Skip to main content

2017 | OriginalPaper | Buchkapitel

Recent Mathematical Models of Axonal Transport

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

An axon is a long thin projection of a neuron that allows for rapid electrochemical communications with other cells over long distances. Axonal transport refers to the stochastic, bidirectional movement of organelles and proteins along cytoskeletal polymers inside an axon, powered by molecular motor proteins. The movement from the cell body to the axon terminal is called anterograde transport and the movement in the opposite direction is called retrograde transport. Axonal transport is a vital process for the axon to survive and maintain its regular shape. Mathematical models have been developed to help understand how cargoes are transported inside an axon and how impairment of axonal transport affects cargo distribution. In this chapter, we review recent mathematical models of axonal transport and discuss open problems in this area.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat M.G.L. Van den Heuvel, M.P. de Graaff, C. Dekker, Microtubule curvatures under perpendicular electric forces reveal a low persistence length. Proc. Natl. Acad. Sci. U. S. A. 105(23), 7941–7946 (2008)CrossRef M.G.L. Van den Heuvel, M.P. de Graaff, C. Dekker, Microtubule curvatures under perpendicular electric forces reveal a low persistence length. Proc. Natl. Acad. Sci. U. S. A. 105(23), 7941–7946 (2008)CrossRef
2.
Zurück zum Zitat S. Tsukita, H. Ishikawa, The cytoskeleton in myelinated axons: serial section study. Biomed. Res. 2, 424–437 (1981) S. Tsukita, H. Ishikawa, The cytoskeleton in myelinated axons: serial section study. Biomed. Res. 2, 424–437 (1981)
3.
Zurück zum Zitat B.J. Schnapp, T.S. Reese, Cytoplasmic structure in rapid frozen axons. J. Cell Biol. 94, 667–679 (1982)CrossRef B.J. Schnapp, T.S. Reese, Cytoplasmic structure in rapid frozen axons. J. Cell Biol. 94, 667–679 (1982)CrossRef
4.
Zurück zum Zitat N. Hirokawa, Axonal transport and the cytoskeleton. Curr. Opin. Neurobiol. 3(5), 724–731 (1993)CrossRef N. Hirokawa, Axonal transport and the cytoskeleton. Curr. Opin. Neurobiol. 3(5), 724–731 (1993)CrossRef
5.
Zurück zum Zitat A. Brown, Axonal transport, in Neuroscience in the 21st Century (Springer, Berlin, 2013) A. Brown, Axonal transport, in Neuroscience in the 21st Century (Springer, Berlin, 2013)
6.
Zurück zum Zitat N. Hirokawa, R. Takemura, Molecular motors and mechanisms of directional transport in neurons. Nat. Rev. Neurosci. 6(3), 201–214 (2005)CrossRef N. Hirokawa, R. Takemura, Molecular motors and mechanisms of directional transport in neurons. Nat. Rev. Neurosci. 6(3), 201–214 (2005)CrossRef
7.
Zurück zum Zitat F. Gittes, B. Mickey, J. Nettleton, J. Howard, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J. Cell Biol. 120(4), 923–934 (1993)CrossRef F. Gittes, B. Mickey, J. Nettleton, J. Howard, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J. Cell Biol. 120(4), 923–934 (1993)CrossRef
8.
Zurück zum Zitat H. Isambert, P. Venier, A.C. Maggs, A. Fattoum, R. Kassab, D. Pantaloni, M.F. Carlier, Flexibility of actin filaments derived from thermal fluctuations. effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J. Biol. Chem. 270(19), 11437–11444 (1995) H. Isambert, P. Venier, A.C. Maggs, A. Fattoum, R. Kassab, D. Pantaloni, M.F. Carlier, Flexibility of actin filaments derived from thermal fluctuations. effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J. Biol. Chem. 270(19), 11437–11444 (1995)
9.
Zurück zum Zitat K. Xu, G. Zhong, X. Zhuang, Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons. Science 339(6118), 452–456 (2013)CrossRef K. Xu, G. Zhong, X. Zhuang, Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons. Science 339(6118), 452–456 (2013)CrossRef
10.
Zurück zum Zitat E.L. Bearer, T.S. Reese, Association of actin filaments with axonal microtubule tracts. J. Neurocytol. 28(2), 85–98 (1999)CrossRef E.L. Bearer, T.S. Reese, Association of actin filaments with axonal microtubule tracts. J. Neurocytol. 28(2), 85–98 (1999)CrossRef
11.
Zurück zum Zitat P.J. Hollenbeck, W.M. Saxton, The axonal transport of mitochondria. J. Cell Sci. 118(Pt 23), 5411–5419 (2005)CrossRef P.J. Hollenbeck, W.M. Saxton, The axonal transport of mitochondria. J. Cell Sci. 118(Pt 23), 5411–5419 (2005)CrossRef
12.
Zurück zum Zitat R. Beck, J. Deek, M. C. Choi, T. Ikawa, O. Watanabe, E. Frey, P. Pincus, C.R. Safinya, Unconventional salt trend from soft to stiff in single neurofilament biopolymers. Langmuir 26(24), 18595–18599 (2010)CrossRef R. Beck, J. Deek, M. C. Choi, T. Ikawa, O. Watanabe, E. Frey, P. Pincus, C.R. Safinya, Unconventional salt trend from soft to stiff in single neurofilament biopolymers. Langmuir 26(24), 18595–18599 (2010)CrossRef
13.
