A model of the spatially dependent mechanical properties of the axon during its growth

CMES - Computer Modeling in Engineering and Sciences

Volumn 87, Issue 5, 2012, Pages 411-432

  Garcia J A ^a,b   Pena J M ^a   McHugh, S ^b   Jerusalem A ^b,c  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b IMDEA MATERIALS INSTITUTE   (Spain)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Axonal growth; Finite difference modeling; Mechanical properties; Microtubule polymerization

Indexed keywords

AXONAL GROWTH; BIOCHEMICAL CHANGES; CELL MIGRATION; COMPLEX PROCESSES; COUPLING MECHANISM; DEPHOSPHORYLATIONS; DIPHOSPHATES; EXTRACELLULAR; FINITE DIFFERENCE; FINITE-DIFFERENCE MODELING; GROWTH CONES; GUANOSINE TRIPHOSPHATE; GUANOSINES; INTRACELLULAR LEVELS; MECHANICAL STIFFNESS; MECHANICAL TENSION; MICROTUBULE POLYMERIZATION; MICROTUBULES; MODELING APPROACH; MULTI-LAYERED STRUCTURE; NEURITES; NEURONAL GROWTH; PATHFINDING; STRUCTURAL EVOLUTION; UNDERLYING MECHANISM;

BIOMECHANICS; ENZYME ACTIVITY; MECHANICAL PROPERTIES; STIFFNESS;

POLYMERIZATION;

EID: 84872106307     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (63)

