Skip to main content
PMC home page
Journal of Biological Physics logoLink to Journal of Biological Physics
. 2003 Dec;29(4):401–428. doi: 10.1023/A:1027318920964

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

JA Tuszynski 1, JA Brown 1, D Sept 2
PMCID: PMC3456179  PMID: 23345857

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.

Full Text

The Full Text of this article is available as a PDF (491.6 KB).

References

  • 1.Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J.D. Molecular Biology of the Cell. London: Garland Publishing; 1994. [Google Scholar]
  • 2.Luby-Phelps K. Physical Properties of Cytoplasm. Curr. Opin. Cell Biol. 1994;6:3–9. doi: 10.1016/0955-0674(94)90109-0. [DOI] [PubMed] [Google Scholar]
  • 3.Hinner B., Tempel M., Sackmann E., Kroy K., Frey E.Entanglement, Elasticity and Viscous Relaxation of Actin Solutions Phys. Rev. Lett. 1998812614–2618.1998PhRvL..81.2614H 10.1103/PhysRevLett.81.2614 [DOI] [Google Scholar]
  • 4.Frey E., Kroy K., Wilhelm J. Viscoelasticity of Biopolymer Networks. Adv. Struct. Biol. 1998;5:135–168. [Google Scholar]
  • 5.Ingber D.E. Tensegrity: The Architectural Basis of Cellular Mechanotransduction. Ann. Rev. Physiology. 1997;59:575–599. doi: 10.1146/annurev.physiol.59.1.575. [DOI] [PubMed] [Google Scholar]
  • 6.Chen C.S., Mrksich M., Huang S., Whitesides G.M., Ingber D.E. Geometric Control of Cell Life and Death. Science. 1997;276:1425–1428. doi: 10.1126/science.276.5317.1425. [DOI] [PubMed] [Google Scholar]
  • 7.King R.W.P., Wu T.T.Electric Field Induced in Cells in the Human Body when This is Exposed to Low-Frequency Electric Fields Phys. Rev. E 1998582363–2369.1998PhRvE..58.2363K 10.1103/PhysRevE.58.2363 [DOI] [Google Scholar]
  • 8.Ledbetter M.C., Porter K.R. A 'Microtubule' in Plant Cell Fine Structure. J. Cell Biol. 1963;19:239–250. doi: 10.1083/jcb.19.1.239. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 9.Amos L.A., Amos W.B. Molecules of the Cytoskeleton. London: Macmillan Press; 1991. [Google Scholar]
  • 10.Chrétien D., Wade R.H. New Data on the Microtubule Surface Lattice. Bio. Cell. 1991;71:161–174. doi: 10.1016/0248-4900(91)90062-R. [DOI] [PubMed] [Google Scholar]
  • 11.Amos L.A. The Microtubule Lattice-20 Years on. Trends Cell Biol. 1995;5:48–51. doi: 10.1016/S0962-8924(00)88938-2. [DOI] [PubMed] [Google Scholar]
  • 12.Chrétien D., Metoz F., Verde F., Karsenti E., Wade R.H. Lattice-Defects in Microtubules: Protofilament Numbers vary within Individual Microtubules. J. Cell Biol. 1992;117:1031–1040. doi: 10.1083/jcb.117.5.1031. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 13.Mitchison T., Kirschner M.Dynamic Instability ofMicrotubule Growth Nature (London) 1984312237–242. 10.1038/312237a01984Natur.312..237M [DOI] [PubMed] [Google Scholar]
  • 14.Horio T., Hotani H.Visualization of the Dynamic Instability of Individual Microtubules by Dark Field Microscopy Nature (London) 1986321605–607.1986Natur.321..605H 10.1038/321605a0 [DOI] [PubMed] [Google Scholar]
  • 15.Cassimeris L. Regulation of Microtubule Dynamic Instability. Cell. Motil. Cyto. 1993;26:275–281. doi: 10.1002/cm.970260402. [DOI] [PubMed] [Google Scholar]
  • 16.Carlier M.F., Melki R., Pantaloni D., Hill T.L., Chen Y.Synchronus Oscillations in Microtubule Polymerization Proc. Natl. Acad. Sci. USA 1987845257–5261.1987PNAS...84.5257C 10.1073/pnas.84.15.5257 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 17.Mandelkow E.-M., Mandelkow E. Microtubule Oscillations. Cell Motil. and Cytoskel. 1992;22:235–244. doi: 10.1002/cm.970220403. [DOI] [PubMed] [Google Scholar]
  • 18.Flyvbjerg H., Holy T.E., Leibler S.Microtubule Dynamics: Caps, Catastrophes, and Coupled Hydrolysis Phys. Rev. E 1996545538–5560.1996PhRvE..54.5538F 10.1103/PhysRevE.54.5538 [DOI] [PubMed] [Google Scholar]
