Axonal Growth and Targeting

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.

[1]  J. Cowan,et al.  Specificity and plasticity of retinotectal connections: a computational model , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[2]  Guo-Hua Li,et al.  Computer model of growth cone behavior and neuronal morphogenesis , 1995 .

[3]  R. M. Gaze,et al.  The arrow model: retinotectal specificity and map formation in the goldfish visual system , 1976, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[4]  Michael A. Arbib,et al.  The Extended Branch-Arrow Model of the formation of retino-tectal connections , 2004, Biological Cybernetics.

[5]  Bruce P. Graham,et al.  Compartmental models of growing neurites , 2001, Neurocomputing.

[6]  P. Gordon-Weeks Microtubules and growth cone function. , 2004, Journal of neurobiology.

[7]  W. Bialek,et al.  Physical limits to biochemical signaling. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Denis Wirtz,et al.  Mechanics and dynamics of actin-driven thin membrane protrusions. , 2006, Biophysical journal.

[9]  D. Wilkinson,et al.  Diverse roles of eph receptors and ephrins in the regulation of cell migration and tissue assembly. , 2004, Developmental cell.

[10]  Paul A Yates,et al.  Topographic Mapping from the Retina to the Midbrain Is Controlled by Relative but Not Absolute Levels of EphA Receptor Signaling , 2000, Cell.

[11]  G H Li,et al.  Neurite branching pattern formation: modeling and computer simulation. , 1992, Journal of theoretical biology.

[12]  H Honda,et al.  Topographic mapping in the retinotectal projection by means of complementary ligand and receptor gradients: a computer simulation study. , 1998, Journal of theoretical biology.

[13]  Geoffrey J. Goodhill,et al.  Adaptation is not required to explain the long-term response of axons to molecular gradients , 2005, Development.

[14]  Troy Shinbrot,et al.  Growth Cone Pathfinding: a competition between deterministic and stochastic events , 2004, BMC Neuroscience.

[15]  H M Buettner,et al.  A model of neurite extension across regions of nonpermissive substrate: simulations based on experimental measurement of growth cone motility and filopodial dynamics. , 1994, Developmental biology.

[16]  H. El-Samad,et al.  Bound attractant at the leading vs. the trailing edge determines chemotactic prowess , 2007, Proceedings of the National Academy of Sciences.

[17]  S B Udin,et al.  Formation of topographic maps. , 1988, Annual review of neuroscience.

[18]  Bruce P. Graham,et al.  Dynamics of outgrowth in a continuum model of neurite elongation , 2006, Journal of Computational Neuroscience.

[19]  Dmitry Tsigankov,et al.  Sperry versus Hebb: Topographic mapping in Isl2/EphA3 mutant mice , 2008, BMC Neuroscience.

[20]  David Holcman,et al.  A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing , 2010, PloS one.

[21]  Helen M. Buettner Analysis of cell‐target encounter by random filopodial projections , 1996 .

[22]  G. Goodhill,et al.  A new chemotaxis assay shows the extreme sensitivity of axons to molecular gradients , 2004, Nature Neuroscience.

[23]  Shin Ishii,et al.  A molecular model for axon guidance based on cross talk between rho GTPases. , 2005, Biophysical journal.

[24]  N R Smalheiser,et al.  The possible role of "sibling neurite bias" in the coordination of neurite extension, branching, and survival. , 1984, Journal of neurobiology.

[25]  Arjen Van Ooyen,et al.  Modeling neural development , 2003 .

[26]  David G. Wilkinson,et al.  Multiple roles of eph receptors and ephrins in neural development , 2001, Nature Reviews Neuroscience.

[27]  J. Molloy Muscle contraction: actin filaments enter the fray. , 2005, Biophysical journal.

[28]  Jun Xu,et al.  The development of retinotectal maps: a review of models based on molecular gradients. , 2005, Network.

[29]  D J Willshaw,et al.  Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology. , 2000, Journal of theoretical biology.

[30]  Geoffrey J. Goodhill,et al.  Predicting Axonal Response to Molecular Gradients with a Computational Model of Filopodial Dynamics , 2004, Neural Computation.

