Hinge, hinges

Compound Electron count av. Wingtip-hinge Hinge-hinge lengths (A) angle (degrees) Reference... 

Keywords homopolymer, block copolymer, hinge, living hinge, plastic hinge, hinge geometry, process parameter, morphology, oriented layers, stacked lamellae, molecular orientation, hard elasticity, deformation mechanism, transmission electron microscopy (TEM). 

Fig. 27 Time history of the displacement v (a), w (b) and of the angle of twist 0 (c) at the midpoint of the hinged-hinged beam of application section Prismatic Beam of Asymmetric Cross Section Under Harmonic Excitation ...

Interestingly, there are many proteins with two domains that show a very clear hinge-bending motion with an obvious functional significance. Such domains have often been reported in the literature, but were never detected on an automated basis. 

Fig. 5. Rigid-body analysis of citrate synthase, using two X-ray structures (after Hayward and Berendsen, Proteins 30 (1998) 144). The decomposition of the protein into two domains (dark gray and white) and two interconnecting regions (light gray) is shown, together with the hinge axis for the closing/opening motion between them.

G., Berendsen, H.J.C. The essential dynamics of thermolysin Confirmation of the hinge-bending motion and comparison of simulations in vacuum and water. Proteins 22 (1995) 45-54. 

The first technique is very intuitive. Out of the few proteins that could be crystallized in a number of different conformations, adenylate kinase is probably the best-studied example. By combining nine observed crystal structures and interpolating between them, a movie was constructed that visualized a hypothetical path of its hinge-bending transition (jVonrhein et al. 1995]). 

In an early study of lysozyme ([McCammon et al. 1976]), the two domains of this protein were assumed to be rigid, and the hinge-bending motion in the presence of solvent was described by the Langevin equation for a damped harmonic oscillator. The angular displacement 0 from the equilibrium position is thus governed by... 

The effective moment of inertia / and the friction coefficient / could easily be estimated. The force constant k associated with the relative motion of the lobes was determined from an empirical energy function. To do so, the molecule was opened in a step-wise fashion by manipulating the hinge region and each resulting structure was energy minimized. Then, the interaction energy between the two domains was measured, and plotted versus 0. 

B. R. Brooks and M. Karplus. Normal modes for specific motions of macromolecules Application to the hinge-bending mode of lysozyme. Proc. Natl. Acad. Sci. USA, 82 4995-4999, 1985. 

Many elements of ehemists pietures of moleeular stmeture hinge on the point of view that separates the eleetronie motions from the vibrational/rotational motions and treats eouplings between these (approximately) separated motions as perturbations. It is essential to understand the origins and limitations of this separated-motions pieture. 

Example The distance between two ends of a large, flexible molecule can provide information about its structural properties or its interaction with solvent. Analysis of an angle can reveal a hinged motion in a macromolecule. 

Fig. 13. Semirigid piping systems (a) two-hinge arrangement (b) universal-type arrangement.

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