A mathematical model explains saturating axon guidance responses to molecular gradients

Correct wiring is crucial for the proper functioning of the nervous system. Molecular gradients provide critical signals to guide growth cones, which are the motile tips of developing axons, to their targets. However, in vitro, growth cones trace highly stochastic trajectories, and exactly how molecular gradients bias their movement is unclear. Here, we introduce a mathematical model based on persistence, bias, and noise to describe this behaviour, constrained directly by measurements of the detailed statistics of growth cone movements in both attractive and repulsive gradients in a microfluidic device. This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values. This work introduces the most accurate predictive model of growth cone trajectories to date, and deepens our understanding of axon guidance events both in vitro and in vivo.

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RHO-1 and the Rho GEF RHGF-1 interact with UNC-6/Netrin signaling to regulate growth cone protrusion and microtubule organization in C. elegans

10.1101/520262 ◽

2019 ◽

Author(s):

Mahekta R. Gujar ◽

Aubrie M. Stricker ◽

Erik A. Lundquist

Keyword(s):

Axon Guidance ◽

Growth Cone ◽

Neural Circuit ◽

Growth Cones ◽

Negative Regulator ◽

Microtubule Organization ◽

C Elegans ◽

Guidance Cue ◽

Rho Gef

AbstractUNC-6/Netrin is a conserved axon guidance cue that directs growth cone migrations in the dorsal-ventral axis of C. elegans and in the vertebrate spinal cord. UNC-6/Netrin is expressed in ventral cells, and growth cones migrate ventrally toward or dorsally away from UNC-6/Netrin. Recent studies of growth cone behavior during outgrowth in vivo in C. elegans have led to a polarity/protrusion model in directed growth cone migration away from UNC-6/Netrin. In this model, UNC-6/Netrin first polarizes the growth cone via the UNC-5 receptor, leading to dorsally biased protrusion and F-actin accumulation. UNC-6/Netrin then regulates protrusion based on this polarity. The receptor UNC-40/DCC drives protrusion dorsally, away from the UNC-6/Netrin source, and the UNC-5 receptor inhibits protrusion ventrally, near the UNC-6/Netrin source, resulting in dorsal migration. UNC-5 inhibits protrusion in part by excluding microtubules from the growth cone, which are pro-protrusive. Here we report that the RHO-1/RhoA GTPase and its activator GEF RHGF-1 inhibit growth cone protrusion and MT accumulation in growth cones, similar to UNC-5. However, growth cone polarity of protrusion and F-actin were unaffected by RHO-1 and RHGF-1. Thus, RHO-1 signaling acts specifically as a negative regulator of protrusion and MT accumulation, and not polarity. Genetic interactions suggest that RHO-1 and RHGF-1 act with UNC-5, as well as with a parallel pathway, to regulate protrusion. The cytoskeletal interacting molecule UNC-33/CRMP was required for RHO-1 activity to inhibit MT accumulation, suggesting that UNC-33/CRMP might act downstream of RHO-1. In sum, these studies describe a new role of RHO-1 and RHGF-1 in regulation of growth cone protrusion by UNC-6/Netrin.Author SummaryNeural circuits are formed by precise connections between axons. During axon formation, the growth cone leads the axon to its proper target in a process called axon guidance. Growth cone outgrowth involves asymmetric protrusion driven by extracellular cues that stimulate and inhibit protrusion. How guidance cues regulate growth cone protrusion in neural circuit formation is incompletely understood. This work shows that the signaling molecule RHO-1 acts downstream of the UNC-6/Netrin guidance cue to inhibit growth cone protrusion in part by excluding microtubules from the growth cone, which are structural elements that drive protrusion.