Zurück zum Zitat O.I. Wagner, S. Rammensee, N. Korde, Q. Wen, J.-F. Leterrier, P.A. Janmey, Softness, strength and self-repair in intermediate filament networks. Exp. Cell Res. 313(10), 2228–2235 (2007)CrossRef O.I. Wagner, S. Rammensee, N. Korde, Q. Wen, J.-F. Leterrier, P.A. Janmey, Softness, strength and self-repair in intermediate filament networks. Exp. Cell Res. 313(10), 2228–2235 (2007)CrossRef
14.
Zurück zum Zitat R. Perrot, P. Lonchampt, A.C. Peterson, J. Eyer, Axonal neurofilaments control multiple fiber properties but do not influence structure or spacing of nodes of Ranvier. J. Neurosci. 27(36), 9573–9584 (2007)CrossRef R. Perrot, P. Lonchampt, A.C. Peterson, J. Eyer, Axonal neurofilaments control multiple fiber properties but do not influence structure or spacing of nodes of Ranvier. J. Neurosci. 27(36), 9573–9584 (2007)CrossRef
15.
Zurück zum Zitat R.L. Friede, T. Samorajski, Axon caliber related to neurofilaments and microtubules in sciatic nerve fibers of rats and mice. Anat. Rec. 167(4), 379–387 (1970)CrossRef R.L. Friede, T. Samorajski, Axon caliber related to neurofilaments and microtubules in sciatic nerve fibers of rats and mice. Anat. Rec. 167(4), 379–387 (1970)CrossRef
16.
Zurück zum Zitat L. Wang, C.L. Ho, D. Sun, R.K. Liem, A. Brown, Rapid movement of axonal neurofilaments interrupted by prolonged pauses. Nat. Cell Biol. 2(3), 137–141 (2000)CrossRef L. Wang, C.L. Ho, D. Sun, R.K. Liem, A. Brown, Rapid movement of axonal neurofilaments interrupted by prolonged pauses. Nat. Cell Biol. 2(3), 137–141 (2000)CrossRef
17.
Zurück zum Zitat N. Trivedi, P. Jung, A. Brown, Neurofilaments switch between distinct mobile and stationary states during their transport along axons. J. Neurosci. 27(3), 507–516 (2007)CrossRef N. Trivedi, P. Jung, A. Brown, Neurofilaments switch between distinct mobile and stationary states during their transport along axons. J. Neurosci. 27(3), 507–516 (2007)CrossRef
18.
Zurück zum Zitat E. Chevalier-Larsen, E.L.F. Holzbaur, Axonal transport and neurodegenerative disease. Biochim. Biophys. Acta 1762(11–12), 1094–1108 (2006)CrossRef E. Chevalier-Larsen, E.L.F. Holzbaur, Axonal transport and neurodegenerative disease. Biochim. Biophys. Acta 1762(11–12), 1094–1108 (2006)CrossRef
19.
Zurück zum Zitat K.J. De Vos, A.J. Grierson, S. Ackerley, C.C.J. Miller, Role of axonal transport in neurodegenerative diseases. Annu. Rev. Neurosci. 31, 151–173 (2008)CrossRef K.J. De Vos, A.J. Grierson, S. Ackerley, C.C.J. Miller, Role of axonal transport in neurodegenerative diseases. Annu. Rev. Neurosci. 31, 151–173 (2008)CrossRef
20.
Zurück zum Zitat S. Millecamps, J.-P. Julien, Axonal transport deficits and neurodegenerative diseases. Nat. Rev. Neurosci. 14(3), 161–176 (2013)CrossRef S. Millecamps, J.-P. Julien, Axonal transport deficits and neurodegenerative diseases. Nat. Rev. Neurosci. 14(3), 161–176 (2013)CrossRef
21.
Zurück zum Zitat C. Zhao, J. Takita, Y. Tanaka, M. Setou, T. Nakagawa, S. Takeda, H.W. Yang, S. Terada, T. Nakata, Y. Takei, M. Saito, S. Tsuji, Y. Hayashi, N. Hirokawa, Charcot-Marie-tooth disease type 2A caused by mutation in a microtubule motor kIF1Bbeta. Cell 105(5), 587–597 (2001)CrossRef C. Zhao, J. Takita, Y. Tanaka, M. Setou, T. Nakagawa, S. Takeda, H.W. Yang, S. Terada, T. Nakata, Y. Takei, M. Saito, S. Tsuji, Y. Hayashi, N. Hirokawa, Charcot-Marie-tooth disease type 2A caused by mutation in a microtubule motor kIF1Bbeta. Cell 105(5), 587–597 (2001)CrossRef
22.
Zurück zum Zitat L. Wang, A. Brown, A hereditary spastic paraplegia mutation in kinesin-1A/KIF5A disrupts neurofilament transport. Mol. Neurodegener. 5, 52 (2010)CrossRef L. Wang, A. Brown, A hereditary spastic paraplegia mutation in kinesin-1A/KIF5A disrupts neurofilament transport. Mol. Neurodegener. 5, 52 (2010)CrossRef
23.
Zurück zum Zitat M.E. MacDonald, C.M. Ambrose, M.P. Duyao, R.H. Myers, C. Lin, L. Srinidhi, G. Barnes, S.A. Taylor, M. James, N. Groot et al., A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington’s disease chromosomes. Cell 72(6), 971–983 (1993)CrossRef M.E. MacDonald, C.M. Ambrose, M.P. Duyao, R.H. Myers, C. Lin, L. Srinidhi, G. Barnes, S.A. Taylor, M. James, N. Groot et al., A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington’s disease chromosomes. Cell 72(6), 971–983 (1993)CrossRef
24.
