A Framework for Modeling DNA Based Molecular Systems

  • Sudheer Sahu
  • Bei Wang
  • John H. Reif
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4287)


In this paper, we propose a framework for a discrete event simulator for simulating the DNA based nano-robotical systems. We describe a physical model that captures the conformational changes of the solute molecules. We also present methods to simulate various chemical reactions due to the molecular collisions, including hybridization, dehybridization and strand displacement. The feasibility of such a framework is demonstrated by some preliminary results.


Collision Detection Physical Simulation Hepatitis Delta Virus Strand Displacement Brownian Dynamic Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Alberti, P., Mergny, J.L.: DNA duplex-quadruplex exchange as the basis for a nanomolecular machine. Proc. Natl. Acad. Sci. USA 100, 1569–1573 (2003)CrossRefGoogle Scholar
  3. 3.
    Allison, S.A., Mazur, S.: Modeling the free solution electrophoretic mobility of short dna fragments. Biopolymers 46, 359–373 (1998)CrossRefGoogle Scholar
  4. 4.
    Allison, S.A., McCammon, J.A.: Multistep brownian dynamics: application to short wormlike chains. Biopolymers 23, 363–375 (1984)CrossRefGoogle Scholar
  5. 5.
    Aragon, S.R., Pecora, R.: Dynamics of wormlike chains. Macromolecules 18, 1868 (1985)CrossRefGoogle Scholar
  6. 6.
    Arridge, R.G.C.: An introduction to polymer mechanics (1985)Google Scholar
  7. 7.
    Arteca, G.A., Edvinsson, T., Elvingson, C.: Compaction of grafted wormlike chains under variable confinement. Phys. Chem. Chem. Phys. 3, 3737–3741 (2001)CrossRefGoogle Scholar
  8. 8.
    Maier, B., Bensimon, B.D., Croquette, V.: Replication by a single dna polymerase of a stretched single-stranded dna. Proc. Natl. Acad. Sci. U.S.A. 97(22), 12002–12007 (2000)CrossRefGoogle Scholar
  9. 9.
    Benenson, Y., Adar, R., Paz-Elizur, T., Livneh, Z., Shapiro, E.: DNA molecule provides a computing machine with both data and fuel. Proc. Natl. Acad. Sci. USA 100, 2191–2196 (2003)CrossRefGoogle Scholar
  10. 10.
    Benenson, Y., Gil, B., Ben-Dor, U., Adar, R., Shapiro, E.: An autonomous molecular computer for logical control of gene expression. Nature 429, 423–429 (2004)CrossRefGoogle Scholar
  11. 11.
    Benenson, Y., Paz-Elizur, T., Adar, R., Keinan, E., Livneh, Z., Shapiro, E.: Programmable and autonomous computing machine made of biomolecules. Nature 414, 430–434 (2001)CrossRefGoogle Scholar
  12. 12.
    Biswas, I., Yamamoto, A., Hsieh, P.: Branch migration through dna sequence heterology. J. Mol. Bio. (1998)Google Scholar
  13. 13.
    Bois, J.S., Venkataraman, S., Choi, H.M.T., Spakowitz, A.J., Wang, G., Pierce, N.A.: Topological constraints in nucleic acid hybridization kinetics. Nucleic Acids Research 33(13), 4090–4095 (2005)CrossRefGoogle Scholar
  14. 14.
    Bouchiat, C., Wang, M.D., Allemand, J., Strick, T., Block, S.M., Croquette, V.: Estimating the persistence length of a worm-like chain molecules from force-extension measurements. Biophys. J. 76, 409 (1999)CrossRefGoogle Scholar
  15. 15.
    Bustamante, C., Marko, J.F., Siggia, E.D., Smith, S.: Entropic elasticity of lambda-phage dna mechanics. Science 265, 1599 (1994)CrossRefGoogle Scholar
  16. 16.
    Bustamante, C., Smith, S., Liphardt, J., Smith, D.: Single-molecule studies of dna mechanics. Current Opinion in Structural Biology 10, 279 (2000)CrossRefGoogle Scholar
  17. 17.