[31]  Troy Shinbrot,et al.  Deterministic and stochastic elements of axonal guidance. , 2005, Annual review of biomedical engineering.

[32]  Neuronal Growth Cones , 2000 .

[33]  D. Lauffenburger,et al.  Receptors: Models for Binding, Trafficking, and Signaling , 1993 .

[34]  D. Willshaw,et al.  Short term interactions between microtubules and actin filaments underlie long term behaviour in neuronal growth cones , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[35]  Bruce Graham,et al.  Biologically plausible models of neurite outgrowth. , 2005, Progress in brain research.

[36]  Laurent Tettoni,et al.  Biophysical model of axonal pathfinding , 2001, Neurocomputing.

[37]  D. O'Leary,et al.  Molecular gradients and development of retinotopic maps. , 2005, Annual review of neuroscience.

[38]  C. Goodman,et al.  The Molecular Biology of Axon Guidance , 1996, Science.

[39]  Alex Mogilner,et al.  Mathematics of Cell Motility: Have We Got Its Number? , 2022 .

[40]  Jaap van Pelt,et al.  Neuritic growth rate described by modeling microtubule dynamics , 1994 .

[41]  D H Perkel,et al.  Competitive and positional cues in the patterning of nerve connections. , 1990, Journal of neurobiology.

[42]  Arjen van Ooyen,et al.  Mathematical modelling and numerical simulation of the morphological development of neurons , 2006, BMC Neuroscience.

[43]  R. Sperry CHEMOAFFINITY IN THE ORDERLY GROWTH OF NERVE FIBER PATTERNS AND CONNECTIONS. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[44]  Geoffrey J. Goodhill,et al.  A simple model can unify a broad range of phenomena in retinotectal map development , 2011, Biological Cybernetics.

[45]  M. Poo,et al.  Calcium signaling in neuronal motility. , 2007, Annual review of cell and developmental biology.

[46]  P. Dayan,et al.  A Bayesian model predicts the response of axons to molecular gradients , 2009, Proceedings of the National Academy of Sciences.

[47]  E. Giniger How do Rho family GTPases direct axon growth and guidance? A proposal relating signaling pathways to growth cone mechanics. , 2002, Differentiation; research in biological diversity.

[48]  G. Goodhill,et al.  Axon guidance by growth-rate modulation , 2010, Proceedings of the National Academy of Sciences.

[49]  D. Willshaw,et al.  On a role for competition in the formation of patterned neural connexions , 1975, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[50]  Hisao Honda,et al.  Competition between Retinal Ganglion Axons for Targets under the Servomechanism Model Explains Abnormal Retinocollicular Projection of Eph Receptor-Overexpressing or Ephrin-Lacking Mice , 2003, The Journal of Neuroscience.

[51]  Cornelius Weber,et al.  DEVELOPMENT AND REGENERATION OF THE RETINOTECTAL MAP IN GOLDFISH : A COMPUTATIONAL STUDY , 1997 .

[52]  D. Bentley,et al.  Pioneer growth cone steering decisions mediated by single filopodial contacts in situ , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[53]  Ajay Gopinathan,et al.  Dynamics of membranes driven by actin polymerization. , 2005, Biophysical journal.

[54]  Peter Dayan,et al.  Bayes-Optimal Chemotaxis , 2011, Neural Computation.

[55]  H. Buettner,et al.  Stochastic dynamics of the nerve growth cone and its microtubules during neurite outgrowth , 2000, Biotechnology and bioengineering.

[56]  Greg Lemke,et al.  A relative signalling model for the formation of a topographic neural map , 2004, Nature.

[57]  A. Mogilner,et al.  The physics of filopodial protrusion. , 2005, Biophysical journal.

[58]  P. Forscher,et al.  Growth cone advance is inversely proportional to retrograde F-actin flow , 1995, Neuron.

[59]  Paola Causin,et al.  Autocatalytic Loop, Amplification and Diffusion: A Mathematical and Computational Model of Cell Polarization in Neural Chemotaxis , 2009, PLoS Comput. Biol..

