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We develop a general method to explore how the function performed by abiological network can constrain both its structural and dynamical networkproperties. This approach is orthogonal to prior studies which examine thefunctional consequences of a given structural feature, for example a scale freearchitecture. A key step is to construct an algorithm that allows us toefficiently sample from a maximum entropy distribution on the space of booleandynamical networks constrained to perform a specific function, or cascade ofgene expression. Such a distribution can act as a "functional null model" totest the significance of any given network feature, and can aid in revealingunderlying evolutionary selection pressures on various network properties.Although our methods are general, we illustrate them in an analysis of theyeast cell cycle cascade. This analysis uncovers strong constraints on thearchitecture of the cell cycle regulatory network as well as significantselection pressures on this network to maintain ordered and convergentdynamics, possibly at the expense of sacrificing robustness to structuralperturbations.Comment: 10 pages, 11 figures, 2 tables Accepted for Physical Review

Function constrains network architecture and dynamics: A case study on the yeast cell cycle Boolean network