Modeling of spindle positioning and hypothesis of the function of ring-like F-actin structure.
(A) The overview of a mitotic cell from three dimensions. X-axis links two spindle poles when the spindle is in its equilibrium position, and Z-axis is vertical to the substrate and passes through the midpoint of spindle poles, and Y-axis is simultaneously vertical to X-axis and Z-axis. Different regions are colored for F-actin (red), microtubule (green), chromosomes (blue), cortex and medium (black). (B) The geometrical hypothesis of cell. A mitotic HeLa cell is supposed to be an ellipsoid with its height H and radius R. Then, the geometry can be described with a formula, and the point on the surface can be positioned with an alterable vector D and two parameters θ, φ. (C) The schematic diagram of spindle rotation in two sections, X-Y and Z-X. The geometrical center of spindle is supposed to be translated from the geometrical center of cell, and the coordinate of two spindle poles can be expressed with A, the distance from spindle pole to equate plate. The rotation in X-Y and Z-X sections can be described with the parameters, Θ, Φ. (D) The hypothesis of oscillation. The microtubule-motor complex is simplified as an oscillator, and the oscillation follows Hooke's Law of Elasticity and is influenced by the obstruction from cytoplasm. Here, D-c represents the vector from spindle pole to cell cortex, which can be decomposed into a regular vector D and the position of one spindle pole. (E) The dynamic transition between effective and ineffective connections or binding state. and were supposed to be two rate constant for this transition. We also supposed that only the oscillators with its |D| in the interval [D1, D2] and a positive momentum make effective connections. Then the number of effective or ineffective connections can be expressed as displayed in the figure.
