Biological systems are noisy by nature. This aspect is reflected in our experimental
measurements and should be reflected in the models we build to better understand these
systems. Noise can be especially consequential when trying to interpret specific regulatory
interactions, i.e. regulatory network edges. In this paper, we propose a method to
explicitly encode edge-noise in Boolean dynamical systems by probabilistic edge-weight
(PEW) operators. PEW operators have two important features: first, they introduce
a form of edge-weight into Boolean models through the noise, second, the noise is
dependent on the dynamical state of the system, which enables more biologically meaningful
modeling choices. Moreover, we offer a simple-to-use implementation in the already
well-established BooleanNet framework. In two application cases, we show how the introduction
of just a few PEW operators in Boolean models can fine-tune the emergent dynamics
and increase the accuracy of qualitative predictions. This includes fine-tuning interactions
which cause non-biological behaviors when switching between asynchronous and synchronous
update schemes in dynamical simulations. Moreover, PEW operators also open the way
to encode more exotic cellular dynamics, such as cellular learning, and to implementing
edge-weights for regulatory networks inferred from omics data.
