Skip to main content
SpringerLink
Log in

Testing a model for the dynamics of actin structures with biological parameter values

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A simple mathematical model for the dynamics of network-bundle transitions in actin filaments has been previously proposed and some of its mathematical properties have been described. Other models in this class have since been considered and investigated mathematically. In this paper, we have made the first steps in connecting parameters in the model with biologically measurable quantities such as published values of rate constants for filament-crosslinker association. We describe how this connection was made, and give some preliminary numerical simulation results for the behavior of the model under biologically realistic parameter regimes. A key result is that filament length influences the bundle-network transition.

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

  • Alberts, B, D. Bray, J. Lewis, M. Raff, M. Roberts and J. D. Watson (1989). Molecular Biology of the Cell. New York: Garland.

    Google Scholar 

  • Bray, D. (1992). Cell Movements. New York: Garland.

    Google Scholar 

  • Burridge K. and J. R. Feramisco (1981). Non-muscle α-actinins are Calcium-sensitive Actin-binding Proteins. Nature 294, 565–567.

    Article  Google Scholar 

  • Civelekoglu, G. and L. Edelstein-Keshet (1994). Models for the formation of actin structures. Bull. Math. Biol. 56, 587–616.

    Article  MATH  Google Scholar 

  • Colombo, R., I. DalleDonne and A. Milzani (1993) α-Actinin Increases Actin Filament End Concentration by Inhibiting Annealing. J. Mol. Biol. 230, 1151–1158.

    Article  Google Scholar 

  • Coppin, C. M. and P. Leavis (1992). Quantitation of liquid-crystaline ordering in F-actin solutions. Biophys J. 63, 794–807.

    Google Scholar 

  • Doi, M. and S. F. Edwards (1986). The Theory of Polymer Dynamics, Oxford: Clarendon Press.

    Google Scholar 

  • Edelstein-Keshet, L. and G. B. Ermentrout (1990). Models for contact-mediated pattern formation: cells that form parallel arrays. J. Math. Biol. 29, 33–58.

    Article  MathSciNet  MATH  Google Scholar 

  • Edelstein-Keshet, L. and G. B. Ermentrout (1998). Models for the length distribution of actin filaments: I Simple polymerization and fragmentation acting alone. Bull. Math. Biol., in press.

  • Ermentrout, G. B. and L. Edelstein-Keshet (1998). Models for the length distribution of actin filaments: II: Polymerization and Fragmentation by Gelsolin acting together. Bull. Math. Biol., in press.

  • Furukawa, R., R. Kundra and M. Fechheimer (1993). Formation of liquid crystals from actin filaments. Biochemistry 32, 12346–12352.

    Google Scholar 

  • Geigant, E., K. Ladizhansky and A. Mogilner (1997). Integro-differential model for orientational distribution of F-actin in cells. SIAM J. Appl. Math., in press.

  • Geigant, E. and M. Stoll, (1996). A non-local model for alignment of oriented particles. Research Summary. Bonn University.

  • Giuliano, K. A. and D. L. Taylor (1995). Measurement and manipulation of cytoskeletal dynamics in living cells. Current Opinion Cell Biol. 7, 4–12.

    Article  Google Scholar 

  • Gorlin, J. B., R. Yamin, S. Eagen, M. Stewart, T. P. Stossel, D. J. Kwiatkowski and J. H. Hartwig (1990). Human endothelial actin-binding protein (ABP-280, nonmuscle filamin): a molecular leaf spring. J. Cell. Biol. 111, 1089–1105.

    Article  Google Scholar 

  • Hartwig, J. H. and D. J. Kwiatkowski (1991). Actin binding proteins. Current Opinion Cell Biol. 3, 87–97.

    Article  Google Scholar 

  • Hartwig, J. H., J. Tyler and T. P. Stossel (1980). Actin-binding protein promotes the bipolar and perpendicular branching of actin filaments. J. Cell. Biol. 87, 841–848.

    Article  Google Scholar 

  • Jacquez J. A. (1972). Compartmental Analysis in Biology and Medicine, Amsterdam: Elsevier.

    Google Scholar 

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

    Google Scholar 

  • Janmey, P. A., J. Peetermans, K. S. Zaner, T. P. Stossel and T. Tanaka (1986). Structure and Mobility of actin filaments as measured by quasielectric light scattering, viscometry and electron microscopy. J. Biol. Chem. 261, 8357–8362.

