Nonlinear Constraint-Based Modeling Of The Function And Evolution Of C4 Photosynthesis

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. The C4 photosynthetic system is a key target of efforts to improve crop yield through biotechnology, and its independent development in dozens of plant species widely separated geographically and phylogenetically is an intriguing example of convergent evolution. The availability of extensive high-throughput experimental data from C4 and non-C4 plants, as well as the origin of the biochemical pathways of C4 photosynthesis in the recruitment of enzymatic reactions already present in the ancestral state, makes it natural to study the development, function and evolution of the C4 system in the context of a plant's complete metabolic network, but the essentially nonlinear relationship between rates of photosynthesis, rates of photorespiration, and carbon dioxide and oxygen levels prevents the application of conventional, linear methods for genome-scale metabolic modeling to these questions. I present an approach which incorporates nonlinear constraints on reaction rates arising from enzyme kinetics and diffusion laws into flux balance analysis problems, and software to enable it. Applying the technique to a new genomescale model, suitable for describing metabolism in the leaves of either Zea mays or generic plants, I show it can reproduce known nonlinear physiological re- sponses of C3 and C4 plants. In combination with a novel method for inferring metabolic activity from enzyme expression data, I use the nonlinear model to interpret multiple channels of transcriptomic and biochemical data in the developing maize leaf, showing that the predicted metabolic state reproduces the transition between carbonimporting tissue at the leaf base and carbon-exporting tissue at the leaf tip while making additional testable predictions about metabolic shifts along the developmental axis. Adapting a method for simulating transition paths in physical and chemical systems, I find the highest-fitness paths connecting C3 and C4 states in the model's high-dimensional parameter space, show that such paths reproduce known aspects of the evolutionary history of the C4 position, and study their response to variation in environmental conditions and C4 biochemistry