Journal of Bionic Engineering

, Volume 5, Issue 4, pp 299–307 | Cite as

An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

  • M. Benke
  • E. Shapiro
  • D. DrikakisEmail author


The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector (FALCO) algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.


multi-scale modelling DNA macromolecule transport meta-modelling particle corrector 


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  1. [1]
    Freemantle M. Microscale technology. Chemical and Engineering News, 1999, 22, 27–36.Google Scholar
  2. [2]
    Ehrfeld W, Hessel V, Lowe H. Microreactors: New Technology for Modern Chemistry, Wiley-VHC, Weiheim, 2000.CrossRefGoogle Scholar
  3. [3]
    Nguyen N T, Wu Z. Micromixers: A review. Journal of Micromechanics and Microengineering, 2005, 15, 1–16.CrossRefGoogle Scholar
  4. [4]
    Squires T M, Quake S R. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 2005, 77, 977–1026.CrossRefGoogle Scholar
  5. [5]
    Whitesides G. The origins and the future of microfluidics. Nature, 2006, 442, 368–373.CrossRefGoogle Scholar
  6. [6]
    Stone H A, Stroock A D, Ajdari A. Engineering flows in small devices: Microfluidics toward a lab-on-a-chip. Annual Review of Fluid Mechanics, 2004, 36, 381–411.CrossRefGoogle Scholar
  7. [7]
    Stroock A D, Dertinger S K W, Ajdari A, Mezic I, Stone H A, Whitesides G M. Chaotic mixer for microchannels. Science, 2002, 295, 647–651.CrossRefGoogle Scholar
  8. [8]
    Ottino J M, Wiggins S. Introduction: Mixing in microfluidics. Philosophical Transactions of Royal Society London A, 2004, 362, 923–935.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Zhang Y, Barber R W, Emerson D R. Part separation in microfluidic devices — SPLITT fractionation and microfluidics. Current Analytical Chemistry, 2005, 1, 345–354.CrossRefGoogle Scholar
  10. [10]
    Gargiuli J, Shapiro E, Gulhane H, Nair G, Drikakis D, Vadgama P. Microfluidic systems for in situ formation of nylon 6,6 membranes. Journal of Membrane Science, 2006, 282, 257–265.CrossRefGoogle Scholar
  11. [11]
    Pasas S A, Lacher N A, Davies M I, Lunte S M. Detection of homocysteine by conventional and microchip capillary electrophoresis/electrochemistry. Electrophoresis, 2002, 23, 759–766.CrossRefGoogle Scholar
  12. [12]
    Fanguy J C, Henry C S. The analysis of uric acid in urine using microchip capillary electrophoresis with electrochemical detection. Electrophoresis, 2002, 23, 767–773.CrossRefGoogle Scholar
  13. [13]
    Shi Y N, Simpson P C, Scherer J R, Wexler D, Skibola C, Smith M T, Mathies R A. Radial capillary array electrophoresis microplate and scanner for high-performance nucleic acid analysis. Analytical Chemistry, 1999, 71, 5354–5361.CrossRefGoogle Scholar
  14. [14]
    Simpson J W, Ruiz-Martinez M C, Mulhern G T, Berka J, Latimer J R, Ball J A, Rothberg J M, Went G T. A transmission imaging spectrograph and microfabricated channel system for DNA analysis. Electrophoresis, 2000, 21, 135–149.CrossRefGoogle Scholar
  15. [15]
    Agarwal U S, Dutta A, Mashelkar R A. Migration of macromolecules under flow: The physical origin and engineering implications. Chemical Engineering Science, 1994, 49, 1693–1717.CrossRefGoogle Scholar
  16. [16]
    Blom M T, Chmela E, Gardeniers J G E, Tijssen R, Elwenspoek M, van den Berg A. Design and fabrication of a hydrodynamic chromatography chip. Sensors and Actuators B, 2002, 82, 111–116.CrossRefGoogle Scholar
  17. [17]
    Wang P C, Gao J, Lee C S. High-resolution chiral separation using microfluidics-based membrane chromatography. Journal of Chromatography A, 2002, 942, 115–122.CrossRefGoogle Scholar
  18. [18]
    Stein D, van der Heyden F H J, Koopmans J A, Dekker C. Pressure-driven transport of confined DNA polymers in fluidic channels. PNAS, 2006, 103, 15853–15858.CrossRefGoogle Scholar
