Construction of a DNA Strand Displacement Memristor and Its Filter Circuit Characteristics
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摘要: 随着生物计算与分子电路技术的发展,基于DNA链置换的分子器件因其高度并行性、可编程性及低功耗特性,已成为构建新一代信息处理系统的重要方向。该文以忆阻器及滤波电路现有研究为基础,开展DNA链置换忆阻器及其在滤波电路中的应用研究。首先,通过忆阻器的DNA链置换反应模块,完成多稳态忆阻器的构建,并通过调控忆阻器内部状态变量,验证了该DNA链置换忆阻器的多稳态性能。其次,基于所设计的忆阻器DNA链置换反应模块,设计1阶低通忆阻器滤波电路,选取方波信号与正弦波信号对该电路进行性能测试,结果表明,DNA链置换1阶忆阻器滤波电路的性能与电路结构及内部状态变量密切相关。最后,依托忆阻器DNA链置换反应模块搭建2阶低通忆阻器滤波电路,通过Visual DSD与MATLAB仿真软件验证了该电路设计的合理性与可行性。研究结果表明,相较于传统滤波电路,DNA链置换忆阻器滤波电路在电路参数调节与工作稳定性方面均具备显著优势。Abstract:
Objective Filter circuits are widely used in modern control and signal-processing systems for noise suppression and signal integrity enhancement. Conventional Resistor-Capacitor (RC) filters are widely applied, but their fixed parameters limit adaptability and miniaturization in emerging molecular and nanoscale computing platforms. To address these limitations, DNA Strand Displacement (DSD) technology is integrated with memristor theory to develop tunable multistable molecular filter circuits. This study aims to design and validate first- and second-order low-pass filter circuits based on the dynamic response and state-dependent behavior of a DSD-based memristor. The proposed filters are designed to improve frequency selectivity, parameter adaptability, and system stability compared with traditional filter architectures. This approach is intended for molecular signal processing, integrated biocircuits, and adaptive filtering systems that require compact size and reconfigurability. Methods The method consists of four stages. First, core DSD reaction modules, including sine, cosine, integration, addition, and multiplication modules, are designed to construct a programmable multistable memristor model. Second, square-wave and sinusoidal input signals are generated through DSD reactions to evaluate the memristor response under different frequencies and amplitudes. Third, the memristor is embedded into low-pass filter structures to construct first- and second-order DSD-based memristor filter circuits. Fourth, simulations are performed using Visual DSD for molecular dynamics analysis and MATLAB for circuit-level analysis. Circuit performance is evaluated using transfer functions, Nyquist plots, Bode diagrams, and time-domain comparisons with classical RC filters. This combined simulation strategy verifies both molecular feasibility and circuit functionality. Results and Discussions The DSD-based memristor exhibits multistable behavior and converges to six stable equilibrium points under different initial conditions ( Fig. 8 ). Its hysteresis characteristics further confirm the state-dependent memory behavior of the designed molecular memristor (Fig. 7 ). The first-order DSD-based memristor filter circuit provides stable attenuation for square-wave and sinusoidal input signals. Its output amplitudes are consistently higher than those of the traditional RC filter across the tested