Chapter 3
Mechanism of Unidirectional Rotation
of γ Subunit in F 1 -ATPase
Abstract In this chapter, the discussion is focused on the functional expression of
F 1 -ATPase, the unidirectional rotation of the γ subunit. In the structure of the α 3 β 3
complex stabilized by the water-entropy effect, the atoms in three β subunits, to which
different chemical compounds (i.e., ATP just before the hydrolysis reaction, ATP,
ADP + Pi, nothing, or Pi) are bound, are closely, moderately, and loosely packed,
respectively. This nonuniformity and the structural asymmetry of the γ subunit play
essential roles. The γ subunit takes a particular orientation in accordance with the
structure of the α 3 β 3 complex so that the water entropy can be maximized. Due to
the occurrence of the ATP binding, ATP hydrolysis, and dissociation of ADP and
Pi during each ATP hydrolysis cycle, the chemical compounds bound to the three
β subunits successively change, in concert with which the α 3 β 3 complex structure
and the orientation of the γ subunit sequentially change to retain the maximized
water entropy. In one hydrolysis cycle, the γ subunit exhibits a 120° rotation. It is
experimentally known that the ATP synthesis occurs when the γ subunit is forced to
rotate in the inverse direction by a sufficiently strong external torque imposed. This
can also be explicated on the basis of the water-entropy effect.
Keywords F 1 -ATPase · Nucleotide · ATP hydrolysis · Entropic force · Entropic
potential · Unidirectional rotation · ATP synthesis
3.1 Definition of Packing Structure for a Protein or Protein
Complex
The free energy for a biomolecule immersed in water is represented by the sum
of conformational energy, hydration energy, conformational entropy, and hydration
entropy. As argued in Sects. 2.6–2.8, upon a structural change of a protein or protein
complex or a binding of two biomolecules, the change in hydration entropy is much
larger than the sum of the changes in conformational energy and in hydration energy
and significantly larger than the change in conformational entropy. Therefore, the
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
M. Kinoshita, Mechanism of Functional Expression of F 1 -ATPase,
SpringerBriefs in Molecular Science,
https://doi.org/10.1007/978-981-33-6232-1_3
29
Mechanism of Unidirectional Rotation
of γ Subunit in F 1 -ATPase
Abstract In this chapter, the discussion is focused on the functional expression of
F 1 -ATPase, the unidirectional rotation of the γ subunit. In the structure of the α 3 β 3
complex stabilized by the water-entropy effect, the atoms in three β subunits, to which
different chemical compounds (i.e., ATP just before the hydrolysis reaction, ATP,
ADP + Pi, nothing, or Pi) are bound, are closely, moderately, and loosely packed,
respectively. This nonuniformity and the structural asymmetry of the γ subunit play
essential roles. The γ subunit takes a particular orientation in accordance with the
structure of the α 3 β 3 complex so that the water entropy can be maximized. Due to
the occurrence of the ATP binding, ATP hydrolysis, and dissociation of ADP and
Pi during each ATP hydrolysis cycle, the chemical compounds bound to the three
β subunits successively change, in concert with which the α 3 β 3 complex structure
and the orientation of the γ subunit sequentially change to retain the maximized
water entropy. In one hydrolysis cycle, the γ subunit exhibits a 120° rotation. It is
experimentally known that the ATP synthesis occurs when the γ subunit is forced to
rotate in the inverse direction by a sufficiently strong external torque imposed. This
can also be explicated on the basis of the water-entropy effect.
Keywords F 1 -ATPase · Nucleotide · ATP hydrolysis · Entropic force · Entropic
potential · Unidirectional rotation · ATP synthesis
3.1 Definition of Packing Structure for a Protein or Protein
Complex
The free energy for a biomolecule immersed in water is represented by the sum
of conformational energy, hydration energy, conformational entropy, and hydration
entropy. As argued in Sects. 2.6–2.8, upon a structural change of a protein or protein
complex or a binding of two biomolecules, the change in hydration entropy is much
larger than the sum of the changes in conformational energy and in hydration energy
and significantly larger than the change in conformational entropy. Therefore, the
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
M. Kinoshita, Mechanism of Functional Expression of F 1 -ATPase,
SpringerBriefs in Molecular Science,
https://doi.org/10.1007/978-981-33-6232-1_3
29