Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors

TL;DR

This paper derives bounds and constructs a phase diagram for the efficiency at maximum power of tight-coupling molecular motors, showing how motor type and parameters influence efficiency relative to 1/2.

Contribution

It provides explicit bounds and a phase diagram for EMP based on constitutive relations and free energy, advancing understanding of motor efficiency limits.

Findings

EMP depends on the constitutive relation between current and force.

Motors can be classified into four types with distinct EMP ranges.

Physiological ATP-fueled motors can exceed 1/2 efficiency at maximum power with small load factors.

Abstract

The efficiency at maximum power (EMP) for tight-coupling molecular motors is investigated within the framework of irreversible thermodynamics. It is found that the EMP depends merely on the constitutive relation between the thermodynamic current and force. The motors are classified into four generic types (linear, superlinear, sublinear, and mixed types) according to the characteristics of the constitutive relation, and then the corresponding ranges of the EMP for these four types of molecular motors are obtained. The exact bounds of the EMP are derived and expressed as the explicit functions of the free energy released by the fuel in each motor step. A phase diagram is constructed which clearly shows how the region where the parameters (the load distribution factor and the free energy released by the fuel in each motor step) are located can determine whether the value of the EMP is larger or smaller than 1/2. This phase diagram reveals that motors using ATP as fuel under physiological conditions can work at maximum power with higher efficiency ($>1/2$) for a small load distribution factor ($<0.1$).