Experimental and theoretical energetics of walking molecular motors under fluctuating environments

Abstract

Molecular motors are nonequilibrium open systems that convert chemical energy to mechanical work. Their energetics are essential for various dynamic processes in cells, but largely remain unknown because fluctuations typically arising in small systems prevent investigation of the nonequilibrium behavior of the motors in terms of thermodynamics. Recently, Harada and Sasa proposed a novel equality to measure the dissipation of nonequilibrium small systems. By utilizing this equality, we have investigated the nonequilibrium energetics of the single-molecule walking motor kinesin-1. The dissipation from kinesin movement was measured through the motion of an attached probe particle and its response to external forces, indicating that large hidden dissipation exists. In this short review, aiming to readers who are not familiar with nonequilibrium physics, we briefly introduce the theoretical basis of the dissipation measurement as well as our recent experimental results and mathematical model analysis and discuss the physiological implications of the hidden dissipation in kinesin. In addition, further perspectives on the efficiency of motors are added by considering their actual working environment: living cells.

Keywords: Fluctuation dissipation theorem; Kinesin; Molecular motor; Nonequilibrium energetics; Single molecule manipulation.

Fig. 1

The molecular motor kinesin. Kinesin walks on a microtubule rail like a bipedal human, whereas the floating head fluctuates wildly (Isojima et al. 2016)

Fig. 2

Single-molecule dissipation measurements of kinesin. a Schematic diagram of the measurement system. A probe particle is attached to a single-molecule kinesin via an antibody. The image of the particle is projected to quadrant photodiodes (QPD). The position signals are processed in a field-programable gate array (FPGA) circuit and feedbacked to the focal point of the optical tweezers via an acousto-optic deflector (AOD). b A typical time-trace of the particle position and the focal point of the optical trap. When the kinesin does not interact with microtubules, the particle shows Brownian motion centered on the trap focus (Waiting). When it begins to interact with a microtubule, kinesin begins to walk. The motion is automatically detected, and feedback is initiated to keep the distance between the particle and the focal point constant (Force clamp). When the kinesin walks to the edge of the detectable range of the QPD, it is forcibly pulled back to the waiting position. c Relationship between kinesin’s fluctuation (red squares) and response (blue circles). The region of the difference between these two (green area) exhibits the violation of the fluctuation dissipation theorem (nonequilibrium dissipation)

Fig. 3

A mathematical model for kinesin. a A two-state transition model for kinesin. b Langevin dynamics including a particle. c Relation between the fluctuation and response of kinesin reproduced by the mathematical model. The dashed lines show fluctuations and responses derived from kinesin molecules