Fig. 2. Robustness properties emerging from the five network designs.

a The table summarizing added features and new emergent properties gained at every design. b The response to perturbations of ROS concentration in Design 1 (model B1), and Design 2 (model B2B). ROS concentration (in nM) is shown for the case of “no design” (solid blue line), which increases rapidly from 0 at time zero to over 100nM within 1h. For numerical reasons, then the simulations was stopped, Design 1 (dotted red line) and Design 2 (solid green line). Both ROS injection (doubling of the initial ROS concentration at day −1, or a decrease in ROS level (the ROS concentration was decreased to 20nM at day −3 was applied. All models are described in detail in Supplementary Information (Sections B1 and B2B). c The response to perturbations of ROS generation in Design 1 (model B1) and Design 2 (model B2B). ROS concentration (in nM) is shown for the case of “no design” (solid blue line), Design 1 (red lines), and Design 2 (green lines). The ROS generation rate constant was either increased twofold on day 1 (responses are shown in solid lines: solid red line for design 1; solid green line for design 2) or first decreased twofold on day 1 and then returned back to the initial value on day 3 (responses are shown in dashed lines: dashed red line for design 1; dashed green line for design 2). All models are described in detail in Supplementary Information (Sections B1 and B2B). d Emergence of homeostasis in Design 3 (model B3). The steady-state concentration of ROS (in nM) is shown against the fold change of the rate constant of ROS generation for Designs 2A (dashed gray line), Design 2B (solid red line), Design 3 (solid green line), Design 4 (dashed yellow line), and Design 5 (purple line). Homeostasis coefficients (H) for each design (shown in boxes) were computed at the point where ROS synthesis fold change was equal to 1. Model is described in Supplementary Information (Section B3). e Emergence of dynamic robustness in Design 4 (model B4). The concentration of healthy mitochondria (in nM) is shown for Designs 3 (dashed gray line) and Design 4 (solid green line). The initial ROS concentration was perturbed (transient increase from 10 to 11nM) at day 1. Dashed red line shows a hypothetical viability that corresponds to the threshold line dissecting 20% (i.e. 10nM) of the initial concentration of healthy mitochondria (i.e. 50 nM). Model is described in Supplementary Information (Section B4). f Emergence of dynamic robustness vis-à-vis with respect to the second pulse of ROS in Design 5 (model B5). The concentration of healthy mitochondria (in nM) is shown for Designs 4 (dashed gray line) and Design 5 (solid green line). The ROS generation rate constant was increased 15-fold on day 1, but, 3h before the increase of ROS generation, the NFκB signaling was increased 15-fold and the system reached a new steady state. On day 8 the ROS generation rate constant was decreased 15-fold causing the growth of healthy mitochondria. At the time point when the concentration of healthy mitochondria was near its peak value, the ROS generation rate constant was increased 15-fold for the second time. Model is described in Supplementary Information (Section B5).