Torsion angles, and

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

To understand the function of a protein at the molecular level, it is important to know its three-dimensional stmcture. The diversity in protein stmcture, as in many other macromolecules, results from the flexibiUty of rotation about single bonds between atoms. Each peptide unit is planar, ie, oJ = 180°, and has two rotational degrees of freedom, specified by the torsion angles ( ) and /, along the polypeptide backbone. The number of torsion angles associated with the side chains, R, varies from residue to residue. The allowed conformations of a protein are those that avoid atomic coUisions between nonbonded atoms. 

Note The formal lUPAC-IUB Commission on Biochemical Nomenclature convention for the definition of the torsion angles polypeptide chain (Biochemistry 9 3471-3479, 1970) is different from that used here, where the atom serves as the point of reference for both rotations, but the result is the same. (Irving Gas)... 

Table 3. Metal-metal bond lengths and torsion angles and -digallanes and their reduced monoanion derivatives...

Let us leave, for a moment, the domain of discrete torsion angles and consider torsion-angle moves in a torsion continuum. Much effort has been directed to the development of efficient phase-space sampling methods for MC [17,23,37,128-138]. The simplest off-lattice move - being a pivotal move [128,131] of a single torsion angle at a time - hardly samples configuration... 

Fig. 3.12. a Displacement of a point in the moving residue compared with the fixed bond length, b First set of solutions for the torsion angles and c Second set of solutions for the torsion angles... 

Despite the strong interest in the correlation between torsion angle and transport properties, suitable model compounds enabling the systematic variation of the torsion angle in biphenyl systems have not been realized so far, and the role of geometric and electric effects of the substituents is still being actively discussed [48, 72, 74, 271, 277]. 

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