FIGURE 3.

3D Purkinje dendrite geometries and the derivation of boundary conditions. (a) Constructed geometry with spines that have uniformly spherical heads and narrow, wide, and medium-sized necks; created using values for spine parameters that fall within ranges obtained from Harris and Stevens (29). The dendrite branchlet is 20 μm long and 2 μm in diameter. Spine 1 is used for most of the simulations. Spines 2 and 3 and the patch of dendrite (*) are used in the PIP2 lateral diffusion studies. (b) Experimentally derived geometry with spines of various shapes and sizes that have narrow, wide, and medium-sized necks; reconstructed in Virtual Cell from a 3D stack of electron microscope images courtesy of Maryanne Martone, Mark Ellisman, and Masako Terada of the National Center for Microscopy and Imaging Research (San Diego, CA). Spine 1 is used in most of the simulations with the experimentally derived geometry. Spines 3 and 6 are used in the PIP2 lateral diffusion studies; and spines 2, 4, and 5 are also stimulated in the stimulated PIP2 synthesis model. (c) IP3 concentration time course at 13.95 μm from the stimulated spine in the 1D model that is used to set a time-varying boundary condition for the constructed 3D geometry (13.95 μm represents the edge of the geometry relative to the stimulated spine at the center of the geometry). The central spine is excited 12 times in succession beginning at t = 0.1 s. Each excitation follows the last by = 0.012 s. A fitted curve with equation y = −3E-14x⁶ + 2E-11x⁵ − 4E-09x⁴ + 3E-07x³ + 6E-06x² − 0.0003x + 0.1618 is superimposed on the simulation results. (d) IP3 concentration at ∼3.52 μm from the stimulated spine in the 1D model that is used to set a time-varying boundary condition for the 3D geometry (3.52 μm represents the edge of the geometry relative to the stimulated spine at the center of the geometry). The central spine is excited 12 times in succession beginning at t = 0.1 s. Each excitation follows the last by = 0.012 s. A fitted curve with equation y = 2E-13x⁶ − 2E-10x⁵ + 4E-08x⁴ − 5E-06x³ + 0.0003x² − 0.0047x + 0.1744 is superimposed on the simulation results.