In silico study of kinetochore control, amplification, and inhibition effects in MCC assembly

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.

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.

Hybrid agent-based model for quantitative in-silico cell-free protein synthesis

An advanced vision of the mRNA translation is presented through a hybrid modeling approach. The dynamics of the polysome formation was investigated by computer simulation that combined agent-based model and fine-grained Markov chain representation of the chemical kinetics. This approach allowed for the investigation of the polysome dynamics under non-steady-state and non-continuum conditions. The model is validated by the quantitative comparison of the simulation results and Luciferase protein production in cell-free system, as well as by testing of the hypothesis regarding the two possible mechanisms of the Edeine antibiotic. Calculation of the Hurst exponent demonstrated a relationship between the microscopic properties of amino acid elongation and the fractal dimension of the translation duration time series. The temporal properties of the amino acid elongation have indicated an anti-persistent behavior under low mRNA occupancy and evinced the appearance of long range interactions within the mRNA-ribosome system for high ribosome density. The dynamic and temporal characteristics of the polysomal system presented here can have a direct impact on the studies of the co-translation protein folding and provide a validated platform for cell-free system studies.

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.

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

Correct DNA segregation is a fundamental process that ensures the precise and reliable inheritance of genomic information for the propagation of cell life. Eukaryotic cells have evolved a conserved surveillance control mechanism for DNA segregation named the Spindle Assembly Checkpoint (SAC).The SAC ensures that the sister chromatids of the duplicated genome are not separated and distributed to the spindle poles before all chromosomes have been properly linked to the microtubules of the mitotic spindle. Biochemically, the SAC delays cell cycle progression by preventing activation of the anaphase-promoting complex (APC/C) or cyclosome whose activation by Cdc20 is required for sister-chromatid separation; this marks the transition into anaphase. In response to activation of the checkpoint, various species control the activity of both APC/C and Cdc20. However, the underlying regulatory pathways remain largely elusive. In this study, five possible model variants of APC/C regulation were constructed, namely BubR1, Mad2, MCC, MCF2, and an all-pathways model variant. These models were validated with experimental data from the literature. A wide range of parameter values has been tested to find the critical values of the APC/C binding rate. The results show that all variants are able to capture the wild-type behavior of the APC/C. However, only one model variant, which included both MCC as well as BubR1 as potent inhibitors of the APC/C, was able to reproduce both wild-type and mutant type behavior of APC/C regulation. In conclusion, the presented work informs the regulation of fundamental processes such as SAC and APC/C in cell biology and has successfully distinguished between five competing dynamical models using a systems biology approach. The results attest that systems-level approaches are vital for molecular and cell biology.

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.

Modeling the mitotic regulatory network identifies highly efficient anti-cancer drug combinations

Targeting mitotic regulation is recognized as an important strategy for cancer therapy. Aurora A/B kinase and polo-like kinase 1 (PLK1) are the key mitotic regulators, and many inhibitors have been developed. Combinations of these inhibitors are anticipated to be more effective therapeutics compared with single-inhibitor treatments; however, a systematic analysis of the combined effects is lacking. Here, we constructed the first mammalian cell mitotic regulation network model, which spans from mitotic entry to anaphase initiation, and contains all key mitotic kinase targets. The combined effects of different kinase inhibitors and microtubule inhibitors were systematically explored. Simultaneous inhibition of Aurora B and PLK1 strongly induces polyploidy. Microtubule inhibitor dosage can be significantly reduced when combined with a PLK1 inhibitor. The efficacy of these inhibitor combinations was validated by our experimental results. The mitotic regulatory network model provides a platform to study the complex interactions during mitosis, enables identification of mitotic regulators, and determines targets for drug discovery research. The suggested use of combining microtubule inhibitors with PLK1 inhibitors is anticipated to enhance microtubule-inhibitor tolerance in a wide range of patients.

Effects of small particle numbers on long-term behaviour in discrete biochemical systems

Motivation: The functioning of many biological processes depends on the appearance of only a small number of a single molecular species. Additionally, the observation of molecular crowding leads to the insight that even a high number of copies of species do not guarantee their interaction. How single particles contribute to stabilizing biological systems is not well understood yet. Hence, we aim at determining the influence of single molecules on the long-term behaviour of biological systems, i.e. whether they can reach a steady state.

Results: We provide theoretical considerations and a tool to analyse Systems Biology Markup Language models for the possibility to stabilize because of the described effects. The theory is an extension of chemical organization theory, which we called discrete chemical organization theory. Furthermore we scanned the BioModels Database for the occurrence of discrete chemical organizations. To exemplify our method, we describe an application to the Template model of the mitotic spindle assembly checkpoint mechanism.

Availability and implementation:http://www.biosys.uni-jena.de/Services.html.

Contact:bashar.ibrahim@uni-jena.de or dittrich@minet.uni-jena.de

Supplementary information:Supplementary data are available at Bioinformatics online.

Structural analysis of in silico mutant experiments of human inner-kinetochore structure

Large multi-molecular complexes like the kinetochore are lacking of suitable methods to determine their spatial structure. Here, we use and evaluate a novel modeling approach that combines rule-bases reaction network models with spatial molecular geometries. In particular, we introduce a method that allows to study in silico the influence of single interactions (e.g. bonds) on the spatial organization of large multi-molecular complexes and apply this method to an extended model of the human inner-kinetochore. Our computational analysis method encompasses determination of bond frequency, geometrical distances, statistical moments, and inter-dependencies between bonds using mutual information. For the analysis we have extend our previously reported human inner-kinetochore model by adding 13 new protein interactions and three protein geometry details. The model is validated by comparing the results of in silico with reported in vitro single protein deletion experiments. Our studies revealed that most simulations mimic the in vitro behavior of the kinetochore complex as expected. To identify the most important bonds in this model, we have created 39 mutants in silico by selectively disabling single protein interactions. In a total of 11,800 simulation runs we have compared the resulting structures to the wild-type. In particular, this allowed us to identify the interaction Cenp-W-H3 and Cenp-S-Cenp-X as having the strongest influence on the inner-kinetochore's structure. We conclude that our approach can become a useful tool for the in silico dynamical study of large, multi-molecular complexes.

