Skip to main content
SpringerLink
Log in

Models of the Collective Behavior of Proteins in Cells: Tubulin, Actin and Motor Proteins

  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

One of the most important issues of molecular biophysics is the complex and multifunctional behavior of the cell's cytoskeleton. Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments with motor proteins providing force and directionality needed for transport processes. Microtubules (MT's) take active part in material transport within the cell, constitute the most rigid elements of the cell and hence found many uses in cell motility (e.g. flagella andcilia). At present there is, however, no quantitatively predictable explanation of how these important phenomena are orchestrated at a molecular level. Moreover, microtubules have been demonstrated to self-organize leading to pattern formation. We discuss here several models which attempt to shed light on the assembly of microtubules and their interactions with motor proteins. Subsequently, an overview of actin filaments and their properties isgiven with particular emphasis on actin assembly processes. The lengths of actin filaments have been reported that were formed by spontaneous polymerization of highly purified actin monomers after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 μm. This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: (1) filaments formed from a wide range of highly purified actin monomer concentrations, and (2) filaments formed from 24 mM actin over a range of CapZ concentrations. In the final part of the paper we briefly review the stochastic models used to describe the motion of motor proteins on protein filaments. The vast majority of these models are based on ratchet potentials with the presence of thermal noise and forcing due to ATP binding and a subsequent hydrolysis. Many outstanding questions remain to be quantitatively addressed on a molecular level in order to explain the structure-to-function relationship for the key elements of the cytoskeleton discussed in this review.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. and Watson, J.D.: Molecular Biology of the Cell, Garland Publishing, London, 1994.

    Google Scholar 

  2. Luby-Phelps, K.: Physical Properties of Cytoplasm, Curr. Opin. Cell Biol. 6 (1994), 3-9.

    Article  Google Scholar 

  3. Hinner, B., Tempel, M., Sackmann, E., Kroy, K. and Frey, E.: Entanglement, Elasticity and Viscous Relaxation of Actin Solutions, Phys. Rev. Lett. 81 (1998), 2614-2618.

    Article  ADS  Google Scholar 

  4. Frey, E., Kroy, K. and Wilhelm, J.: Viscoelasticity of Biopolymer Networks, Adv. Struct. Biol. 5 (1998), 135-168.

    Google Scholar 

  5. Ingber, D.E.: Tensegrity: The Architectural Basis of Cellular Mechanotransduction, Ann. Rev. Physiology 59 (1997), 575-599.

    Article  Google Scholar 

  6. Chen, C.S., Mrksich, M., Huang, S., Whitesides, G.M. and Ingber, D.E.: Geometric Control of Cell Life and Death, Science 276 (1997), 1425-1428.

    Article  Google Scholar 

  7. King, R.W.P. and Wu, T.T.: Electric Field Induced in Cells in the Human Body when This is Exposed to Low-Frequency Electric Fields, Phys. Rev. E 58 (1998), 2363-2369.

    Article  ADS  Google Scholar 

  8. Ledbetter, M.C. and Porter, K.R.: A 'Microtubule' in Plant Cell Fine Structure, J. Cell Biol. 19 (1963), 239-250.

    Article  Google Scholar 

  9. Amos, L.A. and Amos, W.B.: Molecules of the Cytoskeleton, Macmillan Press, London, 1991.

    Google Scholar 

  10. Chrétien, D. and Wade, R.H.: New Data on the Microtubule Surface Lattice, Bio. Cell 71 (1991), 161-174.

    Article  Google Scholar 

  11. Amos, L.A.: The Microtubule Lattice-20 Years on, Trends Cell Biol. 5 (1995), 48-51.

    Article  Google Scholar 

  12. Chrétien, D., Metoz, F., Verde, F., Karsenti, E. and Wade, R.H.: Lattice-Defects in Microtubules: Protofilament Numbers vary within Individual Microtubules, J. Cell Biol. 117 (1992), 1031-1040.

    Article  Google Scholar 

  13. Mitchison, T. and Kirschner, M.: Dynamic Instability ofMicrotubule Growth, Nature (London) 312 (1984), 237-242.

    Article  ADS  Google Scholar 

  14. Horio, T. and Hotani, H.: Visualization of the Dynamic Instability of Individual Microtubules by Dark Field Microscopy, Nature (London) 321 (1986), 605-607.

    Article  ADS  Google Scholar 

  15. Cassimeris, L.: Regulation of Microtubule Dynamic Instability, Cell. Motil. Cyto. 26 (1993), 275-281.

    Article  Google Scholar 

  16. Carlier, M.F., Melki, R., Pantaloni, D., Hill, T.L. and Chen, Y.: Synchronus Oscillations in Microtubule Polymerization, Proc. Natl. Acad. Sci. USA 84 (1987), 5257-5261.

