Synthetic analog feedback control circuits in living cells

Abstract

Models of biochemical reaction networks in cells are important for advancing our understanding of complex biological systems and for designing functional synthetic biological circuits. However, most models are based on a deterministic digital framework that is largely incompatible with nonlinear dynamics, stochastics, high-order feedback, cross talk, loading, and resource consumption in biology. In contrast, analog circuit design is the nearly 100-year-old art of crafting and analyzing nonlinear, stochastic, coupled differential equations to perform a desired task, often to given speed, precision, input sensitivity, power, load, or part-count constraints and in the presence of noise or device mismatch. In this thesis, we develop a canonical analog circuit that maps a wide class of biological circuits, whether at the DNA, RNA, protein, or small-molecule levels to design schematics that represent their underlying dynamical differential equations exactly.

We then apply techniques from analog feedback circuit design to two concrete biological circuits to improve their feedback performance: 1) We show that a novel synthetic microbial operational amplifier (OpAmp) with three amplification stages based on DNA, RNA, and protein stages and a dominant time constant is capable of high open-loop gain, stable, and robust-and-precise closed-loop performance; 2) We show that a synthetic tissue-homeostasis stem-cell circuit with a novel incoherent feed-forward loop attenuates negative phase and thus improves its robustness and precision of response to cell death in Type I diabetes. We also show that our novel use of both asymmetric division and symmetric division of stem cells improves feedback-loop performance w.r.t transients and robustness. To illustrate scalability of our approach to large-scale and high-speed simulations of the future, we use digitally programmable analog microelectronic chips to run complex simulations in parallel.

We develop a mapping that converts our analog schematics to a corresponding configuration on these chips, and demonstrate how to optimize the parameters of the biological OpAmp for high gain and improved performance. Our work illustrates that synthetic analog feed back control in living cells is amenable to rigorous design, analysis, simulation and implementation with the tools of analog circuit design, and leads to novel and experimentally useful synthetic biological circuits.