  We use a model based on the fractional Langevin equation with external noise
to describe the anomalous dynamics observed in microrheology experiments in
living cells. This model reproduces both the subdiffusive short-time and the
superdiffusive long-time behavior. We show that the former reflects the
equilibrium properties of the cell, while the latter is due to the
nonequilibrium external noise. This allows to infer the transport properties of
the system under active measurements from the transient behavior obtained from
passive measurements, extending the connection between active and passive
microrheology to the nonequilibrium regime. The active and passive results can
be linked via a generalized Stokes-Einstein relation based on an effective
time-dependent temperature, which can be determined from the transient passive
behavior. In order to reproduce experimental data, we further find that the
external noise describing the active components of the cell has to be
nonstationary. We establish that the latter leads to a time-dependent noise
spectral density.
