  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. Nonlinear relationships between carbon dioxide and
oxygen levels and reaction rates are key to their physiology but cannot be
handled with standard techniques of constraint-based metabolic modeling. We
demonstrate that incorporating these relationships as constraints on reaction
rates and solving the resulting nonlinear optimization problem yields realistic
predictions of the response of C4 systems to environmental and biochemical
perturbations. Using a new genome-scale reconstruction of maize metabolism, we
build an 18000-reaction, nonlinearly constrained model describing mesophyll and
bundle sheath cells in 15 segments of the developing maize leaf, interacting
via metabolite exchange, and use RNA-seq and enzyme activity measurements to
predict spatial variation in metabolic state by a novel method that optimizes
correlation between fluxes and expression data. Though such correlations are
known to be weak in general, here the predicted fluxes achieve high correlation
with the data, successfully capture the experimentally observed base-to-tip
transition between carbon-importing tissue and carbon-exporting tissue, and
include a nonzero growth rate, in contrast to prior results from similar
methods in other systems. We suggest that developmental gradients may be
particularly suited to the inference of metabolic fluxes from expression data.
