Conformational Geometry of Peptides and Proteins: Before discussing secondary structure, it is important to appreciate the conformational plasticity of proteins. Each residue in a polypeptide has three bonds connecting main chain atoms that are potentially free to rotate. The conformation of the atoms involved in these bonds describes the secondary structure of the protein. The rotation angle about a bond is referred to as a torsional angle. A torsional angle defines the relative orientation of four atoms in space and it is the angle between two planes. The torsional angle between the N and Cα bond is shown below. The torsional angle about the N-Cα bond is defined by the angle between the two intersecting planes. Conformation of the Ci-1 - N (Peptide bond). The four atoms that make up this bond are planar due to the hybridization properties of the carbonyl carbon and the nitrogen (both sp2). In addition, free rotation about the bond is not possible since the pz orbitals of oxygen, carbon, and nitrogen form a delocalized system. Rotation about the peptide bond would break the interaction between the pz orbital of the nitrogen
and carbon atoms, and is therefore unfavorable. The peptide bond is said to be a "partial double bond". The atomic orbitals of the mainchain atoms are shown. The carbonyl carbon uses an sp2 hybrid orbital to bond to the carbonyl oxygen and the nitrogen. Consequently, the oxygen, carbon, and nitrogen all lie in the same plane. Since the nitrogen is also uses sp2 hybrid orbitals, the amide hydrogen is also on the same plane. The second bond between the carbonyl carbon and oxygen is formed by overlap of the pz orbitals. The nitrogen pz orbital is also in a favorable position to overlap with the carbon pz orbital. Consequently, the electrons in all three pz orbitals form a delocalized system resulting in a partial double bond between the carbonyl carbon and the nitrogen. Cis and Trans Peptide Bonds: Two possible orientations of the peptide bond that maintain a favorable interaction between the carbon and nitrogen are possible. They are related by an 180 o flip of the peptide bond, generating the trans form and the cis form. For all peptide bonds, the trans form is more stable than the cis form. The higher energy of the cis form is due, in part, to overlap between the α-protons on adjacent residues (non-proline) or between α and δ protons in the case of proline. Use the buttons on the Jmol images below to highlight these overlaps.
Ala-Ala Trans and Cis Peptide Bonds. In the case of linkages between non-proline residues, the unfavorable overlap of the mainchain (and sidechain) atoms makes the cis form less stable by about 15 kj/mol, giving a ratio of trans to cis of 1000:1. The molecular crowding of the α-hydrogens in the cis form is evident in the Jmol image on the far right. Ala-Pro Trans and Cis Peptide Bonds. Both the trans and cis form of the peptide bond result in overlap of atoms, raising the energy of the trans such that it is only ~4 kj/mol lower than the cis form. In the trans form the molecular crowding involves the α-hydrogen of the preceding residue and the δ-hydrogens on the proline. In the cis form it is the two α- hydrogens. There is free rotation about both of these bonds. Not all torsional angles are equally likely. There are three torsional angles that are more stable than others. They are related to each other by a 120 o rotation about the bond. The three stable positions are more easily seen with a simpler molecule, such as 1-chloro-1-fluoroethane. Note that the three stable conformations minimize the interaction between the atoms on each carbon by maximizing their distance from each other. These conformations are also stabilized by favorable interactions between the molecular orbitals in the molecule.
In the case of amino acid residues in a protein, the presence of the bulky atoms on the sidechain restricts the possible phi and psi angles of a residue to 3 pairs of values that are relatively low in energy: Three possible phi psi angles of a residue Φ = -60, and Ψ = -45 Φ = +60, and Ψ = +45 Φ = -120, and Ψ = -125 Proteins consist of a linear chain of amino acids, with each amino acid representing a build block. The shape of each block depends on the Φ and Ψ angle of each residue. In regular secondary structures these angles are the same for each residue, and thus the shape of each building block, or amino acid, is the same. If a series of identically shaped objects are laid end-to-end they will form some type of geometrical structure. In two dimensions there are two possibilities, either a straight chain or some type of circle (which may or may not be closed). A straight chain occurs if the is no curvature in the block, while a circle will result if there is any degree of curvature. The radius of the circle is related to the degree of curvature.
In the case of three-dimensional building blocks that have some degree of curvature on both faces, the two dimensional circular structure becomes a helix. If the building block is a perfect rectangular prism, then the structure will remain linear. Given the possible values of Φ and Ψ angles, many different shapes of the amino acid building block are possible and therefore many different three-dimensional structures are possible. Only two are commonly observed in proteins, the right-handed alpha helix and beta-structures. A left-handed alpha helix is also stable, but relatively rare. These conformations are stable because they: Maximize mainchain hydrogen bonding Maximize van der Waals interactions of mainchain atoms. Minimizing steric clashes of mainchain and sidechain atoms In all cases these secondary structures of proteins have characteristic values of the Ψ and Φ torsional angles that are the same for each residue within a particular secondary structure. In all cases each peptide bond is rigid and planar in the trans conformation. Non-regular secondary structures Sharp turns in proteins, particularly at the ends of beta-strands and beta-hairpins, have a characteristic geometry and sequence. As with other forms of secondary structure, these turns are stabilized by hydrogen bonding and favorable van der waals interactions. These turns often contain Glycine at position 3 (R3), because of its unique conformational properties. Use the Jmol activity to the right to determine the hydrogen-bonding pattern in a type II turn.
Type II Turn. Tight turns are found at the end of beta-strands. The Jmol on the right shows a type II turn with the sequence Asp-Pro-Gly-Gly.