Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers

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.

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.

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.

Design and Realization of Triple dsDNA Nanocomputing Circuits in Microfluidic Chips

DNA logic gates, nanocomputing circuits, have already implemented basic computations and shown great signal potential for nano logic material application. However, the reaction temperature and computing speed still limit its development. Performing complicated computations requires a more stable component and a better computing platform. We proposed a more stable design of logic gates based on a triple, double-stranded, DNA (T-dsDNA) structure. We demonstrated a half adder and a full adder using these DNA nanocircuits and performed the computations in a microfluidic chip device at room temperature. When the solutions were mixed in the device, we obtained the expected results in real time, which suggested that the T-dsDNA combined microfluidic chip provides a concise strategy for large DNA nanocircuits.

Design of a Single-Channel Chaotic Secure Communication System Implemented by DNA Strand Displacement

DNA strand displacement (DSD) is regarded as a foundation for the construction of biological computing systems because of the predictability of DNA molecular behaviors. Some complex system dynamics can be approximated by cascading DSD reaction modules with different functions. In this paper, four DSD reaction modules are used to realize chaotic secure communication based on drive-response synchronization of four-dimensional chaotic systems. The system adopts the communication technology of chaos masking and uses a single-channel synchronization scheme to achieve high accuracy. The simulation results demonstrate that encryption and decryption of the signal are achieved by the design. Moreover, the system is robust to noise signals and interference during the DNA reactions. This work provides a method for the application of DNA molecular computation in the communication field.

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.

Programmable DNA-Based Boolean Logic Microfluidic Processing Unit

As molecular computing materials, information-encoded deoxyribonucleic acid (DNA) strands provide a logical computing process by cascaded and parallel chain reactions. However, the reactions in DNA-based combinational logic computing are mostly achieved through a manual process by adding desired DNA molecules in a single microtube or a substrate. For DNA-based Boolean logic, using microfluidic chips can afford automated operation, programmable control, and seamless combinational logic operation, similar to electronic microprocessors. In this paper, we present a programmable DNA-based microfluidic processing unit (MPU) chip that can be controlled via a personal computer for performing DNA calculations. To fabricate this DNA-based MPU, polydimethylsiloxane was cast using double-sided molding techniques for alignment between the microfluidics and valve switch. For a uniform surface, molds fabricated using a three-dimensional printer were spin-coated by a polymer. For programming control, the valve switch arms were operated by servo motors. In the MPU controlled via a personal computer or smartphone application, the molecules with two input DNAs and a logic template DNA were reacted for the basic AND and OR operations. Furthermore, the DNA molecules reacted in a cascading manner for combinational AND and OR operations. Finally, we demonstrated a 2-to-1 multiplexer and the XOR operation with a three-step cascade reaction using the simple DNA-based MPU, which can perform Boolean logic operations (AND, OR, and NOT). Through logic combination, this DNA-based Boolean logic MPU, which can be operated using programming language, is expected to facilitate the development of complex functional circuits such as arithmetic logical units and neuromorphic circuits.

DNA strand displacement reactions to accomplish a two-degree-of-freedom PID controller and its application in subtraction gate

Synthesis control circuits can be used to effectively control biochemical molecule processes. In the controller design based on chemical reaction networks (CRNs), generally only the tracking set-point is considered. However, the influence of disturbances, which are frequently encountered in biochemical systems, is often neglected, thus weakening the control effect of the system. In this article, tracking set-point input and suppressing disturbance input are considered in the control effect. Firstly, CRNs are adopted to construct a two-degree-of-freedom PID controller by combining a one-degree-of-freedom PID controller with a feedforward controller for the first time. Then, CRN expressions of the two input functions (step function and ramp function) used as input signals are defined. Furthermore, the two-degree-of-freedom PID controller is founded by DNA strand displacement (DSD) reaction networks, because DNA is an ideal engineering material to constitute molecular devices based on CRNs. The overshoot of the two-degree-of-freedom PID control system is significantly reduced compared to the one-degree-of-freedom PID control system. Finally, a leak reaction is treated as an extraneous disturbance input to a subtraction gate. The influence of external disturbance is solved by the two-degree-of-freedom PID controller. It is worth noting that the two-degree-of-freedom subtraction gate control system better restrains the impact of a disturbance input (leak reaction).

