Skip to main content

Simulations of complex particle transport in heterogeneous active liquids

Abstract

Thermal-fluctuation and external force-induced motion of particles provide mechanical and rheological information for viscoelastic liquids and soft solids. Although particle tracking is well-developed, analysis of particle trajectories in active heterogeneous materials, such as living cells, is usually not simple or straightforward. These trajectories are sometimes composed of several concurrent processes occurring simultaneously or episodically in a complex fluid. Here, we introduce simulations that generate 2-dimensional trajectories of probe transport in a viscous liquid as a tool for complex-trajectory analysis. These computer simulations illustrate cases that are physically relevant and highlight key features, such as spatial confinements or convective speeds, which can for example define a cell’s internal structure and active transport along tubules or fibers. Comparison to experimental data will allow quantitative identification of various concurrent processes and understanding of their time dependence. We examine several well-defined cases of particle motion that occur in soft samples, including living cells, and present information from the analysis as well as new approaches for complex processes.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  1. Addas KM, Schmidt CF, Tang JX (2004) Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry. Phys. Rev. E 70:Art. No. 021503

  2. Apgar J, Tseng Y, Fedorov E, Herwig MB, Almo SC, Wirtz D (2000) Multiple-particle tracking measurements of heterogeneities in solutions of actin filaments and actin bundles. Biophys J 79:1095–1106

    Google Scholar 

  3. Bacher C, Reichenzeller M, Athale C, Herrmann H, Eils R (2004) 4-D single particle tracking of synthetic and proteinaceous microspheres reveals preferential movement of nuclear particles along chromatin-poor tracks. BMC Cell Biol 5:45

    Article  Google Scholar 

  4. Bausch AR, Ziemann F, Boulbitch AA, Jacobson K, Sackmann E (1998) Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. Biophys J 75:2038–2049

    Google Scholar 

  5. Bausch AR, Moller W, Sackmann E (1999) Measurement of local viscoelasticity and forces in living cells by magnetic tweezers. Biophys J 76:573–579

    Google Scholar 

  6. Bird RB, Stewart WE, Lightfoot ED (2002) Transport phenomena. Wiley, New Jersey

    Google Scholar 

  7. Bursac P, Lenormand G, Fabry B, Oliver M, Weitz DA, Viasnoff V, Butler JP, Fredberg JJ (2005) Cytoskeletal remodelling and slow dynamics in the living cell. Nat Mat 4:557–561

    Article  Google Scholar 

  8. Cheng Z, Chaikin PM, Mason TG (2002) Light streak tracking of optically trapped thin microdisks. Phys Rev Lett 89:108303

    Article  Google Scholar 

  9. Cohen AE, Moerner WE (2005) Method for trapping and manipulating nanoscale objects in solution. Appl Phys Lett. 86:Art. No. 093109

  10. Crocker JC, Grier DG (1996) Methods of digital video microscopy for colloidal studies. J Colloid Int Sci 179:298–310

    Article  Google Scholar 

  11. Crocker JC, Valentine MT, Weeks ER, Gisler T, Kaplan PD, Yodh AG, Weitz DA (2000) Two-point microrheology of inhomogeneous soft materials. Phys Rev Lett 85:888–891

    Article  Google Scholar 

  12. Dasgupta BR, Tee SY, Crocker JC, Frisken BJ, Weitz DA (2002) Microrheology of polyethylene oxide using diffusing wave spectroscopy and single scattering. Phys Rev E 65

  13. Dasgupta BR, Weitz DA (2005) Microrheology of cross-linked polyacrylamide networks. Phys Rev E 71

  14. Einstein A (1956) Investigation on the theory of brownian movement. Dover, New York

    Google Scholar 

  15. Evans E, Ritchie K, Merkel R (1995) Sensitive force technique to probe molecular adhesion and structural linkages at biological interfaces. Biophys J 68:2580–2587

    Google Scholar 

  16. Feneberg W, Westphal M, Sackmann E (2001) Dictyostelium cells’ cytoplasm as an active viscoplastic body. Eur Biophys J. Biophys Lett 30:284–294

    Google Scholar 

  17. Fisher ME, Kolomeisky AB (1999) The force exerted by a molecular motor. PNAS 96:6597–6602

    Article  Google Scholar 

  18. Gardel ML, Valentine MT, Crocker JC, Bausch AR, Weitz DA (2003) Microrheology of entangled F-actin solutions. Phys Rev Lett. 91:Art. No. 158302

  19. Gardel ML, Valentine MT, Weitz DA (2005) Microrheology. In: Breuer K (ed) Microdiagnostics. Springer, Berlin Heidelberg New York

    Google Scholar 

  20. Gittes F, Schnurr B, Olmsted PD, MacKintosh FC, Schmidt CF (1997) Microscopic viscoelasticity: shear moduli of soft materials determined from thermal fluctuations. Phys Rev Lett 79:3286–3289

    Article  Google Scholar 

  21. Goodman A, Tseng Y, Wirtz D (2002) Effect of length, topology, and concentration on the microviscosity and microheterogeneity of DNA solutions. J Mol Biol 323:199–215

