Figure 3.

Force-dependent dissociation constants, K_d(F), for three examples of two-state binary interactions. (A–C) Test case 1 is DNA annealing. DNA annealing causes a ssDNA to be paired with the complementary ssDNA to form a dsDNA. The change in the force-dependent conformational free energy Δϕ(F) can be explained by the distinct force–extension curves of naked ssDNA and dsDNA, which leads to the force-dependent interaction affinity of DNA annealing. (D–F) Test case 2 is DNA-stiffening protein binding to dsDNA. Force–extension curves of naked dsDNA and the dsDNA bound by a stiffening protein (e.g., H-NS⁴) that causes an increase in the persistence length of dsDNA from 53 to 174 nm. (G–I) Test case 3 is DNA-bending protein binding to DNA. Force–extension curves of naked dsDNA and dsDNA bound by a bending protein (e.g., IHF⁹) that causes an effective decrease in persistence length of dsDNA from 53 to 30 nm. Panels C, F, and I show the fold change of force-dependent K_d(F) relative to K_d⁰ for DNA annealing, the binding of DNA-stiffening protein to dsDNA, and the binding of DNA-bending protein to dsDNA. As each interaction shown in panels B, E, and H results in different effects on the DNA force–extension curves, the force dependence of the binding constant is markedly different.