Construction of DNA Strand Displacement Memristor and Research on 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。本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，设计一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 链置换一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二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 In modern control and signal processing systems, filter circuits are essential for noise suppression and signal integrity enhancement. Conventional RC filters, while widely used, lack adaptability and miniaturization capabilities required for emerging molecular and nano-scale computing platforms. This study introduces a novel integration of DNA Strand Displacement (DSD) technology with memristor-based circuits to develop tunable, multi-stable molecular filters. The objective is to design and validate first- and second-order low-pass filter circuits that leverage the dynamic response and state-dependent behavior of DSD-based memristors. These filters aim to achieve improved frequency selectivity, parameter adaptability, and system stability compared to traditional filter architectures. The proposed approach targets applications in molecular signal processing, integrated bio-circuits, and adaptive filtering systems where compact size and reconfigurability are critical. Methods The methodology follows a four-stage process. First, core DSD reaction modules (sine, cosine, integration, addition, multiplication) are designed to construct a programmable multi-state memristor model. Second, DSD-based square and sinusoidal inputs are synthesized to evaluate memristor response under varying frequencies and amplitudes. Third, these memristors are integrated into RC filter topologies to build first-order and second-order low-pass filters, replacing fixed resistors with tunable DSD-based memristive elements. Fourth, comprehensive simulations are performed using Visual DSD for molecular dynamics and MATLAB for circuit-level analysis. Performance is assessed via transfer functions, Nyquist plots, Bode diagrams, and time-domain comparisons with classical RC filters. This multi-tool approach rigorously validates both molecular feasibility and electronic functionality. Results and Discussions The DSD-based memristor exhibits multi-stable behavior with six equilibrium states under controlled initial conditions ( Fig. 7 ). The first-order filter provides stable attenuation for square and sinusoidal inputs, with output amplitudes consistently exceeding those of traditional RC filters across tested frequencies (Table 3 ). The second-order filter further reduces signal delay and improves stability, especially under high-frequency inputs (Table 4 ). Frequency response analyses confirm that cutoff frequencies can be dynamically tuned by adjusting DSD reaction rates and initial concentrations (Figs. 8 ,10 ). The system maintains robust performance under varying signal types and environmental simulations, demonstrating adaptability. These results validate the feasibility of DSD-memristor integration for adaptive filtering, offering a promising alternative to conventional rigid circuits in molecular-scale applications.Conclusions This study successfully designs and validates a DSD-based memristor with multi-stable characteristics and its corresponding first- and second-order low-pass filter circuits. The proposed filters demonstrate superior performance in terms of output stability, parameter tunability, and frequency adaptability compared to traditional RC architectures. By integrating DSD technology with memristor theory, we enable a new class of reconfigurable, molecular-scale filtering systems suitable for advanced signal processing applications. The work provides a foundation for future research in adaptive molecular circuits, intelligent filtering, and nano-electronic system design. Further developments could include hardware implementation, real-time tuning algorithms, and integration with machine learning for autonomous signal optimization in IoT and biomedical devices. -
Key words:
- DNA Strand Displacement /
- Memristor /
- Multistability /
- 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} $ 
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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}}Waste;Z_{1}^{+}+Z_{1}^{-}\xrightarrow{{k}_{2}}Waste\end{aligned} $ $ \begin{aligned}{k}_{2}&=10(nMs)^{-1}\\{k}_{5}&=1(nMs)^{-1}\\z_{1}^{+}&=1nM;z_{1}^{-} =1nM\\Z_{1}^{+}&=2nM;Z_{1}^{-} =1nM\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}}Waste;Z_{2}^{+}+Z_{2}^{-}\xrightarrow{{k}_{2}}Waste\end{aligned} $ $ \begin{aligned}z_{2}^{+}&=2nM;z_{2}^{-} =1nM\\Z_{2}^{+}&=1nM;Z_{2}^{-} =1nM\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}}Waste;x_{2}^{+}\xrightarrow{{k}_{5}}{x}^{+}+x_{2}^{+};X_{2}^{+}+X_{2}^{-}\xrightarrow{{k}_{2}}Waste\\& {V}^{-}\xrightarrow{{k}_{5}}{x}^{-}+x_{2}^{-};{v}^{+}+{v}^{-}\xrightarrow{{k}_{2}}Waste;{x}^{+}+{x}^{-}\xrightarrow{{k}_{2}}Waste\end{aligned} $ $ \begin{aligned}{k}_{6}&=2(nMs)^{-1}\\x_{2}^{+}&=1nM;x_{2}^{-} =1nM\\X_{2}^{+}&=2nM;X_{2}^{-} =1nM\\V_{}^{+}&=1nM;V_{}^{-} =1nM\\{v}^{+}&=3nM;{v}^{-} =2nM\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}}Waste\end{aligned} $ $ \begin{aligned}z_{2}^{+}&=3nM\\z_{2}^{-}&=1nM\\x_{}^{+}&=2nM\\x_{}^{-}&=1nM\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}}Waste\\& W(x)^{+}+{V}^{+}\xrightarrow{{k}_{5}}W(x)^{+}+{I}^{+}+{V}^{+}\end{aligned} $ $ \begin{aligned}W(x)^{+}&=2nM\\W(x)^{-}&=1nM\\{V}^{+}&=3nM\\{V}^{-}&=0.5nM\end{aligned} $ 
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表 3 一阶忆阻器滤波电路与一阶 RC 滤波电路的性能对比
$ {V}_{31}({V}_{in}) $ $ {k}_{7} $ $ {V}_{in}(time,peak) $ $ {V}_{M{{C}_{1}}out}(time,peak) $ $ {H}_{1}(s)({V}_{M{{C}_{1}}out}/{V}_{in}) $ $ {V}_{R{{C}_{1}}out}(time,peak) $ $ H_{1}^{\prime}(s)({V}_{R{{C}_{1}}out}/{V}_{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
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表 4 二阶忆阻器滤波电路与二阶 RC 滤波电路的性能对比
$ {V}_{41}({V}_{in}) $ $ {k}_{7} $ $ {V}_{in}(time,peak) $ $ {V}_{M{{C}_{2}}out}(time,peak) $ $ {H}_{1}(s)({V}_{M{{C}_{2}}out}/{V}_{in}) $ $ {V}_{R{{C}_{2}}out}(time,peak) $ $ H_{2}^{\prime}(s)({V}_{R{{C}_{2}}out}/{V}_{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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