  We analyse a continuum model for genetic circuits based on a partial
integro-differential equation initially proposed in Friedman, Cai \& Xie (2006)
as an approximation of a chemical master equation. We use entropy methods to
show exponentially fast convergence to equilibrium for this model with explicit
bounds. The asymptotic equilibration for the multidimensional case of more than
one gene is also obtained under suitable assumptions on the equilibrium
stationary states. The asymptotic equilibration property for networks involving
one and more than one gene is investigated via numerical simulations.
