Abstract
This theoretical research is motivated by a recent model of microtubule (MT) transport put forward by Baas and Mozgova (Cytoskeleton 69:416–425, 2012). According to their model, in an axon all plus-end-distal mobile MTs move anterogradely while all minus-end-distal mobile MTs move retrogradely. Retrograde MT transport thus represents a mechanism by which minus-end-distal MTs are removed from the axon. We suggested equations that implement Baas and Mozgova’s model. We employed these equations to simulate transport of short mobile MTs from a region (such as the site of axonal branch formation) where MT severing activity results in generation of a large number of short MTs of both orientations. We obtained the exact and approximate transient solutions of these equations utilizing the Laplace transform technique. We applied the obtained solutions to calculate the average rates of anterograde and retrograde transport of short MTs.
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References
Baas, P.W., Mozgova, O.I.: A novel role for retrograde transport of microtubules in the axon. Cytoskeleton 69, 416–425 (2012)
Wang, L., Brown, A.: Rapid movement of microtubules in axons. Curr. Biol. 12, 1496–1501 (2002)
Baas, P., Karabay, A., Qiang, L.: Microtubules cut and run. Trends Cell Biol. 15, 518–524 (2005)
Baas, P., Nadar, C., Myers, K.: Axonal transport of microtubules: the long and short of it. Traffic 7, 490–498 (2006)
Goldstein, L.S.B., Yang, Z.H.: Microtubule-based transport systems in neurons: the roles of kinesins and dyneins. Ann. Rev. Neurosci. 23, 39–71 (2000)
Lu, W., Fox, P., Lakonishok, M., Davidson, M.W., Gelfand, V.I.: Initial neurite outgrowth in Drosophila neurons is driven by kinesin-powered microtubule sliding. Curr. Biol. 23, 1018–1023 (2013)
He, Y., Francis, F., Myers, K.A., Yu, W.Q., Black, M.M., Baas, P.W.: Role of cytoplasmic dynein in the axonal transport of microtubules and neurofilaments. J. Cell Biol. 168, 697–703 (2005)
Ahmad, F., He, Y., Myers, K., Hasaka, T., Francis, F., Black, M., Baas, P.: Effects of dynactin disruption and dynein depletion on axonal microtubules. Traffic 7, 524–537 (2006)
Myers, K.A., Baas, P.W.: Microtubule–actin interactions during neuronal development. In: Gallo, G., Lanier, L.M. (eds.) Neurobiology of Actin. Advances in Neurobiology, vol. 5, pp. 73–96. Springer, New York (2011)
Hasaka, T., Myers, K., Baas, P.: Role of actin filaments in the axonal transport of microtubules. J. Neurosci. 24, 11291–11301 (2004)
Zheng, Y., Wildonger, J., Ye, B., Zhang, Y., Kita, A., Younger, S.H., Zimmerman, S., Jan, L.Y., Jan, Y.N.: Dynein is required for polarized dendritic transport and uniform microtubule orientation in axons. Nat. Cell Biol. 10, 1172–1180 (2008)
Dent, E., Callaway, J., Szebenyi, G., Baas, P., Kalil, K.: Reorganization and movement of microtubules in axonal growth cones and developing interstitial branches. J. Neurosci. 19, 8894–8908 (1999)
Yu, W., Liang Qiang, Solowska, J.M., Karabay, A., Korulu, S., Baas, P.W.: The microtubule-severing proteins spastin and katanin participate differently in the formation of axonal branches. Mol. Biol. Cell 19, 1485–1498 (2008)
Gibson, D.A., Ma, L.: Developmental regulation of axon branching in the vertebrate nervous system. Development 138, 183–195 (2011)
Jung, P., Brown, A.: Modeling the slowing of neurofilament transport along the mouse sciatic nerve. Phys. Biol. 6, 046002 (2009)
Li, Y., Jung, P., Brown, A.: Axonal transport of neurofilaments: a single population of intermittently moving polymers. J Neurosci. 32, 746–758 (2012)
Myers, K.A., Baas, P.W.: Kinesin-5 regulates the growth of the axon by acting as a brake on its microtubule array. J. Cell Biol. 178, 1081–1091 (2007)
King, S.J., Schroer, T.A.: Dynactin increases the processivity of the cytoplasmic dynein motor. Nat. Cell Biol. 2, 20–24 (2000)
Toba, S., Watanabe, T.M., Yamaguchi-Okimoto, L., Toyoshima, Y.Y., Higuchi, H.: Overlapping hand-over-hand mechanism of single molecular motility of cytoplasmic dynein. Proc. Nat. Acad. Sci. U. S. A. 103, 5741–5745 (2006)
Kuznetsov, A.V.: An exact solution describing slow axonal transport of cytoskeletal elements: effect of a finite half-life. Proc. R. Soc. A Math. Phys. Eng. Sci. 468, 3384–3397 (2012)
Kuznetsov, A.V.: An exact solution of transient equations describing slow axonal transport. Comput. Methods Biomech Biomed. Eng. 16, 1232–1239 (2013)
Tytell, M., Brady, S., Lasek, R.: Axonal-transport of a subclass of tau-proteins—evidence for the regional differentiation of microtubules in neurons. Proc. Nat. Acad. Sci. U. S. A. 81, 1570–1574 (1984)
Galbraith, J.A., Reese, T.S., Schlief, M.L., Gallant, P.E.: Slow transport of unpolymerized tubulin and polymerized neurofilament in the squid giant axon. Proc. Nat. Acad. Sci. U. S. A. 96, 11589–11594 (1999)
Roll-Mecak, A., Mcnally, F.J.: Microtubule-severing enzymes. Curr. Opin. Cell Biol. 22, 96–103 (2010)
Black, M., Lasek, R.: Slow components of axonal-transport: two cytoskeletal networks. J. Cell Biol. 86, 616–623 (1980)
Oblinger, M., Brady, S., McQuarrie, I., Lasek, R.: Cytotypic differences in the protein-composition of the axonally transported cytoskeleton in mammalian neurons. J. Neurosci. 7, 453–462 (1987)
Kuznetsov, I.A., Kuznetsov, A.V.: Analytical comparison between Nixon-Logvinenko and Jung-Brown theories of slow neurofilament transport in axons. Math. Biosci. 245, 331–339 (2013)
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The authors are indebted to the anonymous reviewers for their constructive comments. AVK gratefully acknowledges support of the Alexander von Humboldt Foundation though the Humboldt Research Award.
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Kuznetsov, I.A., Kuznetsov, A.V. Modeling anterograde and retrograde transport of short mobile microtubules from the site of axonal branch formation. J Biol Phys 40, 41–53 (2014). https://doi.org/10.1007/s10867-013-9334-8
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DOI: https://doi.org/10.1007/s10867-013-9334-8