    Butler, J.E., Shaqfeh, E.S.G.: Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multi-body hydrodynamic interaction. Journal of Chemical Physics 122(014901) (2005)Google Scholar
  18. 18.
    Carri, G.A., Marucho, M.: Statistical mechanics of worm-like polymers from a new generating function. J. Chem. Phys. 121(12), 6064–6077 (2004)CrossRefGoogle Scholar
  19. 19.
    Chelyapov, N., Brun, Y., Gopalkrishnan, M., Reishus, D., Shaw, B., Adleman, L.: DNA triangles and self-assembled hexagonal tilings. J. Am. Chem. Soc. 126, 13924–13925 (2004)CrossRefGoogle Scholar
  20. 20.
    Chen, Y., Mao, C.: Putting a brake on an autonomous DNA nanomotor. J. Am. Chem. Soc. 126, 8626–8627 (2004)CrossRefGoogle Scholar
  21. 21.
    Chen, Y., Wang, M., Mao, C.: An autonomous DNA nanomotor powered by a DNA enzyme. Angew. Chem. Int. Ed. 43, 3554–3557 (2004)CrossRefGoogle Scholar
  22. 22.
    Cocco, S., Marko, J.F., Monasson, R.: Theoretical models for single-molucule dna and rna experiments: from elasticity to unzipping. In: CRAS, special issue dedicated to Single Molecule Experiments (to appear, 2002)Google Scholar
  23. 23.
    Desruisseaux, C., Long, D., Drouin, G., Slater, G.W.: Electrophoresis of composite molecular objects. 1. relation between friction, charge and ionic strength in free solution. Macromolecules 34, 44–59 (2001)CrossRefGoogle Scholar
  24. 24.
    Dessinges, M.N., Maier, B., Zhang, Y., Peliti, M., Bensimon, D., Croquette, V.: Stretching single stranded dna, a model polyelectrolyte. Phys. Rev. Lett. 89, 248102 (2002)CrossRefGoogle Scholar
  25. 25.
    Dimitrakopoulos, P.: Stress and configuration relaxation of an initially straight flexible polymer. J. Fluid Mech. 513, 265–286 (2004)MATHCrossRefGoogle Scholar
  26. 26.
    Doyle, P.S., Underhill, P.T.: Brownian dynamics simulations of polymers and soft matter. In: Yip, S. (ed.) Handbook of Materials Modeling, pp. 2619–2630 (2005)Google Scholar
  27. 27.
    Dirks, R.M., Bois, J.S., Schaeffer, J.M., Winfree, E., Pierce, N.A.: Thermodynamic analysis of interacting nucleic acid strands. In: SIAM Rev. (in press)Google Scholar
  28. 28.
    Feng, L., Park, S.H., Reif, J.H., Yan, H.: A two-state DNA lattice switched by DNA nanoactuator. Angew. Chem. Int. Ed. 42, 4342–4346 (2003)CrossRefGoogle Scholar
  29. 29.
    Fixman, M., Kovac, J.: Polymer conformation statistics iii: Modified gaussian models of the stiff chains. J. Chem. Phys. 58, 1564–1568 (1973)CrossRefGoogle Scholar
  30. 30.
    Flamm, C., Fontana, W., Hofacker, I.L., Schuster, P.: RNA folding at elementary step resolution. RNA 6(3), 325–338 (2000)CrossRefGoogle Scholar
  31. 31.
    Fournier, J.B.: Wormlike chain or tense string? a question of resolution. Continuum Mechanical Thermodynamics 14, 241 (2002)MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Frank-Kamenetskii, M.D.: Biophysics of dna molecule. Phys. Rep. 288, 13–60 (1997)CrossRefGoogle Scholar
  33. 33.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)CrossRefGoogle Scholar
  34. 34.
    Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001)CrossRefGoogle Scholar
  35. 35.
    Hartemink, A.J., Gifford, D.K.: Thermodynamics simulation of deoxyoligonucleotide hybridization for dna computation (1997)Google Scholar
  36. 36.
