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Roland Ewald, Enrico Gutzeit, Sebastian Schwanke, Adelinde Uhrmacher, Christian Lange, Susanne Biermann, and Carsten Maus (2006)

Multi-Level Modeling with DEVS - A Critical Inspection and Steps Towards a Feasible Approach

Poster, Monterey, Winter Simulation Conference.

Multi-level modeling means the description of systems at different abstraction levels. In Systems Biology, different abstraction levels that arise from considering parts of the system at macro (e.g., concentrations) and parts of the system at micro (e.g., individual) level are of particular interest. Many modelling formalisms allow the modular and hierarchical construction of models. Those have often been inspired by DEVS and its construction of hierarchical models via the coupling of other models, but this type of hierarchy does still not allow a direct description of multi-level models, as the composed model has no behavior or state of its own. In DEVS, like in other modeling formalisms, macro and micro models are constructured as modular entities interacting with each other, as if they were equal sub-models. While this approach enables the use of established formalisms, it inhibits a clear distinction between the levels of abstraction and therefore hampers reusability, clearness and expressiveness. To overcome these problems, coupled DEVS models have been enriched by newly introduced high-level models that serve as a representation of the macro-level. Our approach is based on the rhoDEVS modelling formalism, which already provides variables structures, ports, and multi-couplings as key features. As an additional feature, high-level models may completely determine their coupled model's external input and output ports and can filter all inputs and outputs. This enables us to translate macro- and micro-level events over multiple abstraction levels. Furthermore, this behaviour could be very useful for modeling membrane systems. We present the realization of this approach in James II and the individual-based simulation of the canonical Wnt-Pathway as a sample application, in which a high-level model implementing the Gillespie approach serves as a particle collision scheduler. Similarly, a high-level model could include differential equations, or any other approach to model high-level properties of the system at hand. With its ability to survey all structural activities going on at the micro-level and to directly affect individuals by scheduling own events, the upward and downward causation in biological systems is captured. Although it looks as if we left DEVS far behind with this extension, it can be shown that models based on the extended formalism are still equivalent to basic DEVS models. Hence, the DEVS advantages, like modular composition of models via coupling, are preserved. Our approach is feasible to model any number of abstraction levels and can be coupled to other DEVS extensions (including hybrid models). We hope it eases the development of spatial biological models, including membranes, compartments and multiple abstraction levels.