Rank histogram of reactions based on their occurrence. The horizontal axis shows the 2902 reactions in our global reaction set ordered based on their rank. The vertical axis shows the occurrence of each reaction in 1000 randomly sampled genotypes that are viable in a glucose environment, with n = 831 equal to that of E. coli. The occurrence of a reaction is given by the number of sampled genotypes containing the reaction, divided by the sample size of 1000. Reactions have been ordered based on their decreasing occurrence, with rank "1" corresponding to reaction with highest occurrence. All super-essential reactions have an occurrence of 1.0 and contribute to the horizontal plateau on the left of the rank histogram. We also see a larger plateau on the right, with an associated occurrence value of approximately 0.2. The two plateaus are connected by a degraded slope, corresponding to reactions that see their occurrence decrease continuously from 1.0 to 0.2. To study this region of the rank histogram, we have fitted it to two classes of functions: a constant plus an exponential (f(r) = a + b exp[-c r]; a = 0.2267, b = 1.293, c = 0.006827) and a constant plus a power function (f(r) = a + b/rc; a = 0.2052, b = 458.9, c = 1.375). Based on the coefficient of determination R2, the power law provides a better fit (R2 = 0.9645 for the exponential and R2 = 0.9927 for the power).