Geometric Asymmetry Induces Upper Limit of Mitotic Spindle Size

Relaxation and Noise-Driven Oscillations in a Model of Mitotic Spindle Dynamics

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics.

Regulation of organelle size and organization during development

During early embryogenesis, as cells divide in the developing embryo, the size of intracellular organelles generally decreases to scale with the decrease in overall cell size. Organelle size scaling is thought to be important to establish and maintain proper cellular function, and defective scaling may lead to impaired development and disease. However, how the cell regulates organelle size and organization are largely unanswered questions. In this review, we summarize the process of size scaling at both the cell and organelle levels and discuss recently discovered mechanisms that regulate this process during early embryogenesis. In addition, we describe how some recently developed techniques and Xenopus as an animal model can be used to investigate the underlying mechanisms of size regulation and to uncover the significance of proper organelle size scaling and organization.

Modeling reveals cortical dynein-dependent fluctuations in bipolar spindle length

Proper formation and maintenance of the mitotic spindle is required for faithful cell division. Although much work has been done to understand the roles of the key molecular components of the mitotic spindle, identifying the consequences of force perturbations in the spindle remains a challenge. We develop a computational framework accounting for the minimal force requirements of mitotic progression. To reflect early spindle formation, we model microtubule dynamics and interactions with major force-generating motors, excluding chromosome interactions that dominate later in mitosis. We directly integrate our experimental data to define and validate the model. We then use simulations to analyze individual force components over time and their relationship to spindle dynamics, making it distinct from previously published models. We show through both model predictions and biological manipulation that rather than achieving and maintaining a constant bipolar spindle length, fluctuations in pole-to-pole distance occur that coincide with microtubule binding and force generation by cortical dynein. Our model further predicts that high dynein activity is required for spindle bipolarity when kinesin-14 (HSET) activity is also high. To the best of our knowledge, our results provide novel insight into the role of cortical dynein in the regulation of spindle bipolarity.

Spindle scaling mechanisms

The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.

Centering and Shifting of Centrosomes in Cells

Centrosomes have a nonrandom localization in the cells: either they occupy the centroid of the zone free of the actomyosin cortex or they are shifted to the edge of the cell, where their presence is justified from a functional point of view, for example, to organize additional microtubules or primary cilia. This review discusses centrosome placement options in cultured and in situ cells. It has been proven that the central arrangement of centrosomes is due mainly to the pulling microtubules forces developed by dynein located on the cell cortex and intracellular vesicles. The pushing forces from dynamic microtubules and actomyosin also contribute, although the molecular mechanisms of their action have not yet been elucidated. Centrosomal displacement is caused by external cues, depending on signaling, and is drawn through the redistribution of dynein, the asymmetrization of microtubules through the capture of their plus ends, and the redistribution of actomyosin, which, in turn, is associated with basal-apical cell polarization.

Organelle size scaling over embryonic development

Cell division without growth results in progressive cell size reductions during early embryonic development. How do the sizes of intracellular structures and organelles scale with cell size and what are the functional implications of such scaling relationships? Model organisms, in particular Caenorhabditis elegans worms, Drosophila melanogaster flies, Xenopus laevis frogs, and Mus musculus mice, have provided insights into developmental size scaling of the nucleus, mitotic spindle, and chromosomes. Nuclear size is regulated by nucleocytoplasmic transport, nuclear envelope proteins, and the cytoskeleton. Regulators of microtubule dynamics and chromatin compaction modulate spindle and mitotic chromosome size scaling, respectively. Developmental scaling relationships for membrane-bound organelles, like the endoplasmic reticulum, Golgi, mitochondria, and lysosomes, have been less studied, although new imaging approaches promise to rectify this deficiency. While models that invoke limiting components and dynamic regulation of assembly and disassembly can account for some size scaling relationships in early embryos, it will be exciting to investigate the contribution of newer concepts in cell biology such as phase separation and interorganellar contacts. With a growing understanding of the underlying mechanisms of organelle size scaling, future studies promise to uncover the significance of proper scaling for cell function and embryonic development, as well as how aberrant scaling contributes to disease. This article is categorized under: Establishment of Spatial and Temporal Patterns > Regulation of Size, Proportion, and Timing Early Embryonic Development > Fertilization to Gastrulation Comparative Development and Evolution > Model Systems.

Strong static magnetic field delayed the early development of zebrafish

One of the major topics in magnetobiology is the biological effects of strong static magnetic field (SMF) on living organisms. However, there has been a paucity of the comprehensive study of the long-term effects of strong SMF on an animal's development. Here, we explored this question with zebrafish, an excellent model organism for developmental study. In our research, zebrafish eggs, just after fertilization, were exposed to a 9.0 T SMF for 24 h, the critical period of post-fertilization development from cleavage to segmentation. The effects of strong SMF exposure on the following developmental progress of zebrafish were studied until 6 days post-fertilization (dpf). Results showed that 9.0 T SMF exposure did not influence the survival or the general developmental scenario of zebrafish embryos. However, it slowed down the developmental pace of the whole animal, and the late developers would catch up with their control peers after the SMF was removed. We proposed a mechanical model and deduced that the development delaying effect was caused by the interference of SMF in microtubule and spindle positioning during mitosis, especially in early cleavages. Our research data provide insights into how strong SMF influences the developing organisms through basic physical interactions with intracellular macromolecules.

