Glycans, as one of the fundamental biomolecules alongside nucleic acids and proteins, play critical roles in biological processes, including glycoprotein folding, transport, degradation, and cell–cell interactions. Despite their biological importance, the structural analysis of glycans remains challenging due to their high flexibility and complex branched structures. This study addresses these challenges by combining molecular dynamics (MD) simulations and NMR spectroscopy to obtain dynamic conformational ensembles of glycans. Nonlinear correlation analyses, specifically Hilbert–Schmidt independence criterion and maximal information coefficient, were applied to decipher the structural dynamics of glycans. The study focused on GM3 trisaccharides and high-mannose glycans (GM9, M9, and M8B), uncovering the roles of glycosidic dihedral angles and intramolecular hydrogen bonds in stabilizing specific conformations. Key correlations between glycosidic linkages and hydrogen bonds were identified, offering insights into the conformational changes that underpin glycan bioactivity. Notably, the removal of specific mannose residues disrupts hydrogen bond networks, expanding conformational space and influencing glycoprotein fate in the endoplasmic reticulum. By integrating MD simulations, NMR validation, and nonlinear multivariate analysis, this study provides a robust framework for understanding glycan structural dynamics. These findings have broad implications for glycoengineering, glycan-based drug discovery, and the design of therapeutics targeting structurally dynamic biomolecules, such as intrinsically disordered proteins.

Glycans, alongside nucleic acids and proteins, are often referred to as “the third chain of life” and play crucial roles in various biological phenomena. Most secreted and membrane proteins undergo glycosylation, which determines their solubility and thermal stability, and regulates intermolecular interactions.¹⁾ The fate of these glycoproteins in the secretory pathway (folding, transport, and degradation) is also dictated by their glycans.²⁾ Therefore, considering glycan modifications is of paramount importance for enhancing the efficiency and performance of biopharmaceuticals, including therapeutic antibodies.³⁾ Additionally, glycans modify lipids at the cell surface, forming clusters that mediate cell–cell interactions and viral infections. Structural transitions of proteins involved in neurodegenerative diseases are known to progress on these glycan clusters.⁴⁾ Understanding the molecular mechanisms by which glycans exert their functions is essential not only for biopharmaceutical development but also for addressing critical pharmaceutical challenges such as infection control and neurodegenerative disease prevention. To achieve this, precise elucidation of glycan structures is required.

Glycans exhibit unique branched structures and possess numerous isomers, making structural analysis inherently challenging. However, advancements in MS- and HPLC-based techniques have lowered the barriers to glycan structural analysis.⁵⁾ Nonetheless, glycans have high internal mobility and do not adopt fixed 3-dimensional structures, fluctuating significantly in aqueous solutions. This structural flexibility complicates glycan research. However, such fluctuations are fundamentally involved in glycan function. Glycan bioactivity is often mediated through interactions with glycan-binding proteins, collectively termed lectins.⁶⁾ To quantitatively evaluate the energetics of glycan–lectin interactions, it is necessary to assess not only the glycan's conformation when forming complexes but also its structural dynamics in the free state. In fact, modifying the conformational space of free glycans can enhance their affinity for lectins.⁷⁾

We have developed a methodology that explores glycan conformational space by combining molecular dynamics (MD) simulations and NMR spectroscopy.^8,9) Specifically, we employed paramagnetism-assisted NMR methods in which a lanthanide-chelating tag is attached to the reducing end of glycans. This approach enables the observation of pseudocontact shifts in NMR spectra, providing long-range spatial information about the arrangement of individual atoms within glycans. By integrating these data, we are able to construct experimentally validated, dynamic conformational ensembles of glycans. The next challenge is to decipher the information embedded in these ensembles and to identify the factors that govern glycan structural dynamics.

In this study, we applied nonlinear correlation analysis to uncover hidden information within the dynamic structural ensembles of glycans. Specifically, we analyzed the GM3 trisaccharide, αNeu5Ac-(2–3)-βGal-(1–4)-βGlc, which represents the core structure common to ganglioside glycans, and a series panel of high-mannose glycans involved in determining the intracellular fate of glycoproteins.

We first conducted a conformational analysis of the GM3 trisaccharide. The conformational ensemble used in this study was obtained via replica exchange MD (REMD) simulations for 60 ns using 64 replicas, with a temperature range of 300–500 K and the GLYCAM06 force field.⁸⁾ Figure 1 shows the ϕ–ψ plots for the two glycosidic linkages (Neu5Ac–Gal and Gal–Glc) within this glycan. We assessed the independence of these dihedral angles and the presence of intramolecular hydrogen bonds using the Hilbert–Schmidt independence criterion (HSIC)¹⁰⁾ and the maximal information coefficient (MIC)¹¹⁾. These methods allow for the evaluation of dependencies and correlations, including nonlinear ones, providing complementary insights into the conformational landscape.

