ABSTRACT
As described in Chapter 4, several techniques have been proposed to reduce the computational costs of stochastic simulations. Ultimately, however, these methods are still limited in the size of the models that they can analyze. Given the substantial computational requirements for numerical simulation of even modest size genetic circuits, model abstraction is absolutely essential. To reduce the cost of simulation, this chapter describes methods to simplify the original reaction-based model by applying several reaction-based abstractions. These abstractions reduce the model’s size by removing irrelevant or rapid reactions. Each abstraction examines the structure of the reactionbased model and, whenever possible, it applies transformations to simplify the model. The result is a new abstracted reaction-based model with less reactions and species which often substantially lowers the cost of simulation by not only reducing the model size but also eliminating many fast reactions that slow down simulation. The reduced model is also easier to intuitively visualize crucial components and interactions. The remainder of this chapter describes each of the reaction-based abstrac-
tions. Section 5.1 presents irrelevant node elimination. Section 5.2 describes various enzymatic approximations. Section 5.3 presents operator site reduction. An alternative reduction for operator sites that uses statistical thermodynamics is presented in Section 5.4. Section 5.5 describes dimerization reduction. Section 5.6 shows how the reaction-based abstractions reduce the complexity of the analysis for the phage λ model. Finally, Section 5.7 describes stoichiometry amplification.
