We demonstrate that the maximum genotype distance and robustness of metabolic networks can be explained by the number of superessential reactions and by the sizes of minimal metabolic networks viable in an environment.
Fourth, the maximum genotype distance between viable metabolic networks is almost as large as the diameter of genotype space itself, that is, to the maximum distance among all genotypes, regardless of their viability.
Because of the method we used to identify the typical and maximum genotype distance, we know that genotypes at these distances can be connected through individual reaction changes that do not affect viability.
Figure 3A shows the maximum genotype distance D max obtained in such random walks for networks up to 300 reactions, where we required viability on S=1, 5, 10, 20, 40, or 60 different sole sulfur sources.
For example, the viability constraint is invisible for large n, but it strongly affects the maximum genotype distance for n < N/2; not surprisingly, this viability constraint becomes more marked as n decreases to lower values.
For example, for metabolic networks of a given size N and viability on S sulfur sources, the maximum genotype distance within a genotype network is well approximated by one minus the fraction of superessential reactions in minimal metabolic networks.
Connected sets of metabolic networks viable on the same set of sulfur sources exhibit large maximum genotype distances D max.
Random viable metabolic networks of this size would have maximum genotype distances between D max = 0.96 (for S = 1) and D max = 0.60 (for S = 60).
We note that our estimates of maximum genotype distances are only lower bounds, such that this discrepancy may result from our limited ability to find maximal genotype distances accurately.
For maxima detection, we imposed a minimum maxima-to-maxima distance criterion of 10 mm.
However, less overall diversity was detected among the G12 genotype sequences (maximum genetic distance [uncorrected] = 0.0130), with only one major lineage identified, signifying potential recent introduction of this variant.
