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REFERENCES

1.S Lovesey. Theory of Thermal Neutron Scattering from Condensed Matter. Int Seri Monogr Phys Vol 72. Oxford, UK: Oxford Science, 1984.

2.JM Cowley. Diffraction Physics. Amsterdam: North-Holland, 1975.

3.JC Smith. Quart Rev Biophys 24(3):227, 1991.

4.JC Smith. In: WF van Gunsteren, PK Weiner, AJ Wilkinson, eds. Computer Simulation of Biomolecular Systems: Theoretical and Experimental Applications, Vol 3. Dordrecht: Kluwer/ ESCOM, 1997, pp 305–360.

5.L van Hove. Phys Rev 95:249, 1954.

6.L van Hove. Physica 24:404, 1958.

7.M Sampoli, G Ruocco, F Sete. Phys Rev Lett 79:1678, 1997.

8.RL Hayward, HD Middendorf, U Wanderlingh, JC Smith. J Chem Phys 102:5525, 1995.

9.M Barthes, H Kellouai, G Page, J Moret, SW Johnson, J Eckert. Physica D 68, 1993.

10.A Micu, JC Smith. Comput Phys Commun 91:331, 1995.

11.M Gerstein, AM Lesk, C Chothia. Biochemistry 33(22):6739, 1994.

12.P Faure, A Micu, AJ Doucet, JC Smith, J-P Benoıˆt. Nature Struct Biol 2:124, 1994.

13.S He´ry, D Genest, JC Smith. J Mol Biol 279:303–319, 1998.

14.DA McQuarrie. Statistical Mechanics. New York: Harper & Row, 1976.

15.A Micu, D Durand, M Quilichini, MJ Field, JC Smith. J Phys Chem 99:5645, 1995.

16.GR Kneller, V Keiner, VM Kneller, M Schiller. Comput Phys Commun 91:191, 1995.

17.M Be´e. Quasielastic Neutron Scattering: Principles and Applications in Solid State Chemistry, Biology and Materials Science. Philadelphia: Adam Hilger, 1988.

18.M Souaille, F Guillaume, JC Smith. J Chem Phys 105(4):1516–1528, 1996.

19.M Souaille, F Guillaume, JC Smith. J Chem Phys 105(4):1529–1536, 1996.

20.M Souaille, JC Smith, F Guillaume. J Phys Chem 101:6753–6757, 1997.

21.N-D Morelon, GR Kneller, M Ferrand, A Grand, JC Smith, M Be´e. J Chem Phys 109(7): 1–12.

22.W Doster, S Cusack, W Petry. Nature 337:754, 1989.

23.JC Smith, K Kuczera, M Karplus. Proc Natl Acad Sci USA. 87:1601, 1990.

24.GR Kneller, JC Smith. J Mol Biol 242:181, 1994.

25.V Receveur, P Calmettes, JC Smith, M Desmadril, G Coddens, D Durand. Proteins: Struct Funct Genet 28:380–387, 1997.

26.AC Zemach, RJ Glauber. Phys Rev 101:118–129, 1956.

27.JC Smith, S Cusack, B Brooks, U Pezzeca, M Karplus. J Chem Phys 85:3636, 1986.

28.AV Goupil-Lamy, JC Smith, J Yunoki, SF Parker, M Kataoka. J Am Chem Soc 119:9268– 9273, 1997.

13

Applications of Molecular Modeling in

NMR Structure Determination

Michael Nilges

European Molecular Biology Laboratory, Heidelberg, Germany

I.INTRODUCTION

High resolution liquid-state NMR emerged as a structure determination technique for biological macromolecules in 1985. From the beginning, molecular modeling has had a central place in the derivation of NMR solution structures [1–4]. There are several reasons for this. First, the energy parameters, typically derived from a molecular dynamics or molecular mechanics force field, play a central role in calculating and refining the structure. This is because experimental data are scarce, being available for only a fraction of the atoms (mostly the hydrogens). An additional difficulty is that most of the data describe relative positions of atoms and do not directly correspond to the global structure of the molecule. Second, models are not built manually but are automatically calculated by appropriate algorithms. In this way the conformational space consistent with the data is sampled randomly to test whether the data determine the structure uniquely. Consequently, a lot of effort has gone into the development of algorithms to fit the experimental data. The methods used for NMR structure calculations are usually adapted from algorithms originally developed for different purposes in molecular modeling. Third, the wealth of dynamic information obtained by NMR and the difficulties in interpreting it in structural terms have led to a close interaction with MD simulation [5–9].

II. EXPERIMENTAL DATA

A. Deriving Conformational Restraints from NMR Data

The principal sources of structural data [10] are the nuclear Overhauser effect (NOE), which gives information on the spatial proximity of protons (up to a distance of about 4

˚

A); coupling constants, which give information on dihedral angles; and residual dipolar couplings [11,12], which give information on the relative orientation of a bond vector to the molecule (e.g., to the chemical anisotropy tensor or an alignment tensor; see Fig. 1). With residual dipolar couplings one can, for example, define the relative orientation of domains. Because of the increasing number of experimental terms, we can get an increasingly complete description of the molecule in solution. The NOE is, however, still the

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Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons; coupling constants, which give information on dihedral angles φ; and residual dipolar couplings, which give information on the relative orientation θ of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

richest source of structural information and at the same time the most problematic to analyze. Therefore, in this chapter we mostly deal with the treatment of NOEs in determining NMR solution structures. The other energy terms are included in structure refinements in a very similar manner (see, e.g., the literature cited in Ref. 13).

The first step for any structure elucidation is the assignment of the frequencies (chemical shifts) of the protons and other NMR-active nuclei (13C, 15N). Although the frequencies of the nuclei in the magnetic field depend on the local electronic environment produced by the three-dimensional structure, a direct correlation to structure is very complicated. The application of chemical shift in structure calculation has been limited to final structure refinements, using empirical relations [14,15] for proton and 13C chemical shifts and ab initio calculation for 13C chemical shifts of certain residues [16].

In addition, hydrogen bonding can be deduced from NMR data by analyzing the exchange of labile protons [10]. Only the hydrogen bond donor can be determined in this way. The hydrogen bond acceptor is difficult to observe experimentally, and it has only recently been realized that scalar (‘‘through-bond’’) couplings can be measured across hydrogen bonds [17,18]. Most often, the hydrogen bond acceptor is inferred from a prelim-