DNA solution of hard computational problems

Chemical unclonable functions based on operable random DNA pools

Physical unclonable functions (PUFs) based on unique tokens generated by random manufacturing processes have been proposed as an alternative to mathematical one-way algorithms. However, these tokens are not distributable, which is a disadvantage for decentralized applications. Finding unclonable, yet distributable functions would help bridge this gap and expand the applications of object-bound cryptography. Here we show that large random DNA pools with a segmented structure of alternating constant and randomly generated portions are able to calculate distinct outputs from millions of inputs in a specific and reproducible manner, in analogy to physical unclonable functions. Our experimental data with pools comprising up to >1010 unique sequences and encompassing >750 comparisons of resulting outputs demonstrate that the proposed chemical unclonable function (CUF) system is robust, distributable, and scalable. Based on this proof of concept, CUF-based anti-counterfeiting systems, non-fungible objects and decentralized multi-user authentication are conceivable.

Lipid vesicle-based molecular robots

A molecular robot, which is a system comprised of one or more molecular machines and computers, can execute sophisticated tasks in many fields that span from nanomedicine to green nanotechnology. The core parts of molecular robots are fairly consistent from system to system and always include (i) a body to encapsulate molecular machines, (ii) sensors to capture signals, (iii) computers to make decisions, and (iv) actuators to perform tasks. This review aims to provide an overview of approaches and considerations to develop molecular robots. We first introduce the basic technologies required for constructing the core parts of molecular robots, describe the recent progress towards achieving higher functionality, and subsequently discuss the current challenges and outlook. We also highlight the applications of molecular robots in sensing biomarkers, signal communications with living cells, and conversion of energy. Although molecular robots are still in their infancy, they will unquestionably initiate massive change in biomedical and environmental technology in the not too distant future.

Molecular circuit for exponentiation based on the domain coding strategy

DNA strand displacement (DSD) is an efficient technology for constructing molecular circuits. However, system computing speed and the scale of logical gate circuits remain a huge challenge. In this paper, a new method of coding DNA domains is proposed to carry out logic computation. The structure of DNA strands is designed regularly, and the rules of domain coding are described. Based on this, multiple-input and one-output logic computing modules are built, which are the basic components forming digital circuits. If the module has n inputs, it can implement 2n logic functions, which reduces the difficulty of designing and simplifies the structure of molecular logic circuits. In order to verify the superiority of this method for developing large-scale complex circuits, the square root and exponentiation molecular circuits are built. Under the same experimental conditions, compared with the dual-track circuits, the simulation results show that the molecular circuits designed based on the domain coding strategy have faster response time, simpler circuit structure, and better parallelism and scalability. The method of forming digital circuits based on domain coding provides a more effective way to realize intricate molecular control systems and promotes the development of DNA computing.

Programmable Biomolecule-Mediated Processors

Programmable biomolecule-mediated computing is a new computing paradigm as compared to contemporary electronic computing. It employs nucleic acids and analogous biomolecular structures as information-storing and -processing substrates to tackle computational problems. It is of great significance to investigate the various issues of programmable biomolecule-mediated processors that are capable of automatically processing, storing, and displaying information. This Perspective provides several conceptual designs of programmable biomolecule-mediated processors and provides some insights into potential future research directions for programmable biomolecule-mediated processors.

Constructing Double Cyclic Codes over F2+uF2 for DNA Codes

In this article, we investigate the algebraic structure of double cyclic codes of length ( α , β ) over F 2 + u F 2 with u 2 = 0 and construct DNA codes from these codes. The theory of constructing double cyclic codes suitable for DNA codes is studied. We provide the necessary and sufficient conditions for the double cyclic codes to be reversible and reversible-complement codes. As an illustration, we present some of the DNA codes generated from our results.

Facile Strategy to Output Fluorescein from Nucleic Acid Interactions

Biomolecular operations, which involve the conversion of molecular signals or interactions into specific functional outputs, are fundamental to the field of biology and serve as the important foundation for the design of diagnostic and therapeutic systems. To maximize their functionalities and broaden their applicability, it is crucial to develop novel outputs and facile chemical transformation methods. With this aim, in this study, we present a straightforward method for converting nucleic acid signals into fluorescein outputs that exhibit a wide range of functionalities. This operation is designed through a DNA-templated reaction based on riboflavin-photocatalyzed oxidation of dihydrofluorescein, which is readily prepared by simple NaBH4 reduction of the fluorescein with no complicated chemical caging steps. The templated photooxidation exhibits high efficiency (kapp = 2.7 × 10-3/s), generating a clear fluorescein output signal distinguishable from a low background, originating from the high stability of the synthesized dihydrofluorescein. This facile and efficient operation allows the nucleic acid-initiated activation of various fluorescein functions, such as fluorescence and artificial oxidase activity, which are applied in the design of novel bioanalytical systems, including fluorescent and colorimetric DNA sensors. The operation presented herein would expand the scope of biomolecular circuit systems for diagnostic and therapeutic applications.

