Recent Mathematical Models of Axonal Transport



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.



This research was supported by US NSF DMS 1312966 and US NSF CAREER Award 1553637. CX was also supported by the Mathematical Biosciences Institute as a long-term visitor.


  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    S. Tsukita, H. Ishikawa, The cytoskeleton in myelinated axons: serial section study. Biomed. Res. 2, 424–437 (1981)Google Scholar
  3. 3.
    B.J. Schnapp, T.S. Reese, Cytoplasmic structure in rapid frozen axons. J. Cell Biol. 94, 667–679 (1982)CrossRefGoogle Scholar
  4. 4.
    N. Hirokawa, Axonal transport and the cytoskeleton. Curr. Opin. Neurobiol. 3(5), 724–731 (1993)CrossRefGoogle Scholar
  5. 5.
    A. Brown, Axonal transport, in Neuroscience in the 21st Century (Springer, Berlin, 2013)Google Scholar
  6. 6.
    N. Hirokawa, R. Takemura, Molecular motors and mechanisms of directional transport in neurons. Nat. Rev. Neurosci. 6(3), 201–214 (2005)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    K. Xu, G. Zhong, X. Zhuang, Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons. Science 339(6118), 452–456 (2013)CrossRefGoogle Scholar
  10. 10.
    E.L. Bearer, T.S. Reese, Association of actin filaments with axonal microtubule tracts. J. Neurocytol. 28(2), 85–98 (1999)CrossRefGoogle Scholar
  11. 11.
    P.J. Hollenbeck, W.M. Saxton, The axonal transport of mitochondria. J. Cell Sci. 118(Pt 23), 5411–5419 (2005)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    E. Chevalier-Larsen, E.L.F. Holzbaur, Axonal transport and neurodegenerative disease. Biochim. Biophys. Acta 1762(11–12), 1094–1108 (2006)CrossRefGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    S. Millecamps, J.-P. Julien, Axonal transport deficits and neurodegenerative diseases. Nat. Rev. Neurosci. 14(3), 161–176 (2013)CrossRefGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    L. Wang, A. Brown, A hereditary spastic paraplegia mutation in kinesin-1A/KIF5A disrupts neurofilament transport. Mol. Neurodegener. 5, 52 (2010)CrossRefGoogle Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    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)Google Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar
  28. 28.
    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)CrossRefGoogle Scholar
  29. 29.
    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)CrossRefGoogle Scholar
  30. 30.
    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)CrossRefGoogle Scholar
  31. 31.
    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)CrossRefGoogle Scholar
  32. 32.
    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)CrossRefGoogle Scholar
  33. 33.
    P.C. Bressloff, J.M. Newby, Stochastic models of intracellular transport. Rev. Mod. Phys. 85(1), 135 (2013)Google Scholar
  34. 34.
    D. Chowdhury, Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist’s perspective. Phys. Rep. 529(1), 1–197 (2013)MathSciNetCrossRefGoogle Scholar
  35. 35.
    A. Brown, Slow axonal transport. New Encycl. Neurosci. 9, 1–9 (2009)Google Scholar
  36. 36.
    S.I. Rubinow, J.J. Blum, A theoretical approach to the analysis of axonal transport. Biophys. J. 30(1), 137–147 (1980)CrossRefGoogle Scholar
  37. 37.
    T. Takenaka, H. Gotoh, Simulation of axoplasmic transport. J. Theor. Biol. 107(4), 579–601 (1984)CrossRefGoogle Scholar
  38. 38.
    J.J. Blum, M.C. Reed, A model for fast axonal transport. Cell Motil. 5(6), 507–527 (1985)CrossRefGoogle Scholar
  39. 39.
    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)CrossRefGoogle Scholar
  40. 40.
    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)CrossRefGoogle Scholar
  41. 41.
    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)MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    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)Google Scholar
  43. 43.
    G. Craciun, A. Brown, A. Friedman, A dynamical system model of neurofilament transport in axons. J. Theor. Biol. 237(3), 316–322 (2005)MathSciNetCrossRefGoogle Scholar
  44. 44.
    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)CrossRefGoogle Scholar
  45. 45.
    P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve. Phys. Biol. 6(4), 046002 (2009)Google Scholar
  46. 46.
    Y. Li, P. Jung, A. Brown, Axonal transport of neurofilaments: a single population of intermittently moving polymers. J. Neurosci. 32(2), 746–758 (2012)CrossRefGoogle Scholar
  47. 47.
    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)Google Scholar
  48. 48.
    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)CrossRefGoogle Scholar
  49. 49.
