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

A yeast cell cycle pulse generator model shows consistency with multiple oscillatory and checkpoint mutant datasets

Modeling biological systems holds great promise for speeding up the rate of discovery in systems biology by predicting experimental outcomes and suggesting targeted interventions. However, this process is dogged by an identifiability issue, in which network models and their parameters are not sufficiently constrained by coarse and noisy data to ensure unique solutions. In this work, we evaluated the capability of a simplified yeast cell-cycle network model to reproduce multiple observed transcriptomic behaviors under genomic mutations. We matched time-series data from both cycling and checkpoint arrested cells to model predictions using an asynchronous multi-level Boolean approach. We showed that this single network model, despite its simplicity, is capable of exhibiting dynamical behavior similar to the datasets in most cases, and we demonstrated the drop in severity of the identifiability issue that results from matching multiple datasets.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

Mathematical modeling and numerical simulation of the mitotic spindle orientation system

The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. Partial differential equation (PDEs) model as well as linear stability analysis indicate that diffusion play no major role using experimental high diffusion values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division.

Mathematical analysis and modeling of DNA segregation mechanisms

The precise regulation of cell life division is indispensable to the reliable inheritance of genetic material, i.e. DNA, in successive generations of cells. This is governed by dedicated biochemical networks which ensure that all requirements are met before transition from one phase to the next. The Spindle Assembly Checkpoint (SAC) is an evolutionarily mechanism that delays mitotic progression until all chromosomes are properly linked to the mitotic spindle. During some asymmetric cell divisions, such as those observed in budding yeast, an additional mechanism, the Spindle Position Checkpoint (SPOC), is required to delay exit from mitosis until the mitotic spindle is correctly aligned. These checkpoints are complex and their elaborate spatiotemporal dynamics are challenging to understand intuitively. In this study, bistable mathematical models for both activation and silencing of mitotic checkpoints were constructed and analyzed. A one-parameter bifurcation was computed to show the realistic biochemical switches considering all signals. Numerical simulations involving systems of ODEs and PDEs were performed over various parameters, to investigate the effect of the diffusion coefficient. The results provide systems-level insights into mitotic transition and demonstrate that mathematical analysis constitutes a powerful tool for investigation of the dynamic properties of complex biomedical systems.

Mycotoxin zearalenone exposure impairs genomic stability of swine follicular granulosa cells in vitro

Zearalenone (ZEA), a metabolite of Fusarium fungi, is commonly found on moldy grains. Because it can competitively combine to estrogen receptor to disrupt estrogenic signaling, it has been reported to have serious adverse effects on animal reproduction systems. In order to explore the genotoxic effects of ZEA exposure on ovarian somatic cells, porcine granulosa cells were exposed to 10 μM and 30 μM ZEA for 24 or 72 h in vitro. The results showed that ZEA exposure for 24 h remarkably reduced the proliferation of porcine granulosa cells in a dose-dependent manner as determined by MTT analysis and flow cytometry. Furthermore, exposure to ZEA for 72 h induced apoptosis, and RNA sequence analysis also revealed that the expression of apoptosis related genes were altered. RT-qPCR, immunofluorescence and western blot analysis further confirmed the expression of DNA damage and repair related genes (γ-H2AX, BRCA1, RAD51 and PRKDC) were increased in ZEA exposed granulosa cells. When the estrogen antagonist, tamoxifen, was added with ZEA in the culture medium, the DNA damage and repairment by ZEA returned to normal level. Collectively, these results illustrate that ZEA disrupts genome stability and inhibits growth of porcine granulosa cells via the estrogen receptors which may promote granulosa cell apoptosis when the DNA repair system is not enough to rescue this serious damage.

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.

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.