Simulation of Dynamics of Networks with Mutually Inhibitory Operons

<div><p>Black, green, and red indicate activity <i>A</i>, and the expression levels at the two operons, <i>m</i>1 and <i>m</i>2, respectively.</p> <p>Culture conditions were captured by <i>N</i>1, <i>N</i>2 (see Supporting Information). We employed a changing environment: (<i>N</i>1, <i>N</i>2) = (10,10) from 0 to 2000 step, (0,10) to 8000, (10,10) to 10000, (10, 0) to 16000, (10,10) to 20000.</p> <p>The parameters used in this simulation were: <i>S</i>(<i>A</i>) = 6<i>A</i>/(2+<i>A</i>) and <i>D</i>(<i>A</i>) = <i>A</i>, <i>N</i>_<i>thr</i>₁ = <i>N</i>_<i>thr</i>₂ = 2, <i>P</i> = <i>C</i> = 0.01, and <i>n</i>1 = <i>n</i>2 = 5.</p> <p>Initially, the environment contained both nutrients at sufficient levels from <i>t</i> = 0 to 2000, and activity <i>A</i> was less than but very close to 1.</p> <p>Then, following the change in the environment causing depletion of <i>N</i>1 = 0 but with <i>N</i>2 = 10, the system started to lose the activity, which destabilized the Attractor W, and entered the regime with two attractors, where the attractor with higher levels of <i>m</i>1 is selected.</p> <p>When returned to the nutrient-rich environment at <i>t</i> = 8000, the system came back to the single attractor with <i>m</i>1 = <i>m</i>2 = 1.</p> <p>Then, the environmental conditions were changed to depletion of the other nutrient, <i>N</i>1 = 10, <i>N</i>2 = 0 at <i>t</i> = 10000, and the system first deviated to express more of <i>m</i>1 but less <i>m</i>2.</p> <p>This deviation to the side of the non-adaptive attractor occurred by chance, but the small value of <i>m</i>2 did not compensate for the nutrient depletion and the activity is reduced close to zero.</p> <p>Then, the noise term in equations (1) took over in influence on the system.</p> <p>This fluctuation decreased only when <i>m</i>2 happened to rise sufficiently to allow activity to increase again at around <i>t</i> = 11000.</p>