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

Implementation of an Ultrasensitive Biomolecular Controller for Enzymatic Reaction Processes With Delay Using DNA Strand Displacement

In this article, a set of abstract chemical reactions has been employed to construct a novel nonlinear biomolecular controller, i.e, the Brink controller (BC) with direct positive autoregulation (DPAR) (namely BC-DPAR controller). In comparison to dual rail representation-based controllers such as the quasi sliding mode (QSM) controller, the BC-DPAR controller directly reduces the number of CRNs required for realizing an ultrasensitive input-output response because it does not involve the subtraction module, reducing the complexity of DNA implementations. Then, the action mechanism and steady-state condition constraints of two nonlinear controllers, BC-DPAR controller and QSM controller, are investigated further. Considering the mapping relationship between CRNs and DNA implementation, a CRNs-based enzymatic reaction process with delay is constructed, and a DNA strand displacement (DSD) scheme representing time delay is proposed. The BC-DPAR controller, when compared to the QSM controller, can reduce the number of abstract chemical reactions and DSD reactions required by 33.3% and 31.8%, respectively. Finally, an enzymatic reaction scheme with BC-DPAR controller is designed using DSD reactions. According to the findings, the enzymatic reaction process's output substance can approach the target level at a quasi-steady state in both delay-free and non-zero delay conditions, but the target level can only be achieved during a finite-time period, mainly due to the fuel stand depletion.

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.

Exponential Function Computation Based on DNA Strand Displacement Circuits

Due to its high programmability and storage, DNA circuits have been widely used in biological computing. In this paper, the addition, subtraction, multiplication, division, n-order and 1/n-order gates are built through DNA strand displacement reactions. The chemical reaction networks of the exponential function are established by using the six DNA analog computation gates. The integrated DNA strand displacement circuits are built through the chemical reaction networks. The exponential function polynomials can be computed through the integrated DNA strand displacement circuits. Finally, through visual DSD software verification, this design can realise the computation of exponential function polynomials, which provides a reference for solving exponential function equations and neural network computations in the future.

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.

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.