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A Multiscale Computational Model of Chemotactic Axon Guidance

International Journal of Computational Models and Algorithms in Medicine ◽

10.4018/ijcmam.2012100105 ◽

2012 ◽

Vol 3 (4) ◽

pp. 43-60

Author(s):

Giacomo Aletti ◽

Paola Causin ◽

Giovanni Naldi ◽

Matteo Semplice

Keyword(s):

Mathematical Model ◽

Nervous System ◽

Axon Guidance ◽

Growth Cone ◽

Distal Part ◽

Transmembrane Receptors ◽

Axonal Projections ◽

Long Time ◽

Tight Connection ◽

Cytoskeleton Rearrangement

In the development of the nervous system, the migration of neurons driven by chemotactic cues has been known since a long time to play a key role. In this mechanism, the axonal projections of neurons detect very small differences in extracellular ligand concentration across the tiny section of their distal part, the growth cone. The internal transduction of the signal performed by the growth cone leads to cytoskeleton rearrangement and biased cell motility. A mathematical model of neuron migration provides hints of the nature of this process, which is only partially known to biologists and is characterized by a complex coupling of microscopic and macroscopic phenomena. This chapter focuses on the tight connection between growth cone directional sensing as the result of the information collected by several transmembrane receptors, a microscopic phenomenon, and its motility, a macroscopic outcome. The biophysical hypothesis investigated is the role played by the biased re-localization of ligand-bound receptors on the membrane, actively convected by growing microtubules. The results of the numerical simulations quantify the positive feedback exerted by the receptor redistribution, assessing its importance in the neural guidance mechanism.

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RNA-based mechanisms underlying axon guidance

The Journal of Cell Biology ◽

10.1083/jcb.201305139 ◽

2013 ◽

Vol 202 (7) ◽

pp. 991-999 ◽

Cited By ~ 25

Author(s):

Toshiaki Shigeoka ◽

Bo Lu ◽

Christine E. Holt

Keyword(s):

Axon Guidance ◽

Translational Control ◽

Growth Cones ◽

Receptor Activation ◽

Neural Pathways ◽

Neuronal Circuitry ◽

Guidance Cues ◽

Spatiotemporal Control

Axon guidance plays a key role in establishing neuronal circuitry. The motile tips of growing axons, the growth cones, navigate by responding directionally to guidance cues that pattern the embryonic neural pathways via receptor-mediated signaling. Evidence in vitro in the last decade supports the notion that RNA-based mechanisms contribute to cue-directed steering during axon guidance. Different cues trigger translation of distinct subsets of mRNAs and localized translation provides precise spatiotemporal control over the growth cone proteome in response to localized receptor activation. Recent evidence has now demonstrated a role for localized translational control in axon guidance decisions in vivo.

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Gradients and Growth Cone Guidance of Grasshopper Neurons

Journal of Histochemistry & Cytochemistry ◽

10.1177/002215540305100406 ◽

2003 ◽

Vol 51 (4) ◽

pp. 445-454 ◽

Cited By ~ 10

Author(s):

Arthur T. Legg ◽

Timothy P. O'Connor

Keyword(s):

Nervous System ◽

Long Range ◽

Growth Cone ◽

Growth Cones ◽

Path Finding ◽

Guidance Cues ◽

Cone Function ◽

The Absolute ◽

Growth Cone Guidance

The generation of a functional nervous system is dependent on precise path-finding of axons during development. This pathfinding is directed by the distribution of local and long-range guidance cues, the latter of which are believed to be distributed in gradients. Gradients of guidance cues have been associated with growth cone function for over a hundred years. However, little is known about the mechanisms used by growth cones to respond to these gradients, in part owing to the lack of identifiable gradients in vivo. In the developing grasshopper limb, two gradients of the semaphorin Sema-2a are necessary for correct neuronal pathfinding in vivo. The gradients are found in regions where growth cones make critical steering decisions. Observations of different growth cone behaviors associated with these gradients have provided some insights into how growth cones respond to them. Growth cones appear to respond more faithfully to changes in concentration, rather than absolute levels, of Sema-2a expression, whereas the absolute levels may regulate growth cone size.

