Materials for Biomedical Engineering. Mohamed N. Rahaman

that spans a longer distance than the average diameter of a globular protein.

Figure 2.22 Schematic illustration in two dimensions of the overall three‐dimensional shape of (a) globular proteins and (b) fibrous proteins.

      Globular Proteins

      In globular proteins, atoms in the side groups attached to the chain backbone can form covalent bonds and noncovalent bonds, such as ionic, hydrogen and van der Waals bonds, with atoms of other side groups. Unlike hydrogen bonding in the secondary structure that involves the amide bond in the chain backbone without involving the side chains, these bonds can involve side groups of the same chain (intrachain bonding) as well as different chains (interchain bonding). As a result of these interactions, the chain can fold up into various complex three‐dimensional shapes that include lengths of randomly coiled chain along with regions having the regular repeating pattern of the β‐sheet or α‐helix.

      Of the approximately twenty naturally occurring α‐amino acids, only one, cysteine, offers the possibility of forming a covalent bond while approximately five have side groups than can form ionic bonds (Figure 2.17). Consequently, hydrogen and van der Waals bonds often have the largest effect in determining the tertiary structure of a protein. Although these bonds are much weaker than the covalent and ionic bonds (Table 2.2), the combined effect resulting from a large number of such noncovalent bonds determines and stabilizes the globular three‐dimensional shape of the protein. Each type of protein has its own particular conformation but the conformation adopted by any protein is typically the one with the minimum free energy.

      Examples of the main types of interactions between the side groups that can determine the conformation of a protein chain are:

       Covalent bonds: Two residues of the amino acid cysteine, for example, can be oxidized at their thiol (S–H) groups to form a disulfide (S–S) bond, sometimes called a disulfide bridge (Figure 2.23a). Reduction reverses this process.

       Ionic bonds: The side groups of some amino acid residues (Figure 2.17) contain weakly acidic or weakly basic groups that are deprotonated or protonated at the physiological pH (~7.4), giving rise to atoms in these molecules that have a negative or positive charge, respectively. Electrostatic attraction between oppositely charged atoms results in an ionic bond (Figure 2.23b).

Figure 2.23 Illustration of the main types of interactions between side groups of proteins which can determine the conformation of a protein, using examples of specific amino acid residues. (a) Covalent bond between cysteine (Cys) residues; (b) ionic bond between aspartic acid (Asp) and lysine (Lys) residues; (c) hydrogen bond between serine (Ser) residues; (d) van der Waals bonding between leucine (Leu) and valine (Val) residues.

      A common group is the carboxyl group (C=O)OH in which the H atom dissociates to give a (C=O)O⁻ species with a negatively charged oxygen atom. This group is found in the side groups of the negatively charged amino acids (Figure 2.17). On the other hand, weakly basic groups are composed of nitrogen‐containing species such as the amine (NH₂) group. These groups are found in the side groups of the positively charged amino acids. The nitrogen atom in these species become protonated to form a positively charged nitrogen atom.

      It should be noted that in these weakly acidic or basic groups, not all of the (C=O)OH or nitrogen‐containing groups become deprotonated or protonated. Instead, there is an equilibrium reaction that can be expressed generally by the equations

      (2.8)

      (2.9)

      where A–COOH and B–NH₂ represent the side groups, the square brackets denote the concentration of the respective species, and K_a is the equilibrium constant for the reaction. A well‐known indicator of the acidity or basicity of these weak acids or bases is their pK_a value, defined as

      (2.10)

      In general, the higher the pK_a value, the weaker the acid.

      Table 2.4 gives the pK_a values of the molecules in the acidic or basic side groups. As the pK_a value for the side group of aspartic acid is ~3.9, the dissociated side groups (C=O)O⁻ have a negative charge at the physiological pH. On the other hand, the pK_a value for the side group of lysine is ~10.5 and, thus, the protonated side groups (N⁺H₃) in this amino acid have a positive charge at the physiological pH.

       Hydrogen bonds: The amide bonds in the protein chain backbone contain polar C=O and N–H bonds while the side group of some amino acid residues contain these bonds or polar hydroxyl (O–H) bonds. These polar species give rise to hydrogen bonding which can again be intrachain or interchain (Figure 2.23c). Although far weaker than the covalent and ionic bonds, hydrogen bonds are numerous in proteins and, thus, have a significant influence on the conformation of proteins.

        Van der Waals bonds: These weak bonds involve electrostatic interactions between polar species in the side groups that do not take part in hydrogen bonding due to a lack of lone pair electrons in the relevant atoms or between nonpolar side groups (Figure 2.23d).

In an aqueous physiological environment, van der Waals bonding involving the side groups plays an additional role in determining the conformation of proteins. In general, nonpolar molecules are hydrophobic whereas polar and ionic molecules are hydrophilic. Consequently, as the protein chain folds to form a globular three‐dimensional shape, it does so in a manner such that side groups with polar or ionizable molecules gather on the outside of the protein chain backbone whereas side groups with nonpolar molecules are buried on the inside of the chain (Figure 2.24). This manner of chain folding enhances the interaction of the polar or ionizable side groups with the polar water molecules and shields the nonpolar side groups from the aqueous environment. The nonpolar groups cluster together by van der Waals attraction and this, together with the interactions of the polar and ionizable side groups with the water molecules, has a strong influence on the overall three‐dimensional shape of the protein. The protein undergoes conformational changes until the sum of its interaction energy is minimized.

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