biomolecules Article Efficient Construction of Atomic-Resolution Models of Non-Sulfated Chondroitin Glycosaminoglycan Using Molecular Dynamics Data Elizabeth K. Whitmore 1,2 , Gabriel Vesenka 1, Hanna Sihler 1 and Olgun Guvench 1,2,* 1 Department of Pharmaceutical Sciences, University of New England College of Pharmacy, 716 Stevens Avenue, Portland, ME 04103, USA; [email protected] (E.K.W.); [email protected] (G.V.); [email protected] (H.S.) 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: 26 February 2020; Accepted: 1 April 2020; Published: 2 April 2020 Abstract: Glycosaminoglycans (GAGs) are linear, structurally diverse, conformationally complex carbohydrate polymers that may contain up to 200 monosaccharides. These characteristics present a challenge for studying GAG conformational thermodynamics at atomic resolution using existing experimental methods. Molecular dynamics (MD) simulations can overcome this challenge but are only feasible for short GAG polymers. To address this problem, we developed an algorithm that applies all conformational parameters contributing to GAG backbone flexibility (i.e., bond lengths, bond angles, and dihedral angles) from unbiased all-atom explicit-solvent MD simulations of short GAG polymers to rapidly construct models of GAGs of arbitrary length. The algorithm was used to generate non-sulfated chondroitin 10- and 20-mer ensembles which were compared to MD-generated ensembles for internal validation. End-to-end distance distributions in constructed and MD-generated ensembles have minimal differences, suggesting that our algorithm produces conformational ensembles that mimic the backbone flexibility seen in simulation. Non-sulfated chondroitin 100- and 200-mer ensembles were constructed within a day, demonstrating the efficiency of the algorithm and reduction in time and computational cost compared to simulation. Keywords: molecular dynamics; glycosaminoglycan; proteoglycan; chondroitin sulfate; carbohydrate conformation; carbohydrate flexibility; glycosidic linkage; ring pucker; force field; explicit solvent 1. Introduction The diverse group of protein–carbohydrate conjugates called proteoglycans (PGs) is a fundamental component of tissue structure in animals and can be found in the extracellular matrix (ECM) as well as on and within cells. PGs bind growth factors [1–12], enzymes [2,12], membrane receptors [12], and ECM molecules [2,12,13]. By doing so, they modulate signal transduction [13,14], tissue morphogenesis [2,8–11], and matrix assembly [2,15–17]. PG bioactivity is often dependent on the covalently linked carbohydrate chains called glycosaminoglycans (GAGs), which are linear, highly negatively charged, and structurally diverse carbohydrate polymers. GAGs mediate receptor–ligand complex formation by either forming non-covalent complexes with proteins or inhibiting the formation of complexes with other biomolecules. This makes GAGs key modulators in many diseases, giving them potential therapeutic applications. For example, heparan sulfate (HS) is released during sepsis and induces septic shock [18,19]; the removal of chondroitin sulfate (CS) may enhance memory retention and slow neurodegeneration in patients with Alzheimer’s disease [20–22]; and dermatan Biomolecules 2020, 10, 537; doi:10.3390/biom10040537 www.mdpi.com/journal/biomolecules Biomolecules 2020, 10, x FOR PEER REVIEW 2 of 24 Biomolecules 2020, 10, 537 2 of 23 enhance memory retention and slow neurodegeneration in patients with Alzheimer’s disease [20– 22]; and dermatan sulfate (DS) deficiency has been implicated in Ehlers–Danlos syndrome, thus the sulfatescreening (DS) of deficiencyDS in urine has could been be implicated used as an in early Ehlers–Danlos diagnostic tool syndrome, [23,24]. thus the screening of DS in urineGAG could binding be used assites an earlyon proteins diagnostic are tool determined [23,24]. by protein sequence and structure, with requirementsGAG binding for both sites shape on proteins and charge are determined complementarity by protein [12,25]. sequence Thus, and structure,GAG function with requirements depends on forGAG both three shape‐dimensional and charge structure complementarity and conformation. [12,25 Even]. Thus, subtle GAGstructural function differences depends impact on GAG three-dimensionalfunction. For example, structure while and CS conformation. and DS have Even many subtle functional structural differencesdifferences, impact the only GAG structural function. Fordifference example, is in while the chirality CS and of DS the have uronic many acid functional monosaccharides. differences, While the onlymuch structural is known difference about GAG is infunction, the chirality attempting of the to uronic