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Axonal Growth and Targeting

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Computational Systems Neurobiology

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.

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References

  • Aeschlimann M, Tettoni L (2001) Biophysical model of axonal pathfinding. Neurocomp 38–40:87–92

    Article  Google Scholar 

  • Atilgan E, Wirtz D, Sun SX (2006) Mechanics and dynamics of actin-driven thin membrane protrusions. Biophys J 90:65–76

    Article  PubMed  CAS  Google Scholar 

  • Berg HC, Purcell EM (1977) Physics of chemoreception. Biophys J 20:193–219

    Article  PubMed  CAS  Google Scholar 

  • Betz T, Lim D, Käs JA (2006) Neuronal growth: a bistable stochastic process. Phys Rev Lett 96:098103

    Article  PubMed  Google Scholar 

  • Betz T, Koch D, Lim D, Käs JA (2009) Stochastic actin polymerization and steady retrograde flow determine growth cone advancement. Biophys J 96:5130–5138

    Article  PubMed  CAS  Google Scholar 

  • Bialek W, Setayeshgar S (2005) Physical limits to biochemical signaling. Proc Natl Acad Sci USA 102:10040–10045

    Article  PubMed  CAS  Google Scholar 

  • 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 104:11251–11256

    Article  PubMed  CAS  Google Scholar 

  • 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

  • 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):77–88

    Google Scholar 

  • Buettner H (1996) Analysis of cell-target encounter by random filopodial projections. AICHE J 42:1127

    Article  CAS  Google Scholar 

  • 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 163:407–422

    Article  PubMed  CAS  Google Scholar 

  • 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:e1000479

    Article  Google Scholar 

  • Dickson BJ (2002) Molecular mechanisms of axon guidance. Science 298:1959–1964

    Article  PubMed  CAS  Google Scholar 

  • Endres RG, Wingreen NS (2008) Accuracy of direct gradient sensing by single cells. Proc Natl Acad Sci USA 105:15749–15754

    Article  PubMed  CAS  Google Scholar 

  • Fraser SE, Perkel DH (1990) Competitive and positional cues in the patterning of nerve connections. J Neurobiol 21(1):51–72

    Article  PubMed  CAS  Google Scholar 

  • Gierer A (1983) Model for the retino-tectal projection. Proc R Soc Lond B Biol Sci 218(1210):77–93

    Article  PubMed  CAS  Google Scholar 

  • Gierer A (1987) Directional cues for growing axons forming the retinotectal projection. Development 101(3):479–489

    Google Scholar 

  • 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):385–396

    Article  PubMed  CAS  Google Scholar 

  • 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):e1000600

    Article  PubMed  Google Scholar 

  • Goodhill GJ, Urbach JS (1999) Theoretical analysis of gradient detection by growth cones. J Neurobiol 41:230–241

    Article  PubMed  CAS  Google Scholar 

  • Goodhill GJ, Xu J (2005) The development of retinotectal maps: a review of models based on molecular gradients. Network 16(1):5–34

    Article  PubMed  Google Scholar 

  • Goodhill GJ, Gu M, Urbach JS (2004) Predicting axonal response to molecular gradients with a computational model of filopodial dynamics. Neural Comput 16:2221–2243

    Article  PubMed  Google Scholar 

  • Gordon-Weeks PR (2000) Neuronal growth cones. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Gordon-Weeks PR (2004) Microtubules and growth cone function. J Neurobiol 58:70–83

    Article  PubMed  CAS  Google Scholar 

  • Gov NS, Gopinathan A (2006) Dynamics of membranes driven by actin polymerization. Biophys J 90:454–469

    Article  PubMed  CAS  Google Scholar 

  • Graham BP, van Ooyen A (2001) Compartmental models of growing neurites. Neurocomputing 38–40:31–36

    Article  Google Scholar 

  • 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

  • Graham BP, Lauchlan K, McLean DR (2006) Dynamics of outgrowth in a continuum model of neurite elongation. J Comput Neurosci 20:43–60

    Article  PubMed  Google Scholar 

  • Häussler A, von der Malsburg C (1983) Development of retinotopic projections: an analytical treatment. J Theoret Neurobiol 2:47–73

