Temporal logic circuits implementation using a dual cross-inhibition mechanism based on DNA strand displacement

Abstract

Molecular circuits crafted from DNA molecules harness the inherent programmability and biocompatibility of DNA to intelligently steer molecular machines in the execution of microscopic tasks. In comparison to combinational circuits, DNA-based temporal circuits boast supplementary capabilities, allowing them to proficiently handle the omnipresent temporal information within biochemical systems and life sciences. However, the lack of temporal mechanisms and components proficient in comprehending and processing temporal information presents challenges in advancing DNA circuits that excel in complex tasks requiring temporal control and time perception. In this study, we engineered temporal logic circuits through the design and implementation of a dual cross-inhibition mechanism, which enables the acceptance and processing of temporal information, serving as a fundamental building block for constructing temporal circuits. By incorporating the dual cross-inhibition mechanism, the temporal logic gates are endowed with cascading capabilities, significantly enhancing the inhibitory effect compared to a cross-inhibitor. Furthermore, we have introduced the annihilation mechanism into the circuit to further augment the inhibition effect. As a result, the circuit demonstrates sensitive time response characteristics, leading to a fundamental improvement in circuit performance. This architecture provides a means to efficiently process temporal signals in DNA strand displacement circuits. We anticipate that our findings will contribute to the design of complex temporal logic circuits and the advancement of molecular programming.

Fig. 1. Design and implementation of temporal logic gate. (a) Concept of temporal OR gate. (b) Truth table of the temporal OR gate. (c) Architecture design of the temporal OR gate based on DNA strand displacement. The asterisk denotes the complementary sequence of a specific domain. (d) Fluorescence reporting mechanism. (e) Sequences of the essential domains in temporal OR gate. (f) Kinetic characterization of the temporal OR gate. Detector A, Detector B, Reporter X and Reporter Y are added as substrates in advance. [DA] = [DB] = [RX] = [RY] = 300 nM, [SA] = [SB] = 600 nM. The interval between the additions of SA and SB is 30 minutes, and the order of their additions is annotated in the plot labels. Fluorescence values in the experimental data were collected every minute. The measured fluorescence was normalized using a method that involved adding a 10-fold excess input to generate saturation fluorescence values. One unit of normalized fluorescence corresponds to the fluorescence generated by consuming 1 nM DA.

Fig. 2. Dual cross-inhibition mechanism and time–response characteristics. (a) Schematic diagram of the dual cross-inhibition mechanism. (b) Illustration of DA inhibition pathway, demonstrating the rapid consumption of DA by SA when SA inhibits SB, instead of generating SY through interaction with KB. (c) Illustration of DB inhibition pathway, demonstrating the rapid consumption of DB by KA, instead of generating KB through interaction with SB. (d) A bar chart comparing experimental data with simulation results, with SA added 10 minutes, 20 minutes, and 30 minutes before SB. The height of each bar indicates the value of OX or OY collected at 60 min of the reaction. The terms “OX-data” and “OY-data” represent the experimental data for OX and OY, while “OX-sim” and “OY-sim” represent the simulation results for OX and OY. (e) Comparison of the time response characteristics of temporal OR gate and cross-inhibitor. The X-axis represents the time interval between the additions of SA and SB. The Y-axis represents the inhibition degree at 60 min of the reaction at the different time intervals between the two input signals. In all experiments and simulations of (d) and (e), [DA] = [DB] = [RX] = [RY] = 300 nM, [SA] = [SB] = 600 nM. DA, DB, RX and RY are added as substrates in advance.

Fig. 3. Demonstration of the temporal logic gate with the incorporation of the annihilation gate. (a) Comparison of the simulations of temporal OR gates with and without the incorporation of the annihilation gate. “−AG” indicates that the annihilation gate is not incorporated, while “+AG” indicates that the annihilation gate is incorporated. [DA] = [DB] = [RX] = [RY] = 150 nM, [SA] = [SB] = 300 nM. DA, DB, RX and RY are pre-added as substrates. (b) Comparison of the inhibition degrees in (a). “−AG” and “+AG” represent the absence and presence of the annihilation gate. (c) Architecture design of the chemical reaction network of temporal OR gate with the incorporation of the annihilation gate. The reaction process of the reporter mechanism is the same as shown in Fig. 1a. (d) Simulation results of the inhibition degree in a temporal OR gate with the incorporation of the annihilation gate at different orders of magnitude for the reaction rate constant k_a. (e) Simulation results of the three-dimensional surface plot illustrating the inhibition degree id₆₀(B) (Z-axis) as a function of the reaction rate constant k₁ (X-axis), and the ratio of rate constants k₂ to k₁ (Y-axis) for the temporal OR gate with the incorporation of the annihilation gate. (f) Simulation depicting the inhibition degree under different concentrations of AG, with the X-axis representing AG concentration and the Y-axis representing the inhibition degree. The graph includes three curves representing substrate concentrations of 100 nM, 200 nM, and 300 nM. In all cases, the input-to-substrate ratio is maintained at 2 : 1. (g) Time response characteristics of temporal OR gate with the incorporation of annihilation gate. (f) Comparison of time response characteristics between temporal OR gates with and without the incorporation of the annihilation gate. In (d)–(h), all substrates and AG, except for the variables and the specifically annotated, were at a concentration of 300 nM, while the input signals were twice the concentration of the substrates.