A molecular assessment of the practical potential of DNA-based computation

The immense information density of DNA and its potential for massively parallelized computations, paired with rapidly expanding data production and storage needs, have fueled a renewed interest in DNA-based computation. Since the construction of the first DNA computing systems in the 1990s, the field has grown to encompass a diverse array of configurations. Simple enzymatic and hybridization reactions to solve small combinatorial problems transitioned to synthetic circuits mimicking gene regulatory networks and DNA-only logic circuits based on strand displacement cascades. These have formed the foundations of neural networks and diagnostic tools that aim to bring molecular computation to practical scales and applications. Considering these great leaps in system complexity as well as in the tools and technologies enabling them, a reassessment of the potential of such DNA computing systems is warranted.

DNA Arithmetic With Error Correction

DNA design approaches are expected to play an important role in the future design of non-silicon-based computers. However, one of the main challenges for its mass fabrication is the considerable error rate. This paper presents a DNA computing system based on the Redundant Residue Number system (RRNS) that has elegant fault-tolerance features. The proposed method is the first to introduce the sticker model into DNA Arithmetic based on RRNS. The ability of error detection and correction are advantages of the proposed computing system. Moreover, the proposed arithmetic method can operate on large DNA-represented numbers, since RNS split them into smaller numbers. The implementation of arithmetic operations on these small numbers decreases the probability of failure in DNA operations.

Emerging Approaches to DNA Data Storage: Challenges and Prospects

With the total amount of worldwide data skyrocketing, the global data storage demand is predicted to grow to 1.75 × 10¹⁴ GB by 2025. Traditional storage methods have difficulties keeping pace given that current storage media have a maximum density of 10³ GB/mm³. As such, data production will far exceed the capacity of currently available storage methods. The costs of maintaining and transferring data, as well as the limited lifespans and significant data losses associated with current technologies also demand advanced solutions for information storage. Nature offers a powerful alternative through the storage of information that defines living organisms in unique orders of four bases (A, T, C, G) located in molecules called deoxyribonucleic acid (DNA). DNA molecules as information carriers have many advantages over traditional storage media. Their high storage density, potentially low maintenance cost, ease of synthesis, and chemical modification make them an ideal alternative for information storage. To this end, rapid progress has been made over the past decade by exploiting user-defined DNA materials to encode information. In this review, we discuss the most recent advances of DNA-based data storage with a major focus on the challenges that remain in this promising field, including the current intrinsic low speed in data writing and reading and the high cost per byte stored. Alternatively, data storage relying on DNA nanostructures (as opposed to DNA sequence) as well as on other combinations of nanomaterials and biomolecules are proposed with promising technological and economic advantages. In summarizing the advances that have been made and underlining the challenges that remain, we provide a roadmap for the ongoing research in this rapidly growing field, which will enable the development of technological solutions to the global demand for superior storage methodologies.

A Parallel DNA Algorithm for Solving the Quota Traveling Salesman Problem Based on Biocomputing Model

The quota traveling salesman problem (QTSP) is a variant of the traveling salesman problem (TSP), which is a classical optimization problem. In the QTSP, the salesman visits some of the n cities to meet a given sales quota Q while having minimized travel costs. In this paper, we develop a DNA algorithm based on Adleman-Lipton model to solve the quota traveling salesman problem. Its time complexity is O(n²+Q), which is a significant improvement over previous algorithms with exponential complexity. A coding scheme of element information is pointed out, and a reasonable biological algorithm is raised by using limited conditions, whose feasibility is verified by simulation experiments. The innovation of this study is to propose a polynomial time complexity algorithm to solve the QTSP. This advantage will become more obvious as the problem scale increases compared with the algorithm of exponential computational complexity. The proposed DNA algorithm also has the significant advantages of having a large storage capacity and consuming less energy during the operation. With the maturity of DNA manipulation technology, DNA computing, as one of the parallel biological computing methods, has the potential to solve more complex NP-hard problems.

Visual Construction of Logical AND and NAND Gates

DNA logic gates are an important branch of DNA computing and have a wide range of applications in DNA computing. In this study, logic circuits of AND gate and NAND gate are built on origami substrate. The realization of AND gate uses polymerase strand displacement (PSD) reaction and hybridization chain reaction (HCR). If there is a fluorescent band “1” displayed, the result is true. The realization of the NAND gate requires a cyclic reaction. If there is a fluorescent band “A” or “T” displayed, the result is true; if no fluorescent band is displayed, the result is false.

