Robustness Analysis of a Synthetic Translational Resource Allocation Controller

Recent research in Synthetic Biology has highlighted the potential of translational resource allocation controllers to improve circuit modularity by dynamically allocating finite cellular resources in response to fluctuating circuit demands. The design of such controllers is complicated by the significant levels of parametric uncertainty that arise in their biological implementations. Tools from robust control, such as µ-analysis, can be used to determine the robustness of controller designs to parametric uncertainty, but require further development to allow their application to biomolecular control systems, which are typically highly non-linear, and contain multiple uncertainties that cannot be represented using the standard linear fractional transformation formalism. Here, we show how an LFT (Linear Fractional Transformation)-free formulation of the µ-analysis problem can be used to analyse and compare the robustness of alternative potential implementations of a translational resource allocation controller that utilises orthogonal ‘circuit-specific’ ribosomes to translate circuit genes. Our results provide useful guidelines for the construction of robust resource allocation circuitry for multiple future biotechnological applications.