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. Author summary The life and decision-making of cells is regulated by a complex web of dynamically interacting molecules. The strength and nature of individual interactions is very diverse, and it is especially important to understand such diversity when it comes to defects and disease. For example, the mutation of a protein binding site can critically alter the probability and strength of its interactions with its binding partners. Boolean network models have become an increasingly potent tool for understanding the complex dynamical interactions within cellular regulatory systems, however, there is no straightforward and explicit way to encode weights on individual interactions. In this paper we offer a way to add weights to interactions by simple noise operators which alter the behavior of edges (or groups of edges) in in-silico simulations of Boolean network models. We show with multiple applications that adding just a few PEW (probabilistic edge-weight) operators dramatically improves the biological plausibility of Boolean models and reproduces much more nuanced experimental results.