Logic operations with active topological defects

Logic operations performed by semiconductor-based transistors are the basis of modern computing. There is considerable interest in creating autonomous materials systems endowed with the capability to make decisions. In this work, we introduce the concept of using topological defects in active matter to perform logic operations. When an extensile active stress in a nematic liquid crystal is turned on, +1/2 defects can self-propel, in analogy to electron transport under a voltage gradient. By relying on hydrodynamic simulations of active nematics, we demonstrate that patterns of activity, when combined with surfaces imparting certain orientations, can be used to control the formation and transport of +1/2 defects. We further show that asymmetric high- and low-activity patterns can be used to create effective defect gates, tunnels, and amplifiers. The proposed active systems offer the potential to perform computations and transmit information in active soft materials, including actin-, tubulin-, and cell-based systems.

pH Oscillating System for Molecular Computation as a Chemical Turing Machine

It has previously been demonstrated that native chemical Turing machines can be constructed by exploiting the nonlinear dynamics of the homogeneous oscillating Belousov-Zhabotinsky reaction. These Turing machines can perform word recognition of a Chomsky type 1 context sensitive language (CSL), demonstrating their high computing power. Here, we report on a chemical Turing machine that has been developed using the H₂O₂-H₂SO₄-SO₃ ^2--CO₃ ^2- pH oscillating system. pH oscillators are different to bromate oscillators in two key ways: the proton is the autocatalytic agent, and at least one of the reductants is always fully consumed in each turnover-meaning the system has to be operated as a flow reactor. Through careful design, we establish a system that can also perform Chomsky type 1 CSL word recognition and demonstrate its power through the testing of a series of in-language and out-of-language words.

A Review of DNA Data Storage Technologies Based on Biomolecules

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In the information age, data storage technology has become the key to improving computer systems. Since traditional storage technologies cannot meet the demand for massive storage, new DNA storage technology based on biomolecules attracts much attention. DNA storage refers to the technology that uses artificially synthesized deoxynucleotide chains to store and read all information, such as documents, pictures, and audio. First, data are encoded into binary number strings. Then, the four types of base, A(Adenine), T(Thymine), C(Cytosine), and G(Guanine), are used to encode the corresponding binary numbers so that the data can be used to construct the target DNA molecules in the form of deoxynucleotide chains. Subsequently, the corresponding DNA molecules are artificially synthesized, enabling the data to be stored within them. Compared with traditional storage systems, DNA storage has major advantages, such as high storage density, long duration, as well as low hardware cost, high access parallelism, and strong scalability, which satisfies the demands for big data storage. This manuscript first reviews the origin and development of DNA storage technology, then the storage principles, contents, and methods are introduced. Finally, the development of DNA storage technology is analyzed. From the initial research to the cutting edge of this field and beyond, the advantages, disadvantages, and practical applications of DNA storage technology require continuous exploration.

An RNA-Based Theory of Natural Universal Computation

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

A New Conservative Hyperchaotic System-Based Image Symmetric Encryption Scheme with DNA Coding

In the current paper, a new conservative hyperchaotic system is proposed. We make a quantitative analysis of the complexity of the conservative hyperchaotic system from several different aspects, such as phase diagrams, bifurcation diagrams, Lyapunov exponents, and Kaplan–Yorke dimension. The complexity of chaotic time series is tested with various measurement tools, such as the scale index, the multiscale sample entropy and approximate entropy, TESTU01, and NIST test. In addition, a novel hyperchao-based image encryption scheme with dynamic DNA coding is proposed. The encryption algorithm consists of line-by-line scrambling and diffusion of DNA encoding characters. The dynamic DNA coding mechanism is introduced by using the chaotic sequence. The generation of the intermediate secret keys is related to the sum of the image DNA code, and the ciphertext feedback mechanism of the DNA encoding image is introduced in the diffusion procedure. Simulation experiments and various security analyses show that this algorithm has a good effect on encryption, high time efficiency, and can effectively resist brute force attacks, statistical attacks, chosen-plaintext attacks, and differential attacks.

DNA Matrix Operation Based on the Mechanism of the DNAzyme Binding to Auxiliary Strands to Cleave the Substrate

Numerical computation is a focus of DNA computing, and matrix operations are among the most basic and frequently used operations in numerical computation. As an important computing tool, matrix operations are often used to deal with intensive computing tasks. During calculation, the speed and accuracy of matrix operations directly affect the performance of the entire computing system. Therefore, it is important to find a way to perform matrix calculations that can ensure the speed of calculations and improve the accuracy. This paper proposes a DNA matrix operation method based on the mechanism of the DNAzyme binding to auxiliary strands to cleave the substrate. In this mechanism, the DNAzyme binding substrate requires the connection of two auxiliary strands. Without any of the two auxiliary strands, the DNAzyme does not cleave the substrate. Based on this mechanism, the multiplication operation of two matrices is realized; the two types of auxiliary strands are used as elements of the two matrices, to participate in the operation, and then are combined with the DNAzyme to cut the substrate and output the result of the matrix operation. This research provides a new method of matrix operations and provides ideas for more complex computing systems.

