Proteins spherical

What we mean by the molecular weight cut-off of a "diffuse cut-off" membrane must be clearly defined. The convention established by AMICON and adopted by most UF membrane manufacturers is based on the retention of globular proteins (spherical macromolecules). The retention R (in percent) maybe defined as follows ... 

Figure 3.18 shows how this is determined. The retention values of a series of globular proteins (spherical molecules) are measured on the same membrane. The molecular weight at which the retention curve crosses a retentivity of 90% is the "molecular weight cut-off" of the membrane. This means that larger molecules are said to be retained by the membrane and smaller molecules are said to pass. 

Since f is a measurable quantity for, say, a protein, and since the latter can be considered to fail into category (3) in general, the friction factor provides some information regarding the eilipticity and/or solvation of the molecule. In the following discussion we attach the subscript 0 to both the friction factor and the associated radius of a nonsolvated spherical particle and use f and R without subscripts to signify these quantities in the general case. Because of Stokes law, we write... 

Seeds. Seeds are produced in pods, usually containing three almost spherical-to-oval seeds weighing 0.1—0.2 g. Commercial varieties have a yellow seed coat plus two cotyledons, plumule, and hypocotyl-radicle axis. The cotyledons contain primarily protein and Hpid bodies (see Fig. 1). Cottonseed. 

Seeds. The seeds are produced in pods containing two or three seeds. The kernels are almost spherical to roughly cylindrical (0.4—1.1 g each) and consist of a thin coat (testa) containing two cotyledons and the embryo. Cotyledons contain protein bodies, Hpid bodies, and starch granules. 

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

Although the continuum model of the ion could be analyzed by Gauss law together with spherical symmetry, in order to treat more general continuum models of electrostatics such as solvated proteins we need to consider media that have a position-specific permittivity e(r). For these a more general variant of Poisson s equation holds ... 

A nucleic acid can never code for a single protein molecule that is big enough to enclose and protect it. Therefore, the protein shell of viruses is built up from many copies of one or a few polypeptide chains. The simplest viruses have just one type of capsid polypeptide chain, which forms either a rod-shaped or a roughly spherical shell around the nucleic acid. The simplest such viruses whose three-dimensional structures are known are plant and insect viruses the rod-shaped tobacco mosaic virus, the spherical satellite tobacco necrosis virus, tomato bushy stunt virus, southern bean mosaic vims. 

The protein shells of spherical viruses have icosahedral symmetry... 

Two basic principles govern the arrangement of protein subunits within the shells of spherical viruses. The first is specificity subunits must recognize each other with precision to form an exact interface of noncovalent interactions because virus particles assemble spontaneously from their individual components. The second principle is genetic economy the shell is built up from many copies of a few kinds of subunits. These principles together imply symmetry specific, repeated bonding patterns of identical building blocks lead to a symmetric final structure. 

Figure 16.2 The icosahedron (top) and dodecahedron (bottom) have identical symmetries but different shapes. Protein subunits of spherical viruses form a coat around the nucleic acid with the same symmetry arrangement as these geometrical objects. Electron micrographs of these viruses have shown that their shapes are often well represented by icosahedra. One each of the twofold, threefold, and fivefold symmetry axes is indicated by an ellipse, triangle, and pentagon, respectively.

The asymmetric unit of an icosahedron can contain one or several polypeptide chains. The protein shell of a spherical virus with icosahedral symmetry... 

The fact that spherical plant viruses and some small single-stranded RNA animal viruses build their icosahedral shells using essentially similar asymmetric units raises the possibility that they have a common evolutionary ancestor. The folding of the main chain in the protein subunits of these viruses supports this notion. 

The coat proteins of many different spherical plant and animal viruses have similar jelly roll barrel structures, indicating an evolutionary relationship... 

One of the most striking results that has emerged from the high-resolution crystallographic studies of these icosahedral viruses is that their coat proteins have the same basic core structure, that of a jelly roll barrel, which was discussed in Chapter 5. This is true of plant, insect, and mammalian viruses. In the case of the picornaviruses, VPl, VP2, and VP3 all have the same jelly roll structure as the subunits of satellite tobacco necrosis virus, tomato bushy stunt virus, and the other T = 3 plant viruses. Not every spherical virus has subunit structures of the jelly roll type. As we will see, the subunits of the RNA bacteriophage, MS2, and those of alphavirus cores have quite different structures, although they do form regular icosahedral shells. 

The cleft where this drug binds is inside the jelly roll barrel of subunit VPl. Most spherical viruses of known structure have the tip of one type of subunit close to the fivefold symmetry axes (Figure 16.15a). In all the picor-naviruses this position is, as we have described, occupied by the VPl subunit. Two of the four loop regions at the tip are considerably longer in VPl than in the other viral coat proteins. These long loops at the tips of VPl subunits protrude from the surface of the virus shell around its 12 fivefold axes (Figure 16.15b). 

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. 

Chen, Z., et al. Protein-nucleic acid interactions in a spherical virus the structure of beanpod mottle virus at 3.0 A resolution. Science 245 154-159, 1989. 

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