Three dimensional DNA structures in computing

Jonoska, Nataša; Karl, Stephen A.; Saito, Masahico

doi:10.1016/s0303-2647(99)00041-6

Cited by 66 publications

(36 citation statements)

References 12 publications

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“…Self-assembling of molecules mimics the properties of associative memory (Jonoska et al, 1998;Winfree, 1998). This technique has the potential value to analyse large knowledge bases, thereby in principle, paves the way to new methods of programming in logic (Mihalache, 1997).…”

Section: Discussionmentioning

confidence: 99%

The Inference Based on Molecular Computing

Wasiewicz¹

2000

Cybernetics and Systems

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Molecular computing is a new paradigm to perform calculations using nanotechnology. This paper presents the overall research direction from which molecular inference and expert systems are emerging. It introduces the subject matter and a general description of the problems involved. This includes selected methods of knowledge representation by DNA oligonucleotides, strategies of the inference mechanism, concept of the inference engine based on circular DNA molecules, particularly derived from plasmids, practical experience in DNA inference engine implementation, and discussion of the experimental results. The approach allows evaluating logical statements and drawing inferences for generating other statements via DNA computing. Series of experiments have been conducted to confirm practical utility of this approach. In these experiments, parameters of biochemical reactions were varied to determine truth/false recognition accuracy. In addition, we discuss the fundamental issues of inference engine and try to enhance physical insight into the dominating features of the approach proposed.

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Section: Discussionmentioning

confidence: 99%

The Inference Based on Molecular Computing

Wasiewicz¹

2000

Cybernetics and Systems

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“…Apart from this, the potential advantages of three-dimensional structures over two-dimensional structures in nanofabrication includes a considerably increased circuit density. Jonoska et al [10] proposed the use of three-dimensional DNA structures in computing. Simple examples of algorithmic computation in three dimensions includes the generalization of Pascal triangle to 3D [2] and three-dimensional multiplexers (the latter would provide a mechanism for 3D memory addressing with the appropriate affixed molecular electronic components).…”

Section: The Challenge Of 3d Tiling Assembly Error-correctionmentioning

confidence: 99%

“…Its potential to build complex systems from microscale templates can not be overlooked [9,15,28,35]. Besides the assembled three-dimensional structures can be extremely useful in computations [10]. It is possible to simulate a two-dimensional cellular automata, using three-dimensional self-assembly, which then paves way to perform a rich class of computations including matrix multiplication, integer multiplications, context-free language recognition etc.…”

Section: Error Correction In Self-assemblies In Three Dimensionsmentioning

confidence: 99%

Capabilities and Limits of Compact Error Resilience Methods for Algorithmic Self-Assembly

Sahu

Reif

2008

Algorithmica

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Winfree's pioneering work led the foundations in the area of errorreduction in algorithmic self-assembly (Winfree and Bekbolatov in DNA Based Computers 9, LNCS, vol. 2943LNCS, vol. , pp. 126-144, 2004, but the construction resulted in increase of the size of assembly. Reif et al. (Nanotechnol. Sci. Comput. 79-103, 2006) contributed further in this area with compact error-resilient schemes that maintained the original size of the assemblies, but required certain restrictions on the Boolean functions to be used in the algorithmic self-assembly. It is a critical challenge to improve these compact error resilient schemes to incorporate arbitrary Boolean functions, and to determine how far these prior results can be extended under different degrees of restrictions on the Boolean functions. In this work we present a considerably more complete theory of compact error-resilient schemes for algorithmic selfassembly in two and three dimensions. In our error model, is defined to be the probability that there is a mismatch between the neighboring sides of two juxtaposed tiles and they still stay together in the equilibrium. This probability is independent of any other match or mismatch and hence we term this probabilistic model as the independent error model. In our model all the error analysis is performed under the assumption of kinetic equilibrium. First we consider two-dimensional algorithmic self-assembly. We present an error correction scheme for reduction of errors from to 2 for arbitrary Boolean functions in two dimensional algorithmic self-assembly. Then we characterize the class of Boolean functions for which the error can be reduced from to 3 , and present an error correction scheme that achieves this reduction. Then we prove ultimate limits on certain classes of compact error resilient schemes: in particular we show that they can not provide reduction of errors from A preliminary version of this paper was published in DNA12 [22].S. Sahu ( ) · J.H. Reif Department of Computer Science, Duke University, Box 90129, Durham, NC 27708-0129, USA e-mail: sudheer@cs.duke.edu J.H. Reif e-mail: reif@cs.duke.edu Algorithmica to 4 is for any Boolean functions. Further, we develop the first provable compact error resilience schemes for three dimensional tiling self-assemblies. We also extend the work of Winfree on self-healing in two-dimensional self-assembly (Winfree in Nanotechnol. Sci. Comput. 55-78, 2006) to obtain a self-healing tile set for threedimensional self-assembly.