frequencies (Table 3 ). The second-order DSD-based memristor filter circuit further reduces signal delay and improves stability, especially under high-frequency inputs (Table 4 ). Frequency-response analyses show that the cutoff frequency can be dynamically tuned by adjusting DSD reaction rates and initial concentrations (Figs. 9 and11 ). Time-domain simulations further confirm the filtering performance of the first- and second-order circuits (Figs. 10 and12 ). Reliability analysis indicates that lower initial copy numbers increase stochastic molecular noise, whereas higher initial copy numbers make the output distribution closer to the deterministic response and improve the probability of successful filtering. These results verify the feasibility of DSD-memristor integration for adaptive molecular filtering.Conclusions A DSD-based memristor with multistable characteristics and its corresponding first- and second-order low-pass filter circuits are designed and validated. Compared with traditional RC architectures, the proposed filters show improved output stability, parameter tunability, and frequency adaptability. By combining DSD technology with memristor theory, this study provides a reconfigurable molecular-scale filtering framework for signal-processing applications. The results provide a basis for future work on adaptive molecular circuits, intelligent filtering, and nanoelectronic system design. Further studies should focus on experimental validation, real-time tuning strategies, sequence optimization, anti-interference design, signal amplification, and circuit integration. -
Key words:
- DNA Strand Displacement(DSD) /
- Memristor /
- Multistability /
- Low-pass filter circuit
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表 1 DNA 链置换反应的初始值及其对应信号
初始值 初始值 反应速率常数 原始信号 $ \begin{aligned}Y_{2}^{+}(0)&=1\\y_{2}^{+}(0)&=2\end{aligned} $ $ \begin{aligned}Y_{2}^{-}(0)&=1\\y_{2}^{-}(0)&=1\end{aligned} $ $ \begin{aligned}{k}_{4}&=1\\{k}_{4}&=1\end{aligned} $ $ \begin{aligned}{Y}_{2}&=\sin (t)\\{y}_{2}&=\cos (t)\end{aligned} $ $ \begin{aligned}Y_{2}^{+}(0)&=1\\y_{2}^{+}(0)&=3\end{aligned} $ $ \begin{aligned}Y_{2}^{-}(0)&=1\\y_{2}^{-}(0)&=1\end{aligned} $ $ \begin{aligned}{k}_{4}&=2\\{k}_{4}&=2\end{aligned} $ $ \begin{aligned}{Y}_{2}&=\sin (2t)\\{y}_{2}&=\cos (2t)\end{aligned} $ $ \begin{aligned}Y_{2}^{+}(0)&=1\\y_{2}^{+}(0)&=4\end{aligned} $ $ \begin{aligned}Y_{2}^{-}(0)&=1\\y_{2}^{-}(0)&=1\end{aligned} $ $ \begin{aligned}{k}_{4}&=3\\{k}_{4}&=3\end{aligned} $ $ \begin{aligned}{Y}_{2}&=\sin (3t)\\{y}_{2}&=\cos (3t)\end{aligned} $ 表 2 DNA链置换忆阻器反应模块的设计
DNA 链置换反应网络 反应速率和初值 反应模块 DSD 仿真 $ \begin{aligned}& Z_{1}^{+}\xrightarrow{{k}_{5}}Z_{1}^{+}+z_{1}^{+};Z_{1}^{-}\xrightarrow{{k}_{5}}Z_{1}^{-}+z_{1}^{-}\\& z_{1}^{+}\xrightarrow{{k}_{5}}Z_{1}^{-}+z_{1}^{+};z_{1}^{-}\xrightarrow{{k}_{5}}Z_{1}^{+}+z_{1}^{-}\\& z_{1}^{+}+z_{1}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}};Z_{1}^{+}+Z_{1}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}}\end{aligned} $ $ \begin{aligned}{k}_{2}&=10\;({\mathrm{nMs}})^{-1}\\{k}_{5}&=1\;({\mathrm{nMs}})^{-1}\\z_{1}^{+}&=1\;{\mathrm{nM}};z_{1}^{-} =1\;{\mathrm{nM}}\\Z_{1}^{+}&=2\;{\mathrm{nM}};Z_{1}^{-} =1\;{\mathrm{nM}}\end{aligned} $ 

