Abstract
This paper investigates the computational power of a variant of the minimum DNA computation model proposed by Ogihara and Ray. In the variant, two fundamental operations (separation by length and digestion) are dispensed with. To compensate for the loss, the probe arrays are considered as the media for reaction and a wash operation is added to the set of permissible operations. Computation in this model necessarily consists of cycles of five steps: merge, anneal, wash, denature, and wash. It is shown that boolean circuits can be theoretically simulated repetition of the cycle on the same set of four probe arrays.
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References
L. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, 1994.
M. Amos, P. E. Dunne, and A. Gibbons. DNA simulation of boolean circuits. In J. R. Koza, W. Banzhaf, K. Chellapilla, K. D. Deb, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. L. Riolo, editors, Proceedings of 3rd Annual Genetic Programming Conference, pages 679–683, San Francisco, CA, 1998. Morgan Kaufmann.
Y. Benenson, T. Paz-Elizur, R. Adar, E. Keinan, Z. Livneh, and E. Shapiro. Programmable and autonomous computing machine made of biomolecules. Nature, 414:430–434, 2001.
R. S. Braich, N. Chelapov, C. Johnson, P. W. K. Rothemund, and L. Adleman. Solution of a 20-variable 3-SAT problem on a DNA computer. Science, 296:499–502, 2002.
A. Cukras, D. Faulhammer, R. Lipton, and L. Landweber. Chess game: a model for RNA-based computation. In Preliminary Proceedings of 4th DIMACS Workshop on DNA Based Computers, pages 27–37, 1998.
D. R. Dorris, R. Ramakrishnan, D. Trakas, F. Dudzik, R. Belval, C. Zhao, A. Nguyen, M. Domanus, and A. Mazumder. A highly reproducible, linear, and automated sample preparation method for DNA microarrays. Genome Research, 12(6):976–984, 2002.
C. F. Edman, D. E. Raymond, D. J. Wu, E. Tu, R. G. Sosnowski, W. F. Butler, M. Nerenberg, and M. J. Heller. Electric field directed nucleic acid hybridization on microchips. Nucleic Acids Research, 25(24):4907–4914, 1997.
R. Feynman. There’s plenty of room at the bottom. In D. Gilbert, editor, Miniaturization, pages 282–296. Reingold, New York, 1961.
A. Gehani and J. Reif. Microflow bio-molecular computation. Biosystems, 52(1–3):197–216, 1999.
Z. Guo, R. Guigoyle, A. Thiel, R. Wang, and L. Smith. Direct fluorescence analysis of genetic polymorphisms by hybridization with oligonucleotides on glass supports. Nucleic Acids Research, 22:5456–5465, 1994.
H. J. Hoover, M. M. Klawe, and N. J. Pippenger. Bounding fan-out in logical networks. Journal of the Association for Computing Machinery, 31(1):13–18, 1984.
Y. Huang, K. L. Ewalt, M. Tirado, R. Haigis, A. Forster, D. Ackley, M. J. Heller, J. P. O’Connell, and M. Krihak. Electric manipulation of bioparticles and macromolecules on microfabricated electrodes. Analytical Chemistry, 73(7):1549–59, 2001.
J. B. Lamture, K. L. Beattie, B. E. Burke, M. D. Eggers, D. J. Ehrlich, R. Fowler, M. A. Hollis, B. B. Kosicki R. K. Reich, and S. R. Smith. Direct detection of nucleic acid hybridization on the surface of a charge coupled device. Nucleic Acids Research, 22(11):2121–2125, 1994.
K. Lindroos, U. Liljedahl, M. Raitio, and A.-C. Syvanen. Minisequencing on oligonucleotide microarrays: comparison of immobilization chemistries. Nucleic Acids Research, 29:e69, 2001.
R. Lipton. DNA solutions of hard computational problems. Science, 268:542–545, 1995.
Q. Liu, L. Wang, A. G. Frutos, R. M. Corn, and L. M. Smith. DNA computing on surfaces. Nature, 403:175–178, 2000. January, 13.
