Quasi-equivalence

As examples of such quasi-equivalent arrangement of subunits, we will examine the T = 3 and T = 4 packing modes, both of which are found in known virus particles. In the T = 3 structure, which has 180 subunits (3 x 60),... 

Structural versatility gives quasi-equivalent packing in T = 3 plant viruses... 

The molecular basis for quasi-equivalent packing was revealed by the very first structure determination to high resolution of a spherical virus, tomato bushy stunt virus. The structure of this T = 3 virus was determined to 2.9 A resolution in 1978 by Stephen Harrison and co-workers at Harvard University. The virus shell contains 180 chemically identical polypeptide chains, each of 386 amino acid residues. Each polypeptide chain folds into distinct modules an internal domain R that is disordered in the structure, a region (a) that connects R with the S domain that forms the viral shell, and, finally, a domain P that projects out from the surface. The S and P domains are joined by a hinge region (Figure 16.8). 

Small spherical viruses have a protein shell around their nucleic acid that is constructed according to icosahedral symmetry. Objects with icosahedral symmetry have 60 identical units related by fivefold, threefold, and twofold symmetry axes. Each such unit can accommodate one or severed polypeptide chains. Hence, virus shells are built up from multiples of 60 polypeptide chains. To preserve quasi-equivalent symmetry when packing subunits into the shell, only certain multiples (T = 1, 3, 4, 7...) are allowed. 

Tomato bushy stunt virus is a T = 3 plant virus with 180 chemically identical subunits. Each polypeptide chain is divided into several domains. The subunits preserve quasi-equivalent packing in most contact regions by conformational differences of the protein chains, especially a large change in... 

SHAPE CONTROL WITH QUASI-EQUIVALENT DENDRITIC SURFACES - DENDRITIC CYLINDRICAL AND SPHERICAL SHAPES... 

Recent seminal work reported by Percec et al. [45-47] has shown that either spheroidal or cylindrically shaped dendronized polymers may be obtained by the polymerization of a dendronized macromonomer . The degree of polymerization of these monomers determines the ultimate shape which appears to demonstrate the quasi-equivalence of dendritic coats . 

The self-assembly mechanism proposed for these spherical and cylindrical polymer backbones surrounded with quasi-equivalent dendritic coats is outlined in Figure 12.9. This knowledge allows the rational design of polymers with well defined spherical and cylindrical shapes. Quasi-equivalent character of these... 

Figure 12.9 Mechanism of self-assembly of spherical and cylindrical supra-molecules from polymer backbones jacketed with quasi-equivalent dendritic coats [31]...

The transformation from spheres to cyhnders is a peculiar example for the self-adjustment of the molecular conformation. The switching shape can be regarded as an example for the principle of quasi equivalency established by A. Klug for the self-assembly of biomolecules and viruses [145] for the sake of an improved intermolecular packing, the molecules adopt a conformation different from the minimum energy one. This also demonstrates that shape control does not mean a fully constrained structure. Similar to biomolecules, the combination of flexible macromolecules and self-assembly principles is a powerful strategy for preparation of molecules with well-defined but switchable shape [23]. 

DIFFUSION OF LIGAND TO RECEPTOR Biological self-assembly, QUASI-EQUIVALENCE... 

SHIFTED BINDING POLYMERIZATION QUASI-EQUIVALENCE ACTIN ASSEMBLY KINETICS ACTIN-BASED MOTILITY MICROTUBULE ASSEMBLY KINETICS IRREVERSIBLE POLYMERIZATION CRITICAL CONCENTRATION BIOCHEMICAL SELE-ASSEMBLY PROCESSIVITY... 

QUASI-EQUILIBRIUM ASSUMPTION QUASI-EQUIVALENCE Quasi-racemic compound,... 

Quasi-equivalence in virus coats. A large number of icosahedral viruses have coats consisting of 180 identical subunits. For example, the small RNA-containing bacteriophage MS 2 consists of an eicosahedral shell of 180 copies of a 129-residue protein that encloses one molecule of a 3569-residue RNA.89 Tire virus also contains a single molecule of a 44-kDa protein, the A protein, which binds the virus to a bacterial pilus to initiate infection. Related bacteriophages GA, fr, f2, and QP90"1 have a similar... 

The southern bean mosaic virus has an eight-stranded antiparallel (3-barrel structure closely similar to that of the major domain of the bushy stunt viruses but lacking the second hinged domain. The problem of quasi-equivalence is resolved by the presence of an N-terminal extension that binds onto a subunit across the quasi-six-fold axis to give a set of three subunits (labeled C in Fig. 7-19) that associate with true three-fold symmetry and another set (B) with a slightly different conformation fitting between them.68 92 The subunits A, which have a third conformation, fit together around the five-fold axis in true cyclic symmetry. 

Figure 7-19 Schematic icosahedrally symmetric structure with 180 subunits. The quasi-equivalent units A, B, and C are necessarily somewhat differently positioned with respect to their neighbors and must therefore assume different conformations in order to fit together tightly. From Harrison.68...

Newman projection 44 of nucleotides 211 of polysaccharide chains 170 quasi-equivalence 348 random coil 69 sickle 44 skew (S) 166 twist (T) 166... 

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