Zurück zum Zitat M. Katsuno, H. Adachi, M. Minamiyama, M. Waza, K. Tokui, H. Banno, K.e Suzuki, Y. Onoda, F. Tanaka, M. Doyu, G. Sobue, Reversible disruption of dynactin 1-mediated retrograde axonal transport in polyglutamine-induced motor neuron degeneration. J. Neurosci. 26(47), 12106–12117 (2006) M. Katsuno, H. Adachi, M. Minamiyama, M. Waza, K. Tokui, H. Banno, K.e Suzuki, Y. Onoda, F. Tanaka, M. Doyu, G. Sobue, Reversible disruption of dynactin 1-mediated retrograde axonal transport in polyglutamine-induced motor neuron degeneration. J. Neurosci. 26(47), 12106–12117 (2006)
25.
Zurück zum Zitat I. Puls, C. Jonnakuty, B.H. LaMonte, E.L.F. Holzbaur, M. Tokito, E. Mann, M.K. Floeter, K. Bidus, D. Drayna, S.J. Oh, R.H. Brown Jr., C.L. Ludlow, K.H. Fischbeck, Mutant dynactin in motor neuron disease. Nat. Genet. 33(4), 455–456 (2003)CrossRef I. Puls, C. Jonnakuty, B.H. LaMonte, E.L.F. Holzbaur, M. Tokito, E. Mann, M.K. Floeter, K. Bidus, D. Drayna, S.J. Oh, R.H. Brown Jr., C.L. Ludlow, K.H. Fischbeck, Mutant dynactin in motor neuron disease. Nat. Genet. 33(4), 455–456 (2003)CrossRef
26.
Zurück zum Zitat G.M. Fabrizi, T. Cavallaro, C. Angiari, I. Cabrini, F. Taioli, G. Malerba, L. Bertolasi, N. Rizzuto, Charcot-Marie-tooth disease type 2E, a disorder of the cytoskeleton. Brain 130(Pt 2), 394–403 (2007)CrossRef G.M. Fabrizi, T. Cavallaro, C. Angiari, I. Cabrini, F. Taioli, G. Malerba, L. Bertolasi, N. Rizzuto, Charcot-Marie-tooth disease type 2E, a disorder of the cytoskeleton. Brain 130(Pt 2), 394–403 (2007)CrossRef
27.
Zurück zum Zitat D.D. Tshala-Katumbay, V.S. Palmer, M.R. Lasarev, R.J. Kayton, M.I. Sabri, P.S. Spencer, Monocyclic and dicyclic hydrocarbons: structural requirements for proximal giant axonopathy. Acta Neuropathol. 112(3), 317–324 (2006)CrossRef D.D. Tshala-Katumbay, V.S. Palmer, M.R. Lasarev, R.J. Kayton, M.I. Sabri, P.S. Spencer, Monocyclic and dicyclic hydrocarbons: structural requirements for proximal giant axonopathy. Acta Neuropathol. 112(3), 317–324 (2006)CrossRef
28.
Zurück zum Zitat H.H. Goebel, P. Vogel, M. Gabriel, Neuropathologic and morphometric studies in hereditary motor and sensory neuropathy type II with neurofilament accumulation. Ital J. Neurol. Sci. 7(3), 325–332 (1986)CrossRef H.H. Goebel, P. Vogel, M. Gabriel, Neuropathologic and morphometric studies in hereditary motor and sensory neuropathy type II with neurofilament accumulation. Ital J. Neurol. Sci. 7(3), 325–332 (1986)CrossRef
29.
Zurück zum Zitat A.L. Taratuto, G. Sevlever, M. Saccoliti, L. Caceres, M. Schultz, Giant axonal neuropathy (GAN): an immunohistochemical and ultrastructural study report of a Latin American case. Acta Neuropathol. 80(6), 680–683 (1990)CrossRef A.L. Taratuto, G. Sevlever, M. Saccoliti, L. Caceres, M. Schultz, Giant axonal neuropathy (GAN): an immunohistochemical and ultrastructural study report of a Latin American case. Acta Neuropathol. 80(6), 680–683 (1990)CrossRef
30.
Zurück zum Zitat M. Donaghy, R.H. King, P.K. Thomas, J.M. Workman, Abnormalities of the axonal cytoskeleton in giant axonal neuropathy. J. Neurocytol. 17(2), 197–208 (1988)CrossRef M. Donaghy, R.H. King, P.K. Thomas, J.M. Workman, Abnormalities of the axonal cytoskeleton in giant axonal neuropathy. J. Neurocytol. 17(2), 197–208 (1988)CrossRef
31.
Zurück zum Zitat I.R. Griffiths, I.D. Duncan, M. McCulloch, S. Carmichael, Further studies of the central nervous system in canine giant axonal neuropathy. Neuropathol. Appl. Neurobiol. 6(6), 421–432 (1980)CrossRef I.R. Griffiths, I.D. Duncan, M. McCulloch, S. Carmichael, Further studies of the central nervous system in canine giant axonal neuropathy. Neuropathol. Appl. Neurobiol. 6(6), 421–432 (1980)CrossRef
32.
Zurück zum Zitat R. S. Smith. The short term accumulation of axonally transported organelles in the region of localized lesions of single myelinated axons. J. Neurocytol. 9(1), 39–65 (1980)CrossRef R. S. Smith. The short term accumulation of axonally transported organelles in the region of localized lesions of single myelinated axons. J. Neurocytol. 9(1), 39–65 (1980)CrossRef
33.
Zurück zum Zitat P.C. Bressloff, J.M. Newby, Stochastic models of intracellular transport. Rev. Mod. Phys. 85(1), 135 (2013) P.C. Bressloff, J.M. Newby, Stochastic models of intracellular transport. Rev. Mod. Phys. 85(1), 135 (2013)
34.
Zurück zum Zitat D. Chowdhury, Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist’s perspective. Phys. Rep. 529(1), 1–197 (2013)MathSciNetCrossRef D. Chowdhury, Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist’s perspective. Phys. Rep. 529(1), 1–197 (2013)MathSciNetCrossRef
35.
