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

Ibrahim, Bashar

doi:10.1039/c5mb00395d

Cited by 7 publications

(7 citation statements)

References 75 publications

(181 reference statements)

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“…That is, the model should consider the attachment of kinetochores as well as the checkpoint activation and inhibition. Several detailed models of SAC are available, such as 25,41,42 , as well as manually constructed abstract models, such as 4,43–48 . Here, the coarsest model is derived automatically from Model 1 by applying the approximate aggregation.…”

Section: Resultsmentioning

confidence: 99%

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

Henze

Puljiz

et al. 2019

Sci Rep

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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.

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Section: Resultsmentioning

confidence: 99%

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

Henze

Puljiz

et al. 2019

Sci Rep

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“…The ODE or discrete models generally ignore the topology, while PDEs consider the spatial distribution to some extent (e.g., diffusion but not geometry of molecules). EBM does not deal with single entities but rather with describing populations by estimating the mean behavior at a macroscopic level [3,62,64,69,70,88]. It uses a set of equations that are based on the relationships among observables.…”

Section: Spatial Propertiesmentioning

confidence: 99%

Trends in mathematical modeling of host–pathogen interactions

Ewald

Sieber

Garde

et al. 2019

Cell. Mol. Life Sci.

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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.

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“…The operator ∇ refers to the spatial gradient in spherical coordinates ( ∇(r, θ, ϕ) = ∂ ∂r e r + 1 r ∂ ∂θ e θ + 1 rsin(θ) ∂ ∂ϕ e ϕ ). Recent mathematical models of the SAC mechanism show that spherical symmetry can be used without loss of generality [27,20], and this form is used here. The system in Eq.…”

Section: Partial Differential Equations Modelmentioning

confidence: 99%

“…Also, the different components often interact nonlinearly in space and time, and in the presence of various feedback loops, which lead to remarkable phenomena that are difficult to predict [15,28,36,16,14,61]. Mathematical models have helped to illuminate fundamental modules of the SAC controls [8,53,21,40,20,22,27,45,37,25,13,24,26,29,3]. These models yet conceived SAC activation on details molecular level in order to distinguish between different pathways.…”

Section: Introductionmentioning

confidence: 99%

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

Ibrahim

2017

Bull Math Biol

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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.

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

Cited by 7 publications

References 75 publications

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

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

Trends in mathematical modeling of host–pathogen interactions

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

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