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Axonal Growth and Targeting

  • Duncan Mortimer
  • Hugh D. Simpson
  • Geoffrey J. Goodhill
Chapter

Abstract

The growth and guidance of axons is an undertaking of both great complexity and great precision, involving processes at a range of length and time scales. Correct axonal guidance involves directing the tips of individual axons and their branches, interactions between branches of a single axon, and interactions between axons of different neurons. In this chapter, we describe examples of models operating at and between each of these scales.

Keywords

Growth Cone Axon Guidance Tubulin Concentration Molecular Label Axon Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Aeschlimann M, Tettoni L (2001) Biophysical model of axonal pathfinding. Neurocomp 38–40:87–92CrossRefGoogle Scholar
  2. Atilgan E, Wirtz D, Sun SX (2006) Mechanics and dynamics of actin-driven thin membrane protrusions. Biophys J 90:65–76PubMedCrossRefGoogle Scholar
  3. Berg HC, Purcell EM (1977) Physics of chemoreception. Biophys J 20:193–219PubMedCrossRefGoogle Scholar
  4. Betz T, Lim D, Käs JA (2006) Neuronal growth: a bistable stochastic process. Phys Rev Lett 96:098103PubMedCrossRefGoogle Scholar
  5. Betz T, Koch D, Lim D, Käs JA (2009) Stochastic actin polymerization and steady retrograde flow determine growth cone advancement. Biophys J 96:5130–5138PubMedCrossRefGoogle Scholar
  6. Bialek W, Setayeshgar S (2005) Physical limits to biochemical signaling. Proc Natl Acad Sci USA 102:10040–10045PubMedCrossRefGoogle Scholar
  7. Bouzigues C, Morel M, Triller A, Dahan M (2007) Asymmetric redistribution of GABA receptors during GABA gradient sensing by nerve growth cones analyzed by single quantum dot imaging. Proc Natl Acad Sci USA 104:11251–11256PubMedCrossRefGoogle Scholar
  8. Bouzigues C, Holcman D, Dahan M (2010) A mechanism for the polarity formation of chemoreceptors at the growth cone membrane for gradient amplification during directional sensing. PLoS One 5(2):e9243. doi:10.1371/journal.pone.0009243, http://dx.doi.org/10.1371/journal.pone.0009243
  9. Brown A, Yates PA, Burrola P, no DO, Vaidya A, Jessell TM, Pfaff SL, O’Leary DD, Lemke G (2000) Topographic mapping from the retina to the midbrain is controlled by relative but not absolute levels of EphA receptor signaling. Cell 102(1):77–88Google Scholar
  10. Buettner H (1996) Analysis of cell-target encounter by random filopodial projections. AICHE J 42:1127CrossRefGoogle Scholar
  11. Buettner HM, Pittman RN, Ivins JK (1994) A model of neurite extension across regions of nonpermissive substrate: Simulations based on experimental measurements of growth cone motility and filopodial dynamics. Dev Biol 163:407–422PubMedCrossRefGoogle Scholar
  12. Causin P, Facchetti G (2009) Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis. PLoS Comp Biol 5:e1000479CrossRefGoogle Scholar
  13. Dickson BJ (2002) Molecular mechanisms of axon guidance. Science 298:1959–1964PubMedCrossRefGoogle Scholar
  14. Endres RG, Wingreen NS (2008) Accuracy of direct gradient sensing by single cells. Proc Natl Acad Sci USA 105:15749–15754PubMedCrossRefGoogle Scholar
  15. Fraser SE, Perkel DH (1990) Competitive and positional cues in the patterning of nerve connections. J Neurobiol 21(1):51–72PubMedCrossRefGoogle Scholar
  16. Gierer A (1983) Model for the retino-tectal projection. Proc R Soc Lond B Biol Sci 218(1210):77–93PubMedCrossRefGoogle Scholar
  17. Gierer A (1987) Directional cues for growing axons forming the retinotectal projection. Development 101(3):479–489Google Scholar
  18. Giniger E (2002) How do rho family gtpases direct axon growth and guidance? a proposal relating signaling pathways to growth cone mechanics. Differentiation 70(8):385–396PubMedCrossRefGoogle Scholar
  19. Godfrey KB, Eglen SJ, Swindale NV (2009) A multi-component model of the developing retinocollicular pathway incorporating axonal and synaptic growth. PLoS Comput Biol 5(12):e1000600PubMedCrossRefGoogle Scholar
  20. Goodhill GJ, Urbach JS (1999) Theoretical analysis of gradient detection by growth cones. J Neurobiol 41:230–241PubMedCrossRefGoogle Scholar
