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WIREs Comput Mol Sci
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Perspective on computational simulations of glycosaminoglycans

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Glycosaminoglycans (GAGs) represent a formidable frontier for chemists, biochemists, biologists, medicinal chemists, and drug delivery specialists because of massive structural complexity. GAGs are arguably the most complex, natural linear biopolymers with theoretical diversity orders of magnitude higher than proteins and nucleic acids. Yet, this diversity remains generally untapped. Computational approaches offer major routes to understand GAG structure and dynamics so as to enable novel applications of these biopolymers. In fact, computational algorithms, softwares, online tools, and techniques have reached a level of sophistication that help understand atomistic details of conformational variation and protein recognition of individual GAG sequences. This review describes current approaches and challenges in computational study of GAGs. It presents a history of major findings since the earliest mention of GAGs (the 1960s), the development of parameters and force fields specific for GAGs, and the application of these tools in understanding GAG structure–function relationship. This review also presents a section on how to perform simulation of GAGs, which is directed toward researchers interested in entering this promising field with potential to impact therapy. This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Molecular Structures
Structures of common glycosaminoglycans (GAGs). Red—d‐Glucosamine (GlcN); green—N‐acetyl‐d‐galactosamine (GalNAc); purple—d‐glucuronic acid (GlcA); Brown—l‐iduronic acid (IdoA). X = H or SO3; R = Ac or SO3 groups. HA has GlcNAc linked to GlcA by β(1➔4) interglycosidic linkages and GlcA linked to GlcNAc through β(1➔3) interglycosidic linkages. CS has GalNAc linked to GlcA by β(1➔4) linkages and GlcA linked to GalNAc by β(1➔3) interglycosidic bonds. DS's GalNAc is linked to IdoA by β(1–4) linkages, whereas IdoA is α(1➔3) linked to GalNAc. In HP/HS, GlcN is α(1➔4) linked to either GlcA or IdoA. In contrast, GlcA residues are β(1➔4) linked to GlcN residues, whereas IdoA is α(1➔4) linked to GlcN residues
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Ring conformations of GAG. (a) Schematic representation of Cremer–Pople puckering parameter theta (θ) for IdoA ring shown for 4C1, θ = 0° to 60°, 2SO, θ = 60° to 120°, 1C4, θ = 120° to 180°. The structures are shown in right hand side of (a) with representations for observed NOE cross peaks from Hsieh et al. . From this the vicinal coupling based on four torsion is also shown (e.g., H2‐C2‐C3‐H3). (b) The transition path way of ring conformations from chair to skew boat and then to chair observed in microsecond simulation for GlcNAc. (c) The population of ring conformers obtained for IdoA2S and IdoA in the library of eight hexasaccharides sequences (S1–S8) with variation in neighboring residue sulfation are shown. From left to right it shows the increase of sulfation in the sequence . Reprinted with permission from Reference 114. Copyright 2011 Oxford University
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Intermolecular (water) interactions in GAG. (a) Schematic representation of structured water (water molecules shown in blue spheres) around GAG disaccharide and bulk water molecule, which is not close to GAG (shown in red spheres). (b and (c) representation of water molecules close to different polar groups of disaccharide, orange sphere shows water molecules around carboxyl group, green sphere water molecules shown around sulfate group and blue color water spheres shown around one of the hydroxyl group. (d) Shows the structured water molecule around 1–4 linked CS‐C (from A‐D only oxygen atom of water alone shown for better visibility). (e)–(h) shows the radial distribution of water in CS‐C with respect to bulk water–water, hydroxyl group–water, CH–water. (i) schematic representation of water mediated H‐bond interaction. (j) Structure of 1–4 CS‐A. (k) Average number of water mediated H‐bonds with respect to each donor and acceptor