Title: Partial Order on the set of Boolean Regulatory Functions,
Abstract: Logical models have been successfully used to describe regulatory and
signaling networks without requiring quantitative data. However, existing data
is insufficient to adequately define a unique model, rendering the
parametrization of a given model a difficult task.
Here, we focus on the characterization of the set of Boolean functions
compatible with a given regulatory structure, i.e. the set of all monotone
nondegenerate Boolean functions. We then propose an original set of rules to
locally explore the direct neighboring functions of any function in this set,
without explicitly generating the whole set. Also, we provide relationships
between the regulatory functions and their corresponding dynamics.
Finally, we illustrate the usefulness of this approach by revisiting
Probabilistic Boolean Networks with the model of T helper cell differentiation
from Mendoza & Xenarios.