  Positive feedback and cooperativity in the regulation of gene expression are
generally considered to be necessary for obtaining bistable expression states.
Recently, a novel mechanism of bistability termed emergent bistability has been
proposed which involves only positive feedback and no cooperativity in the
regulation. An additional positive feedback loop is effectively generated due
to the inhibition of cellular growth by the synthesized proteins. The
mechanism, demonstrated for a synthetic circuit, may be prevalent in natural
systems also as some recent experimental results appear to suggest. In this
paper, we study the effects of additive and multiplicative noise on the
dynamics governing emergent bistability. The calculational scheme employed is
based on the Langevin and Fokker-Planck formalisms. The steady state
probability distributions of protein levels and the mean first passage times
are computed for different noise strengths and system parameters. In the region
of bistability, the bimodal probability distribution is shown to be a linear
combination of a lognormal and a Gaussian distribution. The variances of the
individual distributions and the relative weights of the distributions are
further calculated for varying noise strengths and system parameters. The
experimental relevance of the model results is also pointed out.
