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 (). The dendrite branchlet is 20

*μ*m long and 2

*μ*m 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

*μ*m 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

*μ*m 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-14

*x*^{6} + 2E-11

*x*^{5} − 4E-09

*x*^{4} + 3E-07

*x*^{3} + 6E-06

*x*^{2} − 0.0003

*x* + 0.1618 is superimposed on the simulation results. (

*d*) IP3 concentration at ∼3.52

*μ*m from the stimulated spine in the 1D model that is used to set a time-varying boundary condition for the 3D geometry (3.52

*μ*m 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-13

*x*^{6} − 2E-10

*x*^{5} + 4E-08

*x*^{4} − 5E-06

*x*^{3} + 0.0003

*x*^{2} − 0.0047

*x* + 0.1744 is superimposed on the simulation results.

## PubMed Commons