  Engineering genetic networks to be both predictable and robust is a key
challenge in synthetic biology. Synthetic circuits must reliably function in
dynamic, stochastic and heterogeneous environments, and simple circuits can be
studied to refine complex gene-regulation models. Although robust behaviours
such as genetic oscillators have been designed and implemented in prokaryotic
and eukaryotic organisms, a priori genetic engineering of even simple networks
remains difficult, and many aspects of cell and molecular biology critical to
engineering robust networks are still inadequately characterized. Particularly,
periodic processes such as gene doubling and cell division are rarely
considered in gene regulatory models, which may become more important as
synthetic biologists utilize new tools for chromosome integration. We studied a
chromosome-integrated, negative-feedback circuit based upon the bacteriophage
{\lambda} transcriptional repressor Cro and observed strong, feedback-dependent
oscillations in single-cell time traces. This finding was surprising due to a
lack of cooperativity, long delays or fast protein degradation. We further show
that oscillations are synchronized to the cell cycle by gene duplication, with
phase shifts predictably correlating with estimated gene doubling times.
Furthermore, we characterized the influence of negative feedback on the
magnitude and dynamics of noise in gene expression. Our results show that
cell-cycle effects must be accounted for in accurate, predictive models for
even simple gene circuits. Cell-cycle-periodic expression of {\lambda} Cro also
suggests an explanation for cell-size dependence in lysis probability and an
evolutionary basis for site-specific {\lambda} integration.
