DNA solution of hard computational problems

QPSO-based adaptive DNA computing algorithm

DNA (deoxyribonucleic acid) computing that is a new computation model based on DNA molecules for information storage has been increasingly used for optimization and data analysis in recent years. However, DNA computing algorithm has some limitations in terms of convergence speed, adaptability, and effectiveness. In this paper, a new approach for improvement of DNA computing is proposed. This new approach aims to perform DNA computing algorithm with adaptive parameters towards the desired goal using quantum-behaved particle swarm optimization (QPSO). Some contributions provided by the proposed QPSO based on adaptive DNA computing algorithm are as follows: (1) parameters of population size, crossover rate, maximum number of operations, enzyme and virus mutation rate, and fitness function of DNA computing algorithm are simultaneously tuned for adaptive process, (2) adaptive algorithm is performed using QPSO algorithm for goal-driven progress, faster operation, and flexibility in data, and (3) numerical realization of DNA computing algorithm with proposed approach is implemented in system identification. Two experiments with different systems were carried out to evaluate the performance of the proposed approach with comparative results. Experimental results obtained with Matlab and FPGA demonstrate ability to provide effective optimization, considerable convergence speed, and high accuracy according to DNA computing algorithm.

The biological microprocessor, or how to build a computer with biological parts

Systemics, a revolutionary paradigm shift in scientific thinking, with applications in systems biology, and synthetic biology, have led to the idea of using silicon computers and their engineering principles as a blueprint for the engineering of a similar machine made from biological parts. Here we describe these building blocks and how they can be assembled to a general purpose computer system, a biological microprocessor. Such a system consists of biological parts building an input / output device, an arithmetic logic unit, a control unit, memory, and wires (busses) to interconnect these components. A biocomputer can be used to monitor and control a biological system.

Non-linear molecular pattern classification using molecular beacons with multiple targets

In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns.

Biologically relevant molecular transducer with increased computing power and iterative abilities

As computing devices, which process data and interconvert information, transducers can encode new information and use their output for subsequent computing, offering high computational power that may be equivalent to a universal Turing machine. We report on an experimental DNA-based molecular transducer that computes iteratively and produces biologically relevant outputs. As a proof of concept, the transducer accomplished division of numbers by 3. The iterative power was demonstrated by a recursive application on an obtained output. This device reads plasmids as input and processes the information according to a predetermined algorithm, which is represented by molecular software. The device writes new information on the plasmid using hardware that comprises DNA-manipulating enzymes. The computation produces dual output: a quotient, represented by newly encoded DNA, and a remainder, represented by E. coli phenotypes. This device algorithmically manipulates genetic codes.

Solving the 0/1 knapsack problem by a biomolecular DNA computer

Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular interest in solving NP-complete and hard combinatorial problems. NP-complete problems such as knapsack problem and other hard combinatorial problems can be easily solved by DNA computers in a very short period of time comparing to conventional silicon-based computers. Sticker-based DNA computing is one of the methods of DNA computing. In this paper, the sticker based DNA computing was used for solving the 0/1 knapsack problem. At first, a biomolecular solution space was constructed by using appropriate DNA memory complexes. Then, by the application of a sticker-based parallel algorithm using biological operations, knapsack problem was resolved in polynomial time.

A Molecular Solution to the Three-Partition Problem

Given a set of numbers, the three-partition problem is to divide them into disjoint triplets that all have the same sum. The problem is NP-complete. This paper presents an algorithm to solve this problem using the biomolecular computing approach. The algorithm uses a distinctive encoding technique that depends on the numbers values which omits the need to an adder to find the sum. The algorithm is explained and an analysis of its complexity in terms of time, the number of strands, number of tubes, and the longest library strand used is presented. A simulation of the algorithm is implemented and tested. This algorithm further proves the ability of molecular computing in solving hard problems.

Binary DNA nanostructures for data encryption

We present a simple and secure system for encrypting and decrypting information using DNA self-assembly. Binary data is encoded in the geometry of DNA nanostructures with two distinct conformations. Removing or leaving out a single component reduces these structures to an encrypted solution of ssDNA, whereas adding back this missing “decryption key” causes the spontaneous formation of the message through self-assembly, enabling rapid read out via gel electrophoresis. Applications include authentication, secure messaging, and barcoding.

