  We extend replica exchange simulation in two ways, and apply our approaches
to biomolecules. The first generalization permits exchange simulation between
models of differing resolution -- i.e., between detailed and coarse-grained
models. Such ``resolution exchange'' can be applied to molecular systems or
spin systems. The second extension is to ``pseudo-exchange'' simulations, which
require little CPU usage for most levels of the exchange ladder and also
substantially reduces the need for overlap between levels. Pseudo exchanges can
be used in either replica or resolution exchange simulations. We perform
efficient, converged simulations of a 50-atom peptide to illustrate the new
approaches.