Concepts and Application of DNA Origami and DNA Self-Assembly: A Systematic Review

With the arrival of the post-Moore Era, the development of traditional silicon-based computers has reached the limit, and it is urgent to develop new computing technology to meet the needs of science and life. DNA computing has become an essential branch and research hotspot of new computer technology because of its powerful parallel computing capability and excellent data storage capability. Due to good biocompatibility and programmability properties, DNA molecules have been widely used to construct novel self-assembled structures. In this review, DNA origami is briefly introduced firstly. Then, the applications of DNA self-assembly in material physics, biogenetics, medicine, and other fields are described in detail, which will aid the development of DNA computational model 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.

Solving the Family Traveling Salesperson Problem in the Adleman-Lipton model based on DNA computing

The Family Traveling Salesperson Problem (FTSP) is a variant of the Traveling Salesperson Problem (TSP), in which all vertices are divided into several different families, and the goal of the problem is to find a loop that concatenates a specified number of vertices with minimal loop overhead. As a Non-deterministic Polynomial Complete (NP-complete) problem, it is difficult to deal with it by the traditional computing. On the contrary, as a computer with strong parallel ability, the DNA computer has incomparable advantages over digital computers when dealing with NP problems. Based on this, a DNA algorithm is proposed to deal with FTSP based on the Adleman-Lipton model. In the algorithm, the solution of the problem can be obtained by executing several basic biological manipulations on DNA molecules with O(N2) computing complexity (N is the number of vertices in the problem without the origin). Through the simulation experiments on some benchmark instances, the results show that the parallel DNA algorithm has better performance than traditional computing. The effectiveness of the algorithm is verified by deducing the algorithm process in detail. Furthermore, the algorithm further proves that DNA computing, as one of the parallel computing methods, has the potential to solve more complex big data problems.

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.

AI in Measurement Science

Measurement of biological systems containing biomolecules and bioparticles is a key task in the fields of analytical chemistry, biology, and medicine. Driven by the complex nature of biological systems and unprecedented amounts of measurement data, artificial intelligence (AI) in measurement science has rapidly advanced from the use of silicon-based machine learning (ML) for data mining to the development of molecular computing with improved sensitivity and accuracy. This review presents an overview of fundamental ML methodologies and discusses their applications in disease diagnostics, biomarker discovery, and imaging analysis. We next provide the working principles of molecular computing using logic gates and arithmetical devices, which can be employed for in situ detection, computation, and signal transduction for biological systems. This review concludes by summarizing the strengths and limitations of AI-involved biological measurement in fundamental and applied research.

Synthesis Strategy of Reversible Circuits on DNA Computers

DNA computers and quantum computers are gaining attention as alternatives to classical digital computers. DNA is a biological material that can be reprogrammed to perform computing functions. Quantum computing performs reversible computations by nature based on the laws of quantum mechanics. In this paper, DNA computing and reversible computing are combined to propose novel theoretical methods to implement reversible gates and circuits in DNA computers based on strand displacement reactions, since the advantages of reversible logic gates can be exploited to improve the capabilities and functionalities of DNA computers. This paper also proposes a novel universal reversible gate library (URGL) for synthesizing n-bit reversible circuits using DNA to reduce the average length and cost of the constructed circuits when compared with previous methods. Each n-bit URGL contains building blocks to generate all possible permutations of a symmetric group of degree n. Our proposed group (URGL) in the paper is a permutation group. The proposed implementation methods will improve the efficiency of DNA computer computations as the results of DNA implementations are better in terms of quantum cost, DNA cost, and circuit length.

