Molecular computing revisited: a Moore's Law? (original) (raw)
Related papers
On the scalability of molecular computational solutions to NP problems
1996
Abstract: A molecular computational procedure in which manipulation of DNA strands may be harnessed to solve a classical problem in NP- the directed Hamiltonian path problem- was recently proposed [Adleman 1994, Gifford 1994]. The procedure is in effect a massively parallel chemical analog computer and has a computational capacity corresponding to approximately ≈ 10 5 CPU years on a typical 10 MFLOP workstation. In this paper limitations on the potential scalability of molecular computation are considered. A simple analysis of the time complexity function shows that the potential of molecular systems to increase the size of generally solvable problems in NP is fundamentally limited to ≈ 10 2. Over the chemically measurable picomolar to molar concentration range the greatest practical increase in problem size is limited to ≈ 10 1.
On the scalability of molecular computational solutions to
1996
A molecular computational procedure in which manipulation of DNA strands may be harnessed to solve a classical problem in NP-the directed Hamiltonian path problem-was recently proposed [Adleman 1994, Gifford 1994]. The procedure is in effect a massively parallel chemical analog computer and has a computational capacity corresponding to approximately ≈ 10 5 CPU years on a typical 10 MFLOP workstation. In this paper limitations on the potential scalability of molecular computation are considered. A simple analysis of the time complexity function shows that the potential of molecular systems to increase the size of generally solvable problems in NP is fundamentally limited to ≈ 10 2. Over the chemically measurable picomolar to molar concentration range the greatest practical increase in problem size is limited to ≈ 10 1 .
DNA computing is essential computation using biological molecules rather than traditional silicon chips. In recent years, DNA computing has been a research tool for solving complex problems. Despite this, it is still not easy to understand. The aim of this paper is present DNA computing in simple terms that a beginner can understand. Introduction Development in traditional electronic computers is restricted by hardware problems. DNA computing will solve that problem and serve as an alternative technology. DNA computing is also known as molecular computing. It is computing using the processing power of molecular information instead the conventional digital components. It is one of the non-silicon based computing approaches. DNA has been shown to have massive processing capabilities that might allow a DNA-based computer to solve complex problems in a reasonable amount of time. DNA computing was proposed by Leonard Adleman, who demonstrated in 1994 that DNA could be applied in computations [1]. He used DNA to solve a small instance of the traveling salesman problem, in which the objective is to find the most efficient route through seven cities connected by 14 one-way flights. Adleman solved this problem by creating strands of DNA to represent each flight and then combined them to generate every possible route [2, 3]. The graph in Adleman's experiment is shown in Figure1. Adleman's work have set imaginations blazing throughout the world and across disciplines. It introduced a new revolutionary era in the field of computing. DNA computing is now an interdisciplinary research field where chemistry, molecular biology, computer science, mathematics, and technology come together.
Solving a Hamiltonian Path Problem with a bacterial computer
Journal of Biological Engineering, 2009
The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time.
Biosystems, 2005
Cook's Theorem . Introduction to Algorithms, second ed., The MIT Press; Garey, M.R., Johnson, D.S., 1979. Computer and Intractability, Freeman, San Fransico, CA] is that if one algorithm for an NPcomplete or an NP-hard problem will be developed, then other problems will be solved by means of reduction to that problem. Cook's Theorem has been demonstrated to be correct in a general digital electronic computer. In this paper, we first propose a DNA algorithm for solving the vertex-cover problem. Then, we demonstrate that if the size of a reduced NP-complete or NP-hard problem is equal to or less than that of the vertex-cover problem, then the proposed algorithm can be directly used for solving the reduced NP-complete or NP-hard problem and Cook's Theorem is correct on DNA-based computing. Otherwise, a new DNA algorithm for optimal solution of a reduced NP-complete problem or a reduced NP-hard problem should be developed from the characteristic of NP-complete problems or NP-hard problems. (M. Guo). strands could be applied for figuring out solutions to 27 an instance of the NP-complete Hamiltonian path prob-28 lem (HPP) . Lipton wrote the second 29 paper in which it was shown that the Adleman tech-30 niques could also be used to solve the NP-complete 31 satisfiability (SAT) problem (the first NP-complete 32 problem) . Adleman and co-workers 33 proposed sticker for enhancing the Adleman-Lipton 34 model (Roweis et al., 1999). 