  Genetic interaction can be defined as a deviation of the phenotypic
quantitative effect of a double gene mutation from the effect predicted from
single mutations using a simple (e.g., multiplicative or linear additive)
statistical model. Experimentally characterized genetic interaction networks in
model organisms provide important insights into relationships between different
biological functions. We describe a computational methodology allowing to
systematically and quantitatively characterize a Boolean mathematical model of
a biological network in terms of genetic interactions between all loss of
function and gain of function mutations with respect to all model phenotypes or
outputs. We use the probabilistic framework defined in MaBoSS software, based
on continuous time Markov chains and stochastic simulations. In addition, we
suggest several computational tools for studying the distribution of double
mutants in the space of model phenotype probabilities. We demonstrate this
methodology on three published models for each of which we derive the genetic
interaction networks and analyze their properties. We classify the obtained
interactions according to their class of epistasis, dependence on the chosen
initial conditions and phenotype. The use of this methodology for validating
mathematical models from experimental data and designing new experiments is
discussed.
