A High Statistical Association between Robustness to Mutations and to Noise

<p>The horizontal axis shows mutational robustness <i>R_μ,</i> which is the fraction of a viable network's neighbors (networks differing from it in only one regulatory interaction) that arrive at the same equilibrium state <b>S</b>_∞ given the initial state <b>S</b>(0). The vertical axes show two different measures of robustness to noise. The left vertical axis (+, solid line) shows <i>R_ν,</i>₁, the probability that a change in <i>one</i> gene's expression state in the initial expression pattern <b>S</b>(0) leaves the network's equilibrium expression pattern <b>S</b>_∞ unchanged. The right vertical axis (circles, dashed line) shows <i>R_ν,</i>_*, the fraction of genes whose expression state in <b>S</b>(0) has to change at random, such that the probability that a network arrives at the equilibrium state <b>S</b>_∞ falls below a value of ½. In a network with large <i>R_ν,</i>_*, perturbation of the expression states of a large fraction of genes affects the equilibrium pattern only rarely. <i>R_μ</i> is highly associated with both <i>R_ν,</i>₁ (Spearman's <i>s</i> = 0.70) and <i>R_ν,</i>_* (Spearman's <i>s</i> = 0.69, <i>p</i> < 10⁻¹⁵; 10³ networks for both). The sample is obtained from a Monte Carlo simulation as described in Methods (<i>N</i> = 20, <i>M</i> ≈ 0.25 <i>N²</i> regulatory interactions, <i>d</i> = 0.5, <i>w_ij</i> = ±1).