group in CS‐A. (l) Life time of established H‐bonds between CS‐A and water molecules (color from blue to red shows the increase in strength in both K and L). (m) Radial distribution of water molecules around heparin trisaccharide with I doA2S in 2SO in red and 1C4 in blue. (n) Bridging water molecular interaction in HA (one water molecular bridging/two water molecular bridging). (o) Bridging water molecular interaction in unsulfated chondroitin (one water molecular bridging/two water molecular bridging). Reprinted with permission from Reference 120. Copyright 1999 Elsevier Science B.V; and Reference 85. Copyright 2012 John Wiley Sons
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Intramolecular H‐bond interactions observed in HP from various MD simulations. (a) and (b) Represents the H‐bond interactions from heparin disaccharides GlcNS6S‐IdoA2S (1C4) and GlcNS6S‐IdoA2S (2SO). (c) and (d) The hydrogen bond interactions from heparin disaccharides GlcNAc6S‐IdoA2S (1C4) and GlcNAc6S‐IdoA2S(2SO). (e) and (f) the hydrogen bond interactions from the sequence (GlcNS6S‐IdoA2s)5 with IdoA2S in both 2SO and 1C4 forms. (g) and (h) various observed stabilizing intra molecular hydrogen bond present in pentasaccharide‐Arixtra with the participating IdoA2S in both 2SO and 1C4 forms. (i)–(k) hydrogen bond distance deviation observed in the individual residue of IdoA in 2SO and 1C4 forms and in between GlcNS3S6S‐IdoA (1C4). All donor‐acceptor atoms and distances are labeled, hydrogen bond interaction shown in dashed line
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Intramolecular H‐bond interactions observed in HA and CS from various MD simulation studies. (a) and (b) Represents the H‐bond interactions established between the possible donor‐acceptor pairs for HA disaccharides. The occupancy in the presence of solvent/vacuum is marked respectively. (c) HA tetrasaccharide H‐bond occupancy in the presence of solvent. (d) and (e) Unsulfated CS disaccharides: Observed hydrogen bond interactions. (f) Unsulfated CS tetrasaccharide in the presence of solvent: H‐bond occupancy. (g) and (h) Donor–acceptor interaction in CS‐A. (i) and (j) Hydrogen bond interactions from CS‐C. (k) and (l) H bond interactions from unsulfated DS with IdoA in 2SO puckering. Note: For all these the disaccharide pairs are shown for both 1–3 and 1–4 linkages with hydrogen bond donor and acceptor atoms labeled, and existence of hydrogen bonds shown in dashed line. The symbol * shows the difference in occurrence and B*, B** shows the first time appearance
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Representation of glycosidic torsion angles Φ,Ψ. (a) and (b) Glycosidic torsional angle Φ, Ψ distribution with respect to GlcN‐IdoA2S and Ido2A‐GlcN linkages for a library of eight sequences . (c) Schematic structure of GAG disaccharide with Δ‐uronic acid and GlcNAc with varying sulfation of total three sequences (1: ΔUA2S‐GlcNAc6S, 2: ΔUA2S‐GlcNS, 3: ΔUA2S‐GlcNS6S). (d) Glycosidic torsional angle Φ, Ψ represented as population distribution heat maps for ΔU2S‐GlcNAc6S, with maximum conformers at Φ = 50°, Ψ = 0°. (e) and (f) Heparin tetra saccharide (E:GlcA‐GlcNAc‐IdoA2S‐GlcNAc, F:GlcA‐GlcNS‐IdoA2S‐GlcNS) with residue E IdoA2S and with varying sulfation in adjacent GlcNAc in E and F. (g)–(i) Glycosidic torsional angle Φ,Ψ represented as population distribution heat maps for all possible disaccharide pairs were reported, here we show (g) distribution of Φ,Ψ for the disaccharide (GlcA‐GlcNS) in sequence E. (h) Distribution of Φ, Ψ with regard to disaccharide pairs in the last IdoA2S‐GlcNAc/GlcNS. (i) Distribution of Φ, Ψ with regard to disaccharide pairs in the last IdoA2S‐GlcNAc with IdoA2S restrained in 2SO form. Reprinted with permission from Reference 102. Copyright 2000 Oxford University Press; and Reference 91. Copyright 2016 NRC Research Press