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.

Information processing based on DNA toehold-mediated strand displacement (TMSD) reaction

SemiSynBio is an emerging topic toward the construction of platforms for next-generation information processing. Recent research has indicated its promising prospect toward information processing including algorithm design and pattern manipulation with the DNA TMSD reaction, which is one of the cores of the SemiSynBio technology route. The DNA TMSD reaction is the process in which an invader strand displaces the incumbent strand from the gate strand through initiation at the exposed toehold domain. Also, the DNA TMSD reaction generally involves three processes: toehold association, branch migration and strand disassociation. Herein, we review the recent progress on information processing with the DNA TMSD reaction. We highlight the diverse developments on information processing with the logic circuit, analog circuit, combinational circuit and information relay with the DNA origami structure. Additionally, we explore the current challenges and various trends toward the design and application of the DNA TMSD reaction in future information processing.

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.

DNA Microsystems for Biodiagnosis

Researchers are continuously making progress towards diagnosis and treatment of numerous diseases. However, there are still major issues that are presenting many challenges for current medical diagnosis. On the other hand, DNA nanotechnology has evolved significantly over the last three decades and is highly interdisciplinary. With many potential technologies derived from the field, it is natural to begin exploring and incorporating its knowledge to develop DNA microsystems for biodiagnosis in order to help address current obstacles, such as disease detection and drug resistance. Here, current challenges in disease detection are presented along with standard methods for diagnosis. Then, a brief overview of DNA nanotechnology is introduced along with its main attractive features for constructing biodiagnostic microsystems. Lastly, suggested DNA-based microsystems are discussed through proof-of-concept demonstrations with improvement strategies for standard diagnostic approaches.

Adjusting Linking Strands to Form Size-Controllable DNA Origami Rings

DNA origami is a powerful tool in nanotechnology that can be used to construct arbitrary structures for several nanoengineering applications. Generally, the more complex and sophisticated the construction, the greater is the number of origamis and connection strands that will be needed. Therefore, developing an effective and low-cost method for multiform DNA architecture is important in nanoengineering. Here, we adopted an oblique linking strategy to connect cross-shaped DNA origami with a controlled curing angle. The size of the DNA rings ranged from four blocks of approximately 200 nm to eleven blocks of c.a. 600 nm. We observed that the minimum size of the DNA ring structure was limited by the width of a single block. The largest rings were negatively affected by thermodynamic randomness, and thus, DNA rings consisting of more than eleven blocks were not observed. This strategy facilitates the generation of various DNA origami rings, whose size can be controlled by adjusting the length of the connection strands.

Programming DNA-Based Biomolecular Reaction Networks on Cancer Cell Membranes

DNA is a highly programmable biomolecule and has been used to construct biological circuits for different purposes. An important development of DNA circuits is to process the information on receptors on cell membranes. In this Communication, we introduce an architecture to program localized DNA-based biomolecular reaction networks on cancer cell membranes. Based on our architecture, various types of reaction networks have been experimentally demonstrated, from simple linear cascades to reaction networks of complex structures. These localized DNA-based reaction networks can be used for medical applications such as cancer cell detection. Compared to prior work on DNA circuits for evaluating cell membrane receptors, the DNA circuits made by our architecture have several major advantages including simpler design, lower leak, lower cost, and higher signal-to-background ratio.

Nonlinear Regulation of Enzyme-Free DNA Circuitry with Ultrasensitive Switches

DNA is used to construct synthetic chemical reaction networks (CRNs), such as inorganic oscillators and gene regulatory networks. Nonlinear regulation with a simpler molecular mechanism is particularly important in large-scale CRNs with complex dynamics, such as bistability, adaptation, and oscillation of cellular functions. Here we introduce a new approach based on ultrasensitive switches as modular regulatory elements to nonlinearly regulate DNA-based CRNs. The nonlinear behavior of the systems can be finely tuned by programmable regulation of the linker length and the ligand binding sites, of which the Hill coefficients (n_H) are in the range of 1.00-2.32. By integrating two different strand displacement reactions with low-order nonlinearities (n_H ≈ 1.44 and 1.54), we could construct CRNs exhibiting high-order nonlinearities with Hill coefficients of up to ∼2.70. In addition, this could provide an efficient approach for designing CRNs at will with complex chemical dynamics by incorporating our design with previously developed enzyme-free DNA circuits.

