Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

S. Swaminathan; F. Ziebert; I. S. Aranson; D. Karpeev

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 119-137
  • ISSN: 0973-5348

Abstract

top
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.

How to cite

top

Swaminathan, S., et al. "Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions." Mathematical Modelling of Natural Phenomena 6.1 (2010): 119-137. <http://eudml.org/doc/197693>.

@article{Swaminathan2010,
abstract = {We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.},
author = {Swaminathan, S., Ziebert, F., Aranson, I. S., Karpeev, D.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {microtubule; molecular motor; stochastic; fokker-planck; mechanics; collision; kinetic; bifurcation; weakly nonlinear analysis; pattern formation; molecular dynamics; active temperature; multiplicative noise; brownian motion.; Fokker-Planck; Brownian motion.},
language = {eng},
month = {6},
number = {1},
pages = {119-137},
publisher = {EDP Sciences},
title = {Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions},
url = {http://eudml.org/doc/197693},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Swaminathan, S.
AU - Ziebert, F.
AU - Aranson, I. S.
AU - Karpeev, D.
TI - Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 119
EP - 137
AB - We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.
LA - eng
KW - microtubule; molecular motor; stochastic; fokker-planck; mechanics; collision; kinetic; bifurcation; weakly nonlinear analysis; pattern formation; molecular dynamics; active temperature; multiplicative noise; brownian motion.; Fokker-Planck; Brownian motion.
UR - http://eudml.org/doc/197693
ER -