study GAG acid monosaccharides. conformational thermodynamics While much is at known atomic aboutresolution GAG presents function, a attemptinglargely unsolved to study problem GAG conformational for existing experimental thermodynamics methods. at atomic This resolution is largely presents due to the a largely structural unsolved and problemconformational for existing complexities experimental of GAGs. methods. For example, This is largelya given due GAG to consists the structural of a repeating and conformational sequence of complexitiesa particular disaccharide, of GAGs. For but example, conformational a given GAG complexity consists is of introduced a repeating through sequence flexibility of a particular in the disaccharide,glycosidic linkages but conformational between monosaccharides complexity is introduced[26–30] (Figure through 1). Additional flexibility in complexity the glycosidic results linkages from betweennon‐template monosaccharides‐based synthesis [26– 30[31]] (Figure and variable1). Additional enzymatic complexity sulfation results [32], which from non-template-based means a biological synthesissample of [a31 GAG] and composed variable of enzymatic a specific sulfation disaccharide [32], repeat which will means be polydisperse a biological and sample heterogeneous of a GAG composedowing to ofthe a specific variable disaccharide length and repeat sulfation will be polydisperse of the individual and heterogeneous polymer owingmolecules. to the variableLiquid lengthchromatography–mass and sulfation of thespectrometry individual polymer(LC‐MS) molecules.[33–35], X‐ Liquidray crystallography chromatography–mass [36–41], spectrometryand nuclear (LC-MS)magnetic [ 33resonance–35], X-ray (NMR) crystallography [42–45] are [36 used–41 ],to and study nuclear GAGs magnetic but are resonancelimited in (NMR)their ability [42–45 to] areaccount used tofor study all of GAGsthese complexities. but are limited Additionally, in their ability some to accountstudies have for all used of these results complexities. from LC‐MS Additionally, [45], X‐ray somecrystallography studies have [46], used and results NMR from [46–51] LC-MS to compare [45], X-ray and crystallography validate conformational [46], and NMR data [46 from–51] to molecular compare anddynamics validate (MD) conformational simulations. data This from suggests molecular that MD dynamics simulations (MD) can simulations. produce results This suggests complementary that MD simulationsto experimental can produce analysis results methods complementary by providing to experimental realistic analysisthree‐dimensional methods by atomic providing‐resolution realistic three-dimensionalmolecular models atomic-resolutionof GAG conformational molecular ensembles models of[52–56]. GAG conformational ensembles [52–56]. Figure 1.1. Compact non non-sulfated‐sulfated chondroitin 20 20-mer‐mer conformation arising from flexibleflexible glycosidic linkages (red) between monosaccharide rings (GalNAc(GalNAc inin blueblue andand GlcAGlcA inin cyan).cyan). The molecular graphics throughout are produced withwith thethe VMDVMD programprogram [[57].57]. A critical challenge with MD simulations of GAGs is that a single biological GAG polymer chain may contain up to 200 monosaccharide units [[9].9]. When fully solvated, the resulting system will have 6 in excess of 10106 atoms. It It is not feasible to routinely simulate such a system using current graphics processing unitunit (GPU)-accelerated (GPU)‐accelerated MD MD codes codes with with a moderna modern GPU GPU and and multi-core multi‐core CPU. CPU. This This limits limits the utilitythe utility of all-atom of all‐atom explicit-solvent explicit‐solvent MD as MD a tool as fora tool routine for routine conformational conformational analysis analysis of GAGs of of GAGs this size. of this size.Coarse-grained (CG) MD simulations are the most feasible current alternative to all-atom explicit-solvent MD as they entail fewer degrees of freedom for the solute [48] and often an implicit Biomolecules 2020, 10, 537 3 of 23 (continuum) description of the solvent [58,59]. This can make CG MD two to three orders of magnitude faster, thereby allowing for the handling of large systems [60], such as GAG 200-mers. Indeed, a recent CG model using glycosidic linkage and ring pucker energy functions has provided previously-unseen details of the structure–dynamics relationship of GAGs in the context of PGs [48]. An important insight from that study was that GAGs, in contrast to the unique ordered conformations of folded proteins, need to be considered as existing in conformational ensembles containing a large diversity of three-dimensional conformations. As an alternative approach to using CG