1. Aeschlimann, M. (2000): Biophysical models of axonal pathfinding. PhD thesis, Université de Lausanne, 2000.
2. Baas, P.; Buster, D. (2004): Slow axonal transport and the genesis of neuronal morphology. J. Neurobiol., vol. 48, pp. 3-17. (Pubitemid 37543334)
3. Bernal, R.; Pullarkat, P.; Melo, F. (2007): Mechanical properties of axon. Physical Review letters, vol. 99, pp. 018301.
4. Betz, T.; Koch, D.; Lu, Y.-B.; Franze, K.; Käs, J. (2011): Growth cones as soft and weak force generators. PNAS, vol. 108, pp. 13420-13425.
5. Bower, J.; Beeman, D. (1998): The book of GENESIS: exploring realistic neural models with the GEneral Neural Simulation System New York. Springer-Verlag.
6. Carnevale, N.; Hines, M. (2006): The NEURON book. Cambridge University Press.
7. Challacombe, J.; Snow, D.; Letourneau, P. (1996): Role of the cytoskeleton in growth cone motility and axonal elongation. Seminar. Neurosci., vol. 8, pp. 67-80.
8. Conde, C.; Cáceres, A. (2009): Microtubule assembly, organization and dynamics in axons and dendrites. Nature Reviews. Neuroscience, vol. 10, pp. 319-332.
9. Dennerll, T.; Joshi, H.; Steel, V.; Buxbaum, R.; Heidemann, S. (1988): Tension and compression in the cytoskeleton of PC-12 neurites II; quantitative measurements. The Journal of Cell Biology, vol. 107, pp. 665-674.
10. Dennerll, T.; Lamoureux, P.; Buxbaum, R.; Heidemann, S. (1989): The cytomechanics of axonal elongation and retraction. The Journal of Cell Biology, vol. 109, pp. 3073-3083. (Pubitemid 20011931)
11. Dent, E.; Gertler, F. (2003): Cytoskeletal dynamics and transport in growth cone motility and axon guidance. Neuron, vol. 40, pp. 209-227. (Pubitemid 37244093)
12. Dogterom, M.; Kerssemakers, J.; Romet-Lemonne, G.; Janson, M. (2005): Force generation by dynamic microtubules. Current Opinion in Cell Biology, vol. 17, pp. 67-74. (Pubitemid 40138090)
13. Dogterom, M.; Yurke, B. (1997): Measurement of the force-velocity relation for growing microtubules. Science, vol. 279, pp. 856-860. (Pubitemid 27467922)
14. Esch, T.; Lemmon, V.; Banker, G. (1999): Local presentation of substrate molecules directs axon specification by cultured hippocampal neurons. J. Neurosci., vol. 19, pp. 6417-6426. (Pubitemid 29347441)
15. F. Bradke, J. F.; Spira, M. (2012): Assembly of a new growth cone after axotomy: the precursor to axon regeneration. Nature Reviews Neuroscience, vol. 13, pp. 183-193.
16. Flyvbjerg, H.; Jobs, E.; Leibler, S. (1996): Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry. Proc. Natl. Acad. Sci. USA, vol. 93, pp. 5979-5979.
17. Glabraith, J.; Reese, T.; Schlief, M.; Gallant, P. (1999): Slow transport of unpolymerized tubulin and polymerized neurofilament in the squid giant axon. Proc. Natl. Acad. Sci, vol. 96, pp. 11589-11594. (Pubitemid 29487425)
18. Gordon-Weeks, P. (2004): Microtubules and growth cone function. Journal of Neurobiology, vol. 58, pp. 70-83. (Pubitemid 37543339)
19. Goslin, K.; Banker, G. (1989): Experimental observations on the development of polarity by hippocampal neurons in culture. J. Cell. Biol., vol. 108, pp. 1507-1516. (Pubitemid 19097054)
20. Graham, B.; Lauchlan, K.; Mclean, D. (2006): Dynamics of outgrowth in a continnuum model of neurite elongation. J. Comput. Neurosci., vol. 20, pp. 43-60.
21. Graham, B.; van Ooyen, A. (2001): Compartmental models of growing neurites. Neurocomputing, vol. 38-40, pp. 31-36. (Pubitemid 35276619)
22. Graham, B.; van Ooyen, A. (2004): Transport limited effects in a model of dendritic branching. Journal of Theoretical Biology, vol. 230, pp. 421-432. (Pubitemid 39092343)
23. Graham, B.; van Ooyen, A. (2006): Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neuroscience, vol. 7, no. 1, pp. S9.
24. Hammele, M.; Zimmermann, W. (2003): Modeling oscillatory microtubule polymerization. Phys. Rev. E, vol. 67, pp. 021903.
25. Hawkins, T.; Mirigian, M.; Yasar, M.; Ross, H. (2010): Mechanics of microtubules. Journal of Biomechanics, vol. 43, pp. 23-30.
26. Heidemann, S.; Buxbaum, R. (1994): Mechanical tension as a regulator of axonal development. NeuroToxicology, vol. 15, pp. 95-108. (Pubitemid 24166892)
27. Hely, T.; Graham, B.; van Ooyen, A. (2001): A computational model of dendrite elongation and branching based on MAP2 phosphorylation. Journal of Theoretical Biology, vol. 210, pp. 375-384. (Pubitemid 32575215)
28. Janulevicius, A.; van Pelt, J.; van Ooyen, A. (2006): Compartment volume influences microtubule dynamic instability: a model study. Biophysical Journal, vol. 90, pp. 788-798.
29. Jobs, E.; Wolf, D.; Flyvbjerg, H. (1997): Modeling microtubule oscillations. Physical Review Letters, vol. 79, pp. 519-522. (Pubitemid 127653661)
30. Keith, C. (1987): Slow transport of tubulin in the neurites of differentiated PC12 cells. Science, pp. 337-339. (Pubitemid 17232561)
31. Kirschner, M.; Mitchinson, T. (1986): Beyond self-assembly: from microtubules to morphogenesis. Cell, vol. 45, pp. 329-342. (Pubitemid 16014983)
32. Klann, M.; Koeppl, H.; Reuss, M. (2012): Spatial modeling of vesicle transport and the cytoskeleton: the challendge of hitting the right road. PLos ONE, vol. 7, pp. e29645.
33. Koch, K. (1999): Biophysics of computation. Information processing in single neurons. Oxford University Press.
