Carsten Maus

Rule-based multi-level modeling of cell biological systems

BackgroundProteins, 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.ResultsMulti-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.ConclusionsRule-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.

Combining micro and macro-modeling in DEVS for computational biology

In computational biology there is an increasing need to combine micro and macro views of the system of interest. Therefore, explicit means to describe micro and macro level and the downward and upward causation that link both are required. Multi-Level-DEVS (or m^-DEVS) supports an explicit description of macro and micro level, information at macro level can be accessed from micro level and vice versa, micro models can be synchronously activated by the macro model and also the micro models can trigger the dynamics at macro level. To link both levels, different methods are combined, to those belong, value coupling, synchronous activations, variable ports, and invariants. The execution semantic of the formalism is given by an abstract simulator and its use is illustrated based on an small extract of the Wnt pathway.

Adapting rule-based model descriptions for simulating in continuous and hybrid space

Space plays an ever increasing role in cell biological modeling and simulation. This ranges from compartmental dynamics, via mesh-based approaches, to individuals moving in continuous space. An attributed, multi-level, rule-based language, ML-Space, is presented that allows to integrate these different types of spatial dynamics within one model. The associated simulator combines Gillespies method, the Next Subvolume method, and Brownian dynamics. This allows the simulation of reaction diffusion systems as well as taking excluded volume effects into account. A small example illuminates the potential of the approach in dealing with complex spatial dynamics like those involved in studying the dynamics of lipid rafts and their role in receptor co-localization.

Discrete event modelling and simulation in systems biology

With Systems Biology, a promising new application area for modelling and simulation emerges. Todays biologists are facing huge amounts of data delivered at different levels of detail by a multitude of advanced experimentation techniques. The Systems Biology approach copes with this information by cycling through phases of forming hypotheses, constructing models, experimenting with or analysing these models, and validating the findings by wet-lab experiments. A crucial point is therefore the way in which the knowledge about a system is formalized, that is, how a biological system is described, as this constrains the perception of the system as well as the scope of possible answers the model might provide. In this article, we compare different discrete event modelling formalisms (PETRI NETS, Stochastic π-CALCULUS, STATECHARTS, and DEVS) regarding their applicability to a cell biological system of current research interest, the Wnt signalling pathway. We then introduce the popular Gillespie algorithm, which is the foundation of many discrete event simulators for molecular-biological systems, and elaborate on some interesting extensions.

Toward a language for the flexible observation of simulations

Simulation studies typically imply the generation and interpretation of data. Collecting, storing, and filtering data can be expensive. Therefore, it is important to allow a user to specify these processes flexibly depending on the modeling language, the model, and the objective of the simulation study. An instrumentation language is presented and applied to collect, aggregate, store, and filter data generated during experimentation with models specified in ML-Rules, a rule-based multilevel modeling language for cell biological systems.

Integrating diverse reaction types into stochastic models: a signaling pathway case study in the imperative π-calculus

We present a case study of reusing parameters and reactions of a deterministic model of a biochemical system in order to implement a stochastic one. Our investigations base on a model of the Wnt signaling pathway and aim to study the influence of the cell cycle on the pathways dynamics. We report on our approaches to solve two major challenges: one is to gather and convert kinetic model parameters, e.g. constants for diffusion and enzymatic reactions. The second challenge is to provide the first implementation of reactions that exhibit Michaelis-Menten kinetics into a π-Calculus based approach by deploying the Imperative π-Calculus.

Hierarchical modeling for computational biology

Diverse hierarchies play a role in modeling and simulation for computational biology, e.g. categories, abstraction hierarchies, and composition hierarchies. Composition hierarchies seem a natural and straightforward focus for our exploration. What are model components and the requirements for a composite approach? How far do they support the quest for building blocks in computational biology? Modeling formalisms provide different means for composing a model. We will illuminate this with DEVS (Discrete event systems specification) and the π calculus. Whereas in DEVS distinctions are emphasized, e.g. between a system and its environment, between properties attributed to a system and the system itself, these distinctions become fluent in the compact description of the π calculus. However, both share the problem that in order to support a comfortable modeling, a series of extensions have been developed which also influence their possibility to support a hierarchical modeling. Thus, not individual formalisms but two families of formalisms and how they support a composite modeling will be presented. In computational biology one type of composite model deserves a closer inspection, as it brings together the wish to compose models and the need to describe a system at different levels in a unique manner, i.e. multi-level models.

One Modelling Formalism & Simulator Is Not Enough! A Perspective for Computational Biology Based on James II

Diverse modelling formalisms are applied in Computational Biology. Some describe the biological system in a continuous manner, others focus on discrete-event systems, or on a combination of continuous and discrete descriptions. Similarly, there are many simulators that support different formalisms and execution types (e.g. sequential, parallel-distributed) of one and the same model. The latter is often done to increase efficiency, sometimes at the cost of accuracy and level of detail. James II has been developed to support different modelling formalisms and different simulators and their combinations. It is based on a plug-in concept which enables developers to integrate spatial and non-spatial modelling formalisms (e.g. stochastic i¾? calculus , Beta binders , Devs , space- i¾?), simulation algorithms (e.g. variants of Gillespies algorithms (including Tau Leaping and Next Subvolume Method ), space- i¾?simulator, parallel Beta binders simulator) and supporting technologies (e.g. partitioning algorithms, data collection mechanisms, data structures, random number generators) into an existing framework. This eases method development and result evaluation in applied modelling and simulation as well as in modelling and simulation research.

Heterogeneity-based guidance for exploring multiscale data in systems biology

In systems biology, analyzing simulation trajectories at multiple scales is a common approach when subtle, detailed behavior and fundamental, overall behavior of a modeled system are to be investigated at the same time. A variety of multiscale visualization techniques provide solutions to handle and depict data at different scales. Yet the mere existence of multiple scales does not necessarily imply the existence of additional information on each of them: Data on a more fine-grained scale may not always yield new details, but instead reflect the already known data from more coarse-grained scales - just at a higher resolution. Nevertheless, to be sure of this, all scales have to be explored. We address this issue by guiding the exploration of simulation trajectories according to information about the deviation of the data between subsequent scales. For this purpose, we apply different dissimilarity measures to the simulation data at subsequent scales to automatically discern heterogeneous regions that exhibit deviating behavior on more fine-grained scales. We mark these regions and display them alongside the actual data in a multiscale visualization. By doing so, our approach provides valuable visual cues on whether it is worthwhile to drill-down further into the multi-scale data and if so, where additional information can be expected. Our approach is demonstrated by an exploratory walk-through of stochastic simulation results of a biochemical reaction network.

Semantics and Efficient Simulation Algorithms of an Expressive Multilevel Modeling Language

The domain-specific modeling and simulation language ML-Rules is aimed at facilitating the description of cell biological systems at different levels of organization. Model states are chemical solutions that consist of dynamically nested, attributed entities. The model dynamics are described by rules that are constrained by arbitrary functions, which can operate on the entities’ attributes, (nested) solutions, and the reaction kinetics. Thus, ML-Rules supports an expressive hierarchical, variable structure modeling of cell biological systems. The formal syntax and semantics of ML-Rules show that it is firmly rooted in continuous-time Markov chains. In addition to a generic stochastic simulation algorithm for ML-Rules, we introduce several specialized algorithms that are able to handle subclasses of ML-Rules more efficiently. The algorithms are compared in a performance study, leading to conclusions on the relation between expressive power and computational complexity of rule-based modeling languages.