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Automated profiling of growth cone heterogeneity defines relations between morphology and motility

The Journal of Cell Biology ◽

10.1083/jcb.201711023 ◽

2018 ◽

Vol 218 (1) ◽

pp. 350-379 ◽

Cited By ~ 2

Author(s):

Maria M. Bagonis ◽

Ludovico Fusco ◽

Olivier Pertz ◽

Gaudenz Danuser

Keyword(s):

Growth Cone ◽

Rho Gtpase ◽

Time Lapse ◽

Growth Cones ◽

Cellular Structures ◽

Unperturbed System ◽

Neurite Length ◽

Manual Curation

Growth cones are complex, motile structures at the tip of an outgrowing neurite. They often exhibit a high density of filopodia (thin actin bundles), which complicates the unbiased quantification of their morphologies by software. Contemporary image processing methods require extensive tuning of segmentation parameters, require significant manual curation, and are often not sufficiently adaptable to capture morphology changes associated with switches in regulatory signals. To overcome these limitations, we developed Growth Cone Analyzer (GCA). GCA is designed to quantify growth cone morphodynamics from time-lapse sequences imaged both in vitro and in vivo, but is sufficiently generic that it may be applied to nonneuronal cellular structures. We demonstrate the adaptability of GCA through the analysis of growth cone morphological variation and its relation to motility in both an unperturbed system and in the context of modified Rho GTPase signaling. We find that perturbations inducing similar changes in neurite length exhibit underappreciated phenotypic nuance at the scale of the growth cone.

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A scanning electron microscope study of the development of a peripheral sensory neurite network

Development ◽

10.1242/dev.69.1.237 ◽

1982 ◽

Vol 69 (1) ◽

pp. 237-250

Author(s):

Alan Roberts ◽

J. S. H. Taylor

Keyword(s):

Electron Microscope ◽

Scanning Electron Microscope ◽

Basal Lamina ◽

Growth Cone ◽

Growth Cones ◽

Sensory Innervation ◽

Scanning Electron Microscope Study ◽

Scanning Electron

The formation of the sensory neurite plexus on the basal lamina of trunk skin in Xenopus embryos has been examined using the scanning electron microscope. It is formed by Rohon-Beard and extramedullary neurons which provide the first sensory innervation of the skin. By observing the distribution of growth cones on the inside surface of the skin of embryos at different ages, the development of the plexus has been followed and related to the development of sensitivity to sensory stimulation. The general features of the plexus are illustrated using a photomontage taken at × 1100. Measurements on neurites from this, and of growth cone orientations demonstrate a general ventral growth pattern with some small regional variations. Interactions of neurites within the plexus are examined. Neurites meeting at shallow angles tend to fasciculate, whilethose meeting at close to 90° tend to cross each other. Angles of incidence and separation of neurites show few angles less than 30°, which suggests that active adjustments occur after a growth cone meets or leaves another neurite. The observations allow comparison of behaviour of growing neurites in vivo and in vitro. Our evidence suggests that adhesion between growth cones and neurites is stronger than that between growth cones and the basal lamina of the skin.

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Frazzled promotes growth cone attachment at the source of a Netrin gradient in the Drosophila visual system

eLife ◽

10.7554/elife.20762 ◽

2016 ◽

Vol 5 ◽

Cited By ~ 42

Author(s):

Orkun Akin ◽

S Lawrence Zipursky

Keyword(s):

Colorectal Cancer ◽

Visual System ◽

Axon Guidance ◽

Growth Cone ◽

Short Range ◽

Growth Cones ◽

Live Imaging ◽

Deleted In Colorectal Cancer ◽

Binding Partner

Axon guidance is proposed to act through a combination of long- and short-range attractive and repulsive cues. The ligand-receptor pair, Netrin (Net) and Frazzled (Fra) (DCC, Deleted in Colorectal Cancer, in vertebrates), is recognized as the prototypical effector of chemoattraction, with roles in both long- and short-range guidance. In the Drosophila visual system, R8 photoreceptor growth cones were shown to require Net-Fra to reach their target, the peak of a Net gradient. Using live imaging, we show, however, that R8 growth cones reach and recognize their target without Net, Fra, or Trim9, a conserved binding partner of Fra, but do not remain attached to it. Thus, despite the graded ligand distribution along the guidance path, Net-Fra is not used for chemoattraction. Based on findings in other systems, we propose that adhesion to substrate-bound Net underlies both long- and short-range Net-Fra-dependent guidance in vivo, thereby eroding the distinction between them.

