Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Molecular logic and computing

Nature Nanotechnology volume 2, pages 399–410 (2007)Cite this article

Abstract

Molecular substrates can be viewed as computational devices that process physical or chemical 'inputs' to generate 'outputs' based on a set of logical operators. By recognizing this conceptual crossover between chemistry and computation, it can be argued that the success of life itself is founded on a much longer-term revolution in information handling when compared with the modern semiconductor computing industry. Many of the simpler logic operations can be identified within chemical reactions and phenomena, as well as being produced in specifically designed systems. Some degree of integration can also be arranged, leading, in some instances, to arithmetic processing. These molecular logic systems can also lend themselves to convenient reconfiguring. Their clearest application area is in the life sciences, where their small size is a distinct advantage over conventional semiconductor counterparts. Molecular logic designs aid chemical (especially intracellular) sensing, small object recognition and intelligent diagnostics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Chemical reactions and computational processes.
Figure 2: Boolean binary logic operations: truth tables, symbols and algebraic expressions.
Figure 3: A molecular logic gate based on photoinduced electron transfer.
Figure 4: A molecular logic gate based on internal charge transfer.
Figure 5: Molecular logic gates based on enzyme cascades.
Figure 6: Integrated molecular logic gates based on colour-forming reactions.
Figure 7: A moleculator based on fluorescein dye.
Figure 8: Molecular computational identification: materials and operation.
Figure 9: 'Lab-on-a-molecule' and its operation.

Similar content being viewed by others

References

  1. Raymo, F. M. Digital processing and communication with molecular switches. Adv. Mater. 14, 401–414 (2002).

    CAS  Google Scholar 

  2. Margulies, D. Felder, C. E., Melman, G. & Shanzer, A. A molecular keypad lock: a photochemical device capable of authorizing password entries. J. Am. Chem. Soc. 129, 347–354 (2007).

    CAS  Google Scholar 

  3. Boole, G. An Investigation of the Laws of Thought (Dover, New York, 1958).

    Google Scholar 

  4. Malvino, A. P. & Brown, J. A. Digital Computer Electronics 3rd edn (Glencoe, New York, 1993).

    Google Scholar 

  5. Bray, D. Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995).

    CAS  Google Scholar 

  6. Williams, K. A. Three-dimensional structure of the ion-coupled transport protein NhaA. Nature 403, 112–115 (2000).

    CAS  Google Scholar 

  7. Lehn, J.-M. Supramolecular Chemistry (VCH, Weinheim, 1995).

    Google Scholar 

  8. Collier, C. P. et al. Electronically configurable molecular-based logic gates. Science 285, 391–394 (1999).

    CAS  Google Scholar 

  9. Amir, R. J., Popkov, M., Lerner, R. A., Barbas III, C. F. & Shabat, D. Prodrug activation gated by a molecular “OR” logic trigger. Angew. Chem. Int. Edn 44, 4378–4381 (2005).

    CAS  Google Scholar 

  10. Grynkiewicz, G., Poenie, M. & Tsien, R. Y. A new generation of Ca2+ indicators with greatly improved fluorescence properties. J. Biol. Chem. 260, 3440–3450 (1985).

    CAS  Google Scholar 

  11. Holman, M. W. & Adams, D. M. Using single-molecule fluorescence spectroscopy to study electron transfer. ChemPhysChem 5, 1831–1836 (2004).

    CAS  Google Scholar 

  12. Uchiyama, S., McClean, G. D., Iwai, K. & de Silva, A. P. Membrane media create small nanospaces for molecular computation. J. Am. Chem. Soc. 127, 8920–8921 (2005).

    CAS  Google Scholar 

  13. Drexler, K. E. Engines of Creation (Anchor Press, New York, 1986).

    Google Scholar 

  14. de Silva, A. P., Gunaratne, H. Q. N. & McCoy, C. P. A molecular photoionic AND gate based on fluorescent signalling. Nature 364, 42–44 (1993).

    Google Scholar 

  15. Bissell, R. A. et al. Fluorescent PET (photoinduced electron transfer) sensors. Top. Curr. Chem. 168, 223–264 (1993).

