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A simple model can unify a broad range of phenomena in retinotectal map development

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Abstract

A paradigm model system for studying the development of patterned connections in the nervous system is the topographic map formed by retinal axons in the optic tectum/superior colliculus. Starting in the 1970s, a series of computational models have been proposed to explain map development in both normal conditions, and perturbed conditions where the retina and/or tectum/superior colliculus are altered. This stands in contrast to more recent models that have often been simpler than older ones, and tend to address more limited data sets, but include more recent genetic manipulations. The original exploration of many of the early models was one-dimensional and limited by the computational resources of the time. This leaves open the ability of these early models to explain both map development in two dimensions, and the genetic manipulation data that have only appeared more recently. In this article, we show that a two-dimensional and updated version of the XBAM model (eXtended Branch Arrow Model), first proposed in 1982, reproduces a range of surgical map manipulations not yet demonstrated by more modern models. A systematic exploration of the parameter space of this model in two dimensions also reveals richer behavior than that apparent from the original one-dimensional versions. Furthermore, we show that including a specific type of axon–axon interaction can account for the map collapse recently observed when particular receptor levels are genetically manipulated in a subset of retinal ganglion cells. Together these results demonstrate that balancing multiple influences on map development seems to be necessary to explain many biological phenomena in retinotectal map formation, and suggest important constraints on the underlying biological variables.

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References

  • Bastmeyer M, Ott H, Leppert CA, Stuermer CA (1995) Fish e587 glycoprotein, a member of the l1 family of cell adhesion molecules, participates in axonal fasciculation and the age-related order of ganglion cell axons in the goldfish retina. J Cell Biol 130(4): 969–976

    Article  PubMed  CAS  Google Scholar 

  • Bonhoeffer F, Huf J (1985) Position-dependent properties of retinal axons and their growth cones. Nature 315(6018): 409–410

    Article  PubMed  CAS  Google Scholar 

  • 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

    Article  PubMed  CAS  Google Scholar 

  • Caras IW (1997) A link between axon guidance and axon fasciculation suggested by studies of the tyrosine kinase receptor EphA5/REK7 and its ligand ephrin-A5/AL-1. Cell Tissue Res 290(2): 261–264

    Article  PubMed  CAS  Google Scholar 

  • Cheng HJ, Nakamoto M, Bergemann AD, Flanagan JG (1995) Complementary gradients in expression and binding of ELF-1 and Mek4 in development of the topographic retinotectal projection map. Cell 82(3): 371–381

    Article  PubMed  CAS  Google Scholar 

  • Cowan J, Friedman A (1991) Studies of a model for the development and regeneration of eye brain maps. In: Touretzky DS (ed) Advances in neural information processing systems III. Morgan Kaufman, San Mateo, pp 3–10

    Google Scholar 

  • Debski EA, Cline HT (2002) Activity-dependent mapping in the retinotectal projection. Curr Opin Neurobiol 12(1): 93–99

    Article  PubMed  CAS  Google Scholar 

  • Drescher U, Kremoser C, Handwerker C, Lschinger J, Noda M, Bonhoeffer F (1995) In vitro guidance of retinal ganglion cell axons by RAGS, a 25 kDa tectal protein related to ligands for Eph receptor tyrosine kinases. Cell 82(3): 359–370

    Article  PubMed  CAS  Google Scholar 

  • Feldheim DA, Kim YI, Bergemann AD, Frisén J, Barbacid M, Flanagan JG (2000) Genetic analysis of ephrin-A2 and ephrin-A5 shows their requirement in multiple aspects of retinocollicular mapping. Neuron 25(3): 563–574

    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. doi:10.1002/neu.480210105

    Article  PubMed  CAS  Google Scholar 

  • Fujisawa H (1981) Retinotopic analysis of fiber pathways in the regenerating retinotectal system of the adult newt cynops pyrrhogaster. Brain Res 206(1): 27–37

    Article  PubMed  CAS  Google Scholar 

  • Gaze RM, Grant P (1978) The diencephalic course of regenerating retinotectal fibres in xenopus tadpoles. J Embryol Exp Morphol 44: 201–216

