A novel activation function based on DNA enzyme-free hybridization reaction and its implementation on nonlinear molecular learning systems.

With the advent of the post-Moore's Law era, the development of traditional silicon-based computers has reached its limit, and there is an urgent need to develop new computing technologies to meet the needs of science, technology, and daily life. Due to its super-strong parallel computing capability and outstanding data storage capacity, DNA computing has become an important branch and hot research topic of new computer technology. DNA enzyme-free hybridization reaction technology is widely used in DNA computing, showing excellent performance in computing power and information processing. Studies have shown that DNA molecules not only have the computing function of electronic devices, but also exhibit certain human brain-like functions. In the field of artificial intelligence, activation functions play an important role as they enable artificial intelligence systems to fit and predict non-linear and complex variable relationships. Due to the difficulty of implementing activation functions in DNA computing, DNA circuits cannot easily achieve all the functions of artificial intelligence. DNA circuits need to rely on electronic computers to complete the training and learning process. Based on the parallel computing characteristics of DNA computing and the kinetic features of DNA molecule displacement reactions, this paper proposes a new activation function. This activation function can not only be easily implemented by DNA enzyme-free hybridization reaction reactions, but also has good nesting properties in DNA circuits, and can be cascaded with other DNA reactions to form a complete DNA circuit. This paper not only provides the mathematical analysis of the proposed activation function, but also provides a detailed analysis of its kinetic features. The activation function is then nested into a nonlinear neural network for DNA computing. This system is capable of fitting and predicting a certain nonlinear function.

Research Progress in Construction and Application of Enzyme-Based DNA Logic Gates.

As a research hotspot in the field of information processing, DNA computing exhibits several important underlying characteristics-from parallel computing and low energy consumption to high-performance storage capabilities-thereby enabling its wide application in nanomachines, molecular encryption, biological detection, medical diagnosis, etc. Based on DNA computing, the most rapidly developed field focuses on DNA molecular logic-gates computing. In particular, the recent advances in enzyme-based DNA logic gates has emerged as ideal materials for constructing DNA logic gates. In this review, we explore protein enzymes that can manipulate DNA, especially, nicking enzymes and polymerases with high efficiency and specificity, which are widely used in constructing DNA logic gates, as well as ribozyme that can construct DNA logic gates following various mechanism with distinct biomaterials. Accordingly, the review highlights the characteristics and applications of various types of DNAzyme-based logic gates models, considering their future developments in information, biomedicine, chemistry, and computers.

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.

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.

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.

Solution of Equations Based on Analog DNA Strand Displacement Circuits.

Deoxyribonucleic acid (DNA) strand displacement can be used to build complex functional circuits due to its highly modular and programmable properties. While DNA strand displacement is most often used to solve logic problems, it can also be used to compute the roots of equations. In this paper, we present the design of novel architectures for catalysis, degradation, and annihilation in ideal formal reaction modules, and we translate these reaction modules to DNA networks. These ideal formal or DNA reaction modules are suitable for building analog circuits for solving tasks. The computing analog DNA circuits are assessed by solving a linear equation, a one-variable quadratic equation, and a set of two simultaneous linear equations. The results were evaluated by simulation.

Visual synchronization of two 3-variable Lotka-Volterra oscillators based on DNA strand displacement.

DNA strand displacement as a theoretic foundation is helpful in constructing reaction networks and DNA circuits. Research on chemical kinetics is significant to exploit the inherent potential property of biomolecular systems. In this study, we investigated two typical reactions and designed DNA strands with a fluorophore and dark quencher for reaction networks using a 3-variable Lotka-Volterra oscillator system as an example to show the convenience of and superiority for observation of dynamic trajectory using our design, and took advantage of the synchronization reaction module to synchronize two 3-variable Lotka-Volterra oscillators. The classical theory of chemical reaction networks can be used to represent biological processes for mathematical modeling. We used this method to simulate the nonlinear kinetics of a 3-variable Lotka-Volterra oscillator system.

Four-Analog Computation Based on DNA Strand Displacement.

DNA strand displacement plays an important role in biological computations. The inherent advantages of parallelism, high storability, and cascading have resulted in increased functional circuit realization of DNA strand displacement on the nanoscale. Herein, we propose an analog computation with minus based on DNA strand displacement. The addition, subtraction, multiplication, and division gates as elementary gates could realize analog computation with minus. The advantages of this proposal are the analog computation with negative value and division computation. In this article, we provide the designs and principles of these elementary gates and demonstrate gate performance by simulation. Furthermore, to show the cascade property of gates, we computed a polynomial as an example by these gates.