    CAS  Google Scholar 

  16. Komura, T., Niu, G. Y., Yamaguchi, T. & Asano, M. Redox and ionic-binding switched fluorescence of phenosafranine and thionine included in Nafion® films. Electrochim. Acta 48, 631–639 (2003).

    CAS  Google Scholar 

  17. Szaciłowski, K., Macyk, W. & Stochel, G. Light-driven OR and XOR programmable chemical logic gates. J. Am. Chem. Soc. 128, 4550–4551 (2006).

    Google Scholar 

  18. Biancardo, M., Bignozzi, C., Doyle, H. & Redmond, G. A potential and ion switched molecular photonic logic gate. Chem. Commun. 3918–3920 (2005).

  19. Matsui, J., Mitsuishi, M., Aoki, A. & Miyashita, T. Molecular optical gating devices based on polymer nanosheets assemblies. J. Am. Chem. Soc. 126, 3708–3709 (2004).

    CAS  Google Scholar 

  20. Yurke, B., Mills Jr., A. P. & Cheng, S. L. DNA implementation of addition in which the input strands are separate from the operator strands. Biosystems 52, 165–174 (1999).

    CAS  Google Scholar 

  21. Schneider, H.-J., Tianjun, L., Lomadze, N. & Palm, B. Cooperativity in a chemomechanical polymer: a chemically induced macroscopic logic gate. Adv. Mater. 16, 613–615 (2004).

    CAS  Google Scholar 

  22. Okamoto, A., Tanaka, K. & Saito, I. DNA logic gates. J. Am. Chem. Soc. 126, 9458–9463 (2004).

    CAS  Google Scholar 

  23. Ashkenasy, G. & Ghadiri, M. R. Boolean logic functions of a synthetic peptide network. J. Am. Chem. Soc. 126, 11140–11141 (2004).

    CAS  Google Scholar 

  24. Blittersdorf, R., Müller, J. & Schneider, F. W. Chemical visualization of Boolean functions: a simple chemical computer. J. Chem. Educ. 72, 760–763 (1995).

    CAS  Google Scholar 

  25. Raymo, F. M. & Giordani, S. All-optical processing with molecular switches. Proc. Natl. Acad. Sci. USA 99, 4941–4944 (2002).

    CAS  Google Scholar 

  26. Szaciłowski, K. Molecular logic gates based on pentacyanoferrate complexes: from simple gates to three-dimensional logic systems. Chem. Eur. J. 10, 2520–2528 (2004).

    Google Scholar 

  27. de Silva, A. P. et al. Signaling recognition events with fluorescent sensors and switches. Chem. Rev. 97, 1515–1566 (1997).

    CAS  Google Scholar 

  28. Balzani, V., Credi, A. & Venturi, M. Molecular Devices and Machines (Wiley-VCH, Weinheim, 2003).

    Google Scholar 

  29. de Silva, A. P. & McClenaghan, N. D. Molecular-scale logic gates. Chem. Eur. J. 10, 574–586 (2004).

    Google Scholar 

  30. de Silva, A. P. & McClenaghan, N. D. Simultaneously multiply-configurable or superposed molecular logic systems composed of ICT (internal charge transfer) chromophores and fluorophores integrated with one- or two-ion receptors. Chem. Eur. J. 8, 4935–4945 (2002).

    Google Scholar 

  31. de Silva, A. P. & McClenaghan, N. D. Proof-of-principle of molecular-scale arithmetic. J. Am. Chem. Soc. 122, 3965–3966 (2000).

    CAS  Google Scholar 

  32. Zhou, Y., Zhang, D., Zhang, Y., Tang, Y. & Zhu, D. Tuning the CD spectrum and optical rotation value of a new binaphthalene molecule with two spiropyran units: mimicking the function of a molecular “AND” logic gate and a new chiral molecular switch. J. Org. Chem. 70, 6164–6170 (2005).

    CAS  Google Scholar 

  33. Tamaki, T. & Ichimura, K. Photochromic chelating spironaphthoxazines. J. Chem. Soc., Chem. Commun. 1477–1479 (1989).

  34. Gobbi, L., Seiler, P. & Diederich, F. A novel three-way chromophoric molecular switch: pH and light controllable switching cycles. Angew. Chem. Int. Edn 38, 674–678 (1999).

