20
2 A New View on Mechanism of Functional Expression …
and p53NTD [24], the water-entropy gain is ~132k B and the conformational-entropy
loss is −59k B . The water-entropy gain was calculated using our recently developed,
accurate method where molecular models are adopted for water and the structures of
biomolecules are treated at the atomic level [22]. The conformational-entropy loss
was calculated by means of the Boltzmann-quasi-harmonic method [27] combined
with MD simulations with all-atom potentials. The calculated values are quantitatively reliable. The gain is more than twice larger than the loss. We can conclude
that the water-entropy gain is a dominant contributor to the binding free energy. The
number of residues of p53NTD is 12. When p53NTD is replaced by another peptide
with 12 residues (actually, two peptides were tested in our earlier work [24]), the
conformational-entropy loss remains almost unchanged but the water-entropy gain
changes to a significant extent. Thus, the water-entropy gain is much more sensitive
to the peptide properties and important as the key quantity governing the binding
affinity of a peptide for the protein.
Protein folding is another good example of biological self-assembly processes.
Protein folding unavoidably undergoes an energetically unfavorable loss of proteinwater hydrogen bonds, but the formation of intramolecular hydrogen bonds using
α-helix and β-sheet works as a factor opposing the loss. Moreover, as illustrated in
Fig. 2.9, the formation of α-helix by a portion of the backbone or the formation of
β-sheet by a lateral contact of portions of the backbone leads to a reduction of the
EV followed by a water-entropy gain. Thus, the formation of α-helix and β-sheet is
favorable both energetically and entropically [28–31]. This is why the folded state
of a protein possesses significantly large percentages of α-helix and β-sheet. On the
other hand, close packing of side chains with diverse geometric characteristics is
crucially important. The presence of a side chain generates an excluded space which
is inaccessible to the centers of water molecules. When the side chains are closely
packed as illustrated in Fig. 2.9, the excluded spaces overlap with the result of a large
gain of water entropy [28–31]. A protein folds so that the backbone and side chains
(i.e., the protein atoms) can closely be packed with the formation of as much α-helix
and β-sheet as possible (see Fig. 2.9).
We demonstrated that the folding of apoplastocyanin (apoPC) with 99 residues at
298 K is characterized by a very large water-entropy gain of ~670k B [32]. This gain
surpasses the conformational-entropy loss of the protein (~−300k B ) and a positive
enthalpy change upon the folding, and the decrease in system free energy upon the
folding is ~−20k B T (T = 298 K) [32]. The water-entropy gain is over twice larger
than the conformational-entropy loss. The gain of protein intramolecular hydrogen
bonds is unavoidably accompanied by the loss of protein-water hydrogen bonds and
the recovery of some of water-water hydrogen bonds, giving rise to the energetic
dehydration penalty [23–26]. The positive enthalpy change, which was measured
at 298 K using a novel experimental technique [33], is ascribed to this penalty. An
important conclusion is that the water-entropy gain drives a protein to fold. The
water-entropy gain consists of the gains of translational, configurational entropy and
rotational entropy. However, we showed that the gain of translational, configurational
entropy is much larger [32].
2 A New View on Mechanism of Functional Expression …
and p53NTD [24], the water-entropy gain is ~132k B and the conformational-entropy
loss is −59k B . The water-entropy gain was calculated using our recently developed,
accurate method where molecular models are adopted for water and the structures of
biomolecules are treated at the atomic level [22]. The conformational-entropy loss
was calculated by means of the Boltzmann-quasi-harmonic method [27] combined
with MD simulations with all-atom potentials. The calculated values are quantitatively reliable. The gain is more than twice larger than the loss. We can conclude
that the water-entropy gain is a dominant contributor to the binding free energy. The
number of residues of p53NTD is 12. When p53NTD is replaced by another peptide
with 12 residues (actually, two peptides were tested in our earlier work [24]), the
conformational-entropy loss remains almost unchanged but the water-entropy gain
changes to a significant extent. Thus, the water-entropy gain is much more sensitive
to the peptide properties and important as the key quantity governing the binding
affinity of a peptide for the protein.
Protein folding is another good example of biological self-assembly processes.
Protein folding unavoidably undergoes an energetically unfavorable loss of proteinwater hydrogen bonds, but the formation of intramolecular hydrogen bonds using
α-helix and β-sheet works as a factor opposing the loss. Moreover, as illustrated in
Fig. 2.9, the formation of α-helix by a portion of the backbone or the formation of
β-sheet by a lateral contact of portions of the backbone leads to a reduction of the
EV followed by a water-entropy gain. Thus, the formation of α-helix and β-sheet is
favorable both energetically and entropically [28–31]. This is why the folded state
of a protein possesses significantly large percentages of α-helix and β-sheet. On the
other hand, close packing of side chains with diverse geometric characteristics is
crucially important. The presence of a side chain generates an excluded space which
is inaccessible to the centers of water molecules. When the side chains are closely
packed as illustrated in Fig. 2.9, the excluded spaces overlap with the result of a large
gain of water entropy [28–31]. A protein folds so that the backbone and side chains
(i.e., the protein atoms) can closely be packed with the formation of as much α-helix
and β-sheet as possible (see Fig. 2.9).
We demonstrated that the folding of apoplastocyanin (apoPC) with 99 residues at
298 K is characterized by a very large water-entropy gain of ~670k B [32]. This gain
surpasses the conformational-entropy loss of the protein (~−300k B ) and a positive
enthalpy change upon the folding, and the decrease in system free energy upon the
folding is ~−20k B T (T = 298 K) [32]. The water-entropy gain is over twice larger
than the conformational-entropy loss. The gain of protein intramolecular hydrogen
bonds is unavoidably accompanied by the loss of protein-water hydrogen bonds and
the recovery of some of water-water hydrogen bonds, giving rise to the energetic
dehydration penalty [23–26]. The positive enthalpy change, which was measured
at 298 K using a novel experimental technique [33], is ascribed to this penalty. An
important conclusion is that the water-entropy gain drives a protein to fold. The
water-entropy gain consists of the gains of translational, configurational entropy and
rotational entropy. However, we showed that the gain of translational, configurational
entropy is much larger [32].