2.5 Entropic Excluded-Volume Effect and Entropic Force …
17
more like the entropic force and potential for the hard-body model, respectively. In
the PMF between two biomolecules, its entropic component usually dominates. It
is worthwhile to note that η S of water is 0.383, much higher than the value set in
Fig. 2.6, 0.3. Therefore, the amplitudes of the entropic force and potential in water
are significantly larger.
When the large sphere is replaced by a polyatomic solute, the structure of the
solute also changes as the solute approaches the wall so that the entropic potential
can be minimized. This effect should be significant especially when the entropic
potential is positive and large. The free-energy barrier for the solute in contact with
the wall to overcome by the thermal fluctuation can be considerably lower than in
the case of the large sphere [21].
2.6 Roles of Electrostatic Interaction in Aqueous Solution
Under Physiological Condition
In a microscopic self-assembly process in a biological system, when a portion with a
positive net charge (portion A) in a biomolecule comes in contact with a portion with a
negative net charge (portion B) in the same biomolecule or another biomolecule, energetic stabilization occurs due to electrostatic attractive interaction between portions A
and B. However, this stabilization is accompanied by the loss of electrostatic attractive
interactions between portion A and oxygen atoms carrying negative partial charges
in water molecules and between portion B and hydrogen atoms carrying positive
partial charges in water molecules, causing energetic destabilization. This destabilization is almost halved because the structure of some of the water near portions
A and B is reorganized upon the contact (i.e., some of the water-water hydrogen
bonds are recovered) [22]. Nevertheless, the net energy change relevant to water is
positive and referred to as the “energetic dehydration penalty”. This penalty, which
is very large, is almost cancelled out by the stabilization energy described above.
The contact of oppositely charged portions is quite important for compensating the
energetic dehydration penalty. The contact of portions with positive net charges, for
instance, causes energetic destabilization arising from not only electrostatic repulsive
interaction between these portions but also the energetic dehydration penalty caused
by the loss of electrostatic attractive interactions between these portions and oxygen
atoms in water molecules. It is now decisive that the contact of portions possessing
net charges in the same sign can hardly occur.
A receptor-ligand binding (binging of two solute molecules) is a good example
of biological self-assembly processes. It is illustrated in Fig. 2.8 [23]. The binding
is accompanied by a decrease in conformational energy of solute molecules and
the energetic dehydration penalty explained above (see Fig. 2.8a). The decrease and
the penalty are compensating (using our accurate statistical-mechanical theory [22]
17
more like the entropic force and potential for the hard-body model, respectively. In
the PMF between two biomolecules, its entropic component usually dominates. It
is worthwhile to note that η S of water is 0.383, much higher than the value set in
Fig. 2.6, 0.3. Therefore, the amplitudes of the entropic force and potential in water
are significantly larger.
When the large sphere is replaced by a polyatomic solute, the structure of the
solute also changes as the solute approaches the wall so that the entropic potential
can be minimized. This effect should be significant especially when the entropic
potential is positive and large. The free-energy barrier for the solute in contact with
the wall to overcome by the thermal fluctuation can be considerably lower than in
the case of the large sphere [21].
2.6 Roles of Electrostatic Interaction in Aqueous Solution
Under Physiological Condition
In a microscopic self-assembly process in a biological system, when a portion with a
positive net charge (portion A) in a biomolecule comes in contact with a portion with a
negative net charge (portion B) in the same biomolecule or another biomolecule, energetic stabilization occurs due to electrostatic attractive interaction between portions A
and B. However, this stabilization is accompanied by the loss of electrostatic attractive
interactions between portion A and oxygen atoms carrying negative partial charges
in water molecules and between portion B and hydrogen atoms carrying positive
partial charges in water molecules, causing energetic destabilization. This destabilization is almost halved because the structure of some of the water near portions
A and B is reorganized upon the contact (i.e., some of the water-water hydrogen
bonds are recovered) [22]. Nevertheless, the net energy change relevant to water is
positive and referred to as the “energetic dehydration penalty”. This penalty, which
is very large, is almost cancelled out by the stabilization energy described above.
The contact of oppositely charged portions is quite important for compensating the
energetic dehydration penalty. The contact of portions with positive net charges, for
instance, causes energetic destabilization arising from not only electrostatic repulsive
interaction between these portions but also the energetic dehydration penalty caused
by the loss of electrostatic attractive interactions between these portions and oxygen
atoms in water molecules. It is now decisive that the contact of portions possessing
net charges in the same sign can hardly occur.
A receptor-ligand binding (binging of two solute molecules) is a good example
of biological self-assembly processes. It is illustrated in Fig. 2.8 [23]. The binding
is accompanied by a decrease in conformational energy of solute molecules and
the energetic dehydration penalty explained above (see Fig. 2.8a). The decrease and
the penalty are compensating (using our accurate statistical-mechanical theory [22]