1208.2524 (Z. C. Tu)

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

Z. C. Tu

The efficiency at maximum power (EMP) for tight-coupling molecular motors is investigated based on the constitutive relation between the flux and thermodynamic force. It is found that the EMP is equal to 1/2 when the flux $J$ and thermodynamic force $F$ satisfy $J=J^\prime F$ where $J^\prime$ represents the derivative with respect to $F$, and that the EMP is smaller (larger) than 1/2 when $JJ^\prime F$). The lower and upper bounds of EMP are proved to be $[1-\mathcal{W}(\mathrm{e}^{1-\Delta\mu})]/\Delta\mu$ and $[\mathcal{W}(\mathrm{e}^{1+\Delta\mu})-1]/\Delta\mu$, respectively, where $\mathcal{W}(.)$ represents the Lambert's W function while $\Delta \mu$ is called the reduced chemical potential which is the ratio of the released free energy of fuel in each motor step to the energy scale of thermal motion at the physiological temperature. A phase diagram with phase boundary $\delta= 2/{\Delta\mu}-1/(\mathrm{e}^{\Delta\mu/2}-1)$ is constructed, which shows how $\Delta \mu$ and the load distribution factor $\delta$ influence on the EMP. It is found that the EMP is larger or smaller than 1/2 when the parameter pair ($\Delta \mu$,$\delta$) takes value in the region below or above the phase boundary. This fact implies that the motors using ATP as fuel can work at maximum power and higher efficiency if $\delta \lesssim 0.1$, which provides a thermodynamic interpretation to several experimental observations on kinesin and myosin motors.

View original: http://arxiv.org/abs/1208.2524