  19. [19]
    Wong P K, Lee Y K, Ho C M. Deformation of DNA molecules by hydrodynamic focusing. Journal of Fluid Mechanics, 2003, 497, 55–65.CrossRefGoogle Scholar
  20. [20]
    Nonaka A, Gulati S, Trebotich D, Miller G H, Muller S J, Liepmann D. Computational model with experimental validation for DNA flow in microchannels. Nanotech: Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show, 2005, 3, 712–715.Google Scholar
  21. [21]
    Chung Y C, Lin Y C, Hsu Y L, Chang W N T, Shiu M Z. The effect of velocity and extensional strain rate on enhancing DNA hybridization. Journal of Micromechanics and Microengineering, 2004, 14, 1376–1383.CrossRefGoogle Scholar
  22. [22]
    Shapiro E, Drikakis D, Gargiuli J, Vadgama P. Microfluidic cell optimization for polymer membrane fabrication. Proceedings of the 4th ASME International Conference on Nanochannels, Microchannels and Minichannels, Limerick, USA, 2006, ICNMM2006-96221.Google Scholar
  23. [23]
    Karniadakis G, Beskok A, Aluru N. Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York, 2005.zbMATHGoogle Scholar
  24. [24]
    Drikakis D, Kalweit M. Coupling strategies for hybrid molecular-continuum simulation methods. Proceedings of the Institution of Mechanical Engineers C, 2008, 222, 797–806.CrossRefGoogle Scholar
  25. [25]
    Gad-el-Hak M. Liquids: The holy grail of microfluidic modelling. Physics of Fluids, 2005, 17, 100612.CrossRefGoogle Scholar
  26. [26]
    Cussler E L. Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, 1997.Google Scholar
  27. [27]
    Doi M, Edwards S F. The Theory of Polymer Dynamics, Clarendon, Oxford, 1986.Google Scholar
  28. [28]
    Trebotich D, Miller G H, Colella P, Graves D T, Martin D F, Schwartz P O. A tightly coupled particle-fluid model for DNA-laden flows in complex microscale geometries. Proceedings of Computational Fluid and Solid Mechanics, MIT, USA, 2005, UCRL-CONF-208132.Google Scholar
  29. [29]
    Goldstein H. Classical Mechanics, Addison-Wesley, USA, 1959.zbMATHGoogle Scholar
  30. [30]
    Happel J, Brenner H. Low Reynolds Number Hydrodynamics, Martinus Nijhoff Publishers, Hague, 1983.zbMATHGoogle Scholar
  31. [31]
    Smith S B, Cui Y, Bustamante C. Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules. Science, 1996, 271, 795–799.CrossRefGoogle Scholar
  32. [32]
    Bustamante C, Smith S B, Liphard J, Smith D. Single-molecule studies of DNA mechanics. Current Opinion in Structural Biology, 2000, 10, 279–285.CrossRefGoogle Scholar
  33. [33]
    Ryckaert J P, Ciccotti G, Berendsen H J C. Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes. Journal of Computational Physics, 1977, 23, 327–341.CrossRefGoogle Scholar
  34. [34]
    Chorin A J. Numerical solution of the Navier-Stokes equations. Mathematics of Computation, 1968, 22, 745–762.MathSciNetCrossRefGoogle Scholar
  35. [35]
    Shapiro E, Drikakis D. Non-conservative and conservative formulations of characteristics-based numerical reconstructions for incompressible flows. International Journal of Numerical Methods for Engineering, 2006, 66, 1466–1482.MathSciNetCrossRefGoogle Scholar
  36. [36]
    Drikakis D, Rider W. High-Resolution Methods for Incompressible and Low-Speed Flows, Springer-Verlag, Berlin, 2004.Google Scholar
  37. [37]
    Tothova J, Brutovsky B, Lisy V. Addendum to “Monomer motion in single- and double-stranded DNA coils”. arXiv:cond-mat/0701523v1 [cond-mat.soft], 2005.Google Scholar

Copyright information

© Jilin University 2008

Authors and Affiliations

  1. 1.Fluid Mechanics and Computational Science Group, Department of Aerospace SciencesCranfield UniversityCranfieldUK

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