Nonequilibrium Energetics of Molecular Motor Kinesin

Abstract

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.Kinesin-1 (hereafter called kinesin) is a molecular motor that transports various cargos along microtubules throughout the cell [1,2]. Single molecule kinesin takes 8 nm steps [3] per ATP hydrolysis [4,5] on a microtubule rail and generates ≈7 pN maximum force [6][7][8]. The two catalytic sites (heads) hydrolyze ATP in a "hand-over-hand" manner that mimics bipedal walking [9-11] by alternating its two heads in coordination with different nucleotide/microtubule binding states [12]. Kinesin shows backward steps occasionally at no load and frequently at high loads [13][14][15]. Recent experiments indicate that the biased unidirectional motion is achieved by regulating selective binding/unbinding of the head to/from the appropriate binding site [16][17][18][19][20]. Contrary to the molecular mechanism of the motility, the thermodynamic energetics of the motor is poorly understood due to kinesin's stochastic and nonequilibrium behavior.The energetics of single-molecule motors were historically discussed when their stall forces were measured [21]. Kinesin's stall force of ≈7 pN indicates that maximum work per 8-nm step (≈56 pN•nm) is smaller than the physiological free energy change per ATP hydrolysis (≈85 pN•nm). This is in contrast to rotary motor F 1 -ATPase, whose stall force explains all input free energy [22]. Kinesin's inefficient work at stall has been regarded as an "open problem" [23]. However, it may not be appropriate to evaluate kinesin efficiency from the stall force for two reasons. First, it is believed that kinesin consumes ATP at backsteps instead of synthesizing ATP [13][14][15], indicating that the stall condition is not thermodynamically (quasi-)static. Second, the physiological role of kinesin is to carry vesicles against viscous media, meaning that the input energy is dissipated as "heat" rather than "work." Thus, measuring the "dissipation" from the motor is essential when discussing kinesin's nonequilibrium energetics in physiologically relevant conditions.The Harada-Sasa equality is best suited for this purpose [24,25] :Here, J x is total heat dissipation per unit time from the system through specific degrees of freedom indicated with subscript x. γ is viscous drag, and x  v is mean velocity, where  denotes the ensemble average. () Cf , with frequency f, is a Fourier transform of the correlation function of velocity fluctuations,is a Fourier transform of the velocity response function, and the prime indicates the re...

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