M. Ogihara. Relating the minimum model for DNA computation and Boolean circuits. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, editors, Genetic and Evolutionary Computation Conference, pages 1817–1822. Morgan Kaufmann Publishers, San Francisco, CA, 1999.
M. Ogihara and A. Ray. A DNA-based self-propagating algorithm for solving bounded-fan-in Boolean circuits. In J. R. Koza, W. Banzhaf, K. Chellapilla, K. D. Deb, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. L. Riolo, editors, Genetic Programming 1998: Proceedings of the Third Annual Conference, pages 725–730, San Francisco, CA, July 1998. Morgan Kaufman.
M. Ogihara and A. Ray. The minimum DNA model and its computational power. In Unconventional Models of Computation, pages 309–322. Springer, Singapore, 1998.
M. Ogihara and A. Ray. Biomolecular computing-recent theoretical and experimental advances. SIGACT News, 30(2):22–30, 1999.
M. Ogihara and A. Ray. Simulating boolean circuits on DNA computers. Algorithmica, 25:239–250, 1999.
M. Ogihara, A. Ray, and K. Smith. Biomolecular computing-a shape of computation to come. SIGACT News, 28(3):2–11, 1997.
B. W. Pontius and P. Berg. Rapid renaturation of complementary DNA strands mediated by cationic detergents: A role for high-probability binding domains in enhancing the kinetics of molecular assembly processes. Proceedings of the National Academy of Science, 88:8237–8241, 1991.
R. Radtkey, L. Feng, M. Muralhidar, M. Duhon, D. Canter, D. DiPierro, S. Fallon, E. Tu, K. McElfresh, M. Nerenberg, and R. G. Sosnowski. Rapid, high fidelity analysis of simple sequence repeats on an electronically active DNA microchip. Nucleic Acids Research, 28(7):E17, 2000.
R. Ramakrishnan, D. Dorris, A. Lublinsky, A. Nguyen, M. Domanus, A. Prokhorova, L. Gieser, E. Touma, R. Lockner, and M. Tata. Development and use of analytical tools in the dissection and optimization of microarray performance. Nucleic Acids Research, 30:E30, 2002.
J. H. Reif. Parallel biomolecular computation: methods and simulations. Algorithmica, 25:142–175, 1999.
P. Rothemund. A DNA and restriction enzyme implementation of Turing machines. In R. Lipton and E. Baum, editors, DNA Based Computers, pages 75–119. The American Mathematical Society DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 27, 1996.
S. Roweis, E. Winfree, R. Burgoyne, N. Chelapov, M. Goodman, P. Rothemund, and L. Adleman. A sticker based model for DNA computation. In L. Landweber and E. Baum, editors, DNA Based Computers II, pages 1–30. The American Mathematical Society DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 44, 1999.
J. Sakamoto, H. Gouzu, K. Komiya, D. Kiga, S. Yokoyama, T. Yokomori, and M. Hagiya. Molecular computation by DNA hairpin formation. Science, 288:1223–1226, 2000.
M. Schena, D. Shalon, R. w. Davis, and P. O. Brown. Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science, 270:467–470, 1995.
J. Watson, M. Gilman, J. Witkowski, and M. Zoller. Recombinant DNA. Scientific American Books, New York, NY, 2nd edition, 1992.
J. Watson, N. Hopkins, J. Roberts, J. Steiz, and A. Weiner. Molecular Biology of the Gene. Benjamin-Cummings, Menlo Part, CA, 4 edition, 1987.
E. Winfree, F. Liu, L. A. Wenzler, and N. C. Seeman. Design and self-assembly of two-dimensional DNA crystals. Nature, 394:539–544, 1998.
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Ogihara, M., Ray, A. (2002). The Minimum-Model DNA Computation on a Sequence of Probe Arrays. In: Unconventional Models of Computation. UMC 2002. Lecture Notes in Computer Science, vol 2509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45833-6_4
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DOI: https://doi.org/10.1007/3-540-45833-6_4
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