Growth Cone Pathfinding: a competition between deterministic and stochastic events

BACKGROUND: Growth cone migratory patterns show evidence of both deterministic and stochastic search modes. RESULTS: We quantitatively examine how these two different migration modes affect the growth cone's pathfinding response, by simulating growth cone contact with a repulsive cue and measuring the resultant turn angle. We develop a dimensionless number, we call the determinism ratio Ψ, to define the ratio of deterministic to stochastic influences driving the growth cone's migration in response to an external guidance cue. We find that the growth cone can exhibit three distinct types of turning behaviors depending on the magnitude of Ψ. CONCLUSIONS: We conclude, within the context of these in silico studies, that only when deterministic and stochastic migration factors are in balance (i.e. Ψ ~ 1) can the growth cone respond constructively to guidance cues

The turn angle φ is plotted (a) as a function of the determinism ratio Ψ, and (b) as a function of the contact angle θ

<p><b>Copyright information:</b></p><p>Taken from "Growth Cone Pathfinding: a competition between deterministic and stochastic events"</p><p>BMC Neuroscience 2004;5():22-22.</p><p>Published online 8 Jul 2004</p><p>PMCID:PMC499546.</p><p>Copyright © 2004 Maskery et al; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.</p> As demonstrated in both (a) and (b), when τ >1 s, φ is always ~0°. Only at τ~10 s is guided migration possible through modulation of cue geometry and strength

The determinism ratio Ψ is a dimensionless number calculated from θ, δ, and τ

<p><b>Copyright information:</b></p><p>Taken from "Growth Cone Pathfinding: a competition between deterministic and stochastic events"</p><p>BMC Neuroscience 2004;5():22-22.</p><p>Published online 8 Jul 2004</p><p>PMCID:PMC499546.</p><p>Copyright © 2004 Maskery et al; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.</p> The turn angle φ is plotted as a function of Ψ. hree states emerge when the turn angle φ is plotted as a function of the determinism ratio Ψ. At φ = -180° random migration dominates. The growth cone always collapses. The second state is a transition region where deterministic and stochastic motions are balanced. This region occurs over a narrow region where random migration and deterministic migration are comparable. At φ = 0° deterministic migration dominates. Growth cone migration is unaffected by size or placement of the constraint region