  Inspired by problems in biochemical kinetics, we study statistical properties
of an overdamped Langevin process whose friction coefficient depends on the
state of a similar, unobserved process. Integrating out the latter, we derive
the long time behaviour of the mean square displacement. Anomalous diffusion is
found. Since the diffusion exponent can not be predicted using a simple scaling
argument, anomalous scaling appears as well. We also find that the coupling can
lead to ergodic or non-ergodic behaviour of the studied process. We compare our
theoretical predictions with numerical simulations and find an excellent
agreement. The findings caution against treating biochemical systems coupled
with unobserved dynamical degrees of freedom by means of standard, diffusive
Langevin descriptions.