    Heath, P.J., Gebe, J.A., Allison, S.A., Schurr, J.M.: Comparison of analytical theory with brownian dynamics simulations for small linear and circular dnas. Macromolecules 29, 3583 (1996)CrossRefGoogle Scholar
  37. 37.
    Hur, J.S., Shaqfeh, E.S.G.: Brownian dynamics simulations of single dna molecule in shear flow. J. Rheol. 44(4), 713–742 (2000)CrossRefGoogle Scholar
  38. 38.
    Isambert, H., Siggia, E.D.: Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. Proc. Natl. Acad. Sci. USA 97(12), 6515–6520 (2000)CrossRefGoogle Scholar
  39. 39.
    James, H.M., Guth, E.: Theory of the elastic properties of rubber. Journal of Chemical Physics 10, 455–481 (1943)CrossRefGoogle Scholar
  40. 40.
    Jendrejack, R.M., Pablo, J.J., Graham, M.D.: Stochastic simulations of dna in flow: Dynamics and the effects of hydrodynamic interactions. Journal of Chemical Physics 116(17), 7752 (2002)CrossRefGoogle Scholar
  41. 41.
    Santalucia Jr., J.: A unified view of polymer, dumbbell and oligonucleotide dna nearest-neighbor thermodynamics. PNAS 95, 1460–1465 (1998)CrossRefGoogle Scholar
  42. 42.
    Kierzek, A.M.: Stocks: Stochastic kinetic simulations of biochemical systems with gillespie algorithm. Bioinformatics 18, 470–481 (2002)CrossRefGoogle Scholar
  43. 43.
    Klenin, K., Merlitz, H., Langowski, J.: A brownian dynamics program for the simulation of linear and circular dna and other wormlike chain polyelectrolytes. Biophys. J 74(2), 780–788 (1998)CrossRefGoogle Scholar
  44. 44.
    Kovac, J., Crabb, C.: Modified gaussian model for rubber elasticity. 2. the wormlike chain. Macromolecules 15(2), 537 (1982)CrossRefGoogle Scholar
  45. 45.
    Kuhn, M., Grun, F.: Relationships between elastic constants and stretching double refraction of highly elastic substances. Kolloid-Z 101, 294 (1942)CrossRefGoogle Scholar
  46. 46.
    Kutter, S.: Elasticity of polymers with internal topological constraints. PhD Thesis (August 2002)Google Scholar
  47. 47.
    LaBean, T.H., Yan, H., Kopatsch, J., Liu, F., Winfree, E., Reif, J.H., Seeman, N.C.: The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc. 122, 1848–1860 (2000)CrossRefGoogle Scholar
  48. 48.
    Ladoux, B., Quivy, J.P., Doyle, P.S., Almouzni, G., Viovy, J.L.: Direct imaging of single-molecules: from dynamics of a single dna chain to the study of complex dna-protein interactions. Sci. Prog. 84, 267 (2001)CrossRefGoogle Scholar
  49. 49.
    Langowski, J.: Polymer chain models of dna and chromatin (manuscript, 2006)Google Scholar
  50. 50.
    Larson, R.G., Hu, H., Smith, D.E., Chu, S.: Brownian dynamics simulation of a dna molecule in an extensional flow field. J. Rheol. 43(2), 267–304 (1999)CrossRefGoogle Scholar
  51. 51.
    Larson, R.G., Perkins, T., Smith, D., Chu, S.: Hydrodynamics of a dna molecule in a flow field. Phys. Rev. E. 55, 1794–1797 (1997)CrossRefGoogle Scholar
  52. 52.
    Larson, R.G., Perkins, T.T., Smith, D.E., Chu, S.: Brownian dynamics simulations of a dna molecule in an extensional flow field. J. Rheol. 43, 267 (1999)CrossRefGoogle Scholar
  53. 53.
    Li, J., Tan, W.: A single DNA molecule nanomotor. Nano Lett. 2, 315–318 (2002)CrossRefGoogle Scholar
  54. 54.
    Liu, D., Wang, M., Deng, Z., Walulu, R., Mao, C.: Tensegrity: Construction of rigid DNA triangles with flexible four-arm dna junctions. J. Am. Chem. Soc. 126, 2324–2325 (2004)CrossRefGoogle Scholar
  55. 55.