34. Krottje, J.; van Ooyen, A. (2007): A mathematical framework for modeling axon guidance. Bulletin of Mathematical Biology, vol. 69, pp. 3-31. (Pubitemid 46155342)
35. Lamoureux, P.; Buxbaum, R.; Heidemann, S. (1998): Axonal outgrowth of cultured neurons is not limited by growth cone competition. Journal of Cell Science, vol. 111, pp. 3245-3252. (Pubitemid 28532434)
36. Lee, A.; Suter, D. (2008): Quantitative analysis of microtubule dynamics during adhesion-mediated growth cone guidance. Dev. Neurobi., vol. 68, pp. 1363-1377.
37. Lee, J.; Bashur, C.; Gomez, N.; Goldstein, A.; Schmidt, C. (2010): Enhanced polarization of embyonic hippocampal neurons on micron scale electrospun fibers. J. Biomed. Mater. Res. A., vol. 92, pp. 1398-1406.
38. Li, G.; Qin, C.;Wang, L. (1995): Computer model of growth cone behavior and neuronal morphogenesis. J. theor. Biol, vol. 174, pp. 381-389.
39. Lindsley, T.; Kerlin, A.; Rising, L. (2003): Time-lapse analysis of ethanol's effects on axon growth in vitro. Developmental Brain Reseach, vol. 147, pp. 191-199.
40. Lu, Y.-B.; Franze, K.; Seifert, G.; Steinhaüser, C.; Kirchhoff, F.;Wolburg, H.; Guck, J.; Janmey, P.;Wei, E.-Q.; Käs, J.; Reichenbach, A. (2006): Viscoelastic properties of individual glial cells and neurons in the CNS. PNAS, vol. 103, pp. 17759-17764. (Pubitemid 44852233)
41. Ma, Y.; Shakiryanova, D.; Vardya, I.; Popov, S. (2004): Quantitative analysis of microtubule transport in growing nerve process. Curr. Biol., vol. 14, pp. 725-730. (Pubitemid 38503611)
42. Margolin, G.; Gregoretti, I.; Goodson, H.; Alber, M. (2006): Analysis of a microscopic stochastic model of microtubule dynamic instability. Phys. Rev. E, vol. 74, pp. 041-920.
43. McGarry, J.; Prendergast, P. (2004): A three-dimensional finite element model of an adherent eukaryotic cell. European Cells and Materials, vol. 7, pp. 27-33.
44. McLean, D.; van Ooyen, A.; Graham, B. (2004): Continuum model for tubulindriven neurite elongation. Neurocomputing, vol. 58-60, pp. 511-516.
45. Miller, M.; Samuels, D. (1996): The axon as a metabolic compartment: protein degradation, transport and maximum length of an axon. J. theor. Biol., vol. 186, pp. 373-379. (Pubitemid 27281524)
46. Mitchison, T.; Kirschner, M. (1984): Microtubule assembly nucleated by isolated centrosomes. Nature, vol. 312, pp. 232-237. (Pubitemid 15201997)
47. Odde, D. (1997): Estimation of the diffusion-limited rate of microtubule assembly. Biophys. J., vol. 73, pp. 88-96. (Pubitemid 27274107)
48. Ouyang, H.; Nauman, E.; Shi, R. (2010): Contribution of cytoskeletal elements to the mechanical property of axons. In Micro/Nano Symposium (UGIM), 2010 18th Biennial University/Government/Industry, pp. 1-5.
49. Ouyang, H.; Nauman, E.; Shi, R. (2010): Contribution of cytoskeletal elements to the mechanical property of axons. In Micro/Nano Symposium (UGIM), 2010 18th Biennial University/Government/Industry, pp. 1-5.
50. Pascual-Leone, A.; Amedi, A.; Fregni, F.; Merabet, L. (2005): The plastic human brain cortex. Annual Review of Neuroscience, vol. 28, pp. 377-401. (Pubitemid 41098910)
51. Peter, S.; Mofrad, M. (2012): Computational modeling of axonal microtubule bundles under tension. Biophys. J., vol. 102, pp. 749-757.
52. Poulain, F.; Sobel, A. (2010): The microtubule network and neuronal morphogenesis: Dynamics and coordinated orchestration through multiple players. Molecular and Cellular Neuroscience, vol. 43, pp. 15-32.
53. Suresh, S. (2007): Biomechanics and biophysics of cancer cells. Acta Biomaterialia, vol. 3, pp. 413-438. (Pubitemid 46865787)
54. Tanaka, E.; Kirschner, M. (1991): Microtubule behavior in the growth cones of living neurons during axon elongation. The Journal of Cell Biology, vol. 115, pp. 345-363. (Pubitemid 21926032)
55. Twiss, J.; Fainzilber, M. (2009): Ribosomes in axons - scrounging from the neighbors? Trends in Cell Biology, vol. 19, pp. 236-243.
56. Uchida, A.; Alami, N.; Brown, A. (2009): Tight functional coupling of kinesin-1A and dynein motors in the bidirectional transport of neurofilaments. Mol. Biol. Cell, vol. 20, pp. 4997-5006.
57. van Ooyen, A.; Graham, B.; Ramakers, G. (1994): Competition for tubulin between growing neurites during development. Neurocomputing, vol. 38-40, pp. 73-78.
58. van Pelt, J.; Dityatev, A.; Uylings, H. (1997): Natural variability in the number of dendritic segments: model-based inferences about branching during neurite outgrowth. The Journal of Comparative Neurology, vol. 387, pp. 325-340. (Pubitemid 27430333)
59. van Pelt, J.; Schierwagen, A. (2004): Morphological analysis and modeling of neuronal dendrites. Mathematical Biosciences, vol. 188, pp. 147-155. (Pubitemid 38177310)
60. van Veen, M.; van Pelt, J. (1992): A model for outgrowth of branching neurites. J. theor. Biol., vol. 159, pp. 1-23. (Pubitemid 23010720)
61. van Veen, M.; van Pelt, J. (1994): Neuritic growth rate described by modeling microtubule dynamics. Bull Math Biol, vol. 56, pp. 249-273.
62. Williamson, T.; Gordon-Weeks, P.; Schachner, M.; Taylor, J. (1996): Microtubule reorganization is obligaroty fro growth cone turning. Proc. Natl. Acad. Sci. USA, vol. 93, pp. 15221-15226. (Pubitemid 27009580)
63. Zubler, F.; Douglas, R. (2009): A framework for modeling the growth and development of neurons and networks. Frontiers in Computational Neuroscience, vol. 3, pp. 25.