Programming Molecules and Cells: Design Architectures for Chemical Reaction and Gene Regulatory Networks

Abstract

The stages of cell differentiation are often illustrated as a sequence of events and chemical cues that move a cell from one state to another. Differentiated cells send and receive signals to compute functions on their environments and perform complex tasks such as pattern formation. But how would one program a cell, <italic>de novo</italic>, to have these behaviors? Great strides have been made in developing tools for genetically modifying organisms to carry out simple tasks, and the wealth of literature in quantitative biology and genome engineering speaks to these efforts. However, what may be missing is an engineering framework—a formal layering of mathematical abstractions connected to physical implementations via a “biomolecular compiler”. Engineering frameworks and compilers are instrumental to the design and implementation of other technological systems—it is the reason that complex commercial airplanes can be proven safe, and that computers are useful tools and not one–of–a–kind nests of unreliable circuitry. It seems clear that similar technomimetic frameworks for synthetic biology should exist, however may questions remain. What abstractions or specification languages are suitable for engineering living organisms? Are the abstractions for specifying single celled behaviors suitable for specifying multicellular behaviors? How are such specifications physically instantiated? The original contribution of this thesis is to develop two frameworks for engineering dynamical and computational systems: a compiler taking a linear I/O system as input and producing a chemical reaction network as output, and a framework for compiling a finite state machine specification into a gene regulatory network. Linear I/O systems are a fundamental tool in systems theory, and have been used to design complex circuits and control systems in a variety of settings. In Chapter 2 I present a principled design method for implementing arbitrary linear I/O systems with biochemical reactions. This method relies on two levels of abstraction: first, an implementation of linear I/O systems using idealized chemical reactions, and second, an approximate implementation of the ideal chemical reactions with enzyme-free, entropy-driven DNA reactions. The ideal linear dynamics are shown to be closely approximated by the chemical reactions model and the DNA implementation. The approach is illustrated with integration, gain, and summation as well as with the ubiquitous robust proportional-integral (PI) controller. Finite state machines are fundamental computing devices at the core of many models of computation. In biology, finite state machines are commonly used as models of development in multicellular organisms. In Chapter 3 I describe a method by which any finite state machine can be built using nothing more than a suitably engineered network of readily available repressing transcription factors. In particular, I show the mathematical equivalence of finite state machines with a Boolean model of gene regulatory networks. I describe how such networks can be realized with a small class of promoters and transcription factors. To demonstrate the robustness of our approach, I show that the behavior of the ideal Boolean network model approximates a more realistic delay differential equation model of gene expression. Finally, I explore a framework for the design of more complex systems via an example, synthetic bacterial microcolony edge detection, that illustrates how finite state machines could be used together with cell signaling to construct novel multicellular behaviors. The results presented in this work contribute to both engineering and basic science. To the engineer, these frameworks provide a possible method by which living dynamical and computational systems may be specified and physically realized. To the scientist these frameworks provide a hypothesis about the computational limits of single cells, and a new light in which examine and compare multicellular behavior.