Zurück zum Zitat A. Brown, Slow axonal transport. New Encycl. Neurosci. 9, 1–9 (2009) A. Brown, Slow axonal transport. New Encycl. Neurosci. 9, 1–9 (2009)
36.
Zurück zum Zitat S.I. Rubinow, J.J. Blum, A theoretical approach to the analysis of axonal transport. Biophys. J. 30(1), 137–147 (1980)CrossRef S.I. Rubinow, J.J. Blum, A theoretical approach to the analysis of axonal transport. Biophys. J. 30(1), 137–147 (1980)CrossRef
37.
Zurück zum Zitat T. Takenaka, H. Gotoh, Simulation of axoplasmic transport. J. Theor. Biol. 107(4), 579–601 (1984)CrossRef T. Takenaka, H. Gotoh, Simulation of axoplasmic transport. J. Theor. Biol. 107(4), 579–601 (1984)CrossRef
38.
Zurück zum Zitat J.J. Blum, M.C. Reed, A model for fast axonal transport. Cell Motil. 5(6), 507–527 (1985)CrossRef J.J. Blum, M.C. Reed, A model for fast axonal transport. Cell Motil. 5(6), 507–527 (1985)CrossRef
39.
Zurück zum Zitat M.C. Reed, J.J. Blum, Theoretical analysis of radioactivity profiles during fast axonal transport: effects of deposition and turnover. Cell Motil. Cytoskeleton 6(6), 620–627 (1986)CrossRef M.C. Reed, J.J. Blum, Theoretical analysis of radioactivity profiles during fast axonal transport: effects of deposition and turnover. Cell Motil. Cytoskeleton 6(6), 620–627 (1986)CrossRef
40.
Zurück zum Zitat J.J. Blum, M.C. Reed, A model for slow axonal transport and its application to neurofilamentous neuropathies. Cell Motil. Cytoskeleton 12(1), 53–65 (1989)CrossRef J.J. Blum, M.C. Reed, A model for slow axonal transport and its application to neurofilamentous neuropathies. Cell Motil. Cytoskeleton 12(1), 53–65 (1989)CrossRef
41.
Zurück zum Zitat M.C. Reed, S. Venakides, J.J. Blum, Approximate traveling waves in linear reaction-hyperbolic equations. SIAM J. Appl. Math. 50(1), 167–180 (1990)MathSciNetCrossRefMATH M.C. Reed, S. Venakides, J.J. Blum, Approximate traveling waves in linear reaction-hyperbolic equations. SIAM J. Appl. Math. 50(1), 167–180 (1990)MathSciNetCrossRefMATH
42.
Zurück zum Zitat S. Roy, P. Coffee, G. Smith, R.K. Liem, S.T. Brady, M.M. Black, Neurofilaments are transported rapidly but intermittently in axons: implications for slow axonal transport. J. Neurosci. 20(18), 6849–6861 (2000) S. Roy, P. Coffee, G. Smith, R.K. Liem, S.T. Brady, M.M. Black, Neurofilaments are transported rapidly but intermittently in axons: implications for slow axonal transport. J. Neurosci. 20(18), 6849–6861 (2000)
43.
Zurück zum Zitat G. Craciun, A. Brown, A. Friedman, A dynamical system model of neurofilament transport in axons. J. Theor. Biol. 237(3), 316–322 (2005)MathSciNetCrossRef G. Craciun, A. Brown, A. Friedman, A dynamical system model of neurofilament transport in axons. J. Theor. Biol. 237(3), 316–322 (2005)MathSciNetCrossRef
44.
Zurück zum Zitat A. Brown, L. Wang, P. Jung, Stochastic simulation of neurofilament transport in axons: the “stop-and-go” hypothesis. Mol. Biol. Cell 16(9), 4243–4255 (2005)CrossRef A. Brown, L. Wang, P. Jung, Stochastic simulation of neurofilament transport in axons: the “stop-and-go” hypothesis. Mol. Biol. Cell 16(9), 4243–4255 (2005)CrossRef
45.
Zurück zum Zitat P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve. Phys. Biol. 6(4), 046002 (2009) P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve. Phys. Biol. 6(4), 046002 (2009)
46.
Zurück zum Zitat Y. Li, P. Jung, A. Brown, Axonal transport of neurofilaments: a single population of intermittently moving polymers. J. Neurosci. 32(2), 746–758 (2012)CrossRef Y. Li, P. Jung, A. Brown, Axonal transport of neurofilaments: a single population of intermittently moving polymers. J. Neurosci. 32(2), 746–758 (2012)CrossRef
47.
Zurück zum Zitat Y. Li, A. Brown, P. Jung, Deciphering the axonal transport kinetics of neurofilaments using the fluorescence photoactivation pulse-escape method. Phys. Biol. 11(2), 026001 (2014) Y. Li, A. Brown, P. Jung, Deciphering the axonal transport kinetics of neurofilaments using the fluorescence photoactivation pulse-escape method. Phys. Biol. 11(2), 026001 (2014)
48.
Zurück zum Zitat P.C. Monsma, Y. Li, J.D. Fenn, P. Jung, A. Brown, Local regulation of neurofilament transport by myelinating cells. J. Neurosci. 34(8), 2979–2988 (2014)CrossRef P.C. Monsma, Y. Li, J.D. Fenn, P. Jung, A. Brown, Local regulation of neurofilament transport by myelinating cells. J. Neurosci. 34(8), 2979–2988 (2014)CrossRef
49.
