Mathematical models and modular composition rules for synthetic genetic circuits

One major challenge in synthetic biology is how to design genetic circuits with predictable behaviors in various biological contexts. There are two limitations to addressing this challenge in mammalian cells. First, models that can predict circuit behaviors accurately in bacteria cells cannot be directly translated to mammalian cells. Second, upon interconnection, the behavior of a module, the building block of a circuit, may be different from its behavior in a standalone setting. In this thesis, I present a bottom-up modeling framework that can be used to predict circuit behaviors in transiently transfected mammalian cells (TTMC). The first part of the framework is based on a novel bin-dependent ODE model that can describe the behavior of modules in TTMC accurately. The second part of the framework rests upon a method of modular composition that allows model-based design of circuits. The efficacies of the bin-dependent model and the method of modular composition are validated via experimental data. The effects of retroactivity, a loading effect that arises from modular composition, on circuit behaviors are also investigated

Modeling genetic circuit behavior in transiently transfected mammalian cells

Binning cells by plasmid copy number is a common practice for analyzing transient transfection data. In many kinetic models of transfected cells, protein production rates are assumed to be proportional to plasmid copy number. The validity of this assumption in transiently transfected mammalian cells is not clear; models based on this assumption appear unable to reproduce experimental flow cytometry data robustly. We hypothesize that protein saturation at high plasmid copy number is a reason previous models break down and validate our hypothesis by comparing experimental data and a stochastic chemical kinetics model. The model demonstrates that there are multiple distinct physical mechanisms that can cause saturation. On the basis of these observations, we develop a novel minimal bin-dependent ODE model that assumes different parameters for protein production in cells with low versus high numbers of plasmids. Compared to a traditional Hill-function-based model, the bin-dependent model requires only one additional parameter, but fits flow cytometry input-output data for individual modules up to twice as accurately. By composing together models of individually fit modules, we use the bin-dependent model to predict the behavior of six cascades and three feed-forward circuits. The bin-dependent models are shown to provide more accurate predictions on average than corresponding (composed) Hill-function-based models and predictions of comparable accuracy to EQuIP, while still providing a minimal ODE-based model that should be easy to integrate as a subcomponent within larger differential equation circuit models. Our analysis also demonstrates that accounting for batch effects is important in developing accurate composed models.Accepted manuscrip