    Article  ADS  Google Scholar 

  17. Mandelkow, E.-M. and Mandelkow, E.: Microtubule Oscillations, Cell Motil. and Cytoskel. 22 (1992), 235-244.

    Article  Google Scholar 

  18. Flyvbjerg, H., Holy, T.E. and Leibler, S.: Microtubule Dynamics: Caps, Catastrophes, and Coupled Hydrolysis, Phys. Rev. E 54 (1996), 5538-5560.

    Article  ADS  Google Scholar 

  19. Houchmandzadeh, B. and Vallade, M.: Collective Oscillations in Microtubule Growth, Phys. Rev. E 6320 (1996), 53.

    Google Scholar 

  20. Sept, D., Limbach, H.-J., Bolterauer, H. and Tuszynski, J.A.: A Chemical Kinetics Model for Microtubule Oscillations, J. theor. Biol. 197 (1999), 77-88.

    Article  Google Scholar 

  21. Mandelkow, E.M., Mandelkow, E. and Milligan, R.: Microtubule Dynamics and Microtubule Caps: A Time Resolved Cryo-Electron Microscopy Study, J. Cell Biol. 114 (1991), 977-991.

    Article  Google Scholar 

  22. Tran, P.T., Walker, R.A. and Salmon, E.D.: A Metastable Intermediate State of Microtubule Dynamic Instability that Differs Significantly between Plus and Minus Ends, J. Cell Biol. 138 (1997), 105-117.

    Article  Google Scholar 

  23. Sept, D.: Models of Assembly and Disassembly of Individual Microtubules and their Ensembles, PhD thesis, University of Alberta, 1997.

  24. Fygenson, D.K., Braun, E. and Libchaber, A.: Phase Diagram of Microtubules, Phys. Rev. D 50 (1994), 1579-1588.

    ADS  Google Scholar 

  25. Tabony, J. and Job, D.: Spatial Structures in Microtubular Solutions Requiring a Sustained Energy Source, Nature (London) 346 (1990), 448-451.

    Article  ADS  Google Scholar 

  26. Nogales, E., Wolf, S.G. and Downing, K.: Structure of the Alpha-Beta Tubulin Dimer by Electron Crystallography, Nature (London) 391 (1998), 199-203.

    Article  ADS  Google Scholar 

  27. Kraulis, Per J.: MOLSCRIPT, A Program to Produce Both Detailed and Schematic Plots of Protein Structures, J. Appl. Crystallogr. 24 (1991), 946-950.

    Article  Google Scholar 

  28. Bairoch, A. and Apweiler, R.: The SWISS-PROT Protein Sequence Data Bank and its Supplement TrEMBL in 1998, Nucleic Acids Res. 26 (1998), 38-42.

    Article  Google Scholar 

  29. Lu, Q., Moore, G.D., Walss, C. and Luduena, R.F.: Structural and Functional Properties of Tubulin Isotypes, Adv. Struct. Biol. 5 (1998), 203-227.

    Google Scholar 

  30. Hyman, A.A., Salser, S., Dreschel, D.N., Unwin, N. and Mitchison, T.J.: Role of GTP Hydrolysis in Microtubule Dynamics: Information from a Slowly Hydrolyzable Analogue, GMPCPP, Molec. Biol. Cell 3 (1992), 1155-1167.

    Google Scholar 

  31. Hyman, A.A., Chrétien, D., Arnal, I. and Wade, R.H.: Structural Changes Accompanying GTP Hydrolysis in Microtubules: Information from a Slowly Hydrolyzable Analogue Guanlyl-(α,β)-Methylene-Diphosphonate, J. Cell. Biol. 128 (1995), 117-125.

    Article  Google Scholar 

  32. Semënov, M.V.: New Concept of Microtubule Dynamics and Microtubule Motor Movement and New Model of Chromosome Movement in Mitosis, J. theor. Biol. 179 (1996), 91-117.

    Article  Google Scholar 

  33. Gittes, F., Mickey, E. and Nettleton, J.: Flexural Rigidity of Microtubules and Actin Filaments measured from Thermal Fluctuations in Shape, J. Cell Biol. 120 (1993), 923-934.

    Article  Google Scholar 

  34. Felgner, H., Frank, R. and Schliwa, M.: Flexural Rigidity of Microtubules measured with the Use of Optical Tweezers, J. Cell. Sci. 109 (1996), 509-516.

    Google Scholar 

  35. Mickey, B. and Howard, J.: Rigidity of Microtubules is Increased by Stabilizing Agents, J. Cell Biol. 130 (1995), 909-917.