    CAS  Google Scholar 

  35. Wojtyk, J. T. C., Kazmaier, P. M. & Buncel, E. Effects of metal ion complexation on the spiropyran–merocyanine interconversion: development of a thermally stable photo-switch. Chem. Commun. 1703–1704 (1998).

  36. Raymo, F. M. & Giordani, S. Multichannel digital transmission in an optical network of communicating molecules. J. Am. Chem. Soc. 124, 2004–2007 (2002).

    CAS  Google Scholar 

  37. Baron, R., Lioubashevski, O., Katz, E., Niazov, T. & Willner, I. Two coupled enzymes perform in parallel the 'AND' and 'InhibAND' logic gate operations. Org. Biomol. Chem. 4, 989–991 (2006).

    CAS  Google Scholar 

  38. Baron, R., Lioubashevski, O., Katz, E., Niazov, T. & Willner, I. Elementary arithmetic operations by enzymes: a model for metabolic pathway based computing. Angew. Chem. Int. Edn 45, 1572–1576 (2006).

    CAS  Google Scholar 

  39. Zauner, K.-P. & Conrad, M. Enzymatic Computing. Biotechnol. Prog. 17, 553–559 (2001).

    CAS  Google Scholar 

  40. Deonarine, A. S., Clark, S. M. & Konermann, L. Implementation of a multifunctional logic gate based on folding/unfolding transitions of a protein. Future Gener. Comp. Sy. 19, 87–97 (2003).

    Google Scholar 

  41. Sivan, S., Tuchman, S. & Lotan, N. A biochemical logic gate using an enzyme and its inhibitor. Part II: The logic gate. BioSystems 70, 21–33 (2003).

    CAS  Google Scholar 

  42. Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994).

    CAS  Google Scholar 

  43. Stojanovic, M. N., Mitchell, T. E. & Stefanovic, D. Deoxyribozyme-based logic gates. J. Am. Chem. Soc. 124, 3555–3561 (2002).

    CAS  Google Scholar 

  44. Hod, O., Baer, R. & Rabani, E. A parallel electromagnetic molecular logic gate. J. Am. Chem. Soc. 127, 1648–1649 (2005).

    CAS  Google Scholar 

  45. Tour, J. M. in Stimulating Concepts in Chemistry (eds. Vögtle, F. Stoddart, J. F. & Shibasaki, M.) 237–253 (Wiley-VCH, Weinheim, 2000).

    Google Scholar 

  46. Kele, P., Orbulescu, J., Gawley, R. E. & Leblanc, R. M. Spectroscopic detection of saxitoxin: An alternative to mouse bioassay. Chem. Commun. 1494–1496 (2006).

  47. Hall, M. J., Allen, L. T. & O'Shea, D. F. PET modulated fluorescent sensing from the BF2 chelated azadipyrromethene platform. Org. Biomol. Chem. 4, 776–780 (2006).

    CAS  Google Scholar 

  48. Kwon, J. Y. et al. A highly selective fluorescent chemosensor for Pb2+. J. Am. Chem. Soc. 127, 10107–10111 (2005).

    CAS  Google Scholar 

  49. Yoon, S., Albers, A. E., Wong, A. P. & Chang, C. J. Screening mercury levels in fish with a selective fluorescent chemosensor. J. Am. Chem. Soc. 127, 16030–16031 (2005).

    CAS  Google Scholar 

  50. Banthia, S. & Samanta, A. A two-dimensional chromogenic sensor as well as fluorescence inverter: selective detection of copper(II) in aqueous medium. New J. Chem. 29, 1007–1010 (2005).

    CAS  Google Scholar 

  51. Dale, T. J. & Rebek Jr., J. Fluorescent sensors for organophosphorus nerve agent mimics. J. Am. Chem. Soc. 128, 4500–4501 (2006).

    CAS  Google Scholar 

  52. Bencic-Nagale, S., Sternfeld, T. & Walt, D. R. Microbead chemical switches: An approach to detection of reactive organophosphate chemical warfare agent vapors. J. Am. Chem. Soc. 128, 5041–5048 (2006).