Quantum Speedup and Mathematical Solutions of Implementing Bio-Molecular Solutions for the Independent Set Problem on IBM Quantum Computers

In this paper, we propose a bio-molecular algorithm with O( n² + m ) biological operations, O( 2ⁿ ) DNA strands, O( n ) tubes and the longest DNA strand, O( n ), for solving the independent-set problem for any graph G with m edges and n vertices. Next, we show that a new kind of the straightforward Boolean circuit yielded from the bio-molecular solutions with m NAND gates, ( m +n × ( n + 1 )) AND gates and (( n × ( n + 1 ))/2) NOT gates can find the maximal independent-set(s) to the independent-set problem for any graph G with m edges and n vertices. We show that a new kind of the proposed quantum-molecular algorithm can find the maximal independent set(s) with the lower bound Ω ( 2^n/2 ) queries and the upper bound O( 2^n/2 ) queries. This work offers an obvious evidence for that to solve the independent-set problem in any graph G with m edges and n vertices, bio-molecular computers are able to generate a new kind of the straightforward Boolean circuit such that by means of implementing it quantum computers can give a quadratic speed-up. This work also offers one obvious evidence that quantum computers can significantly accelerate the speed and enhance the scalability of bio-molecular computers. Next, the element distinctness problem with input of n bits is to determine whether the given 2ⁿ real numbers are distinct or not. The quantum lower bound of solving the element distinctness problem is Ω ( 2^n×(2/3) ) queries in the case of a quantum walk algorithm. We further show that the proposed quantum-molecular algorithm reduces the quantum lower bound to Ω (( 2^n/2 )/( [Formula: see text]) queries. Furthermore, to justify the feasibility of the proposed quantum-molecular algorithm, we successfully solve a typical independent set problem for a graph G with two vertices and one edge by carrying out experiments on the backend ibmqx4 with five quantum bits and the backend simulator with 32 quantum bits on IBM's quantum computer.

Biocomputing Based on DNA Strand Displacement Reactions

The high sequence specificity and precise base complementary pairing principle of DNA provides a rich orthogonal molecular library for molecular programming, making it one of the most promising materials for developing bio-compatible intelligence. In recent years, DNA has been extensively studied and applied in the field of biological computing. Among them, the toehold-mediated strand displacement reaction (SDR) with properties including enzyme free, flexible design and precise control, have been extensively used to construct biological computing circuits. This review provides a systemic overview of SDR design principles and the applications. Strategies for designing DNA-only, enzymes-assisted, other molecules-involved and external stimuli-controlled SDRs are described. The recently realized computing functions and the application of DNA computing in other fields are introduced. Finally, the advantages and challenges of SDR-based computing are discussed.

Toward Smart Information Processing with Synthetic DNA Molecules

DNA, a biological macromolecule, is a naturally evolved information material. From the structural point of view, an individual DNA strand can be considered as a chain of data with its bases working as single units. For decades, due to the high biochemical stability, large information storage capacity, and high recognition specificity, DNA has been recognized as an attractive material for information processing. Especially, the chemical synthesis strategies and DNA sequencing techniques have been rapidly developed recently, further enabling encoding information with synthetic DNA molecules. Herein, recent progresses are summarized on information processing based on synthetic DNA molecules from three aspects including information storage, computation, and encryption, and proposed the challenges and future development directions.

Nanopore decoding for a Hamiltonian path problem

DNA computing has attracted attention as a tool for solving mathematical problems due to the potential for massive parallelism with low energy consumption. However, decoding the output information to a human-recognizable signal is generally time-consuming owing to the requirement for multiple steps of biological operations. Here, we describe simple and rapid decoding of the DNA-computed output for a directed Hamiltonian path problem (HPP) using nanopore technology. In this approach, the output DNA duplex undergoes unzipping whilst passing through an α-hemolysin nanopore, with information electrically decoded as the unzipping time of the hybridized strands. As a proof of concept, we demonstrate nanopore decoding of the HPP of a small graph encoded in DNA. Our results show the feasibility of nanopore measurement as a rapid and label-free decoding method for mathematical DNA computation using parallel self-assembly.

Leveraging autocatalytic reactions for chemical domain image classification

Autocatalysis is fundamental to many biological processes, and kinetic models of autocatalytic reactions have mathematical forms similar to activation functions used in artificial neural networks. Inspired by these similarities, we use an autocatalytic reaction, the copper-catalyzed azide-alkyne cycloaddition, to perform digital image recognition tasks. Images are encoded in the concentration of a catalyst across an array of liquid samples, and the classification is performed with a sequence of automated fluid transfers. The outputs of the operations are monitored using UV-vis spectroscopy. The growing interest in molecular information storage suggests that methods for computing in chemistry will become increasingly important for querying and manipulating molecular memory.

A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

A Parallel Bioinspired Algorithm for Chinese Postman Problem Based on Molecular Computing

The Chinese postman problem is a classic resource allocation and scheduling problem, which has been widely used in practice. As a classical nondeterministic polynomial problem, finding its efficient algorithm has always been the research direction of scholars. In this paper, a new bioinspired algorithm is proposed to solve the Chinese postman problem based on molecular computation, which has the advantages of high computational efficiency, large storage capacity, and strong parallel computing ability. In the calculation, DNA chain is used to properly represent the vertex, edge, and corresponding weight, and then all possible path combinations are effectively generated through biochemical reactions. The feasible solution space is obtained by deleting the nonfeasible solution chains, and the optimal solution is solved by algorithm. Then the computational complexity and feasibility of the DNA algorithm are proved. By comparison, it is found that the computational complexity of the DNA algorithm is significantly better than that of previous algorithms. The correctness of the algorithm is verified by simulation experiments. With the maturity of biological operation technology, this algorithm has a broad application space in solving large-scale combinatorial optimization problems.

