Solution of Equations Based on Analog DNA Strand Displacement Circuits

Projection Synchronization of Three-Dimensional Chaotic Systems With Active Control Based on DNA Strand Displacement

The emergence of biological computing based on DNA strand displacement has allowed chaotic systems to have more abundant dynamic behaviors. So far, the synchronization of chaotic systems based on DNA strand displacement has been mainly realized by coupling control and PID control. In this paper, the projection synchronization of chaotic systems based on DNA strand displacement is achieved using an active control method. First, some basic catalytic reaction modules and annihilation reaction modules are constructed based on the theoretical knowledge of DNA strand displacement. Second, the chaotic system and the controller are designed according to the above mentioned modules. On the basis of chaotic dynamics, the complex dynamic behavior of the system is verified by the lyapunov exponents spectrum and the bifurcation diagram. Third, the active controller based on DNA strand displacement is used to realize the projection synchronization between the drive system and the response system, where the projection can be adjusted within a certain range by changing the value of the scale factor. The result of projection synchronization of chaotic system is more flexible, which is realized by active controller. Our control method provides an efficient way to achieve synchronization of chaotic systems based on DNA strand displacement. The designed projection synchronization is verified to have excellent timeliness and robustness by the results Visual DSD simulation.

A nonlinear neural network based on an analog DNA toehold mediated strand displacement reaction circuit

The DNA toehold mediated strand displacement reaction is one of the semi-synthetic biology technologies for next-generation computers. In this article, we present a framework for a novel nonlinear neural network based on an engineered biochemical circuit, which is constructed by several reaction modules including catalysis, degradation and adjustment reaction modules. The proposed neural network possesses an architecture that is similar to that of an error back propagation neural network, and is built of an input layer, hidden layer and output layer. As a proof of concept, we utilize this nonlinear neural network based on an analog DNA toehold mediated strand displacement reaction circuit to learn the standard quadratic form function and analyze the robustness of the nonlinear neural network toward DNA strand concentration detection, DNA strand displacement reaction rate and noise. Unlike in error back propagation neural networks, the adaptive behavior of this DNA molecular neural network system endows it with supervised learning capability. This investigation will highlight the potential of analog DNA displacement reaction circuits for implementing artificial intelligence.

Synchronization of Hyper-Lorenz System Based on DNA Strand Displacement

Lorenz system is depicted by chemical reaction equations of an ideal formal chemical reaction network, and a series of reversible reactions are added into chemical reaction network in order to construct a cluster of hyper-Lorenz system. DNA as a universal substrate for chemical dynamics can approximate arbitrary dynamical characteristics of ideal formal chemical reaction network through auxiliary DNA strands and displacement reactions. Based on Lyapunov's stableness theory, a novel synchronization strategy is proposed. A 6-dimensional hyper-Lorenz system is taken as examples for simulation and shows that DNA strands displacement reactions can implement the synchronization of ideal formal chemical reaction networks. Numerical simulations indicate that synchronization based on DNA strand displacement is robust to the detection of DNA strand concentration, control of reaction rate, and noise.

A Novel Adaptive Linear Neuron Based on DNA Strand Displacement Reaction Network

Analog DNA strand displacement circuits can be used to build artificial neural network due to the continuity of dynamic behavior. In this study, DNA implementations of novel catalysis, novel degradation and adjustment reaction modules are designed and used to build an analog DNA strand displacement reaction network. A novel adaptive linear neuron (ADALINE) is constructed by the ordinary differential equations of an ideal formal chemical reaction network, which is built by reaction modules. When reaction network approaches equilibrium, the weights of the ADALINE are updated without learning algorithm. Simulation results indicate that, ADALINE based on the analog DNA strand displacement circuit has ability to implement the learning function of the ADALINE based on the ideal formal chemical reaction networks, and fit a class of linear function.