    Liu, Q., Wang, L., Frutos, A.G., Condon, A.E., Corn, R.M., Smith, L.M.: DNA computing on surfaces. Nature 403, 175–179 (2000)CrossRefGoogle Scholar
  56. 56.
    Malevanets, A., Yoemans, J.M.: Dynamics of short polymer chains in solution. Europhysics Letters 52(2), 231 (2000)CrossRefGoogle Scholar
  57. 57.
    Mao, C., LaBean, T.H., Reif, J.H., Seeman, N.C.: Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407, 493–496 (2000)CrossRefGoogle Scholar
  58. 58.
    Mao, C., Sun, W., Seeman, N.C.: Designed two-dimensional DNA holliday junction arrays visualized by atomic force microscopy. J. Am. Chem. Soc. 121, 5437–5443 (1999)CrossRefGoogle Scholar
  59. 59.
    Mao, C., Sun, W., Shen, Z., Seeman, N.C.: A DNA nanomechanical device based on the B-Z transition. Nature 397, 144–146 (1999)CrossRefGoogle Scholar
  60. 60.
    Marko, J., Siggia, E.D.: Bending and twisting elasticity of dna. Macromolecules 27, 981 (1994)CrossRefGoogle Scholar
  61. 61.
    Marko, J.F., Siggia, E.D.: Stretching dna. Macromolecules 28, 8759 (1995)CrossRefGoogle Scholar
  62. 62.
    Meagher, R.J., Won, J., McCormick, L.C., Nedelcu, S., Bertrand, M.M., Bertarm, J.L., Drouin, G., Barron, A.E., Slaters, G.W.: End-labeled free-solution electrophoresis of dna. Electrophoresis 26, 331–350 (2005)CrossRefGoogle Scholar
  63. 63.
    Mercier, J., Slater, G.W.: Solid phase dna amplification: a brownian dynamics study of crowding effects. Biophysical Journal 89, 32–42 (2005)CrossRefGoogle Scholar
  64. 64.
    Murphy, M.C., Rasnik, I., Cheng, W., Lohman, T.M., Ha, T.: Probing single-stranded dna conformation flexibility using fluorescence spectroscopy. Biophysical Journal 86, 2530–2537 (2004)CrossRefGoogle Scholar
  65. 65.
    Odijk, T.: Stiff chains and filaments under tension. Macromolecule 28, 7016–7018 (1995)CrossRefGoogle Scholar
  66. 66.
    Panyutin, I.G., Hsieh, P.: The kinetics of spontaneous dna branch migration. Proc. Natl. Acad. Sci. USA 91(6), 2021–2025 (1994)CrossRefGoogle Scholar
  67. 67.
    Pedersen, J.S., Laso, M., Schurtenberger, P.: Monte carlo study of excluded volume effects in wormlike micelles and semiflexible polymers. Phys. Rev. E 54(6), 5917–5920 (1996)CrossRefGoogle Scholar
  68. 68.
    Peyret, N., Seneviratne, P.A., Allawi, H.T., Santalucia, J.: Nearest-neighbor thermodynamics and nmr of dna sequences with internal aa,cc,gg and tt mismatches. Biochemistry 38, 3468 (1999)CrossRefGoogle Scholar
  69. 69.
    Rao, C., Arkin, A.: Stochastic chemical kinetics and the quasi-steady-state assumption: application to the gillespie algorithm. J. of Chem. Phys. 118, 4999–5010 (2003)CrossRefGoogle Scholar
  70. 70.
    Reif, J.H.: The design of autonomous DNA nanomechanical devices: Walking and rolling DNA. In: The 8th International Meeting on DNA Based Computers (DNA 8) (2002)Google Scholar
  71. 71.
    Rief, M., Clausen-Schaumann, H., Gaub, H.E.: Sequence-dependent mechanics of single dna molecules. Nature Structural Biology 6, 346–349 (1999)CrossRefGoogle Scholar
  72. 72.
