| Achoimre: | <p>This thesis is concerned with large-scale systems of Ordinary Differential Equations that model Biomolecular Reaction Networks (BRNs) in Systems and Synthetic Biology. It addresses the strategies of model reduction and decomposition used to overcome the challenges posed by the high dimension and stiffness typical of these models. A number of developments of these strategies are identified, and their implementation on various BRN models is demonstrated.</p> <p>The goal of model reduction is to construct a simplified ODE system to closely approximate a large-scale system. The <em>error estimation problem</em> seeks to quantify the approximation error; this is an example of the <em>trajectory comparison problem</em>. The first part of this thesis applies semi-definite programming (SDP) and dissipativity theory to this problem, producing a single <em>a priori</em> upper bound on the difference between two models in the presence of parameter uncertainty and for a range of initial conditions, for which exhaustive simulation is impractical.</p> <p>The second part of this thesis is concerned with the <em>BRN decomposition problem</em> of expressing a network as an interconnection of subnetworks. A novel framework, called layered decomposition, is introduced and compared with established modular techniques. Fundamental properties of <em>layered</em> decompositions are investigated, providing basic criteria for choosing an appropriate layered decomposition. Further aspects of the layering framework are considered: we illustrate the relationship between decomposition and scale separation by constructing singularly perturbed BRN models using layered decomposition; and we reveal the inter-layer signal propagation structure by decomposing the steady state response to parametric perturbations.</p> <p>Finally, we consider the <em>large-scale SDP problem</em>, where large scale SDP techniques fail to certify a system’s dissipativity. We describe the framework of S<em>tructured Storage Functions</em> (<em>SSF</em>), defined where systems admit a cascaded decomposition, and demonstrate a significant resulting speed-up of large-scale dissipativity problems, with applications to the trajectory comparison technique discussed above.</p>
|
|---|