Bashar Ibrahim

Rule-based spatial modeling with diffusing, geometrically constrained molecules

BackgroundWe suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.ResultsOur simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.ConclusionsWe conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Elm1 kinase activates the spindle position checkpoint kinase Kin4

Elm1 phosphorylates a conserved residue within the Kin4 kinase domain to coordinate spindle position with cell cycle progression.

Monitoring spindle orientation: Spindle position checkpoint in charge

Every cell division in budding yeast is inherently asymmetric and counts on the correct positioning of the mitotic spindle along the mother-daughter polarity axis for faithful chromosome segregation. A surveillance mechanism named the spindle position checkpoint (SPOC), monitors the orientation of the mitotic spindle and prevents cells from exiting mitosis when the spindle fails to align along the mother-daughter axis. SPOC is essential for maintenance of ploidy in budding yeast and similar mechanisms might exist in higher eukaryotes to ensure faithful asymmetric cell division. Here, we review the current model of SPOC activation and highlight the importance of protein localization and phosphorylation for SPOC function.

In-silico modeling of the mitotic spindle assembly checkpoint.

Background The Mitotic Spindle Assembly Checkpoint (MSAC) is an evolutionary conserved mechanism that ensures the correct segregation of chromosomes by restraining cell cycle progression from entering anaphase until all chromosomes have made proper bipolar attachments to the mitotic spindle. Its malfunction can lead to cancer. Principle Findings We have constructed and validated for the human MSAC mechanism an in silico dynamical model, integrating 11 proteins and complexes. The model incorporates the perspectives of three central control pathways, namely Mad1/Mad2 induced Cdc20 sequestering based on the Template Model, MCC formation, and APC inhibition. Originating from the biochemical reactions for the underlying molecular processes, non-linear ordinary differential equations for the concentrations of 11 proteins and complexes of the MSAC are derived. Most of the kinetic constants are taken from literature, the remaining four unknown parameters are derived by an evolutionary optimization procedure for an objective function describing the dynamics of the APC:Cdc20 complex. MCC:APC dissociation is described by two alternatives, namely the “Dissociation” and the “Convey” model variants. The attachment of the kinetochore to microtubuli is simulated by a switching parameter silencing those reactions which are stopped by the attachment. For both, the Dissociation and the Convey variants, we compare two different scenarios concerning the microtubule attachment dependent control of the dissociation reaction. Our model is validated by simulation of ten perturbation experiments. Conclusion Only in the controlled case, our models show MSAC behaviour at meta- to anaphase transition in agreement with experimental observations. Our simulations revealed that for MSAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding.

Mad2 binding is not sufficient for complete Cdc20 sequestering in mitotic transition control (an in silico study).

For successful mitosis, metaphase has to be arrested until all centromeres are properly attached. The onset of anaphase, which is initiated by activating the APC, is controlled by the spindle assembly checkpoint (M)SAC. Mad2, which is a constitutive member of the (M)SAC, is supposed to inhibit the activity of the APC by sequestering away its co-activator Cdc20. Mad1 recruits Mad2 to unattached kinetochores and is compulsory for the establishment of the Mad2 and Cdc20 complexes. Recently, based on results from in vivo and in vitro studies, two biochemical models were proposed: the Template and the Exchange model. Here, we derive a mathematical description to compare the dynamical behaviour of the two models. Our simulation analysis supports the Template model. Using experimentally determined values for the model parameters, the Cdc20 concentration is reduced down to only about half. Thus, although the Template model displays good metaphase-to-anaphase switching behaviour, it is not able to completely describe (M)SAC regulation. This situation is neither improved by amplification nor by p31(comet) inhibition. We speculate that either additional reaction partners are required for total inhibition of Cdc20 or an extended mechanism has to be introduced for (M)SAC regulation.

A dynamical model of the spindle position checkpoint

The orientation of the mitotic spindle with respect to the polarity axis is crucial for the accuracy of asymmetric cell division. In budding yeast, a surveillance mechanism called the spindle position checkpoint (SPOC) prevents exit from mitosis when the mitotic spindle fails to align along the mother‐to‐daughter polarity axis. SPOC arrest relies upon inhibition of the GTPase Tem1 by the GTPase‐activating protein (GAP) complex Bfa1–Bub2. Importantly, reactions signaling mitotic exit take place at yeast centrosomes (named spindle pole bodies, SPBs) and the GAP complex also promotes SPB localization of Tem1. Yet, whether the regulation of Tem1 by Bfa1–Bub2 takes place only at the SPBs remains elusive. Here, we present a quantitative analysis of Bfa1–Bub2 and Tem1 localization at the SPBs. Based on the measured SPB‐bound protein levels, we introduce a dynamical model of the SPOC that describes the regulation of Bfa1 and Tem1. Our model suggests that Bfa1 interacts with Tem1 in the cytoplasm as well as at the SPBs to provide efficient Tem1 inhibition.

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.

The role of localization in the operation of the mitotic spindle assembly checkpoint

The mitotic spindle assembly checkpoint (MSAC) is an important regulatory mechanism of the cell cycle, ensuring proper chromosome segregation in mitosis. It delays the transition to anaphase until all chromosomes are properly attached to the mitotic spindle by emitting a diffusible “wait anaphase”-signal from unattached kinetochores. Current models of the checkpoint disregard important spatial properties like localization, diffusion and realistic numbers of kinetochores. To allow for in silico studies of the dynamics of these models in a more realistic environment, we introduce a mathematical framework for quasi-spatial simulation of localized biochemical processes that are typically observed during checkpoint activation and maintenance. The “emitted inhibition” model of the MSAC by Doncic et al. (Proc Natl Acad Sci USA 2005; 102:6332–7) assumes instantaneous activation of the diffusible “wait anaphase”-signal upon kinetochore encounter. We modify this model to account for binding kinetics with finite rates and use the developed framework to determine the feasible range of the binding parameters. We find that for proper activation, the binding rate constant has to be fast and above a critical value. Furthermore, this critical value depends significantly on the amount of local binding sites at each kinetochore. The critical values lie in a physiological realistic regime (104–106 M-1s-1). We also determine the feasible parameter range for fast checkpoint activation of the “Mad2 template” model, for which the kinetic parameters have recently been studied in vitro by Simonetta et al. (PLoS Biology 2009; 7:1000010). We find critical values for binding and catalysis rate constants, both significantly higher than the measured values. Our results suggest that yet unknown mechanisms at the kinetochores facilitate binding and catalysis in vivo. We conclude that quantitative models of the MSAC have to account for the limited availability of binding sites at kinetochores.

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.

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.