Figure 6.

Kinetics of TelK-induced dimerization and target search. (a) Model of TelK target search. TelK monomers in solution bind DNA with rate k_on and scan rapidly along non-target DNA with mean diffusion coefficient D_monomer = 1.8 µm²/s. Monomers localize the target site with rate k_target and bind tightly or dissociate from non-target DNA with average rate k_off = 0.24 s⁻¹. Preferential and stable binding of a TelK monomer allows a second monomer to dimerize at the target site and form a kinked DNA–TelK complex primed for catalysis. Occasionally, mobile monomers encounter each other on non-target DNA with rate k_dimer and form stable, immobile dimers (D_dimer < 1 × 10⁻⁴ µm²/s) that ‘test’ their substrate by condensing the DNA transiently. Eventually, dimers on non-target DNA dissociate or separate into mobile monomers again (rate < 0.01 s⁻¹). (b) Implementation of kinetic model in (a) via stochastic simulations using experimentally derived kinetic parameters. Average rates for first dimerization k_dimer (blue, black), and first target localization k_target (red) as a function of average protein occupancy, <N>, on DNA. For mean occupancies >1, target-finding and dimerization rates obey simple scaling laws of N² and N⁴, respectively. For mean occupancies <1, dimerization follows of N² scaling. Provided TelK occupancy is reasonably small, target localization consistently occurs faster than dimerization. Simulated rates are in good agreement with experimentally derived rates of first dimerization.