    CAS  Google Scholar 

  53. de Silva, A. P., Gunaratne, H. Q. N. & Gunnlaugsson, T. Fluorescent PET (photoinduced electron transfer) reagents for thiols. Tetrahedron Lett. 39, 5077–5080 (1998).

    CAS  Google Scholar 

  54. Cooper, C. R. & James, T. D. Selective D-glucosamine hydrochloride fluorescence signalling based on ammonium cation and diol recognition. Chem. Commun. 1419–1420 (1997).

  55. Fages, F. et al. Synthesis and fluorescence emission properties of a bis-anthracenyl macrotricyclic ditopic receptor. Crystal structure of its dinuclear rubidium cryptate. J. Chem. Soc., Chem. Commun. 655–658 (1990).

  56. de Silva, A. P. & Sandanayake, K. R. A. S. Fluorescence “off-on” signalling upon linear recognition and binding of α,ω-alkanediyldiammonium ions by 9,10-bis{(1-aza-4,7,10,13,16-pentaoxacyclooctadecyl)methyl}anthracene. Angew. Chem. Int. Edn Engl. 29, 1173–1175 (1990).

    Google Scholar 

  57. Misumi, S. Recognitory coloration of cations with chromoacerands. Top. Curr. Chem. 165, 163–192 (1993).

    CAS  Google Scholar 

  58. Secor, K., Plante, J., Avetta, C. & Glass, T. Fluorescent sensors for diamines. J. Mater. Chem. 15, 4073–4077 (2005).

    CAS  Google Scholar 

  59. Zhao, J., Fyles, T. M. & James, T. D. Chiral binol-bisboronic acid as fluorescence sensor for sugar acids. Angew. Chem. Int. Edn 43, 3461–3464 (2004).

    CAS  Google Scholar 

  60. James, T. D., Sandanayake, K. R. A. S. & Shinkai, S. Chiral discrimination of monosaccharides using a fluorescent molecular sensor. Nature 374, 345–347 (1995).

    CAS  Google Scholar 

  61. Gray Jr., C. W. & Houston, T. A. Boronic acid receptors for α-hydroxycarboxylates: high affinity of Shinkai's glucose receptor for tartrate. J. Org. Chem. 67, 5426–5428 (2002).

    CAS  Google Scholar 

  62. He, J. X. et al. Metal-free silicon-molecule-nanotube testbed and memory device. Nature Mater. 5, 63–68 (2006).

    CAS  Google Scholar 

  63. de Silva, A. P. et al. Integration of logic functions and sequential operation of gates at the molecular-scale. J. Am. Chem. Soc. 121, 1393–1394 (1999).

    CAS  Google Scholar 

  64. Mu, L. X., Wang, Y., Zhang, Z. & Jin, W. J. Room temperature phosphorescence pH switch based on photo-induced electron transfer. Chinese Chem. Lett. 15, 1131–1134 (2004).

    CAS  Google Scholar 

  65. de Sousa, M., de Castro, B., Abad, S., Miranda, M. A. & Pischel, U. A molecular tool kit for the variable design of logic operations (NOR, INH, EnNOR). Chem. Commun. 2051–2053 (2006).

  66. Cheng, P.-N., Chiang, P.-T. & Chiu, S.-H. A switchable macrocycle-clip complex that functions as a NOR logic gate. Chem. Commun. 1285–1287 (2005).

  67. Giordani, S., Cejas, M. A. & Raymo, F. M. Photoinduced proton exchange between molecular switches. Tetrahedron 60, 10973–10981 (2004).

    CAS  Google Scholar 

  68. Margulies, D., Melman, G. & Shanzer, A. Fluorescein as a model molecular calculator with reset capability. Nature Mater. 4, 768–771 (2005).

    CAS  Google Scholar 

  69. Shiraishi, Y., Tokitoh, Y. & Hirai, T. A fluorescent molecular logic gate with multiply-configurable dual outputs. Chem. Commun. 5316–5318 (2005).