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Representation of glycosidic torsion angles (Φ, Ψ). (a) and (b) Energy contour exploration of glycosidic angles Φ,Ψ from alternate tetrasaccharide of hyaluronan (HA) shown for middle linkage, extracted from molecular dynamics simulation. The filled diamond boxes represent values of Φ, Ψ extracted from X‐ray fiber diffraction refinements. (c) and (d) Energy contour exploration of glycosidic angles Φ,Ψ from alternate tetrasaccharide of chondroitin shown for middle linkage, extracted from molecular dynamics simulation. The filled circle represents the value of Φ,Ψ with different helical folds from X‐ray‐fiber diffraction data . (e)–(h) Contour plots of heparin glycosidic linkages as a function on IdoA conformation. (e) GlcNS6S(1➔4)IdoA2S linkage shown with IdoA2S in 1C4, (f) with IdoA2S in 2SO. (g) GlcNAc6S(1➔4)IdoA2S linkage shown with IdoA2S in 1C4. (h) IdoA2S(1➔4)GlcNS6S linkage with IdoA in 1C4, # represents the final conformation after 200 ns and * represents the input minimum‐energy conformation for MD refinement. Reprinted with permission from References 73 and 74. Copyright 1998 Academic Press; Reference 122. Copyright 2000 Oxford University Press; and Reference 84. Copyright 2008 Elsevier Ltd
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Schematic flow chart for performing MD simulations. (1) The atomic coordinates of GAG should be extracted from the protein data Bank (www.rcsb.org) or Cambridge structural data base (https://www.ccdc.cam.ac.uk) or from other structural data bases (details are provided in Table ). (2) if the structure is not available in any of these databases, it can be built using 3D model building tools (Table ). Once the 3D structure is built, check for missing atoms and add hydrogens at appropriate places. Appropriate sugar puckering (1C4, 4C1, 2SO) should be included, for example, IdoA. (3) After successfully building GAG structure, select the force field and relevant MD program to perform dynamic simulation (GLYCAM06‐AMBER, CHARMM‐NAMD/CHARMM, or GROMOS/GROMACS). (4) Using the respective program, call the force field and load the structure obtained from 1 or 2. The loaded structure should be checked for any error and rectified. (5) An example of a loaded structure is shown (e.g., IdoA2S(2SO)‐GlcNS6S). (6) Check the charge of the GAG sequence and add required number of counter ions (using respective programs like addion, genion and autoionize). (7) Solvate the molecule in a pre‐equilibrated solvent box with defined box size such as cubic 12 Å (e.g., water model: TIP3P, SPC/SPCE). (8) Once the GAG and ions are solvated save the initial parameter/topology and coordinates to perform further steps. Steps 9–12: A typical way of conducting molecular dynamics (MD) simulations. (9) Energy minimize the system to remove steric clashes, if any, with defined protocols. (10) After minimization slowly bring the system to desired temperature using thermostat by restraining the GAG. (11) Apply constant pressure by coupling the system to a barostat; bring the system to NPT ensemble (different ensembles could be used NVT, NVE) and record outputs at constant time intervals. (12) Once the system is well equilibrated, perform the final MD production run ranging from nanoseconds (ns) to microseconds (μs) of choice; record system trajectory at constant interval of time (e.g., for every 1, 2, or 10 ps). Apply periodic boundary condition and particle—Meash–Ewald for long range interactions. Steps 13–16: Analyzing the recorded trajectory to extract information. (13) Extract the interglycosidic torsional space and understanding their density/probability/distribution in 2D contour plot by binning the Φ and Ψ. (14) Trace H‐bond interactions within and in‐between GAG residues by calculating their occupancy, average number and lifetimes. (15) Evaluate caging of GAGs in water molecules with respect to time during the simulation using pair distribution function, average number, lifetimes and bridging water molecules. (16) Analyze the individual puckering states using ring conformational analysis, Cremer–Pople parameters, theoretical and experimental vicinal coupling constants 3JHH and interproton distance using NOE and MD for adjacent residues. Free energy of conformational transition from one ring to other ring form can also be calculated
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Time line of advances in computational studies of GAGs. Key findings are listed in chronological order from left to right
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