LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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238 Nataˇsa Jonoska, Shiping Liao, and Nadrian C. Seeman 6 Discussion What is the feasibility of this proposed system for a finite state machine? The TX tiles have already been developed and have been successfully self-assembled into a periodic 2D array [13]. Thus, we feel it is a reasonable extension of this previous work to extend this system to prototiles in a Wang tile system. Likewise, we have developed and purified a short double diamond-like system of connected PX-JX2 devices. The experimental problems that we envision are the following: (i) Purifying a long linear system so that we do not have a mixture of input components. We expect that this can be done as done with the short system, using specifically biotinylated molecules on the end members of the input array. If the system is to be run similarly to the PX-JX2 device previously constructed, we will need to remove the biotin groups from the system before operation. (ii) A second problem that we envision is that three sticky ends need to bind, but two sticky ends must be rejected. We have noted above two different methods by which this goal might be achieved. The most obvious form of competition is to make all of the sticky ends imperfect hairpins that require perfect mates to come undone. Experimentation will be required to identify the most effective protocol for this purpose. An iterated computation (or a composition) of the machine can be obtained by allowing third, fourth etc. rows of assembly and hence recursive functions can be obtained. Although theoretically this has already been observed, the proposed way to simulate a transducer provides a much faster computational device than simulating a CA. As shown by examples in Figure 1 and 2 functions like addition and division as well as encoding devices can be simulated with a single row of tiles. However, the theoretical proofs for composition and recursion use transducers that perform a single rewriting step and are not much different from the computational steps simulated by CA. It is a theoretical question to characterize the functions that can be computed by a single application of a transducer. Knowing these functions, we can get a better understanding of the computational complexity of their iterations and compositions and with that a better understanding of the practical power of the proposed method. From another point, it is clear that errors can be minimized with minimal number of prototiles. It is known that the iterations of a four-state gsm provide universal computation [15], but what will be the minimal number of transitions in a transducer whose iterations provide universal computation remains to be determined. With this paper we have presented ideas how to obtain a finite state nanomachine that is programmable, produces an output and is potentially reusable. Success in this objective relies on contributions of multiple disciplines, including biochemistry and information theory. Chemistry and biochemistry provide the infrastructure for dealing with biomolecules such as DNA and RNA. The development of programmable nano-devices provides us with a tool for building new (bio)molecules. Information theory provides the algorithms as well as the understanding of the potential and limitations of these devices as information processing machines. In turn, we expect that information technology will gain
Transducers with Programmable Input by DNA Self-assembly 239 improved molecular based methods that ultimately will prove to be of value for difficult applications and computational problems. Acknowledgements. This research has been supported by grants GM-29554 from the National Institute of General Medical Sciences, N00014-98-1-0093 from the Office of Naval Research, grants DMI-0210844, EIA-0086015, EIA-0074808, DMR- 01138790, and CTS-0103002 from the National Science Foundation, and F30602- 01-2-0561 from DARPA/AFSOR. References 1. L. Adleman, Molecular computation of solutions of combinatorial problems, Science 266 (1994) 1021-1024. 2. Y. Benenson, T. Paz-Elizur, R. Adar, E. Keinan, E. Shapiro: Programmable and autonomous computing machine made of biomolecules, Nature414 (2001) 430-434. 3. R. S. Braich, N. Chelyapov, C. Johnson, P.W.K. Rothemund, L. Adleman, Solution of a 20-variable 3-SAT problem on a DNA Computer, Science 296 (2002) 499-502. 4. J.H. Chen, N.C. Seeman, Synthesis from DNA of a molecule with the connectivity of a cube, Nature 350 (1991) 631-633. 5. N.J. Cutland, Computability, an introduction to recursive function theory, Cambridge University Press, Cambridge 1980. 6. D. Faulhammer, A.R. Curkas, R.J. Lipton, L.F. Landweber, Molecular computation: RNA solution to chess problems, PNAS 97 (2000) 1385-1389. 7. T.J. Fu, N.C. Seeman, DNA double crossover structures, Biochemistry 32 3211- 3220 (1993). 8. T. Head et.al, Computing with DNA by operating on plasmids, BioSystems57 (2000) 87-93. 9. J.E. Hopcroft, J.D. Ullman, Introduction to automata theory, languages and computation, Addison-Wesley 1979. 10. N. Jonoska, P. Sa-Ardyen, N.C. Seeman, Computation by self-assembly of DNA graphs, Genetic Programming and Evolvable Machines 4 (2003) 123-137. 11. N. Jonoska, S. Karl, M. Saito, Three dimensional DNA structures in computing, BioSystems 52 (1999) 143-153. 12. N.R. Kallenbach, R.-I. Ma, N.C. Seeman, An immobile nucleic acid junction constructed from oligonucleotides, Nature305 (1983) 829-831. 13. T.H. LaBean, H. Yan, J. Kopatsch, F. Liu, E. Winfree, J.H. Reif, N.C. Seeman, The construction, analysis, ligation and self-assembly of DNA triple crossover complexes, J.Am.Chem.Soc.122 (2000) 1848-1860. 14. V. Manca, C. Martin-Vide, Gh. Păun, New computing paradigms suggested by DNA computing: computing by carving, BioSystems52 (1999) 47-54. 15. V. Manca, C. Martin-Vide, Gh. Păun, Iterated gsm mappings: a collapsing hierarchy, inJewels are forever, (J. Karhumaki, H. Maurer, Gh. Păun, G. Rozenberg eds.) Springer-Verlag 1999, 182-193. 16. C. Mao, T.H. LaBean, J.H. Reif, N.C. Seeman, Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature407 (2000) 493-496. 17. C. Mao, W. Sun, Z. Shen, N.C. Seeman, A nanomechanical device based on the B-Z transition of DNA, Nature397 (2000) 144-146.
