Fig. 4.

The TLD translator system. (A) The intended pathway of the translator $X\to Y$ that translates strand $X$ to strand $Y$. (B) One possible leak pathway of the TLD translator in the absence of the input strand $X$. After the clamp domain in F2 is open, the unbound domain $y_1$ in fuel F1 displaces the $y_1$ domain in fuel F2 through toeless strand displacement, resulting in a short-lived four-stranded complex, which could quickly reverse (unimolecular reaction; green) to the original configuration. Then, after the clamp domain in F3 is open, F3 reacts with this four-stranded complex and forms a six-stranded species $Y_{complex}$, which can similarly quickly reverse. Finally, the downstream reporter needs to capture this transient six-stranded complex before the reverse reaction occurs. This pathway suggests that the leak rate in the TLD translator should be even slower than that in the DLD translator, since this leak pathway requires a longer series of slow reactions to occur, and each transient in the leak pathway is more likely to quickly reverse toward the nonleak state. (Inset) Thermodynamic analysis shows that leak has an energy penalty of two units of entropy, which is one unit of entropy more than in the DLD design. The change in the number of base pairs due to the net leak reactions is equal to $\left\{\text{toehold size}\right\}-3\times \left\{\text{clamp size}\right\}=-1$. The number of separate components decreases by two after leak.