Factors Stabilizing β‑Sheets in Protein Structures from a Quantum-Chemical Perspective

Protein
folds are determined by the interplay between various (de)­stabilizing
forces, which can be broadly divided into a local strain of the protein
chain and intramolecular interactions. In contrast to the α-helix,
the β-sheet secondary protein structure is significantly stabilized
by long-range interactions between the individual β-strands.
It has been observed that quite diverse amino acid sequences can form
a very similar small β-sheet fold, such as in the three-β-strand
WW domain. Employing “calibrated” quantum-chemical methods,
we show herein on two sequentially diverse examples of the WW domain
that the internal strain energy is higher in the β-strands and
lower in the loops, while the interaction energy has an opposite trend.
Low strain energy computed for peptide sequences in the loop 1 correlates
with its postulated early formation in the folding process. The relatively
high strain energy within the β-strands (up to 8 kcal mol–1 per amino acid residue) is compensated by even higher
intramolecular interaction energy (up to 15 kcal mol–1 per residue). It is shown in a quantitative way that the most conserved
residues across the structural family of WW domains have the highest
contributions to the intramolecular interaction energy. On the other
hand, the residues in the regions with the lowest strain are not conserved.
We conclude that the internal interaction energy is the physical quantity
tuned by evolution to define the β-sheet protein fold.