Chemical Reaction Networks’ Programming for Solving Equations

The computational ability of the chemical reaction networks (CRNs) using DNA as the substrate has been verified previously. To solve more complex computational problems and perform the computational steps as expected, the practical design of the basic modules of calculation and the steps in the reactions have become the basic requirements for biomolecular computing. This paper presents a method for solving nonlinear equations in the CRNs with DNA as the substrate. We used the basic calculation module of the CRNs with a gateless structure to design discrete and analog algorithms and realized the nonlinear equations that could not be solved in the previous work, such as exponential, logarithmic, and simple triangle equations. The solution of the equation uses the transformation method, Taylor expansion, and Newton iteration method, and the simulation verified this through examples. We used and improved the basic calculation module of the CRN++ programming language, optimized the error in the basic module, and analyzed the error’s variation over time.

An Operational DNA Strand Displacement Encryption Approach

DeoxyriboNucleic Acid (DNA) encryption is a new encryption method that appeared along with the research of DNA nanotechnology in recent years. Due to the complexity of biology in DNA nanotechnology, DNA encryption brings in an additional difficulty in deciphering and, thus, can enhance information security. As a new approach in DNA nanotechnology, DNA strand displacement has particular advantages such as being enzyme free and self-assembly. However, the existing research on DNA-strand-displacement-based encryption has mostly stayed at a theoretical or simulation stage. To this end, this paper proposes a new DNA-strand-displacement-based encryption framework. This encryption framework involves three main strategies. The first strategy was a tri-phase conversion from plaintext to DNA sequences according to a Huffman-coding-based transformation rule, which enhances the concealment of the information. The second strategy was the development of DNA strand displacement molecular modules, which produce the initial key for information encryption. The third strategy was a cyclic-shift-based operation to extend the initial key long enough, and thus increase the deciphering difficulty. The results of simulation and biological experiments demonstrated the feasibility of our scheme for encryption. The approach was further validated in terms of the key sensitivity, key space, and statistic characteristic. Our encryption framework provides a potential way to realize DNA-strand-displacement-based encryption via biological experiments and promotes the research on DNA-strand-displacement-based encryption.

Solution of Simultaneous Higher Order Equations Based on DNA Strand Displacement Circuit

Currently, DNA strand displacement is often used to build neural networks or solve logical problems. While there are few studies on the use of DNA strand displacement to solve the higher order equations. In this paper, the catalysis, degradation, annihilation and adjusted reaction modules are built through DNA strand displacement. The chemical reaction networks of the corresponding higher order equations and simultaneous equations are established through these modules, and these chemical reaction networks can be used to build analog circuits to solve binary primary simultaneous equations and binary quadratic simultaneous equations. Finally, through Visual DSD software verification, this design can realize the solution of binary primary simultaneous equations and binary quadratic simultaneous equations, which provides a reference for DNA computation in the future.

Solving 0-1 Integer Programming Problem Based on DNA Strand Displacement Reaction Network

Chemical reaction networks (CRNs) based on DNA strand displacement (DSD) can be used as an effective programming language for solving various mathematical problems. In this paper, we design three chemical reaction modules by using the DNA strand displacement reaction as the basic principle, with a weighted reaction module, sum reaction module, and threshold reaction module. These modules are used as basic elements to form chemical reaction networks that can be used to solve 0-1 integer programming problems. The problem can be solved through the three steps of weighting, sum, and threshold, and then the results of the operations can be expressed through a single-stranded DNA output with fluorescent molecules. Finally, we use biochemical experiments and Visual DSD simulation software to verify and evaluate the chemical reaction networks. The results have shown that the DSD-based chemical reaction networks constructed in this paper have good feasibility and stability.

Stability Based on PI Control of Three-Dimensional Chaotic Oscillatory System via DNA Chemical Reaction Networks

The classical proportional integral (PI) controller of SISO linear system is realized by DNA chemical reaction networks (CRNs) in the previous work. Up to now, few works have been done to realize PI controller of chaotic system through DNA CRNs. In this paper, a three-dimensional chaotic oscillatory system and a PI controller of three-dimensional chaotic oscillatory system are proposed by DNA CRNs. The CRNs of chaotic oscillatory system are made up of catalysis modules, degradation module and annihilation module then chemical reaction equations can be compiled into three-dimensional chaotic oscillatory system by the law of mass action to generate chaotic oscillatory signals. The CRNs of PI controller are designed by an integral module, a proportion module and an addition module, which can be compiled into PI controller for stabilizing chaotic oscillatory signals. The simulations of Matlab and Visual DSD are given to show our design achieving the PI control of a three-variable chaotic oscillatory system.

