Introduction 1 2 3 d l N N 1 4 Fig. 1 n 1 3 2 3 4  O 5 6 8 9 10 l 7 11 13 14 6 15 16 18 et al. 18 et al. 16 11 15 15 1 15 15 13 15 19 15 E. coli 15 20 15 1 1 15 T 1 J- 21 22 23 Theory 15 T 1 T 2 η 9 15 T 1 T 2 1 15 T 1 η 19 J ω 1 2 γ ħ π ω σ N 15 N r NH 1 \documentclass[12pt]{minimal}
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\frac{1}
{{T_{1} }} = \frac{1}
{{10}}\gamma ^{2}_{{\text{N}}} \gamma ^{2}_{{\text{H}}} {\hbar }^{2} \frac{1}
{{r^{6}_{{{\text{NH}}}} }}{\left[ {3J{\left( {\omega _{{\text{N}}} } \right)} + 6J{\left( {\omega _{{\text{N}}}  + \omega _{{\text{H}}} } \right)} + J{\left( {\omega _{{\text{N}}}  - \omega _{{\text{H}}} } \right)}} \right]} + \frac{2}
{{15}}{\left( {\omega _{{\text{N}}} \Delta \sigma _{{\text{N}}} } \right)}^{2} J{\left( {\omega _{{\text{N}}} } \right)}
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\begin{document}$$\eta  = \frac{1}{{10}}\frac{{\gamma _{\text{H}} }}{{\gamma _{\text{N}} }}\gamma _{\text{N}}^2 \gamma _{\text{H}}^2 \hbar ^2 \frac{1}{{r_{{\text{NH}}}^6 }}\left[ {6J\left( {\omega _{\text{N}}  + \omega _{\text{H}} } \right) - J\left( {\omega _{\text{N}}  - \omega _{\text{H}} } \right)} \right]T_1 $$\end{document} 3 −1 4 5 \documentclass[12pt]{minimal}
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\begin{document}$$\tau _\parallel   < \tau _ \bot  $$\end{document} α 3 \documentclass[12pt]{minimal}
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\begin{document}$$J_{{\text{iso}}} \left( {\omega ,\tau } \right) = \frac{\tau }{{1 + \left( {\tau \omega } \right)^2 }},{\text{ }}\tau  = \left( {6D} \right)^{ - 1} $$\end{document} 4 \documentclass[12pt]{minimal}
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\begin{document}$$J_{{\text{aniso}}} \left( \omega  \right) = \sum\limits_{i = 1}^3 {A_i J_{{\text{iso}}} \left( {\omega ,\tau _i } \right)} $$\end{document} 5 \documentclass[12pt]{minimal}
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\begin{document}$$\begin{array}{*{20}c}  {\tau _1^{ - 1}  = 6D_ \bot   = \tau _ \bot ^{ - 1} }{A_1  = \frac{1}{4}\left[ {3\cos ^2 \alpha  - 1} \right]^2 } \\  {\tau _2^{ - 1}  = 5D_ \bot   + D_{||}  = 5\left( {6\tau _ \bot  } \right)^{ - 1}   + \left( {6\tau _{||} } \right)^{ - 1} }{A_2  = 3\sin ^2 \alpha \cos ^2 \alpha } \\  {\tau _3^{ - 1}  = 2D_ \bot   + 4D_{||}  = \left( {3\tau _ \bot  } \right)^{ - 1}  + 2\left( {3\tau _{||} } \right)^{ - 1} }{A_3  = \frac{3}{4}\sin ^4 \alpha } \\ \end{array} $$\end{document} τ e τ M 15 6 7 S 2 8 J aniso ω 4 \documentclass[12pt]{minimal}
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\begin{document}$$\widetilde\tau _i $$\end{document} 9 6 \documentclass[12pt]{minimal}
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\begin{document}$$J_{{\text{dyn\_iso}}} \left( \omega   \right) = S^2 J_{{\text{iso}}} \left( {\omega ,\tau _{\text{M}} } \right) + \left( {1 - S^2 } \right)J_{{\text{iso}}} \left( {\omega ,\tau } \right)$$\end{document} 7 \documentclass[12pt]{minimal}
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\begin{document}$$\tau ^{ - 1}  = \tau _{\text{M}}^{ - 1}  + \tau _{\text{e}}^{ - 1} $$\end{document} 8 \documentclass[12pt]{minimal}
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\begin{document}$$J_{{\text{dyn\_aniso}}} \left( \omega  \right) = S^2 \sum\limits_{i = 1}^3 {A_i J_{{\text{iso}}} \left( {\omega ,\tau _i } \right)}  + \left( {1 - S^2 } \right)\sum\limits_{i = 1}^3 {A_i J_{{\text{iso}}} \left( {\omega ,\widetilde\tau _i } \right)} $$\end{document} 9 \documentclass[12pt]{minimal}
