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

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.

Compressing molecular dynamics trajectories: Breaking the one-bit-per-sample barrier.

Molecular dynamics simulations yield large amounts of trajectory data. For their durable storage and accessibility an efficient compression algorithm is paramount. State of the art domain-specific algorithms combine quantization, Huffman encoding and occasionally domain knowledge. We propose the high resolution trajectory compression scheme (HRTC) that relies on piecewise linear functions to approximate quantized trajectories. By splitting the error budget between quantization and approximation, our approach beats the current state of the art by several orders of magnitude given the same error tolerance. It allows storing samples at far less than one bit per sample. It is simple and fast enough to be integrated into the inner simulation loop, store every time step, and become the primary representation of trajectory data. © 2016 Wiley Periodicals, Inc.

Structural analysis of in silico mutant experiments of human inner-kinetochore structure.

Large multi-molecular complexes like the kinetochore are lacking of suitable methods to determine their spatial structure. Here, we use and evaluate a novel modeling approach that combines rule-bases reaction network models with spatial molecular geometries. In particular, we introduce a method that allows to study in silico the influence of single interactions (e.g. bonds) on the spatial organization of large multi-molecular complexes and apply this method to an extended model of the human inner-kinetochore. Our computational analysis method encompasses determination of bond frequency, geometrical distances, statistical moments, and inter-dependencies between bonds using mutual information. For the analysis we have extend our previously reported human inner-kinetochore model by adding 13 new protein interactions and three protein geometry details. The model is validated by comparing the results of in silico with reported in vitro single protein deletion experiments. Our studies revealed that most simulations mimic the in vitro behavior of the kinetochore complex as expected. To identify the most important bonds in this model, we have created 39 mutants in silico by selectively disabling single protein interactions. In a total of 11,800 simulation runs we have compared the resulting structures to the wild-type. In particular, this allowed us to identify the interaction Cenp-W-H3 and Cenp-S-Cenp-X as having the strongest influence on the inner-kinetochore's structure. We conclude that our approach can become a useful tool for the in silico dynamical study of large, multi-molecular complexes.

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.