Negative CG dinucleotide bias: An explanation based on feedback loops between Arginine codon assignments and theoretical minimal RNA rings

Theoretical minimal RNA rings are candidate primordial genes evolved for non-redundant coding of the genetic code's 22 coding signals (one codon per biogenic amino acid, a start and a stop codon) over the shortest possible length: 29520 22-nucleotide-long RNA rings solve this min-max constraint. Numerous RNA ring properties are reminiscent of natural genes. Here we present analyses showing that all RNA rings lack dinucleotide CG (a mutable, chemically instable dinucleotide coding for Arginine), bearing a resemblance to known CG-depleted genomes. CG in "incomplete" RNA rings (not coding for all coding signals, with only 3-12 nucleotides) gradually decreases towards CG absence in complete, 22-nucleotide-long RNA rings. Presumably, feedback loops during RNA ring growth during evolution (when amino acid assignment fixed the genetic code) assigned Arg to codons lacking CG (AGR) to avoid CG. Hence, as a chemical property of base pairs, CG mutability restructured the genetic code, thereby establishing itself as genetically encoded biological information.

A DNA algorithm for the job shop scheduling problem based on the Adleman-Lipton model

A DNA (DeoxyriboNucleic Acid) algorithm is proposed to solve the job shop scheduling problem. An encoding scheme for the problem is developed and DNA computing operations are proposed for the algorithm. After an initial solution is constructed, all possible solutions are generated. DNA computing operations are then used to find an optimal schedule. The DNA algorithm is proved to have an O(n2) complexity and the length of the final strand of the optimal schedule is within appropriate range. Experiment with 58 benchmark instances show that the proposed DNA algorithm outperforms other comparative heuristics.

Design, Bioanalytical, and Biomedical Applications of Aptamer-Based Hydrogels

Aptamers are special types of single-stranded DNA generated by a process called systematic evolution of ligands by exponential enrichment (SELEX). Due to significant advances in the chemical synthesis and biotechnological production, aptamers have gained considerable attention as versatile building blocks for the next generation of soft materials. Hydrogels are high water-retainable materials with a three-dimensional (3D) polymeric network. Aptamers, as a vital element, have greatly expanded the applications of hydrogels. Due to their biocompatibility, selective binding, and molecular recognition, aptamer-based hydrogels can be utilized for bioanalytical and biomedical applications. In this review, we focus on the latest strategies of aptamer-based hydrogels in bioanalytical and biomedical applications. We begin this review with an overview of the underlying design principles for the construction of aptamer-based hydrogels. Next, we will discuss some bioanalytical and biomedical applications of aptamer-based hydrogel including biosensing, target capture and release, logic devices, gene and cancer therapy. Finally, the recent progress of aptamer-based hydrogels is discussed, along with challenges and future perspectives.

Simultaneous polydirectional transport of colloidal bipeds

Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. We design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. Using such loops, we induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. Our ideas and methodology might be transferred to other systems for which topological protection is at work.

Detailed control over motions of colloidal particles holds promise for many applications such as lab-on-chip devices. Mirzaee-Kakhki et al. show transport of self-assembled colloidal rods with different lengths into different directions simultaneously on a checkerboard pattern under a magnetic field.

Parallelizing Assignment Problem with DNA Strands

Background

Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and is not applicable up to now.

Objectives

DNA (Deoxyribonucleic acid) computing provides a fantastic method to solve NP-hard problems in polynomial time. Accordingly, one of the famous NP-hard problems is assignment problem, which is designed to find the best assignment of n jobs to n persons in a way that it could maximize the profit or minimize the cost.

Material and Methods

Applying bio molecular operations of Adelman Lipton model, a novel parallel DNA algorithm have been proposed for solving the assignment problem.

Results

The proposed algorithm can solve the problem in time complexity, and just O(n²) initial DNA strand in comparison with nn initial sequence, which is used by the other methods.

Conclusions

In this article, using DNA computing, we proposed a parallel DNA algorithm to solve the assignment problem in linear time.

