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Decoupling between activation time and steady-state level in input-output responses
Fig 3
Decoupling under rate scale separation in the ladder model, 
, for case 1.III in Table 1 (A–E) and a generalization of case 2.I in Table 2 (F–J).
(A) Schematic of 
with regulation of 
(case 1.III). (B) Distribution of coupling scores after termination of the PSO. Each PSO run was terminated whenever f < 1 for more than 5 consecutive generations. For almost all the runs (n = 99) f < 0.1. (C) Evolution of f over each PSO run. The red curve represents the “best” optimized parameter set with the smallest value of f. (D) Input-output responses of optimized parameter sets for which f < 1 and the steady-state level increases monotonically with x. (E) Distributions of parameter values corresponding to the curves in panel D, with 
and 
. The green curve represents the best parameter set (red curve in C). (F) Schematic of 
with regulation of 
and 
(generalization of case 2.I). (G) Distribution of coupling scores after termination of the PSO. Each PSO run was terminated after 23 hours of computation time. For almost all the runs (n = 99) f < 0.1. (H) Evolution of f over each PSO run. The red curve represents the best parameter set. (I) Distributions of optimized parameter values for which f < 1 and the steady-state level increases monotonically with x. The green curve corresponds to the best parameter set (red curve in H). (J) Normalized dynamic ranges for two families of parameter sets, with the parameters set as follows: 
, 
, 
, 
, 
, 
or 10, and 
varied over a logarithmic range. The dots represent numerical computations (Materials and Methods), and the dashed lines represent the formulas in Table 2 (case 2.I).
doi: https://doi.org/10.1371/journal.pcbi.1014288.g003