Fig. 4

Mathematical model for neurite outgrowth regulated by LOVTRAP-Rho-kinase. a The model neurite was modeled based on one-dimensional reaction-diffusion of LOVTRAP-Rho-kinase, which was activated in the cell body by illumination, diffused along the neurite, and was then inactivated or degraded. C _s (t), C _i (x,t) and R _i indicate the concentrations of LOVTRAP-Rho-kinase in the cell body at time t, along the neurite at x μm from the neck of neurite i at time t, and in the growth cone, respectively. b The steady state distribution of LOVTRAP-Rho-kinase along the long axon (red line) or the short minor neurites (blue line) during photoactivation. Equation (4) was plotted. c The concentration of LOVTRAP-Rho-kinase at the tip of the neurite depended on its length, which was mathematically described by Equation (1). d Migration of the model growth cone driven by constitutive growth force, Rho-kinase-regulated growth force and retraction force. e The simulation dynamics of neurites of various lengths in response to photoactivation of LOVTRAP-Rho-kinase. Red and blue lines represent typical behaviors of the long axon and short minor neurites, respectively. f Model prediction of the relationship between initial neurite length and LOVTRAP-Rho-kinase-dependent neurite retraction. The black line was plotted by varying F _i , which controls initial neurite length. g, h The neurite retraction caused by a 1-h photoactivation of LOVTRAP-Rho-kinase g and LOVTRAP-Control h was plotted against the initial length of each axon (red dots) and minor neurite (blue dots). The black lines indicate the relationship generated by a simulation in which the parameters (F _o , K/C _o , h, c) were adjusted for the best fit to the red and blue dots. The parameter values used are listed in Methods