Macromolecules dimensionality

A number of structured databases have been developed to classify proteins according to the three-dimensional structures. Many of these are accessible via the World Wide Web, T1 protein databanlc (PDB [Bernstein d al. 1977]) is the primary source of data about the stru tures of biological macromolecules and contains a large number of structures, but many i these are of identical proteins (complexed with different ligands or determined at differet resolutions) or are of close homologues. 

Unsaturated polyester resins prepared by condensation polymerization constitute the largest industrial use for maleic anhydride. Typically, maleic anhydride is esterified with ethylene glycol [107-21-1] and a vinyl monomer or styrene is added along with an initiator such as a peroxide to produce a three-dimensional macromolecule with rigidity, insolubiUty, and mechanical strength. 

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. 

Early efforts to develop molecular models emphasized ways of representing three-dimensional aspects in two-dimensional projections. Some of the problems addressed were the folding of macromolecules (43,44) and two-dimensional projections with hidden surfaces (45,46). The state of the art in the early 1970s has been reviewed (47). 

High-resolution observation of dynamics of bio-macromolecules in cells and bio-organisms atomic or molecular level, regional or focused observation, three-dimensional analysis ... 

The well-known difficulties in calculating tliree-dimensional structures of macromolecules from NMR data mentioned above (sparseness of the data, imprecision of the restraints due to spin diffusion and internal dynamics) also make the validation of the structures a challenging task. The quality of the data [88] and the energy parameters used in the refinement [89] can be expected to influence the quality of structures. Several principles can be used to validate NMR structures. 

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

The processes of ordering in polymer systems consisting of linear polymers are related, at least on one level of supermolecular organization, to the development of a predominant localization of macromolecules (or their parts) along some directions the orientation axes, i.e. to the transition of the system into the oriented state. The most simple and most widely spread type of polymer orientation is the uniaxial orientation, i.e. the one-dimensional orientation in the direction of the axes of macromolecules. 

Any extended part of a linear polymer molecule exhibits a strong anisotropy of many properties since its atoms and atomic groups are oriented and the macromolecule is actually a one-dimensional crystal . The parallel packing of these parts during the formation of a uniaxially oriented polymer substance imparts the anisotropie properties of a single molecule to the whole polymeric material. 

The formation of ECC is not only an extension of a portion of the macromolecule but also a mutual orientational ordering of these portions belonging to different molecules (intermolecular crystallization), as a result of which the structure of ECC is similar to that of a nematic liquid crystal. After the melt is supercooled below the melting temperature, the processes of mutual orientation related to the displacement of molecules virtually cannot occur because the viscosity of the system drastically increases and the chain mobility decreases. Hence, the state of one-dimensional orientational order should be already attained in the melt. During crystallization this ordering ensures the aggregation of extended portions to crystals of the ECC type fixed by intermolecular interactons on cooling. 

Although the conjugated gradient and related methods are very effective in finding local minima, they do not overcome the problems associated with the enormous dimensionality of macromolecules. That is, in systems with... 

Yethiraj, A. (2003) Computer simulation study of two-dimensional polymer solutions. Macromolecules, 36, 5854-5862. 

Shuto, K., Oishi, Y, Kajiyama, T. and Han, C. C. (1993) Aggregation structure of a two-dimensional ultrathin polystyrene film prepared by the water casting method. Macromolecules, 26, 6589-6594. 

Sato, N., Ito, S. and Yamamoto, M. (1998) Molecular weight dependence of shear viscosity of a polymer monolayer evidence for the lack of chain entanglement in the two-dimensional plane. Macromolecules, 31, 2673-2675. 

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