An Exploration of Dynamics of the Moving Mechanism of the Growth Cone

A stochastic, nonlinear dynamic model is proposed to explain the growth cone at the tip of a cell process, such as a growing axon or dendrite of a neuron. The model explains the outward motion of the tip as an extension of the cytoskeleton, using the actin-myosin system as a molecular motor. The kinetic energy is supplied by heat from ATP hydrolysis in the form of random motion of water molecules embedding the actin-myosin. The mechanical structure is provided by the F-actin macromolecules forming a spiral filament. The myosin heads form a stochastic distribution of small spheres. They are attached by elastic springs to the spiral rods of the myosin filaments. Under thermal agitation the system sustains oscillation, which is directed by the interaction between the myosin heads and the actin filament. As the energy of oscillation is dissipated, the actin filament is moved toward the center of the growth cone. The joint probability density of movement of the actin filament is obtained by solving a non-stationary version of the FPK equation. By incorporating a probability distribution of actin filaments provided by the geometry of the tip, the directed motion of the tip is explained.