Protein Structure: a -helix, b -sheet and turns

1. Hierarchical Structure of Proteins

Amino acids are covalently linked through peptide bonds to form linear polymers called peptides or proteins. These linear polymers can spontaneously fold into three dimensional structures, called native fold, i.e., a biologically active form. The structure of proteins (and peptides) can be analyzed on 4 different levels. These four levels are summarized in the table below:
 

I	primary	linear sequence	1°-D
II	secondary	local, repetitive spatial arrangements	2°-D
		(II/III supersecondary; motif)
III	tertiary	three dimensional structure of native fold	3°-D
IV	quaternary	non-covalent oligomerization of subunits (single polypeptides) into protein complexes	4°-D

2. Peptide bond formation

Two amino acids can undergo a condensation reaction, where the carboxyl group reacts with the amine group. The formation of this peptide bond (see box in figure) produces a dipeptide and a H₂O molecule, exhibiting a dipole moment m = 3.7 Debye for the peptide bond (arrow in figure). Note that the dipole moment of the dipeptide is different from the peptide bond dipole moment because of its charged amine and carboxyl groups.

Fig. Chemical structure of a dipeptide

Adding additional amino acids to the growing peptide chain (always form N-term to C-term direction in living cells) produces a polypeptide chain or protein. The order in which amino acids are linked to the growing chain defines its primary structure or sequence.

The geometrical character of the peptide bond is that of a rigid plane between the two flanking a -carbon atoms. The reason for this structural stability (there is no rotation around the C-N bond) can be explained by the electronic resonance character of the O=C-N structure. The double bond character changes between the O-C and C-N bonds.

Fig. Electronic resonance character of peptide bond due to the p -like molecular orbital that extends over all 3 atoms (O-C-N)

Evidence for this structure comes from X-ray crystallographic studies of simple peptides showing that the N-Ca bond length is 1.46Å as expected for a single bond. The C-N peptide bond is 1.33Å long, only a little longer than the value of 1.27Å for the average C=N bond length in model compounds. Similar X-ray studies show the six atoms Ca NHCOCa very close to being co-planar (Pethig, p.41).
 

3. Secondary structure

Immersed in water a polypeptide chain will not stay in an elongated form, but fold up according to the polarity of the side chains it contains and the rotation of peptide backbone bond angels largely determined by Van der Waals radii of side chains.

To understand protein structures we can measure two torsion angles ( also called dihedral angles) in the backbone which define the tilt between two neighboring amide planes (the plane of the peptide bond) with the Ca at the center of rotation:

                                        F Ca¾ N Y Ca¾ C

Thus we can calculate the allowed backbone conformations of a peptide through interplay of rotation around the bonds defined by the torsion angles Phi (F ) and Psi (Y ) and the steric hindrance of side groups determined by their Van der Waals radii. The resulting conformational map is called Ramachandran plot (after Ramachandran, who invented it). A free rotation (no energy needed, due to thermal motion) around a C-C bond is possible in the absence of any steric (i.e., Van der Waals radii) constraints. (Note that the peptide bond torsion angle w has a fixed value and can be neglected in a Ramachandran plot.)
 

Fig. Peptide backbone and torsion angles

from Richardson and Richardson, pp.4/5

Fig. Ramachandran plot for all residues except Gly and Pro

Note: values come from structure data sets
(from Richardson and Richardson, p. 6)

Ramachandran plots for proteins show three confined regions of the conformational map which are physically accessible to them. The Ramachandran plot of a protein is a full description of the polypeptide backbone conformation (excludes side chain conformations). Three important regions of the Ramachandran plot describe the most commonly found secondary structures in proteins:

a -helix : a right handed helical structure with average torsion angles F =-57 and Y =-47

b -sheet: parallel (F =-119 and Y =113) or anti-parallel pleated sheet structures

b -turn: minimal loop structures of 3 to 4 amino acids with defined torsion angles
 

4. The a -helix

The a -helix is one of two secondary structures (the other being the b -sheet) predicted and discovered by Linus Pauling in 1951. It is a right-handed helix with the following spatial parameters:

F = -57°
Y = -47°
n = 3.6 (number of residues per turn)
pitch 0.54nm (or 5.4Å)

The helix has a specific hydrogen bonding pattern, where the backbone C=O group of residue n bonds with the N-H of residue n+4. The atomic distance between the N and O measures 0.28nm. The H-bonds are almost parallel to the helix axis and the total dipole moment gives the helix a dipole moment that points from the N-term (+) to the C-term (-). This helix dipole is important in the interaction of neighboring helices in the packing of secondary structural motifs into the 3-D structure. An example of the functional importance of a helical dipole moment is shown in section 2.3.

Fig. Orientation of dipole moment(s) in an a -helix as defined by chemists (m +® -)

The core of the helix is packed. The backbone atoms are in Van der Waals contact with each other across the helix axis. A helix can be represented in its so called wheel presentation. A helical wheel is a projection in 2-D along the helix axis and displays the orientation of the side chains on a 360 degree map with respect to the side of the helix. This wheel presentation is helpful for the detection of potential amphipathic helices. Amphipathic helices have a polar and a non-polar side and this plays a crucial role in helix-helix interaction and in the interaction of small peptides that have a helical conformation with the interaction with membranes, air-water interfaces, and self-assembly processes.

                    Fig. Helical wheel representation of a 15 amino acid long a -helix

5. The b -strand and b -pleated sheet

In 1952, Pauling and Corey predicted the b -pleated sheet structure as an alternative secondary structure to the a -helix in proteins. b -strands are elongated peptide segments with atomic distances from side chain n to side chain n+2 of 0.7nm.

