Conformational Populations of β-(1→4) O-Glycosidic Linkages Using Redundant NMR J-Couplings and Circular Statistics

Abstract

Twelve disaccharides containing β-(1→4) linkages and displaying systematic structural variations in the vicinity of these linkages were selectively labeled with ¹³C to facilitate measurements of multiple NMR spin-spin (scalar; J) coupling constants (J_CH and J_CC values) across their O-glycosidic linkages. Ensembles of spin-couplings (²J_COC, ³J_COCH, ³J_COCC) sensitive to the two linkage torsion angles, phi (ϕ) and psi (ψ), were analyzed by using parametrized equations obtained from density functional theory (DFT) calculations, Fredholm theory, and circular statistics to calculate experiment-based rotamer populations for ϕ and ψ in each disaccharide. With the statistical program MA'AT, torsion angles ϕ and ψ were modeled as a single von Mises distribution, which yielded two parameters, the mean position and the circular standard deviation (CSD) for each angle. The NMR-derived rotamer populations were compared to those obtained from 1 μs aqueous molecular dynamics (MD) simulations and crystallographic database statistical analyses. Conformer populations obtained exclusively from the MA'AT treatment of redundant J-couplings were in very good agreement with those obtained from the MD simulations, providing evidence that conformational populations can be determined by NMR for mobile molecular elements such as O-glycosidic linkages with minimal input from theory. The approach also provides an experimental means to validate the conformational preferences predicted from MD simulations. The conformational behaviors of ϕ in the 12 disaccharides were very similar, but those of ψ varied significantly, allowing a classification of the 12 disaccharides based on preferred linkage conformation in solution.

Figure 1

Contour plot of DFT-calculated ³J_C1′,C5 values in βGal14βXylOCH₃ 13 as a function of ϕ and ψ, showing a secondary dependence on ϕ at some values of ψ (ϕ = H1′–C1′–O1′–C4; ψ = C1′–O1′–C4–H4).

Figure 2

Calculated ³J_C1′,C5 values in βGal14βXylOCH₃ 13 as a function of ψ before (A) and after (B) the application of a 10 kcal/mol energy cutoff to the data. In both plots, the blue line is the best fit of the data. ψ = C1′–O1′–C4–H4.

Figure 3

(A) Calculated ³J_C2′,C4 values in disaccharides 2 and 4–14 as a function of ϕ. (B) Plots of the three generalized eqs 3 – 5, showing the effects of structure and configuration at C2′ on ³J_C2′,C4 in β-(1→4) linkages. ϕ = H1′–C1′–O1′–C4.

Figure 4

(A) Calculated ³J_C1′,C5 values in disaccharides 2 and 4–14 as a function of ψ. See Figure 3 for color definitions. (B) Plots of generalized eqs 6 and 7 showing the effect of different substituents at C5 (–CH₂OH vs – H) on ³J_C1′,C5 in β-(1→4) linkages. ψ = C1′–O1′–C4–H4.

Figure 5

(A) Calculated ³J_C1′,C3 values in disaccharides 2 and 4–14 as a function of ψ. See Figure 3 for color definitions. (B) Plots of eqs 8 and 9 used to treat ³J_C1′,C3 values in β-(1→4) linkages for coupling pathways with axial and equatorial orientations of the terminal O3. ψ = C1′–O1′–C4–H4.

Figure 6

Calculated ²J_C1′,C4 values in disaccharides 2 and 4–14 as a function of ϕ. This geminal ²J_COC is negative in sign and exhibits a dynamic range of ~3 Hz, with the least negative (most positive) values observed at ϕ = 300° (O5′ anti to C4). Each curve represents the average of 24 ²J_C1′,C4 vs ϕ curves at different ψ values to account for the indirect effects of ψ on ²J_C1′,C4. See Figure 3 for color definitions. ϕ = H1′–C1′–O1′–C4.

