"Efficiency in molecular motors"

Molecular motors exploit the free energy released in the hydrolysis of 
energetic molecules like ATP to perform work useful for the cell. It 
is therefore important to know the efficiency of this process, i.e., 
the ratio between the performed work and the released free energy. The 
efficiency could reach 100% if the motor worked reversibly, i.e., 
infinitely slowly, but then its output power would vanish. Thus the 
relevant quantity is the Efficiency at Maximum Power (EMP). It has 
been shown that EMP reaches 50% when the motor operates in the linear 
regime close to equilibrium, but only recently it has been 
investigated further from equilibrium in models describing the motor 
as a discrete random process.

One can provide a more fundamental model of a molecular motor as a 
Brownian particle evolving in a two-dimensional continuous space, in 
which one coordinate represents its spatial position on the substrate 
and the other coordinate the advancement of the ATP-hydrolysis 
reaction, subject to a periodic “egg-carton” potential, whose tilt
in the direction of the chemical coordinate expresses the
free-energy imbalance. We have evaluated the EMP for such a model,
with special choices of the potential, and found that it reaches the
highest values when the displacements in the spatial and chemical
coordinate are tightly bound: in this regime, efficiencies larger that
50% can be reached sufficiently far from equilibrium. When the binding
is not tight, the EMP decreases since the motor can perform a chemical
hydrolysis cycle without advancing. Our formalism thus allows us to
gain a deeper insight into the connection between the mechanics and
the thermodynamics of molecular motors.