The first terms in Eqs. 1 and 2 denote the spatial diffusion of T † ABi and L † AB, respectively; 𝐷(𝒙) is the diffusion coefficient depending on the position x (x = "inside" or "outside" of A:B-droplet). The term 𝑓(⋯ ) denotes the consumption of division triggers T † AB1 via hybridization with L † AB and other molecules (details in Supplemental Note S1). 𝑔(⋯ ) denotes the time delay reaction (defined by Eq.3), modulated by the concentrations of RNase H and the inhibitor RNAs; 𝐾 # and 𝑘 $%& are the Michaelis-Menten parameters for the RNase H reaction; 𝑐 ' "# is the total RNase H concentration; 𝑘 ( $% and 𝑘 ) $&! are the hybridization rates of the division triggers with linker LAB and the inhibitor RNAs, respectively. The second term of Eq.2 denotes the hybridizations of L † AB with T † ABi. We also obtained partial differential equations for the other molecules; the details of the full numerical model and numerical simulations are described in Supplemental Note S1.