    Google Scholar 

  • Janson, L. W. and D. L. Taylor (1994). Actin-crosslinking protein regulation of filament movement in motility assays: a theoretical model. Biophys. J. 67, 973–982.

    Google Scholar 

  • Jockusch, B. M. and G. Isenberg (1981). Interaction of α-Actinin and Vinculin with Actin: Opposite effects on Filament Network Formation. Proc. Nat. Acad. Sci. USA. 78, 3005–3009.

    Article  Google Scholar 

  • Ladizhansky, K. (1994). Distribution of generalized aspect with applications to actin fibers and social interactions, Technical Report, MSc thesis Weizmann Institute of Science, Rehovot, Israel.

  • Luby-Phelps, K. (1994). Physical Properites of Cytoplasm. Current Opinion Cell Biol. 6, 3–9.

    Article  Google Scholar 

  • Lumsden, C. J. and P. A. Dufort (1993). Cellular Automaton Model of the Actin Cytoskeleton. Cell Motil. Cytoskel. 25, 87–104.

    Article  Google Scholar 

  • McGough, A. (1997). Structural Studies of Gelsolin: Actin Interactions, Baylor College of Medicine, Houston, http://dali.bcm.tmc.edu/amy/Gelsolin.html.

    Google Scholar 

  • Maciver, S. K., D. H. Wachsstock, W. H. Schwarz and T. D. Pollard (1991). The actin filament severing protein acotophorin promotes the formation of rigid bundles of actin filaments crosslinked with α-actinin. J. Cell Biol. 115, 1621–1628.

    Article  Google Scholar 

  • Meyer, R. K. and U. Aebi (1990). Bundling of actin filaments by α-actinin depends on its molecular length. J. Cell Biol. 110, 2013–2024.

    Article  Google Scholar 

  • Mogilner, A. and L. Edelstein-Keshet (1995). Selecting a common direction I. How orientational order can arise from simple contact responses between interacting cells. J. Math. Biol. 33, 619–660.

    Article  MathSciNet  MATH  Google Scholar 

  • Mogilner, A. and L. Edelstein-Keshet (1996). Spatio-angular order in populations of self-aligning objects: formation of oriented patches. Physica D89, 346–367.

    MathSciNet  Google Scholar 

  • Niederman, R. R., P. C. Amrein and J. Hartwig (1983). Three-dimensional structure of actin filaments and of an actin gel made with actin-binding protein. J. Cell. Biol. 96, 1400–1413.

    Article  Google Scholar 

  • Oster, G. F. (1994). Biophysics of Cell Motility, Lecture Notes, University of California Berkeley.

  • Otto, J. J. (1994). Actin-bundling proteins. Current Opinion Cell Biol. 6, 105–109.

    Article  Google Scholar 

  • Parfenov, V. N., D. S. Davis, G. N. Pochukalina, C. E. Sample, E. A. Bugaeva and K. G. Murti (1995). Nuclear actin filaments and their topological changes in frog oocytes. Exp. Cell Res. 217, 385–394.

    Article  Google Scholar 

  • Suzuki, A., T. Maeda and T. Ito (1991). Formation of liquid crystalline phase of actin filament solutions and its dependence on filament length as studied by optical birefringence. Biophys. J. 59, 25–30.

    Google Scholar 

  • Taylor, K. A. and D. W. Taylor (1994). Formation of two-dimensional complexes of F-Actin and crosslinking proteins on Lipid monolayers: demonstration of unipolar α-actinin—F-actin crosslinking. Biophys. J. 67, 1976–1983.

    Google Scholar 

  • Wachsstock, D. H., W. H. Schwarz and T. D. Pollard (1993). Affinity of α—Actinin for actin determines the structure and mechanical properties of actin filament gels. Biophys. J., 65, 205–214.

    Google Scholar 

  • Wachsstock, D. H., W. H. Schwarz and T. D. Pollard (1994). Cross—linker dynamics determine the mechanical properties of actin gels. Biophys. J. 66, 801–809.

    Google Scholar 

  • Zaner, K. S. (1995). Physics of actin networks. I. Rheology of semi-dilute F-Actin. Biophys. J. 68, 1019–1026.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Athan Spiros & Leah Edelstein-Keshet

Authors
  1. Athan Spiros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leah Edelstein-Keshet
    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

Spiros, A., Edelstein-Keshet, L. Testing a model for the dynamics of actin structures with biological parameter values. Bull. Math. Biol. 60, 275–305 (1998). https://doi.org/10.1006/bulm.1997.0022

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1006/bulm.1997.0022

Keywords

Search

Navigation