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Lecture Notes in Computer Science 2
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Nata˘sa Jonoska Gheorghe Păun Grz
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Thomas J. Head
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VIII Preface portant to keep in min
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X Table of Contents Formal Properti
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Solving Graph Problems by P Systems
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where Solving Graph Problems by P S
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Writing Information into DNA Masano
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Writing Information into DNA 25 Ham
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Writing Information into DNA 27 Fig
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Writing Information into DNA 29 Dea
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5 Results 5.1 DNA Code for the Engl
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Writing Information into DNA 33 3.
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Writing Information into DNA 35 101
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Balance Machines: Computing = Balan
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+ .. . + Balance Machines: Computin
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x Balance Machines: Computing = Bal
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1 Balance Machines: Computing = Bal
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Eilenberg P Systems with Symbol-Obj
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2 Definitions Definition 1. A strea
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5 Conclusions Eilenberg P Systems w
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Molecular Tiling and DNA Self-assem
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3 Molecular Self-assembly Processes
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8 Hierarchical Tiling Molecular Til
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References Molecular Tiling and DNA
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On Some Classes of Splicing Languag
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ˆxa ˆby ✬ ✩✬ ✩ a b x y
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The Power of Networks of Watson-Cri
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Fixed Point Approach to Commutation
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Here the last one holds if and only
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� � � � � Fixed Point App
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Remarks on Relativisations and DNA
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Splicing Test Tube Systems and Thei
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Splicing Test Tube Systems 141 the
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Splicing Test Tube Systems 143 to a
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Splicing Test Tube Systems 145 6. R
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Splicing Test Tube Systems 147 (c)
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I0 Ai i Splicing Test Tube Systems
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Splicing Test Tube Systems 151 4. J
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Digital Information Encoding on DNA
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DNA-based Cryptography Ashish Gehan
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DNA-based Cryptography 169 concern.
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DNA-based Cryptography 171 The one-
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DNA-based Cryptography 173 of DNA t
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DNA-based Cryptography 175 Fig. 3.
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DNA-based Cryptography 177 the comp
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DNA-based Cryptography 179 can be c
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DNA-based Cryptography 181 4.4 DNA-
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DNA-based Cryptography 183 Fig. 7.
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DNA-based Cryptography 185 offer li
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A DNA Algorithm for the Hamiltonian
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Formal Languages Arising from Gene
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A Proof of Regularity for Finite Sp
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--- ◦ ❄ ⊗ γ ✲ A Proof of R
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The Duality of Patterning in Molecu
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The Duality of Patterning in Molecu
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Membrane Computing: Some Non-standa
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The P Versus NP Problem Through Cel
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Realizing Switching Functions Using
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Realizing Switching Functions Using
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AND Gate Realizing Switching Functi
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NOR Gate Realizing Switching Functi
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Plasmids to Solve #3SAT Rani Siromo
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Plasmids to Solve #3SAT 363 A comme
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Plasmids to Solve #3SAT 365 from th
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Communicating Distributed H Systems
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Proof Communicating Distributed H S
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Books: Publications by Thomas J. He
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LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

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