$ \begin{aligned}& Z_{2}^{+}\xrightarrow{{k}_{5}}Z_{2}^{+}+z_{2}^{-};Z_{2}^{-}\xrightarrow{{k}_{5}}Z_{2}^{-}+z_{2}^{+}\\& z_{2}^{+}\xrightarrow{{k}_{5}}Z_{2}^{+}+z_{1}^{+};z_{2}^{-}\xrightarrow{{k}_{5}}Z_{2}^{-}+z_{1}^{-}\\& z_{2}^{+}+z_{2}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}};Z_{2}^{+}+Z_{2}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}}\end{aligned} $ $ \begin{aligned}z_{2}^{+}&=2\;{\mathrm{nM}};z_{2}^{-} =1\;{\mathrm{nM}}\\Z_{2}^{+}&=1\;{\mathrm{nM}};Z_{2}^{-} =1\;{\mathrm{nM}}\end{aligned} $ 

$ \begin{aligned}& X_{2}^{+}\xrightarrow{{k}_{5}}x_{2}^{+}+X_{2}^{+};X_{2}^{-}\xrightarrow{{k}_{5}}x_{2}^{-}+X_{2}^{-};x_{2}^{+}\xrightarrow{{k}_{5}}x_{2}^{+}+X_{2}^{-}\\& x_{2}^{-}\xrightarrow{{k}_{5}}x_{2}^{-}+X_{2}^{+};{v}^{+}\xrightarrow{{k}_{6}}{V}^{+}+{v}^{+};{v}^{-}\xrightarrow{{k}_{6}}{V}^{-}+{v}^{-}\\& {V}^{+}\xrightarrow{{k}_{6}}{v}^{-}+{V}^{+};{V}^{-}\xrightarrow{{k}_{6}}{v}^{+}+{V}^{-}{V}^{+}\xrightarrow{{k}_{5}}{V}^{+}+{x}^{+};\\& x_{2}^{+}+x_{2}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}};x_{2}^{+}\xrightarrow{{k}_{5}}{x}^{+}+x_{2}^{+};X_{2}^{+}+X_{2}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}}\\& {V}^{-}\xrightarrow{{k}_{5}}{x}^{-}+x_{2}^{-};{v}^{+}+{v}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}};{x}^{+}+{x}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}}\end{aligned} $ $ \begin{aligned}{k}_{6}&=2\;({\mathrm{nMs}})^{-1}\\x_{2}^{+}&=1\;{\mathrm{nM}};x_{2}^{-} =1\;{\mathrm{nM}}\\X_{2}^{+}&=2\;{\mathrm{nM}};X_{2}^{-} =1\;{\mathrm{nM}}\\V_{}^{+}&=1\;{\mathrm{nM}};V_{}^{-} =1\;{\mathrm{nM}}\\{v}^{+}&=3\;{\mathrm{nM}};{v}^{-} =2\;{\mathrm{nM}}\end{aligned} $ 
$ \dot{x}=\sin (x)+V $
$ \begin{aligned}& {V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{x}^{+};{x}^{-}\xrightarrow{{k}_{5}}W(x)^{-}+{x}^{-}\\& z_{2}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+z_{2}^{+};z_{2}^{-}\xrightarrow{{k}_{5}}W(x)^{-}+z_{2}^{-}\\& W(x)^{+}\xrightarrow{{k}_{5}}W(x)^{-}+W(x)^{+}\\& W(x)^{-}\xrightarrow{{k}_{5}}W(x)^{+}+W(x)^{-}\\& W(x)^{+}+W(x)^{-}\xrightarrow{{k}_{5}}{\mathrm{Waste}}\end{aligned} $ $ \begin{aligned}z_{2}^{+}&=3\;{\mathrm{nM}}\\z_{2}^{-}&=1\;{\mathrm{nM}}\\x_{}^{+}&=2\;{\mathrm{nM}}\\x_{}^{-}&=1\;{\mathrm{nM}}\end{aligned} $ 
$ W(x)=x+{z}_{2} $
$ \begin{aligned}& W(x)^{+}+{V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{I}^{+}+{V}^{+};{I}^{+}\xrightarrow{{k}_{5}}{I}^{+}+{I}^{-}\\& W(x)^{+}+{V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{I}^{+}+{V}^{+};{I}^{-}\xrightarrow{{k}_{5}}{I}^{+}+{I}^{-}\\& W(x)^{+}+{V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{I}^{+}+{V}^{+};{I}^{+}+{I}^{-}\xrightarrow{{k}_{2}}{\mathrm{Waste}}\\& W(x)^{+}+{V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{I}^{+}+{V}^{+}\end{aligned} $ $ \begin{aligned}W(x)^{+}&=2\;{\mathrm{nM}}\\W(x)^{-}&=1\;{\mathrm{nM}}\\{V}^{+}&=3\;{\mathrm{nM}}\\{V}^{-}&=0.5\;{\mathrm{nM}}\end{aligned} $ 