    Article  Google Scholar 

  36. Elbaum, M., Fygenson, D.K. and Libchaber, A.: Buckling Microtubules in Vesicles, Phys. Rev. Lett. 76 (1996), 4078-4081.

    Article  ADS  Google Scholar 

  37. Vale, R.D., Coppin, C.M., Malik, F., Kull, F.J. and Milligan, R.A.: Tubulin GTP Hydrolysis Influences the Structure, Mechanical Properties, and Kinesin-Driven Transport of Microtubules, J. Biol. Chem. 269 (1994), 23769-23775.

    Google Scholar 

  38. Venier, P., Maggs, A.C., Carlier, M.-F. and Pantaloni, D.: Analysis of Microtubule Rigidity using Hydrodynamic Flow and Thermal Fluctuations, J. Biol. Chem. 269 (1994), 13353-13360.

    Google Scholar 

  39. Edelstein-Keshet, L.: A Mathematical Approach to Skeletal Assembly, Eur. Biophys. J. 27 (1998), 521-531.

    Article  Google Scholar 

  40. Civelecoglu, G. and Edelstein-Keshet, L.: Modeling the Dynamics of F-Actin in the Cell, Bull. Math. Biol. 56 (1998), 587-616.

    Article  Google Scholar 

  41. Oosawa, F. and Asakura, S.: Thermodynamics of the Polymerization of Protein, Academic Press, London, New York, 1975.

    Google Scholar 

  42. Pollard, T.D.: Rate Constants for the Reactions of ATP-and ADP-Actin with the Ends of Actin Filaments, J. Cell Biol. 103 (1986), 2747-2754.

    Article  Google Scholar 

  43. Tobacman, L.S. and Korn, E.D.: The Kinetics of Actin Nucleation and Polymerization, J. Biol. Chem. 258 (1983), 3207-3214.

    Google Scholar 

  44. Cooper, J.A., Buhle, E.L., Jr., Walker, S.B., Tsong, T.Y. and Pollard, T.D.: Kinetic Evidence for a Monomer Activation Step in Actin Polymerization, Biochemistry 22 (1983), 2193-2202.

    Article  Google Scholar 

  45. Frieden, C.: Polymerization of Actin: Mechanism of the Mg2+-induced Process at pH 8 and 20?C, Proc. Natl. Acad. Sci. USA 80 (1983), 6513-6517.

    Article  ADS  Google Scholar 

  46. Frieden, C. and Goddette, D.: Polymerization of Actin and Actin-like Systems: Evaluation of the Time Course of Polymerization in Relation to the Mechanism, Biochemistry 22 (1983), 5836-5843.

    Article  Google Scholar 

  47. Wegner, A. and Savko, P.: Fragmentation of Actin Filaments, Biochemistry 21 (1982), 1909-1913.

    Article  Google Scholar 

  48. Buzan, J.M. and Frieden, C.: Yeast Actin: Polymerization Kinetic Studies of Wild Type and a Poorly Polymerizing Mutant, Proc. Natl. Acad. Sci. USA 93 (1996), 91-95.

    Article  ADS  Google Scholar 

  49. Kinosian, H.J., Selden, L.A., Estes, J.E. and Gershman, L.C.: Actin Filament Annealing in the Presence of ATP and Phalloidin, Biochem. 32 (1993), 12353-12357.

    Article  Google Scholar 

  50. Rickard, J.E. and Sheterline, P.: Effect of ATP Removal and Inorganic Phosphate on Length Redistribution of Sheared Actin Filaments Populations: Evidence for a Mechanism of End-to-End Annealing, J. Mol. Biol. 201 (1988), 675-681.

    Article  Google Scholar 

  51. Carlier, M.F., Pantaloni, D. and Korn, E.D.: Steady State Length Distribution of F-actin under Controlled Fragmentation and Mechanism of Length Redistribution following Fragmentation, J. Biol. Chem. 259 (1984), 9987-9991.

    Google Scholar 

  52. Murphy, D.B., Gray, R.O., Grasser, W.A. and Pollard, T.D.: Direct Demonstration of Actin Filament Annealing in Vitro, J. Cell Biol. 106 (1988), 1947-1954.

    Article  Google Scholar 

  53. Press, W., Teukolsky, S., Vetterling, W. and Flannery, B.: Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  54. de Gennes, P.-G.: Introduction to Polymer Dynamics, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  55. Doi, M.: Rotational Relaxation Time of Rigid Rod-Like Macromolecule in Concentrated Solution, J. Physiol. (Paris) 36 (1975), 607-617.

    Google Scholar 

  56. Janmey, P.A., Hvidt, S., Käs, J., Lerche, D., Maggs, A., Sackmann, E., Schliwa, M. and Stossel, T.P.: The Mechanical Properties of Actin Gels. J. Biol. Chem. 269 (1994), 32503-32513.

