Andreucci D, Bisegna P, Caruso G, Hamm H E, DiBenedetto E
Dipartimento di Metodi e Modelli Matematici, Università di Roma La Sapienza, 00161 Rome, Italy.
Biophys J. 2003 Sep;85(3):1358-76. doi: 10.1016/S0006-3495(03)74570-6.
A model describing the role of transversal and longitudinal diffusion of cGMP and Ca(2+) in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP and Ca(2+) in the inter-disc spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 microm, consistent with experimental data. This approach represents a tool to analyze point-wise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.
建立了一个描述环磷酸鸟苷（cGMP）和钙离子（Ca(2+)）的横向和纵向扩散在脊椎动物视杆外段信号传导中作用的模型。利用表面-体积反应的新概念以及均匀化和集中容量的数学理论，证明了cGMP和Ca(2+)在盘间空间中的扩散可简化为在单个视杆横截面上发生的单参数扩散过程族；而外壳中的扩散可简化为圆柱面上的扩散。此外，前者的外部通量作为后者的源项，减轻了对充分搅拌的胞质溶胶的假设。通过施加“总体”假设，可以从该模型中恢复先前假设视杆外段胞质溶胶充分搅拌（因此不包含空间信息）的视觉转导模型。该模型表明，在单个视紫红质激活后，cGMP变化是局部的，并且呈现纵向和横向分量。因此，膜电流也高度局部化。预测单个光子响应沿外段纵轴的空间传播为3-5微米，与实验数据一致。这种方法代表了一种分析逐点信号动力学的工具，无需通过全局米氏动力学对整个细胞进行平均。
