Abstract
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.
Highlights
Biological processes like cell-cycle control[1] are complex due to the number of components involved and due to non-linearity and ubiquitous feed-back loops[2]
We will see that in practice it appears beneficial to depart from the strict mathematical definition of a coarse-graining in favor of obtaining a more elegant model through an approximate coarse-graining, as we will do by using organizational coarse-graining based on chemical organization theory[10]
We model the dynamics of a reaction network as a continuous-time Markov chain (CTMC)
Summary
Biological processes like cell-cycle control[1] are complex due to the number of components involved and due to non-linearity and ubiquitous feed-back loops[2]. There is usually a trade-off between the accuracy of a model, desirable for representing biological knowledge in detail[3], and the simplicity of a model, which is beneficial for understanding and generalizing the fundamental mechanisms involved, e.g.4,5. If both are required, a multi-model approach is useful, where a set of models with different granularity is derived. The mitotic spindle assembly checkpoint (SAC) is a central regulatory mechanism to achieve this goal. Kinetochores of unattached or misaligned chromosomes generate a diffusible “wait-anaphase” signal, which is the basis for downstream events to inhibit the anaphase promoting complex/cyclosome (APC/C or APC)[15,16,17].
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