Zurück zum Zitat A. Friedman, G. Craciun, Approximate traveling waves in linear reaction-hyperbolic equations. SIAM J. Math. Anal. 38(3), 741–758 (2006)MathSciNetCrossRefMATH A. Friedman, G. Craciun, Approximate traveling waves in linear reaction-hyperbolic equations. SIAM J. Math. Anal. 38(3), 741–758 (2006)MathSciNetCrossRefMATH
50.
Zurück zum Zitat A. Friedman, G. Craciun, A model of intracellular transport of particles in an axon. J. Math. Biol. 51(2), 217–246 (2005)MathSciNetCrossRefMATH A. Friedman, G. Craciun, A model of intracellular transport of particles in an axon. J. Math. Biol. 51(2), 217–246 (2005)MathSciNetCrossRefMATH
51.
Zurück zum Zitat A. Friedman, B. Hu, Uniform convergence for approximate traveling waves in linear reaction–diffusion–hyperbolic systems. Arch. Ration. Mech. Anal. 186(2), 251–274 (2007)MathSciNetCrossRefMATH A. Friedman, B. Hu, Uniform convergence for approximate traveling waves in linear reaction–diffusion–hyperbolic systems. Arch. Ration. Mech. Anal. 186(2), 251–274 (2007)MathSciNetCrossRefMATH
52.
Zurück zum Zitat A. Friedman, B. Hu, Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Indiana University Math. J. 56(5), 2133–2158 (2007)MathSciNetCrossRefMATH A. Friedman, B. Hu, Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Indiana University Math. J. 56(5), 2133–2158 (2007)MathSciNetCrossRefMATH
53.
Zurück zum Zitat E.A. Brooks, Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients. Ann. Appl. Probab. 9(3), 719–731 (1999)MathSciNetCrossRefMATH E.A. Brooks, Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients. Ann. Appl. Probab. 9(3), 719–731 (1999)MathSciNetCrossRefMATH
54.
Zurück zum Zitat L. Popovic, S.A. McKinley, M.C. Reed, A stochastic compartmental model for fast axonal transport. SIAM J. Appl. Math. 71(4), 1531–1556 (2011)MathSciNetCrossRefMATH L. Popovic, S.A. McKinley, M.C. Reed, A stochastic compartmental model for fast axonal transport. SIAM J. Appl. Math. 71(4), 1531–1556 (2011)MathSciNetCrossRefMATH
55.
Zurück zum Zitat P.C. Bressloff, Stochastic model of protein receptor trafficking prior to synaptogenesis. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031910 (2006) P.C. Bressloff, Stochastic model of protein receptor trafficking prior to synaptogenesis. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031910 (2006)
56.
Zurück zum Zitat J.M. Newby, P.C. Bressloff, Directed intermittent search for a hidden target on a dendritic tree. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2 Pt 1), 021913 (2009) J.M. Newby, P.C. Bressloff, Directed intermittent search for a hidden target on a dendritic tree. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(2 Pt 1), 021913 (2009)
57.
Zurück zum Zitat J.M. Newby, P.C. Bressloff, Quasi-steady state reduction of molecular motor-based models of directed intermittent search. Bull. Math. Biol. 72(7), 1840–1866 (2010)MathSciNetCrossRefMATH J.M. Newby, P.C. Bressloff, Quasi-steady state reduction of molecular motor-based models of directed intermittent search. Bull. Math. Biol. 72(7), 1840–1866 (2010)MathSciNetCrossRefMATH
58.
Zurück zum Zitat P.C. Bressloff, J.M. Newby, Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11(1), 016006 (2014) P.C. Bressloff, J.M. Newby, Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11(1), 016006 (2014)
59.
Zurück zum Zitat R.L. Price, P. Paggi, R.J. Lasek, M.J. Katz, Neurofilaments are spaced randomly in the radial dimension of axons. J. Neurocytol. 17(1), 55–62 (1988)CrossRef R.L. Price, P. Paggi, R.J. Lasek, M.J. Katz, Neurofilaments are spaced randomly in the radial dimension of axons. J. Neurocytol. 17(1), 55–62 (1988)CrossRef
60.
Zurück zum Zitat S.T. Hsieh, G.J. Kidd, T.O. Crawford, Z. Xu, W.M. Lin, B.D. Trapp, D.W. Cleveland, J.W. Griffin, Regional modulation of neurofilament organization by myelination in normal axons. J. Neurosci. 14(11 Pt 1), 6392–6401 (1994) S.T. Hsieh, G.J. Kidd, T.O. Crawford, Z. Xu, W.M. Lin, B.D. Trapp, D.W. Cleveland, J.W. Griffin, Regional modulation of neurofilament organization by myelination in normal axons. J. Neurosci. 14(11 Pt 1), 6392–6401 (1994)
61.
Zurück zum Zitat S.C. Papasozomenos, L. Autilio-Gambetti, P. Gambetti, Reorganization of axoplasmic organelles following beta, beta′-iminodipropionitrile administration. J. Cell Biol. 91(3 Pt 1), 866–871 (1981)CrossRef S.C. Papasozomenos, L. Autilio-Gambetti, P. Gambetti, Reorganization of axoplasmic organelles following beta, beta′-iminodipropionitrile administration. J. Cell Biol. 91(3 Pt 1), 866–871 (1981)CrossRef
62.
Zurück zum Zitat S.C. Papasozomenos, M. Yoon, R. Crane, L. Autilio-Gambetti, P. Gambetti, Redistribution of proteins of fast axonal transport following administration of beta,beta′-iminodipropionitrile: a quantitative autoradiographic study. J. Cell Biol. 95(2 Pt 1), 672–675 (1982)CrossRef S.C. Papasozomenos, M. Yoon, R. Crane, L. Autilio-Gambetti, P. Gambetti, Redistribution of proteins of fast axonal transport following administration of beta,beta′-iminodipropionitrile: a quantitative autoradiographic study. J. Cell Biol. 95(2 Pt 1), 672–675 (1982)CrossRef
63.
