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Modelling the dynamics of F-actin in the cell

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Abstract

The regulation of the interactions between the actin binding proteins and the actin filaments are known to affect the cytoskeletal structure of F-actin. We develop a model depicting the formation of actin cytoskeleton, bundles and orthogonal networks, via activation or inactivation of different types of actin binding proteins. It is found that as the actin filament density increases in the cell, a spontaneous tendency to organize into bundles or networks occurs depending on the active actin binding protein concentration. Also, a minute change in the relative binding affinity of the actin binding proteins in the cell may lead to a major change in the actin cytoskeleton. Both the linear stability analysis and the numerical results indicate that the structures formed are highly sensitive to changes in the parameters, in particular to changes in the parameter ϕ, denoting the relative binding affinity and concentration of the actin binding proteins.

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Literature

  • Alt, W. 1987. Mathematical models in actin-myosin interaction. InFortschiritte der Zoology, Nature and Function of Cytoskeletal Proteins in Motility and Transport, Band 34, K. E. Wohlfarth-Bottermann (Ed.), pp. 219–230. Stuttgart: Gustav Fisher Verlag.

    Google Scholar 

  • Alt, W. 1992. Personal communication.

  • Civelekoglu, G. and A. Mogilner. 1994. The actin tail ofListeria monocytogenes. Submitted.

  • Cooper, J. A. 1991. The role of actin polymerization in cell motility.Ann. Rev. Physiol. 53, 585–605.

    Article  Google Scholar 

  • Cooper, J. A., E. L. Buhle, Jr., S. B. Walker, T. Y. Tsong and T. J. Pollard. 1983. Kinetic evidence for a monomer activation step in actin polymerization.Biochemistry 22, 2193–2202.

    Article  Google Scholar 

  • Dembo, M. 1989. Field theories of the cytoplasm.Com. theor. Biol. 1(3), 159–177.

    MathSciNet  Google Scholar 

  • Edelstein-Keshet, L. and G. B. Ermentrout. 1990. Models for contact mediated pattern formation.J. math. Biol. 29, 33–58.

    Article  MATH  MathSciNet  Google Scholar 

  • Harris, H. 1987. Few answers but many questions.Nature 330, 310–311.

    Article  Google Scholar 

  • Hartwig, J. H. 1992. Mechanisms of actin rearrangements mediating platelet activation.J. Cell. Biol. 118(6), 1421–1442.

    Article  Google Scholar 

  • Hartwig, J. H. and T. P. Stossel. 1981. Structure of macrophage actin-binding protein molecules in solution and interacting with actin filaments.J. molec. Biol. 145, 563–581.

    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 

  • Hartwig, J. H., M. Thelen, A. Rosen, P. A. Janmey, A. C. Nairn and A. Aderem. 1992. Marcks is an actin filament crosslinking protein regulated by protein kinease C and calcium-calmodulin.Nature 356, 618–622.

    Article  Google Scholar 

  • Korn, E. D. 1982. Actin polymerization and its regulation by proteins from nonmuscle cells.Physiol. Rev. 62(2), 672–729.

    Google Scholar 

  • Meulemans, W. and A. De Loof. 1992. Changes in cytoskeletal actin patterns in the malphigian tubules of the fishfly,Sarcophage bullata, during metamorphosis.Int. J. Insect Morphol. Embryol. 21(1), 1–16.

    Article  Google Scholar 

  • Mogilner, A. and L. Edelstein-Keshet. 1994a. Selecting a common direction: How orientational order can arise from simple contact responses between interacting cells. Submitted.

  • Mogilner, A. and L. Edelstein-Keshet. 1994b. Spatio-angular order in populations of self-aligning objects: formation of oriented patches. Submitted.

  • Mossakowska, M., J. Belagyi and H. Strzelecka-Golaszewska. 1988. An EPR study of the rotational dynamics of actins from striated and smooth muscle and their complexes with heavy meromyosin.Eur. J. Biochem. 175, 557–564.

    Article  Google Scholar 

  • Oster, G. 1989. Cell motility and tissue morphogenesis. InCell Shape: Determinants, Regulation and Regulatory Role, pp. 33–61. New York: Aademic Press.

    Google Scholar 

  • Oster, G. F. and G. M. Odell. 1984. Mechanics of cytogels. I: oscillations in physarum.Cell Motil. 4, 464–503.

    Article  Google Scholar 

  • Oster, G., J. D. Murray and G. M. Odell. 1985. The formation of microvilli. InMolecular Determinants of Animal Form, pp. 365–384. New York: Alan R. Liss.

