Odell G M
J Mechanochem Cell Motil. 1977 Mar;4(1):1-13.
A continuum theory is proposed for the chemically controlled cytoplasmic streaming observed in pseudopodium extension in Chaos Carolinensis. Amoeboid cytoplasm is assumed to consist of submicroscopic contractile fibers bathed by viscous fluid. The fiber constituent models the actin-like and myosin-like contractile machinery known to be present in Chaos Carolinensis cytoplasm. A "trigger chemical", produced at the pseudopodium tip, moves by diffusion in, and convection by, the viscous fluid, and causes the contractile fibers to contract in their own length. The contracting fibers, attached at the tip and running continuously back toward the amoeba cell body, pull the fluid constituent of the cytoplasm forward and ultimately crosslink to form the outer gel tube of the advancing pseudopodium. That is, streaming cytoplasm is modeled as a two constituent porous medium, with the fluid constituent free to flow through a porous matrix of oriented (contractile fiber) rods, while the matrix of rods itself moves as the fibers contract, with fiber contraction controlled by a trigger chemical born by the fluid constituent. According to this theory, in the region behind the advancing pseudopodium tip, the contractile fiber rods move forward toward the tip faster than the fluid constituent. The hydrostatic pressure in the fluid therefore increases from the cell body toward the tip (Just the opposite from flow driven by pressure excess generated in the cell body). The excess of hydrostatic pressure above ambient built up at the tip provides the force to roll out the advancing pseudopodium tip. The cell membrane plays no active mechanical role. The mathematical transcription makes a precise theory of R. D. Allen's "frontal (or fountain zone) contraction model". The general system of coupled, non-linear, partial differential equations is solved for its simplest non-trivial special case, that of a steady-state motion, as seen from a coordinate system attached to the advancing tip. Solutions exist, and, for each distinct forward speed (which is left to the discretion of the amoeba) the solution is unique. The theory predicts both upper and lower bounds for possible pseudopodium lengths.
针对在卡罗琳裸变形虫伪足伸展过程中观察到的化学控制的细胞质流动，提出了一种连续介质理论。假定变形虫细胞质由被粘性流体包围的亚微观收缩纤维组成。纤维成分模拟了已知存在于卡罗琳裸变形虫细胞质中的肌动蛋白样和肌球蛋白样收缩机制。在伪足尖端产生的一种“触发化学物质”，通过在粘性流体中的扩散和对流移动，并使收缩纤维在其自身长度上收缩。收缩纤维附着在尖端并持续向变形虫细胞体向后延伸，将细胞质的流体成分向前拉动，并最终交联形成前进伪足的外部凝胶管。也就是说，流动的细胞质被建模为一种双组分多孔介质，流体成分可自由流过由定向（收缩纤维）杆组成的多孔基质，而杆的基质本身随着纤维收缩而移动，纤维收缩由流体成分携带的触发化学物质控制。根据该理论，在前进的伪足尖端后面的区域，收缩纤维杆向尖端的移动速度比流体成分快。因此，流体中的静水压力从细胞体向尖端增加（与细胞体中产生的压力过剩驱动的流动相反）。在尖端积累的高于环境压力的静水压力过剩提供了展开前进伪足尖端的力。细胞膜不发挥主动的机械作用。数学推导为R.D.艾伦的“前端（或喷泉区）收缩模型”建立了精确的理论。针对其最简单的非平凡特殊情况，即从附着在前进尖端的坐标系中观察到的稳态运动，求解了耦合的非线性偏微分方程组的一般系统。解是存在的，并且对于每个不同的前进速度（由变形虫自行决定），解是唯一的。该理论预测了可能的伪足长度的上限和下限。
