Spatial-temporal model for silencing of the mitotic spindle assembly checkpoint

An autonomous mathematical model for the mammalian cell cycle

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APC^Cdh1, SCF^βTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

Spindle Architectural Features Must Be Considered Along With Cell Size to Explain the Timing of Mitotic Checkpoint Silencing

Mitosis proceeds through a defined series of events that is largely conserved, but the amount of time needed for their completion can vary in different cells and organisms. In many systems, mitotic duration depends on the time required to satisfy and silence the spindle assembly checkpoint (SAC), also known as the mitotic checkpoint. Because SAC silencing involves trafficking SAC molecules among kinetochores, spindle, and cytoplasm, the size and geometry of the spindle relative to cell volume are expected to affect mitotic duration by influencing the timing of SAC silencing. However, the relationship between SAC silencing, cell size, and spindle dimensions is unclear. To investigate this issue, we used four DLD-1 tetraploid (4N) clones characterized by small or large nuclear and cell size. We found that the small 4N clones had longer mitotic durations than the parental DLD-1 cells and that this delay was due to differences in their metaphase duration. Leveraging a previous mathematical model for spatiotemporal regulation of SAC silencing, we show that the difference in metaphase duration, i.e., SAC silencing time, can be explained by the distinct spindle microtubule densities and sizes of the cell, spindle, and spindle poles in the 4N clones. Lastly, we demonstrate that manipulating spindle geometry can alter mitotic and metaphase duration, consistent with a model prediction. Our results suggest that spindle size does not always scale with cell size in mammalian cells and cell size is not sufficient to explain the differences in metaphase duration. Only when a number of spindle architectural features are considered along with cell size can the kinetics of SAC silencing, and hence mitotic duration, in the different clones be explained.

Implications of alternative routes to APC/C inhibition by the mitotic checkpoint complex

The mitotic checkpoint (also called spindle assembly checkpoint) is a signaling pathway that ensures faithful chromosome segregation. Mitotic checkpoint proteins inhibit the anaphase-promoting complex (APC/C) and its activator Cdc20 to prevent precocious anaphase. Checkpoint signaling leads to a complex of APC/C, Cdc20, and checkpoint proteins, in which the APC/C is inactive. In principle, this final product of the mitotic checkpoint can be obtained via different pathways, whose relevance still needs to be fully ascertained experimentally. Here, we use mathematical models to compare the implications on checkpoint response of the possible pathways leading to APC/C inhibition. We identify a previously unrecognized funneling effect for Cdc20, which favors Cdc20 incorporation into the inhibitory complex and therefore promotes checkpoint activity. Furthermore, we find that the presence or absence of one specific assembly reaction determines whether the checkpoint remains functional at elevated levels of Cdc20, which can occur in cancer cells. Our results reveal the inhibitory logics behind checkpoint activity, predict checkpoint efficiency in perturbed situations, and could inform molecular strategies to treat malignancies that exhibit Cdc20 overexpression.

Cell division is a fundamental event in the life of cells. It requires that a mother cell gives rise to two daughters which carry the same genetic material of their mother. Thus, during each cell cycle the genetic material needs to be replicated, compacted into chromosomes and redistributed to the two daughter cells. Any mistake in chromosome segregation would attribute the wrong number of chromosomes to the progeny. Hence, the process of chromosome segregation is closely watched by a surveillance mechanism known as the mitotic checkpoint. The molecular players of the checkpoint pathway are well known: we know both the input (ie, the species to be inhibited and their inhibitors), and the output (ie, the inhibited species). However, we do not exactly know the path that leads from the former to the latter. In this manuscript, we use a mathematical approach to explore the properties of plausible mitotic checkpoint networks. We find that seemingly similar circuits show very different behaviors for high levels of the protein targeted by the mitotic checkpoint, Cdc20. Interestingly, this protein is often overexpressed in cancer cells. For physiological levels of Cdc20, instead, all the models we have analyzed are capable to mount an efficient response. We find that this is due to a series of consecutive protein-protein binding reactions that funnel Cdc20 towards its inhibited state. We call this the funneling effect. Our analysis helps understanding the inhibitory logics underlying the checkpoint, and proposes new concepts that could be applied to other inhibitory pathways.

Spindle Size Scaling Contributes to Robust Silencing of Mitotic Spindle Assembly Checkpoint

Chromosome segregation during mitosis hinges on proper assembly of the microtubule spindle that establishes bipolar attachment to each chromosome. Experiments demonstrate allometry of mitotic spindles and a universal scaling relationship between spindle size and cell size across metazoans, which indicates a conserved principle of spindle assembly at play during evolution. However, the nature of this principle is currently unknown. Researchers have focused on deriving the mechanistic underpinning of the size scaling from the mechanical aspects of the spindle assembly process. In this work we take a different standpoint and ask: What is the size scaling for? We address this question from the functional perspectives of spindle assembly checkpoint (SAC). SAC is the critical surveillance mechanism that prevents premature chromosome segregation in the presence of unattached or misattached chromosomes. The SAC signal gets silenced after and only after the last chromosome-spindle attachment in mitosis. We previously established a model that explains the robustness of SAC silencing based on spindle-mediated spatiotemporal regulation of SAC proteins. Here, we refine the previous model, and find that robust and timely SAC silencing entails proper size scaling of mitotic spindle. This finding provides, to our knowledge, a novel, function-oriented angle toward understanding the observed spindle allometry, and the universal scaling relationship between spindle size and cell size in metazoans. In a broad sense, the functional requirement of robust SAC silencing could have helped shape the spindle assembly mechanism in evolution.

