Screw-axis motion

Translation, libration, and screw-axis motions of NCP elements... 

Fig. 17. Composite structural motions of subunits can be described with translation, libration, and screw-axis (TLS) analysis of the NCP. Analysis of the histone subunits are shown here, (a) Composite motion of histones H2A (blue) and H2B (blue) considered as individual elements and combined as H2A H2B dimer (red). Note for the individual histones that the axis of motion is parallel with the medial a-helix of the histone. The origin of the TLS axes are within the structural positions of the histone. The composite motion for the H2A H2B dimer is dominated by the motion of H2A, as is seen in the similarity of orientation and position of the two axes, (b) The orientation and motion of the two H2A H2B dimers appear symmetric across the dyad axis of the NCP. (c) H3 H4 composite motions when considered as dimers (blue) and as the tetramer (red). Interpretation is more complex because of the asymmetric magnitude of motion for the two dimers, and the different position in the axis of primary motion for the tetramer. These motions are most likely the consequence of packing interactions, described in greater detail in the text.

Fig. 2.6. The dynamic domains of goat a-lactalbumin, domain 1 (dark gray) and domain 2 (light gray), and the screw axis of the interdomain motion [24]. The C-helix is involved in domain 2 and moves together with the Ca2+-binding site and the 13-domain. Reproduced with permission from [24]...

The principal component analysis of the dynamics revealed the hingebending motions of the protein. One end of the screw axis of the motions... 

Fig. 4 Molecular structure of the Sg molecule in orthorhombic a-sulfur with bond lengths in pm, bond angles (left) and torsion angles (right). The twofold screw axis of the molecule is indicated. Molecular parameters taken from [80], The values of the bond lengths are those after correction for librational motion giving a mean of 205.5(2) pm in comparison with the uncorrected mean of 204.6(3) pm (Table 5)...

FIGURE 49.11 Approximate location of the optimal axis (case 1 — nonsymmetric, case 3 — symmetric), and the screw axis (case 2) on the medial and lateral condyles of the femur of a human subject for the range of motion of 0 to 90° flexion (standing to sitting, respectively). (From Lewis J.L. and Lew W.D. 1978. /. Biomech. Eng. 100 187. With permission.)... 

The excited state of a single extended polypeptide chain is made up of a band of states with an energy spread which depends on the magnitude of the coupling constants. The transition moment to any one of these states is the sum of all the individual transition moments in the molecule, each multiplied by a phase factor (Schellman and Schellman, 1964). In the important special situation of the polypeptide chain with a twofold screw axis (sheet structures), a group of two peptide groups in sequence can be considered as a unit cell. In this situation (Davydov, 1962) the allowed motions can be described in terms of transition moments that are either in phase with one another or 180° out of phase n radians). The former case produces a parallel absorption band, the latter a perpendicular band thus, the component of the transition moments in the direction of the molecular axis contributes only to the parallel band and the component perpendicular to this axis contributes to the perpendicular band. 

On the other hand, the yield stress of the control specimen can be interpreted in terms of screw dislocation motion. The tensile axis orientation dependence of the yield stress of b.c.c. metals is generally regarded as the effect of the core structure of a screw dislocation on its motion [ ]. A simplistic explanation of this effect is as follows. The screw dislocation is most mobile on a 110 plane. On a 112 plane, the structure of the dislocation core is asymmetric with respect to the (110) direction (direction of motion). Dislocation mobility is not equal in the forward and reverse directions. The higher mobility direction is represented by the [100] tensile axis in the present work and is called the soft 112 slip. The [110] tensile axis represents another case, the hard 112 slip. Hence, the yield stress of the control specimen behaved as shown in Fig. 4. Since the tensile axis orientation dependence is characteristic of the screw dislocation motion, SFS should not be strongly orientation... 

The resulting description of the average rigid-body motion is in terms of six independently distributed instantaneous motions—three screw librations about nonintersecting axes (with screw pitches given by S11/Lll, etc.) and three translations. The parameter set consists of three libration and three translation amplitudes six angles of orientation for the principal axes of L and T six coordinates of axis displacement and three screw pitches, one of which has to be chosen arbitrarily again, for a total of 20 variables. 

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