Figure 6. A Math Model-Aided Analysis Reveals Gene-Specific Requirements for TA1 and TA2.

(A) Schematic of the ordinary differential equation (ODE) used to obtain simulated mRNA dynamics from quantified NF-κB activity time courses.

(B) Schematic of the particle swarm optimization (PSO) pipeline used to quantify the activation strengths (k_act) for TAD mutants. First K_D, n_hill, k_deg are fit to RelA-wt data with k_act = 1. The identified parameters are then maintained with the new k_act fit for each TAD mutant to obtain the remaining activation strength (see Method Details).

(C) Experimental (left, RNA-seq) and simulated best-fit mRNA time-course (middle) heatmaps, along with identified k_act for TA2^CI (yellow) and TA1^Δ (pink). k_act is shown relative to RelA-wt with brighter colors indicating closer activity to RelA-wt (no effect of mutation) and white indicating complete loss of activity in the mutant (k_act = 0). Gray indicating a fit with ln (dist) < − 2:5 (see Method Details) was not found.

(D) Scatterplot of k_act for TA2^CI and TA1^Δ for 76 genes with a good fit in (C). Center color represents the effect of either a single mutation (from green k_act = 1 with no change from RelA-wt and redundancy with respect to a single mutation, to blue k_act = 0 where either mutation abrogates gene induction and both domains work synergistically to achieve full gene activation). Border colors represent an off-diagonal effect in which a gene shows a specific loss of induction in TA2^CI (pink) or TA1^Δ (yellow). Gray lines indicate the standard deviation of k_act from three repeated runs of optimization pipeline.

(E) Bar graphs of k_act (relative to the mean RelA-wt k_act) for RelA-wt, TA2^CI, TA1^Δ, and TA2^CITA1^Δ mutants, shown for four example genes arranged to indicate their relative positions in (D). Error bars indicate standard deviations of k_act from three repeated runs of optimization pipeline.