Protein regulatory networks are the hallmark of many important biological functionalities. Two of these functionalities are mammalian cell cycle progression and near-perfect adaptive responses. Modeling and simulating these functionalities are crucial stages to understanding and predicting them as systems-level properties of cells.

In the context of the mammalian cell cycle, the timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. To avoid this problem, modelers often resort to "qualitative" modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this work, we describe a hybrid approach that combines features of continuous and discrete networks. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. Using our hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks found in various contexts within cells.

Large-scale protein regulatory networks, such as the one that controls the progression of the mammalian cell cycle, also contain small-scale motifs or modules that carry out specific dynamical functions. Systematic characterization of smaller, interacting, network motifs whose individual behavior is well known under certain conditions is therefore of great interest to systems biologists. We model and simulate various 3-node network motifs to find near-perfect adaptation behavior. This behavior entails that a system responds to a change in its environmental cues, or signals, by coming back nearly to its pre-signal state even in the continued presence of the signal. We let various topologies evolve in their parameter space such that they eventually stumble upon a region where they score well under a pre-defined scoring metric. We find many such parameter sample sets across various classes of topologies.