Rule-based multi-level modeling of cell biological systems

<p>Abstract</p> <p>Background</p> <p>Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.</p> <p>Results</p> <p>Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.</p> <p>Conclusions</p> <p>Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.</p

Supporting the Integrated Visual Analysis of Input Parameters and Simulation Trajectories

The visualization of simulation trajectories is a well-established approach to analyze simulated processes. Likewise, the visualization of the parameter space that configures a simulation is a well-known method to get an overview of possible parameter combinations. This paper follows the premise that both of these approaches are actually two sides of the same coin: Since the input parameters influence the simulation outcome, it is desirable to visualize and explore both in a combined manner. The main challenge posed by such an integrated visualization is the combinatorial explosion of possible parameter combinations. It leads to insurmountably high simulation runtimes and screen space requirements for their visualization. The Visual Analytics approach presented in this paper targets this issue by providing a visualization of a coarsely sampled subspace of the parameter space and its corresponding simulation outcome. In this visual representation, the analyst can identify regions for further drill-down and thus finer subsampling. We aid this identification by providing visual cues based on heterogeneity metrics. These indicate in which regions of the parameter space deviating behavior occurs at a more fine-grained scale and thus warrants further investigation and possible re-computation. We demonstrate our approach in the domain of systems biology by a visual analysis of a rule-based model of the canonical Wnt signaling pathway that plays a major role in embryonic development. In this case, the aim of the domain experts was to systematically explore the parameter space to determine those parameter configurations that match experimental data sufficiently well

Hinzu reproduzierbare Simulationsstudien mit JAMES II

This thesis proposes a workflow-based approach for conducting simulation studies, using software aided documentation of workflow executions. A simulation study is divided into two layers, one dealing with the creation of a simulation model while the other deals with the execution of a simulation experiment with this model. In this thesis workflows for both layers, covering a broad range of different types of simulation studies are presented and a framework for executing those workflows as well as automatically collecting provenance data and documentation is developed and implemented.In dieser Arbeit wird ein workflow-basierter Ansatz vorgestellt, um Simulationsstudien abzubilden und zu dokumentieren. Damit dies funktioniert, wird eine Simulationstudie in 2 Stufen unterteilt, zum Einen in die Erstellung des Simulationsmodells und zum Anderen in die Ausführung eines Simulationsexperiments mit diesem Modell. Diese Arbeit stellt dabei für beide Stufen Workflows vor, um eine Vielzahl von verschiedenen Simulationsstudien abzubilden. Für die Ausführung der Workflows und automatische Dokumentation derer Ausführung wird ein Framework konzipiert und umgesetzt

Error-bounded GPU-supported terrain visualisation

The interactive visualisation of digital terrain datasets deals with their interrelated issues: quality, time and resources. In this paper a GPU-supported rendering technique is introduced, which finds a tradeoff between these issues. For this we use the projective grid method as the foundation. Even though the method is simple and powerful, its most significant problem is the loss of relevant features. Our contribution is a definition of a view-dependent grid distribution on the view-plane and an error-bounded rendering. This leads to a better approximation of the original terrain surface compared to previous GPU-based approaches. A higher quality is achieved with respect to the grid resolution. Furthermore the combination with an error metric and ray casting enables us to render a terrain representation within a given error threshold. Hence, high quality interactive terrain rendering is guaranteed, without expensive preprocessing

Calculated Vogel number for each specimen used in this study.

<p>Vogel number is calculated as the square root of the surface area of the chamber divided by the cube root of the volume of the chamber. Linearizing these values allow direct comparisons between the two while removing scaling effects due to size. It is important to note that the difference between ammonites and <i>S</i>. <i>spirula</i> in early ontogeny exists even when corrected for size. The high values shown by the early chambers of <i>A</i>. <i>scrobiculatus</i> may be an artifact due to resolution and should be interpreted with care.</p

Calculated Vogel number for each specimen used in this study.

<p>Vogel number is calculated as the square root of the surface area of the chamber divided by the cube root of the volume of the chamber. Linearizing these values allow direct comparisons between the two while removing scaling effects due to size. It is important to note that the difference between ammonites and <i>S</i>. <i>spirula</i> in early ontogeny exists even when corrected for size. The high values shown by the early chambers of <i>A</i>. <i>scrobiculatus</i> may be an artifact due to resolution and should be interpreted with care.</p

The Evolution and Development of Cephalopod Chambers and Their Shape - Fig 2

<p>A) Comparison between the surface area to volume ratio (SA_C:V_C) of each segmented chamber against chamber number for all specimens. B) SA_C:V_C against shell diameter at each chamber for <i>A</i>. <i>scrobiculatus</i>, <i>S</i>. <i>spirula</i>, <i>Arnsbergites</i> sp., <i>Amauroceras</i> sp., and <i>Kosmoceras</i> sp. SA_C:V_C is a parameter that reflects the capacity of the shell to compensate for potential buoyancy changes due to the water storing, organic lining in each chamber (Kroger, 2002). Chamber volume (C) and chamber surface area (D) comparisons between <i>S</i>. <i>spirula</i> and selected ammonoids. <i>A</i>. <i>scrobiculatus</i> and <i>N</i>. <i>pompilius</i> have an overall larger volume and surface area due to the much larger size of the animal, maximum diameter is an order of magnitude larger than <i>S</i>. <i>spirula</i> or <i>Kosmoceras</i>. Comparison between <i>S</i>. <i>spirula</i> and the ammonoids is a comparison between extreme morphologies as <i>S</i>. <i>spirula</i> has a whorl interspace, conservative shell cross-section through ontogeny and simple sutures while ammonoids have overlapping whorls, more complex septa (complexity changes through ontogeny), and variable conch morphology and ornamentation. Hm is the potential hatching point, Pa is the pathological chamber, TC is the terminal countdown.</p

Three-dimensional surface renderings of the segmented chambers of all specimens used in this study.

<p>A) <i>Spirula spirula</i>, B) pathological <i>S</i>. <i>spirula</i> (pathological chamber indicated by black arrow), C) <i>Nautilus pompilius</i> D) <i>Allonautilus scrobiculatus</i> E) <i>Arnsbergites</i> sp. F) <i>Amauroceras</i> sp. G) <i>Cadoceras</i> sp. H) <i>Kosmoceras</i> sp. Segmented chambers appear in sequentially different colors; only six chambers of <i>Kosmoceras</i> were segmented. The largest segmented chamber is shown in dorsal/ventral view (top) and lateral view (bottom). The boundaries of the chamber volumes trace the shape of the septa. Images are not to scale.</p

Comparison of the curvature between one chamber of <i>A</i>. <i>scrobiculatus</i> and <i>Kosmoceras</i> sp.

<p>Both chambers have similar volume and the chamber of <i>Kosmoceras</i> sp. was resampled to the same voxel size to make the datasets comparable. Curvature is measured at the vertices of the surface mesh. Overall, <i>Kosmoceras</i> sp. shows a consistently higher curvature over a greater percentage of its available surface area. Both chambers show highest curvature along the suture line.</p

Specimen Data and Tomographic Scan Meta-Data.

<p>Specimen Data and Tomographic Scan Meta-Data.</p