Experimental thermodynamics of single molecular motor

Distribution of energy in the ideal gas that lacks equipartition

The energy and velocity distributions of ideal gas particles were first obtained by Boltzmann and Maxwell in the second half of the nineteenth century. In the case of a finite number of particles, the particle energy distribution was obtained by Boltzmann in 1868. However, it appears that this distribution is not valid for all vessels. A round vessel is a special case due to the additional integral of motion, the conservation of the gas angular momentum. This paper is intended to fill this gap, it provides the exact distribution of particle energy for a classical non-rotating ideal gas of a finite number of colliding particles in a round vessel. This previously unknown distribution was obtained analytically from the first principles, it includes the dependence on all the particle masses. The exact mean energies of gas particles are also found to depend on the system parameters, i.e., the distribution of energy over the degrees of freedom is not uniform. Therefore, the usual ideal gas model allows for the uneven energy partitioning, which we study here both theoretically and in simple numerical experiments.

Pushing the limits of luminescence thermometry: probing the temperature of proteins in cells

Proteins are involved in numerous cellular activities such as transport and catalysis. Misfolding during biosynthesis and malfunctioning as a molecular machine may lead to physiological disorders and metabolic problems. Protein folding and mechanical work may be viewed as thermodynamic energetically favorable processes in which stochastic nonequilibrium intermediate states may be present with conditions such as thermal fluctuations. In my opinion, measuring those thermal fluctuations may be a way to access the energy exchange between the protein and the physiological environment and to better understand how those nonequilibrium states may influence the misfolding/folding process and the efficiency of the molecular engine cycle. Here, I discuss luminescence thermometry as a possible way to measure those temperature fluctuations from a single-molecule experimental perspective with its current technical limitations and challenges.

Is F1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip

We present a chemomechanical network model of the rotary molecular motor F₁-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F₁-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.

Evaluation of the Duty Ratio of the Bacterial Flagellar Motor by Dynamic Load Control

The bacterial flagellar motor is one of the most complex and sophisticated nanomachineries in nature. A duty ratio D is a fraction of time that the stator and the rotor interact and is a fundamental property to characterize the motor but remains to be determined. It is known that the stator units of the motor bind to and dissociate from the motor dynamically to control the motor torque depending on the load on the motor. At low load, at which the kinetics such as proton translocation speed limits the rotation rate, the dependency of the rotation rate on the number of stator units N implies D: the dependency becomes larger for smaller D. Contradicting observations supporting both the small and large D have been reported. A dilemma is that it is difficult to explore a broad range of N at low load because the stator units easily dissociate, and N is limited to one or two at vanishing load. Here, we develop an electrorotation method to dynamically control the load on the flagellar motor of Salmonella with a calibrated magnitude of the torque. By instantly reducing the load for keeping N high, we observed that the speed at low load depends on N, implying a small duty ratio. We recovered the torque-speed curves of individual motors and evaluated the duty ratio to be 0.14 ± 0.04 from the correlation between the torque at high load and the rotation rate at low load.