  21. Goodhill GJ, Xu J (2005) The development of retinotectal maps: a review of models based on molecular gradients. Network 16(1):5–34PubMedCrossRefGoogle Scholar
  22. Goodhill GJ, Gu M, Urbach JS (2004) Predicting axonal response to molecular gradients with a computational model of filopodial dynamics. Neural Comput 16:2221–2243PubMedCrossRefGoogle Scholar
  23. Gordon-Weeks PR (2000) Neuronal growth cones. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Gordon-Weeks PR (2004) Microtubules and growth cone function. J Neurobiol 58:70–83PubMedCrossRefGoogle Scholar
  25. Gov NS, Gopinathan A (2006) Dynamics of membranes driven by actin polymerization. Biophys J 90:454–469PubMedCrossRefGoogle Scholar
  26. Graham BP, van Ooyen A (2001) Compartmental models of growing neurites. Neurocomputing 38–40:31–36CrossRefGoogle Scholar
  27. Graham BP, van Ooyen A (2006) Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neurosci 7(1):S9. doi:10.1186/1471-2202-7-S1-S9, http://dx.doi.org/10.1186/1471-2202-7-S1-S9
  28. Graham BP, Lauchlan K, McLean DR (2006) Dynamics of outgrowth in a continuum model of neurite elongation. J Comput Neurosci 20:43–60PubMedCrossRefGoogle Scholar
  29. Häussler A, von der Malsburg C (1983) Development of retinotopic projections: an analytical treatment. J Theoret Neurobiol 2:47–73Google Scholar
  30. Hely TA, Willshaw DJ (1998) Short-term interactions between microtubules and actin filaments underlie long-term behaviour in neuronal growth cones. Proc R Soc Lond B 265:1801–1807CrossRefGoogle Scholar
  31. Herzmark P, Campbell K, Wang F, Wong K, El-Samad H, Groisman A, Bourne HR (2007) Bound attractant at the leading vs. the trailing edge determines chemotactic prowess. Proc Natl Acad Sci USA 104:13349–13354PubMedCrossRefGoogle Scholar
  32. Honda H (1998) Topographic mapping in the retinotectal projection by means of complementary ligand and receptor gradients: a computer simulation study. J Theor Biol 192(2):235–246PubMedCrossRefGoogle Scholar
  33. Honda H (2003) Competition between retinal ganglion axons for targets under the servomechanism model explains abnormal retinocollicular projection of Eph receptor-overexpressing or ephrin-lacking mice. J Neurosci 23(32):10368–10377PubMedGoogle Scholar
  34. Hope RA, Hammond BJ, Gaze RM (1976) The arrow model: retinotectal specificity and map formation in the goldfish visual system. Proc R Soc Lond B Biol Sci 194(1117):447–466PubMedCrossRefGoogle Scholar
  35. Kiddie G, McLean D, Van Ooyen A, Graham B (2005) Biologically plausible models of neurite outgrowth. Progr Brain Res 147:67–80CrossRefGoogle Scholar
  36. Koulakov AA, Tsigankov DN (2004) A stochastic model for retinocollicular map development. BMC Neurosci 5:30PubMedCrossRefGoogle Scholar
  37. Lamoureux P, Buxbaum RE, Heidemann SR (1998) Axonal outgrowth of cultured neurons is not limited by growth cone competition. J Cell Sci 111:3245–3252PubMedGoogle Scholar
  38. Lauffenburger DA, Linderman JL (1993) Receptors: models for binding, trafficking and signaling. Oxford university press, OxfordGoogle Scholar
  39. Li GH, Qin CD, Wang ZS (1992) Neurite branching pattern formation: modeling and computer simulation. J Theor Biol 157:463–486PubMedCrossRefGoogle Scholar
  40. Li GH, Qin CD, Wang LW (1995) Computer model of growth cone behavior and neuronal morphogenesis. J Theor Biol 174:381–389CrossRefGoogle Scholar
  41. Lin CH, Forscher P (1995) Growth cone advance is inversely proportional to retrograde F-actin flow. Neuron 14:763–771PubMedCrossRefGoogle Scholar
  42. Lowery LA, van Vactor D (2009) The trip of the tip: understanding the growth cone machinery. Nat Rev Mol Cell Biol 10:332–343PubMedCrossRefGoogle Scholar
  43. Maskery S, Shinbrot T (2005) Deterministic and stochastic elements of axonal guidance. Annu Rev Biomed Eng 7:187–221. doi:10.1146/annurev.bioeng.7.060804.100446, http://dx.doi.org/10.1146/annurev.bioeng.7.060804.100446 Google Scholar
  44. Maskery S, Buettner H, Shinbrot T (2004) Growth cone pathfinding: a competition between deterministic and stochastic events. BMC Neurosci 5:22PubMedCrossRefGoogle Scholar
