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An Exploration of Dynamics of the Moving Mechanism of the Growth Cone
School of Science, Donghua University, 1882 West Yan-An Road, Shanghai 200051, China
Institute for Computational Science and Engineering, Ocean University of China, Shandong 266003, China
Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, Wakamatsu-Ku, Kitakyushu 808-0196, Japan
Shanghai Telecommunication Corporation, Shanghai 200092, China
Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC V6T 1Z1, Canada
* Author to whom correspondence should be addressed.
Received: 1 January 2003; Published: 31 January 2003
Abstract: 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.
Keywords: Actin-myosin system; the growth cone; random noise and dissipation; stochastic elastic collision; the joint probability density; the non-stationary FPK equation
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Wang, R.; Hayashi, H.; Zhang, Z.; Duan, Y.-B. An Exploration of Dynamics of the Moving Mechanism of the Growth Cone. Molecules 2003, 8, 127-138.
Wang R, Hayashi H, Zhang Z, Duan Y-B. An Exploration of Dynamics of the Moving Mechanism of the Growth Cone. Molecules. 2003; 8(1):127-138.
Wang, Rubin; Hayashi, Hatsuo; Zhang, Zhikang; Duan, Yun-Bo. 2003. "An Exploration of Dynamics of the Moving Mechanism of the Growth Cone." Molecules 8, no. 1: 127-138.