Rule-based modeling and simulations of the inner kinetochore structure

Cell cycle control of kinetochore assembly

The kinetochore is a large proteinaceous structure assembled on the centromeres of chromosomes. The complex machinery links chromosomes to the mitotic spindle and is essential for accurate chromosome segregation during cell division. The kinetochore is composed of two submodules: the inner and outer kinetochore. The inner kinetochore is assembled on centromeric chromatin and persists with centromeres throughout the cell cycle. The outer kinetochore attaches microtubules to the inner kinetochore, and assembles only during mitosis. The review focuses on recent advances in our understanding of the mechanisms governing the proper assembly of the outer kinetochore during mitosis and highlights open questions for future investigation.

Performance Analysis of a Solar-Powered Multi-Purpose Supply Container

In this article, the performance of a solar-powered multi-purpose supply container used as a service module for first-aid, showering, freezing, refrigeration and water generation purposes in areas of social emergency is analyzed. The average daily energy production of the solar panel is compared to the average daily energy demands of the above-mentioned types of service modules. The comparison refers to five different locations based on the Köppen–Geiger classification of climatic zones with the data for energy demand being taken from another publication. It is shown that in locations up to mid-latitudes, the supply container is not only able to power all types of modules all year round but also to provide up to 15 m3 of desalinated water per day for drinking, domestic use and irrigation purposes. This proves and quantifies the possibility of combining basic supply with efficient transport and self-sufficiency by using suitably equipped shipping containers. Thus, flexible solutions are provided to some of the most challenging problems humans will face in the future, such as natural disasters, water scarcity, starvation and homelessness.

Ccp1-Ndc80 switch at the N terminus of CENP-T regulates kinetochore assembly

Precise chromosome segregation relies on kinetochores. How kinetochores are precisely assembled on centromeres through the cell cycle remains poorly understood. Centromeres in most eukaryotes are epigenetically marked by nucleosomes containing the histone H3 variant, CENP-A. Here, we demonstrated that Ccp1, an anti–CENP-A loading factor, interacts with the N terminus of CENP-T to promote the assembly of the outer kinetochore Ndc80 complex. This work further suggests that competitive exclusion between Ccp1 and Ndc80 at the N terminus of CENP-T via phosphorylation ensures precise kinetochore assembly during mitosis. In addition, CENP-T is critical for Ccp1 centromeric localization, which in turn regulates CENP-A distribution. Our results reveal a previously unrecognized mechanism underlying kinetochore assembly through the cell cycle.

Kinetochores, a protein complex assembled on centromeres, mediate chromosome segregation. In most eukaryotes, centromeres are epigenetically specified by the histone H3 variant CENP-A. CENP-T, an inner kinetochore protein, serves as a platform for the assembly of the outer kinetochore Ndc80 complex during mitosis. How CENP-T is regulated through the cell cycle remains unclear. Ccp1 (counteracter of CENP-A loading protein 1) associates with centromeres during interphase but delocalizes from centromeres during mitosis. Here, we demonstrated that Ccp1 directly interacts with CENP-T. CENP-T is important for the association of Ccp1 with centromeres, whereas CENP-T centromeric localization depends on Mis16, a homolog of human RbAp48/46. We identified a Ccp1-interaction motif (CIM) at the N terminus of CENP-T, which is adjacent to the Ndc80 receptor motif. The CIM domain is required for Ccp1 centromeric localization, and the CIM domain–deleted mutant phenocopies ccp1Δ. The CIM domain can be phosphorylated by CDK1 (cyclin-dependent kinase 1). Phosphorylation of CIM weakens its interaction with Ccp1. Consistent with this, Ccp1 dissociates from centromeres through all stages of the cell cycle in the phosphomimetic mutant of the CIM domain, whereas in the phospho-null mutant of the domain, Ccp1 associates with centromeres during mitosis. We further show that the phospho-null mutant disrupts the positioning of the Ndc80 complex during mitosis, resulting in chromosome missegregation. This work suggests that competitive exclusion between Ccp1 and Ndc80 at the N terminus of CENP-T via phosphorylation ensures precise kinetochore assembly during mitosis and uncovers a previously unrecognized mechanism underlying kinetochore assembly through the cell cycle.

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.