  45. McLaughlin T, O’Leary DDM (2005) Molecular gradients and development of retinotopic maps. Annu Rev Neurosci 28:327–355PubMedCrossRefGoogle Scholar
  46. McLean DR, van Ooyen A, Graham BP (2004) Continuum model for tubulin-driven neurite elongation. Neurocomp 58–60:511–516CrossRefGoogle Scholar
  47. Medeiros NA, Burnette DT, Forscher P (2006) Myosin II functions in actin-bundle turnover in neuronal growth cones. Nature Cell Biol 8:215–226PubMedCrossRefGoogle Scholar
  48. Mitchison T, Kirschner M (1984) Dynamic instability of microtubule growth. Nature 312:237–242PubMedCrossRefGoogle Scholar
  49. Mogilner A (2009) Mathematics of cell motility: have we got its number? J Math Biol 58:105–134PubMedCrossRefGoogle Scholar
  50. Mogilner A, Rubinstein B (2005) The physics of filopodial protrusion. Biophys J 89:1–14CrossRefGoogle Scholar
  51. Mortimer D, Fothergill T, Pujic Z, Richards LJ, Goodhill GJ (2008) Growth cone chemotaxis. Trends Neurosci 31:90–98PubMedCrossRefGoogle Scholar
  52. Mortimer D, Feldner J, Vaughan T, Vetter I, Pujic Z, Rosoff WJ, Burrage K, Dayan P, Richards LJ, Goodhill GJ (2009) A bayesian model predicts the response of axons to molecular gradients. Proc Natl Acad Sci USA 106(25):10296–10301PubMedCrossRefGoogle Scholar
  53. Mortimer D, Dayan P, Burrage K, Goodhill G (2010a) Optimizing chemotaxis by measuring unbound-bound transitions. Physica D 239:477–484CrossRefGoogle Scholar
  54. Mortimer D, Pujic Z, Vaughan T, Thompson AW, Feldner J, Vetter I, Goodhill GJ (2010b) Axon guidance by growth-rate modulation. Proc Natl Acad Sci USA 107:5202–5207PubMedCrossRefGoogle Scholar
  55. Mortimer D, Dayan P, Burrage K, Goodhill GJ (2011) Bayes-optimal chemotaxis. Neural Comput 23:336–373PubMedCrossRefGoogle Scholar
  56. Nakamoto M, Cheng HJ, Friedman GC, McLaughlin T, Hansen MJ, Yoon CH, O’Leary DD, Flanagan JG (1996) Topographically specific effects of ELF-1 on retinal axon guidance in vitro and retinal axon mapping in vivo. Cell 86(5):755–766PubMedCrossRefGoogle Scholar
  57. O’Connor TP, Duerr JS, Bentley D (1990) Pioneer growth cone steering decisions mediated by single filopodial contacts in situ. J Neurosci 10:3935PubMedGoogle Scholar
  58. Odde D, Tanaka E, Hawkins S, Buettner H (1996) Stochastic dynamics of the nerve growth cone and its microtubules during neurite outgrowth. Biotechnol Bioeng 50:452–461PubMedCrossRefGoogle Scholar
  59. Overton KJ, Arbib MA (1982) The extended branch-arrow model of the formation of retino-tectal connections. Biol Cybern 45(3):157–175PubMedCrossRefGoogle Scholar
  60. Poliakov A, Cotrina M, Wilkinson DG (2004) Diverse roles of eph receptors and ephrins in the regulation of cell migration and tissue assembly. Dev Cell 7(4):465–480PubMedCrossRefGoogle Scholar
  61. Prestige MC, Willshaw DJ (1975) On a role for competition in the formation of patterned neural connexions. Proc R Soc Lond B Biol Sci 190(1098):77–98PubMedCrossRefGoogle Scholar
  62. Reber M, Burrola P, Lemke G (2004) A relative signalling model for the formation of a topographic neural map. Nature 431(7010):847–853PubMedCrossRefGoogle Scholar
  63. Rosoff WJ, Urbach JS, Esrick MA, McAllister RG, Richards LJ, Goodhill GJ (2004) A new chemotaxis assay shows the extreme sensitivity of axons to molecular gradients. Nat Neurosci 7(6):678–682PubMedCrossRefGoogle Scholar
  64. Sakumura Y, Tsukada Y, Yamamoto N, Ishii S (2005) A molecular model for axon guidance based on cross talk between rho gtpases. Biophys J 89(2):812–822PubMedCrossRefGoogle Scholar
  65. Simpson HD, Goodhill GJ (2011) A simple model can unify a broad range of phenomena in retinotectal map development. Biol Cybern 104(1):9–29. doi:10.1007/ s00422-011-0417-yPubMedCrossRefGoogle Scholar
  66. Simpson HD, Mortimer D, Goodhill GJ (2009) Theoretical models of neural circuit development. In: Hobert O (ed )The development of neural circuitry. Current topics in developmental biology, vol 87. Elsevier, Amsterdam, pp 1–51Google Scholar
  67. Smalheiser NR, Crain SM (1984) The possible role of “sibling neurite bias” in the coordination of neurite extension, branching, and survival. J Neurobiol 15:517–529PubMedCrossRefGoogle Scholar