    Google Scholar 

  • Phillips, L., F. Seperovic, B. A. Cornell, J. A. Barden and C. G. dos Remedios. 1991. Actin dynamics studied by solid-state NMR spectroscopy.Eur. Biophys. J. 19, 147–155.

    Article  Google Scholar 

  • Pohl, T. 1990. Periodic contraction waves in cytoplasmic extracts. InBiological Motion: Lecture Notes in Biomathematics, Vol. 89, W. Alt and G. Hoffmann (Eds), pp. 85–94. Berlin: Springer.

    Google Scholar 

  • Pollard, T. D. 1990. Actin.Curr. Opin. Cell Biol. 2, 33–40.

    MathSciNet  Google Scholar 

  • Pollard, T. D. and J. A. Cooper. 1986. Actin and actin-binding proteins. A critical evaluation of mechanisms and functions.Ann. Rev. Biochem. 55, 987–1035.

    Article  Google Scholar 

  • Pollard, T. D., L. Satterwhite, L. Cisek, J. Corden, M. Sato and P. Maupin. 1990. Actin and myosin biochemistry in relation to cytokinesis.Ann. N.Y. Acad. Sci. 582, 120–130.

    Google Scholar 

  • Sato, M., W. H. Schwartz and T. D. Pollard. 1987. Dependence of the mechanical properties of actin/α-actinin gels on deformation rate.Nature 325, 828–830.

    Article  Google Scholar 

  • Sawyer, W. H., A. G. Woodhouse, J. J. Csarnecki and E. Blatt. 1988. Rotational dynamics of actin.Biochemistry 27, 7733–7740.

    Article  Google Scholar 

  • Sherratt, J. A. and J. Lewis. 1993. Stress induced alignment of actin filaments and the mechanism of cytogel.Bull. math. Biol. 55, 637–654.

    Article  MATH  Google Scholar 

  • Small, J. V., G. Rinnerthaler and H. Hinssen. 1982. Organization of actin meshworks in cultured cells: the leading edge.Cold Spring Harbor Symp. quant. Biol. 46, 599–611.

    Google Scholar 

  • Stossel, T. P. 1984. Contribution of actin to the structure of the cytoplasmic matrix.J. Cell Biol. 99(1), 15s-21s.

    Article  Google Scholar 

  • Stossel, T. P. 1990. How cells crawl.Am. Sci. 78, 408–423.

    Google Scholar 

  • Stossel, T. P., C. Chaponnier, R. M. Ezzel, J. H. Hartwig, P. A. Janmeyet al. 1985. Nonmuscle actin-binding proteins.Ann. Rev. Cell Biol. 1, 353–402.

    Article  Google Scholar 

  • Theriot, J. A. and T. J. Mitchison. 1992. The rate of actin based motility of intracellularListeria monocytogenes equals the rate of actin polymerization.Nature 357, 257–261.

    Article  Google Scholar 

  • Thomas, D. D., J. C. Seidel and J. Gergely. 1979. Rotational dynamics of spin-labeled F-actin in the sub-millisecond time range.J. molec. Biol. 132, 257–273.

    Article  Google Scholar 

  • Tilney, L. G., D. J. DeRosier and M. S. Tilney. 1992a. HowListeria exploits host cell actin to form its own cytoskeleton. I. Formation of a tail and how that tail might be involved in movement.J. Cell Biol. 118(1), 71–81.

    Article  Google Scholar 

  • Tilney, L. G., D. J. DeRosier and M. S. Tilney. 1992b. HowListeria exploits host cell actin to form its own cytoskeleton. II. Nucleation, actin filament polarity, filament assembly, and evidence for a pointed end capper.J. Cell Biol. 118(1), 83–93.

    Article  Google Scholar 

  • Vandekerckhove, J. 1990. Actin-binding proteins.Curr. Op. Cell Biol. 2, 41–50.

    Google Scholar 

  • Way, M. and A. Weeds. 1990. Cytoskeletal ups and downs.Nature 344, 292–294.

    Article  Google Scholar 

  • Weeds, A. 1982. Actin-binding proteins—regulators of cell architecture and motility.Nature 296, 811–816.

    Article  Google Scholar 

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Civelekoglu, G., Edelstein-Keshet, L. Modelling the dynamics of F-actin in the cell. Bltn Mathcal Biology 56, 587–616 (1994). https://doi.org/10.1007/BF02460713

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