Zurück zum Zitat J.W. Griffin, K.E. Fahnestock, D.L. Price, P.N. Hoffman, Microtubule-neurofilament segregation produced by beta, beta′-iminodipropionitrile: evidence for the association of fast axonal transport with microtubules. J. Neurosci. 3(3), 557–566 (1983) J.W. Griffin, K.E. Fahnestock, D.L. Price, P.N. Hoffman, Microtubule-neurofilament segregation produced by beta, beta′-iminodipropionitrile: evidence for the association of fast axonal transport with microtubules. J. Neurosci. 3(3), 557–566 (1983)
64.
Zurück zum Zitat J.W. Griffin, K.E. Fahnestock, D.L. Price, L.C. Cork, Cytoskeletal disorganization induced by local application of β,β′-iminodipropionitrile and 2,5-hexanedione. Ann. Neurol. 14, 55–61 (1983)CrossRef J.W. Griffin, K.E. Fahnestock, D.L. Price, L.C. Cork, Cytoskeletal disorganization induced by local application of β,β′-iminodipropionitrile and 2,5-hexanedione. Ann. Neurol. 14, 55–61 (1983)CrossRef
65.
Zurück zum Zitat J.W. Griffin, D.L. Price, P.N. Hoffman, Neurotoxic probes of the axonal cytoskeleton. Trends Neurosci. 6, 490–495 (1983)CrossRef J.W. Griffin, D.L. Price, P.N. Hoffman, Neurotoxic probes of the axonal cytoskeleton. Trends Neurosci. 6, 490–495 (1983)CrossRef
66.
Zurück zum Zitat S.C. Papasozomenos, L.I. Binder, P.K. Bender, M.R. Payne, Microtubule-associated protein 2 within axons of spinal motor neurons: associations with microtubules and neurofilaments in normal and beta,beta′-iminodipropionitrile-treated axons. J. Cell Biol. 100(1), 74–85 (1985)CrossRef S.C. Papasozomenos, L.I. Binder, P.K. Bender, M.R. Payne, Microtubule-associated protein 2 within axons of spinal motor neurons: associations with microtubules and neurofilaments in normal and beta,beta′-iminodipropionitrile-treated axons. J. Cell Biol. 100(1), 74–85 (1985)CrossRef
67.
Zurück zum Zitat N. Hirokawa, G.S. Bloom, R.B. Vallee, Cytoskeletal architecture and immunocytochemical localization of microtubule-associated proteins in regions of axons associated with rapid axonal transport: the beta,beta′-iminodipropionitrile-intoxicated axon as a model system. J. Cell Biol. 101(1), 227–239 (1985)CrossRef N. Hirokawa, G.S. Bloom, R.B. Vallee, Cytoskeletal architecture and immunocytochemical localization of microtubule-associated proteins in regions of axons associated with rapid axonal transport: the beta,beta′-iminodipropionitrile-intoxicated axon as a model system. J. Cell Biol. 101(1), 227–239 (1985)CrossRef
68.
Zurück zum Zitat S.C. Papasozomenos, M.R. Payne, Actin immunoreactivity localizes with segregated microtubules and membranous organelles and in the subaxolemmal region in the beta,beta′-iminodipropionitrile axon. J. Neurosci. 6(12), 3483–3491 (1986) S.C. Papasozomenos, M.R. Payne, Actin immunoreactivity localizes with segregated microtubules and membranous organelles and in the subaxolemmal region in the beta,beta′-iminodipropionitrile axon. J. Neurosci. 6(12), 3483–3491 (1986)
69.
Zurück zum Zitat R.G. Nagele, K.T. Bush, H.Y. Lee, A morphometric study of cytoskeletal reorganization in rat sciatic nerve axons following beta,beta′-iminodipropionitrile (IDPN) treatment. Neurosci. Lett. 92(3), 241–246 (1988)CrossRef R.G. Nagele, K.T. Bush, H.Y. Lee, A morphometric study of cytoskeletal reorganization in rat sciatic nerve axons following beta,beta′-iminodipropionitrile (IDPN) treatment. Neurosci. Lett. 92(3), 241–246 (1988)CrossRef
70.
Zurück zum Zitat A. Bizzi, R.C. Crane, L. Autilio-Gambetti, P. Gambetti, Aluminum effect on slow axonal transport: a novel impairment of neurofilament transport. J. Neurosci. 4(3), 722–731 (1984) A. Bizzi, R.C. Crane, L. Autilio-Gambetti, P. Gambetti, Aluminum effect on slow axonal transport: a novel impairment of neurofilament transport. J. Neurosci. 4(3), 722–731 (1984)
71.
Zurück zum Zitat M.R. Gottfried, D.G. Graham, M. Morgan, H.W. Casey, J.S. Bus, The morphology of carbon disulfide neurotoxicity. Neurotoxicology 6(4), 89–96 (1985) M.R. Gottfried, D.G. Graham, M. Morgan, H.W. Casey, J.S. Bus, The morphology of carbon disulfide neurotoxicity. Neurotoxicology 6(4), 89–96 (1985)
72.
Zurück zum Zitat I. Jirmanová, E. Lukás, Ultrastructure of carbon disulphie neuropathy. Acta Neuropathol. 63(3), 255–263 (1984)CrossRef I. Jirmanová, E. Lukás, Ultrastructure of carbon disulphie neuropathy. Acta Neuropathol. 63(3), 255–263 (1984)CrossRef
73.
