Molecular Structure Refinement of a ß-Heptapeptide Based on Residual Dipolar Couplings: The Challenge of Extracting...

The experimental determination of residual dipolar couplings (RDCs) rests on sampling the rotational motion of a molecule in an environment that induces a slightly nonuniform, unfortunately immeasurable, orientation distribution of the molecule in solution. Averaging over this slightly nonuniform, anisotropic distribution reduces the size of the dipolar couplings (DCs) from the kHz range to the Hz range for the resulting RDCs by a factor of 10³ to 10⁴. These features hamper the use of measured RDCs to contribute to the structure determination or refinement of (bio)molecules. The commonly used alignment-tensor (AT) methodology assumes that the immeasurable, unknown orientation distribution of the molecule can be expressed in terms of five spherical harmonic functions of order 2. Staying close to experiment, RDCs can, alternatively, be calculated from a molecular simulation by sampling the rotational motion of the molecule (MRS method) or, instead, of a vector (mfv) representing the magnetic field (HRS method). The AT and HRS methods were applied to a β-heptapeptide solvated in methanol, for which 131 NOE atom-atom distance upper bounds and 21 ³J-couplings derived from NMR experiments are available and, in addition, 39 RDC values obtained for the molecule solvated in methanol with polyvinyl acetate added. In methanol at room temperature and pressure, the molecule adopts a relatively stable helical fold. It appears that MD simulation of the molecule in methanol using the GROMOS biomolecular force field already satisfies virtually all experimental data. Application of RDC restraining shows the limitations caused by the assumptions on which the AT and HRS methods rest and suggests that experimentally measured RDCs are less useful for molecular structure determination or refinement than other observable quantities that can be measured by NMR techniques. The results illustrate that in structure determination or refinement of a (bio)molecule based on experimentally measured data, it is mandatory (i) to refrain from the vacuum boundary condition and (ii) from torsional-angle restraints that do not account for the multiplicity of the inverse function of the Karplus relation expressing ³J-couplings in terms of molecular torsional angles, (iii) to allow for Boltzmann-weighted time- or molecule-averaging and, not the least, (iv) to use a force field that has an adequate basis in thermodynamic data of biomolecules.