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 spatial modeling with diffusing, geometrically constrained molecules.

BACKGROUND: We 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. RESULTS: Our 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. CONCLUSIONS: We 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.

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 (10(4)-10(6) M(-1)s(-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.