Composite Motions

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. 18. TLS analysis of the palindromic DNA on the NCP. (a) Composite motions of the DNA gyres looking at the ventral surface with the DNA colored by atom type. The two gyres reflect the structural asymmetry of the NCP with non-coincident axes of motion and different orientations for the primary axis of motion. The ventral gyre TLS axes more closely resemble the composite motions of the individual H3 H4 dimers (Fig. 17c), the dorsal TLS axes resemble the composite motion of the tetramer. (b) The composite motions of the DNA gyres are shown in a view down the dyad axis. The DNA is shown in a surface representation colored by atom type. Note that axes of motion appear parallel and in plane with the pitch of the DNA. In this view the ventral surface is on the bottom of the image.

Fig. 19. TLS analysis of the NCP, DNA, and histone core. In these ventral and dorsal views of the NCP model, the composite motion axes of the DNA, histones, and the NCP are shown in red, blue, and green, respectively. The center of motion axes for the DNA and the histones are non-coincident, the TLS axis for the DNA is furthest from the center of mass of the NCP. This may reflect the dominance of the DNA ends in the overall displacement of the DNA. The TLS analysis shows that DNA regions with high B-values, seen in Fig. 15, have little contribution to the overall motion of the DNA on the NCP. The overall motion of the NCP appears dominated by the DNA motion, with the TLS origin shifted in the direction and appearing congruent with the DNA. Overall, the primary axes of motion are in plane with the DNA, hence the interpretation that the composite motions are dominated by dynamic tension between the DNA and the histones, with deviation from these general motions the consequence of packing interactions.

The best way to demonstrate the motion was found [94] to be starting with a rotation tt rad about a horizontal axis to produce a configuration shown in figure 5. The ball can be rotated indefinitely about its vertical axis without the wires becoming permanently entangled. The initial arrangement is restored after each rotation of 47r, i.e. two complete revolutions. The total motion differs from normal rotation about an axis the difference arises with the initial half twist about a horizontal axis. As the ball is then rotated about the vertical axis, the axis of the initial half turn also rotates. The composite motion is more like a continuous wobble than a rotation and the three dimensions of space therefore participate more symmetrically in the motion. 

A no less important point to note is that the six symmetry coordinates comprise a complete set, in terms of which any arbitrary molecular motion can be described. A composite motion like the one in Fig. 3.9 can be constructed by a superposition of symmetry coordinates with suitably chosen phase and amplitude, and is therefore assigned to a reducible representation, the direct sum of its component irreps. It is easy to see that the motion of a single atom also belongs to a reducible representation Displacement of the left-hand X atom parallel to x is clearly a superposition of Tx and the negative phase of Ry, so it belongs to bsu b2g, whereas that of the right-hand atom along z, composed of Tz and transforms as ag... 

The motions observed in the elbow joint are flexion, extension, and rotation (supination and pronation). Flexion and extension are the only motions that involve the true elbow joint, the ulna with the humerus. The elbow joint has the composite motions of elbow flexion, with forearm supination, and elbow extension, with forearm pronation. Therefore, the superior radioulnar joint and its motions complicate, and are part of, elbow joint motion. 

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