    Sales-Pardo, M., Guimera, R., Moreira, A.A., Widom, J., Amaral, L.A.: Mesoscopic modeling for nucleic acid chain dynamics. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 71, 051902 (2005)CrossRefGoogle Scholar
  73. 73.
    Santalucia, J., Hicks, D.: The thermodynamics of dna structural motifs. Annu. Rev. Biophys. Biomol. Struct. 33, 415 (2004)CrossRefGoogle Scholar
  74. 74.
    Sahu, S., Wang, B., Reif, J.H.: A Framework for Modeling DNA Based Molecular Systems. Technical Report, Duke University (2006)Google Scholar
  75. 75.
    Sha, R., Liu, R., Millar, D.P., Seeman, N.C.: Atomic force microscopy of parallel DNA branched junction arrays. Chemistry and Biology 7, 743–751 (2000)CrossRefGoogle Scholar
  76. 76.
    Sherman, W.B., Seeman, N.C.: A precisely controlled DNA biped walking device. Nano Lett. 4, 1203–1207 (2004)CrossRefGoogle Scholar
  77. 77.
    Shin, J.S., Pierce, N.A.: A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126, 10834–10835 (2004)CrossRefGoogle Scholar
  78. 78.
    Simmel, F.C., Yurke, B.: Using DNA to construct and power a nanoactuator. Phys. Rev. E 63, 041913 (2001)CrossRefGoogle Scholar
  79. 79.
    Simmel, F.C., Yurke, B.: A DNA-based molecular device switchable between three distinct mechanical states. Appl. Phys. Lett. 80, 883–885 (2002)CrossRefGoogle Scholar
  80. 80.
    Smith, S.B., Finzi, L., Bustamante, B.: Direct mechanical measurements of the elasticity of single dna molecules by using magnetic beads. Science 258, 1122 (1992)CrossRefGoogle Scholar
  81. 81.
    Smith, S.B., Cui, Y., Bustamante, C.: Overstretching b-dna: the elastic response of individual double-stranded and single-stranded dna molecules. Science 271, 795–799 (1996)CrossRefGoogle Scholar
  82. 82.
    Somasi, M., Khomami, B., Woo, N.J., Hur, J.S., Shaqfeh, E.S.G.: Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues. J. Non-Newtonian Fluid Mech. 108, 227–255 (2002)MATHCrossRefGoogle Scholar
  83. 83.
    Stellwagen, E., Stellwagen, N.C.: Determining the electrophoretic mobility and translational diffusion coefficients of dna molecules in free solution. Electrophoresis 23(16), 2794–2803 (2002)CrossRefGoogle Scholar
  84. 84.
    Storm, C., Nelson, P.C.: Theory of high-force dna stretching and overstretching. Physical Review E 67, 051906 (2003)CrossRefMathSciNetGoogle Scholar
  85. 85.
    Thompson, B.J., Camien, M.N., Warner, R.C.: Kinetics of branch migration in double-stranded dna. Proc. Natl. Acad. Sci. USA 73(7), 2299–2303 (1976)CrossRefGoogle Scholar
  86. 86.
    Tian, Y., He, Y., Chen, Y., Yin, P., Mao, C.: Molecular devices - a DNAzyme that walks processively and autonomously along a one-dimensional track. Angew. Chem. Intl. Ed. 44, 4355–4358 (2005)CrossRefGoogle Scholar
  87. 87.
    Tinoco, I., Bustamante, C.: The effect of force on thermodynamics and kinetics of single molecule reactions. Biophys Chem 513, 101–102 (2002)Google Scholar
  88. 88.
    Turberfield, A.J., Mitchell, J.C., Yurke, B., Mills Jr., A.P., Blakey, M.I., Simmel, F.C.: DNA fuel for free-running nanomachines. Phys. Rev. Lett. 90, 118102 (2003)CrossRefGoogle Scholar
  89. 89.
    Turberfield, A.J., Yurke, B., Mills Jr., A.P.: DNA hybridization catalysts and molecular tweezers. In: DNA5 (2000)Google Scholar
  90. 90.
    Turner, T.E., Schnell, S., Burrage, K.: Stochastic approaches for modelling in vivo reactions. Computational Biology and Chemistry (2004)Google Scholar
  91. 91.
