How to Compute with DNA

An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.

P-systems recently were introduced by Gheorghe Pă un as a new model for computations based on membrane structures. Using the membranes as a kind of filter for specific objects when transferring them into an inner compartment turned out to be a very powerful mechanism in combination with suitable rules to be applied within the membranes in the model of generalized P-systems, GP-systems for short. In general, GP-systems allow for the simulation of graph controlled grammars of arbitrary type based on productions working on single objects. In this paper we consider GP-systems as computing devices using splicing or cutting and recombination of strings. Various variants of such systems are proved to have universal computational power, e.g., we show how test tube systems based on splicing or cutting and recombination of strings can be simulated by the corresponding GP-systems.

<p class="Abstract">Much of our scientific, technological, and economic future depends on the availability of an ever-increasing supply of computational power. However, the increasing demand for such power has pushed electronic technology to the limit of physical feasibility and has raised the concern that this technology may not be able to sustain our growth in the near future. It became important to consider an alternative means of achieving computational power. In this regard, DNA computing was introduced based on the usage of DNA and molecular biology hardware instead of the typical silicon based technology. The molecular computers could take advantage of DNA's physical properties to store information and perform calculations. These include extremely dense information storage, enormous parallelism and extraordinary energy efficiency. One of the main advantages that DNA computations would add to computation is its self - parallel processing while most of the electronic computers now use linear processing. In this paper, the DNA computation is reviewed and its state of the art challenges and applications are presented. Some of these applications are those require fast processing, at which DNA computers would be able to solve the hardest problems faster than the traditional ones. For example, 10 trillion DNA molecules can fit in one cubic centimeter that would result in a computer that holds 10 terabytes of data. Moreover, this work focuses on whether a large scale molecular computer can be built.</p>

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional silicon-chips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate double-stranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented.

Turing machines based on quantum logic can solve undecidableproblems. In this paper we will give recursion-theoreticalcharacterization of the computational power of this kind of quantumTuring machines. In detail, for the unsharp case, it is proved that&#931<sup>0</sup><sub>1</sub>&#8746&#928<sup>0</sup><sub>1</sub>&#8838L<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))&#8838&#928<sup>0</sup><sub>2</sub>when the truth value lattice is locally finite and the operation &#8743is computable, whereL<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))denotes theclass of quantum language accepted by these Turing machine indepth-first model (respectively, width-first model);for the sharp case, we can obtain similar results for usual orthomodular lattices.

Since the first author became involved in research on molecular computing, we have been consistently working on molecular computations using secondary structures of DNA, whose simplest forms are hairpins. In particular, we have been interested in the computational power of formation and dissociation of such secondary structures. In this chapter, we first review our previous research on computing with hairpins, and show that hairpin formation and dissociation have enough computational power in themselves. We then report our recent experiments on implementing logic gates by loop dissociation. The paper is organized as follows. In Section 2, we briefly describe our research that shows the computational power of hairpin formation. We then survey the Whiplash Machine, a kind of molecular machine based on repeated formation and dissociation of hairpins, in Section 3. In Section 4, after describing our model of general-purpose molecular systems, we report the experimental results concerning the scheme of logical circuits based on loop dissociation.

DNA computer is a new type of computer which computing by biological molecular techniques. If DNA computer want to realize its practicability, it must be the same as a traditional computer. In order to settle the issues of representation and organizational in DNA computer, we need a reasonable data structures to effectively represent and organize the information of DNA computer. The thesis designs a stack structure model based on DNA computing, which can express limited stack constraints through hairpin structure. At the same time, it can complete the operations of entering stack and leaving stack using two different restrictive enzymes.

Design of data structure is valuable to the concrete realization of DNA computer.Therefore,a method of designing a binary tree based on sequential storage model in DNA computer was proposed,which utilized the biological characteristics of DNA molecules and restriction endonucleases to complete sequential storage structure and basic operations of the binary tree.All the biological technology mentioned here could be practically implemented in the laboratory.To prove the feasibility of this method,an actual binary tree with detailed nucleotide encodings and an instance of algorithm were given.The process of an algorithm implemented on this binary tree was demonstrated.

DNA computing aims at using nucleic acids for computing. Since micromolar DNA solutions can act as billions of parallel nanoprocessors, DNA computers can in theory solve optimization problems that require vast search spaces. However, the actual parallelism currently being achieved is at least a hundred million-fold lower than the number of DNA molecules used. This is due to the quantity of DNA molecules of one species that is required to produce a detectable output to the computations. In order to miniaturize the computation and considerably reduce the amount of DNA needed, we proposed that fluorescence labeling techniques can be applied to DNA computing. In the paper, we solved the simple 0-1 programming problem with fluorescence labeling techniques based on surface chemistry. It is attempt to apply DNA computing to programming problem.

