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Articles

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

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Pages 71-83 | Received 18 Feb 2018, Accepted 07 Oct 2018, Published online: 24 Dec 2018

References

  • Ballatore C, Lee VMY, Trojanowski JQ. 2007. Tau-mediated neurodegeneration in Alzheimer’s disease and related disorders. Nat Rev Neurosci. 8(9):663–672.
  • Beck JV, Arnold KJ. 1977. Parameter estimation in science and engineering. New York (NY): Wiley.
  • Black MM, Slaughter T, Moshiach S, Obrocka M, Fischer I. 1996. Tau is enriched on dynamic microtubules in the distal region of growing axons. J Neurosci. 16(11):3601–3619.
  • Bloom GS. 2014. Amyloid-beta and tau: the trigger and bullet in Alzheimer disease pathogenesis. JAMA Neurol. 71(4):505–508.
  • Boutajangout A, Sigurdsson EM, Krishnamurthy PK. 2011. Tau as a therapeutic target for Alzheimer’s disease. Curr Alzheimer Res. 8(6):666–677.
  • Butner KA, Kirschner MW. 1991. Tau-protein binds to microtubules through a flexible array of distributed weak sites. J Cell Biol. 115(3):717–730.
  • Cuchillo-Ibanez I, Seereeram A, Byers HL, Leung K, Ward MA, Anderton BH, Hanger DP. 2008. Phosphorylation of tau regulates its axonal transport by controlling its binding to kinesin. Faseb J. 22(9):3186–3195.
  • DeVos SL, Miller RL, Schoch KM, Holmes BB, Kebodeaux CS, Wegener AJ, Chen G, Shen T, Tran H, Nichols B, et al. 2017. Tau reduction prevents neuronal loss and reverses pathological tau deposition and seeding in mice with tauopathy. Sci Transl Med. 9(374):eaag0481.
  • Hinrichs MH, Jalal A, Brenner B, Mandelkow E, Kumar S, Scholz T. 2012. Tau protein diffuses along the microtubule lattice. J Biol Chem. 287(46):38559–38568.
  • Igaev M, Janning D, Sündermann F, Niewidok B, Brandt R, Junge W. 2014. A refined reaction-diffusion model of tau-microtubule dynamics and its application in FDAP analysis. Biophys J. 107(11):2567–2578.
  • Ittner A, Ke YD, van Eersel J, Gladbach A, Götz J, Ittner LM. 2011. Brief update on different roles of tau in neurodegeneration. IUBMB Life. 63(7):495–502.
  • Jung P, Brown A. 2009. Modeling the slowing of neurofilament transport along the mouse sciatic nerve. Phys Biol. 6(4):046002
  • Kacser H, Burns J, Fell D. 1995. The control of flux. Biochem Soc Trans. 23(2):341–366.
  • Kirk PDW, Babtie AC, Stumpf MPH. 2015. Systems biology (un)certainties. Science. 350(6259):386–388.
  • Konzack S, Thies E, Marx A, Mandelkow EM, Mandelkow E. 2007. Swimming against the tide: Mobility of the microtubule-associated protein tau in neurons. J Neurosci. 27(37):9916–9927.
  • Kuznetsov AV. 2012. An exact solution describing slow axonal transport of cytoskeletal elements: effect of a finite half-life. Proc R Soc A. 468(2147):3384–3397.
  • Kuznetsov AV, Avramenko AA, Blinov DG. 2011. Investigation of the role of diffusivity on spreading, rate, and merging of the bell-shaped waves in slow axonal transport. Int J Numer Meth Biomed Eng. 27(7):1040–1053.
  • Kuznetsov IA, Kuznetsov AV. 2015. A comparison between the diffusion-reaction and slow axonal transport models for predicting tau distribution along an axon. Math Med Biol. 32(3):263–283.
  • Kuznetsov IA, Kuznetsov AV. 2016. Can numerical modeling help understand the fate of tau protein in the axon terminal? Comput Methods Biomech Biomed Engin. 19(2):115–125.
  • Kuznetsov IA, Kuznetsov AV. 2017a. Simulating tubulin-associated unit transport in an axon: Using bootstrapping for estimating confidence intervals of best fit parameter values obtained from indirect experimental data. Proc R Soc A. 473(2201):20170045.
  • Kuznetsov IA, Kuznetsov AV. 2017b. Utilization of the bootstrap method for determining confidence intervals of parameters for a model of MAP1B protein transport in axons. J Theor Biol. 419:350–361.