Fig. 1. (a) Superimposition of 100 Conformers and (b) Torsion Angle Density Maps Derived from the REMD Simulation of the GM3 Trisaccharide

The Neu5Ac, Gal, and Glc residues are colored purple, yellow, and orange, respectively, with each conformer aligned along the Gal and Glc residues.

HSIC exploits reproducing kernel Hilbert space properties to evaluate the independence between two probabilistic variables, where values close to 0 indicate independence (Table 1). The results suggest that the conformations of the two glycosidic linkages are primarily influenced by distinct subsets of hydrogen bonds, highlighting that HSIC is highly sensitive to subtle relationships and effective for detecting weak dependencies. However, it requires the selection of hyperparameters such as the kernel function and bandwidth, which can introduce a degree of arbitrariness.¹⁰⁾ In contrast, MIC is a grid-based method that identifies both linear and nonlinear associations by maximizing mutual information. Its key advantage lies in its independence from hyperparameters, making it robust and versatile across diverse datasets.¹²⁾ However, compared to HSIC, MIC is slightly less sensitive to weak correlations.¹³⁾ Taking advantage of the complementary strengths of HSIC and MIC, we were able to comprehensively evaluate the dependencies and correlations among the parameters. This dual approach provided a deeper understanding of the conformational dynamics and the role of intramolecular hydrogen bonds.

Table 1. Independence Test of the Glycosidic Bonds and Intramolecular Hydrogen Bonds of the GM3 Trisaccharide Using HSIC

Our findings revealed that the ψ angle of Gal–Glc is correlated with the hydrogen bonding between Gal-O5 and Glc-O3H (Table 2). This hydrogen bond stabilizes the major conformation of Gal–Glc but has little influence on the conformation of Neu5Ac–Gal. In contrast, the conformational state of the Neu5Ac–Gal glycosidic linkage correlates with hydrogen bonds between Neu5Ac-O6 and Gal-O2H, as well as Neu5Ac-COO and Gal-O4H. These hydrogen bonds contribute to stabilizing a major conformation of Neu5Ac–Gal while having minimal impact on Gal–Glc conformation. In related ganglioside glycans, such as the GM1 pentasaccharide and GM2 tetrasaccharide, Gal-O4H is substituted with GalNAc, preventing hydrogen bond formation and resulting in the loss of the conformation of Neu5Ac–Gal.

Table 2. Correlation Analysis of the Glycosidic Bonds and Intramolecular Hydrogen Bonds of the GM3 Trisaccharide Using MIC

The heatmaps provide a visual representation of potential inter-hydrogen bond correlations (Supplementary Figs. S1 and S2). Our analysis using HSIC suggests that such correlations can be detected, particularly in regions where hydrogen bonds are spatially proximal. While there are some challenges, such as quantifying the strength of these correlations and distinguishing direct interactions from indirect effects mediated by the overall molecular structure, these findings provide valuable insights into the dynamic coordination of hydrogen bonds.

Next, we applied correlation analysis to study the conformations of high-mannose glycans. N-Glycans share a common core structure consisting of two N-acetylglucosamine, i.e., βGlcNAc-(1–4)-βGlcNAc, and three mannose residues, forming a pentasaccharide. The common precursor of N-glycans is a triantennary high-mannose glycan with three glucose residues on the D1 arm, which is transferred to nascent proteins in the endoplasmic reticulum (ER).²⁾ Enzymatic trimming in the ER removes these glucose residues, leaving a single glucose on the D1 arm and resulting in the GM9 dodecasaccharide (Glc₁Man₉GlcNAc₂), which is recognized by lectins acting as ER chaperones. The removal of this glucose generates the M9 undecasaccharide, which is no longer recognized by the lectins serving as ER chaperones. If the glycoprotein is properly folded, M9 is recognized by lectins functioning as cargo receptors and is transported to the Golgi apparatus. If proper folding of the glycoprotein is not achieved and mannose trimming progresses further, it is recognized by another ER lectin, retrotranslocated into the cytoplasm, and degraded by the ubiquitin–proteasome system. Mannose trimming begins at the central D2 arm of the mannose branches, producing the M8B decasaccharide, marks the entry into the degradation pathway. This sequential mannose-trimming program appears to be encoded within the dynamic conformational ensemble of glycans. Analyzing the dynamic conformational ensembles of GM9, M9, and M8B will provide insights into this molecular program.

The ensemble models of these high-mannose-type oligosaccharides were constructed by analyzing 1000 conformers extracted at equal intervals from the trajectories of REMD simulations (with a simulation time of 52 ns for each replica) and validated with NMR data⁹⁾ (Fig. 2). These conformers were subjected to HSIC and MIC analyses (Supplementary Figs. S3–S8). Using HSIC analysis, correlations between internal dihedral angles were tested, and results with p-values smaller than 0.001 were summarized in Table 3. These findings indicate that, in all glycan structures, significant correlations exist between the trimannosyl core and the outer branches (Fig. 3a). Particularly, the dihedral angles at the Man4’–Man3 positions were suggested to act as critical hubs in these correlation networks. In contrast, the motion of the glucose residue at the terminus of the D1 arm, which serves as the molecular recognition target of ER chaperones, appears relatively independent, showing weak coupling with other regions.

