10
1 Brownian Ratchets and Molecular Motors
When U(x) =
1
2 κx 2 the integral is not algebraically tractable, and it is assumed that
the height of the energy barrier is high, U L ≡ U(L) k B T , then Eq. 1.24, gives
t K = τ
π
4
k B T
U L
exp
U L
k B T
(1.26)
where τ = γ /κ is the drag coefficient divided by the spring constant, t K is called
the Kramers time, after Kramers, who first derived it in 1940, [35].
For properties of First Passage Phenomena see Appendix D.1.
1.6 Power Stroke
We saw that a ratchet is a motor in which the motion is driven directly by thermal
fluctuations and rectified, or biased, by chemical reactions. In contrast, a powerstroke motor directly drives the motion. As an example we consider the rotation
experiments of the F 1 ATPase, the load is the long actin filament attached to the γ
subunit, see Fig. 1.5a, [24, 36, 37]. Similarly, in kinesin experiments the motor tows
a large bead (the load).
Compare this case with the ratchet one at Fig. B.1, Appendix B in Stochastic
Energetics. In both cases the ratchet and the power-stroke the energy to drive the
motion ultimately comes from chemical reactions taking place in the catalytic site(s)
of the motor. For Numerical computation of mechanochemical coupling see Chap. 4.
Indeed, a power stroke is large, rapid structural change in a protein that can be
used to do mechanical work, see Fig. 1.6. A power stroke has a size on the order of
the dimension of the protein itself (several nanometers); this distinguishes it from
the much smaller localized structural changes that occur when a protein binds to
a ligand or catalyzes a chemical reaction (the size of a chemical bond or a few
Ångstroms) [38]. The concept was first formulated for the protein myosin II which
drives the contraction of muscle [39].
The γ -subunit acts as a crankshaft that converts conformational changes in the
α3β3 ring to a unidirectional rotation and it also transmits conformational changes
in an αβ pair to another. Literature treating the rotation of the γ -subunit and the
effects that produces see [40–45].
1 Brownian Ratchets and Molecular Motors
When U(x) =
1
2 κx 2 the integral is not algebraically tractable, and it is assumed that
the height of the energy barrier is high, U L ≡ U(L) k B T , then Eq. 1.24, gives
t K = τ
π
4
k B T
U L
exp
U L
k B T
(1.26)
where τ = γ /κ is the drag coefficient divided by the spring constant, t K is called
the Kramers time, after Kramers, who first derived it in 1940, [35].
For properties of First Passage Phenomena see Appendix D.1.
1.6 Power Stroke
We saw that a ratchet is a motor in which the motion is driven directly by thermal
fluctuations and rectified, or biased, by chemical reactions. In contrast, a powerstroke motor directly drives the motion. As an example we consider the rotation
experiments of the F 1 ATPase, the load is the long actin filament attached to the γ
subunit, see Fig. 1.5a, [24, 36, 37]. Similarly, in kinesin experiments the motor tows
a large bead (the load).
Compare this case with the ratchet one at Fig. B.1, Appendix B in Stochastic
Energetics. In both cases the ratchet and the power-stroke the energy to drive the
motion ultimately comes from chemical reactions taking place in the catalytic site(s)
of the motor. For Numerical computation of mechanochemical coupling see Chap. 4.
Indeed, a power stroke is large, rapid structural change in a protein that can be
used to do mechanical work, see Fig. 1.6. A power stroke has a size on the order of
the dimension of the protein itself (several nanometers); this distinguishes it from
the much smaller localized structural changes that occur when a protein binds to
a ligand or catalyzes a chemical reaction (the size of a chemical bond or a few
Ångstroms) [38]. The concept was first formulated for the protein myosin II which
drives the contraction of muscle [39].
The γ -subunit acts as a crankshaft that converts conformational changes in the
α3β3 ring to a unidirectional rotation and it also transmits conformational changes
in an αβ pair to another. Literature treating the rotation of the γ -subunit and the
effects that produces see [40–45].