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Decoupling between activation time and steady-state level in input-output responses
Fig 4
Decoupling under rate scale constraint arises under incoherent regulation.
(A) Distributions of the coupling score, f, obtained from optimization with various rate scale constraints (RSC). The lower the RSC, the more similar the horizontal transition rates are forced to be. Optimisations were terminated after a predefined compute time (Materials and Methods). Only the parameter sets for which f < 1 are shown, and their number for each RSC value is given underneath the corresponding set of points. (B) Input-output responses corresponding to the parameter sets obtained from optimisation with RSC = 0.005, for which f < 1 and 
increases with x. (C) Values of 
and 
in the parameter sets corresponding to the responses in B (RSC = 0.005). (D) Parameter values corresponding to the responses in B (RSC = 0.005). The green line represents the best parameter set (minimum f). Each parameter is plotted in units of 
, except for kon, which is in units of 
. (E) Heatmap of the coupling score, f, with respect to 
and 
, with the other parameters set to the most optimal parameter set (green curve in D), along with select choices of 
and 
(crosses) whose corresponding input-output curves are shown in F. (F) Input-output curves corresponding to the parameter sets indicated in E. (G) Overlap between the concentration ranges over which the input-output curves in B change by 90%. Given two intervals [a,b] and [c,d], the overlap is computed as 
. The closer this value is to zero, the less overlap there is between the concentration ranges over which 
and 
exhibit the greatest change. (H) Values of 
and 
in the best parameter set for each choice of RSC.
doi: https://doi.org/10.1371/journal.pcbi.1014288.g004