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“…do parallel arithmetic on multiple inputs, or determine satisfying inputs of a circuit), so they are an enhancement of the power of DP-BMC. Jonoska et al [JKS98] describes techniques for solving the Hamiltonian path problem by self assembly of single strand DNA into three dimensional DNA structures representing a Hamiltonian path. (D) The Cellular Processor Paradigm.…”

Section: Enabling Technologies and Experimental Paradigms For Bmcmentioning

confidence: 99%

Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation

Reif

1998

Lecture Notes in Computer Science

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Molecular Computation (MC) is massively parallel computation where data is stored and processed within objects of molecular size. Biomolecular Computation (BMC) is MC using biotechnology techniques, e.g. recombinant DNA operations. In contrast, Quantum Computation (QC) is a type of computation where unitary and measurement operations are executed on linear superpositions of basis states. Both BMC and QC may be executed at the micromolecular scale by a variety of methodologies and technologies. This paper surveys various methods for doing BMC and QC and discusses the considerable theoretical and practical advances in BMC and QC made in the last few years. We compare bounds on key resource such as time, volume (number of molecules times molecular density), energy and error rates achievable, taking particular note of the scalability of these methods with the size of the problem solved. In addition to NP search problems and database search problems, we enumerate a wide variety of further potential practical applications of BMC and QC.We observe that certain problems (e.g., NP search problems), if solved with polynomial time bounds, requires exponentially large volume for BMC, so BMC does not scale well to solve very large NP search problems. However, we describe a number of applications (e.g., search within large data bases and simulation of parallel machines) where the volume grows polynomial.Also, we note that the observation operation of QC, which is a fundamental operation of QC used for obtaining classical output, may potentially suffer from exponentially large volume requirements. Observation operations in quantum physics are generally done by a macroscopic measurement apparatus, and the original formulations of QC implicity assumed that macroscopic measurement apparatus would be used for QC. However, if the measurement apparatus is very small, it will be subject to quantum effects. At this time, no one has demonstrated or proved that the observation operation (for a quantum system with n entangled qubits) can even be approximated within a larger unitary quantum system in volume growing less than exponentially with n. Hence it is unknown whether QC (with the observation operation) scales to even moderate numbers of qubits within small volume. We pose a major open problem in QC: to determine (i.e., provide a formal proof) whether or not observation, in a closed quantum system, can be approximated in small volume: say, growing as a polynomial in the number of qubits.We also discuss techniques for decreasing errors in BMC (e.g., annealing errors) and QC (e.g., decoherence errors), and volume where possible, to insure the scalability of BMC and QC to problems of large input size. In addition, we consider how BMC might be used to assist QC (e.g., to do observation operations for Bulk QC) and also how quantum techniques might be used to assist BMC (e.g., to do exquisite detection of very small quantities of a molecule in solution within a large volume).

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Three dimensional DNA structures in computing

Cited by 66 publications

References 12 publications

The Inference Based on Molecular Computing

The Inference Based on Molecular Computing

Capabilities and Limits of Compact Error Resilience Methods for Algorithmic Self-Assembly

Alternative Computational Models: A Comparison of Biomolecular and Quantum Computation

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