Figure 2

The space of viable genotypes gets rarefied with decreasing n. The horizontal axis shows the number n of reactions in a genotype and the vertical axis shows, on a logarithmic scale, the estimated fraction of random genotypes contained in the viable space V(n) for three different chemical environments, glucose, acetate and succinate, respectively. The estimated fraction of viable genotypes shown in this figure has been obtained as a product of two terms. The first term is an analytic prefactor which gives the fraction of genotypes in Ω(n) containing all super-essential reactions. The black dashed curve shows this analytic prefactor as function of n. The second term, that we estimated numerically, is the probability for a genotype to be viable given that it has all super-essential reactions. The numerical estimation of the fraction of viable genotypes in Ω(n) becomes extremely difficult for n < 2100 reactions even with the decomposition method.