A model for Dictyostelium motion.
(A) The blue line is hand drawn to guide the eye and represents θ, a one-dimensional random walk. The black line ϕ, is an enlarged view of the data in box 3 of Fig. 6. In our model, ϕ is the net effect of θ and colored noise centered on θ. The stochastic differential equations used to describe the behavior of ϕ and θ are explained in detail in the text. (B) θ is the angle assumed to be fixed by a cell's intrinsic polarity, possibly a vector directed from the center of nucleus (light blue) to the position of the centrosome . Black arrow, pseudopod extensions and retractions lead to stochastic oscillations. New pseudopods bifurcate from old, and they swing back and forth about the internal vector. (C) A cartoon describing directional control.