35 In this paper, we use sticker to construct solution 36 space of DNA library sequences for the vertex-cover 37 1 BIO 2404 1-12 2 M. Guo et al. / BioSystems xxx (2004) xxx-xxx problem. Simultaneously, we also apply DNA opera-38 tions in the Adleman-Lipton model to develop a DNA 39 algorithm. The main result of the proposed DNA algo-40 rithm shows that the vertex-cover problem is solved 41 with biological operations in the Adleman-Lipton 42 model from the solution space of stickers. Furthermore, 43 if the size of a reduced NP-complete or a reduced NP-44 hard problem is equal to or less than that of the vertex-45 cover problem, then the proposed algorithm can be di-46 rectly used for solving the reduced NP-complete, or 47 NP-hard problem. 48 The rest of this paper is organized as follows. In Sec-49 tion 2, the Adleman-Lipton model is introduced and 50 the comparison is made with other models. In Section 51 3, the first DNA algorithm is proposed for solving the 52 vertex-cover problem from solution space of sticker 53 in the Adleman-Lipton model. In Section 4, the ex-54 perimental result of simulated DNA computing is also 55 given. Conclusions are drawn in Section 5. 56 2. DNA model of computation 57 In Section 2.1, a summary of DNA structure and 58 the Adleman-Lipton model is described in detail. In 59 Section 2.2, the comparison of the Adleman-Lipton 60 model with other models is also introduced. 61 2.1. The Adleman-Lipton model 62 A DNA is a molecule that plays the main role in 63 DNA based computing (Paun et al., 1998). In the bio-64 chemical world of large and small molecules, polymers 65 and monomers, DNA is a polymer, which is strung 66 together from monomers called deoxyribonucleotides. 67 The monomers used for the construction of DNA are 68 deoxyribonucleotides which each deoxyribonucleotide 69 containing three components: a sugar, a phosphate 70 group and a nitrogenous base. This sugar has five car-71 bon atoms-for the sake of reference there is a fixed 72 numbering of them. Because the base also has carbons, 73 to avoid confusion the carbons of the sugar are num-74 bered from 1 to 5 (rather than from 1 to 5). The phos-75 phate group is attached to the 5 carbon, and the base 76 is attached to the 1 carbon. Within the sugar structure 77 there is a hydroxyl group attached to the 3 carbon. 78 Distinct nucleotides are detected only with their 79 bases, which come in two sorts: purines and pyrim-80 In the Adleman-Lipton model (Adleman, 1994; 130 Lipton, 1995), splints were used to correspond to the 131 edges of a particular graph the paths of which repre-132 sented all possible binary numbers. A s it stands, their 133 construction indiscriminately builds all splints that lead 134 to a complete graph. This is to say that hybridization 135 has higher probabilities of errors. Hence, Adleman et al. 136 (Roweis et al., 1999) proposed the sticker-based model, 137 which was an abstract model of molecular computing 138 based on DNAs with a random access memory and a 139 new form of encoding the information, to enhance the 140 Adleman-Lipton model.
A general resolution of intractable problems in polynomial time through DNA Computing
Biosystems, 2016
Based on a set of known biological operations, a general resolution of intractable problems in polynomial time through DNA Computing is presented. This scheme has been applied to solve two NP-Hard problems (Minimization of Open Stacks Problem and Matrix Bandwidth Minimization Problem) and three co-NP-Complete problems (associated with Hamiltonian Path, Traveling Salesman and Hamiltonian Circuit), which have not been solved with this model. Conclusions and open questions concerning the computational capacity of this model are presented, and research topics are suggested.
Active Transport in Biological Computing (preliminary Version) 1.1 an Easy Case
1996
Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimpliied chemical models. In this paper, we reintroduce complexity to the chemical model by considering the eeect problem size has on the initial concentrations of reactants, and the eeect this has in turn on the rate of production and quantity of nal reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires time (n 2) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more diicult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the nal yield also drops exponentially. These issues are not objections to biological computing per se, but rather diiculties to be overcome in its development as a viable technology...
Active Transport in Biological Computing (Preliminary Version)
Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimplified chemical models. In this paper, we reintroduce complexity to the chemical model by considering the effect problem size has on the initial concentrations of reactants, and the effect this has in turn on the rate of production and quantity of final reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires timeOmegaGamma n 2 ) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more difficult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the final yield also drops exponentially. These issues are not objections to biological computing per se, but rather difficulties to be overcome in its deve...