology 2018, 29, 36–44. [CrossRef] 79. Jo, S.; Kim, T.; Iyer, V.G.; Im, W. CHARMM-GUI: A web-based graphical user interface for CHARMM. J. Comput. Chem. 2008, 29, 1859–1865. [CrossRef][PubMed] 80. Jo, S.; Song, K.C.; Desaire, H.; MacKerell, A.D., Jr.; Im, W. Glycan Reader: Automated sugar identification and simulation preparation for carbohydrates and glycoproteins. J. Comput. Chem. 2011, 32, 3135–3141. [CrossRef] 81. Park, S.-J.; Lee, J.; Patel, D.S.; Ma, H.; Lee, H.S.; Jo, S.; Im, W. Glycan Reader is improved to recognize most sugar types and chemical modifications in the Protein Data Bank. Bioinformatics 2017, 33, 3051–3057. [CrossRef][PubMed] 82. Park, S.-J.; Lee, J.; Qi, Y.; Kern, N.R.; Lee, H.S.; Jo, S.; Joung, I.; Joo, K.; Lee, J.; Im, W. CHARMM-GUI glycan modeler for modeling and simulation of carbohydrates and glycoconjugates. Glycobiology 2019, 29, 320–331. [CrossRef][PubMed] 83. Brooks, B.R.; Bruccoleri, R.E.; Olafson, B.D.; States, D.J.; Swaminathan, S.; Karplus, M. CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J. Comput. Chem. 1983, 4, 187–217. [CrossRef] 84. Brooks, B.R.; Brooks, C.L., III; Mackerell, A.D., Jr.; Nilsson, L.; Petrella, R.J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; et al. CHARMM: The biomolecular simulation program. J. Comput. Chem. 2009, 30, 1545–1614. [CrossRef] 85. MacKerell, A.D., Jr.; Brooks, B.; Brooks, C.L., III; Nilsson, L.; Roux, B.; Won, Y.; Karplus, M. CHARMM: The energy function and its parameterization with an overview of the program. In Encyclopedia of Computational Chemistry; John Wiley and Sons, Ltd.: New York, NY, USA, 1998; Volume 1, pp. 271–277. 86. Jorgensen, W.L.; Chandrasekhar, J.; Madura, J.D.; Impey, R.W.; Klein, M.L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926–935. [CrossRef] 87. Durell, S.R.; Brooks, B.R.; Ben-Naim, A. Solvent-induced forces between two hydrophilic groups. J. Phys. Chem. 1994, 98, 2198–2202. [CrossRef] 88. Beglov, D.; Roux, B. Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations. J. Chem. Phys. 1994, 100, 9050–9063. [CrossRef] 89. Phillips, J.C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R.D.; Kale, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781–1802. [CrossRef] [PubMed] 90. Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33–38. [CrossRef] 91. Cremer, D.; Pople, J. General definition of ring puckering coordinates. J. Am. Chem. Soc. 1975, 97, 1354–1358. [CrossRef] 92. Banerji, S.; Wright, A.J.; Noble, M.; Mahoney, D.J.; Campbell, I.D.; Day, A.J.; Jackson, D.G. Structures of the CD44–hyaluronan complex provide insight into a fundamental carbohydrate-protein interaction. Nat. Struct. Mol. Biol. 2007, 14, 234. [CrossRef] 93. Jedrzejas, M.J.; Mello, L.V.; de Groot, B.L.; Li, S. Mechanism of hyaluronan degradation by Streptococcus pneumoniae Hyaluronate Lyase. J. Biol. Chem. 2002, 277, 28287–28297. [CrossRef][PubMed] 94. Mello, L.V.; de Groot, B.L.; Li, S.; Jedrzejas, M.J. Structure and flexibility of Streptococcus agalactiae hyaluronate lyase complex with its substrate. J. Biol. Chem. 2002, 277, 36678–36688. [CrossRef][PubMed] 95. Marković-Housley, Z.; Miglierini, G.; Soldatova, L.; Rizkallah, P.J.; Müller, U.; Schirmer, T. Crystal structure of hyaluronidase, a major allergen of bee venom. Structure 2000, 8, 1025–1035. [CrossRef] 96. Tashima, T.; Nagatoishi, S.; Caaveiro, J.M.; Nakakido, M.; Sagara, H.; Kusano-Arai, O.; Iwanari, H.; Mimuro, H.; Hamakubo, T.; Ohnuma, S.-i. Molecular basis for governing the morphology of type-I collagen fibrils by Osteomodulin. Commun. Biol. 2018, 1, 1–10. [CrossRef] 97. Paracuellos, P.; Kalamajski, S.; Bonna, A.; Bihan, D.; Farndale, R.W.; Hohenester, E. Structural and functional analysis of two small leucine-rich repeat proteoglycans, fibromodulin and chondroadherin. Matrix Biol. 2017, 63, 106–116. [CrossRef][PubMed] 98. Ohto, U.; Usui, K.; Ochi, T.; Yuki, K.; Satow, Y.; Shimizu, T. Crystal structure of human β-galactosidase structural basis of gm1 gangliosidosis and morquio b diseases. J. Biol. Chem. 2012, 287, 1801–1812. [CrossRef] Int. J. Mol. Sci. 2020, 21, 7699 40 of 41