  • 19.Houchmandzadeh B., Vallade M. Collective Oscillations in Microtubule Growth. Phys. Rev. E. 1996;6320:53. doi: 10.1103/physreve.53.6320. [DOI] [PubMed] [Google Scholar]
  • 20.Sept D., Limbach H.-J., Bolterauer H., Tuszynski J.A. A Chemical Kinetics Model for Microtubule Oscillations. J. theor. Biol. 1999;197:77–88. doi: 10.1006/jtbi.1998.0861. [DOI] [PubMed] [Google Scholar]
  • 21.Mandelkow E.M., Mandelkow E., Milligan R. Microtubule Dynamics and Microtubule Caps: A Time Resolved Cryo-Electron Microscopy Study. J. Cell Biol. 1991;114:977–991. doi: 10.1083/jcb.114.5.977. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Tran P.T., Walker R.A., Salmon E.D. A Metastable Intermediate State of Microtubule Dynamic Instability that Differs Significantly between Plus and Minus Ends. J. Cell Biol. 1997;138:105–117. doi: 10.1083/jcb.138.1.105. [DOI] [PMC free article] [PubMed] [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., Libchaber A.Phase Diagram of Microtubules Phys. Rev. D 1994501579–1588.1994PhRvE..50.1579F [DOI] [PubMed] [Google Scholar]
  • 25.Tabony J., Job D.Spatial Structures in Microtubular Solutions Requiring a Sustained Energy Source Nature (London) 1990346448–451.1990Natur.346..448T 10.1038/346448a0 [DOI] [PubMed] [Google Scholar]
  • 26.Nogales E., Wolf S.G., Downing K.Structure of the Alpha-Beta Tubulin Dimer by Electron Crystallography Nature (London) 1998391199–203.1998Natur.391..199N 10.1038/34465 [DOI] [PubMed] [Google Scholar]
  • 27.Kraulis P. J. MOLSCRIPT, A Program to Produce Both Detailed and Schematic Plots of Protein Structures. J. Appl. Crystallogr. 1991;24:946–950. doi: 10.1107/S0021889891004399. [DOI] [Google Scholar]
  • 28.Bairoch A., Apweiler R. The SWISS-PROT Protein Sequence Data Bank and its Supplement TrEMBL in 1998. Nucleic Acids Res. 1998;26:38–42. doi: 10.1093/nar/26.1.38. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 29.Lu Q., Moore G.D., Walss C., Luduena R.F. Structural and Functional Properties of Tubulin Isotypes. Adv. Struct. Biol. 1998;5:203–227. [Google Scholar]
  • 30.Hyman A.A., Salser S., Dreschel D.N., Unwin N., Mitchison T.J. Role of GTP Hydrolysis in Microtubule Dynamics: Information from a Slowly Hydrolyzable Analogue, GMPCPP. Molec. Biol. Cell. 1992;3:1155–1167. doi: 10.1091/mbc.3.10.1155. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 31.Hyman A.A., Chrétien D., Arnal I., Wade R.H. Structural Changes Accompanying GTP Hydrolysis in Microtubules: Information from a Slowly Hydrolyzable Analogue Guanlyl-(α,β)-Methylene-Diphosphonate. J. Cell. Biol. 1995;128:117–125. doi: 10.1083/jcb.128.1.117. [DOI] [PMC free article] [PubMed] [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. 1996;179:91–117. doi: 10.1006/jtbi.1996.0052. [DOI] [PubMed] [Google Scholar]
  • 33.Gittes F., Mickey E., Nettleton J. Flexural Rigidity of Microtubules and Actin Filaments measured from Thermal Fluctuations in Shape. J. Cell Biol. 1993;120:923–934. doi: 10.1083/jcb.120.4.923. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Felgner H., Frank R., Schliwa M. Flexural Rigidity of Microtubules measured with the Use of Optical Tweezers. J. Cell. Sci. 1996;109:509–516. doi: 10.1242/jcs.109.2.509. [DOI] [PubMed] [Google Scholar]
  • 35.Mickey B., Howard J. Rigidity of Microtubules is Increased by Stabilizing Agents. J. Cell Biol. 1995;130:909–917. doi: 10.1083/jcb.130.4.909. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 36.Elbaum M., Fygenson D.K., Libchaber A.Buckling Microtubules in Vesicles Phys. Rev. Lett. 1996764078–4081.1996PhRvL..76.4078E 10.1103/PhysRevLett.76.4078 [DOI] [PubMed] [Google Scholar]