Zurück zum Zitat Z. Sahenk, J.R. Mendell, Alterations in slow transport kinetics induced by estramustine phosphate, an agent binding to microtubule-associated proteins. J. Neurosci. Res. 32(4), 481–493 (1992)CrossRef Z. Sahenk, J.R. Mendell, Alterations in slow transport kinetics induced by estramustine phosphate, an agent binding to microtubule-associated proteins. J. Neurosci. Res. 32(4), 481–493 (1992)CrossRef
74.
Zurück zum Zitat D.D. Tshala-Katumbay, V.S. Palmer, R.J. Kayton, M.I. Sabri, P.S. Spencer, A new murine model of giant proximal axonopathy. Acta Neuropathol. 109(4), 405–410 (2005)CrossRef D.D. Tshala-Katumbay, V.S. Palmer, R.J. Kayton, M.I. Sabri, P.S. Spencer, A new murine model of giant proximal axonopathy. Acta Neuropathol. 109(4), 405–410 (2005)CrossRef
75.
Zurück zum Zitat M.K. Lee, J.R. Marszalek, D.W. Cleveland, A mutant neurofilament subunit causes massive, selective motor neuron death: implications for the pathogenesis of human motor neuron disease. Neuron 13(4), 975–988 (1994)CrossRef M.K. Lee, J.R. Marszalek, D.W. Cleveland, A mutant neurofilament subunit causes massive, selective motor neuron death: implications for the pathogenesis of human motor neuron disease. Neuron 13(4), 975–988 (1994)CrossRef
76.
Zurück zum Zitat H. Selye, Lathyrism. Rev. Can. Biol. 16, 1–73 (1957) H. Selye, Lathyrism. Rev. Can. Biol. 16, 1–73 (1957)
77.
Zurück zum Zitat J.L. Cadet, The iminodipropionitrile (IDPN)-induced dyskinetic syndrome: behavioral and biochemical pharmacology. Neurosci. Biobehav. Rev. 13(1), 39–45 (1989)MathSciNetCrossRef J.L. Cadet, The iminodipropionitrile (IDPN)-induced dyskinetic syndrome: behavioral and biochemical pharmacology. Neurosci. Biobehav. Rev. 13(1), 39–45 (1989)MathSciNetCrossRef
78.
Zurück zum Zitat P.S. Spencer, H.H. Schaumburg, Lathyrism: a neurotoxic disease. Neurobehav. Toxicol. Teratol. 5(6), 625–629 (1983) P.S. Spencer, H.H. Schaumburg, Lathyrism: a neurotoxic disease. Neurobehav. Toxicol. Teratol. 5(6), 625–629 (1983)
79.
Zurück zum Zitat P.S. Spencer, C.N. Allen, G.E. Kisby, A.C. Ludolph, S.M. Ross, D.N. Roy, Lathyrism and western pacific amyotrophic lateral sclerosis: etiology of short and long latency motor system disorders. Adv. Neurol. 56, 287–299 (1991) P.S. Spencer, C.N. Allen, G.E. Kisby, A.C. Ludolph, S.M. Ross, D.N. Roy, Lathyrism and western pacific amyotrophic lateral sclerosis: etiology of short and long latency motor system disorders. Adv. Neurol. 56, 287–299 (1991)
80.
Zurück zum Zitat J. Llorens, C. Soler-Martín, B. Cutillas, S. Saldaña-Ruíz, Nervous and vestibular toxicities of acrylonitrile and iminodipropionitrile. Toxicol. Sci. 110(1), 244–245; Author reply 246–248 (2009) J. Llorens, C. Soler-Martín, B. Cutillas, S. Saldaña-Ruíz, Nervous and vestibular toxicities of acrylonitrile and iminodipropionitrile. Toxicol. Sci. 110(1), 244–245; Author reply 246–248 (2009)
81.
Zurück zum Zitat J. Llorens, Toxic neurofilamentous axonopathies – accumulation of neurofilaments and axonal degeneration. J. Intern. Med. 273(5), 478–489 (2013)CrossRef J. Llorens, Toxic neurofilamentous axonopathies – accumulation of neurofilaments and axonal degeneration. J. Intern. Med. 273(5), 478–489 (2013)CrossRef
82.
Zurück zum Zitat J.W. Griffin, P.N. Hoffman, A.W. Clark, P.T. Carroll, D.L. Price, Slow axonal transport of neurofilament proteins: impairment of beta,beta′-iminodipropionitrile administration. Science 202(4368), 633–635 (1978)CrossRef J.W. Griffin, P.N. Hoffman, A.W. Clark, P.T. Carroll, D.L. Price, Slow axonal transport of neurofilament proteins: impairment of beta,beta′-iminodipropionitrile administration. Science 202(4368), 633–635 (1978)CrossRef
83.
Zurück zum Zitat C. Xue, B. Shtylla, A. Brown, A stochastic multiscale model that explains the segregation of axonal microtubules and neurofilaments in toxic neuropathies. PLoS Comput. Biol. 11(8), e1004406 (2015) C. Xue, B. Shtylla, A. Brown, A stochastic multiscale model that explains the segregation of axonal microtubules and neurofilaments in toxic neuropathies. PLoS Comput. Biol. 11(8), e1004406 (2015)
84.
Zurück zum Zitat Q. Zhu, M. Lindenbaum, F. Levavasseur, H. Jacomy, J.P. Julien, Disruption of the NF-H gene increases axonal microtubule content and velocity of neurofilament transport: relief of axonopathy resulting from the toxin beta,beta′-iminodipropionitrile. J. Cell Biol. 143(1), 183–193 (1998)CrossRef Q. Zhu, M. Lindenbaum, F. Levavasseur, H. Jacomy, J.P. Julien, Disruption of the NF-H gene increases axonal microtubule content and velocity of neurofilament transport: relief of axonopathy resulting from the toxin beta,beta′-iminodipropionitrile. J. Cell Biol. 143(1), 183–193 (1998)CrossRef
85.