    Article  Google Scholar 

  22. Haber C, Wirtz D (2000) Magnetic tweezers for DNA micromanipulation. Rev Sci Instr 71:4561–4570

    Article  Google Scholar 

  23. Helfer E, Harlepp S, Bourdieu L, Robert J, MacKintosh FC, Chatenay D (2000) Microrheology of biopolymer-membrane complexes. Phys Rev Lett 85:457–460

    Article  Google Scholar 

  24. Kole TP, Tseng Y, Huang L, Katz JL, Wirtz D (2004) Rho kinase regulates the intracellular micromechanical response of adherent cells to rho activation. Mol Biol Cell 15:3475–3484

    Article  Google Scholar 

  25. Lindemann CB (2003) Structural-functional relationships of the dynein, spokes, and central-pair projections predicted from an analysis of the forces acting within a flagellum. Biophys J 84:4115–4126

    Google Scholar 

  26. Mason TG (2000) Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation. Rheol Acta 39:371–378

    Article  Google Scholar 

  27. Mason TG, Weitz DA (1995) Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys Rev Lett 74:1250–1253

    Article  Google Scholar 

  28. Mason TG, Ganesan K, vanZanten JH, Wirtz D, Kuo SC (1997a) Particle tracking microrheology of complex fluids. Phys Rev Lett 79:3282–3285

    Article  Google Scholar 

  29. Mason TG, Dhople A, Wirtz D (1997b) Concentrated DNA rheology and microrheology. MRS proc stat mech phys biol 463:153–156

    Google Scholar 

  30. Mason TG, Gang H, Weitz DA (1997c) Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids. J Opt Soc Am A 14:139–149

    Google Scholar 

  31. Mizuno D, Kimura Y, Hayakawa R (2004) Electrophoretic microrheology of a dilute lamellar phase: Relaxation mechanisms in frequency-dependent mobility of nanometer-sized particles between soft membranes. Phys Rev E 70

  32. Panorchan P, Schafer BW, Wirtz D, Tseng Y (2004) Nuclear envelope breakdown requires overcoming the mechanical integrity of the nuclear lamina. J Biol Chem 279:43462–43467

    Article  Google Scholar 

  33. Qian H, Sheetz M, Elson E (1991) Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys J 60:910–921

    Article  Google Scholar 

  34. Salman H, Gil Y, Granek R, Elbaum M (2002) Microtubules, motor proteins, and anomalous mean squared displacements. Chem Phys 284:389–397

    Article  Google Scholar 

  35. Saxton MJ, Jacobson K (1997) Single-particle tracking: Applications to membrane dynamics. Annu Rev Biophys Biomol Struct 26:373–399

    Article  Google Scholar 

  36. Suh JH, Wirtz D, Hanes J (2004) Real-time intracellular transport of gene nanocarriers studied by multiple particle tracking. Biotech. Progr. 20:598–602

    Article  Google Scholar 

  37. Tseng Y, Kole TP, Wirtz D (2002) Micromechanical mapping of live cells by multiple-particle-tracking microrheology. Biophys. J. 83:3162–3176

    Google Scholar 

  38. Tseng Y, Lee JSH, Kole TP, Jiang I, Wirtz D (2004) Micro-organization and visco-elasticity of the interphase nucleus revealed by particle nanotracking. J Cell Sci 117:2159–2167

    Article  Google Scholar 

  39. Valentine MT, Kaplan PD, Thota D, Crocker JC, Gisler T, Prud’homme RK, Beck M, Weitz DA (2001) Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking. Phys Rev E 6406:Art. No. 061506

  40. Valentine MT, Perlman ZE, Gardel ML, Shin JH, Matsudaira P, Mitchison TJ, Weitz DA (2004) Colloid surface chemistry critically affects multiple particle tracking measurements of biomaterials. Biophys J 86:4004–4014

    Article  Google Scholar 

  41. Weeks ER, Crocker JC, Levitt AC, Schofield A, Weitz DA (2000) Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287:627–631

    Article  Google Scholar 

  42. Yamada S, Wirtz D, Kuo SC (2000) Mechanics of living cells measured by laser tracking microrheology. Biophys J 78:1736–1747

    Google Scholar 

  43. Yamada S, Wirtz D, Coulombe PA (2002) Pairwise assembly determines the intrinsic potential for self-organization and mechanical properties of keratin filaments. Mol Biol Cell 13:382–391

    Article  Google Scholar 

  44. Xu JY, Viasnoff V, Wirtz D (1998) Compliance of actin filament networks measured by particle-tracking microrheology and diffusing wave spectroscopy. Rheologica Acta 37:387–398

    Article  Google Scholar 

Download references

Acknowledgements

Supported by National Institute of Health grants PN2EY018228-01, CA90571, CA107300, and GM073981 and CMISE, a National Aeronautics and Space Administration URETI Institute Award NCC 2-1364. M.A.T. is a Scholar of the Leukemia and Lymphoma Society. T.G.M. is supported by the American Chemical Society PRF 42858-AC7.

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Daphne Weihs or Michael A. Teitell.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Weihs, D., Teitell, M.A. & Mason, T.G. Simulations of complex particle transport in heterogeneous active liquids. Microfluid Nanofluid 3, 227–237 (2007). https://doi.org/10.1007/s10404-006-0117-4

Download citation

Keywords

  • Bio-microrheology
  • Brownian motion
  • Particle tracking
  • Mean square displacement