stabilize it. This is comparable to the formation of a molecular crystal from
a solution, where bond energies often are 1 or 2kBTper molecule. Doublets
of these molecules would be very short-lived, but a crystal of sufficient size is
stable, mainly because each molecule now is involved in a number of bonds,
e.g., six. A prerequisite, both in a crystal and in a helix, is a very good fit of
the bonds. This is the case in ana-helix, where the H-bonds are almost
perfectly aligned. The cooperativity principle implies that an a-helix cannot
be very short, as is indeed observed.
In theb-strandthe peptide chain is almost fully extended, although
slightly twisted (the translation equals about 0.34 nm per residue rather than
0.36 nm when stretched). A singleb-strand is unstable, but several of them
can be aligned to formb-sheets, which can either be parallel or, more
commonly, antiparallel. Note that the strands in one sheet need not be from
nearby regions in the primary structure. In the sheets, several H-bonds are
formed, again stabilizing the conformation by the cooperativity principle.
The antiparallelb-sheet seems to be somewhat more stable than the parallel
one. A singleb-strand can also be stabilized by other structures, e.g., by
alignment with ana-helix.
The presence and abundance of the various secondary structure
elements in a protein in solution can in principle be determined by
spectroscopic techniques. This also relates to some smaller scale structure,
like reverse turns. However, definitive results on secondary structure can
only be obtained by determination of the complete conformation.
7.1.4 Tertiary Structure
By means of x-ray diffraction of crystalline protein and of NMR
spectroscopy of the molecules in solution, the complete three-dimensional
structure of a protein can be established. Many proteins show an intricate,
tightly folded structure, which includes secondary structure elements.
Generally, hydrophilic amino acid side groups are predominantly at the
surface, and hydrophobic ones in the core of the structure. The driving
forces for folding are discussed in Section 7.2.1. The role of water is essential
and it may be stated that
polypeptide chainþwater¼proteinIt depends on the proportions of hydrophobic and hydrophilic residues, as
well as on the length of the peptide chain, what the overall structure can be.
This is illustrated in Figure 7.3. Assuming a hydrophilic outer layer of one
peptide chain, i.e., about 0.5 nm in thickness, a larger protein molecule can
accommodate a greater proportion of hydrophobic residues in its core. A