66
4 Concluding Remarks
The porter and drug-efflux domains are immersed in water molecules but the TM
domain is immersed in nonpolar chains of lipid molecules. These nonpolar chains
as well as water molecules act as the “solvent”. We showed that the translational,
configuration entropy of hydrocarbon groups in the nonpolar chains (CH 2 , CH 3 , and
CH) and water molecules provide a clue to the structural stability of a membrane
protein [6–10] and to the mechanism of the functional rotation of AcrB [11, 12].
We showed that the packing structure of AcrB with a proton or two protons bound
is characterized by significant ununiformity and this ununiformity plays essential
roles in the functional rotation through the solvent-entropy effect [11, 12]. There are
similarities between the rotations for the α 3 β 3 complex in F 1 -ATPase and AcrB. The
solvent is not the external system for AcrB. The force required for the functional
rotation of AcrB is generated by the solvent.
As argued in Sect. 3.3.2 through 3.3.4, in the most stable packing structure of the
α 3 β 3 complex in F 1 -ATPase, the packing efficiencies of subcomplexes I−γ, II−γ,
and III−γ are substantially different from one another. Due to the ATP hydrolysis
cycle, the most stable packing structure is perturbed and the structural reorganization
of the α 3 β 3 complex occurs to retain the most stable packing structure. The physical
essence can be described as follows: When the structure of one of the three portions
forming the complex is perturbed in the direction that a solvent-entropy loss is caused,
the structures of the other two portions are always reorganized to make up for the loss
and thus prevent a decrease in solvent entropy. This physical essence should also be
applicable to the functional rotation of AcrB. In AcrB, the three portions correspond
to the protomers in access (A), binding (B), and extrusion (E) states, respectively.
The solvent is composed of water molecules for F 1 -ATPase while it is composed of
the hydrocarbon groups mentioned above as well as water molecules for AcrB.
The functional rotation of AcrB suggested by us is depicted in Fig. 4.3. Consult our
earlier publications [11, 12] for more details. Significant points are briefly described
in what follows. The protomers in access (A), binding (B), and extrusion (E) states are
referred to as protomers A, B, and E, respectively. A drug molecule is accommodated
in protomer B, it is inserted during the structural reorganization from protomer A to
protomer A’, and it is extruded during the structural reorganization from protomer
B’ to protomer E. In conformation (a), only the proton binding site of protomer
B is exposed to the higher-concentration side, and a proton binds to protomer B
((a)→(b)). The binding is accompanied by a decrease in system free energy. During
the reorganization of the AcrB structure following the proton binding ((b)→(c)),
a drug molecule is entropically introduced. The introduction leads to a solvententropy gain. The proton binding site of protomer E’ is then exposed to the lowerconcentration side with the result of the dissociation of the proton from protomer
E’ ((c)→(d)). The dissociation is accompanied by a decrease in system free energy.
During the reorganization of the AcrB structure following the proton dissociation
((d)→(e)), the drug molecule is entropically released. The release leads to a solvententropy gain.
The net decrease in system free energy in each drug-transport cycle (or equivalently, each proton-transfer cycle) is F P (F P < 0). F P is ~−9k B T +ξ (ξ > 0).
4 Concluding Remarks
The porter and drug-efflux domains are immersed in water molecules but the TM
domain is immersed in nonpolar chains of lipid molecules. These nonpolar chains
as well as water molecules act as the “solvent”. We showed that the translational,
configuration entropy of hydrocarbon groups in the nonpolar chains (CH 2 , CH 3 , and
CH) and water molecules provide a clue to the structural stability of a membrane
protein [6–10] and to the mechanism of the functional rotation of AcrB [11, 12].
We showed that the packing structure of AcrB with a proton or two protons bound
is characterized by significant ununiformity and this ununiformity plays essential
roles in the functional rotation through the solvent-entropy effect [11, 12]. There are
similarities between the rotations for the α 3 β 3 complex in F 1 -ATPase and AcrB. The
solvent is not the external system for AcrB. The force required for the functional
rotation of AcrB is generated by the solvent.
As argued in Sect. 3.3.2 through 3.3.4, in the most stable packing structure of the
α 3 β 3 complex in F 1 -ATPase, the packing efficiencies of subcomplexes I−γ, II−γ,
and III−γ are substantially different from one another. Due to the ATP hydrolysis
cycle, the most stable packing structure is perturbed and the structural reorganization
of the α 3 β 3 complex occurs to retain the most stable packing structure. The physical
essence can be described as follows: When the structure of one of the three portions
forming the complex is perturbed in the direction that a solvent-entropy loss is caused,
the structures of the other two portions are always reorganized to make up for the loss
and thus prevent a decrease in solvent entropy. This physical essence should also be
applicable to the functional rotation of AcrB. In AcrB, the three portions correspond
to the protomers in access (A), binding (B), and extrusion (E) states, respectively.
The solvent is composed of water molecules for F 1 -ATPase while it is composed of
the hydrocarbon groups mentioned above as well as water molecules for AcrB.
The functional rotation of AcrB suggested by us is depicted in Fig. 4.3. Consult our
earlier publications [11, 12] for more details. Significant points are briefly described
in what follows. The protomers in access (A), binding (B), and extrusion (E) states are
referred to as protomers A, B, and E, respectively. A drug molecule is accommodated
in protomer B, it is inserted during the structural reorganization from protomer A to
protomer A’, and it is extruded during the structural reorganization from protomer
B’ to protomer E. In conformation (a), only the proton binding site of protomer
B is exposed to the higher-concentration side, and a proton binds to protomer B
((a)→(b)). The binding is accompanied by a decrease in system free energy. During
the reorganization of the AcrB structure following the proton binding ((b)→(c)),
a drug molecule is entropically introduced. The introduction leads to a solvententropy gain. The proton binding site of protomer E’ is then exposed to the lowerconcentration side with the result of the dissociation of the proton from protomer
E’ ((c)→(d)). The dissociation is accompanied by a decrease in system free energy.
During the reorganization of the AcrB structure following the proton dissociation
((d)→(e)), the drug molecule is entropically released. The release leads to a solvententropy gain.
The net decrease in system free energy in each drug-transport cycle (or equivalently, each proton-transfer cycle) is F P (F P < 0). F P is ~−9k B T +ξ (ξ > 0).