As discussed in Chapter 2, atoms behave almost as if they were hard spheres with a definite radius (their van der Waals radius). The requirement that no two atoms overlap plus other constraints limit the possible bond angles in a polypeptide chain (Figure 3–3), severely restricting the possible three-dimensional arrangements (or conformations) of atoms. Nevertheless, a long flexible chain such as a protein can still fold in an enormous number of ways.
The folding of a protein chain is also determined by many different sets of weak noncovalent bonds that form between one part of the chain and another. These involve atoms in the polypeptide backbone, as well as atoms in the amino acid side chains. There are three types of these weak bonds: hydrogen bonds, electrostatic attractions, and van der Waals attractions, as explained in Chapter 2 (see p. 44). Individual noncovalent bonds are 30–300 times weaker than the typical covalent bonds that create biological molecules. But many weak bonds acting in parallel can hold two regions of a polypeptide chain tightly together. In this way, the combined strength of large numbers of such noncovalent bonds determines the stability of each folded shape (Figure 3–4).
Figure 3–2 The 20 amino acids commonly found in proteins. Each amino acid has a three-letter and a one-letter abbreviation. There are equal numbers of polar and nonpolar side chains; however, some side chains listed here as polar are large enough to have some nonpolar properties (for example, Tyr, Thr, Arg, Lys). For atomic structures, see Panel 3–1 (pp. 112–113).
Figure 3–3 Steric limitations on the bond angles in a polypeptide –180 chain. (A) Each amino acid contributes three bonds (red) to the backbone –180 0 +180 of the chain. The peptide bond is planar (gray shading) and does not permit rotation. By contrast, rotation can occur about the Cα–C bond, whose angle of rotation is called psi (ψ), and about the N–Cα bond, whose angle of left-handed rotation is called phi (ϕ). By convention, an R group is often used to denote helix an amino acid side chain (purplecircles). (B) The conformation of the main-chain atoms in a protein is determined by one pair of ϕ and ψ angles for each amino acid; because of steric collisions between atoms within each amino acid, most of the possible pairs of ϕ and ψ angles do not occur. In this so-called Ramachandran plot, each dot represents an observed pair of angles in a protein. The three differently shaded clusters of dots reflect three different “secondary structures” repeatedly found in proteins, as will be described in the text. (B, from J. Richardson, Adv. Prot. Chem. 34:174–175, 1981. © Academic Press.)
A fourth weak force—a hydrophobic clustering force—also has a central role in determining the shape of a protein. As described in Chapter 2, hydrophobic molecules, including the nonpolar side chains of particular amino acids, tend to be forced together in an aqueous environment in order to minimize their disruptive effect on the hydrogen-bonded network of water molecules (see Panel 2–2, pp. 92–93). Therefore, an important factor governing the folding of any protein is
Figure 3–4 Three types of noncovalent bonds help proteins fold. Although a single one of these bonds is quite weak, many of them act together to create a strong bonding arrangement, as in the example shown. As in the previous figure, R is used as a general designation for an amino acid side chain.
112 Panel 3–1:  The 20 amino acids Found in Proteins
THE AMINO ACID OPTICAL ISOMERS The ˜-carbon atom is asymmetric, which allows for two mirror images (or stereo-)
The general formula of an amino acid is isomers, L and D. ˜-carbon atom