99. Scally, S.W.; Petersen, J.; Law, S.C.; Dudek, N.L.; Nel, H.J.; Loh, K.L.; Wijeyewickrema, L.C.; Eckle, S.B.; van Heemst, J.; Pike, R.N. A molecular basis for the association of the HLA-DRB1 locus, citrullination, and rheumatoid arthritis. J. Exp. Med. 2013, 210, 2569–2582. [CrossRef][PubMed] 100. Sattelle, B.M.; Almond, A. Is N-acetyl-d-glucosamine a rigid 4C1 chair? Glycobiology 2011, 21, 1651–1662. [CrossRef] 101. Siciˇnska,W.; Adams, B.; Lerner, L. A detailed 1H and 13C NMR study of a repeating disaccharide of hyaluronan: The effects of temperature and counterion type. Carbohydr. Res. 1993, 242, 29–51. [CrossRef] 102. Gargiulo, V.; Morando, M.A.; Silipo, A.; Nurisso, A.; Pérez, S.; Imberty, A.; Cañada, F.J.; Parrilli, M.; Jiménez-Barbero, J.; De Castro, C. Insights on the conformational properties of hyaluronic acid by using NMR residual dipolar couplings and MD simulations. Glycobiology 2010, 20, 1208–1216. [CrossRef][PubMed] 103. Ikemizu, S.; Sparks, L.M.; van der Merwe, P.A.; Harlos, K.; Stuart, D.I.; Jones, E.Y.; Davis, S.J. Crystal structure of the CD2-binding domain of CD58 (lymphocyte function-associated antigen 3) at 1.8-Å resolution. Proc. Natl. Acad. Sci. USA 1999, 96, 4289–4294. [CrossRef][PubMed] 104. Chang, C.; Magracheva, E.; Kozlov, S.; Fong, S.; Tobin, G.; Kotenko, S.; Wlodawer, A.; Zdanov, A. Crystal structure of interleukin-19 defines a new subfamily of helical cytokines. J. Biol. Chem. 2003, 278, 3308–3313. [CrossRef][PubMed] 105. Xu, R.; McBride, R.; Paulson, J.C.; Basler, C.F.; Wilson, I.A. Structure, receptor binding, and antigenicity of influenza virus hemagglutinins from the 1957 H2N2 pandemic. J. Virol. 2010, 84, 1715–1721. [CrossRef] [PubMed] 106. Maveyraud, L.; Niwa, H.; Guillet, V.; Svergun, D.I.; Konarev, P.V.; Palmer, R.A.; Peumans, W.J.; Rougé, P.; Van Damme, E.J.; Reynolds, C.D. Structural basis for sugar recognition, including the Tn carcinoma antigen, by the lectin SNA-II from Sambucus nigra. Proteins Struct. Funct. Bioinf. 2009, 75, 89–103. [CrossRef] [PubMed] 107. Alibay, I.; Bryce, R.A. Ring puckering landscapes of glycosaminoglycan-related monosaccharides from molecular dynamics simulations. J. Chem. Inf. Model. 2019, 59, 4729–4741. [CrossRef] 108. Alibay, I.; Burusco, K.K.; Bruce, N.J.; Bryce, R.A. Identification of rare Lewis oligosaccharide conformers in aqueous solution using enhanced sampling molecular dynamics. J. Phys. Chem. B 2018, 122, 2462–2474. [CrossRef] 109. Nyerges, B.; Kovacs, A. Density functional study of the conformational space of 4C1 D-glucuronic acid. J. Phys. Chem. A 2005, 109, 892–897. [CrossRef] 110. Blundell, C.D.; Roberts, I.S.; Sheehan, J.K.; Almond, A. Investigating the molecular basis for the virulence of Escherichia coli K5 by nuclear magnetic resonance analysis of the capsule polysaccharide. J. Mol. Microbiol. Biotechnol. 2009, 17, 71–82. [CrossRef] 111. Furlan, S.; La Penna, G.; Perico, A.; Cesàro, A. Hyaluronan chain conformation and dynamics. Carbohydr. Res. 2005, 340, 959–970. [CrossRef] 112. Almond, A.; DeAngelis, P.L.; Blundell, C.D. Hyaluronan: The local solution conformation determined by NMR and computer modeling is close to a contracted left-handed 4-fold helix. J. Mol. Biol. 2006, 358, 1256–1269. [CrossRef][PubMed] 113. Holmbeck, S.M.; Petillo, P.A.; Lerner, L.E. The solution conformation of hyaluronan: A combined NMR and molecular dynamics study. Biochemistry 1994, 33, 14246–14255. [CrossRef][PubMed] 114. Adrian-Scotto, M.; Abdallah, K.B.; Mallet, G.; Vasilescu, D. Quantum molecular modeling of free radical saccharides from hyaluronan. J. Molec. Struct. 