  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 ($<0.1$).