A Dynamical Model for Activating and Silencing the Mitotic Checkpoint

The spindle assembly checkpoint (SAC) is an evolutionarily conserved mechanism, exclusively sensitive to the states of kinetochores attached to microtubules. During metaphase, the anaphase-promoting complex/cyclosome (APC/C) is inhibited by the SAC but it rapidly switches to its active form following proper attachment of the final spindle. It had been thought that APC/C activity is an all-or-nothing response, but recent findings have demonstrated that it switches steadily. In this study, we develop a detailed mathematical model that considers all 92 human kinetochores and all major proteins involved in SAC activation and silencing. We perform deterministic and spatially-stochastic simulations and find that certain spatial properties do not play significant roles. Furthermore, we show that our model is consistent with in-vitro mutation experiments of crucial proteins as well as the recently-suggested rheostat switch behavior, measured by Securin or CyclinB concentration. Considering an autocatalytic feedback loop leads to an all-or-nothing toggle switch in the underlying core components, while the output signal of the SAC still behaves like a rheostat switch. The results of this study support the hypothesis that the SAC signal varies with increasing number of attached kinetochores, even though it might still contain toggle switches in some of its components.

A Mathematical Framework for Kinetochore-Driven Activation Feedback in the Mitotic Checkpoint

Proliferating cells properly divide into their daughter cells through a process that is mediated by kinetochores, protein-complexes that assemble at the centromere of each sister chromatid. Each kinetochore has to establish a tight bipolar attachment to the spindle apparatus before sister chromatid separation is initiated. The spindle assembly checkpoint (SAC) links the biophysical attachment status of the kinetochores to mitotic progression and ensures that even a single misaligned kinetochore keeps the checkpoint active. The mechanism by which this is achieved is still elusive. Current computational models of the human SAC disregard important biochemical properties by omitting any kind of feedback loop, proper kinetochore signals, and other spatial properties such as the stability of the system and diffusion effects. To allow for more realistic in silico study of the dynamics of the SAC model, a minimal mathematical framework for SAC activation and silencing is introduced. A nonlinear ordinary differential equation model successfully reproduces bifurcation signaling switches with attachment of all 92 kinetochores and activation of APC/C by kinetochore-driven feedback. A partial differential equation model and mathematical linear stability analyses indicate the influence of diffusion and system stability. The conclusion is that quantitative models of the human SAC should account for the positive feedback on APC/C activation driven by the kinetochores which is essential for SAC silencing. Experimental diffusion coefficients for MCC subcomplexes are found to be insufficient for rapid APC/C inhibition. The presented analysis allows for systems-level understanding of mitotic control, and the minimal new model can function as a basis for developing further quantitative-integrative models of the cell division cycle.

The mitotic checkpoint complex (MCC): looking back and forth after 15 years

The mitotic checkpoint is a specialized signal transduction pathway that contributes to the fidelity of chromosome segregation. The signaling of the checkpoint originates from defective kinetochore-microtubule interactions and leads to formation of the mitotic checkpoint complex (MCC), a highly potent inhibitor of the Anaphase Promoting Complex/Cyclosome (APC/C)—the E3 ubiquitin ligase essential for anaphase onset. Many important questions concerning the MCC and its interaction with APC/C have been intensively investigated and debated in the past 15 years, such as the exact composition of the MCC, how it is assembled during a cell cycle, how it inhibits APC/C, and how the MCC is disassembled to allow APC/C activation. These efforts have culminated in recently reported structure models for human MCC:APC/C supra-complexes at near-atomic resolution that shed light on multiple aspects of the mitotic checkpoint mechanisms. However, confusing statements regarding the MCC are still scattered in the literature, making it difficult for students and scientists alike to obtain a clear picture of MCC composition, structure, function and dynamics. This review will comb through some of the most popular concepts or misconceptions about the MCC, discuss our current understandings, present a synthesized model on regulation of CDC20 ubiquitination, and suggest a few future endeavors and cautions for next phase of MCC research.

