Enumeration of Architectures with Perfect Matchings
In this thesis, we present two approaches for designing genetic regulatory networks in the field of synthetic biology. The core problem is to capture topological properties and dynamical mechanisms in such a way that enables generation of large-scale and complex genetic regulatory networks. Synthetic biologists design and construct artificial biological systems to create novel biological functions for a range of applications . While a number of design methods for genetic regulatory networks have been studied, these investigations have been limited to small-scale networks, and the design of larger-scale complex networks is not well understood yet. To address the issue, we introduce two new methods for gene circuit design. The first is based on direct transcription (DT) and mathematical programs with complementarity constraints (MPCCs). Since genetic regulatory networks are dynamic systems, DT is an appropriate optimization strategy, and is used to determine optimal network parameter values. An MPCC formulation is introduced that supports network structure optimization. The approach is applied to a genetic regulatory network where the adaptive capabilities of a network are optimized. This new approach supports the design of larger systems than established methods that are based on exhaustive enumeration [133, 134, 175]. It reduces computational expense and yields better designs. The second design method introduced here capitalizes on the representational power of generative algorithms. Inspired by preferential attachment  and generative graph grammars , we present new generative models that can incorporate both growth processes and “if-then” statement rules. These generative models are used as an abstract design representation of genetic regulatory networks. Genetic algorithms (GAs) operate on the underlying rules of these algorithms instead of on the design directly. This allows the use of a fixed-length GA encoding to uniquely characterize a variable-dimension network topology (phenotype). By adjusting elements of the GA encoding, the model can generate different network patterns, including larger and complex networks. Algorithms were developed initially for undirected graphs. These algorithms were tested using a graph matching problem. The results show that the generative algorithm is capable of producing networks with a range of topologies. Genetic regulatory networks can be represented using directed signed graphs, and algorithms were developed to generate this class of graphs. Instead of optimizing for adaptation, a robustness measure was chosen as the objective. A GA with a generative algorithm encoding was compared to a directly encoded GA, and a comprehensive analysis of these two approaches indicates that generative algorithm abstractions improve the ability to identify high-utility network designs in complex design spaces.