Analysis, design, and in vitro implementation of robust biochemical networks

The functionalities of every living organism are wired in the biochemical interactions among proteins, nucleic acids, and all the other molecules that constitute life's building blocks. Understanding the general design principles of this "hardware of life" is an exciting and challenging task for modern bioengineers. In this thesis, I focus on the topic of molecular network robustness: I investigate several design rules guaranteeing desired functionalities in specific systems, despite their components variability. Experimental verifications of such design schemes are carried out using \emph{in vitro} transcriptional circuits, a minimal analogue of cellular genetic networks. The first problem I consider is flux control, which is a fundamental feature for the correct performance of biochemical systems. I describe a simple model problem where two reagents bind stoichiometrically to form an output product. In the absence of any regulation, imbalances in the reagent production rates can cause accumulation of unused molecules, and limit the output flow. To match the reagents' flux robustly with respect to the open loop rates, I propose the use of negative or positive feedback schemes that rely on competitive binding. Such schemes are modeled through ordinary differential equations and implemented using transcriptional circuits; data are presented showing the performance of the two approaches. The second topic I examine is the functional robustness of interconnected networks. Molecular devices characterized in isolation may lose their properties once interconnected. This challenge is illustrated with a case study: a synthetic transcriptional clock is used to time conformational changes in a molecular nanomachine called DNA tweezers. Mass conservation introduces parasitic interactions that perturb the oscillator trajectories proportionally to the total amount of tweezers "load". To overcome this problem, we can use a transcriptional switch that acts as a buffer amplifier, achieving signal propagation and at the same time reducing the perturbations on the source of signal. Finally, I describe a general class of control-theoretic methods to analyze structural robustness in natural biological systems. Using Lyapunov theory and set invariance, the stability properties of several well-known case studies are analytically demonstrated. The key feature of this analysis is its reliance on parameter-independent models, which only capture essential dynamic interactions between molecular species.