Encryption Algorithm Based on DNA Strand Displacement and DNA Sequence Operation

DNA strand displacement is introduced in this study and used to construct an analog DNA strand displacement chaotic system based on six reaction modules in nanoscale size. The DNA strand displacement circuit is employed in encryption as a chaotic generator to produce chaotic sequences. In the encryption algorithm, we convert chaotic sequences to binary ones by comparing the concentration of signal DNA strand. Simulation results show that the encryption scheme is sensitive to the keys, and key space is large enough to resist the brute-force attacks, furthermore algorithm has a high capacity to resist statistic attack. Based on robustness analysis, our proposed encryption scheme is robust to the DNA strand displacement reaction rate control, noise and concentration detection to a certain extent.

Compilation of a Coupled Hyper-Chaotic Lorenz System Based on DNA Strand Displacement Reaction Network

Ideal formal chemical reaction network is an effective programming language to design complex system dynamical behavior. In this article, a coupled hyper-chaotic Lorenz system can be described by the ordinary differential equations of an ideal formal reaction network, which is constructed by catalysis, annihilation and adjust reaction modules, where the variables of system are represented by the difference in concentration of two chemical species. The ideal formal reaction network can be implemented by DNA strand displacement reaction network. Through Lyapunov exponent, we have analyzed hyper-chaotic dynamical behavior of coupled Lorenz system. In discussion and analysis, we have analyzed effect of noise, reaction rate control error and concentration detection error to DNA strand displacement reaction network.

Three-Variable Chaotic Oscillatory System Based on DNA Strand Displacement and Its Coupling Combination Synchronization

The synchronization control of two chaotic oscillatory systems is designed based on DNA strand displacement in the present work. Thus, combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement. Firstly, five chemical reaction modules of double, displacement, adjustment, catalysis and degradation are designed. Based on these five modules, a 3-variable chaotic oscillatory system is designed. Secondly, based on the design principle of coupling terms and theory of stability, synchronization modules and coupling terms are added to three chaotic oscillatory systems to design combination synchronization of three 3-variable chaotic oscillatory systems based on DNA strand displacement. Modules and systems are implemented and tested using visual DSD and Matlab, and the simulation results are presented to demonstrate the effectiveness and correctness of the chemical reaction modules and systems. The combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement, which may be extended to the reaction networks of DNA strand displacement and to the combination synchronization of multivariable chaotic oscillatory systems based on DNA strand displacement.

DNA circuits driven by conformational changes in DNAzyme recognition arms

DNA computing plays an important role in nanotechnology due to the unique programmability and parallelism of DNA molecules. As an important tool to realize DNA computation, various logic computing devices have great application potential. The application of DNAzyme makes the achievements in the field of logical computing more diverse. In order to improve the efficiency of the logical units run by DNAzyme, we proposed a strategy to regulate the DNA circuit by the conformational change of the E6-type DNAzyme recognition arms driven by Mg2+. This strategy changes the single mode of DNAzyme signal transmission, extends the functions of E6-type DNAzyme, and saves the time of signal transmission in the molecular scale. To verify the feasibility of this strategy, first, we constructed DNA logic gates (YES, OR, and AND). Second, we cascade different logic gates (YES-YES, YES-AND) to prove the scalability. Finally, a self-catalytic DNA circuit is established. Through the experimental results, we verified that this DNAzyme regulation strategy relatively reduces the cost of logic circuits to some extent and significantly increases the reaction rate, and can also be used to indicate the range of Mg2+ concentrations. This research strategy provides new thinking for logical computing and explores new directions for detection and biosensors.