Dihedral angle space

The conformational distance does not have to be defined in Cartesian coordinates. Eor comparing polypeptide chains it is likely that similarity in dihedral angle space is more important than similarity in Cartesian space. Two conformations of a linear molecule separated by a single low barrier dihedral torsion in the middle of the molecule would still be considered similar on the basis of dihedral space distance but will probably be considered very different on the basis of their distance in Cartesian space. The RMS distance is dihedral angle space differs from Eq. (12) because it has to take into account the 2n periodicity of the torsion angle. 

B. Normal Mode Analysis in Dihedral Angle Space... 

Lee, B., Kurochkina, N. and Kang, H. S. (1996). Protein folding by a biased Monte Carlo procedure in the dihedral angle space. Faseb J, 10,119-125. 

Optimal filtering was proposed by Altman and Jardetzky (1989) as a heuristic refinement method of structure determination and has also been applied to the dihedral angle space (KoeU et al., 1992). Optimal filtering uses the exclusion paradigm, and during the search aU possible conformations are retained except where they are incompatible with the data. This allows a more systematic search of the allowed conformational space. As in the case of distance geometry, it is a ptire geometric method, and it calculates the mean positions and standard deviations of each atom. The output also needs to be refined to add information fi om the empirical force field. 

Figure 59. Probability distribution for the alanine dipeptide in the (, 1/9 dihedral-angle space at 300 K (a) vacuum potential surface (b) solvent-modified potential surface.

Thus, /(Ni,C i), J(Ni,C i), and possibly other J-couplings could definitely be used as a secondary structure index, that is, to discriminate between most different conformations such as helical and beta-sheet, but one should abstain to use the corresponding Karplus fits to establish quantitative relations with dihedral angles. The use of these Karplus fits to estimate the J-coupling values from the averaging over an MD simulation trajectory that does sample the entire dihedral angle space is questionable [110]. 

Yang YD, Liu HY (2006) Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space. J Comput Chem 27 1593-1602... 

It is remarked that the use of internal coordinate models is also of interest for normal mode calculations since a reduced number of variables simplifies the eigenvalue problem and also eliminates the high frequency movements associated with bond stretching, which are only weakly coupled to the low frequency collective modes. It has also been demonstrated that the harmonicity of the energy hypersurface can be assumed over a wider range in dihedral angle space than in Cartesian space. This approach, however, requires a special treatment to exclude any motion of the center of mass of the system. ... 

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