    Google Scholar 

  • 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 265:1801–1807

    Article  CAS  Google Scholar 

  • 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 104:13349–13354

    Article  PubMed  Google Scholar 

  • 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):235–246

    Article  PubMed  CAS  Google Scholar 

  • 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):10368–10377

    PubMed  CAS  Google Scholar 

  • 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):447–466

    Article  PubMed  CAS  Google Scholar 

  • Kiddie G, McLean D, Van Ooyen A, Graham B (2005) Biologically plausible models of neurite outgrowth. Progr Brain Res 147:67–80

    Article  CAS  Google Scholar 

  • Koulakov AA, Tsigankov DN (2004) A stochastic model for retinocollicular map development. BMC Neurosci 5:30

    Article  PubMed  Google Scholar 

  • Lamoureux P, Buxbaum RE, Heidemann SR (1998) Axonal outgrowth of cultured neurons is not limited by growth cone competition. J Cell Sci 111:3245–3252

    PubMed  CAS  Google Scholar 

  • Lauffenburger DA, Linderman JL (1993) Receptors: models for binding, trafficking and signaling. Oxford university press, Oxford

    Google Scholar 

  • Li GH, Qin CD, Wang ZS (1992) Neurite branching pattern formation: modeling and computer simulation. J Theor Biol 157:463–486

    Article  PubMed  CAS  Google Scholar 

  • Li GH, Qin CD, Wang LW (1995) Computer model of growth cone behavior and neuronal morphogenesis. J Theor Biol 174:381–389

    Article  Google Scholar 

  • Lin CH, Forscher P (1995) Growth cone advance is inversely proportional to retrograde F-actin flow. Neuron 14:763–771

    Article  PubMed  CAS  Google Scholar 

  • Lowery LA, van Vactor D (2009) The trip of the tip: understanding the growth cone machinery. Nat Rev Mol Cell Biol 10:332–343

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • Maskery S, Buettner H, Shinbrot T (2004) Growth cone pathfinding: a competition between deterministic and stochastic events. BMC Neurosci 5:22

    Article  PubMed  Google Scholar 

  • McLaughlin T, O’Leary DDM (2005) Molecular gradients and development of retinotopic maps. Annu Rev Neurosci 28:327–355

    Article  PubMed  CAS  Google Scholar 

  • McLean DR, van Ooyen A, Graham BP (2004) Continuum model for tubulin-driven neurite elongation. Neurocomp 58–60:511–516

    Article  Google Scholar 

  • Medeiros NA, Burnette DT, Forscher P (2006) Myosin II functions in actin-bundle turnover in neuronal growth cones. Nature Cell Biol 8:215–226

    Article  PubMed  CAS  Google Scholar 

  • Mitchison T, Kirschner M (1984) Dynamic instability of microtubule growth. Nature 312:237–242

    Article  PubMed  CAS  Google Scholar 

  • Mogilner A (2009) Mathematics of cell motility: have we got its number? J Math Biol 58:105–134

    Article  PubMed  Google Scholar 

  • Mogilner A, Rubinstein B (2005) The physics of filopodial protrusion. Biophys J 89:1–14

    Article  Google Scholar 

  • Mortimer D, Fothergill T, Pujic Z, Richards LJ, Goodhill GJ (2008) Growth cone chemotaxis. Trends Neurosci 31:90–98

    Article  PubMed  CAS  Google Scholar 

  • 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):10296–10301

    Article  PubMed  CAS  Google Scholar 

  • Mortimer D, Dayan P, Burrage K, Goodhill G (2010a) Optimizing chemotaxis by measuring unbound-bound transitions. Physica D 239:477–484

    Article  CAS  Google Scholar 

  • 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 107:5202–5207

    Article  PubMed  CAS  Google Scholar 

  • Mortimer D, Dayan P, Burrage K, Goodhill GJ (2011) Bayes-optimal chemotaxis. Neural Comput 23:336–373

    Article  PubMed  Google Scholar 

  • 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):755–766

    Article  PubMed  CAS  Google Scholar 

  • O’Connor TP, Duerr JS, Bentley D (1990) Pioneer growth cone steering decisions mediated by single filopodial contacts in situ. J Neurosci 10:3935