Zurück zum Zitat K. Visscher, M.J. Schnitzer, S.M. Block, Single kinesin molecules studied with a molecular force clamp. Nature 400(6740), 184–189 (1999)CrossRef K. Visscher, M.J. Schnitzer, S.M. Block, Single kinesin molecules studied with a molecular force clamp. Nature 400(6740), 184–189 (1999)CrossRef
86.
Zurück zum Zitat R.P. Erickson, Z. Jia, S.P. Gross, C.C. Yu, How molecular motors are arranged on a cargo is important for vesicular transport. PLoS Comput. Biol. 7(5), e1002032 (2011) R.P. Erickson, Z. Jia, S.P. Gross, C.C. Yu, How molecular motors are arranged on a cargo is important for vesicular transport. PLoS Comput. Biol. 7(5), e1002032 (2011)
87.
Zurück zum Zitat N. Hirokawa, K.K. Pfister, H. Yorifuji, M.C. Wagner, S.T. Brady, G.S. Bloom, Submolecular domains of bovine brain kinesin identified by electron microscopy and monoclonal antibody decoration. Cell 56(5), 867–878 (1989)CrossRef N. Hirokawa, K.K. Pfister, H. Yorifuji, M.C. Wagner, S.T. Brady, G.S. Bloom, Submolecular domains of bovine brain kinesin identified by electron microscopy and monoclonal antibody decoration. Cell 56(5), 867–878 (1989)CrossRef
88.
Zurück zum Zitat C.M. Coppin, J.T. Finer, J.A. Spudich, R.D. Vale, Measurement of the isometric force exerted by a single kinesin molecule. Biophys. J. 68(4 Suppl.), 242S–244S (1995) C.M. Coppin, J.T. Finer, J.A. Spudich, R.D. Vale, Measurement of the isometric force exerted by a single kinesin molecule. Biophys. J. 68(4 Suppl.), 242S–244S (1995)
89.
Zurück zum Zitat F. Ziebert, M. Vershinin, S.P. Gross, I.S. Aranson, Collective alignment of polar filaments by molecular motors. Eur. Phys. J. E Soft Matter 28(4), 401–409 (2009)CrossRef F. Ziebert, M. Vershinin, S.P. Gross, I.S. Aranson, Collective alignment of polar filaments by molecular motors. Eur. Phys. J. E Soft Matter 28(4), 401–409 (2009)CrossRef
90.
Zurück zum Zitat R.G. Cox, The motion of long slender bodies in a viscous fluid. Part 1. general theory. J. Fluid Mech. 44(Part 3), 790–810 (1970) R.G. Cox, The motion of long slender bodies in a viscous fluid. Part 1. general theory. J. Fluid Mech. 44(Part 3), 790–810 (1970)
91.
Zurück zum Zitat C. Brennen, H. Winet, Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9(1), 339–398 (1977)CrossRefMATH C. Brennen, H. Winet, Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9(1), 339–398 (1977)CrossRefMATH
92.
Zurück zum Zitat K. Svoboda, C.F. Schmidt, B.J. Schnapp, S.M. Block, Direct observation of kinesin stepping by optical trapping interferometry. Nature 365(6448), 721–727 (1993)CrossRef K. Svoboda, C.F. Schmidt, B.J. Schnapp, S.M. Block, Direct observation of kinesin stepping by optical trapping interferometry. Nature 365(6448), 721–727 (1993)CrossRef
93.
Zurück zum Zitat M.J. Schnitzer, S.M. Block, Kinesin hydrolyses one ATP per 8-nm step. Nature 388(6640), 386–390 (1997)CrossRef M.J. Schnitzer, S.M. Block, Kinesin hydrolyses one ATP per 8-nm step. Nature 388(6640), 386–390 (1997)CrossRef
94.
Zurück zum Zitat A. Kunwar, M. Vershinin, J. Xu, S.P. Gross, Stepping, strain gating, and an unexpected force-velocity curve for multiple-motor-based transport. Curr. Biol. 18(16), 1173–1183 (2008)CrossRef A. Kunwar, M. Vershinin, J. Xu, S.P. Gross, Stepping, strain gating, and an unexpected force-velocity curve for multiple-motor-based transport. Curr. Biol. 18(16), 1173–1183 (2008)CrossRef
95.
Zurück zum Zitat J. Kerssemakers, J. Howard, H. Hess, S. Diez, The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy. Proc. Natl. Acad. Sci. U. S. A. 103(43), 15812–15817 (2006)CrossRef J. Kerssemakers, J. Howard, H. Hess, S. Diez, The distance that kinesin-1 holds its cargo from the microtubule surface measured by fluorescence interference contrast microscopy. Proc. Natl. Acad. Sci. U. S. A. 103(43), 15812–15817 (2006)CrossRef
96.
Zurück zum Zitat I.G Currie, Fundamental Mechanics of Fluids (CRC Press, Boca Raton, 2012) I.G Currie, Fundamental Mechanics of Fluids (CRC Press, Boca Raton, 2012)
97.
Zurück zum Zitat R. Swaminathan, C.P. Hoang, A.S. Verkman, Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-s65t in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion. Biophys. J. 72, 1900–1907 (1997)CrossRef R. Swaminathan, C.P. Hoang, A.S. Verkman, Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-s65t in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion. Biophys. J. 72, 1900–1907 (1997)CrossRef
Metadaten
Titel
Recent Mathematical Models of Axonal Transport
verfasst von
Chuan Xue
Gregory Jameson
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-62627-7_12