Brownian diffusion is the chaotic and irregular movement of a particle immersed in a fluid, caused by its collisions with the surrounding molecules of much smaller size. The mathematical model of this random path is called Wiener process, and consists of a real-valued centred time-homogeneous Gaussian process that starts at zero and has independent increments.
Published in Chapter:
A Multiscale Computational Model of Chemotactic Axon Guidance
Giacomo Aletti (University of Milan, Italy), Paola Causin (University of Milan, Italy), Giovanni Naldi (University of Milan, Italy), and Matteo Semplice (University of Insubria, Italy)
Copyright: © 2011
|Pages: 18
DOI: 10.4018/978-1-60960-491-2.ch028
Abstract
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.