    PubMed  Google Scholar 

  • Odde D, Tanaka E, Hawkins S, Buettner H (1996) Stochastic dynamics of the nerve growth cone and its microtubules during neurite outgrowth. Biotechnol Bioeng 50:452–461

    Article  PubMed  CAS  Google Scholar 

  • Overton KJ, Arbib MA (1982) The extended branch-arrow model of the formation of retino-tectal connections. Biol Cybern 45(3):157–175

    Article  PubMed  CAS  Google Scholar 

  • 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):465–480

    Article  PubMed  CAS  Google Scholar 

  • 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):77–98

    Article  PubMed  CAS  Google Scholar 

  • Reber M, Burrola P, Lemke G (2004) A relative signalling model for the formation of a topographic neural map. Nature 431(7010):847–853

    Article  PubMed  CAS  Google Scholar 

  • 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):678–682

    Article  PubMed  CAS  Google Scholar 

  • 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):812–822

    Article  PubMed  CAS  Google Scholar 

  • 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-y

    Article  PubMed  Google Scholar 

  • 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 1–51

    Google Scholar 

  • Smalheiser NR, Crain SM (1984) The possible role of “sibling neurite bias” in the coordination of neurite extension, branching, and survival. J Neurobiol 15:517–529

    Article  PubMed  CAS  Google Scholar 

  • Sperry R (1963) Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc Natl Acad Sci USA 50:703–710

    Article  PubMed  CAS  Google Scholar 

  • Suter DM, Forscher P (2000) Substrate-cytoskeletal coupling as a mechanism for the regulation of growth cone motility and guidance. J Neurobiol 44:97–113

    Article  PubMed  CAS  Google Scholar 

  • Tessier-Lavigne M, Goodman CS (1996) The molecular biology of axon guidance. Science 274:1123

    Article  PubMed  CAS  Google Scholar 

  • 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

  • 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):101–114

    Article  PubMed  Google Scholar 

  • Udin SB, Fawcett JW (1988) Formation of topographic maps. Annu Rev Neurosci 11:289–327

    Article  PubMed  CAS  Google Scholar 

  • Ueda M, Shibata T (2007) Stochastic signal processing and transduction in chemotactic response of eukaryotic cells. Biophys J 93:11–20

    Article  PubMed  CAS  Google Scholar 

  • van Ooyen A (2001) Competition in the development of nerve connections: a review of models. Network 12(1):R1–47

    Article  PubMed  Google Scholar 

  • van Ooyen A (ed) (2003) Modeling Neural Development. MIT Press, Cambridge

    Google Scholar 

  • 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):195–210

    Article  PubMed  Google Scholar 

  • Van Veen MP, Van Pelt J (1994) Neuritic growth rate described by modeling microtubule dynamics. Bull Math Biol 56:249–273

    Article  PubMed  Google Scholar 

  • 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):1603–1623

    Article  Google Scholar 

  • Whitelaw VA, Cowan JD (1981) Specificity and plasticity of retinotectal connections: a computational model. J Neurosci 1(12):1369–1387

    PubMed  CAS  Google Scholar 

  • Wilkinson DG (2001) Multiple roles of Eph receptors and ephrins in neural development. Nat Rev Neurosci 2(3):155–164

    Article  PubMed  CAS  Google Scholar 

  • 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):2705–2717

    Article  PubMed  CAS  Google Scholar 

  • 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):203–243

    Article  PubMed  CAS  Google Scholar 

  • Willshaw DJ, Price DJ (2003) Models for topographic map formation. In: van Ooyen A (ed) Modeling neural development. MIT Press, Cambridge, pp 213–244

    Google Scholar 

  • 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):4545–4552

    Google Scholar 

  • 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):8548–8563

    PubMed  CAS  Google Scholar 

  • 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):95–113

    Article  PubMed  CAS  Google Scholar 

  • Zheng JQ, Poo MM (2007) Calcium signaling in neuronal motility. Ann Rev Cell Dev Biol 23:375–404

    Article  CAS  Google Scholar 

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Correspondence to Geoffrey J. Goodhill .

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Mortimer, D., Simpson, H.D., Goodhill, G.J. (2012). Axonal Growth and Targeting. In: Le Novère, N. (eds) Computational Systems Neurobiology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3858-4_14

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