Mathematical aspects of protein structure determination with NMR orientational restraints
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The field of structural biology is becoming increasingly important as new technological developments facilitate the collection of data on the atomic structures of proteins and nucleic acids. The solid-state NMR method is a relatively new biophysical technique that holds particular promise for determining the structures of peptides and proteins that are located within the cell membrane. This method provides information on the orientation of the peptide planes relative to an external magnetic field. In this article, we discuss some of the mathematical methods and tools that are useful in deriving the atomic structure from these orientational data. We first discuss how the data are viewed as tensors, and how these tensors can be used to construct an initial atomic model, assuming ideal stereochemistry. We then discuss methods for refining the models using global optimization, with stereochemistry constraints treated as penalty functions. These two processes, initial model building followed by refinement, are the two crucial steps between data collection and the final atomic model.
KeywordsNuclear Magnetic Resonance Dipolar Coupling Quine Residual Dipolar Coupling Nuclear Magnetic Resonance Method
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- Anfinsen, C. B. (1973). Principles that govern the folding of protein chains. Science 181, 223–230.Google Scholar
- Brünger, A. T. (1992b). X-Plor Version 3.1, A System for Crystallography and NMR, New Haven, CT: Yale University Press.Google Scholar
- Brünger, A. T. and L. M. Rice (1997). Crystallographic refinement by simulated annealing: methods and applications. Methods Enzymol. 277, 243–269.Google Scholar
- Evans, J. N. S. (1995). Biomolecular NMR Spectroscopy, New York: Oxford University Press.Google Scholar
- Lee, D.-K., Y. Wei and A. Ramamoorthy (2001). A two-dimensional magic-angle decoupling and magic-angle turning solid-state NMR method: an application to study chemical shift tensors from peptides that are nonselectively labeled with 15N isotope. J. Phys. Chem. B 105, 4752–4762.CrossRefGoogle Scholar
- MacKerell, A. D. Jr et al. (1998). All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. 102, 3586–3616.Google Scholar
- Mascioni, A. and G. Veglia (2003). Theoretical analysis of residual dipolar coupling patterns in regular secondary structures of proteins. J. Am. Chem. Soc. 41, 12520–12526.Google Scholar
- Mazur, A. K. and R. A. Abagyan (1989). New methodology for computer-aided modelling of biomolecular structure and dynamics. (I) Non-cyclic structures. J. Biomol. Struct. Dynam. 4, 815–832.Google Scholar
- Prestegard, J. H., J. R. Tolman, H. M. Al-Hashimi and M. Andrec (1999). Protein structure and dynamics from field-induced residual dipolar couplings, in Biological Magnetic Resonance, Volume 17: Structure and Dynamics in Protein NMR, Krishna and Berliner (Eds), New York: Plenum Publishers, pp. 311–355.Google Scholar
- Ramamoorthy, A., F. Marassi, M. Zasloff and S. J. Opella (1995). Three-dimensional solid-state NMR spectroscopy of a peptide oriented in membrane bilayers. J. Biol. NMR 6, 329–334.Google Scholar
- Vaidehi, N. and W. A. Goddard III (2001). Atomic-level simulation and modeling of biomacromolecules, in Computational Modeling of Genetic and Biochemical Networks, J. M. Bower and H. Bolouri (Eds), Cambridge, MA: MIT Press, pp. 161–188.Google Scholar