  70. Alves, S. et. al. Open-chain polyamine ligands bearing an anthracene unit–chemosensors for logic operations at the molecular level. Eur. J. Inorg. Chem. 405–412 (2001).

    Google Scholar 

  71. Callan, J. F., de Silva, A. P. & McClenaghan, N. D. Switching between molecular switch types by module rearrangement: Ca2+-enabled, H+-driven 'off-on-off', H+-driven YES and PASS 0 as well as H+, Ca2+-driven AND logic operations. Chem. Commun. 2048–2049 (2004).

  72. Qu, D.-H., Wang, Q.-C. & Tian, H. A half adder based on a photochemically driven [2]rotaxane. Angew. Chem. Int. Edn 44, 5296–5299 (2005).

    CAS  Google Scholar 

  73. Andréasson, J. et al. Molecule-based photonically switched half-adder. J. Am. Chem. Soc. 126, 15926–15927 (2004).

    Google Scholar 

  74. Lederman, H., Macdonald, J., Stefanovic, D. & Stojanovic, M. N. Deoxyribozyme-based three-input logic gates and construction of a molecular full adder. Biochemistry 45, 1194–1199 (2006).

    CAS  Google Scholar 

  75. Guo, X., Zhang, D., Zhang, G. & Zhu, D. Monomolecular logic: “half-adder” based on multistate/multifunctional photochromic spiropyrans. J. Phys. Chem. B 108, 11942–11945 (2004).

    CAS  Google Scholar 

  76. Stojanovic, M. N. & Stefanovic, D. A deoxyribozyme-based molecular automaton. Nature Biotechnol. 21, 1069–1074 (2003).

    CAS  Google Scholar 

  77. Wild, U. P., Bernet, S., Kohler, B. & Renn, A. From supramolecular photochemistry to the molecular computer. Pure Appl. Chem. 64, 1335–1342 (1992).

    CAS  Google Scholar 

  78. Margulies, D., Melman, G. & Shanzer, A. A molecular full-adder and full-subtractor, an additional step toward a moleculator. J. Am. Chem. Soc. 128, 4865–4871 (2006).

    CAS  Google Scholar 

  79. Tour, J. M. Molecular electronics. Synthesis and testing of components. Acc. Chem. Res. 33, 791–804 (2000).

    CAS  Google Scholar 

  80. Williams, R. S., quoted in Ball, P. Chemistry meets computing. Nature 406, 118–120 (2000).

    Google Scholar 

  81. Cox, J. C., Cohen, D. S. & Ellington, A. D. The complexities of DNA computation. Trends Biotechnol. 17, 151–154 (1999).

    CAS  Google Scholar 

  82. Lam, K. S. et al. A new type of synthetic peptide library for identifying ligand-binding activity. Nature 354, 82–84 (1991).

    CAS  Google Scholar 

  83. Furka, Á., Sebestyén, F., Asgedom, M. & Dibó, G. General-method for rapid synthesis of multicomponent peptide mixtures. Int. J. Pept. Prot. Res. 37, 487–493 (1991).

    CAS  Google Scholar 

  84. Shepard, S. RFID: Radio Frequency Identification (McGraw-Hill, New York, 2005).

    Google Scholar 

  85. Nicolaou, K. C., Xiao, X.-Y., Parandoosh, Z., Senyei, A. & Nova, M. P. Radiofrequency encoded combinatorial chemistry. Angew. Chem. Int. Edn Engl. 34, 2289–2291 (1995).

    CAS  Google Scholar 

  86. Moran, E. J. et al. Radio frequency tag encoded combinatorial library method for discovery of tripeptide-substituted cinnamic acid inhibitors of the protein tyrosine phosphatase PTP1B. J. Am. Chem. Soc. 117, 10787–10788 (1995).

    CAS  Google Scholar 

  87. Walt, D. R. Bead-based fiber-optic arrays. Science 287, 451–452 (2000).

    CAS  Google Scholar 

  88. Battersby, B. J., Lawrie, G. A., Johnston, A. P. R. & Trau, M. Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery. Chem. Commun. 1435–1441 (2002).

  89. de Silva, A. P., James, M. R., McKinney, B. O. F., Pears, P. A. & Weir, S. M. Molecular computational elements encode large populations of small objects. Nature Mater. 5, 787–790 (2006).

