Fig. 8: Different regimes in cascades of CMCs.

a Scheme representing a cascade with two CMC cycles. S₁ and S₂ are the unmodified substrates, and P₁ and P₂ are the products (modified substrates), in each level. E₁ and E₁’ are the modifying enzymes or kinase and phosphatase in the upper level, C₁ and C₁’ are the complexes substrate–kinase and substrate-phosphatase in the upper level, P₁ and E₂’ are the modifying enzymes in the lower level, C₂ and C₂’ are the complexes in the lower level. The three kinetic parameters associated with each enzymatic reaction are a_i, d_i, k_i, the association, dissociation, and catalytic rates, respectively (more details in the Methods section). The conservation conditions are listed in the scheme. b Table summarizing the five representative numerical studies carried out. In all of them, step stimulation is applied. In studies 1 and 2, parameter values of the first cycle are selected so that this cycle in isolation exhibits signal termination or monotonic response, respectively, whereas the parameter values of the second cycle are randomly selected from predefined ranges. In studies 3 and 4, parameter values of the second cycle are selected so that this cycle in isolation exhibits signal termination or monotonic response, respectively, whereas the parameter values of the first cycle are randomly selected from predefined ranges. In Study 5, all the parameter values, first and second cycle, are randomly selected from the mentioned ranges. In all, 5,000 results of numerical simulations were analyzed in studies 1–4, and 10,000 in Study 5. Parameter values for each study are listed in Supplementary Table 1. The ranges for random exploration are concentrations: 10–100, association and dissociation rates: 0.1–10, and catalytic rates: 1–50. The results were classified into four groups (right): (i) those exhibiting signal termination in the first cycle but not in the second one (red bar); (ii) the inverse of (i) (light blue bar); (iii) those exhibiting signal termination in both cycles (orange bar); (iv) those with monotonic behavior in both cycles (light green bar). These groups are schematized next to the table (with the same color pattern as in the last row of the table). The criteria used to classify the outputs in groups are described in Methods. The lowest row in the table contains the results of each study, with a bar plot representing the percentage of cases in groups i–iv.