Figure 2

Regulation of multiple factors by using hierarchical pairs and approximated error. (a–d) Stochastic processes of competitive amplification with β = 1 and MSE-dependent decay are repeated in the model with two, four, and eight factors. (a) Target ratios of each factor in three simulation conditions are shown as three lines with markers. (b) Competition and MSE are calculated in one list that include all factors. The ratios of each factor after 10⁶ repeats are shown. (c, d) The ratios of eight or four factors are determined by hierarchical pairs (d). Each pair independently repeats the stochastic processes 10⁵ times. (e–h) The results after 10⁵ repeats in the model regulating 64 factors in hierarchical pairs. In MSE, the error is calculated with full accuracy. In “stepwise”, MSE is rounded every 10 folds. The number of steps of error (g) indicates the possible error levels. In “shuffle” (h), the factor with each target value is randomly set in the hierarchical pairs. In (e), correlation coefficient between the target and result ratios in 10 tests are shown in box and whisker plots indicating the interquartile range, 1.5 × the interquartile range, the mean (cross), and the data in outlier region (circle). Black lines in (f–h) indicate the target ratios. (i–m) The results in the model with 2¹² factors after 10⁵ repeats. Accurate MSE (i) or approximated stepwise error (j–m) is applied to decay probability. (i, j) The factor with each target value (range 1–4096 as indicated by a red line) is randomly set in the hierarchical pairs. (k) The target ratio is set using the expression ratio in E. coli without antibiotics. Initial condition of pairs is an even distribution. (l, m) Subsequently, from the (k) state, the target ratios for the next 10⁵ repeats are reset using gene expression data in the presence of antibiotics. The ratios of the factors before (l) and after (m) the second 10⁵ repeats are shown, where r is the correlation coefficient.