Torsion angle space

Usually, two conformations are regarded as geometrically different if their minimized RMS deviation is equal to or larger than 0.3 A in Cartesian space RMSx z)> or 30 " in torsion angle space (RMSja). respectively. 

Recently, MD constrained to torsion angle space [torsion angle dynamics (TAD)] was introduced to refinement calculations [33,57,58]. Earlier versions of the equations of... 

Schaumann T, Braun W, Wilthrich K. The program FANTOM for energy refinement of polypeptides and proteins using a Newton-Raphson minimizer in torsion angle space. Biopolymers 1990 29 679-694. 

One possibility is to run simulated annealing refinement in torsion angle space as implemented in CNS (Briinger et ah, 1998). As this is one of the most powerful programs in terms of radius of convergence, it is especially useful to look for the decrease of the free-R-factor (Adams et al., 1999), but this is a rather cpu-intensive task if several possible solutions are to be tested. 

FANTOM for Energy Refinement of Polypeptides and Proteins Using a Newton—Raphson Minimizer in Torsion Angle Space. 

Torsion angle space minimization (variable target function method) 242... 

The second method developed is the torsion angle space minimization algorithm.32 This is a method to optimize the target function in the torsion angle space. The degrees of freedom are the torsion angles. Basically, the... 

Molecular dynamics calculation is solving Newton s equation of motion using a hybrid target function between empirical force fields and experimental data. The degrees of freedom are the Cartesian coordinates of the atoms. The dynamics aim to cross potential barriers caused by inappropriately folded structures. This can reduce the problem of being trapped in local minima more than the torsion angle space minimization. Usually, a... 

Fig. 2. Schematic representation of conformational space exploration efficiencies and their dependency for the different sampling scale with, insufficient (A), nearly sufficient (B), and almost sufficient (C) number of initial structures. In this example, preliminary calculations are distance geometry or torsion angle space algorithms, and refinement is restraint molecular dynamics with same set of NMR-derived structural information. The exploration extents of the refinements are assumed to be similar for selected preliminary calculation s results (i.e., initial structures of the refinement calculations).

To describe correlated peptide conformation fluctuations in internal coordinates, the multivariate Gaussian distribution fiG used for characteristic packets and integration kernels in Cartesian space must be adapted to the periodic and multiply connected torsion angle space. Although the Carte-... 

Macromolecules can pose a special problem—even after coarse-grained dissection the macrostate probability distributions at high temperatures are seldom well modeled by Gaussian kernels, even in torsion-angle space. For example, we examined arbitrarily selected macrostates of Met-enkephalin and found that ( . > a useful goodness-of-fit measure, was typically... 

Fig. 1 illustrates torsional potentials in HS-SH and HSe-SeH molecules obtained from moment truncated multicenter multipole expansion combined with Frozen Fragment (FF) approximation [13] and compared with corresponding SCF results. Apparently the torsional potentials are controlled in this case solely by quadrupole moments (M—k -l- -m- -2). Dominant contribution of electrostatic effects in torsional potentials seems to be limited to systems with unusually long bonds [13,26], where also delocalization is excluded. The leading role of quadrupole term could explain why d polarization functions are sometimes required to obtain proper results in conformational analysis in torsional angle space. 

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