Fig. 2. Superimpositions of 100 Conformers Derived from the REMD Simulations of GM9, M9, and M8B Glycans

The Glc, Man, and GlcNAc residues are colored orange, green, and blue, respectively, with each conformer aligned along the GlcNAc residues at the reducing terminus.

Table 3. Summary of the Glycosidic Bonds of the High-Mannose Glycans GM9, M9, and M8B with p-Values Smaller than 0.001 Determined by the HSIC Independence Tests

Fig. 3. Schematic Diagram of the Dynamic Correlation (a) between the Glycosidic Bonds and (b) between the Glycosidic Bonds and the Hydrogen Bonds of GM9, M9, and M8B Glycans

The orange line indicates hydrogen bonds.

Next, the intramolecular hydrogen bonds were investigated, and the correlations between key hydrogen bonds and glycosidic dihedral angles were evaluated using MIC analysis. Table 4 and Fig. 3b compare the MIC analysis results for the structural ensembles of GM9, M9, and M8B. A key observation is that in GM9 and M9, conformational changes in the D2 arm—particularly variations in the ω angle of Man3 and the ϕ angle of ManA–Man4′—are closely linked to fluctuations in multiple hydrogen bonds. Notably, the hydrogen bond frequently formed between the distal ManD2 and GlcNAc2 is tightly correlated with internal dihedral angle variations.

Table 4. Summary of the Dynamic Correlation between the Glycosidic Bonds and the Hydrogen Bonds of the High-Mannose Glycans GM9, M9, and M8B with Values Greater than 0.2 by the MIC Analysis

In M8B, where ManD2 is absent, the correlation between glycosidic dihedral angles and hydrogen bonds weakens. This suggests that hydrogen bonding between the outer branch of the D2 arm and the core region restricts the conformational space of the D2 arm. The removal of ManD2 disrupts this hydrogen bond network, leading to an expanded conformational space in M8B. These findings offer crucial insights into the sequential mannose-trimming molecular program.

By applying nonlinear correlation analysis to ensemble models obtained from MD simulations, we identified key structural determinants of glycan conformations, primarily hydrogen bonds. The two methods employed here complement each other in computational efficiency and sensitivity to correlations, allowing for a comprehensive and quantitative assessment of complex relationships beyond chemical intuition. This study demonstrates the application of nonlinear correlation analysis methods in MD simulations of glycans, enabling a more objective and comprehensive extraction of structural insights compared to previous intuition-based approaches. In particular, we identified that the dihedral angles in the trimannosyl core serve as a critical hub in the glycosidic linkage network of high mannose-type glycans, a novel finding not observed in our previous work. Furthermore, we previously developed a quantitative method for characterizing glycan conformational ensembles using nonlinear multivariate analysis.¹⁴⁾ This method maps glycan conformers into a reproducing kernel Hilbert space, applies Gaussian mixture model clustering, and classifies glycan conformations based on the free-energy landscape. Integrating these approaches enables systematic exploration and rational remodeling of glycan conformational spaces. Such data-driven strategies have broad applicability, extending beyond glycan-based drug discovery and glycoengineering to include structurally fluctuating biomolecules, such as intrinsically disordered proteins, thereby opening new avenues for molecular design and therapeutic innovation.

Data extraction from MD trajectories was performed using the CPPTRAJ module in the AMBER program package. For each glycan, 1000 conformers extracted at equal intervals from the trajectory were used for the analyses. The dihedral angles ϕ, ψ, and ω were defined as O5–C1–O'x–C'x, C1–O'x–C'x–C'x-1, and O'6–C'5–C'5–O'5, respectively. For the Neu5Ac–Gal linkage, the torsion angles ϕ and ψ are defined as O6–C2–O'3–C'3 and C2–O'3–C'3–C'2, respectively. An intramolecular hydrogen bond was defined using simple geometric criteria with an acceptor (A) to donor (D) distance (3.0 Å) and A–H–D angular (135°) cutoffs. The nonlinear correlation analyses of the data were performed with the R packages dHSIC and minerva at the Research Center for Advanced Computing Infrastructure, JAIST. For the HSIC independence test, a Gaussian kernel with the median heuristic as the bandwidth was used.

This work was supported in part by JST-CREST (JP MJCR21E3), JSPS KAKENHI (JP24H00599), Joint Research of ExCELLS (24EXC901 and 25EXC603), Cooperative Research by IMS (24IMS1210), and the Naito Foundation Research Grant. This work was also supported by MEXT through the Promotion of Development of a Joint Usage/Research System Project: Spin-L (JPMXP1323015488 and spin24XN014), the J-GlycoNet cooperative network, and the Human Glycome Atlas Project.

The authors declare no conflict of interest.

This article contains supplementary materials.

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