  Neuronal growth cones are the most sensitive amongst eukaryotic cells in
responding to directional chemical cues. Although a dynamic microtubule
cytoskeleton has been shown to be essential for growth cone turning, the
precise nature of coupling of the spatial cue with microtubule polarization is
less understood. Here we present a computational model of microtubule
polarization in a turning neuronal growth cone (GC). We explore the limits of
directional cues in modifying the spatial polarization of microtubules by
testing the role of microtubule dynamics, gradients of regulators and
retrograde forces along filopodia. We analyze the steady state and transition
behavior of microtubules on being presented with a directional stimulus. The
model makes novel predictions about the minimal angular spread of the chemical
signal at the growth cone and the fastest polarization times. A regulatory
reaction-diffusion network based on the cyclic
phosphorylation-dephosphorylation of a regulator predicts that the receptor
signal magnitude can generate the maximal polarization of microtubules and not
feedback loops or amplifications in the network. Using both the
phenomenological and network models we have demonstrated some of the physical
limits within which the MT polarization system works in turning neuron.
