Fig. 3: Numerical investigation of timing-controlled linker-cleavage for DNA droplet division.

a Schematics of time-delay circuit to regulate cleaving rate of a DNA linker. (i) Excess inhibitor RNAs hybridize with released division triggers, producing inhibited division triggers. (ii) Released division triggers are released from inhibited division triggers by RNase H reaction. Released division triggers hybridize with the DNA linker, cleaving the linker via strand displacement. b Compositions of a binary-mixed DNA droplet (A:B-droplet). c Schematic of the timing-controlled division of A:B-droplet using a time-delay circuit. L_AB is initially cleaved using T_ABi followed by the cleaving of L^†_AB, resulting in the division of A:B-droplet. The time-delayed cleaving of L^†_AB is achieved by the release of T^†_ABi from iT^†_ABi. The degree of time delay of the T^†_ABi release decides the timing control of the droplet division. Linkers and triggers with “†” indicate those that can achieve a time-delay circuit if inhibitor RNAs and RNase H are added. d, e Snapshots of numerically calculated concentrations of L_AB and L^†_AB in the A:B-droplet using the reaction-diffusion simulation. The white broken-line circle indicates the surface of the A:B-droplet. f Time course of L_AB of the A:B-droplet in the numerical simulation. g, h Time courses of L^†_AB concentrations of the A:B-droplet in the numerical simulation via changing the RNase H concentration \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) or inhibitor RNA concentration \({u}_{{{{{\rm{R}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}\), respectively. Normalized initial total concentration of inhibitor RNA is defined as \({\widetilde{c}}_{{{\rm{AB}}}}\) = \({u}_{{{{{\rm{R}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{{{\rm{tot}}}}/{u}_{{{{{\rm{T}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{{{\rm{tot}}}}\) (i = 1,2), where \({u}_{{{{{\rm{R}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{{{\rm{tot}}}}\) = \({u}_{{{{{\rm{R}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}+{u}_{{{{{\rm{iT}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}\) is the initial total concentration of excess and hybridized inhibitor RNAs, and \({u}_{{{{{\rm{T}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{{{\rm{tot}}}}\) = \({u}_{{{{{\rm{T}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}+{u}_{{{{{\rm{iT}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}\) is the initial total concentration of released and inhibited triggers. g \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) = 1.25, 2.5, and 5.0 × 10⁻² U/µL; \({\widetilde{c}}_{{{\rm{AB}}}}\) = 1.5. h \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) = 2.5 × 10⁻² U/µL; \({\widetilde{c}}_{{{\rm{AB}}}}\) = 1.0, 1.5, and 2.0. i, j Time courses of the division ratio r_div in the reaction-diffusion simulation with changing the \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) or \({u}_{{{{{\rm{R}}}}^{{\dagger} }}_{{{\rm{AB}}}i}}^{0}\), respectively. i \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) = 1.25, 2.5, and 5.0 × 10⁻² U/µL; \({\widetilde{c}}_{{{\rm{AB}}}}\) = 1.5. j \({c}_{{{{\rm{E}}}}_{{{\rm{RH}}}}}\) = 2.5 × 10⁻² U/µL; \({\widetilde{c}}_{{{\rm{AB}}}}\) = 1.0, 1.5, and 2.0. Source data are provided as a Source Data file.