  • Kuznetsov IA, Kuznetsov AV. 2017c. What mechanisms of tau protein transport could be responsible for the inverted tau concentration gradient in degenerating axons? Math Med Biol. 34:125–150.
  • Kuznetsov IA, Kuznetsov AV. 2018. How the formation of amyloid plaques and neurofibrillary tangles may be related – a mathematical modelling study. Proc R Soc A. 474(2210):20170777.
  • Lee RH, Mitchell CS. 2015. Axonal transport cargo motor count versus average transport velocity: Is fast versus slow transport really single versus multiple motor transport? J Theor Biol. 370:39–44.
  • Li Y, Jung P, Brown A. 2012. Axonal transport of neurofilaments: A single population of intermittently moving polymers. J Neurosci. 32(2):746–758.
  • Lippens G, Landrieu I, Smet C, Huvent I, Gandhi NS, Gigant B, Despres C, Qi H, Lopez J. 2016. NMR meets tau: Insights into its function and pathology. Biomolecules. 6(2):28.
  • Lloret-Villas A, Varusai TM, Juty N, Laibe C, Le Novere N, Hermjakob H, Chelliah V. 2017. The impact of mathematical modeling in understanding the mechanisms underlying neurodegeneration: evolving dimensions and future directions. CPT Pharmacometrics Syst Pharmacol. 6(2):73–86.
  • Mercken M, Fischer I, Kosik K, Nixon R. 1995. Three distinct axonal transport rates for tau, tubulin, and other microtubule-associated proteins: Evidence for dynamic interactions of tau with microtubules in vivo. J Neurosci. 15(12):8259–8267.
  • Millecamps S, Julien J. 2013. Axonal transport deficits and neurodegenerative diseases. Nat Rev Neurosci. 14(3):161–176.
  • Moreno H, Morfini G, Buitrago L, Ujlaki G, Choi S, Yu E, Moreira JE, Avila J, Brady ST, Pant H, et al. 2016. Tau pathology-mediated presynaptic dysfunction. Neuroscience. 325:30–38.
  • Pachima YI, Zhou L, Lei P, Gozes I. 2016. Microtubule-tau interaction as a therapeutic target for Alzheimer’s disease. J Mol Neurosci. 58(2):145–152.
  • Poppek D, Keck S, Ermak G, Jung T, Stolzing A, Ullrich O, Davies KJA, Grune T. 2006. Phosphorylation inhibits turnover of the tau protein by the proteasome: Influence of RCAN1 and oxidative stress. Biochem J. 400(3):511–520.
  • Samsonov A, Yu JZ, Rasenick M, Popov SV. 2004. Tau interaction with microtubules in vivo. J Cell Sci. 117(Pt 25):6129–6141.
  • Scholz T, Mandelkow E. 2014. Transport and diffusion of tau protein in neurons. Cell Mol Life Sci. 71(16):3139–3150.
  • Tai H, Serrano-Pozo A, Hashimoto T, Frosch MP, Spires-Jones TL, Hyman BT. 2012. The synaptic accumulation of hyperphosphorylated tau oligomers in Alzheimer disease is associated with dysfunction of the ubiquitin-proteasome system. Am J Pathol. 181(4):1426–1435.
  • Utton M, Connell J, Asuni A, van Slegtenhorst M, Hutton M, de Silva R, Lees A, Miller C, Anderton B. 2002. The slow axonal transport of the microtubule-associated protein tau and the transport rates of different isoforms and mutants in cultured neurons. J Neurosci. 22(15):6394–6400.
  • Utton M, Noble W, Hill J, Anderton B, Hanger D. 2005. Molecular motors implicated in the axonal transport of tau and alpha-synuclein. J Cell Sci. 118(Pt 20):4645–4654.
  • Walsh DM, Selkoe DJ. 2016. A critical appraisal of the pathogenic protein spread hypothesis of neurodegeneration. Nat Rev Neurosci. 17(4):251–260.
  • Wang Y, Mandelkow E. 2016. Tau in physiology and pathology. Nat Rev Neurosci. 17(1):5–21.
  • Weissmann C, Reyher H, Gauthier A, Steinhoff H, Junge W, Brandt R. 2009. Microtubule binding and trapping at the tip of neurites regulate tau motion in living neurons. Traffic. 10(11):1655–1668.
  • Zadeh KS. 2009. Multi-objective optimization in variably saturated fluid flow. J Comput Appl Math. 223(2):801–819.
  • Zadeh KS, Montas HJ. 2010. A class of exact solutions for biomacromolecule diffusion-reaction in live cells. J Theor Biol. 264(3):914–933.

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