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\begin{document}$$\widetilde\tau _1^{ - 1}  = \tau _1^{ - 1}  + \tau _{\text{e}}^{ - 1} ,{\text{ }}\widetilde\tau _2^{ - 1}  = \tau _2^{ - 1}  + \tau _{\text{e}}^{ - 1} ,{\text{ }}\widetilde\tau _3^{ - 1}  = \tau _3^{ - 1}  + \tau _{\text{e}}^{ - 1} $$\end{document} 8 15 24 Diffusion measurements 25 21 22 g 10 26 10 \documentclass[12pt]{minimal}
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\begin{document}$$S = S_0 {\text{e}}^{ - D_{\text{t}} \gamma ^2 \delta ^2 g^2 \Delta '} $$\end{document} 10 S S 0 D t δ D t 11 12 27 c n 11 \documentclass[12pt]{minimal}
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\begin{document}$$S = S_0 {\text{e}}^{ - \sum\limits_{n = 1}^N {c_n \sigma ^n } } $$\end{document} 12 \documentclass[12pt]{minimal}
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\begin{document}$$\sigma  = D_{\text{t}} \gamma ^2 \delta ^2 g^2 \Delta '$$\end{document} D t D t v M 13 v 28 θ v 28 13 \documentclass[12pt]{minimal}
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\begin{document}$$D_{\text{t}}  \propto M^\nu  $$\end{document} Results 15 E. coli. 1 15 1 15 2 Fig. 2 15 1 1  1 15 T 1 1 15 T 1 3 1 15 1 Fig. 3 T 1 2  1 T 1 η T 1 A 2 14 14 \documentclass[12pt]{minimal}
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\eta _{{{\text{error}}}}  = {\left| {\frac{{A_{{{\text{NH}} - \alpha }}  + A_{{{\text{NH}} - \beta }} }}
{{A_{{{\text{NH}} - \omega }} }} - 1} \right|}
$$\end{document} Table 1 1 15 T 1 η   14.1T 18.1T 21.1T η T 1 η T 1 η T 1 1 α −1.35 1,790 −1.23 1,625 −0.42 1,526 β −1.63 1,614 −1.22 1,524 −0.56 1,445 ω −1.89 1,255 −0.95 1,183 −0.39 1,116 2 α −0.96 1,613 −0.85 1,473 −0.28 1,400 β −1.12 1,456 −0.79 1,368 −0.34 1,310 γ −1.07 995 −0.33 942 0.14 889 ω −1.17 1,050 −0.38 978 −0.01 939 3 α −0.81 1,437 −0.84 1,362 −0.14 1,342 β −0.99 1,318 −0.75 1,278 −0.33 1,252 γ −0.58 755 0.04 797 0.50 a ψ −0.77 831 −0.17 824 0.40 a ω −0.92 946 −0.18 910 0.25 908 a The heteronuclear experiments for the octasaccharide (3) were collected using two different sweep-widths. In the first experiment a larger sweep width was used, where all nuclei were present and unfolded, but in which the γ- and ψ-amide groups could not be resolved. These resonances were resolved using a second, narrower spectral width (not shown). The spectral width of the second experiment was chosen so that aliased peaks did not interfere with the resonances of interest. 1 2 6 8 τ e 29 τ e 16 19 30 2 S 2 S 2 a priori Table 2 Calculated model-free parameters for the tetra-, hexa- and octa-saccharides (1, 2 and 3 respectively) of the NA-domain of heparan sulfate, using a constant internal correlation time of 30 ps, fitted to isotropic and anisotropic models of rotational diffusion Models of rotational diffusion Isotropic S 2 S 2 calc 1 M 0.57 α 0.32 0.46 e 0.03 β 0.35 0.59   ω 0.48 0.62 2 M 0.71 α 0.35 0.49 e 0.03 β 0.36     γ 0.60 0.70   ω 0.55 0.61 3 M 0.74 α 0.32   e 0.03 β 0.34     γ 0.87     Ψ 0.82     ω 0.67 Anisotropic S 2 α S 2 calc α calc 1 \documentclass[12pt]{minimal}
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\begin{document}$$\tau _{||} $$\end{document} 0.35 α 0.33 15.4 0.46 64.2 \documentclass[12pt]{minimal}
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\begin{document}$${{\tau _ \bot  } \mathord{\left/ {\vphantom {{\tau _ \bot  } {\tau _{||} }}} \right. \kern-\nulldelimiterspace} {\tau _{||} }}$$\end{document} 1.88 ω 0.56 58.6 0.62 63.1 e 0.03       2 \documentclass[12pt]{minimal}
