Nonequilibrium Energetics of Molecular Motor Kinesin

Nonequilibrium energetics of single molecule translational motor kinesin was investigated by measuring heat dissipation from the violation of the fluctuation-response relation of a probe attached to the motor using optical tweezers. The sum of the dissipation and work did not amount to the input free energy change, indicating large hidden dissipation exists. Possible sources of the hidden dissipation were explored by analyzing the Langevin dynamics of the probe, which incorporates the two-state Markov stepper as a kinesin model. We conclude that internal dissipation is dominant.

Figure 1

(a) Schematic of the experimental setup for force clamp measurement of kinesin movement (not to scale). (b) Typical trace of probe (red) and trap (black) position with the FPGA force clamp. Both sampling and feedback rates are 20 kHz. Trap stiffness is $0.02\mathrm{pN}/\mathrm{nm}$.

Figure 2

(a) Typical examples of experimental results of FRR at high ATP (1 mM ATP, 0.1 mM ADP, 1 mM Pi) and (b) low ATP ($10\mu \mathrm{M}$ ATP, $1\mu \mathrm{M}$ ADP, 1 mM Pi). Square dots: velocity fluctuations, Circles: response functions. Lines are cubic spline interpolations. (c) Model predictions of FRR at high ATP and (d) low ATP. Dots and circles: numerical simulations. Lines indicate analytical solutions. Dashed lines are analytical solutions from the kinesin motor. Shaded areas indicate violation of the FRR.

Figure 3

(a) Schematic of a two-state kinesin stepper model. (b) Langevin model of a probe connected to the kinesin stepper. (c) Force-velocity relationship of single molecule kinesin movements at high ATP and (d) low ATP ($\text{mean}\pm \mathrm{s}.\mathrm{d}.$). Lines are fitted by Eq. (6). Fit parameters for high and low ATP are: $k_f^0=981$ and 889, $k_b^0=22.8$ and $0.61{\mathrm{s}}^{-1}$, $k_c=129$ and $32.5{\mathrm{s}}^{-1}$, $d_f=3.3$ and 4.0 nm, and $d_b=0.47$ and $-0.83\mathrm{nm}$, respectively.