    Google Scholar 

  90. Hayes, B. Third base. Am. Scientist 89, 490–494 (2001).

    Google Scholar 

  91. Callan, J. F., de Silva, A. P., Ferguson, J., Huxley, A. J. M. & O'Brien, A. M. Fluorescent photoionic devices with two receptors and two switching mechanisms: applications to pH sensors and implications for metal ion detection. Tetrahedron 60, 11125–11131 (2004).

    CAS  Google Scholar 

  92. Magri, D. C., Brown, G. J., McClean, G. D. & de Silva, A. P. Communicating chemical congregation: a molecular AND logic gate with three chemical inputs as a “lab-on-a-molecule” prototype. J. Am. Chem. Soc. 128, 4950–4951 (2006).

    CAS  Google Scholar 

  93. Gunnlaugsson, T., Lee, T. C. & Parkesh, R. A highly selective and sensitive fluorescent PET (photoinduced electron transfer) chemosensor for Zn(II). Org. Biomol. Chem. 1, 3265–3267 (2003).

    CAS  Google Scholar 

  94. Lankshear, M. D., Cowley, A. R. & Beer, P. D. Cooperative AND receptor for ion-pairs. Chem. Commun. 612–614 (2006).

  95. Koskela, S. J. M., Fyles, T. M. & James, T. D. A ditopic fluorescent sensor for potassium fluoride. Chem. Commun. 945–947 (2005).

  96. Saghatelian, A., Völcker, N. H., Guckian, K. M., Lin, V. S.-Y. & Ghadiri, M. R. DNA-based photonic logic gates: AND, NAND, and INHIBIT. J. Am. Chem. Soc. 125, 346–347 (2003).

    CAS  Google Scholar 

  97. Gust, D., Moore, T. A. & Moore, A. L. Molecular switches controlled by light. Chem. Commun. 1169–1178 (2006).

  98. Pina, F. et al. Multistate/multifunctional molecular-level systems: light and pH switching between the various forms of a synthetic flavylium salt. Chem. Eur. J. 4, 1184–1191 (1998).

    CAS  Google Scholar 

  99. Uchiyama, S., Kawai, N., de Silva, A. P. & Iwai, K. Fluorescent polymeric AND logic gate with temperature and pH as inputs. J. Am. Chem. Soc. 126, 3032–3033 (2004).

    CAS  Google Scholar 

  100. Leigh, D. A. et al. Patterning through controlled submolecular motion: rotaxane-based switches and logic gates that function in solution and polymer films. Angew. Chem. Int. Edn 44, 3062–3067 (2005).

    CAS  Google Scholar 

  101. Penchovsky, R. & Breaker, R. R. Computational design and experimental validation of oligonucleotide-sensing allosteric ribozymes. Nature Biotechnol. 23, 1424–1433 (2005).

    CAS  Google Scholar 

  102. Remacle, F., Speiser, S. & Levine, R. D. Intermolecular and intramolecular logic gates. J. Phys. Chem. B 105, 5589–5591 (2001).

    CAS  Google Scholar 

  103. Remacle, F., Weinkauf, R. & Levine, R. D. Molecule-based photonically switched half and full adder. J. Phys. Chem. A 110, 177–184 (2006).

    CAS  Google Scholar 

Download references

Acknowledgements

We are grateful for support from Avecia, The Daiwa Anglo-Japanese Foundation, DEL, EPSRC, Invest NI (RTD COE 40), Japan Society for the Promotion of Science and Procter and Gamble. This paper is dedicated to Fraser Stoddart.

Author information

Authors and Affiliations

  1. School of Chemistry and Chemical Engineering, Queen's University, Belfast, BT9 5AG, Northern Ireland

    A. Prasanna de Silva

  2. Graduate School of Pharmaceutical Sciences, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Seiichi Uchiyama

Authors
  1. A. Prasanna de Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seiichi Uchiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Silva, A., Uchiyama, S. Molecular logic and computing. Nature Nanotech 2, 399–410 (2007). https://doi.org/10.1038/nnano.2007.188

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2007.188

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing