Figure 6.
Comparison of simulation results for detailed and condensed domain-level reaction networks at increasing initial concentrations. We calculate the time point when a product species reaches 50% of its final concentration in the detailed and condensed network, and plot the ratio of t1/2 for detailed and condensed systems. At low initial concentrations (all initial complexes less than or equal to 10 pM), this ratio is close to 1 in all our examples, which confirms that bimolecular steps are rate-limiting. All examples shown here are taken from literature [34,37,66] and will be explained in more detail in §5 (figures 7 and 8). Triangles denote single condensed reactions: Zhang & Winfree [34] - 5s and - 7s are single condensed three-way strand displacement reactions with a 5 nt and 7 nt toehold, respectively. Dabby [37] - (2,2) and - (4,4) are each single condensed four-way strand displacement reactions with two 2 nt and 4 nt toeholds. Simulations start to differ between 1 μM and 1 mM initial concentrations of complexes. Kotani & Hughes [66] - F4s is a slow condensed reaction isolated from a complex autocatalytic DSD system ({I5 + S6 → P2 + P8 + P9 + C} cf. figure 8). The detailed reaction pathway requires multiple four-way branch migration reactions to succeed, and can only be considered fast at concentrations below 10 pM. Circles denote two condensed reactions: Zhang & Winfree [34] - 5 and - 7 show the original experimental setup to measure reaction rates, which involves a separate reporter reaction. The full detailed network contains an unproductive toehold interaction between substrate and reporter that slows down the system at concentrations above 10 nM. When using rate-independent enumeration, this effect (called toehold occlusion) can only be observed in the detailed CRN. Squares show a complex system of many reactions: Kotani & Hughes [66] - F4 is an autocatalytic system, which contains slow four-way branch migration reactions (such as in the single condensed reaction discussed earlier). As a consequence, already at low concentrations the rate-limiting steps are not always bimolecular, and we will use rate-dependent enumeration and condensation when analysing this system.