  We introduce a minimal model for the evolution of functional
protein-interaction networks using a sequence-based mutational algorithm, and
apply the model to study neutral drift in networks that yield oscillatory
dynamics. Starting with a functional core module, random evolutionary drift
increases network complexity even in the absence of specific selective
pressures. Surprisingly, we uncover a hidden order in sequence space that gives
rise to long-term evolutionary memory, implying strong constraints on network
evolution due to the topology of accessible sequence space.
