2.8 Essential Roles of Water-Entropy Effect in Biological Processes
23
and properties of the protein upon the folding in (I) and by the structural change of
the transporter in (II) (see Fig. 1.1c). Diverse proteins are inserted and released in
(I), and a variety of substrates are carried across the membrane in (II). We showed
that the entropic force and potential generated by water play essential roles in the
insertion process in (I) [14, 40] and the insertion and release processes in (II) [14,
41–43]. (An energetic factor plays a pivotal role in the release process in (I) [14, 40].)
A molecular motor, an ATP-driven protein or protein complex, functions in
aqueous solution under the physiological condition. As described in Sect. 2.5.1, the
entropic EV effect is remarkably large for a protein or protein complex immersed
in water. The importance of the translational, configurational entropy of water over
the electrostatic interaction, which is argued above, holds true for the functional
expression of the molecular motor as well.
2.9 Recent Papers Pointing Out Crucial Importance
of Hydration Effect on Unidirectional Movement
of Myosin Along F-Actin
In the literature, there are two pioneering papers [44, 45] pointing out the essential
roles of hydration effect in the unidirectional movement of myosin along F-actin. The
first [44] and second [45] papers were written by us and Suzuki et al., respectively.
S1 was considered as a simple but physically insightful model of myosin. The claim
shared by these papers is that the force for moving myosin is generated by water.
First, we review the second paper [45] (it was revisited in a recently published
book [46]). The key quantity is claimed to be the hydration free energy of S1, μ,
which takes a significantly large, negative value. After ATP bound to S1 is hydrolyzed
into ADP and Pi, S1 weakly binds to F-actin. During this weak binding, S1 repeats
the detachment from and the attachment to F-actin. While S1 is detached from Factin, S1 is driven to move in the right direction for the following reason. S1 feels the
negative electric field emanated from F-actin. Importantly, μ becomes lower (i.e.,
|μ| becomes larger) as the field strength increases. The structure of F-actin on the
left side of S1 is different from that on the right side of S1, and the electric field
emanated from F-actin on the right side of S1 is stronger than that on the left side of
S1. Therefore, S1 moves in the right direction so that μ can be lowered.
We then comment on the second paper [45, 46]. The quantity to be looked at is not
the hydration free energy of S1 but the system free energy represented by the sum of
the hydration free energy (a), conformational energy (b) (i.e., energy in vacuum), and
conformational entropy (c) of the protein complex (i.e., actomyosin) comprising S1
and F-actin. S1 is moved so that the system free energy can be lowered. The hydration
free energy can be decomposed into the hydration energy (a−1) and entropy (a−2).
We note that factors (a−1) and (b) are compensating: When (a−1) becomes lower,
for example, (b) always becomes higher. Factor (c) is relatively smaller. Therefore,
the change in system free energy can be approximated by that in factor (a−2). It
23
and properties of the protein upon the folding in (I) and by the structural change of
the transporter in (II) (see Fig. 1.1c). Diverse proteins are inserted and released in
(I), and a variety of substrates are carried across the membrane in (II). We showed
that the entropic force and potential generated by water play essential roles in the
insertion process in (I) [14, 40] and the insertion and release processes in (II) [14,
41–43]. (An energetic factor plays a pivotal role in the release process in (I) [14, 40].)
A molecular motor, an ATP-driven protein or protein complex, functions in
aqueous solution under the physiological condition. As described in Sect. 2.5.1, the
entropic EV effect is remarkably large for a protein or protein complex immersed
in water. The importance of the translational, configurational entropy of water over
the electrostatic interaction, which is argued above, holds true for the functional
expression of the molecular motor as well.
2.9 Recent Papers Pointing Out Crucial Importance
of Hydration Effect on Unidirectional Movement
of Myosin Along F-Actin
In the literature, there are two pioneering papers [44, 45] pointing out the essential
roles of hydration effect in the unidirectional movement of myosin along F-actin. The
first [44] and second [45] papers were written by us and Suzuki et al., respectively.
S1 was considered as a simple but physically insightful model of myosin. The claim
shared by these papers is that the force for moving myosin is generated by water.
First, we review the second paper [45] (it was revisited in a recently published
book [46]). The key quantity is claimed to be the hydration free energy of S1, μ,
which takes a significantly large, negative value. After ATP bound to S1 is hydrolyzed
into ADP and Pi, S1 weakly binds to F-actin. During this weak binding, S1 repeats
the detachment from and the attachment to F-actin. While S1 is detached from Factin, S1 is driven to move in the right direction for the following reason. S1 feels the
negative electric field emanated from F-actin. Importantly, μ becomes lower (i.e.,
|μ| becomes larger) as the field strength increases. The structure of F-actin on the
left side of S1 is different from that on the right side of S1, and the electric field
emanated from F-actin on the right side of S1 is stronger than that on the left side of
S1. Therefore, S1 moves in the right direction so that μ can be lowered.
We then comment on the second paper [45, 46]. The quantity to be looked at is not
the hydration free energy of S1 but the system free energy represented by the sum of
the hydration free energy (a), conformational energy (b) (i.e., energy in vacuum), and
conformational entropy (c) of the protein complex (i.e., actomyosin) comprising S1
and F-actin. S1 is moved so that the system free energy can be lowered. The hydration
free energy can be decomposed into the hydration energy (a−1) and entropy (a−2).
We note that factors (a−1) and (b) are compensating: When (a−1) becomes lower,
for example, (b) always becomes higher. Factor (c) is relatively smaller. Therefore,
the change in system free energy can be approximated by that in factor (a−2). It