Cell shape and intercellular adhesion regulate mitotic spindle orientation

Cell division orientation plays an essential role in tissue morphogenesis and cell fate decision. Recent studies showed that either cell shape or adhesion geometry can regulate the orientation of mitotic spindles and thereby the cell division orientation. However, how they together regulate the spindle orientation remains largely unclear. In this work, we use a general computational model to investigate the competitive mechanism of determining the spindle orientation between cell shape and intercellular adhesion in epithelial cells. We find the spindle orientation is dominated by the intercellular adhesion when the cell shape anisotropy is small, but dominated by the cell shape when the shape anisotropy is large. A strong adhesion and moderate adhesive size can ensure the planar division of epithelial cells with large apico-basal elongation. We also find the spindle orientation could be perpendicular to the adhesive region when only one side of the cell is adhered to an E-cadherin-coated matrix. But after the cell is compressed, the spindle orientation is governed by the cell shape and the spindle will be parallel to the adhesive region when the cell shape anisotropy is large. Finally, we demonstrate the competition between cell shape and tricellular junctions can also effectively regulate the spindle orientation.

In vivo mitotic spindle scaling can be modulated by changing the levels of a single protein: the microtubule polymerase XMAP215

In many organisms, early embryonic development is characterized by a series of reductive cell divisions that result in rapid increases in cell number and concomitant decreases in cell size. Intracellular organelles, such as the nucleus and mitotic spindle, also become progressively smaller during this developmental window, but the molecular and mechanistic underpinnings of these scaling relationships are not fully understood. For the mitotic spindle, changes in cytoplasmic volume are sufficient to account for size scaling during early development in certain organisms. This observation is consistent with models that evoke a limiting component, whereby the smaller absolute number of spindle components in smaller cells limits spindle size. Here we investigate the role of a candidate factor for developmental spindle scaling, the microtubule polymerase XMAP215. Microinjection of additional XMAP215 protein into Xenopus laevis embryos was sufficient to induce the assembly of larger spindles during developmental stages 6.5, 7, and 8, whereas addition of a polymerase-incompetent XMAP215 mutant resulted in a downward shift in the in vivo spindle scaling curve. In sum, these results indicate that even small cells are able to produce larger spindles if microtubule growth rates are increased and suggest that structural components are not limiting.

Regulating positioning and orientation of mitotic spindles via cell size and shape

Proper location of the mitotic spindle is critical for chromosome segregation and the selection of the cell division plane. However, how mitotic spindles sense cell size and shape to regulate their own position and orientation is still largely unclear. To investigate this question systematically, we used a general model by considering chromosomes, microtubule dynamics, and forces of various molecular motors. Our results show that in cells of various sizes and shapes, spindles can always be centered and oriented along the long axis robustly in the absence of other specified mechanisms. We found that the characteristic time of positioning and orientation processes increases with cell size. Spindles sense the cell size mainly by the cortical force in small cells and by the cytoplasmic force in large cells. In addition to the cell size, the cell shape mainly influences the orientation process. We found that more slender cells have a faster orientation process, and the final orientation is not necessarily along the longest axis but is determined by the radial profile and the symmetry of the cell shape. Finally, our model also reproduces the separation and repositioning of the spindle poles during the anaphase. Therefore, our work provides a general tool for studying the mitotic spindle across the whole mitotic phase.

Eml1 loss impairs apical progenitor spindle length and soma shape in the developing cerebral cortex

The ventricular zone (VZ) of the developing cerebral cortex is a pseudostratified epithelium that contains progenitors undergoing precisely regulated divisions at its most apical side, the ventricular lining (VL). Mitotic perturbations can contribute to pathological mechanisms leading to cortical malformations. The HeCo mutant mouse exhibits subcortical band heterotopia (SBH), likely to be initiated by progenitor delamination from the VZ early during corticogenesis. The causes for this are however, currently unknown. Eml1, a microtubule (MT)-associated protein of the EMAP family, is impaired in these mice. We first show that MT dynamics are perturbed in mutant progenitor cells in vitro. These may influence interphase and mitotic MT mechanisms and indeed, centrosome and primary cilia were altered and spindles were found to be abnormally long in HeCo progenitors. Consistently, MT and spindle length regulators were identified in EML1 pulldowns from embryonic brain extracts. Finally, we found that mitotic cell shape is also abnormal in the mutant VZ. These previously unidentified VZ characteristics suggest altered cell constraints which may contribute to cell delamination.