2003, 636, 89–113. [CrossRef] 115. Moulabbi, M.; Broch, H.; Robert, L.; Vasilescu, D. Quantum molecular modeling of hyaluronan. J. Mol. Struct. 1997, 395, 477–508. [CrossRef] 116. Guss, J.; Hukins, D.; Smith, P.; Winter, W.; Arnott, S.; Moorhouse, R.; Rees, D. Hyaluronic acid: Molecular conformations and interactions in two sodium salts. J. Mol. Biol. 1975, 95, 359–384. [CrossRef] 117. Rees, D. Conformational analysis of polysaccharides. Part II. Alternating copolymers of the agar–carrageenan–chondroitin type by model building in the computer with calculation of helical parameters. J. Chem. Soc. B 1969, 217–226. [CrossRef] 118. Mitra, A.; Arnott, S.; Atkins, E.; Isaac, D. Dermatan sulfate: Molecular conformations and interactions in the condensed state. J. Mol. Biol. 1983, 169, 873–901. [CrossRef] 119. Virudachalam, R.; Rao, V.S. Theoretical investigations on 2-acetamido-2-deoxy aldohexopyranoses: Conformation and the anomeric effect. Carbohydr. Res. 1976, 51, 135–139. [CrossRef] Int. J. Mol. Sci. 2020, 21, 7699 41 of 41

120. Hsieh, P.-H.; Thieker, D.F.; Guerrini, M.; Woods, R.J.; Liu, J. Uncovering the relationship between sulphation patterns and conformation of iduronic acid in heparan sulphate. Nature 2016, 6, 29602. [CrossRef] 121. Gatti, G.; Casu, B.; Torri, G.; Vercellotti, J.R. Resolution-enhanced 1H-nmr spectra of dermatan sulfate and chondroitin sulfates: Conformation of the uronic acid residues. Carbohydr. Res. 1979, 68, C3–C7. [CrossRef] 122. Ernst, S.; Venkataraman, G.; Sasisekharan, V.; Langer, R.; Cooney, C.L.; Sasisekharan, R. Pyranose ring flexibility. Mapping of physical data for iduronate in continuous conformational space. J. Am. Chem. Soc. 1998, 120, 2099–2107. [CrossRef] 123. Van Boeckel, C.; Van Aelst, S.; Wagenaars, G.; Mellema, J.R.; Paulsen, H.; Peters, T.; Pollex, A.; Sinnwell, V. Conformational analysis of synthetic heparin-like oligosaccharides containing α-L-idopyranosyluronic acid. Recl. Trav. Chim. Pays Bas. 1987, 106, 19–29. [CrossRef] 124. Inoue, Y.; Inouye, Y.; Nagasawa, K. Conformational equilibria of the L-iduronate residue in non-sulphated di-, tetra-and hexa-saccharides and their alditols derived from dermatan sulphate. Biochem. J. 1990, 265, 533–538. [CrossRef][PubMed] 125. Ragazzi, M.; Provasoli, A.; Ferro, D. Molecular mechanics and the structure of iduronate-containing carbohydrates. In Computer Modeling of Carbohydrate Molecules; French, A., Ed.; ACS Publications: Washington, DC, USA, 1990; pp. 332–344. 126. Forster, M.J.; Mulloy, B. Molecular dynamics study of iduronate ring conformation. Biopolymers 1993, 33, 575–588. [CrossRef] 127. Venkataraman, G.; Sasisekharan, V.; Cooney, C.L.; Langer, R.; Sasisekharan, R. A stereochemical approach to pyranose ring flexibility: Its implications for the conformation of dermatan sulfate. Proc. Natl. Acad. Sci. USA 1994, 91, 6171–6175. [CrossRef] 128. Arnott, S.; Guss, J.; Hukins, D.; Dea, I.; Rees, D. Conformation of keratan sulphate. J. Mol. Biol. 1974, 88, 175–184. [CrossRef] 129. Rudrum, M.; Shaw, D. 10. The structure and conformation of some monosaccharides in solution. J. Chem. Soc. 1965, 52–57. [CrossRef] 130. Angyal, S.J. Conformational analysis in carbohydrate chemistry: I. Conformational free energies. The conformations and α: β ratios of aldopyranoses in aqueous solution. Aust. J. Chem. 1968, 21, 2737–2746. [CrossRef] 131. Bush, C.A.; Feeney, R.E. Conformation of the glycotripeptide repeating unit of antifreeze glycoprotein of polar fish as determined from the fully assigned proton nmr spectrum. Int. J. Pept. Prot. Res. 1986, 28, 386–397. [CrossRef][PubMed] 132. Mulloy, B.; Forster, M.J. Conformation and dynamics of heparin and heparan sulfate. Glycobiology 2000, 10, 1147–1156. [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional aﬃliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).