Abstract: We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional consequences of a given structural feature, for example a scale free architecture. A key step is to construct an algorithm that allows us to efficiently sample from a maximum entropy distribution on the space of Boolean dynamical networks constrained to perform a specific function, or cascade of gene expression. Such a distribution can act as a "functional null model" to test the significance of any given network feature, and can aid in revealing underlying evolutionary selection pressures on various network properties. Although our methods are general, we illustrate them in an analysis of the yeast cell cycle cascade. This analysis uncovers strong constraints on the architecture of the cell cycle regulatory network as well as significant selection pressures on this network to maintain ordered and convergent dynamics, possibly at the expense of sacrificing robustness to structural perturbations.