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Deuterium isotope effects on 15N backbone chemical shifts in proteins.

Abildgaard J, Hansen PE, Manalo MN, LiWang A - J. Biomol. NMR (2009)

Bottom Line: The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N-H bond length.Another contributing factor is the effect of increased anharmonicity of the N-H stretching vibrational state upon hydrogen bonding, which results in an altered N-H/N-D equilibrium bond length ratio.For residues with uncharged side chains a very good prediction of isotope effects can be made.

View Article: PubMed Central - PubMed

Affiliation: Department of Science, Systems and Models, Roskilde University, Roskilde, Denmark.

ABSTRACT
Quantum mechanical calculations are presented that predict that one-bond deuterium isotope effects on the (15)N chemical shift of backbone amides of proteins, (1)Delta(15)N(D), are sensitive to backbone conformation and hydrogen bonding. A quantitative empirical model for (1)Delta(15)N(D) including the backbone dihedral angles, Phi and Psi, and the hydrogen bonding geometry is presented for glycine and amino acid residues with aliphatic side chains. The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N-H bond length. Another contributing factor is the effect of increased anharmonicity of the N-H stretching vibrational state upon hydrogen bonding, which results in an altered N-H/N-D equilibrium bond length ratio. The N-H stretching anharmonicity contribution falls off with the cosine of the N-H...O bond angle. For residues with uncharged side chains a very good prediction of isotope effects can be made. Thus, for proteins with known secondary structures, (1)Delta(15)N(D) can provide insights into hydrogen bonding geometries.

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Experimental versus predicted 1Δ15N(D) values for aliphatic residues using Eq. 2 for the protein ubiquitin. The solid circle and solid squares are for (apparently) non-hydrogen bonded backbone amides of glycine and leucine residues, respectively. The line is along the diagonal. The residues used in this plot are listed in Table 2. The pairwise root mean square difference between the experimental and calculated values is 0.014 ppm
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Fig7: Experimental versus predicted 1Δ15N(D) values for aliphatic residues using Eq. 2 for the protein ubiquitin. The solid circle and solid squares are for (apparently) non-hydrogen bonded backbone amides of glycine and leucine residues, respectively. The line is along the diagonal. The residues used in this plot are listed in Table 2. The pairwise root mean square difference between the experimental and calculated values is 0.014 ppm

Mentions: Thus, calculations suggest that 1Δ15N(D) are sensitive to (1) backbone conformation, (2) electric-field effects and (3) anharmonicity effects from hydrogen bonding. We therefore performed a fit of the experimental 1Δ15N(D) data against backbone dihedral angles and geometric parameters of the hydrogen bonds for all amino acids with aliphatic side chains and glycine (Table 2) and obtained the following empirical equation for 1Δ15N(D):2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ ^{1} {{\Updelta}}^{15} {\text{N}}({\text{D}}) = A + B\Upphi^\prime + C\Uppsi^\prime + D\cos \theta_{{{\text{N}}-{\text{H}} \cdots {\text{O}}}} $$\end{document}where Φ′ = cos(Φ + 88° ± 8°), Ψ′ = cos(Ψ−68° ± 9°), A = 0.66 ± 0.02 ppm, B = 0.06 ± 0.01 ppm, C = 0.043 ± 0.009 ppm Å, and D = 0.03 ± 0.02 ppm. The coefficients are the averages of 10,000 fits where each time six out of 22 data points were randomly removed, and the values of the coefficients A, B, and C were randomly set between −1.0 and +1.0 ppm prior to each fit, whereas D was randomly set between −5.0 and +5.0 ppm. The standard deviations of the averages from these fits are used as estimates of the uncertainties in the coefficients. Angles were obtained as explained above using the BPW91/6-31G(d) level of theory. F-test analysis showed that including the factor 1/r, where r is the hydrogen bond distance, in term D does not statistically improve the fit for Eq. 2. A plot of the experimental 1Δ15N(D) values versus predictions from Eq. 2 for the protein ubiquitin are shown in Fig. 7. The pairwise root mean square difference between the experimental and predicted 1Δ15N(D) values is 0.014 ppm.Table 2


Deuterium isotope effects on 15N backbone chemical shifts in proteins.

