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

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.

Trends in mathematical modeling of host–pathogen interactions

“…As discussed in detail by Schleicher et al [109], the combination and integration of different approaches is valuable to exploit the large amount of biological data and complex networks of HPI. A combined approach often improves the applicability and value of mathematical models, as pointed out in Section "Defense, counter defense and counter-counter defense" with respect to game theory and ODEs [9,19,29,56,88]. Moreover, game-theoretical approaches can be combined with ABM, dynamic optimization [29], or in the form of games on grids or graphs [107].…”

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

“…Furthermore, our approach is open to include other dynamically relevant components like treatment and vaccination strategies. Another task for future work would be to study the transient virus immune system in more detail, for example, by mapping the basin of attraction of each organization or by systematically analyzing the transition dynamics in-between organizations [33,34].…”

Persistent Subspaces of Reaction-Based Dynamical Systems

“…The concept of the chemical organization was applied successfully in various constructive systems like chemical computing [15], social systems [16], virus dynamics [17][18][19][20] or checking systems biology models for inconsistencies [21] as well as in cell cycle control [22][23][24]. For the time being, the theory was completed in [14] and here it is presented in a brief and clear manner that omits mathematical details.…”