    Vologodskii, A.V.: Monte carlo simulation of dna topological properties (preprint, 2004)Google Scholar
  92. 92.
    Voter, A.F.: Introduction to kinetic monte carlo method. Springer, NATO publishing unit (2005)Google Scholar
  93. 93.
    Wetmur, J.G., Davidson, N.: Kinetics of renaturation of dna. J. Mol. Biol. 31, 349–370 (1968)CrossRefGoogle Scholar
  94. 94.
    Winfree, E.: Complexity of restricted and unrestricted models of molecular computation. In: Lipton, R.J., Baum, E.B. (eds.) DNA Based Computers 1. DIMACS, vol. 27, pp. 187–198. American Mathematical Society (1996)Google Scholar
  95. 95.
    Winfree, E.: Simulation of computing by self-assembly. Technical Report 1998.22, Caltech (1998)Google Scholar
  96. 96.
    Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and self-assembly of two-dimensional DNA crystals. Nature 394(6693), 539–544 (1998)CrossRefGoogle Scholar
  97. 97.
    Winfree, E., Yang, X., Seeman, N.C.: Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber, L.F., Baum, E.B. (eds.) DNA Based Computers II. DIMACS, vol. 44, pp. 191–213. American Mathematical Society (1999)Google Scholar
  98. 98.
    Wolfinger, M.T., Svrcek-Seiler, W.A., Flamm, C., Hofacker, I.L., Stadler, P.F.: Exact Folding Dynamics of RNA Secondary Structures. J. Phys. A: Math. Gen. 37, 4731–4741 (2004)MATHCrossRefMathSciNetGoogle Scholar
  99. 99.
    Yamakawa, H., Yoshizaki, T.: Dynamics of helical wormlike chains. Journal of Chemical Physics 75(2), 1016 (1981)CrossRefMathSciNetGoogle Scholar
  100. 100.
    Yan, H., LaBean, T.H., Feng, L., Reif, J.H.: Directed nucleation assembly of DNA tile complexes for barcode patterned DNA lattices. Proc. Natl. Acad. Sci. USA 100(14), 8103–8108 (2003)CrossRefGoogle Scholar
  101. 101.
    Yan, H., Park, S.H., Finkelstein, G., Reif, J.H., LaBean, T.H.: DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science 301(5641), 1882–1884 (2003)CrossRefGoogle Scholar
  102. 102.
    Yan, H., Zhang, X., Shen, Z., Seeman, N.C.: A robust DNA mechanical device controlled by hybridization topology. Nature 415, 62–65 (2002)CrossRefGoogle Scholar
  103. 103.
    Yan, J., Marko, J.F.: Localized single-stranded bubble mechanism for cyclization of short double helix dna. Phys. Rev. Lett. 93(10), 108108 (2004)CrossRefGoogle Scholar
  104. 104.
    Yin, P., Sahu, S., Turberfield, A.J., Reif, J.H.: Design of autonomous DNA cellular automata. In: Proc. 11th International Meeting on DNA Computing, pp. 376–387 (2005)Google Scholar
  105. 105.
    Yin, P., Turberfield, A.J., Sahu, S., Reif, J.H.: Design of an autonomous DNA nanomechanical device capable of universal computation and universal translational motion. In: Proc. 10th International Meeting on DNA Computing, pp. 344–356 (2004)Google Scholar
  106. 106.
    Yurke, B., Mills, A.P., Turberfield, A.J.: A molecular machine made of and powdered by DNA. Biophysics 78, 2629 (2000)Google Scholar
  107. 107.
    Yurke, B., Turberfield, A.J., Mills Jr., A.P., Simmel, F.C., Neumann, J.L.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)CrossRefGoogle Scholar
  108. 108.
    Zhang, Y., Zhou, H., Ou-Yang, Z.: Stretching single-stranded dna: Interplay of electrostatic, base-pairing, and base-pair stacking interactions. Biophys J 81(2), 1133–1143 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sudheer Sahu
    • 1
  • Bei Wang
    • 1
  • John H. Reif
    • 1
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA

Personalised recommendations