Figure 3.

Characterization of the cooperative search process and steady-state levels as a function of the cooperativity ω and for different on-state levels p_ab, given N = 1 molecule of each TF species. (A) Dimerization probability P_dimer at equilibrium. The dimerization threshold is given by the entropic cost of dimerization and corresponds approximately to the length of the genome L_G. (B) The fold-change ϕ increases with the cooperativity as $\sqrt{\omega }$ below the dimerization threshold and then approaches a maximal value. (C) The cooperative search time τ displays a maximum at an intermediate cooperativity. For large ω, the search time decreases again and settles at an on-state independent value, corresponding to the dimer search time; compare to Fig. 4. (D) The probability W_D that the cooperative target state is reached via the dimer pathway is distinct from P_dimer in panel A, because independent monomeric search and dimeric search have different timescales. Note that the transition from the monomer to the dimer pathway marks the position of the maximal search time.