Spatial Rule-Based Simulations: The SRSim Software

SRSim combines rule-based reaction network models with spatial particle simulations allowing to simulate the dynamics of large molecular complexes changing according to a set of chemical reaction rules. As the rule can contain patterns of molecular complexes and specific states of certain binding sites, a combinatorially complex or even infinitely sized reaction network can be defined. Particles move in a three-dimensional space according to molecular dynamics implemented by LAMMPS, while the BioNetGen language is used to formulate reaction rules. Geometric information is added in a specific XML format. The simulation protocol is exemplified by two different variants of polymerization as well as a toy model of DNA helix formation. SRSim is open source and available for download.

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.

CENP-C/H/I/K/M/T/W/N/L and hMis12 but not CENP-S/X participate in complex formation in the nucleoplasm of living human interphase cells outside centromeres

Kinetochore proteins assemble onto centromeric chromatin and regulate DNA segregation during cell division. The inner kinetochore proteins bind centromeres while most outer kinetochore proteins assemble at centromeres during mitosis, connecting the complex to microtubules. Here, we measured the co-migration between protein pairs of the constitutive centromere associated network (CCAN) and hMis12 complexes by fluorescence cross-correlation spectroscopy (FCCS) in the nucleoplasm outside centromeres in living human interphase cells. FCCS is a method that can tell if in living cells two differently fluorescently labelled molecules migrate independently, or co-migrate and thus are part of one and the same soluble complex. We also determined the apparent dissociation constants (Kd) of the hetero-dimers CENP-T/W and CENP-S/X. We measured co-migration between CENP-K and CENP-T as well as between CENP-M and CENP-T but not between CENP-T/W and CENP-S/X. Furthermore, CENP-C co-migrated with CENP-H, and CENP-K with CENP-N as well as with CENP-L. Thus, in the nucleoplasm outside centromeres, a large fraction of the CENP-H/I/K/M proteins interact with CENP-C, CENP-N/L and CENP-T/W but not with CENP-S/X. Our FCCS analysis of the Mis12 complex showed that hMis12, Nsl1, Dsn1 and Nnf1 also form a complex outside centromeres of which at least hMis12 associated with the CENP-C/H/I/K/M/T/W/N/L complex.

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.

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.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

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.

The CENP-T C-terminus is exclusively proximal to H3.1 and not to H3.2 or H3.3

The kinetochore proteins assemble onto centromeric chromatin and regulate DNA segregation during cell division. The inner kinetochore proteins bind centromeres while most outer kinetochore proteins assemble at centromeres during mitosis, connecting the complex to microtubules. The centromere-kinetochore complex contains specific nucleosomes and nucleosomal particles. CENP-A replaces canonical H3 in centromeric nucleosomes, defining centromeric chromatin. Next to CENP-A, the CCAN multi-protein complex settles which contains CENP-T/W/S/X. These four proteins are described to form a nucleosomal particle at centromeres. We had found the CENP-T C-terminus and the CENP-S termini next to histone H3.1 but not to CENP-A, suggesting that the Constitutive Centromere-Associated Network (CCAN) bridges a CENP-A- and a H3-containing nucleosome. Here, we show by in vivo FRET that this proximity between CENP-T and H3 is specific for H3.1 but neither for the H3.1 mutants H3.1(C96A) and H3.1(C110A) nor for H3.2 or H3.3. We also found CENP-M next to H3.1 but not to these H3.1 mutants. Consistently, we detected CENP-M next to CENP-S. These data elucidate the local molecular neighborhood of CCAN proteins next to a H3.1-containing centromeric nucleosome. They also indicate an exclusive position of H3.1 clearly distinct from H3.2, thus documenting a local, and potentially also functional, difference between H3.1 and H3.2.

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.

Multi-state modeling of biomolecules

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behavior of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: the problem of how to describe and specify a multi-state system (the “specification problem”) and the problem of how to use a computer to simulate the progress of the system over time (the “computation problem”). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus [1], BioNetGen [2]–[5], the Allosteric Network Compiler [6], and others [7], [8]. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm[9], [10]. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators fall into two further categories: nonspatial simulators, such as StochSim [11], DYNSTOC [12], RuleMonkey [9], [13], and the Network-Free Stochastic Simulator (NFSim) [14], and spatial simulators, including Meredys [15], SRSim [16], [17], and MCell [18]–[20]. Modelers can thus choose from a variety of tools, the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

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.

On some recent insights in Integral Biomathics

This paper summarizes the results in Integral Biomathics obtained to this moment and provides an outlook for future research in the field.