    A. Friedman, G. Craciun, Approximate traveling waves in linear reaction-hyperbolic equations. SIAM J. Math. Anal. 38(3), 741–758 (2006)MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    A. Friedman, G. Craciun, A model of intracellular transport of particles in an axon. J. Math. Biol. 51(2), 217–246 (2005)MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    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)MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    A. Friedman, B. Hu, Uniform convergence for approximate traveling waves in linear reaction-hyperbolic systems. Indiana University Math. J. 56(5), 2133–2158 (2007)MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    E.A. Brooks, Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients. Ann. Appl. Probab. 9(3), 719–731 (1999)MathSciNetCrossRefMATHGoogle Scholar
  54. 54.
    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)MathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    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)Google Scholar
  56. 56.
    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)Google Scholar
  57. 57.
    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)MathSciNetCrossRefMATHGoogle Scholar
  58. 58.
    P.C. Bressloff, J.M. Newby, Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11(1), 016006 (2014)Google Scholar
  59. 59.
    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)CrossRefGoogle Scholar
  60. 60.
    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)Google Scholar
  61. 61.
    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)CrossRefGoogle Scholar
  62. 62.
    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)CrossRefGoogle Scholar
  63. 63.
    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)Google Scholar
  64. 64.
    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)CrossRefGoogle Scholar
  65. 65.
    J.W. Griffin, D.L. Price, P.N. Hoffman, Neurotoxic probes of the axonal cytoskeleton. Trends Neurosci. 6, 490–495 (1983)CrossRefGoogle Scholar
  66. 66.
    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)CrossRefGoogle Scholar
  67. 67.
    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)CrossRefGoogle Scholar
  68. 68.
    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)Google Scholar
  69. 69.
    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)CrossRefGoogle Scholar
  70. 70.
    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)Google Scholar
  71. 71.
    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)Google Scholar
  72. 72.
    I. Jirmanová, E. Lukás, Ultrastructure of carbon disulphie neuropathy. Acta Neuropathol. 63(3), 255–263 (1984)CrossRefGoogle Scholar
  73. 73.
    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)CrossRefGoogle Scholar
  74. 74.
    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)CrossRefGoogle Scholar
  75. 75.
    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)CrossRefGoogle Scholar
  76. 76.
    H. Selye, Lathyrism. Rev. Can. Biol. 16, 1–73 (1957)Google Scholar
  77. 77.
    J.L. Cadet, The iminodipropionitrile (IDPN)-induced dyskinetic syndrome: behavioral and biochemical pharmacology. Neurosci. Biobehav. Rev. 13(1), 39–45 (1989)MathSciNetCrossRefGoogle Scholar
  78. 78.
    P.S. Spencer, H.H. Schaumburg, Lathyrism: a neurotoxic disease. Neurobehav. Toxicol. Teratol. 5(6), 625–629 (1983)Google Scholar
  79. 79.
    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)Google Scholar
  80. 80.
    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)Google Scholar
  81. 81.
    J. Llorens, Toxic neurofilamentous axonopathies – accumulation of neurofilaments and axonal degeneration. J. Intern. Med. 273(5), 478–489 (2013)CrossRefGoogle Scholar
  82. 82.
    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)CrossRefGoogle Scholar
  83. 83.
    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)Google Scholar
  84. 84.
    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)CrossRefGoogle Scholar
  85. 85.
    K. Visscher, M.J. Schnitzer, S.M. Block, Single kinesin molecules studied with a molecular force clamp. Nature 400(6740), 184–189 (1999)CrossRefGoogle Scholar
  86. 86.
    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)Google Scholar
  87. 87.
    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)CrossRefGoogle Scholar
  88. 88.
    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)Google Scholar
  89. 89.
    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)CrossRefGoogle Scholar
  90. 90.
    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)Google Scholar
  91. 91.
    C. Brennen, H. Winet, Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9(1), 339–398 (1977)CrossRefMATHGoogle Scholar
  92. 92.
    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)CrossRefGoogle Scholar
  93. 93.
    M.J. Schnitzer, S.M. Block, Kinesin hydrolyses one ATP per 8-nm step. Nature 388(6640), 386–390 (1997)CrossRefGoogle Scholar
  94. 94.
    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)CrossRefGoogle Scholar
  95. 95.
    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)CrossRefGoogle Scholar
  96. 96.
    I.G Currie, Fundamental Mechanics of Fluids (CRC Press, Boca Raton, 2012)Google Scholar
  97. 97.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Biophysics Graduate ProgramOhio State UniversityColumbusUSA

Personalised recommendations