Axon guidance is of primary importance in the formation
of the nervous system. Understanding it represents a question of enormous
complexity at the forefront of modern biology. We would like to study the
molecular mechanisms of axon guidance in the presence graded spatial distributions
of non-diffusible substrate-bounded molecules. We will use a neurite outgrowth
promoting molecule (L1) and a neurite outgrowth inhibiting molecule (RAGS)
as graded substrates. The effect of substrate gradients on axon guidance
will be assayed by monitoring growth cone motility by video timelapse microscopy
and quantitative morphometry. To obtain a quantitative understanding of
the effect of haptotaxis on axon guidance, We will construct a mathematical
model to describe the growth cone motility in the presence of substrate
gradients. The model is based on the Langevin equation for Brownian motion
and incorporates essential features of growth cone motility and haptotaxis.
We will compare the theoretically predicted mean square displacement of
the centroid of the growth cone, growth cone shape, and filopodial motility
with that of the experimentally measured values for neurons on uniform
and graded substrates. We will also analyze data obtained by others in
the lab to address potential molecular components that contribute to the
terms in the equation, including haptotactic responsiveness, intracellular
signaling, and cytoskeletal dynamics. It is these interactions which induce
cytoplasmic changes that ultimately causes the growth cone turning and
thus axonal guidance. By refining our mathematical model and defining the
terms of the equation with respect to molecular components of the growth
cone, we hope to contribute to a theoretical understanding of axon guidance. |
