Systems Biology Modeling of Five Pathways for Regulation and Potent Inhibition of the Anaphase-Promoting Complex (APC/C): Pivotal Roles for MCC and BubR1

Cell Cycle Complexity: Exploring the Structure of Persistent Subsystems in 414 Models

Background: The regulation of cellular proliferation and genomic integrity is controlled by complex surveillance mechanisms known as cell cycle checkpoints. Disruptions in these checkpoints can lead to developmental defects and tumorigenesis. Methods: To better understand these mechanisms, computational modeling has been employed, resulting in a dataset of 414 mathematical models in the BioModels database. These models vary significantly in detail and simulated processes, necessitating a robust analytical approach. Results: In this study, we apply the chemical organization theory (COT) to these models to gain insights into their dynamic behaviors. COT, which handles both ordinary and partial differential equations (ODEs and PDEs), is utilized to analyze the compartmentalized structures of these models. COT's framework allows for the examination of persistent subsystems within these models, even when detailed kinetic parameters are unavailable. By computing and analyzing the lattice of organizations, we can compare and rank models based on their structural features and dynamic behavior. Conclusions: Our application of the COT reveals that models with compartmentalized organizations exhibit distinctive structural features that facilitate the understanding of phenomena such as periodicity in the cell cycle. This approach provides valuable insights into the dynamics of cell cycle control mechanisms, refining existing models and potentially guiding future research in this area.

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.

Multi-scale stochastic organization-oriented coarse-graining exemplified on the human mitotic checkpoint

The complexity of biological models makes methods for their analysis and understanding highly desirable. Here, we demonstrate the orchestration of various novel coarse-graining methods by applying them to the mitotic spindle assembly checkpoint. We begin with a detailed fine-grained spatial model in which individual molecules are simulated moving and reacting in a three-dimensional space. A sequence of manual and automatic coarse-grainings finally leads to the coarsest deterministic and stochastic models containing only four molecular species and four states for each kinetochore, respectively. We are able to relate each more coarse-grained level to a finer one, which allows us to relate model parameters between coarse-grainings and which provides a more precise meaning for the elements of the more abstract models. Furthermore, we discuss how organizational coarse-graining can be applied to spatial dynamics by showing spatial organizations during mitotic checkpoint inactivation. We demonstrate how these models lead to insights if the model has different “meaningful” behaviors that differ in the set of (molecular) species. We conclude that understanding, modeling and analyzing complex bio-molecular systems can greatly benefit from a set of coarse-graining methods that, ideally, can be automatically applied and that allow the different levels of abstraction to be related.

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.

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.

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.

Chelidonine induces mitotic slippage and apoptotic-like death in SGC-7901 human gastric carcinoma cells

The aim of the present study was to investigate the effect of chelidonine on mitotic slippage and apoptotic-like death in SGC-7901 human gastric cancer cells. The MTT assay was performed to detect the antiproliferative effect of chelidonine. Following treatment with chelidonine (10 µmol/l), the ultrastructure changes in SGC-7901, MCF-7 and HepG2 cells were observed by transmission electron microscopy. The effects of chelidonine on G2/M phase arrest and apoptosis of SGC-7901 cells were determined by flow cytometry. Indirect immunofluorescence assay and laser scanning confocal microscopy (LSCM) were used to detect the phosphorylation level of histone H3 (Ser10) and microtubule formation was detected using LSCM following immunofluorescent labeling. Subsequent to treatment with chelidonine (10 µmol/l), expression levels of mitotic slippage-associated proteins, including BUB1 mitotic checkpoint serine/threonine kinase B (BubR1), cyclin-dependent kinase 1 (Cdk1) and cyclin B1, and apoptosis-associated protein, caspase-3 were examined by western blotting at 24, 48 and 72 h. The half maximal inhibitory concentration of chelidonine was 23.13 µmol/l over 48 h and chelidonine induced G2/M phase arrest of cells. The phosphorylation of histone H3 at Ser10 was significantly increased following treatment with chelidonine for 24 h, indicating that chelidonine arrested the SGC-7901 cells in the M phase. Chelidonine inhibited microtubule polymerization, destroyed microtubule structures and induced cell cycle arrest in the M phase. Giant cells were observed with multiple micronuclei of varying sizes, which indicated that following a prolonged arrest in the M phase, the cells underwent mitotic catastrophe. Western blotting demonstrated that the protein expression levels of BubR1, cyclin B1 and Cdk1 decreased significantly between 48 and 72 h. Low expression levels of BubR1 and inactivation of the cyclin B1-Cdk1 complex results in the cells being arrested at mitosis and leads to mitotic slippage. In addition, apoptotic morphological changes in multinucleated cells were observed, the apoptosis rates increased gradually with administration of chelidonine in a time-dependent manner and the protein levels of caspase-3 increased significantly between 24 and 72 h. Thus, chelidonine induces mitotic slippage, and apoptotic-like death occurs in SGC-7901 cells undergoing mitotic catastrophe. Gastric cancer is a common malignancy, and ranks second in overall cancer-associated mortalities worldwide. The present study demonstrated that chelidonine induces M phase arrest and mitotic slippage of SGC-7901 human gastric carcinoma cells via downregulating the expression of BubR1, Cdk1 and cyclin B1 proteins. With the prolongation of chelidonine treatment, the giant cells with multiple micronuclei underwent mitotic slippage and were maintained in the G1 phase and did not survive. A number of multinucleated cells underwent apoptosis via a caspase-dependent signaling pathway. The current study proposes that chelidonine induces mitotic slippage and apoptotic-like death of SGC-7901 cells.

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.