DNA computing is an area of natural computing based on the idea that molecular biology processes can be used to perform arithmetic and logic operations on information encoded as DNA strands. The first part of this review outlines basic molecular biology notions necessary for understanding DNA computing, recounts the first experimental demonstration of DNA computing (Adleman’s 7-vertex Hamiltonian Path Problem), and recounts the milestone wet laboratory experiment that first demonstrated the potential of DNA computing to outperform the computational ability of an unaided human (20 variable instance of 3-SAT).The second part of the review describes how the properties of DNA-based information, and in particular the Watson–Crick complementarity of DNA single strands, have influenced areas of theoretical computer science such as formal language theory, coding theory, automata theory and combinatorics on words. More precisely, we describe the problem of DNA encodings design, present an analysis of intramolecular bonds, define and characterize languages that avoid certain undesirable intermolecular bonds, and investigate languages whose words avoid even imperfect bindings between their constituent strands. We also present another, vectorial, representation of DNA strands, and two computational models based on this representation: sticker systems and Watson–Crick automata. Lastly, we describe the influence that properties of DNA-based information have had on research in combinatorics on words, by enumerating several natural generalizations of classical concepts of combinatorics of words: pseudopalindromes, pseudoperiodicity, Watson–Crick conjugate and commutative words, involutively bordered words, pseudoknot bordered words. In addition, we outline natural extensions in this context of two of the most fundamental results in combinatorics of words, namely Fine and Wilf's theorem and the Lyndon–Schutzenberger result.

Molecular computers (also called DNA computers), as an alternative to traditional electronic computers, are smaller in size but more energy efficient, and have massive parallel processing capacity. However, DNA computers may not outperform electronic computers owing to their higher error rates and some limitations of the biological laboratory. The stickers model, as a typical DNA-based computer, is computationally complete and universal, and can be viewed as a bit-vertically operating machine. This makes it attractive for silicon implementation. Inspired by the information processing method on the stickers computer, we propose a novel parallel computing model called DEM (DNA Electronic Computing Model) on System-on-a-Programmable-Chip (SOPC) architecture. Except for the significant difference in the computing medium—transistor chips rather than bio-molecules—the DEM works similarly to DNA computers in immense parallel information processing. Additionally, a plasma display panel (PDP) is used to show the change of solutions, and helps us directly see the distribution of assignments. The feasibility of the DEM is tested by applying it to compute a maximum clique problem (MCP) with eight vertices. Owing to the limited computing sources on SOPC architecture, the DEM could solve moderate-size problems in polynomial time.

A goal of research on DNA computing is to solve problems that are beyond the capabilities of the fastest silicon-based supercomputers. Adleman and Lipton present exhaustive search algorithms for 3Sat and 3-Coloring, which can only be run on small instances and hence are not practical. In this paper, we show how improved algorithms can be developed for the 3-Coloring and Independent Set problems. Our algorithms use only the DNA operations proposed by Adleman and Lipton, but combine them in more powerful ways, and use polynomial preprocessing on a standard computer to tailor them to the specific instance to be solved. The main contribution of this paper is a more general model of DNA algorithms than that proposed by Lipton. We show that DNA computation for NP-complete problems can do more than just exhaustive search. Further research in this direction will help determine whether or not DNA computing is viable for NP-hard problems. A second contribution is the first analysis of errors that arise in generating the solution space for DNA computation.

We introduce a new model of molecular computation that we call the sticker model. Like many previous proposals it makes use of DNA strands as the physical substrate in which information is represented and of separation by hybridization as a central mechanism. However, unlike previous models, the stickers model has a random access memory that requires no strand extension and uses no enzymes; also (at least in theory), its materials are reusable. The paper describes computation under the stickers model and discusses possible means for physically implementing each operation. Finally, we go on to propose a specific machine architecture for implementing the stickers model as a microprocessor-controlled parallel robotic workstation. In the course of this development a number of previous general concerns about molecular computation (Smith, 1996; Hartmanis, 1995; Linial et al., 1995) are addressed. First, it is clear that general-purpose algorithms can be implemented by DNA-based computers, potentially solving a wide class of search problems. Second, we find that there are challenging problems, for which only modest volumes of DNA should suffice. Third, we demonstrate that the formation and breaking of covalent bonds is not intrinsic to DNA-based computation. Fourth, we show that a single essential biotechnology, sequence-specific separation, suffices for constructing a general-purpose molecular computer. Concerns about errors in this separation operation and means to reduce them are addressed elsewhere (Karp et al., 1995; Roweis and Winfree, 1999). Despite these encouraging theoretical advances, we emphasize that substantial engineering challenges remain at almost all stages and that the ultimate success or failure of DNA computing will certainly depend on whether these challenges can be met in laboratory investigations.

Recently, in the research field of DNA Computing, the improvement of reliability of computation has been expected. Since DNA Computing consists of some chemical reactions, it seems to be clearly important to optimize each reaction protocol in order to improve the reliability of computing. Moreover, the purpose of the reaction in DNA Computing crosses variably. We consider that the optimization of reaction protocol according to each purpose will be necessary. We try to derive positive impact factors on the reaction result from actual experiments by using DOE. From the results of experiments, we show the importance and necessity of optimizing reaction protocol according to each desired reaction.KeywordsPolymerase Chain ReactionOrthogonal ArrayReaction CharacteristicPolymerase Chain Reaction ProtocolReaction ProtocolThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356For further resources related to this article, please visit the WIREs website.