  Metabolic networks are complex systems that comprise hundreds of chemical
reactions which synthesize biomass molecules from chemicals in an organism's
environment. The metabolic network of any one organism is encoded by a
metabolic genotype, defined by a set of enzyme-coding genes whose products
catalyze the network's reactions. Each metabolic genotype has a metabolic
phenotype, such as the ability to synthesize biomass on a spectrum of different
sources of chemical elements and energy. We here focus on sulfur metabolism,
which is attractive to study the evolution of metabolic networks, because it
involves many fewer reactions than carbon metabolism. Specifically, we study
properties of the space of all possible metabolic genotypes, and analyze
properties of random metabolic genotypes that are viable on different numbers
of sulfur sources. We show that metabolic genotypes with the same phenotype
form large connected genotype networks that extend far through metabolic
genotype space. How far they reach through this space is a linear function of
the number of super-essential reactions in such networks, the number of
reactions that occur in all networks with the same phenotype. We show that
different neighborhoods of any genotype network harbor very different novel
phenotypes, metabolic innovations that can sustain life on novel sulfur
sources. We also analyze the ability of evolving populations of metabolic
networks to explore novel metabolic phenotypes. This ability is facilitated by
the existence of genotype networks, because different neighborhoods of these
networks contain very different novel phenotypes. In contrast to
macromolecules, where phenotypic robustness may facilitate phenotypic
innovation, we show that here the ability to access novel phenotypes does not
monotonically increase with robustness.
