A Theoretical Model of Axon Guidance by the Robo Code

After crossing the midline, different populations of commissural axons in Drosophila target specific longitudinal pathways at different distances from the midline. It has recently been shown that this choice of lateral position is governed by the particular combination of Robo receptors expressed by these axons, presumably in response to a gradient of Slit released by the midline. Here we propose a simple theoretical model of this combinatorial coding scheme. The principal results of the model are that purely quantitative rather than qualitative differences between the different Robo receptors are sufficient to account for the effects observed following removal or ectopic expression of specific Robo receptors, and that the steepness of the Slit gradient in vivo must exceed a certain minimum for the results observed experimentally to be consistent.

[1]  Julie H. Simpson,et al.  Short-Range and Long-Range Guidance by Slit and Its Robo Receptors Robo and Robo2 Play Distinct Roles in Midline Guidance , 2000, Neuron.

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

[3]  Geoffrey J. Goodhill,et al.  Mathematical guidance for axons , 1998, Trends in Neurosciences.

[4]  Y. Rao,et al.  Local inhibition guides the trajectory of early longitudinal tracts in the developing chick brain , 2004, Mechanisms of Development.

[5]  S. Pfaff,et al.  Transcriptional codes and the control of neuronal identity. , 2002, Annual review of neuroscience.

[6]  B. Dickson,et al.  Crossing the Midline Roles and Regulation of Robo Receptors , 2000, Neuron.

[7]  Julie H. Simpson,et al.  Short-Range and Long-Range Guidance by Slit and Its Robo Receptors A Combinatorial Code of Robo Receptors Controls Lateral Position , 2000, Cell.

[8]  G. Barton.  The Mathematics of Diffusion 2nd edn , 1975 .

[9]  T. Jessell,et al.  The netrins define a family of axon outgrowth-promoting proteins homologous to C. elegans UNC-6 , 1994, Cell.

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

[11]  C. Goodman,et al.  Slit Proteins Bind Robo Receptors and Have an Evolutionarily Conserved Role in Repulsive Axon Guidance , 1999, Cell.

[12]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[13]  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.

[14]  James R. Schott,et al.  Principles of Multivariate Analysis: A User's Perspective , 2002 .

[15]  Mu-ming Poo,et al.  cAMP-induced switching in turning direction of nerve growth cones , 1997, Nature.

[16]  Geoffrey J. Goodhill,et al.  Retinotectal maps: molecules, models and misplaced data , 1999, Trends in Neurosciences.

[17]  Y. Hiromi,et al.  The Drosophila Netrin receptor Frazzled guides axons by controlling Netrin distribution , 2000, Nature.

[18]  J. Westwater,et al.  The Mathematics of Diffusion. , 1957 .

[19]  Timothy E. Kennedy,et al.  Netrins are diffusible chemotropic factors for commissural axons in the embryonic spinal cord , 1994, Cell.

[20]  Jennifer L. Doyle,et al.  Genetic Analysis of Netrin Genes in Drosophila: Netrins Guide CNS Commissural Axons and Peripheral Motor Axons , 1996, Neuron.

[21]  L. Rosenhead.  Conduction of Heat in Solids , 1947, Nature.

[22]  C. Goodman,et al.  Slit Is the Midline Repellent for the Robo Receptor in Drosophila , 1999, Cell.

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

[24]  B. Dickson,et al.  Selecting a Longitudinal Pathway Robo Receptors Specify the Lateral Position of Axons in the Drosophila CNS , 2000, Cell.

[25]  Julie H. Simpson,et al.  Ectopic Expression in the Giant Fiber System ofDrosophila Reveals Distinct Roles for Roundabout (Robo), Robo2, and Robo3 in Dendritic Guidance and Synaptic Connectivity , 2002, The Journal of Neuroscience.

[26]  B. Mueller,et al.  Growth cone guidance: first steps towards a deeper understanding. , 1999, Annual review of neuroscience.

[27]  H. Gutfreund,et al.  Kinetics for the life sciences , 1995 .

[28]  L. Buck,et al.  Combinatorial Receptor Codes for Odors , 1999, Cell.

[29]  G. Goodhill.  Diffusion in Axon Guidance , 1997, The European journal of neuroscience.

[30]  Z. Kaprielian,et al.  Axon guidance at the midline of the developing CNS , 2000, The Anatomical record.

[31]  M. Poo,et al.  The cell biology of neuronal navigation , 2001, Nature Cell Biology.

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

[33]  M. Nieto.  Molecular Biology Meeting Review of Axon Guidance , 1996 .