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Mechanical tension produced by nerve cells in tissue culture

Journal of Cell Science ◽

10.1242/jcs.37.1.391 ◽

1979 ◽

Vol 37 (1) ◽

pp. 391-410 ◽

Cited By ~ 1

Author(s):

D. Bray

Keyword(s):

Tissue Culture ◽

Sensory Neurons ◽

Growth Cone ◽

High Probability ◽

Growth Cones ◽

Cultured Neurons ◽

Mechanical Tension ◽

Standard Methods

Evidence is presented that (a) the growth cone of cultured neurons can exert mechanical tension, and (b) that the direction of advance of the growth cone is determined by the tension existing between it and the rest of the cell. (a) The evidence that growth cones can pull comes from a vectorial analysis of the outlines of individually isolated sensory neurons. The angles formed in these outgrowths are very close to those of tension-generated networks anchored at their free ends and these values are restored shortly after an experimental displacement. The relative mechanical tension on each segment of an outgrowth can be calculated by standard methods and is found to decrease at each branch point. It appears to be correlated with the diameter of the fibre so that thicker fibres maintain more tension than thinner ones. (b) The influence of tension on the direction of advance of the growth cone is shown by 2 kinds of experient. If a growing neurite is pulled to one side with a microelectrode then the direction of its advance is changed immediately according to the new stress. If the mechanical tension on the growth cone of a neurite is released by amputation or displacement the growth cone is found to have a high probability of branching shortly afterwards. The ability of the growth cone to exert tension is discussed in relation to evidence that microspikes have contractile properties and in terms of the distribution of microfilaments within the neurite. It is suggested that the exertion of tension by a growth cone could serve to guide the neurite along paths of high adhesivity both in vitro and in vivo.

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UNC-6/Netrin and its Receptors UNC-5 and UNC-40/DCC Control Growth Cone Polarity, Microtubule Accumulation, and Protrusion

10.1101/294215 ◽

2018 ◽

Author(s):

Mahekta R. Gujar ◽

Lakshmi Sundararajan ◽

Aubrie Stricker ◽

Erik A. Lundquist

Keyword(s):

Axon Guidance ◽

Growth Cone ◽

Growth Cones ◽

Microtubule Organization ◽

C Elegans ◽

Control Growth ◽

Receptor Interactions ◽

Independent Mechanism ◽

Actin Localization

AbstractMany axon guidance ligands and their receptors have been identified, but it is still unclear how these ligand-receptor interactions regulate events in the growth cone, such as protrusion and cytoskeletal arrangement, during directed outgrowth in vivo. In this work, we dissect the multiple and complex effects of UNC-6/Netrin on the growth cone. Previous studies showed that in C. elegans, the UNC-6/Netrin receptor UNC-5 regulates growth cone polarity, as evidenced by loss of asymmetric dorsal F-actin localization and protrusion in unc-5 mutants. UNC-5 and another UNC-6/Netrin receptor UNC-40/DCC also regulate the extent of protrusion, with UNC-40/DCC driving protrusion and UNC-5 inhibiting protrusion. In this work we analyze the roles of UNC-6/Netrin, UNC-40/DCC, and UNC-5 in coordinating growth cone F-actin localization, microtubule organization, and protrusion that results in directed outgrowth away from UNC-6/Netrin. We find that a previously-described pathway involving the UNC-73/Trio Rac GEF and UNC-33/CRMP that acts downstream of UNC-5, regulates growth cone dorsal asymmetric F-actin accumulation and protrusion. unc-5 and unc-33 mutants also display excess EBP-2::GFP puncta, suggesting that MT + end accumulation is important in growth cone polarity and/or protrusion. unc-73 Rac GEF mutants did not display excess EBP-2::GFP puncta despite larger and more protrusive growth cones, indicating a MT-independent mechanism to polarize the growth cone and to inhibit protrusion, possibly via actin. Finally, we show that UNC-6/Netrin and UNC-40/DCC are required for excess protrusion in unc-5 mutants, but not for loss of F-actin asymmetry or MT + end accumulation, indicating that UNC-6/Netrin and UNC-40/DCC are required for protrusion downstream of F-actin asymmetry and MT + end entry. Our data suggest a model in which UNC-6/Netrin polarizes the growth cone via UNC-5, and then regulates a balance of pro- and anti-protrusive forces driven by UNC-40 and UNC-5, respectively, that result in directed protrusion and outgrowth.

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