References

top
  1. I. S. Aranson, L. S. Tsimring. Pattern formation of microtubules and motors: Inelastic interaction of polar rods. Phys Rev E, 71 (2005), No. 5, 050901. 
  2. I. S. Aranson, L. S. Tsimring. Theory of self-assembly of microtubules and motors. Phys Rev E, 74 (2006), No. 3, 031915. 
  3. I. S. Aranson, L. S. Tsimring, V. M. Vinokur. Continuum theory of axial segregation in a long rotating drum. Phys Rev E, 60 (1999), No. 2, 1975-1987. 
  4. I. S. Aranson, D. Volfson, L. S. Tsimring. Swirling motion in a system of vibrated elongated particles. Phys Rev E, 75 (2007), No. 5, 051301. 
  5. E. Ben-Naim, P. L. Krapivsky. Alignment of rods and partition of integers. Phys Rev E, 73 (2006), No. 3, 031109. 
  6. O. Campas, Y. Kafri, K. B. Zeldovich, J. Casademunt, J. F. Joanny. Collective dynamics of interacting molecular motors. Phys Rev Lett, 97 (2006), No. 3, 038101. 
  7. C. M. Coppin, T. Finer, J. A. Spudich, R. D. Vale. Measurement of the isometric force exerted by a single kinesin molecule. Biophys. J., 68 (1995), 242s–244s. 
  8. C. M. Coppin, D. W. Pierce, L. Hsu, R. D. Vale. The load dependence of kinesin’s mechanical cycle. Proc. Natl. Acad. Sci., 94 (1997), No. 16, 8539–8544. 
  9. P. G. de Gennes, J. Prost. The Physics of Liquid Crystals. Clarendon Press, Oxford, 1993.  
  10. M. Doi, S. F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford, 1986.  
  11. S. J. Fiedor, J. M. Ottino. Dynamics of axial segregation and coarsening of dry granular materials and slurries in circular and square tubes. Phys Rev Lett, 91 (2003), No. 24, 244301. 
  12. T. Finger, A. Voigt, J. Stadler, H. G. Niessen, L. Naji, R. Stannarius. Coarsening of axial segregation patterns of slurries in a horizontally rotating drum. Phys Rev E, 74 (2006), No. 3, 031312. 
  13. T. L. Gilbert. A phenomenological theory of damping in ferromagnetic materials, IEEE Trans. Magn, 40 (2004), No. 6, 3443–3449. 
  14. S. W. Grill, K. Kruse, F. Jülicher. Theory of mitotic spindle oscillations. Phys Rev Lett, 94 (2005), No. 10, 108104. 
  15. J. Howard. Mechanics of Motor Proteins and the Cytoskeleton, Springer, New York, 2001.  
  16. D. Humphrey, C. Duggan, D. Saha, D. Smith, J. Käs. Active fluidization of polymer networks through molecular motors. Nature (London), 416 (2002), No. 6879, 413–416. 
  17. L. C. Kapitein, E. J. G. Peterman, B. H. Kwok, J. H. Kim, T. M. Kapoor, C. F. Schmidt. The bipolar mitotic kinesin Eg5 moves on both microtubules that it crosslinks. Letters to Nature, 435 (2005), No. 7038, 114–118. 
  18. D. Karpeev, I. S. Aranson, L. S. Tsimring, H. G. Kaper. Interactions of Semiflexible Filaments and Molecular Motors, Phys Rev E, 76 (2007), No. 5, 051905. 
  19. S. Klumpp, R. Lipowski. Cooperative cargo transport by several molecular motors. Proc. Natl. Acad. Sci., 102 (2005), No. 48, 17284–17289. 
  20. K. Kruse, J. F. Joanny, F. Jülicher, J. Prost, K. Sekimoto. Asters, vortices, and rotating spirals in active gels of polar filaments. Phys Rev Lett, 92 (2004), No.7, 078101.1–078101.4.  
  21. K. Kruse, F. Jülicher. Self-organization and mechanical properties of active filament bundles. Phys Rev E, 67 (2004), No. 5051913.1–051913.16.  
  22. L. D. Landau, E. M. Lifshitz,On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sovietunion, 8 (1935), 153–169.  Zbl0012.28501
  23. H. Y. Lee, M. Kardar. Macroscopic equations for pattern formation in mixtures of microtubules and motors. Phys Rev E, 64 (2001), No. 5056113.1–056113.8.  
  24. D. Loi, S. Mossa, L. F. Cugliandolo. Effective temperature of active matter. Phys Rev E, 77 (2008), No. 5, 051111. 
  25. T. B. Liverpool, A. C. Maggs, A. Ajdari. Viscoelasticity of solutions of motile polymers. Phys Rev Lett, 86 (2001), No. 18, 4171–4174. 
  26. T. B. Liverpool, M. C. Marchetti. Instabilities of isotropic solutions of active polar filaments. Phys Rev Lett, 90 (2003), No. 13, 138102. 
  27. H. Lodish, A. Berk, S. L. Zipursky, P. Matsudaira, D. Baltimore J. Darnell. Molecular Cell Biology, W.H. Freeman, New York, 1999.  
  28. D. Mizuno, C. Tardin, C. F. Schmidt, F. C. MacKintosh. Nonequilibrium mechanics of active cytoskeletal networks. Science, 315 (2007), No. 5810, 370–373. 
  29. F. Nédélec, T. Surrey, A. C. Maggs. Dynamic Concentration of Motors in Microtubule Arrays. Phys Rev Lett, 86 (2001), No. 14, 3192–3195. 
  30. F. J. Nédélec, T. Surrey, A. C. Maggs, S. Leibler. Self-organization of microtubules and motors. Nature (London), 389 (1997), No. 6648, 305–308. 
  31. L. Onsager. Effects of shape on the interaction of colloidal particles. Ann. N.Y. Acad. Sci., 51 (1949), No. 4, 627–659. 
  32. A. Parmeggiani, F. Jülicher, L. Peliti, J. Prost. Detachment of molecular motors under tangential loading. Europhys Lett, 56 (2001), No. 4, 603–609. 
  33. H. Risken. The Fokker-Planck Equation, Springer, Berlin (1989).  Zbl0665.60084
  34. R. A. Simha, S. Ramaswamy. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys Rev Lett, 89 (2002), No. 5, 058101. Zbl0994.76099
  35. D. Smith, F. Ziebert, D. Humphrey, C. Duggan, M. Steinbeck, W. Zimmermann, J. Kas. Molecular motor-induced instabilities and cross-linkers determine biopolymer organization. Biophysical Journal, 93 (2007), No. 12, 4445–4452. 
  36. A. Sokolov, I. S. Aranson, J. O.Kessler, R. E. Goldstein. Concentration dependence of the collective dynamics of swimming bacteria. Phys Rev Lett, 98 (2007), No. 15, 158102. 
  37. T. Surrey, F. Nédélec, S. Leibler, E. Karsenti. Physical properties determining self-organization of motors and microtubules. Science, 292 (2001), No. 5519, 1167–1171. 
  38. S. Swaminathan, D. Karpeev, I. S. Aranson. Bundle dynamics of interacting polar rods. Phys Rev E, 77 (2008), No. 6, 066206. 
  39. S. Swaminathan, F. Ziebert, D. Karpeev, I. S. Aranson. Motor-mediated alignment of microtubules in semidilute mixtures. Phys Rev E, 79 (2009), No. 3, 036207. 
  40. K. Takiguch. Heavy meromyosin induces sliding movements between antiparallel actin filaments. J. Biochem, 109 (1991), No. 4, 520–527. 
  41. R. Urrutia, M. A. McNiven, J. P. Albanesi, D. B. Murphy, B. Kachar. Purified kinesin promotes vesicle motility and induces active sliding between microtubules in vitro. Proc Natl Acad Sci, 88 (1991), No. 15, 6701–6705. 
  42. R. D. Vale, R .A. Milligan. The way things move: Looking under the hood of molecular motor proteins. Science, 288 (2000), No. 5463, 88–95. 
  43. F. Ziebert, I. S. AransonRheological and structural properties of dilute active filament solutions, Phys Rev E, 77 (2008), No. 1, 011918. 
  44. F. Ziebert, I. S. Aranson, L. S. Tsimring. Effects of crosslinks on filament-motor organization. New J. Phys., 9 (2007), No. 11, 421. 
  45. F. Ziebert, M. Vershinin, S. P. Gross, I. S. Aranson. Collective alignment of polar filaments by molecular motors. Eur. Phys. J. E, 28 (2009), No. 4, 401–409. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.