Absence of furrowing activity following regional cortical tension reduction in sand dollar blastomere and fertilized egg fragment surfaces

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Cytokinesis mechanics and mechanosensing

Cytokinesis shape change occurs through the interfacing of three modules, cell mechanics, myosin II-mediated contractile stress generation and sensing, and a control system of regulatory proteins, which together ensure flexibility and robustness. This integrated system then defines the stereotypical shape changes of successful cytokinesis, which occurs under a diversity of mechanical contexts and environmental conditions.

The stress and strain of cytokinesis

The ultimate goal of all signaling pathways in cytokinesis is to control the mechanical separation of the mother cell into two daughter cells. Because of the intrinsic mechanical nature of cytokinesis, it is essential to understand fully how cell shapes and the material properties of the cell are generated, how these shapes and material properties create force, and how motor proteins such as myosin-II modify the system to achieve successful cytokinesis. In this review (which is part of the Cytokinesis series), we discuss the relevant physical properties of cells, how these properties are measured and the basic models that are used to understand cell mechanics. Finally, we present our current understanding of how cytokinesis mechanics work.

Site selection for the cleavage furrow at cytokinesis

The question of how the site for division of the cytoplasm is determined at the end of mitosis has been studied for over a century, and it remains an active, controversial and fascinating problem in cell biology. This problem draws on the use of several model cell types, with the goal of understanding and identifying how the cell cycle regulates signals between the mitotic apparatus and the cell cortex. Studies in different cell types and using a vast array of techniques reveal different answers: these might reflect differences in experimental approaches, multiple and redundant mechanisms and, importantly, diversity in biology. In this article (which is part of the Cytokinesis series), we present a summary and critique of the major models for the roles of the mitotic apparatus microtubules in stimulating furrow formation at cytokinesis.

Why does a cleavage plane develop parallel to the spindle axis in conical sand dollar eggs? A key question for clarifying the mechanism of contractile ring positioning

Three types of models have been proposed about how the mitotic apparatus determines the position of the cleavage furrow in animal cells. In the first and second types, the contractile ring appears in a cortical region that least and most astral microtubules reach, respectively. The third type is that the spindle midzone positions the contractile ring. In the previous study, a new model was proposed through analyses of cytokinesis in sand dollar and sea urchin eggs. Gradients of the surface density of microtubule plus ends are assumed to drive membrane proteins whose accumulation causes the formation of contractile-ring microfilaments. In the present study, the validity of each model is examined by simulating the furrow formation in conical sand dollar eggs with the mitotic apparatus oriented perpendicular to the cone axis. The new model predicts that unilateral furrows with cleavage planes roughly parallel to the spindle axis appear between the mitotic apparatus and the vertex besides the normally positioned furrow. The predictions are consistent with the observations by Rappaport & Rappaport (1994, Dev. Biol.164, 258-266). The other three types of models do not predict the formation of the ectopic furrows. Furthermore, it is pointed out that only the new model has the ability to explain the geometrical relationship between the mitotic apparatus and the contractile ring under various experimental conditions. These results strongly suggest the real existence of the membrane proteins postulated in the model.

Analysis of cortical flow models in vivo

Cortical flow, the directed movement of cortical F-actin and cortical organelles, is a basic cellular motility process. Microtubules are thought to somehow direct cortical flow, but whether they do so by stimulating or inhibiting contraction of the cortical actin cytoskeleton is the subject of debate. Treatment of Xenopus oocytes with phorbol 12-myristate 13-acetate (PMA) triggers cortical flow toward the animal pole of the oocyte; this flow is suppressed by microtubules. To determine how this suppression occurs and whether it can control the direction of cortical flow, oocytes were subjected to localized manipulation of either the contractile stimulus (PMA) or microtubules. Localized PMA application resulted in redirection of cortical flow toward the site of application, as judged by movement of cortical pigment granules, cortical F-actin, and cortical myosin-2A. Such redirected flow was accelerated by microtubule depolymerization, showing that the suppression of cortical flow by microtubules is independent of the direction of flow. Direct observation of cortical F-actin by time-lapse confocal analysis in combination with photobleaching showed that cortical flow is driven by contraction of the cortical F-actin network and that microtubules suppress this contraction. The oocyte germinal vesicle serves as a microtubule organizing center in Xenopus oocytes; experimental displacement of the germinal vesicle toward the animal pole resulted in localized flow away from the animal pole. The results show that 1) cortical flow is directed toward areas of localized contraction of the cortical F-actin cytoskeleton; 2) microtubules suppress cortical flow by inhibiting contraction of the cortical F-actin cytoskeleton; and 3) localized, microtubule-dependent suppression of actomyosin-based contraction can control the direction of cortical flow. We discuss these findings in light of current models of cortical flow.