The Shape of Macromolecules

The external shape of macromolecules is determined by the number and distribution of the conformations as well as by the interaction between chain segments. Chain segments, or segments, are defined as portions of the chain of any desired length. 

Molecules of perfect helical conformation are rod or cylinder shaped. They are characterized by their external dimensions such as length and diameter. 

It is given by measuring the contour length of the chain, and, so, it is independent of the angle between main chain atoms. The physical maximum possible chain length, on the other hand, is also dependent on t, the 

The shape and size of macromolecules together with the segment distribution within these forms determine the excluded volume of the polymer. Compact molecular shapes such as helices, ellipsoids, and spheres have only an external (intermolecular) excluded volume the space occupied by a given volume in space cannot be occupied by others, and so is an excluded volume for other molecules. Coils, on the other hand, with their loose internal structure, also have, additionally, an internal (intramolecular) excluded volume, since the space occupied by one segment is not available to another segment of the same molecule. 

A perfect helical main chain conformation always leads to a rodlike or cylindrical external shape. But each monomeric unit in such a rod contributes a certain flexibility. So, the flexibility of the rod, as a whole, must increase with increasing degree of polymerization, even when the flexibility per monomeric unit remains constant. A macroscopic example of this would be the flexibility of steel wires of equal diameter but different lengths. Thus, even a perfect helix will adopt coil shape if the molecular mass is very high. Because of this, helically occurring macromolecules, and other stiff macromolecules, can often be well represented by what is known as the wormlike screw model for macromolecular chains at low molecular masses, the chains behave like a stiff rod, but for high molecular masses, the behavior is more coil-like. Examples are nucleic acids, many poly(a-amino acids), and highly tactic poly(a-olefins). 

---

The Einstein equation is now used as a reference to estimate the shape of macromolecules. Any deviation can be interpreted as the fact that the molecules are not a sphere. 

The shapes of macromolecules, both synthetic and natural, can be described in terms of primary, secondary, tertiary, and quaternary structure (Figure 10.1), and these will be illustrated with protein structures. 

The main purpose of the method is to define molecular shapes through isodensity surfaces. Tests on a number of small molecules show that this aim is achieved with a great efficiency in computer time. Discrepancies between MEDLA densities and theoretical distributions, averaged over the grid points, are typically below 10% of the total density. While this does not correspond to an adequate accuracy for an X-ray scattering model, the results do provide important information on the shapes of macromolecules. 

The shape of macromolecules within a folded lamella is not the same for all polymers. In crystalline polyethylene, for example, the chains assume a planar zigzag conformation, but in some other polymers like polypropylene and polyoxymethylene the chains prefer a helical shape, as in proteins. The helix might have three, four, or five monomer units per turn, i.e., the helices are three-, four-, or five-fold (Fig. 1.12)... 

The stiffness of the main chain of a polymer is of great importance for the solution viscosity the stiffer the chain is, the higher is the viscosity for polymers with the same molecular weight (see Sect. 2.3.3.3.1 for the dependency of K and a in the viscosity equation on the shape of macromolecules in solution). 

The shapes of macromolecules, large and complex molecular systems such as polypeptides, proteins, and polysaccharides, can be studied considering different... 

Luisi addressed this problem and recognized that the phenomenon can be dissected into two concepts.In the first case, flexibility describes an equilibrium in which the molecule exists in a small number of conformations relative to all those conceivably based on the molecular structure. This thermodynamic conformational flexibility describes a situation in which many rapidly interconverting conformations exist. The second concept relates to the rate of interconversion among different conformations hence, this is a kinetic conformational flexibility related to the energy barriers between conformations. The potential energy barriers govern the shape of macromolecules. 

When using molar mass as the calibration parameter, one has to consider the shape of macromolecules in solution during the data evaluation e.g., it is not possible to calculate directly the molar mass of the randomly coiled proteins from the calibration curve obtained by means of the globular proteins. 

Perrin in 1936 derived equations that relate frictional coefficients to the shape of macromolecules formed as ellipsoids of revolution. The frictional coefficients (/) of prolate and oblate ellipsoids (see Chapter 8) are both greater than the frictional coefficients of spheres (/( or /o) of equal volume. The difference depends on the ratio of the major to the minor axis. Let p = b/a be the axial ratio, where b is the equatorial radius and a is the semiaxis of revolution. For prolate ellipsoids or elongated ellipsoids a/b > 1), we have... 

Elucidation of Protein Structure UV absorption has been used to study the intra-and intermolecular interactions of biological chromophores in different environments. These interactions are often manifested in the shapes of macromolecules. For example, poly-L-lysine hydrochloride exists in three dfferent forms in aqueous solution, depending on the pH and temperature of the solution random cod, pH 6.0, 25°C helix, pH 10.8, 25 C and p-form, pH 10.8,52°C. The UV absorption spectra of poly-L-lysine hydrochloride for these three forms are shown in Figure 17.5. 

The nature of water in the cell can be discussed in terms of how this three-dimensional liquid-state stmcture is perturbed by the presence of solutes and surfaces, such as globular proteins, salts and membranes. This perturbation is itself intrinsically dynamic, since the shapes of macromolecules and molecular assemblies fluctuate. The water that hydrates these biomolecular entities must also be reconfigured during biochemical reactions and interactions - for example, as two or more proteins join in particular unions, or as a protein binds its substrate. 

J. L. Richards, Viscosity and the shapes of macromolecules a physical chemistry experiment using molecular-level models in the interpretation of macroscopic data obtained from simple measurements, Journal of Chemical Education, vol. 70, no. 8, pp. 685—689, 1993. 

---