  Modeling stochasticity in gene regulatory networks is an important and
complex problem in molecular systems biology. To elucidate intrinsic noise,
several modeling strategies such as the Gillespie algorithm have been used
successfully. This paper contributes an approach as an alternative to these
classical settings. Within the discrete paradigm, where genes, proteins, and
other molecular components of gene regulatory networks are modeled as discrete
variables and are assigned as logical rules describing their regulation through
interactions with other components. Stochasticity is modeled at the biological
function level under the assumption that even if the expression levels of the
input nodes of an update rule guarantee activation or degradation there is a
probability that the process will not occur due to stochastic effects. This
approach allows a finer analysis of discrete models and provides a natural
setup for cell population simulations to study cell-to-cell variability. We
applied our methods to two of the most studied regulatory networks, the outcome
of lambda phage infection of bacteria and the p53-mdm2 complex.