Encoding scheme for data storage and retrieval on DNA computers

There has been exponential growth in the amount of data being generated on a daily basis. Such a huge amount of data creates a need for efficient data storage techniques. Due to the limitations of existing storage media, new storage solutions have always been of interest. There have been recent developments in order to efficiently use synthetic deoxyribonucleic acid (DNA) for information storage. DNA storage has attracted researchers because of its extremely high data storage density, about 1 exabyte/mm3 and long life under easily achievable conditions. This work presents an encoding scheme for DNA-based data storage system with controllable redundancy and reliability, the authors have also talked about the feasibility of the proposed method. The authors have also analysed the proposed algorithm for time and space complexity. The proposed encoding scheme tries to minimise the bases per letter ratio while controlling the redundancy. They have experimented with three different types of data with a value of redundancy as 0.75. In the randomised simulation setup, it was observed that the proposed algorithm was able to correctly retrieve the stored data in our experiments about 94% of the time. In the situation, where redundancy was increased to 1, the authors were able to retrieve all the information correctly in the proposed experiments.

DNA steganography: hiding undetectable secret messages within the single nucleotide polymorphisms of a genome and detecting mutation-induced errors

BACKGROUND

As cell engineering technology advances, more complex synthetically designed cells and metabolically engineered cells are being developed. Engineered cells are important resources in industry. Similar to image watermarking, engineered cells should be watermarked for protection against improper use.

RESULTS

In this study, a DNA steganography methodology was developed to hide messages in variable regions (single nucleotide polymorphisms) of the genome to create hidden messages and thereby prevent from hacking. Additionally, to detect errors (mutations) within the encrypted messages, a block sum check algorithm was employed, similar to that used in network data transmission to detect noise-induced information changes.

CONCLUSIONS

This DNA steganography methodology could be used to hide secret messages in a genome and detect errors within the encrypted messages. This approach is expected to be useful for tracking cells and protecting biological assets (e.g., engineered cells).

In Vitro Identification of the Hamiltonian Cycle Using a Circular Structure Assisted DNA Computer

Adleman's illustration of molecular computing using DNA paved the way toward an entirely new direction of computing (Adleman, L. M. Science 1994, 266, 1021). The exponential time complex combinatorial problem on a traditional computer turns out to be a separation problem involving a polynomial number of steps in DNA computing experiments. Despite being a promising concept, the implementations of existing DNA computing procedures were restricted only to the smaller size formulations. In this work, we demonstrate a structure assisted DNA computing procedure on a bigger size Hamiltonian cycle problem involving 18 vertices. The developed model involves the formation and digestion of circular structure DNA, iteratively over multiple stages to eliminate the incorrect solutions to the given combinatorial problem. A high accuracy is obtained compared to other structure assisted models, which enable one to solve the bigger size problems.

Programmable DNA Nanoindicator-Based Platform for Large-Scale Square Root Logic Biocomputing

The prospect of programming molecular computing systems to realize complex autonomous tasks has advanced the design of synthetic biochemical logic circuits. One way to implement digital and analog integrated circuits is to use noncovalent hybridization and strand displacement reactions in cell-free and enzyme-free nucleic acid systems. To date, DNA-based circuits involving tens of logic gates capable of implementing basic and complex logic functions have been demonstrated experimentally. However, most of these circuits are still incapable of realizing complex mathematical operations, such as square root logic operations, which can only be carried out with 4 bit binary numbers. A high-capacity DNA biocomputing system is demonstrated through the development of a 10 bit square root logic circuit. It can calculate the square root of a 10 bit binary number (within the decimal integer 900) by designing DNA sequences and programming DNA strand displacement reactions. The input signals are optimized through the output feedback to improve performance in more complex logical operations. This study provides a more universal approach for applications in biotechnology and bioengineering.

A new DNA-based model for finite field arithmetic

A Galois fieldG F ( p n ) withp ≥ 2 a prime number and n ≥ 1 is a mathematical structure widely used in Cryptography and Error Correcting Codes Theory. In this paper, we propose a novel DNA-based model for arithmetic overG F ( p n ) . Our model has three main advantages over other previously described models. First, it has a flexible implementation in the laboratory that allows the realization arithmetic calculations in parallel forp ≥ 2 , while the tile assembly and the sticker models are limited to p = 2 . Second, the proposed model is less prone to error, because it is grounded on conventional Polymerase Chain Reaction (PCR) amplification and gel electrophoresis techniques. Hence, the problems associated to models such as tile-assembly and stickers, that arise when using more complex molecular techniques, such as hybridization and denaturation, are avoided. Third, it is simple to implement and requires 50 ng/μL per DNA double fragment used to develop the calculations, since the only feature of interest is the size of the DNA double strand fragments. The efficiency of our model has execution times of orderO ( 1 ) andO ( n ) , for the addition and multiplication overG F ( p n ) , respectively. Furthermore, this paper provides one of the few experimental evidences of arithmetic calculations for molecular computing and validates the technical applicability of the proposed model to perform arithmetic operations over G F ( p n ) .

