  Many single molecule experiments for molecular motors comprise not only the
motor but also large probe particles coupled to it. The theoretical analysis of
these assays, however, often takes into account only the degrees of freedom
representing the motor. We present a coarse-graining method that maps a model
comprising two coupled degrees of freedom which represent motor and probe
particle to such an effective one-particle model by eliminating the dynamics of
the probe particle in a thermodynamically and dynamically consistent way. The
coarse-grained rates obey a local detailed balance condition and reproduce the
net currents. Moreover, the average entropy production as well as the
thermodynamic efficiency is invariant under this coarse-graining procedure. Our
analysis reveals that only by assuming unrealistically fast probe particles,
the coarse-grained transition rates coincide with the transition rates of the
traditionally used one-particle motor models. Additionally, we find that for
multicyclic motors the stall force can depend on the probe size. We apply this
coarse-graining method to specific case studies of the F1-ATPase and the
kinesin motor.