  • 37.Vale R.D., Coppin C.M., Malik F., Kull F.J., Milligan R.A. Tubulin GTP Hydrolysis Influences the Structure, Mechanical Properties, and Kinesin-Driven Transport of Microtubules. J. Biol. Chem. 1994;269:23769–23775. [PubMed] [Google Scholar]
  • 38.Venier P., Maggs A.C., Carlier M.-F., Pantaloni D. Analysis of Microtubule Rigidity using Hydrodynamic Flow and Thermal Fluctuations. J. Biol. Chem. 1994;269:13353–13360. [PubMed] [Google Scholar]
  • 39.Edelstein-Keshet L. A Mathematical Approach to Skeletal Assembly. Eur. Biophys. J. 1998;27:521–531. doi: 10.1007/s002490050162. [DOI] [PubMed] [Google Scholar]
  • 40.Civelecoglu G., Edelstein-Keshet L. Modeling the Dynamics of F-Actin in the Cell. Bull. Math. Biol. 1998;56:587–616. doi: 10.1016/S0092-8240(05)80305-2. [DOI] [PubMed] [Google Scholar]
  • 41.Oosawa F., Asakura S. Thermodynamics of the Polymerization of Protein. London, New York: Academic Press; 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. 1986;103:2747–2754. doi: 10.1083/jcb.103.6.2747. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 43.Tobacman L.S., Korn E.D. The Kinetics of Actin Nucleation and Polymerization. J. Biol. Chem. 1983;258:3207–3214. [PubMed] [Google Scholar]
  • 44.Cooper J.A., Buhle E.L., Jr., Walker S.B., Tsong T.Y., Pollard T.D. Kinetic Evidence for a Monomer Activation Step in Actin Polymerization. Biochemistry. 1983;22:2193–2202. doi: 10.1021/bi00278a021. [DOI] [PubMed] [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 1983806513–6517.1983PNAS...80.6513F 10.1073/pnas.80.21.6513 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 46.Frieden C., Goddette D. Polymerization of Actin and Actin-like Systems: Evaluation of the Time Course of Polymerization in Relation to the Mechanism. Biochemistry. 1983;22:5836–5843. doi: 10.1021/bi00294a023. [DOI] [PubMed] [Google Scholar]
  • 47.Wegner A., Savko P. Fragmentation of Actin Filaments. Biochemistry. 1982;21:1909–1913. doi: 10.1021/bi00537a032. [DOI] [PubMed] [Google Scholar]
  • 48.Buzan J.M., Frieden C.Yeast Actin: Polymerization Kinetic Studies of Wild Type and a Poorly Polymerizing Mutant Proc. Natl. Acad. Sci. USA 19969391–95.1996PNAS...93...91B 10.1073/pnas.93.1.91 [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 49.Kinosian H.J., Selden L.A., Estes J.E., Gershman L.C. Actin Filament Annealing in the Presence of ATP and Phalloidin. Biochem. 1993;32:12353–12357. doi: 10.1021/bi00097a011. [DOI] [PubMed] [Google Scholar]
  • 50.Rickard J.E., 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. 1988;201:675–681. doi: 10.1016/0022-2836(88)90466-4. [DOI] [PubMed] [Google Scholar]
  • 51.Carlier M.F., Pantaloni D., Korn E.D. Steady State Length Distribution of F-actin under Controlled Fragmentation and Mechanism of Length Redistribution following Fragmentation. J. Biol. Chem. 1984;259:9987–9991. [PubMed] [Google Scholar]
  • 52.Murphy D.B., Gray R.O., Grasser W.A., Pollard T.D. Direct Demonstration of Actin Filament Annealing in Vitro. J. Cell Biol. 1988;106:1947–1954. doi: 10.1083/jcb.106.6.1947. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 53.Press W., Teukolsky S., Vetterling W., Flannery B. Numerical Recipes in C: The Art of Scientific Computing. Cambridge: Cambridge University Press; 1992. [Google Scholar]
  • 54.de Gennes P.-G. Introduction to Polymer Dynamics. Cambridge: Cambridge University Press; 1990. [Google Scholar]
  • 55.Doi M. Rotational Relaxation Time of Rigid Rod-Like Macromolecule in Concentrated Solution. J. Physiol. (Paris) 1975;36:607–617. [Google Scholar]
  • 56.Janmey P.A., Hvidt S., Käs J., Lerche D., Maggs A., Sackmann E., Schliwa M., Stossel T.P. The Mechanical Properties of Actin Gels. J. Biol. Chem. 1994;269:32503–32513. [PubMed] [Google Scholar]
