Understanding robustness in Random Boolean Networks

Long used as a framework for abstract modelling of genetic regulatory networks, the Random Boolean Network model possesses interesting robustness-related behaviour. We introduce coherency, a new measure of robustness based on a system’s state space, and defined as the probability of switching between attraction basins due to perturbation. We show that this measure has both upper and random-case bounds, and that these bounds are based on the size of individual attractor basins within the system. A mechanism for calculating these bounds is introduced, and the bounds are then used to define structural coherency, a measure of robustness attributable to system structure. Using these measures, we show that the decrease in coherency that occurs in the Random Boolean Network as its connectivity increases is related to a loss of structure in the system’s state space.