Active transport can greatly enhance Cdc20:Mad2 formation

To guarantee genomic integrity and viability, the cell must ensure proper distribution of the replicated chromosomes among the two daughter cells in mitosis. The mitotic spindle assembly checkpoint (SAC) is a central regulatory mechanism to achieve this goal. A dysfunction of this checkpoint may lead to aneuploidy and likely contributes to the development of cancer. Kinetochores of unattached or misaligned chromosomes are thought to generate a diffusible “wait-anaphase” signal, which is the basis for downstream events to inhibit the anaphase promoting complex/cyclosome (APC/C). The rate of Cdc20:C-Mad2 complex formation at the kinetochore is a key regulatory factor in the context of APC/C inhibition. Computer simulations of a quantitative SAC model show that the formation of Cdc20:C-Mad2 is too slow for checkpoint maintenance when cytosolic O-Mad2 has to encounter kinetochores by diffusion alone. Here, we show that an active transport of O-Mad2 towards the spindle mid-zone increases the efficiency of Mad2-activation. Our in-silico data indicate that this mechanism can greatly enhance the formation of Cdc20:Mad2 and furthermore gives an explanation on how the “wait-anaphase” signal can dissolve abruptly within a short time. Our results help to understand parts of the SAC mechanism that remain unclear.

Spatial rule-based modeling: a method and its application to the human mitotic kinetochore

A common problem in the analysis of biological systems is the combinatorial explosion that emerges from the complexity of multi-protein assemblies. Conventional formalisms, like differential equations, Boolean networks and Bayesian networks, are unsuitable for dealing with the combinatorial explosion, because they are designed for a restricted state space with fixed dimensionality. To overcome this problem, the rule-based modeling language, BioNetGen, and the spatial extension, SRSim, have been developed. Here, we describe how to apply rule-based modeling to integrate experimental data from different sources into a single spatial simulation model and how to analyze the output of that model. The starting point for this approach can be a combination of molecular interaction data, reaction network data, proximities, binding and diffusion kinetics and molecular geometries at different levels of detail. We describe the technique and then use it to construct a model of the human mitotic inner and outer kinetochore, including the spindle assembly checkpoint signaling pathway. This allows us to demonstrate the utility of the procedure, show how a novel perspective for understanding such complex systems becomes accessible and elaborate on challenges that arise in the formulation, simulation and analysis of spatial rule-based models.

Rule-based modeling and simulations of the inner kinetochore structure

BACKGROUND

Combinatorial complexity is a central problem when modeling biochemical reaction networks, since the association of a few components can give rise to a large variation of protein complexes. Available classical modeling approaches are often insufficient for the analysis of very large and complex networks in detail. Recently, we developed a new rule-based modeling approach that facilitates the analysis of spatial and combinatorially complex problems. Here, we explore for the first time how this approach can be applied to a specific biological system, the human kinetochore, which is a multi-protein complex involving over 100 proteins.

RESULTS

Applying our freely available SRSim software to a large data set on kinetochore proteins in human cells, we construct a spatial rule-based simulation model of the human inner kinetochore. The model generates an estimation of the probability distribution of the inner kinetochore 3D architecture and we show how to analyze this distribution using information theory. In our model, the formation of a bridge between CenpA and an H3 containing nucleosome only occurs efficiently for higher protein concentration realized during S-phase but may be not in G1. Above a certain nucleosome distance the protein bridge barely formed pointing towards the importance of chromatin structure for kinetochore complex formation. We define a metric for the distance between structures that allow us to identify structural clusters. Using this modeling technique, we explore different hypothetical chromatin layouts.

CONCLUSIONS

Applying a rule-based network analysis to the spatial kinetochore complex geometry allowed us to integrate experimental data on kinetochore proteins, suggesting a 3D model of the human inner kinetochore architecture that is governed by a combinatorial algebraic reaction network. This reaction network can serve as bridge between multiple scales of modeling. Our approach can be applied to other systems beyond kinetochores.

Cycles and the qualitative evolution of chemical systems

Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks' cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.

A quantitative systems view of the spindle assembly checkpoint

The idle assembly checkpoint acts to delay chromosome segregation until all duplicated sister chromatids are captured by the mitotic spindle. This pathway ensures that each daughter cell receives a complete copy of the genome. The high fidelity and robustness of this process have made it a subject of intense study in both the experimental and computational realms. A significant number of checkpoint proteins have been identified but how they orchestrate the communication between local spindle attachment and global cytoplasmic signalling to delay segregation is not yet understood. Here, we propose a systems view of the spindle assembly checkpoint to focus attention on the key regulators of the dynamics of this pathway. These regulators in turn have been the subject of detailed cellular measurements and computational modelling to connect molecular function to the dynamics of spindle assembly checkpoint signalling. A review of these efforts reveals the insights provided by such approaches and underscores the need for further interdisciplinary studies to reveal in full the quantitative underpinnings of this cellular control pathway.