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Original Articles

Mathematical modelling and computer simulation of Brownian motion and hybridisation of nanoparticle–bioprobe–polymer complexes in the low concentration limit

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Pages 66-71 | Received 24 Sep 2010, Accepted 28 Jun 2011, Published online: 25 Nov 2011

References

  • Kim , D. , Daniel , W.L. and Mirkin , C.A. 2009 . Microarray-based multiplexed scanometric immunoassay for protein cancer markers using gold nanoparticle probes . Anal. Chem , 81 ( 21 ) : 9183 – 9187 .
  • Lim , S.F. , Riehn , R. , Tung , C.-K. , Ryu , W.S. , Zhuo , R. , Dalland , J. and Austin , R.H. 2009 . Upconverting nanophosphors for bioimaging . Nanotechnology , 20 ( 40 ) : 405701/1 – 405701/6 .
  • Xiang , M. , Xu , X. , Liu , F. , Li , N. and Li , K.-A. 2009 . Gold nanoparticle based plasmon resonance light-scattering method as a new approach for glycogen–biomacromolecule interactions . J. Phys. Chem. B , 113 ( 9 ) : 2734 – 2738 .
  • Graham , D. , Faulds , K. , Thompson , D. , McKenzie , F. , Stokes , R. , Dalton , C. , Stevenson , R. , Alexander , J. , Garside , P. and McFarlane , E. 2009 . Functionalized nanoparticles for bioanalysis by serrs . Biochem. Soc. Trans. , 37 ( Pt 4 ) : 697 – 701 .
  • Radwan , S.H. and Azzazy , H.M.E. 2009 . Gold nanoparticles for molecular diagnostics . Expert. Rev. Mol. Diagn , 9 ( 5 ) : 511 – 524 .
  • Koenig , G.M. , Ong , R. , Cortes , A.D. , Antonio Moreno-Razo , J. , de Pablo , J.J. and Abbott , N.L. 2009 . Single nanoparticle tracking reveals influence of chemical functionality of nanoparticles on local ordering of liquid crystals and nanoparticle diffusion coefficients . Nano Lett. , 9 ( 7 ) : 2794 – 2801 .
  • Azzazy , H.M.E. and Mansour , M.M.H. 2009 . In vitro diagnostic prospects of nanoparticles . Clin. Chim. Acta , 403 ( 1–2 ) : 1 – 8 .
  • Fang , S.-B. , Tseng , W.Y. , Lee , H.-C. , Tsai , C.-K. , Huang , J.-T. and Hou , S.-Y. 2009 . Identification of salmonella using colony-print and detection with antibody-coated gold nanoparticles . J. Microbiol. Methods , 77 ( 2 ) : 225 – 228 .
  • Ngoc Bui , M.-P. , Baek , T.J. and Seong , G.H. 2007 . Gold nanoparticle aggregation-based highly sensitive DNA detection using atomic force microscopy . Anal. Bioanal. Chem. , 388 ( 5–6 ) : 1185 – 1190 .
  • Wang , Y.-F. , Shen , J.-T. and Liu , H.-H. 2004 . Analytical performance of and real sample analysis with an hbv gene visual detection chip . J. Virol. Methods , 121 ( 1 ) : 79 – 84 .
  • Elsner , H.I. and Lindblad , E.B. 1989 . Ultrasonic degradation of DNA . DNA , 8 : 697 – 701 .
  • Berg , H.C. 1993 . Random Walks in Biology , Princeton, NJ : Princeton University Press .
  • Schulten , Z. and Schulten , K. 1977 . The generation, diffusion, spin motion, and recombination of radical pairs in solution in the nanosecond time domain . J. Chem. Phys. , 66 : 4616 – 4634 .
  • Szabo , A. , Schulten , K. and Schulten , Z. 1980 . First passage time approach to diffusion controlled reactions . J. Chem. Phys. , 72 : 4350 – 4357 .
  • Axelrod , D. and Wang , M.D. 1994 . Reduction-of-dimensionality kinetics at reaction-limited cell surface receptors . Biophys. J. , 66 : 588 – 600 .
  • Erickson , D. , Li , D. and Krull , U.J. 2003 . Modeling of DNA hybridization kinetics for spatially resolved biochips . Anal. Biochem. , 317 ( 2 ) : 186 – 200 .
  • Wetmur , J.G. and Davidson , N. 1968 . Kinetics of renaturation of DNA . J. Mol. Biol. , 31 : 349 – 370 .
  • Redner , S. 2001 . Guide to First Passage Processes , Cambridge, UK : Cambridge University Press .
  • Marsaglia , G. and Tsang , W.W. 2000 . The ziggurat method for generating random variables . J. Stat. Software , 5 ( 8 ) : 1 – 7 .
  • Einstein , A. 1905 . Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen . Annelen der Physik , 17 : 549 – 560 .
  • Peskir , G. 2003 . On the diffusion coefficient: The Einstein relation and beyond . Stochastic Models. , 19 ( 3 ) : 383 – 405 .
  • Given , J.A. , Hubbard , J.B. and Douglas , J.F. 1997 . A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules . J. Chem. Phys , 106 ( 9 ) : 3761 – 3771 .
  • Donev , A. , Bulatov , V.V. , Oppelstrup , T. , Gilmer , G.H. , Sadigh , B. and Kalos , M.H. 2010 . A first-passage kinetic Monte Carlo algorithm for complex diffusion-reaction systems . J. Chem. Phys , 229 ( 9 ) : 3214 – 3236 .

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