[60]  Paul A Yates,et al.  Computational modeling of retinotopic map development to define contributions of EphA-ephrinA gradients, axon-axon interactions, and patterned activity. , 2004, Journal of neurobiology.

[61]  Dylan T Burnette,et al.  Myosin II functions in actin-bundle turnover in neuronal growth cones , 2006, Nature Cell Biology.

[62]  B. Dickson Molecular Mechanisms of Axon Guidance , 2002, Science.

[63]  Maxime Dahan,et al.  Asymmetric redistribution of GABA receptors during GABA gradient sensing by nerve growth cones analyzed by single quantum dot imaging , 2007, Proceedings of the National Academy of Sciences.

[64]  N. Wingreen,et al.  Accuracy of direct gradient sensing by single cells , 2008, Proceedings of the National Academy of Sciences.

[65]  Alexei A. Koulakov,et al.  A unifying model for activity-dependent and activity-independent mechanisms predicts complete structure of topographic maps in ephrin-A deficient mice , 2005, Journal of Computational Neuroscience.

[66]  P. Forscher,et al.  Substrate-cytoskeletal coupling as a mechanism for the regulation of growth cone motility and guidance. , 2000, Journal of neurobiology.

[67]  Alfred Gierer,et al.  Directional cues for growing axons forming the retinotectal projection , 1987 .

[68]  Timo Betz,et al.  Stochastic actin polymerization and steady retrograde flow determine growth cone advancement. , 2009, Biophysical journal.

[69]  P. Dayan,et al.  Optimizing chemotaxis by measuring unbound–bound transitions , 2010 .

[70]  M. Ueda,et al.  Stochastic signal processing and transduction in chemotactic response of eukaryotic cells. , 2007, Biophysical journal.

[71]  Alexei A Koulakov,et al.  A stochastic model for retinocollicular map development , 2003, BMC Neuroscience.

[72]  Arjen van Ooyen,et al.  Competition in the development of nerve connections: a review of models , 2001 .

[73]  L. A. Lowery,et al.  The trip of the tip: understanding the growth cone machinery , 2009, Nature Reviews Molecular Cell Biology.

[74]  I. Nikolaidis Web Caching and Content Delivery [Book Review] , 2002, IEEE Network.

[75]  Geoffrey J Goodhill,et al.  Theoretical models of neural circuit development. , 2009, Current topics in developmental biology.

[76]  D J Willshaw,et al.  A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. , 1979, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[77]  G. Goodhill,et al.  Theoretical analysis of gradient detection by growth cones. , 1999, Journal of neurobiology.

[78]  David Willshaw Analysis of mouse EphA knockins and knockouts suggests that retinal axons programme target cells to form ordered retinotopic maps , 2006, Development.

[79]  H. Berg,et al.  Physics of chemoreception. , 1977, Biophysical journal.

[80]  M. Kirschner,et al.  Dynamic instability of microtubule growth , 1984, Nature.

[81]  T. McLaughlin,et al.  Topographic-Specific Axon Branching Controlled by Ephrin-As Is the Critical Event in Retinotectal Map Development , 2001, The Journal of Neuroscience.

[82]  John G Flanagan,et al.  Topographically Specific Effects of ELF-1 on Retinal Axon Guidance In Vitro and Retinal Axon Mapping In Vivo , 1996, Cell.

[83]  G. Goodhill,et al.  Growth cone chemotaxis , 2008, Trends in Neurosciences.

[84]  J. Käs,et al.  Neuronal growth: a bistable stochastic process. , 2006, Physical review letters.

[85]  R. Buxbaum,et al.  Axonal outgrowth of cultured neurons is not limited by growth cone competition. , 1998, Journal of cell science.

[86]  A Gierer,et al.  Model for the retino-tectal projection , 1983, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[87]  Stephen J. Eglen,et al.  A Multi-Component Model of the Developing Retinocollicular Pathway Incorporating Axonal and Synaptic Growth , 2009, PLoS Comput. Biol..

[88]  Bruce P. Graham,et al.  Continuum model for tubulin-driven neurite elongation , 2004, Neurocomputing.