Abildgaard J, Hansen PE, Manalo MN, LiWang A - J. Biomol. NMR (2009)

Experimental versus predicted 1Δ15N(D) values for aliphatic residues using Eq. 2 for the protein ubiquitin. The solid circle and solid squares are for (apparently) non-hydrogen bonded backbone amides of glycine and leucine residues, respectively. The line is along the diagonal. The residues used in this plot are listed in Table 2. The pairwise root mean square difference between the experimental and calculated values is 0.014 ppm
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Fig7: Experimental versus predicted 1Δ15N(D) values for aliphatic residues using Eq. 2 for the protein ubiquitin. The solid circle and solid squares are for (apparently) non-hydrogen bonded backbone amides of glycine and leucine residues, respectively. The line is along the diagonal. The residues used in this plot are listed in Table 2. The pairwise root mean square difference between the experimental and calculated values is 0.014 ppm
Mentions: Thus, calculations suggest that 1Δ15N(D) are sensitive to (1) backbone conformation, (2) electric-field effects and (3) anharmonicity effects from hydrogen bonding. We therefore performed a fit of the experimental 1Δ15N(D) data against backbone dihedral angles and geometric parameters of the hydrogen bonds for all amino acids with aliphatic side chains and glycine (Table 2) and obtained the following empirical equation for 1Δ15N(D):2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ ^{1} {{\Updelta}}^{15} {\text{N}}({\text{D}}) = A + B\Upphi^\prime + C\Uppsi^\prime + D\cos \theta_{{{\text{N}}-{\text{H}} \cdots {\text{O}}}} $$\end{document}where Φ′ = cos(Φ + 88° ± 8°), Ψ′ = cos(Ψ−68° ± 9°), A = 0.66 ± 0.02 ppm, B = 0.06 ± 0.01 ppm, C = 0.043 ± 0.009 ppm Å, and D = 0.03 ± 0.02 ppm. The coefficients are the averages of 10,000 fits where each time six out of 22 data points were randomly removed, and the values of the coefficients A, B, and C were randomly set between −1.0 and +1.0 ppm prior to each fit, whereas D was randomly set between −5.0 and +5.0 ppm. The standard deviations of the averages from these fits are used as estimates of the uncertainties in the coefficients. Angles were obtained as explained above using the BPW91/6-31G(d) level of theory. F-test analysis showed that including the factor 1/r, where r is the hydrogen bond distance, in term D does not statistically improve the fit for Eq. 2. A plot of the experimental 1Δ15N(D) values versus predictions from Eq. 2 for the protein ubiquitin are shown in Fig. 7. The pairwise root mean square difference between the experimental and predicted 1Δ15N(D) values is 0.014 ppm.Table 2

Bottom Line: The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N-H bond length.Another contributing factor is the effect of increased anharmonicity of the N-H stretching vibrational state upon hydrogen bonding, which results in an altered N-H/N-D equilibrium bond length ratio.For residues with uncharged side chains a very good prediction of isotope effects can be made.

View Article: PubMed Central - PubMed

Affiliation: Department of Science, Systems and Models, Roskilde University, Roskilde, Denmark.

ABSTRACT
Quantum mechanical calculations are presented that predict that one-bond deuterium isotope effects on the (15)N chemical shift of backbone amides of proteins, (1)Delta(15)N(D), are sensitive to backbone conformation and hydrogen bonding. A quantitative empirical model for (1)Delta(15)N(D) including the backbone dihedral angles, Phi and Psi, and the hydrogen bonding geometry is presented for glycine and amino acid residues with aliphatic side chains. The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N-H bond length. Another contributing factor is the effect of increased anharmonicity of the N-H stretching vibrational state upon hydrogen bonding, which results in an altered N-H/N-D equilibrium bond length ratio. The N-H stretching anharmonicity contribution falls off with the cosine of the N-H...O bond angle. For residues with uncharged side chains a very good prediction of isotope effects can be made. Thus, for proteins with known secondary structures, (1)Delta(15)N(D) can provide insights into hydrogen bonding geometries.

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