    Fig. b -strand

Single b -strands are not stable structures but occur in association with neighboring strands. Thus they can be found as either parallel or anti-parallel with respect to the N- to C-terminal direction of the adjacent peptide strands.

anti-parallel  N® C     parallel  N® C
                   C¬ N                  N® C

Like a -helices, b -pleated sheet backbones are fully hydrogen bonded, but here the H-bonds occur between neighboring strands (intermolecular). The H-bond geometry is different in the parallel and anti-parallel conformations (see also section 1.8).
 

Fig. Hydrogen bonding in antiparallel b sheet

from Richardson and Richardson, p.18

More than two strands can form into sheets which form extended right-handed twists. Such extended b -pleated sheets (called super secondary structures) can often been found in the cores of proteins. Alternatively, bundles of 4 closely packed a -helices (so called a -helical bundles) are also found at the center of globular proteins.

If the b -strand contains alternating polar and non-polar residues it forms an amphipathic b -sheet. This distribution of hydrophilic and hydrophobic residues has been observed in the membrane protein porin that forms a b -barrel structure (section 2.3), where the non-polar residues stick into the hydrophobic part of the lipid membrane and the hydrophilic residues form part of the channel interior responsible for the passage of small molecules across the membrane.
 

6. The b -turns

To combine helices and sheets in their various combinations, protein structures must contain turns that allow the peptide backbone to fold back. Two turn structures will be discussed here using their Ramachandran plot coordinates:

from Richardson and Richardson, p.24

These turns can be found almost always on the surface of proteins and often contain Pro and/or Gly. Proline gives the backbone a special rigidity (fixed Phi torsion angle at -60° , Ca -N) and glycine has a high flexibility because of its hydrogen substituent. Turn structures are also stabilized through H-bond formation.
 

7. Super Secondary Structures or folds

There are many structural motifs that are formed by the combination of a -helices and b -strands. They can be classified in groups as shown below (see also section 3.9). The 4 most common (among >300) motifs are:
 

1. bab

2. b -hairpin (or anti-parallel b -pleated sheet)

3. aa (the most common member being the 4 helical bundle)

4. b -barrels (see Greek key motif)

All these motifs can be found in many different proteins and enzymes that have very diverse functional and structural properties. a and b -structures are often found in combination as seen for carboxypeptidase and trios phosphateisomerase and for pyruvate kinase as shown in the figure below.

Fig. The three domains of pyruvate kinase (PDB entry 1A3W)

The three domains are shown separately below:

from Richardson and Richardson, p.29

This motif classification can be important in finding protein domains and study protein structure evolution. The functional variability associated with homologous motifs, however, makes the classification of proteins according to their functional properties more useful.
 

8. Tertiary structure

The tertiary structure is the 3 dimensional, native structure of a single polypeptide or protein. A protein normally is folded into a compact structure, usually referred to as 'globular protein', a term traditionally associated with water soluble proteins. The secondary structures are stabilized by the final, native fold. The nativefold is defined as the active conformation.

Amino acids are the components of proteins and their sequence determines the native fold. Of course this is always in combination with the solvent, in this case water. The location of an amino acid in a protein fold correlates with the energy of hydration of each individual amino acid residue and the entropy of the side chain, polypeptide backbone, and solvent molecules (see section 2.7). As mentioned earlier, polar and charged amino acids are likely to be hydrated, whereas the non-polar residues stick to each other and often form the core of a protein, forming a usually hydrophobic core that stabilizes the fold of water soluble, globular proteins. For membrane proteins exhibiting both hydrophobic and hydrophilic surfaces, the amino acid distribution is different from globular proteins but the same rules of the hydrophobic effect apply. Here is a list of the distribution of amino acids in globular and membraneproteins:

Table Distribution of amino acids in proteins
 

Residue

Globular protein

Membrane proteins

_____________________________________________________________________________
 

non-polar V, L, I, M, F, Y, W	in interior, hydrophobic core	surface, lipid anchor
polar, charged R, K, D, E, H	surface, in interior function often as catalytic sites	extra membranous, electrostatic interaction, functional group of channel proteins, forming a hydrophilic core
polar, neutral S, T, N, Q, Y, W	surface & interior (H-bond network)	surface, inside part of channel, H-bond network

Note: all amino acids can be found inside or at the surface, if their chemical properties are complemented (e.g. ion pair in hydrophobic core)

The following list is a selection describing the special roles of amino acids in protein structures (from Richardson&Richardson, pp.43-75): .

                                                   m² = 2D_oMkTd /N_A

where d is the dielectric weight increment, M the molecular weight of the protein, D_o the dielectric constant of water. The dielectric weight increment d can be calculated from the dielectric constant of the protein solution (D), water (D_o), and the protein concentration (c):

                                                        d = (D - D_o)/c

The following table lists the protein dipole moments for a few proteins as given by R.Pethig, p.86 (Table 3.4)
 
 

Single polypeptides can associate with each other to form larger protein complexes of geometrically specific arrangements, called quaternary structures. Individual polypeptides in protein complexes are referred to as subunits (and should not be confused with domains). We will encounter many examples of quaternary structures or subunit composition of protein complexes. Most enzymes are complexes of proteins and the symmetry and stoichiometry of the composition of the complexes is crucial for their activity.

We can distinguish two different compositions, the homomeric and heteromeric complexes. Heteromeric composition of most protein complexes gives the cells an additional level of variability and complexity it can use for its activity. Often, heteromeric compositions of protein complexes are tissue specific or developmental specific and multiple genes can control the activity of a single heteromeric protein complex.