Erroneous Silencing of the Mitotic Checkpoint by Aberrant Spindle Pole-Kinetochore Coordination

To segregate chromosomes during cell division, microtubules that form the bipolar spindle attach to and pull on paired chromosome kinetochores. The spindle assembly checkpoint (SAC) is activated at unattached and misattached kinetochores to prevent further mitotic progression. The SAC is silenced after all the kinetochores establish proper and stable attachment to the spindle. Robust timing of SAC silencing after the last kinetochore-spindle attachment herein dictates the fidelity of chromosome segregation. Chromosome missegregation is rare in typical somatic cell mitosis, but frequent in cancer cell mitosis and in meiosis I of mammalian oocytes. In the latter cases, SAC is normally activated in response to disruptions of kinetochore-spindle attachments, suggesting that frequent chromosome missegregation ensues from faulty SAC silencing. In-depth understanding of how SAC silencing malfunctions in these cases is yet missing, but is believed to hold promise for treatment of cancer and prevention of human miscarriage and birth defects. We previously established a spatiotemporal model that, to the best of our knowledge, explained the robustness of SAC silencing in normal mitosis for the first time. In this article, we take advantage of the whole-cell perspective of the spatiotemporal model to identify possible causes of chromosome missegregation out of the distinct features of spindle assembly exhibited by cancer cells and mammalian oocytes. The model results explain why multipolar spindle could inhibit SAC silencing and spindle pole clustering could promote it-albeit accompanied by more kinetochore attachment errors. The model also eliminates geometric factors as the cause for nonrobust SAC silencing in oocyte meiosis, and instead, suggests atypical kinetochore-spindle attachment in meiosis as a potential culprit. Overall, the model shows that abnormal spindle-pole formation and its aberrant coordination with atypical kinetochore-spindle attachments could compromise the robustness of SAC silencing. Our model highlights systems-level coupling between kinetochore-spindle attachment and spindle-pole formation in SAC silencing.

In silico spatial simulations reveal that MCC formation and excess BubR1 are required for tight inhibition of the anaphase-promoting complex

In response to the activation of the mitotic spindle assembly checkpoint (SAC), distinct inhibitory pathways control the activity of the anaphase-promoting complex (APC/C). It remains unclear whether the different regulatory mechanisms function in separate pathways or as part of an integrated signalling system. Here, five variant models of APC/C regulation were constructed and analysed. The simulations showed that all variant models were able to reproduce the wild type behaviour of the APC. However, only one model, which included both the mitotic checkpoint complex (MCC) as well as BubR1 as direct inhibitors of the APC/C, was able to reproduce both wild and mutant type behaviour of APC/C regulation. Interestingly, in this model, the MCC as well as the BubR1 binding rate to the APC/C was comparable to the known Cdc20-Mad2 binding rate and could not be made higher. Mad2 active transport towards the spindle mid-zone accelerated the inhibition speed of the APC/C but not its concentration level. The presented study highlights the principle that a systems biology approach is critical for the SAC mechanism and could also be used for predicting hypotheses to design future experiments. The presented work has successfully distinguished between five potent inhibitors of the APC/C using a systems biology approach. Here, the favoured model contains both BubR1 and MCC as direct inhibitors of the APC/C.

Spatial organization of the Ran pathway by microtubules in mitosis

Concentration gradients of soluble proteins are believed to be responsible for control of morphogenesis of subcellular systems, but the mechanisms that generate the spatial organization of these subcellular gradients remain poorly understood. Here, we use a newly developed multipoint fluorescence fluctuation spectroscopy technique to study the ras-related nuclear protein (Ran) pathway, which forms soluble gradients around chromosomes in mitosis and is thought to spatially regulate microtubule behaviors during spindle assembly. We found that the distribution of components of the Ran pathway that influence microtubule behaviors is determined by their interactions with microtubules, resulting in microtubule nucleators being localized by the microtubules whose formation they stimulate. Modeling and perturbation experiments show that this feedback makes the length of the spindle insensitive to the length scale of the Ran gradient, allows the spindle to assemble outside the peak of the Ran gradient, and explains the scaling of the spindle with cell size. Such feedback between soluble signaling pathways and the mechanics of the cytoskeleton may be a general feature of subcellular organization.

Spindle assembly checkpoint is sufficient for complete Cdc20 sequestering in mitotic control

The spindle checkpoint assembly (SAC) ensures genome fidelity by temporarily delaying anaphase onset, until all chromosomes are properly attached to the mitotic spindle. The SAC delays mitotic progression by preventing activation of the ubiquitin ligase anaphase-promoting complex (APC/C) or cyclosome; whose activation by Cdc20 is required for sister-chromatid separation marking the transition into anaphase. The mitotic checkpoint complex (MCC), which contains Cdc20 as a subunit, binds stably to the APC/C. Compelling evidence by Izawa and Pines (Nature 2014; 10.1038/nature13911) indicates that the MCC can inhibit a second Cdc20 that has already bound and activated the APC/C. Whether or not MCC per se is sufficient to fully sequester Cdc20 and inhibit APC/C remains unclear. Here, a dynamic model for SAC regulation in which the MCC binds a second Cdc20 was constructed. This model is compared to the MCC, and the MCC-and-BubR1 (dual inhibition of APC) core model variants and subsequently validated with experimental data from the literature. By using ordinary nonlinear differential equations and spatial simulations, it is shown that the SAC works sufficiently to fully sequester Cdc20 and completely inhibit APC/C activity. This study highlights the principle that a systems biology approach is vital for molecular biology and could also be used for creating hypotheses to design future experiments.