Graphene-based aptamer logic gates and their application to multiplex detection

In this work, a GO/aptamer system was constructed to create multiplex logic operations and enable sensing of multiplex targets. 6-Carboxyfluorescein (FAM)-labeled adenosine triphosphate binding aptamer (ABA) and FAM-labeled thrombin binding aptamer (TBA) were first adsorbed onto graphene oxide (GO) to form a GO/aptamer complex, leading to the quenching of the fluorescence of FAM. We demonstrated that the unique GO/aptamer interaction and the specific aptamer-target recognition in the target/GO/aptamer system were programmable and could be utilized to regulate the fluorescence of FAM via OR and INHIBIT logic gates. The fluorescence changed according to different input combinations, and the integration of OR and INHIBIT logic gates provided an interesting approach for logic sensing applications where multiple target molecules were present. High-throughput fluorescence imagings that enabled the simultaneous processing of many samples by using the combinatorial logic gates were realized. The developed logic gates may find applications in further development of DNA circuits and advanced sensors for the identification of multiple targets in complex chemical environments.

Biomolecular computing systems: principles, progress and potential

The task of information processing, or computation, can be performed by natural and man-made 'devices'. Man-made computers are made from silicon chips, whereas natural 'computers', such as the brain, use cells and molecules. Computation also occurs on a much smaller scale in regulatory and signalling pathways in individual cells and even within single biomolecules. Indeed, much of what we recognize as life results from the remarkable capacity of biological building blocks to compute in highly sophisticated ways. Rational design and engineering of biological computing systems can greatly enhance our ability to study and to control biological systems. Potential applications include tissue engineering and regeneration and medical treatments. This Review introduces key concepts and discusses recent progress that has been made in biomolecular computing.

Chromatin computation

In living cells, DNA is packaged along with protein and RNA into chromatin. Chemical modifications to nucleotides and histone proteins are added, removed and recognized by multi-functional molecular complexes. Here I define a new computational model, in which chromatin modifications are information units that can be written onto a one-dimensional string of nucleosomes, analogous to the symbols written onto cells of a Turing machine tape, and chromatin-modifying complexes are modeled as read-write rules that operate on a finite set of adjacent nucleosomes. I illustrate the use of this “chromatin computer” to solve an instance of the Hamiltonian path problem. I prove that chromatin computers are computationally universal – and therefore more powerful than the logic circuits often used to model transcription factor control of gene expression. Features of biological chromatin provide a rich instruction set for efficient computation of nontrivial algorithms in biological time scales. Modeling chromatin as a computer shifts how we think about chromatin function, suggests new approaches to medical intervention, and lays the groundwork for the engineering of a new class of biological computing machines.

Biomolecular theorem proving on a chip: a novel microfluidic solution to a classical logic problem

Biomolecules inside a microfluidic system can be used to solve computational problems, such as theorem proving, which is an important class of logical reasoning problems. In this article, the Boolean variables (literals) were represented using single-stranded DNA molecules, and theorem proving was performed by the hybridization and ligation of these variables into a double-stranded "solution" DNA. Then, a novel sequential reaction mixing method in a microfluidic chip was designed to solve a theorem proving problem, where a reaction loop and three additional chambers were integrated and controlled by pneumatic valves. DNA hybridization, ligation, toehold-mediated DNA strand displacement, exonuclease I digestion, and fluorescence detection of the double-stranded DNA were sequentially performed using this platform. Depending on the computational result, detection of the correct answer was demonstrated based on the presence of a fluorescence signal. This result is the first demonstration that microfluidics can be used to facilitate DNA-based logical inference.

A mechanical Turing machine: blueprint for a biomolecular computer

We describe a working mechanical device that embodies the theoretical computing machine of Alan Turing, and as such is a universal programmable computer. The device operates on three-dimensional building blocks by applying mechanical analogues of polymer elongation, cleavage and ligation, movement along a polymer, and control by molecular recognition unleashing allosteric conformational changes. Logically, the device is not more complicated than biomolecular machines of the living cell, and all its operations are part of the standard repertoire of these machines; hence, a biomolecular embodiment of the device is not infeasible. If implemented, such a biomolecular device may operate in vivo, interacting with its biochemical environment in a program-controlled manner. In particular, it may ‘compute’ synthetic biopolymers and release them into its environment in response to input from the environment, a capability that may have broad pharmaceutical and biological applications.

A SEMI-GENERAL METHOD TO SOLVE THE COMBINATORIAL OPTIMIZATION PROBLEMS BASED ON NANOCOMPUTING

Nanocomputing describes computing that uses nanoscale devices. It is reasonable to search for nanoscale particles, such as molecules, that do not require difficult fabrication steps. DNA is recognized as a nanomaterial, not as a biological material, in the research field of nanotechnology. This paper proposes a semi-general method to solve combinatorial optimization problems based on DNA computing. It is obvious that the DNA molecule is one of the most promising functional nanomaterials. However, the application of DNA molecules is still under study because of the big gap that exists between theory and practice.

