  The regulation of cellular function is often controlled at the level of gene
transcription. Such genetic regulation usually consists of interacting
networks, whereby gene products from a single network can act to control their
own expression or the production of protein in another network. Engineered
control of cellular function through the design and manipulation of such
networks lies within the constraints of current technology. Here we develop a
model describing the regulation of gene expression, and elucidate the effects
of noise on the formulation. We consider a single network derived from
bacteriophage $\lambda$, and construct a two-parameter deterministic model
describing the temporal evolution of the concentration of $\lambda$ repressor
protein. Bistability in the steady-state protein concentration arises
naturally, and we show how the bistable regime is enhanced with the addition of
the first operator site in the promotor region. We then show how additive and
multiplicative external noise can be used to regulate expression. In the
additive case, we demonstrate the utility of such control through the
construction of a protein switch, whereby protein production is turned ``on''
and ``off'' using short noise pulses. In the multiplicative case, we show that
small deviations in the transcription rate can lead to large fluctuations in
the production of protein, and describe how these fluctuations can be used to
amplify protein production significantly. These novel results suggest that an
external noise source could be used as a switch and/or amplifier for gene
expression. Such a development could have important implications for gene
therapy.
