Overall shape

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

FIGURE 7 12 Chohc acid Its 11 chirality centers are those carbons at which stereochemistry is indicated in the structural drawing at the left The molecular model at the right more dearly shows the overall shape of the molecule... 

As Figure 25 8 shows the glucose units of cellulose are turned with respect to each other The overall shape of the chain however is close to linear Consequently neigh boring chains can pack together m bundles where networks of hydrogen bonds stabilize the structure and impart strength to cellulose fibers... 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

Tertiary structure also refers to the overall shape of a molecule, especially to structures stabilized by disulfide bridges (cystine) formed by the oxidation of cysteine mercapto groups. 

The three levels of structure listed above are also useful categories for describing nonprotein polymers. Thus details of the microstructure of a chain is a description of the primary structure. The overall shape assumed by an individual molecule as a result of the rotation around individual bonds is the secondary structure. Structures that are locked in by chemical cross-links are tertiary structures. 

As useful as molecular models are, they are limited in that they only show the location of the atoms and the space they occupy. Another important dimension to molecular structure is its electron distribution. We introduced electrostatic potential maps in Section 1.5 as a way of illustrating charge distribution and will continue to use them throughout the text. Figure 1.6(d) shows the electrostatic potential map of methane. Its overall shape is similar to the volume occupied by the space-filling model. The most electron-rich regions are closer to carbon and the most electron-poor ones are closer to the hydrogens. 

The small change in stereochemistry between cellulose and amylose creates a large difference in their overall shape and in their properties. Some of this difference can be seen in the strorcture of a short portion of fflnylose in Figure 25.9. The presence of the a-glycosidic linkages imparts a twist to the fflnylose chain. Where the main chain is roughly linear- in cellulose, it is helical in anylose. Attractive forces between chains are weaker in fflnylose, and fflnylose does not form the same kind of strong fibers that cellulose does. 

The processes of electron transport and oxidative phosphorylation are membrane-associated. Bacteria are the simplest life form, and bacterial cells typically consist of a single cellular compartment surrounded by a plasma membrane and a more rigid cell wall. In such a system, the conversion of energy from NADH and [FADHg] to the energy of ATP via electron transport and oxidative phosphorylation is carried out at (and across) the plasma membrane. In eukaryotic cells, electron transport and oxidative phosphorylation are localized in mitochondria, which are also the sites of TCA cycle activity and (as we shall see in Chapter 24) fatty acid oxidation. Mammalian cells contain from 800 to 2500 mitochondria other types of cells may have as few as one or two or as many as half a million mitochondria. Human erythrocytes, whose purpose is simply to transport oxygen to tissues, contain no mitochondria at all. The typical mitochondrion is about 0.5 0.3 microns in diameter and from 0.5 micron to several microns long its overall shape is sensitive to metabolic conditions in the cell. 

Draw a line-bond structure for propane, CH3CH2CH3. Predict the value of each bond angle, and indicate the overall shape of the molecule. 

Don t be intimidated by the size of the molecule most of the structure is there to provide an overall shape for binding to the enzyme and to provide appropriate solubility behavior. When looking at biological molecules, focus on the small part of the molecule where the chemical change takes place. 

As outlined in Section III.A, knowledge of the molecular wavefunction implies knowledge of the electron distribution. By setting a threshold value for this function, the molecular boundaries can be established, and the path is open to a definition of molecular shape. A quicker, but quite effective, approach to this entity is taken by assuming that each atom in a molecule contributes an electron sphere, and that the overall shape of a molecular object results from interpenetration of these spheres. The necessary radii can be obtained by working backwards from the results of MO calculations21, or from some kind of empirical fitting22. 

Figure 46. Separation of the overall oxidation curve into its two components a relaxation curve, responsible for the initial slope and the position of the chronoamperometric maximum, and a diffusion curve that controls the overall shape of the chronoampero-gram. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, J. Phys. Chem. 101, 3688, 1997, Figs. 1, 3, 6, 7, 13. Copyright 1997. Reprinted with permission from the American Chemical Society.)...

STRATEGY Write down the Lewis structure and identify the electron arrangement around each central atom (each C atom, in this case). Treat each multiple bond as a single unit. Then identify the overall shape of the molecule (refer to Fig. 3.2 if necessary). 

Now consider the overall shape of the pH curve. The slow change in pH about halfway to the stoichiometric point indicates that the solution acts as a buffer in that region (see Fig. 11.3). At the halfwayr point of the titration, [HA] = [A ] and pH = pfCa. In fact, one way to prepare a buffer is to neutralize half the amount of weak acid present with strong base. The flatness of the curve near pH = pKa illustrates very clearly the ability of a buffer solution to stabilize the pH of the solution. Moreover, we can now see how to determine pKa plot the pH curve during a titration, identify the pH halfway to the stoichiometric point, and set pKa equal to that pH (Fig. 11.8). To obtain the pfCh of a weak base, we find pK3 in the same way but go on to use pKa -1- pfq, = pKw. The values recorded in Tables 10.1 and 10.2 were obtained in this way. 

FIGURE 1119 The lysozyme molecule is a typical enzyme molecule. Lysozyme is present in a number of places in the body, including tears and the mucus in the nose. One of its functions is to attack the cell walls of bacteria and destroy them. This "ribbon" representation shows only the general arrangement of the atoms to emphasize the overall shape of the molecule the ribbon actually consists of amino acids linked together (Section 19.13). 

Even though dynein, kinesin, and myosin serve similar ATPase-dependent chemomechanical functions and have structural similarities, they do not appear to be related to each other in molecular terms. Their similarity lies in the overall shape of the molecule, which is composed of a pair of globular heads that bind microtubules and a fan-shaped tail piece (not present in myosin) that is suspected to carry the attachment site for membranous vesicles and other cytoplasmic components transported by MT. The cytoplasmic and axonemal dyneins are similar in structure (Hirokawa et al., 1989 Holzbaur and Vallee, 1994). Current studies on mutant phenotypes are likely to lead to a better understanding of the cellular roles of molecular motor proteins and their mechanisms of action (Endow and Titus, 1992). 

This relatively small catalog of molecular shapes accounts for a remarkable number of molecules. Even complicated molecules such as proteins and other polymers have shapes that can be traced back to these relatively simple templates. The overall shape of a large molecule is a composite of the shapes associated with its inner atoms. The shape around each inner atom is determined by steric numbers and the number of lone pairs. 

---