    PubMed  CAS  Google Scholar 

  • Gaze RM, Keating MJ (1972) The visual system and “neuronal specificity”. Nature 237(5355): 375–378

    Article  PubMed  CAS  Google Scholar 

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

    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 

  • 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. doi:10.1371/journal.pcbi.1000600

    Article  PubMed  Google Scholar 

  • Goodhill GJ, Richards LJ (1999) Retinotectal maps: molecules, models and misplaced data. Trends Neurosci 22(12): 529–534

    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 

  • Gosse NJ, Nevin LM, Baier H (2008) Retinotopic order in the absence of axon competition. Nature 452(7189): 892–895. doi:10.1038/nature06816

    Article  PubMed  CAS  Google Scholar 

  • Hansen MJ, Dallal DJ, Flanagan JG (2004) Retinal axon response to ephrin-As shows a graded, concentration-dependent transition from growth promotion to inhibition. Neuron 42(5): 717–730. doi:10.1016/j.neuron.2004.05.009

    Article  PubMed  CAS  Google Scholar 

  • Harris WA, Holt CE, Bonhoeffer F (1987) Retinal axons with and without their somata, growing to and arborizing in the tectum of xenopus embryos: a time-lapse video study of single fibres in vivo. Development 101(1): 123–133

    PubMed  CAS  Google Scholar 

  • Harris WA (1982) The transplantation of eyes to genetically eyeless salamanders: visual projections and somatosensory interactions. J Neurosci 2(3): 339–353

    PubMed  CAS  Google Scholar 

  • Hayes WP, Meyer RL (1988) Normal and regenerating optic fibers in goldfish tectum: HRP-EM evidence for rapid synaptogenesis and optic fiber-fiber affinity. J Comp Neurol 274(4): 516–538. doi:10.1002/cne.902740404

    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): 10,368–10,377

    CAS  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. doi:10.1006/jtbi.1998.0662

    Article  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 

  • Horder TJ (1971) Retention, by fish optic nerve fibres regenerating to new terminal sites in the tectum, of ‘chemospecific’ affinity for their original sites. J Physiol 216(2): 53P–55P

    PubMed  CAS  Google Scholar 

  • Kaas JH (1997) Topographic maps are fundamental to sensory processing. Brain Res Bull 44(2): 107–112

    Article  PubMed  CAS  Google Scholar 

  • Kaethner RJ, Stuermer CA (1992) Dynamics of terminal arbor formation and target approach of retinotectal axons in living zebrafish embryos: a time-lapse study of single axons. J Neurosci 12(8): 3257–3271

    PubMed  CAS  Google Scholar 

  • Koulakov AA, Tsigankov DN (2004) A stochastic model for retinocollicular map development. BMC Neurosci 5: 30. doi:10.1186/1471-2202-5-30

    Article  PubMed  Google Scholar 

  • McLaughlin T, O’Leary DDM (2005) Molecular gradients and development of retinotopic maps. Annu Rev Neurosci 28: 327–355. doi:10.1146/annurev.neuro.28.061604.135714

    Article  PubMed  CAS  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 

  • Overton KJ, Arbib MA (1982a) Systems matching and topographic maps: the branch-arrow model (BAM). In: Amari S, Arbib MA (eds) Competition and cooperation in neural nets. Lecture Notes in Biomathematics. Springer, Berlin, Heidelberg, New York. A5:202–225

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

    Article  PubMed  CAS  Google Scholar 

  • Pasquale EB (2005) Eph receptor signalling casts a wide net on cell behaviour. Nat Rev Mol Cell Biol 6(6): 462–475. doi:10.1038/nrm1662

    Article  PubMed  CAS  Google Scholar 

  • Pittman AJ, Law MY, Chien CB (2008) Pathfinding in a large vertebrate axon tract: isotypic interactions guide retinotectal axons at multiple choice points. Development 135(17): 2865–2871. doi:10.1242/dev.025049