Detection of multiple disease indicators by an autonomous biomolecular computer

The promise of biomolecular computers is their ability to interact with naturally occurring biomolecules, enabling in the future the development of context-dependent programmable drugs. Here we show a context-sensing mechanism of a biomolecular automaton that can simultaneously sense different types of molecules, allowing future integration of biomedical knowledge on a broad range of molecular disease symptoms in the decision of a biomolecular computer to release a drug molecule.

An unenumerative DNA computing model for vertex coloring problem

The solution space exponential explosion caused by the enumeration of the candidate solutions maybe is the biggest obstacle in DNA computing. In the paper, a new unenumerative DNA computing model for graph vertex coloring problem is presented based on two techniques: 1) ordering the vertex sequence for a given graph in such a way that any two consecutive labeled vertices i and i+1 should be adjacent in the graph as much as possible; 2) reducing the number of encodings representing colors according to the construture of the given graph. A graph with 12 vertices without triangles is solved and its initial solution space includes only 283 DNA strands, which is 0.0532 of 3(12) (the worst complexity).

Padlock probe-mediated qRT-PCR for DNA computing answer determination

Padlock probe-mediated quantitative real time PCR (PLP-qRT-PCR) was adapted to quantify the abundance of sequential 10mer DNA sequences for use in DNA computing to identify optimal answers of traveling salesman problems. The protocol involves: (i) hybridization of a linear PLP with a target DNA sequence; (ii) PLP circularization through enzymatic ligation; and (iii) qRT-PCR amplification of the circularized PLP after removal of non-circularized templates. The linear PLP was designed to consist of two 10-mer sequence-detection arms at the 5' and 3' ends separated by a core sequence composed of universal PCR primers, and a qRT-PCR reporter binding site. Circularization of each PLP molecule is dependent upon hybridization with target sequence and high-fidelity ligation. Thus, the number of PLP circularized is determined by the abundance of target in solution. The amplification efficiency of the PLP was 98.7% within a 0.2 pg-20 ng linear detection range between thermal cycle threshold (C(t) value) and target content. The C(t) values derived from multiplex qRT-PCR upon three targets did not differ significantly from those obtained with singleplex assays. The protocol provides a highly sensitive and efficient means for the simultaneous quantification of multiple short nucleic acid sequences that has a wide range of applications in biotechnology.

DNA-based computing of strategic assignment problems

DNA-based computing is a novel technique to tackle computationally difficult problems, in which computing time grows exponentially corresponding to problematic size. A strategic assignment problem is a typical nondeterministic polynomial problem, which is often associated with strategy applications. In this Letter, a new approach dealing with strategic assignment problems is proposed based on manipulating DNA strands, which is believed to be better than the conventional silicon-based computing in solving the same problem.

Logic integration of mRNA signals by an RNAi-based molecular computer

Synthetic in vivo molecular 'computers' could rewire biological processes by establishing programmable, non-native pathways between molecular signals and biological responses. Multiple molecular computer prototypes have been shown to work in simple buffered solutions. Many of those prototypes were made of DNA strands and performed computations using cycles of annealing-digestion or strand displacement. We have previously introduced RNA interference (RNAi)-based computing as a way of implementing complex molecular logic in vivo. Because it also relies on nucleic acids for its operation, RNAi computing could benefit from the tools developed for DNA systems. However, these tools must be harnessed to produce bioactive components and be adapted for harsh operating environments that reflect in vivo conditions. In a step toward this goal, we report the construction and implementation of biosensors that 'transduce' mRNA levels into bioactive, small interfering RNA molecules via RNA strand exchange in a cell-free Drosophila embryo lysate, a step beyond simple buffered environments. We further integrate the sensors with our RNAi 'computational' module to evaluate two-input logic functions on mRNA concentrations. Our results show how RNA strand exchange can expand the utility of RNAi computing and point toward the possibility of using strand exchange in a native biological setting.

The simulation of virus life cycle with quantum gates

Quantum physics and molecular biology are two disciplines that have evolved relatively independently. However, recently a wealth of evidence has demonstrated the importance of quantum mechanics for biological systems and thus a new field of quantum biology is emerging. There are many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms. We consider the nucleonic acid of virus as a quantum system in this paper and discuss virus life cycle from the view-point of quantum and simulate it using quantum gates for the first time. The maximally entangled states show infected cell can change to entire cell, the virus can switch from the lysogenic to the lytic and the prophages can remain latent in the bacterial chromosome for many generations.

