  Computational models of biological processes provide one of the most powerful
methods for a detailed analysis of the mechanisms that drive the behavior of
complex systems. Logic-based modeling has enhanced our understanding and
interpretation of those systems. Defining rules that determine how the output
activity of biological entities is regulated by their respective inputs has
proven to be challenging, due to increasingly larger models and the presence of
noise in data, allowing multiple model parameterizations to fit the
experimental observations.
  We present several Boolean function metrics that provide modelers with the
appropriate framework to analyze the impact of a particular model
parameterization. We demonstrate the link between a semantic characterization
of a Boolean function and its consistency with the model's underlying
regulatory structure. We further define the properties that outline such
consistency and show that several of the Boolean functions under study violate
them, questioning their biological plausibility and subsequent use. We also
illustrate that regulatory functions can have major differences with regard to
their asymptotic output behavior, with some of them being biased towards
specific Boolean outcomes when others are dependent on the ratio between
activating and inhibitory regulators.
  Application results show that in a specific signaling cancer network, the
function bias can be used to guide the choice of logical operators for a model
that matches data observations. Moreover, graph analysis indicates that the
standardized Boolean function bias becomes more prominent with increasing
numbers of regulators, confirming the fact that rule specification can
effectively determine regulatory outcome despite the complex dynamics of
biological networks.