Figure 7

2D Contour plot of calculated ²J_C1′,C4 values in βGal14βGlcOCH₃ 2 as a function of ϕ and ψ. ϕ = H1′–C1′–O1′– C4; ψ = C1′–O1′–C4–H4.

Figure 8

Calculated ³J_C4,H1′ (A) and ³J_C1′,H4 (B) values in disaccharides 2 and 4–14 as a function of ϕ and ψ, respectively. See Figure 3 for color definitions. ϕ = H1′–C1′–O1′–C4; ψ = C1′–O1′–C4–H4.

Figure 9

(A) Contour plot of calculated ³J_C4,H1′ values in 2, showing a primary dependency on ϕ. (B) Contour plot of calculated ³J_C1′,H4 values in 2, showing a primary dependency on ψ.ϕ = H1′–C1′–O1′–C4; ψ = C1′–O1′–C4–H4.

Figure 10

Single-state von Mises models of ϕ-dependent J-couplings (A) and ψ-dependent J-couplings (B) in disaccharides 2 and 4–14. In (A), a common mean position of ϕ at ~29° is observed. In (B), three different mean positions at ~−22°, ~−9°, and ~15° are observed (Table 3). See Figure 3 for color definitions. ϕ = H1′–C1′–O1′–C4; ψ = C1′–O1′–C4–H4.

Figure 11

Single-state von Mises models of ψ for disaccharides in Groups I–III. Distributions were determined using DFT-derived eqs 3–11 and the average experimental J-couplings in each group (Table 1). Group I: μ = −8.8° (±6), σ = 15.5° (±12), RMS = 0.23 Hz. Group II: μ = –18.1° (±7), σ = 20.3° (±11), RMS = 0.16 Hz. Group III: μ = 12.4° (±9), σ = 25.2° (±9), RMS = 0.43 Hz. μ = mean, σ = CSD.

Figure 12

Parameter space for the single-state von Mises model of ψ in 2. At least two local minima are observed in addition to the global minimum at μ = −8°/σ = 18° (μ = mean; σ = CSD). The local minimum at μ = 130°/σ = 36° has an RMS error of 0.60 Hz. The local minimum at μ = 210°/σ = 60° has an RMS error of 0.76 Hz.

Figure 13

Histograms from 1 μs aqueous MD simulations for ϕ (A)–(C) and ψ (D)–(F) in disaccharides 2, 12, and 13. Mean positions for ϕ are +44°, + 44°, and +46° for 2, 12, and 13, respectively. Mean positions for ψ are −3°, − 20°, and +16° for 2, 12, and 13, respectively. Red = 2; green = 12, blue = 13. See Table 5 for CSDs.

Figure 14

Newman projections for ϕ and ψ in disaccharides 2, 12, and 13 superimposed on statistical distributions determined by NMR J-coupling analysis (blue lines) and aqueous MD simulations (red histograms).

Scheme 1

Redundant J-Couplings across a “Two-Bond” β-(1→4) O-Glycosidic Linkage, Illustrated in Disaccharide 2

Scheme 2

Redundant J-Couplings across a “Three-Bond” β-(1→6) O-Glycosidic Linkage, Illustrated in Disaccharide 3

Scheme 3

Structures of the 12 ¹³C-Labeled β-(1→4)-Linked Disaccharides Studied in This Investigation ^{a a}Their classification into three groups is based on conformational preferences about their internal O-glycosidic linkages (see text). Modes of ¹³C-labeling are described in Scheme 4.

Scheme 4

Two ¹³C-Labeling Modes Used To Measure J-Couplings across the “Two-Bond” O-Glycosidic Linkages in 2 and 4–14, Illustrated in 2

Scheme 5

Definitions of the ϕ and ψ Rotamers in 2 and 4–14

Scheme 6

Newman Projections for ψ Superimposed on von Mises Models of ψ in Representative Disaccharides in Groups I (2), II (12), and III (13)