    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 

  • Rashid T, Upton AL, Blentic A, Ciossek T, Knöll B, Thompson ID, Drescher U (2005) Opposing gradients of ephrin-As and EphA7 in the superior colliculus are essential for topographic mapping in the mammalian visual system. Neuron 47(1): 57–69. doi:10.1016/j.neuron.2005.05.030

    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. doi:10.1038/nature02957

    Article  PubMed  CAS  Google Scholar 

  • Ruthazer ES, Cline HT (2004) Insights into activity-dependent map formation from the retinotectal system: a middle-of-the-brain perspective. J Neurobiol 59(1): 134–146. doi:10.1002/neu.10344

    Article  PubMed  CAS  Google Scholar 

  • Schmidt JT, Cicerone CM, Easter SS (1978) Expansion of the half retinal projection to the tectum in goldfish: an electrophysiological and anatomical study. J Comp Neurol 177(2): 257–277. doi:10.1002/cne.901770206

    Article  Google Scholar 

  • Scicolone G, Ortalli AL, Carri NG (2009) Key roles of Ephs and ephrins in retinotectal topographic map formation. Brain Res Bull 79(5): 227–247. doi:10.1016/j.brainresbull.2009.03.008

    Article  PubMed  CAS  Google Scholar 

  • Simon DK, O’Leary DD (1992) Development of topographic order in the mammalian retinocollicular projection. J Neurosci 12(4): 1212–1232

    PubMed  CAS  Google Scholar 

  • Simpson HD, Mortimer D, Goodhill GJ (2009) Theoretical models of neural circuit development. Curr Top Dev Biol 87: 1–51

    Article  PubMed  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 

  • Straznicky K, Gaze RM (1971) The growth of the retina in Xenopus laevis: an autoradiographic study. J Embryol Exp Morphol 26(1): 67–79

    PubMed  CAS  Google Scholar 

  • Stuermer CA, Raymond PA (1989) Developing retinotectal projection in larval goldfish. J Comp Neurol 281(4): 630–640. doi:10.1002/cne.902810411

    Article  PubMed  CAS  Google Scholar 

  • Stuermer CA (1988) Trajectories of regenerating retinal axons in the goldfish tectum: II. Exploratory branches and growth cones on axons at early regeneration stages. J Comp Neurol 267(1): 69–91. doi:10.1002/cne.902670106

    Article  PubMed  CAS  Google Scholar 

  • Thivierge JP, Marcus GF (2007) The topographic brain: from neural connectivity to cognition. Trends Neurosci 30(6): 251–259. doi:10.1016/j.tins.2007.04.004

    Article  PubMed  CAS  Google Scholar 

  • 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. doi:10.1007/s10827-006-9575-7

    Article  PubMed  Google Scholar 

  • Udin SB, Fawcett JW (1988) Formation of topographic maps. Annu Rev Neurosci 11: 289–327. doi:10.1146/annurev.ne.11.030188.001445

    Article  PubMed  CAS  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 Biol Sci 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. doi:10.1242/dev.02430

    Article  PubMed  CAS  Google Scholar 

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

    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 

  • 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. doi:10.1002/neu.10341

    Article  PubMed  CAS  Google Scholar 

  • Yoon MG (1976) Progress of topographic regulation of the visual projection in the halved optic tectum of adult goldfish. J Physiol 257(3): 621–643

    PubMed  CAS  Google Scholar 

  • Yoon MG (1973) Retention of the original topographic polarity by the 180 degrees rotated tectal reimplant in young adult goldfish. J Physiol 233(3): 575–588

    PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Queensland Brain Institute, The University of Queensland, Brisbane, QLD, 4072, Australia

    Hugh D. Simpson & Geoffrey J. Goodhill

  2. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia

    Geoffrey J. Goodhill

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  1. Hugh D. Simpson
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  2. Geoffrey J. Goodhill
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Correspondence to Geoffrey J. Goodhill.

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Simpson, H.D., Goodhill, G.J. A simple model can unify a broad range of phenomena in retinotectal map development. Biol Cybern 104, 9–29 (2011). https://doi.org/10.1007/s00422-011-0417-y

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  • DOI: https://doi.org/10.1007/s00422-011-0417-y

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