  68. Sperry R (1963) Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc Natl Acad Sci USA 50:703–710PubMedCrossRefGoogle Scholar
  69. Suter DM, Forscher P (2000) Substrate-cytoskeletal coupling as a mechanism for the regulation of growth cone motility and guidance. J Neurobiol 44:97–113PubMedCrossRefGoogle Scholar
  70. Tessier-Lavigne M, Goodman CS (1996) The molecular biology of axon guidance. Science 274:1123PubMedCrossRefGoogle Scholar
  71. Tsigankov D, Koulakov AA (2010) Sperry versus hebb: topographic mapping in isl2/epha3 mutant mice. BMC Neurosci 11:155. doi:10.1186/1471-2202-11-155, http://dx.doi.org/10.1186/1471-2202-11-155
  72. Tsigankov DN, Koulakov AA (2006) A unifying model for activity-dependent and activity-independent mechanisms predicts complete structure of topographic maps in ephrin-A deficient mice. J Comput Neurosci 21(1):101–114PubMedCrossRefGoogle Scholar
  73. Udin SB, Fawcett JW (1988) Formation of topographic maps. Annu Rev Neurosci 11:289–327PubMedCrossRefGoogle Scholar
  74. Ueda M, Shibata T (2007) Stochastic signal processing and transduction in chemotactic response of eukaryotic cells. Biophys J 93:11–20PubMedCrossRefGoogle Scholar
  75. van Ooyen A (2001) Competition in the development of nerve connections: a review of models. Network 12(1):R1–47PubMedCrossRefGoogle Scholar
  76. van Ooyen A (ed) (2003) Modeling Neural Development. MIT Press, CambridgeGoogle Scholar
  77. van Ooyen A, Willshaw DJ (2000) Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology. J Theor Biol 206(2):195–210PubMedCrossRefGoogle Scholar
  78. Van Veen MP, Van Pelt J (1994) Neuritic growth rate described by modeling microtubule dynamics. Bull Math Biol 56:249–273PubMedCrossRefGoogle Scholar
  79. Weber C, Ritter H, Cowan J, Klaus Obermayer K (1997) Development and regeneration of the retinotectal map in goldfish: a computational study. Philos Trans 352(1361):1603–1623CrossRefGoogle Scholar
  80. Whitelaw VA, Cowan JD (1981) Specificity and plasticity of retinotectal connections: a computational model. J Neurosci 1(12):1369–1387PubMedGoogle Scholar
  81. Wilkinson DG (2001) Multiple roles of Eph receptors and ephrins in neural development. Nat Rev Neurosci 2(3):155–164PubMedCrossRefGoogle Scholar
  82. Willshaw D (2006) Analysis of mouse EphA knockins and knockouts suggests that retinal axons programme target cells to form ordered retinotopic maps. Development 133(14):2705–2717PubMedCrossRefGoogle Scholar
  83. Willshaw DJ, von der Malsburg C (1979) A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. Philos Trans R Soc Lond B Biol Sci 287(1021):203–243PubMedCrossRefGoogle Scholar
  84. Willshaw DJ, Price DJ (2003) Models for topographic map formation. In: van Ooyen A (ed) Modeling neural development. MIT Press, Cambridge, pp 213–244Google Scholar
  85. Xu J, Rosoff WJl, Urbach JS, Goodhill GJ (2005) Adaptation is not required to explain the long-term response of axons to molecular gradients. Development 132(20):4545–4552Google Scholar
  86. Yates PA, Roskies AL, McLaughlin T, O’Leary DD (2001) Topographic-specific axon branching controlled by ephrin-As is the critical event in retinotectal map development. J Neurosci 21(21):8548–8563PubMedGoogle Scholar
  87. Yates PA, Holub AD, McLaughlin T, Sejnowski TJ, O’Leary DDM (2004) Computational modeling of retinotopic map development to define contributions of EphA-ephrinA gradients, axon–axon interactions, and patterned activity. J Neurobiol 59(1):95–113PubMedCrossRefGoogle Scholar
  88. Zheng JQ, Poo MM (2007) Calcium signaling in neuronal motility. Ann Rev Cell Dev Biol 23:375–404CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Duncan Mortimer
    • 1
  • Hugh D. Simpson
    • 2
  • Geoffrey J. Goodhill
    • 3
  1. 1.Electronics and Computer Science, Faculty of Physical and Applied SciencesUniversity of SouthamptonSouthamptonUK
  2. 2.The Queensland Brain InstituteThe University of QueenslandBrisbaneAustralia
  3. 3.The School of Mathematics and Physics, The Queensland Brain InstituteThe University of QueenslandBrisbaneAustralia

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