Fig. 4

Slow and fast pathways to TF specialization. a Temporal traces of TF–TF match M (top), and TF–BS mismatches k _ij (middle: TF1, bottom: TF2) with the corresponding signal specificity mutations denoted on dashed lines, for one example evolutionary trajectory at baseline parameters. Macrostates are color-coded as in the top legend and Fig. 3. b Average dynamics of fitness NF (blue, left scale) and TF–TF match M (red, right scale). For every timepoint, the dominant macrostate is denoted in color. c Snapshots of dominant macrostates (at increasing time post-duplication as indicated in the panels), shown for different combinations of selection strength Ns and signal correlation ρ as in Fig. 3. Contours mark dwell times in the dominant macrostates (in units of μ⁻¹). Red cross=baseline parameters. d Schematic of the two alternative pathways to specialization. τ _slow and τ _fast are the total times to specialization for the ‘slow’ and the ‘fast’ pathway, respectively. e Relative duration of the two pathways, as a function of binding site length L (gray line, top axis), TF consensus sequence mutation rate r _TF (red), and signal domain mutation rate r _S (blue, bottom axis). Pie charts indicate the fraction of slow (pink) and fast (green) pathways at each parameter value