Journal of Biomolecular NMR 29: 517–524, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 517 Alignment of chain-like molecules Martti Louhivuori a , Kai Fredriksson b , Kimmo Pääkkönen c , Perttu Permi c & Arto Annila a,b,c,∗ Departments of a Physical Sciences, b Biosciences, c NMR Laboratory, Structural Biology and Biophysics Program, Institute of Biotechnology, University of Helsinki, Finland Received 5 January 2004; Accepted 30 March 2004 Key words: characteristic ratio, denatured protein, persistence length, random-flight chain, residual dipolar couplings, valence chain Abstract The steric obstruction model, that describes the enhanced alignment of folded proteins by anisotropic medium, is extended to account for the residual dipolar couplings of chain-like polypeptides. The average alignment of each chain segment is calculated from an ensemble of conformations represented by a spatial probability distribution. The segmental alignment depends on chain length, flexibility and segment’s position in the chain. Residual dipolar couplings in turn depend on internuclear vector directions within each fragment. The results of calculations and simulations explain salient features of the experimental data. With this insight residual dipolar couplings can be interpreted to assess the degree of denaturation, local structures and spatial organization of weakly structured proteins. Introduction Residual dipolar couplings (RDCs) are particularly in- formative NMR parameters for studies of biological macromolecules in solution (Tjandra and Bax, 1997; Mueller et al., 2000; Prestegard et al., 2000; Bax et al., 2001; De Alba and Tjandra, 2002). Most notably RDCs relate to orientations of chemical bonds with respect to a molecular coordinate system. RDCs have been used to determine and refine three-dimensional structures, to build models of macromolecular com- plexes from known sub-units (Clore, 2000; Fischer et al., 1999; Mattinen et al., 2002), to construct three- dimensional protein models from protein fragments deposited in the PDB (Delaglio et al., 2000; Andrec et al., 2001), to study spatial arrangements of modular proteins (Fischer et al., 1999; Chou et al., 2001), and to recognize (Annila et al., 1999) and classify protein folds (Valafar and Prestegard, 2003). For diamagnetic proteins RDCs are intrinsically small (Tjandra et al., 1996) but become readily observable and applicable when anisotropic molecular tumbling is enhanced by ∗ To whom correspondence should be addressed. E-mail: arto.annila@helsinki.fi liquid crystal particles (Tjandra and Bax, 1997; Meier et al., 2002) or axial polymer matrices (Tycko et al., 2000). The enhanced alignment due to the obstruction is a well-understood phenomenon for structured mac- romolecules (Zweckstetter and Bax, 2000; Bax et al., 2001; Fernandes et al., 2001), i.e., for folded proteins. Recently RDCs were also recorded from denatured proteins (Shortle and Ackerman, 2001; Ackerman and Shortle, 2002; Ohnishi and Shortle, 2003). However, the first interpretations were based on an incorrect im- plicit assumption that only a molecule with a defined three-dimensional architecture may give rise to non- vanishing RDCs. It was subsequently shown through an analytical calculation that the mere structure of a random-flight chain is sufficient to yield non-zero RDCs (Louhivuori et al., 2003). To progress in in- terpreting RDCs acquired from denatured proteins we have formulated a valence chain model to account for steric hindrance between residues and simulated chains of varying flexibility.