    Google Scholar 

  57. Käs, J., Strey, H., Tang, J.X., Finger, D., Ezzell, R., Sackmann, E. and Janmey, P.A.: F-Actin, a Model Polymer for Semiflexible Chains in Dilute, Semidilute, and Liquid Crystalline Solutions, Biophys. J. 70 (1996), 609-625.

    Article  Google Scholar 

  58. Erickson, H.P.: Co-Operativity in Protein-Protein Association, J. Molec. Biol. 206 (1989), 465-474.

    Article  Google Scholar 

  59. Schafer, D., Jennings, P. and Cooper, J.: Dynamics of Capping Protein and Actin Assembly In Vitro: Uncapping Barbed Ends by Polyphosphoinositides, J. Cell Biol. 135 (1996), 169-179.

    Article  Google Scholar 

  60. Casella, J.F., Barron-Casella, E.A. and Torres, M.A.: Quantitation of CapZ in Conventional Actin Preparations and Methods for Further Purification of Actin, Cell Motil. Cytoskel. 30 (1995), 164-170.

    Article  Google Scholar 

  61. Leibler, S. and Huse, D.A.: Porters versus Rowers: A Unified Stochastic Model of Motor Proteins, J. Cell Biol. 121 (1993), 1357-1368.

    Article  Google Scholar 

  62. Brown, J.A. and Tuszynski, J.A.: Dipole Interactions in Axonal Microtubules as a Mechanism of Signal Propagation, Phys. Rev. E 56 (1997), 5834-5840.

    Article  ADS  Google Scholar 

  63. Woehlke, G., Ruby, A.K., Hart, C.L., Ly, B., Hom-Booher, N. and Vale, R.D.: Microtubule Interaction Site of the Kinesin Motor, Cell 90 (1997), 207-216.

    Article  Google Scholar 

  64. Jülicher, F., Adjari, A. and Prost, J.: Modeling Molecular Motors, Rev. Mod. Phys. 69 (1997), 1269-1281.

    Article  ADS  Google Scholar 

  65. Ruppel, K.M., Lorenz, M. and Spudich, J.A.: Myosin Structure/Function: A Combined Mutagenesis-Crystallography Approach, Curr. Opin. Struct. Bio. 5 (1995), 181-186.

    Article  Google Scholar 

  66. Buttiker, M.: Z. Phys. B 68 (1987), 161.

    Article  ADS  Google Scholar 

  67. Landauer, R.: J. Stat. Phys. 53 (1988), 233.

    Article  ADS  Google Scholar 

  68. Feynman, R.P., Leighton, R.B. and Sands, M.: The Feynman Lectures on Physics, Addison-Wesley, Reading MA, 1969.

    Google Scholar 

  69. Doering, C.R., Horsthemke, W. and Riordan, J.: Phys. Rev. Lett. 72 (1994), 2984.

    Article  ADS  Google Scholar 

  70. Astumian, R.D. and Bier, M.: Phys. Rev. Lett. 72 (1994), 1766.

    Article  ADS  Google Scholar 

  71. Risken, H.: The Fokker-Planck Equation, Springer-Verlag, Berlin, 1989.

    MATH  Google Scholar 

  72. Svoboda, K. and Block, S.M.: Cell 77 (1994), 773.

    Article  Google Scholar 

  73. Hays, T.S. and Salmon, E.D.: Poleward Force at the Kinetochore in Metaphase depends on the Number of Kinetochore Microtubules, J. Cell Biol. 110 (1990), 391-404.

    Article  Google Scholar 

  74. Spurck, T.P. and Pickett, H.J.: On the Mechanism of Anaphase A: Evidence that ATP is needed for Microtubule Disassembly and not Generation of Poleward force, J. Cell Biol. 105 (1987), 1691-1705.

    Article  Google Scholar 

  75. Sept, D., Xu, J., Pollard, T.D. and McCammon, J.A.: Annealing accounts for the length of actin filaments formed by spontaneous polymenization. Biophys. J. 77, 2911-2919 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2J1, Canada

    J.A. Tuszynski & J.A. Brown

  2. Department of Biomedical Engineering, Center for Computational Biology, Washington University, Campus Box 1097, One Brookings Drive, St. Louis, MO, 63130-4899, USA

    D. Sept

Authors
  1. J.A. Tuszynski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.A. Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Sept
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tuszynski, J., Brown, J. & Sept, D. Models of the Collective Behavior of Proteins in Cells: Tubulin, Actin and Motor Proteins. Journal of Biological Physics 29, 401–428 (2003). https://doi.org/10.1023/A:1027318920964

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1027318920964

Keywords

Search

Navigation