Temporal Pattern Recognition through Analog Molecular Computation

Living cells communicate information about physiological conditions by producing signaling molecules in a specific timed manner. Different conditions can result in the same total amount of a signaling molecule, differing only in the pattern of the molecular concentration over time. Such temporally coded information can be completely invisible to even state-of-the-art molecular sensors with high chemical specificity that respond only to the total amount of the signaling molecule. Here, we demonstrate design principles for circuits with temporal specificity, that is, molecular circuits that respond to specific temporal patterns in a molecular concentration. We consider pulsatile patterns in a molecular concentration characterized by three fundamental temporal features: time period, duty fraction, and number of pulses. We develop circuits that respond to each one of these features while being insensitive to the others. We demonstrate our design principles using general chemical reaction networks and with explicit simulations of DNA strand displacement reactions. In this way, our work develops building blocks for temporal pattern recognition through molecular computation.

Enzymatic Weight Update Algorithm for DNA-Based Molecular Learning

Recent research in DNA nanotechnology has demonstrated that biological substrates can be used for computing at a molecular level. However, in vitro demonstrations of DNA computations use preprogrammed, rule-based methods which lack the adaptability that may be essential in developing molecular systems that function in dynamic environments. Here, we introduce an in vitro molecular algorithm that ‘learns’ molecular models from training data, opening the possibility of ‘machine learning’ in wet molecular systems. Our algorithm enables enzymatic weight update by targeting internal loop structures in DNA and ensemble learning, based on the hypernetwork model. This novel approach allows massively parallel processing of DNA with enzymes for specific structural selection for learning in an iterative manner. We also introduce an intuitive method of DNA data construction to dramatically reduce the number of unique DNA sequences needed to cover the large search space of feature sets. By combining molecular computing and machine learning the proposed algorithm makes a step closer to developing molecular computing technologies for future access to more intelligent molecular systems.

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.

Improving the Performance of DNA Strand Displacement Circuits by Shadow Cancellation

DNA strand displacement circuits are powerful tools that can be rationally engineered to implement molecular computing tasks because they are programmable, cheap, robust, and predictable. A key feature of these circuits is the use of catalytic gates to amplify signal. Catalytic gates tend to leak; that is, they generate output signal even in the absence of intended input. Leaks are harmful to the performance and correct operation of DNA strand displacement circuits. Here, we present "shadow cancellation", a general-purpose technique to mitigate leak in catalytic DNA strand displacement circuits. Shadow cancellation involves constructing a parallel shadow circuit that mimics the primary circuit and has the same leak characteristics. It is situated in the same test tube as the primary circuit and produces "anti-background" DNA strands that cancel "background" DNA strands produced by leak. We demonstrate the feasibility and strength of the shadow leak cancellation approach through a challenging test case, a cross-catalytic feedback DNA amplifier circuit that leaks prodigiously. Shadow cancellation dramatically reduced the leak of this circuit and improved the signal-to-background difference by several fold. Unlike existing techniques, it makes no modifications to the underlying amplifier circuit and is agnostic to its leak mechanism. Shadow cancellation also showed good robustness to concentration errors in multiple scenarios. This work introduces a direction in leak reduction techniques for DNA strand displacement amplifier circuits and can potentially be extended to other molecular amplifiers.

DNA-Based Analog Computing

The field of DNA computation makes use of DNA reactions to do molecular-scale computation. Most works in DNA computation execute digital computations such as evaluation of Boolean circuits. This chapter surveys novel DNA computation methods that execute analog computations, where the inputs and outputs are real values specified by the concentrations of particular DNA strands.