2.0 Sheets

Beta sheets are repetitive secondary structures, like helices, because their backbone phi and psi angles are repeated geometrically along the structure. The basic component of a 'sheet' is a 'strand' and has phi = -139 and psi = +135. A strand may be thought of as a 'helix' with n=2 residues (this forms a flat ribbon see Figure 1.1). Consequently, strands can also be described by the five parameters as shown earlier for helices and shown below and in Table 2.1:

d= distance traveled per repeating unit (parallel to the 'helix axis')

n=number of 'repeating units' (ie residues) per turn of the 'helix'

p=pitch distance between successive points between one complete turn of the helix

r=radius of 'helix'

angle = the angle of rotation of each residue within the 'helix' - this is 160 degrees for a beta strand.

shows the parameters for some sheet structures.

Table 2.1 Parameters of beta strand structures (using helix parameters) found in Proteins

Secondary Structure	Residues per turn n	Rise per residue d (Å)	Radius of helix r (Å)
Parallel sheet - planar	+/-2.0	3.2	1.1
Antiparallel sheet - planer	+/-2.0	3.4	0.9
Parallel or antiparallel sheet - twisted	-2.3	3.3	1.0
Note that the plus sign indicates a right-handed 'helix' and negative sign a left-handed 'helix'

Summary of beta strand and beta sheet characteristics:

2.1 beta strands and beta sheets

• formed from a combination of several regions of the polypeptide - each region being a ' beta strand'

• second major structural element in protein accounting for about 20 to 28% of all residues in protein

• a beta strand is about 5-10 residues long (Figure 2.1)

• phi and psi angles almost fully extended in the strands of about -139 and +135 respectively in both parallel and antiparallel strands and lie in the top left of the Ramachandran plot. (Figure 1.7)

• strands are aligned adjacent to each other (Figure 2.2 and Figure 2.3)

• Hydrogen bonds between C=O of one beta strand to NH group of adjacent strand (and vice versa)

• beta sheets are formed from about 2 to 6 strands. Although OmpF - an outer membrane protein in E.coli - has 16 strands in an antiparallel beta sheet (Figure 2.5)

• pleated structure of sheets due to alpha carbon and side chains alternating above and below the plane of the sheet

• three types of sheets
  1. antiparallel where alternate strands run in opposite directions (Figure 2.2)
  2. parallel - where strands run in the same direction (Figure 2.3)
  3. mixed - where both parallel and antiparallel. Note that only 20% of strands have parallel bonds on one side and antiparallel bonds on the other.

   

• The 'ideal' parallel and antiparallel sheets are planar but these are rarely observed in proteins. The more stable structures are twisted by up to 30 degrees per residue (Figure 2.4)

• It is thought that antiparallel sheets are more stable than parallel sheets because they can withstand greater twisting and other distortions (eg beta bulges Figure 2.6) and exposure to solvent.