Experimental evidence for UNC-6 (netrin) axon guidance by stochastic fluctuations of intracellular UNC-40 (DCC) outgrowth activity.

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Abstract

How the direction of axon guidance is determined is not understood. In Caenorhabditis elegans the UNC-40 (DCC) receptor mediates a response to the UNC-6 (netrin) guidance cue that directs HSN axon development. UNC-40 becomes asymmetrically localized within the HSN neuron to the site of axon outgrowth. Here we provide experimental evidence that the direction of guidance can be explained by the stochastic fluctuations of UNC-40 asymmetric outgrowth activity. We find that the UNC-5 (UNC5) receptor and the cytoskeletal binding protein UNC-53 (NAV2) regulate the induction of UNC-40 localization by UNC-6. If UNC-40 localization is induced without UNC-6 by using an unc-53 mutation, the direction of UNC-40 localization undergoes random fluctuations. Random walk models describe the path made by a succession of randomly directed movement. This model was experimentally tested using mutations that affect Wnt/PCP signaling. These mutations inhibit UNC-40 localization in the anterior and posterior directions. As the axon forms in Wnt/PCP mutants, the direction of UNC-40 localization randomly fluctuates; it can localize in either the anterior, posterior, or ventral direction. Consistent with a biased random walk, over time the axon will develop ventrally in response to UNC-6, even though at a discrete time UNC-40 localization and outgrowth can be observed anterior or posterior. Also, axon formation is slower in the mutants than in wild-type animals. This is also consistent with a random walk since this model predicts that the mean square displacement (msd) will increase only linearly with time, whereas the msd increases quadratically with time for straight-line motion.

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Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

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Allen C. Goodman, Peter Tessier (1996)

Neuronal growth cones navigate over long distances along specific pathways to find their correct targets. The mechanisms and molecules that direct this pathfinding are the topics of this review. Growth cones appear to be guided by at least four different mechanisms: contact attraction, chemoattraction, contact repulsion, and chemorepulsion. Evidence is accumulating that these mechanisms act simultaneously and in a coordinated manner to direct pathfinding and that they are mediated by mechanistically and evolutionarily conserved ligand-receptor systems.