  The digital nature of genes combined with the associated low copy numbers of
proteins regulating them is a significant source of stochasticity, which
affects the phase of biochemical oscillations. We provide a theoretical
framework for understanding the dephasing evolution of genetic oscillations by
combining the phenomenological stochastic limit cycle dynamics and the discrete
Markov state models that describe the genetic oscillations. Through simulations
of the realistic model of the NF\kappa B/I\kappa B network we illustrate the
dephasing phenomena which are important for reconciling single cell and
population based experiments on this system.