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\begin{document}$${{\tau _ \bot  } \mathord{\left/ {\vphantom {{\tau _ \bot  } {\tau _{||} }}} \right. \kern-\nulldelimiterspace} {\tau _{||} }}$$\end{document} 1.39 γ 0.62 58.6 0.70 64.4 e 0.03 ω 0.61 84.7 0.61 63.3 3 \documentclass[12pt]{minimal}
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\begin{document}$${{\tau _ \bot  } \mathord{\left/ {\vphantom {{\tau _ \bot  } {\tau _{||} }}} \right. \kern-\nulldelimiterspace} {\tau _{||} }}$$\end{document} 2.59 γ 0.65 2.2    e 0.03 Ψ 0.66 23.2      ω 0.54 31.1    S 2 calc α calc 3 10 ν 13 4 D t M ν \documentclass[12pt]{minimal}
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\begin{document}$$\left( {D_{\text{t}}  = 9.4 \times 10^{ - 8} M^{0.48} } \right)$$\end{document} Fig. 4 D t M D t M 13  Table 3 Calculated translational diffusion times using the methyl resonance of the various oligomers (tetra-, hexa- and octasaccharides labeled in table as 1, 2 and 3 respectively) of the NA-domain from heparan sulfate at a proton frequency of 400 MHz Compound D −6 2 1 3.08 ± 0.0004 2 2.55 ± 0.0007 3 2.22 ± 0.0007 5 S 2 α 2 S 2 α Fig. 5 Overlay of 40 snapshots from 50 ns of molecular dynamics simulations of the hexasaccharide of unsulfated heparan sulfate. The molecules are superimposed using the atoms in the adjacent linkages. The position of the nitrogen atom (blue sphere) in each structure is highlighted  1 1 15 4 Table 4 3 J (H2−HN)   3 J (α− [H2−HN]) 3 J (β− [H2−HN]) 3 J (γ− [H2−HN]) 3 J (ω− [H2−HN]) 1 8.43 8.55  9.14 2 8.30 8.65 9.14 9.24 All values have an estimated error of ±0.05 Hz. Discussion Analysis of the NMR relaxation data 15 2 15 1 η η T 1 1 15 1 13 15 15 18 6 11 16 18 30 31 \documentclass[12pt]{minimal}
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\begin{document}$$\left( {\tau _ \bot  } \right)$$\end{document} τ e S 2 α Isotropic or anisotropic model of rotational diffusion? 3 4 4 ν S 2 S 2 α T 1 η α 2 α α S 2 1 S 2 3 i.e. 2 \documentclass[12pt]{minimal}
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\begin{document}$$\left( {\tau _ \bot  } \right)$$\end{document} 5 2 2 J 32 3 J (H2−HN) 4 i.e. 32 S 2 S 2 15 S 2 S 2 2 S 2 4 C 1 S 2 Role of dynamics in HS 16 \documentclass[12pt]{minimal}
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\begin{document}$$\tau _ \bot  $$\end{document} S 2 33 6 34 8 2 4 35 Fig. 6 Schematic diagram illustrating the proposed increase in flexibility due to the NA-domains of heparan sulfate and the concomitant increase in spatial range that can be covered together with the potential for mediating multivalent interactions  i.e. etc 36 36 Conclusions 1 15 15 S 2 S 2 16 Methods and materials Biochemical preparation of oligosaccharides Escherichia coli 15 15 37 15 2 4 4 Sample preparation 2 3 NMR spectroscopy T 1 40 T 1 1 15 41 J et al. 38 39 32 39 37 et al. 38 39 1 15 Model-free NMR relaxation analysis S 2 \documentclass[12pt]{minimal}
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\begin{document}$$\left( {\tau _{||} } \right)$$\end{document} α χ 2 19 ab initio N d 32 42 43 in vacuo 42 44 2 Molecular dynamics simulations 45 S 2 i i−1 d i+1 i+1 i + 1 α α Diffusion ordered spectroscopy (DOSY) experiments −1 46 δ i.e. −1 25 10 −3 −4 −5 27 Electronic supplementary material Below is the link to the electronic supplementary material.
 Supporting Table 1 1 Supporting Table 2 Calculated model-free parameters for the tetra-, hexa-, and octa sacchrides (1, 2, and 3 respectively) of the NA-domain of heparan sulfate, using a constant internal correlation time of 30 ps, fitted to isotopic and anisotropic models of rotational diffusion (PDF 23.5 kb)