  • 57.Käs J., Strey H., Tang J.X., Finger D., Ezzell R., Sackmann E., Janmey P.A. F-Actin, a Model Polymer for Semiflexible Chains in Dilute, Semidilute, and Liquid Crystalline Solutions. Biophys. J. 1996;70:609–625. doi: 10.1016/S0006-3495(96)79630-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 58.Erickson H.P. Co-Operativity in Protein-Protein Association. J. Molec. Biol. 1989;206:465–474. doi: 10.1016/0022-2836(89)90494-4. [DOI] [PubMed] [Google Scholar]
  • 59.Schafer D., Jennings P., Cooper J. Dynamics of Capping Protein and Actin Assembly In Vitro: Uncapping Barbed Ends by Polyphosphoinositides. J. Cell Biol. 1996;135:169–179. doi: 10.1083/jcb.135.1.169. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 60.Casella J.F., Barron-Casella E.A., Torres M.A. Quantitation of CapZ in Conventional Actin Preparations and Methods for Further Purification of Actin. Cell Motil. Cytoskel. 1995;30:164–170. doi: 10.1002/cm.970300208. [DOI] [PubMed] [Google Scholar]
  • 61.Leibler S., Huse D.A. Porters versus Rowers: A Unified Stochastic Model of Motor Proteins. J. Cell Biol. 1993;121:1357–1368. doi: 10.1083/jcb.121.6.1357. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 62.Brown J.A., Tuszynski J.A.Dipole Interactions in Axonal Microtubules as a Mechanism of Signal Propagation Phys. Rev. E 1997565834–5840.1997PhRvE..56.5834B 10.1103/PhysRevE.56.5834 [DOI] [Google Scholar]
  • 63.Woehlke G., Ruby A.K., Hart C.L., Ly B., Hom-Booher N., Vale R.D. Microtubule Interaction Site of the Kinesin Motor. Cell. 1997;90:207–216. doi: 10.1016/S0092-8674(00)80329-3. [DOI] [PubMed] [Google Scholar]
  • 64.Jülicher F., Adjari A., Prost J.Modeling Molecular Motors Rev. Mod. Phys. 1997691269–1281.1997RvMP...69.1269J 10.1103/RevModPhys.69.1269 [DOI] [Google Scholar]
  • 65.Ruppel K.M., Lorenz M., Spudich J.A. Myosin Structure/Function: A Combined Mutagenesis-Crystallography Approach. Curr. Opin. Struct. Bio. 1995;5:181–186. doi: 10.1016/0959-440X(95)80073-5. [DOI] [PubMed] [Google Scholar]
  • 66.Buttiker M.Z. Phys. B 198768161. 10.1007/BF013042211987ZPhyB..68..161B [DOI] [Google Scholar]
  • 67.Landauer R.J. Stat. Phys. 198853233. 10.1007/BF010115551988JSP....53..233L [DOI] [Google Scholar]
  • 68.Feynman R.P., Leighton R.B., Sands M. The Feynman Lectures on Physics. Reading MA: Addison-Wesley; 1969. [Google Scholar]
  • 69.Doering C.R., Horsthemke W., Riordan J.Phys. Rev. Lett. 19947229841994PhRvL..72.2984D 10.1103/PhysRevLett.72.2984 [DOI] [PubMed] [Google Scholar]
  • 70.Astumian R.D., Bier M.Phys. Rev. Lett. 19947217661994PhRvL..72.1766A 10.1103/PhysRevLett.72.1766 [DOI] [PubMed] [Google Scholar]
  • 71.Risken H. The Fokker-Planck Equation. Berlin: Springer-Verlag; 1989. [Google Scholar]
  • 72.Svoboda K., Block S.M. Cell. 1994;77:773. doi: 10.1016/0092-8674(94)90060-4. [DOI] [PubMed] [Google Scholar]
  • 73.Hays T.S., Salmon E.D. Poleward Force at the Kinetochore in Metaphase depends on the Number of Kinetochore Microtubules. J. Cell Biol. 1990;110:391–404. doi: 10.1083/jcb.110.2.391. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 74.Spurck T.P., 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. 1987;105:1691–1705. doi: 10.1083/jcb.105.4.1691. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 75.Sept D., Xu J., Pollard T.D., McCammon J.A. Annealing accounts for the length of actin filaments formed by spontaneous polymenization. Biophys. J. 1999;77:2911–2919. doi: 10.1016/s0006-3495(99)77124-9. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Journal of Biological Physics are provided here courtesy of Springer Science+Business Media B.V.

RESOURCES