表 3 1阶忆阻器滤波电路与1阶RC滤波电路的性能对比
$ {V}_{31}({V}_{{\mathrm{in}}}) $ $ {k}_{7} $ $ {V}_{{\mathrm{in}}}({\mathrm{time}},{\mathrm{peak}}) $ $ {V}_{{\mathrm{M}}{{{\mathrm{C}}}_{1}}{\mathrm{out}}}({\mathrm{time}},{\mathrm{peak}}) $ $ {H}_{1}(s)({V}_{{\mathrm{M}}{{{\mathrm{C}}}_{1}}{\mathrm{out}}}/{V}_{{\mathrm{in}}}) $ $ {V}_{{\mathrm{R}}{{{\mathrm{C}}}_{1}}{\mathrm{out}}}({\mathrm{time}},{\mathrm{peak}}) $ $ H_{1}^{\prime}(s)({V}_{{\mathrm{R}}{{{\mathrm{C}}}_{1}}{\mathrm{out}}}/{V}_{{\mathrm{in}}}) $ $ T=3.14,P=2 $ 1 (10.99, 2) (10.99, 1.943) 0.9715 (10.99, 2.0000 )0.6565 $ T=2.1,P=1 $ 1 (11.52, 1) (11.52, 0.8385 )0.8385 (11.52, 0.4689 )0.4689 $ T=6.28,P=3 $ 1 (9.24, 3) (9.42, 3) 1.0000 (9.24, 2.7490 )0.9163 $ T=3.14,P=2 $ 1.5 (10.99, 2) (10.99, 1.933) 0.9965 (10.99, 1.654) 0.827 $ T=3.14,P=2 $ 0.8 (10.99, 2) (10.99, 1.8721 )0.9361 (10.99, 1.116) 0.558 $ T=3.14,P=2 $ 0.4 (10.99, 2) (10.99, 1.462) 0.7130 (10.99, 0.6218 )0.3109 $ \sin (t) $ 2 (14.13, 1) (14.33, 0.9816 )0.9816 (14.61, 0.8941 )0.9841 $ \sin (t)+\cos (t) $ 2 (13.35, 1.414) (13.53, 1.392) 0.9844 (13.81, 1.265) 0.8946 $ \sin (3t) $ 2 (13.09, 1) (13.29, 0.8176 )0.8176 (13.42, 0.554) 0.5540 $ \sin (2t) $ 1 (10.21, 1) (10.57, 0.7404 )0.7404 (10.77, 0.4467 )0.4467 $ \sin (2t) $ 1.5 (10.21, 1) (10.49, 0.8543 )0.8543 (10.67, 0.5995 )0.5995 $ \sin (2t) $ 0.5 (10.21, 1) (10.73, 0.4924 )0.4924 (10.87, 0.2433 )0.2433 表 4 2阶忆阻器滤波电路与2阶RC滤波电路的性能对比
$ {V}_{41}({V}_{{\mathrm{in}}}) $ $ {k}_{7} $ $ {V}_{{\mathrm{in}}}({\mathrm{time}},{\mathrm{peak}}) $ $ {V}_{{\mathrm{M}}{{{\mathrm{C}}}_{2}}{\mathrm{out}}}({\mathrm{time}},{\mathrm{peak}}) $ $ {H}_{1}(s)({V}_{{\mathrm{M}}{{{\mathrm{C}}}_{2}}{\mathrm{out}}}/{V}_{{\mathrm{in}}}) $ $ {V}_{{\mathrm{R}}{{{\mathrm{C}}}_{2}}{\mathrm{out}}}({\mathrm{time}},{\mathrm{peak}}) $ $ H_{2}^{\prime}(s)({V}_{{\mathrm{R}}{{{\mathrm{C}}}_{2}}{\mathrm{out}}}/{V}_{{\mathrm{in}}}) $ $ T=3.14,P=2 $ 1 (10.99, 2) (10.99, 2) 1 (11.19, 0.4282 )0.2141 $ T=2.1,P=1 $ 1 (11.52, 1) (11.53, 0.9964 )0.9964 (11.73, 0.1075 )0.1075 $ T=6.28,P=3 $ 1 (9.42, 3) (9.42, 3) 1 (9.55, 1.465) 0.4833 $ T=3.14,P=2 $ 1.5 (10.99, 2) (11.01, 2) 1 (11.11, 0.7047 )0.3524 $ T=3.14,P=2 $ 0.8 (10.99, 2) (11.01, 1.998) 0.9990 (10.25, 0.3216 )0.1068 $ T=3.14,P=2 $ 0.4 (10.99, 2) (11.01, 1.906) 0.9530 (10.43, 0.1482 )0.0741 $ \sin (t) $ 2 (14.13, 1) (14.23, 0.9957 )0.9957 (12.26, 0.6013 )0.6013 $ \sin (t)+\cos (t) $ 2 (13.35, 1.414) (13.45, 1.408) 0.9958 (14.45, 0.8504 )0.6014 $ \sin (3t) $ 2 (13.09, 1) (13.19, 0.9628 )0.9628 (13.71, 0.217) 0.2170 $ \sin (2t) $ 1 (10.21, 1) (10.41, 0.9488 )0.9488 (11.23, 0.1529 )0.1529 $ \sin (2t) $ 1.5 (10.21, 1) (10.35, 0.9756 )0.9756 (11.09, 0.2482 )0.2482 $ \sin (2t) $ 0.5 (10.21, 1) (10.57, 0.8241 )0.8241 (11.45, 0.0646 )0.0646 -
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