Universal translators for nucleic acid diagnosis

Defined broadly, molecular translators are constructs that can convert any designated molecular input into a unique output molecule. In particular, the development of universal nucleic acid translators would be of significant practical value in view of the expanding biomedical importance of gene diagnostics. Currently, diagnostic assays for nucleic acids must be individually developed and optimized for each new sequence because inputs for one assay are sequence-specific and are therefore incompatible with any other assay designed for the detection of a different nucleic acid. However, if a desired nucleic acid sequence could be translated in vitro into a predetermined nucleic acid output for which there is already a known diagnostic assay, then that single assay could be easily adapted to detect nearly any strand. Here we investigate PCR-independent isothermal molecular translation strategies that function without the need for post-translation purification and can be implemented with commercially available components. Translation yields up to 96% are obtained in 5 min at room temperature with minimal background reaction (<1%) and with discrimination of single nucleotide polymorphisms in the input sequence. Furthermore, we apply these translators to adapt a high-gain HIV diagnostic system for high-throughput detection of hepatitis C, avian influenza (H5N1), and smallpox without making changes to the underlying assay. Finally, we show the feasibility of translating small-molecule interactions into nucleic acid outputs by demonstrating the utility of a DNA aptamer for translating adenosine into a readily detectable output DNA sequence. Additionally, equilibrium expressions are described in order to facilitate rational engineering of aptameric translators for label-free detection of any molecule that an aptamer can recognize.

Intelligent medical diagnostics via molecular logic

In this communication, we describe the integration of microarray sensor technology with logic capability for screening combinations of proteins and DNA in a biological sample. In this system, we have demonstrated the use of a single platform amenable to both protein detection and protein-DNA detection using molecular logic gates. The pattern of protein and DNA inputs results in fluorescence outputs according to a truth table for AND and INHIBIT gates, thereby demonstrating the feasibility of performing medical diagnostics using a logic gate design. One possible application of this technique would be direct screening of various medical conditions that are dependent on combinations of diagnostic markers.

Production of random DNA oligomers for scalable DNA computing

While remarkably complex networks of connected DNA molecules can form from a relatively small number of distinct oligomer strands, a large computational space created by DNA reactions would ultimately require the use of many distinct DNA strands. The automatic synthesis of this many distinct strands is economically prohibitive. We present here a new approach to producing distinct DNA oligomers based on the polymerase chain reaction (PCR) amplification of a few random template sequences. As an example, we designed a DNA template sequence consisting of a 50-mer random DNA segment flanked by two 20-mer invariant primer sequences. Amplification of a dilute sample containing about 30 different template molecules allows us to obtain around 10(11) copies of these molecules and their complements. We demonstrate the use of these amplicons to implement some of the vector operations that will be required in a DNA implementation of an analog neural network.

Construction of a DNA nano-object directly demonstrates computation

We demonstrate a computing method in which a DNA nano-object representing the solution of a problem emerges as a result of self-assembly. We report an experiment in which three-vertex colorability for a six-vertex graph with nine edges is solved by constructing a DNA molecule representing the colored graph itself. Our findings show that computation based on "shape processing" is a viable alternative to symbol processing when computing by molecular self-assembly.

Biocomputers: from test tubes to live cells

Biocomputers are man-made biological networks whose goal is to probe and control biological hosts--cells and organisms--in which they operate. Their key design features, informed by computer science and engineering, are programmability, modularity and versatility. While still a work in progress, biocomputers will eventually enable disease diagnosis and treatment with single-cell precision, lead to "designer" cell functions for biotechnology, and bring about a new generation of biological measurement tools. This review describes the intellectual foundation of the "biocomputer" concept as well as surveys the state of the art in the field.

Solving the fully-connected 15-city TSP using probabilistic DNA computing

Implementation of DNA computers has lagged behind the theoretical advances due to several technical limitations. These limitations include the amount of DNA required, the efficiency and accuracy of methods to generate and purify answers, and the lack of a reliable method to read the answer. Here we show how to perform calculations using a reasonable amount of DNA with greater efficiency and accuracy and a new readout method that was used to successfully solve a problem with 15 vertices and 210 edges, the largest problem ever solved with DNA. These advances will provide new opportunities for DNA computing to perform practical computations that utilize the massively parallel nature of DNA hybridization.

The use of gold nanoparticle aggregation for DNA computing and logic-based biomolecular detection

The use of DNA molecules as a physical computational material has attracted much interest, especially in the area of DNA computing. DNAs are also useful for logical control and analysis of biological systems if efficient visualization methods are available. Here we present a quick and simple visualization technique that displays the results of the DNA computing process based on a colorimetric change induced by gold nanoparticle aggregation, and we apply it to the logic-based detection of biomolecules. Our results demonstrate its effectiveness in both DNA-based logical computation and logic-based biomolecular detection.

Quantum algorithms for biomolecular solutions of the satisfiability problem on a quantum machine

In this paper, we demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented more efficiently by our proposed quantum algorithm on the quantum machine proposed by Deutsch. To test our theory, we carry out a three-quantum bit nuclear magnetic resonance experiment for solving the simplest satisfiability problem.