Figure 2.

Strand displacement models. (a) Concurrent displacement model (yin-yang model). Strand displacement is preceded by a state occupied by the incumbent only (C). Branch migration begins after the toehold annealing step $\left(k_a\right)$. The branch point can take any value (i) between 0 and n − 1 and migrate toward nearest neighbors with a forward rate (f_i) and a reverse rate (r_i). V is the invader-only state. Concurrently with branch migration, the invader and the incumbent can dissociate from any intermediate state with rates $\left(d_i^{\prime }\text{and}{d}_i\right)$ that depend on the number of base pairs. (b) Sequential displacement model. The initial state and the final state are identical to C and V. The orange, black, and blue line segments represent the incumbent, substrate, and invader, respectively. The invader may anneal (k_a) and dissociate $\left(k_d^{\prime }\right)$ with the toehold reversibly. Afterward, branch migration (k_b) proceeds until a mismatch is encountered at state j – 1 or the incumbent strand is significantly destabilized at state n_th. From either state, the incumbent can irreversibly dissociate (k_d). To see this figure in color, go online.