Flexible molecules, structure determination

Each class of molecules has a similar structural hierarchy subunits of fixed structure are connected by bonds of limited flexibility to form macromolecules with three-dimensional structures determined by noncovalent interactions. These macromolecules then interact to form the supramolecular structures and organelles that allow a cell to carry out its many metabolic functions. Together, the molecules described in Part I are the stuff of life. We begin with water. 

Novel properties of peptides can be obtained by incorporation of Saa. Peptides are characteristically highly flexible molecules whose 3D structure is strongly influenced by their environment. Their often unordered conformation in solution complicates their use in determining the receptor bound bioactive structure.182,831 Conformational constraints,184-881 cyclization/891 and/or replacement of the peptide backbone or parts of it162 90-921 can provide information on the required conformation for biological activity. 

However, one of the interesting aspects of NMR structural results is that they often suggest no discernible solution structure for small systems, such as a tri- or tetra-peptides. This is due to the flexibility and structural variance displayed by these sample systems. However, the lack of interactions between parts of the molecule, which normally are detected via Nuclear Overhauser enhancements and refined into molecular structures during NMR structural determinations, should not be interpreted as a lack of a solution structure. It is the slow time scale of NMR, coupled with the rapidly interconverting conformations, which weakens these effects to the point where they can no longer be detected with certainty, and structural techniques which operate on a much faster time scale (e.g., UV-CD spectroscopy, or forms of vibrational spectroscopy) demonstrate that there is a preferred class of solution conformers even in small peptide systems. 

However, all standard NMR parameters are of short-ranged nature chemical shifts are typically affected by the first and second sphere of atoms surrounding the nucleus and usually provide only qualitative measures 3/-couplings are limited to dihedral angles via three covalent bonds and through space connectivities via NOE can only be found up to 5 A in favourable cases. As soon as the chain of short-range information is interrupted by NMR-inactive nuclei or a flexible linker, distant parts of a molecule cannot be correlated and the structure determination is bound to fail. 

Rigid Molecule Group theory will be given in the main part of this paper. For example, synunetry adapted potential energy function for internal molecular large amplitude motions will be deduced. Symmetry eigenvectors which factorize the Hamiltonian matrix in boxes will be derived. In the last section, applications to problems of physical interest will be forwarded. For example, conformational dependencies of molecular parameters as a function of temperature will be determined. Selection rules, as wdl as, torsional far infrared spectrum band structure calculations will be predicted. Finally, the torsional band structures of electronic spectra of flexible molecules will be presented. 

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