Dufort P A, Lumsden C J
Membrane Biology Group, University of Toronto, Canada.
Cell Motil Cytoskeleton. 1993;25(1):87-104. doi: 10.1002/cm.970250110.
We describe a cellular automaton model of the actin cytoskeleton. The model incorporates spatial and temporal behavior at the macromolecular level and is relevant to the viscous nonequilibrium conditions suspected to occur in vivo. The model includes cation and nucleotide binding to actin monomers, actin nucleation and polymerization into filaments, cross-linking with alpha-actinin, monomer sequestration with profilin, filament severing, capping and nucleation with gelsolin, binding of profilin and gelsolin to membrane-bound phosphatidylinositide biphosphate (PIP2), and regulation of cross-linking and severing by changing calcium levels. We derive 1) equations for the molecular translation and rotation probabilities required for the cellular automaton simulation in terms of molecular size, shape, cytoplasmic viscosity, and temperature; and 2) equations for the binding probabilities of adjacent molecules in terms of experimentally determined reaction rate constants. The model accurately captures the known characteristics of actin polymerization and subsequent ATP hydrolysis under different cation and nucleotide conditions. An examination of gelation and sol-gel transitions resulting from calcium regulation of alpha-actinin and gelsolin predicts an inhomogeneous distribution of bound alpha-actinin and F-actin. The double-bound alpha-actinin (both ends bound to F-actin) is tightly bunched, while single-bound alpha-actinin is moderately bunched and unbound alpha-actinin is homogeneously distributed. The spatial organization of the alpha-actinin is quantified using estimates of fractal dimension. The simulation results also suggest that actin/alpha-actinin gels may shift from an isotropic to an amorphous phase after shortening of filaments. The gel-sol transition of the model shows excellent agreement with the present theory of polymer gels. The close correspondence of the model's predictions with previous experimental and theoretical results suggests that the model may be pertinent to better understanding the spatial and temporal properties of complex cytoskeletal processes.
我们描述了一种肌动蛋白细胞骨架的元胞自动机模型。该模型纳入了大分子水平的空间和时间行为，与怀疑在体内发生的粘性非平衡条件相关。该模型包括阳离子和核苷酸与肌动蛋白单体的结合、肌动蛋白的成核和聚合成丝、与α - 辅肌动蛋白的交联、与胸腺素β4的单体隔离、丝的切断、凝溶胶蛋白的封端和成核、胸腺素β4和凝溶胶蛋白与膜结合的磷脂酰肌醇二磷酸（PIP2）的结合，以及通过改变钙水平对交联和切断的调节。我们推导了1）根据分子大小、形状、细胞质粘度和温度，用于元胞自动机模拟所需的分子平移和旋转概率的方程；以及2）根据实验确定的反应速率常数，用于相邻分子结合概率的方程。该模型准确地捕捉了在不同阳离子和核苷酸条件下肌动蛋白聚合以及随后的ATP水解的已知特征。对由α - 辅肌动蛋白和凝溶胶蛋白的钙调节导致的凝胶化和溶胶 - 凝胶转变的研究预测了结合的α - 辅肌动蛋白和F - 肌动蛋白的不均匀分布。双结合的α - 辅肌动蛋白（两端与F - 肌动蛋白结合）紧密聚集，而单结合的α - 辅肌动蛋白适度聚集，未结合的α - 辅肌动蛋白均匀分布。使用分形维数估计对α - 辅肌动蛋白的空间组织进行了量化。模拟结果还表明，肌动蛋白/α - 辅肌动蛋白凝胶在丝缩短后可能从各向同性相转变为无定形相。该模型的凝胶 - 溶胶转变与当前的聚合物凝胶理论显示出极好的一致性。该模型的预测与先前的实验和理论结果的密切对应表明，该模型可能有助于更好地理解复杂细胞骨架过程的空间和时间特性。
