  We analyze three simple genetic circuits which involve transcriptional
regulation and feedback: the autorepressor, the switch and the repressilator,
that consist of one, two and three genes, respectively. Such systems are
commonly simulated using rate equations, that account for the concentrations of
the mRNAs and proteins produced by these genes. Rate equations are suitable
when the concentrations of the relevant molecules in a cell are large and
fluctuations are negligible. However, when some of the proteins in the circuit
appear in low copy numbers, fluctuations become important and the rate
equations fail. In this case stochastic methods, such as direct numerical
integration of the master equation or Monte Carlo simulations are required.
Here we present deterministic and stochastic simulations of the autorepressor,
the switch and the repressilator. We show that fluctuations give rise to
quantitative and qualitative changes in the dynamics of these systems. In
particular, we demonstrate a fluctuations-induced bistability in a variant of
the genetic switch and and noisy oscillations obtained in the repressilator
circuit.