Pathways to cellular supremacy in biocomputing

Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.

Synthetic biology uses cells as its computing substrate, often based on the genetic circuit concept. In this Perspective, the authors argue that existing synthetic biology approaches based on classical models of computation limit the potential of biocomputing, and propose that living organisms have under-exploited capabilities.

A novel bio-heuristic computing algorithm to solve the capacitated vehicle routing problem based on Adleman-Lipton model

DNA computing, as one of potential means to solve complicated computational problems, is a new field of interdisciplinary research, including computational mathematics, parallel algorithms, bioinformatics. Capacitated vehicle routing problem is one of famous NP-hard problems, which includes determining the path of a group same vehicles serving a set of clients, while minimizing the total transportation cost. Based on the bio-heuristic computing model and DNA molecular manipulations, parallel biocomputing algorithms for solving capacitated vehicle routing problem are proposed in this paper. We appropriately use different biological chains to mean vertices, edges, weights, and adopt appropriate biological operations to search the solutions of the problem with O(n²) time complexity. We enrich the application scope of biocomputing, reduce computational complexity, and verify practicability of DNA parallel algorithms through simulations.

Probe computing model based on small molecular switch

Background

DNA is a promising candidate for the construction of biological devices due to its unique properties, including structural simplicity, convenient synthesis, high flexibility, and predictable behavior. And DNA has been widely used to construct the advanced logic devices.

Results

Herein, a molecular probe apparatus was constructed based on DNA molecular computing to perform fluorescent quenching and fluorescent signal recovery, with an ’ ON/OFF’ switching function. In this study, firstly, we program the streptavidin-mediated fluorescent quenching apparatus based on short-distance strand migration. The variation of fluorescent signal is acted as output. Then DNAzyme as a switching controller was involved to regulate the fluorescent signal increase. Finally, on this base, a cascade DNA logic gate consists of two logic AND operations was developed to enrich probe machine.

Conclusion

The designed probe computing model can be implemented with readout of fluorescence intensity, and exhibits great potential applications in the field of bioimaging as well as disease diagnosis.

Recent Progress in Fluorescence Signal Design for DNA-Based Logic Circuits

DNA-based logic circuits, encoding algorithms in DNA and processing information, are pushing the frontiers of molecular computers forward, owing to DNA's advantages of stability, accessibility, manipulability, and especially inherent biological significance and potential medical application. In recent years, numerous logic functions, from arithmetic to nonarithmetic, have been realized based on DNA. However, DNA can barely provide a detectable signal by itself, so that the DNA-based circuits depend on extrinsic signal actuators. The signal strategy of carrying out a response is becoming one of the design focuses in DNA-based logic circuit construction. Although work on sequence and structure design for DNA-based circuits has been well reviewed, the strategy on signal production lacks comprehensive summary. In this review, we focused on the latest designs of fluorescent output for DNA-based logic circuits. Several basic strategies are summarized and a few designs for developing multi-output systems are provided. Finally, some current difficulties and possible opportunities were also discussed.

Something has to give: scaling combinatorial computing by biological agents exploring physical networks encoding NP-complete problems

On-chip network-based computation, using biological agents, is a new hardware-embedded approach which attempts to find solutions to combinatorial problems, in principle, in a shorter time than the fast, but sequential electronic computers. This analytical review starts by describing the underlying mathematical principles, presents several types of combinatorial (including NP-complete) problems and shows current implementations of proof of principle developments. Taking the subset sum problem as example for in-depth analysis, the review presents various options of computing agents, and compares several possible operation 'run modes' of network-based computer systems. Given the brute force approach of network-based systems for solving a problem of input size C, 2C solutions must be visited. As this exponentially increasing workload needs to be distributed in space, time, and per computing agent, this review identifies the scaling-related key technological challenges in terms of chip fabrication, readout reliability and energy efficiency. The estimated computing time of massively parallel or combinatorially operating biological agents is then compared to that of electronic computers. Among future developments which could considerably improve network-based computing, labelling agents 'on the fly' and the readout of their travel history at network exits could offer promising avenues for finding hardware-embedded solutions to combinatorial problems.

DNA computing over the ring ℤ4[v]/〈v2 − v〉

In this paper, we discuss the DNA construction of general length over the finite ring [Formula: see text], with [Formula: see text], which plays a very significant role in DNA computing. We discuss the GC weight of DNA codes over [Formula: see text]. Several examples of reversible cyclic codes over [Formula: see text] are provided, whose [Formula: see text]-images are [Formula: see text]-linear codes with good parameters.