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Theory and Algorithms for Modular Network Analysis

Applicant Stelling Jörg
Number 141264
Funding scheme Project funding (Div. I-III)
Research institution Computational Systems Biology Department of Biosystems, D-BSSE ETH Zürich
Institution of higher education ETH Zurich - ETHZ
Main discipline Information Technology
Start/End 01.12.2012 - 30.11.2014
Approved amount 207'287.00
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All Disciplines (2)

Information Technology

Keywords (7)

qualitative dynamics; fixed-parameter tractable ; dynamic model; system identification; monotone system; structural network analysis; system decomposition

Lay Summary (English)

Lay summary

Mathematical modeling is a key ingredient for describing and understanding the behavior of complex dynamic systems over time. Such systems are ubiquitous in engineering and the natural sciences and they are fundamental to study biological systems in the new discipline of systems biology. Increasing computational power allows us to simulate ever larger models and to make predictions of a given system without the need of exhaustive experimental work. Such simulations require that all parameters and the initial states of a system are given with sufficient accuracy. In many cases, however, these parameter values are unknown and can only be guessed with great uncertainty, making reliable predictions difficult or even impossible. Finding suitable parameter values is difficult and expensive for larger models and typically requires laborious experimentation.

On the other hand, non-trivial conclusion on the feasible dynamics of a system can be drawn from the equation structure alone, at least for certain classes of systems. This often allows one to select the most promising models, to exclude a particular model, or to detect missing components in a given model even without knowledge of parameter values, thus saving the time and resources for extensive experimental work. A typical example in biology is so-called multistationarity. Here, a particular biological system is known to be able to arrive at two stable equilibria (e.g., two states in a cell cycle) and a useful model must thus be able to do the same. For large classes of models, the equation structure alone is sufficient to determine this dynamic feature of a model.

This project aims at developing theoretical concepts and implementing algorithms for analyzing complex dynamic models by decomposing them into smaller modules with particular desired properties. These modules  will serve at least two different  purposes: (i) they will allow us to study large models that do not fall into one of the classes that allow immediate analysis by splitting the work into modules and their interconnections and (ii) they will enable us to find which parts of a large model need further data for parameter identification and what kind of experiments need to be performed to gather this data.

In this project we will concentrate on dynamic models from systems biology. Many conceptual problems are still open, including the best mathematical representation of these models for modular analysis and a useful and general enough description of the interconnections of modules. With a good representation at hand, we will be able to unite several existing approaches under the same framework and combine their strengths and scopes. Moreover, many of the most promising approaches for modular analysis require efficient algorithms to be of practical use and we will develop and implement such algorithms.

Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants


Name Institute


A unified view on bipartite species-reaction and interaction graphs for chemical reaction networks
Kaltenbach H.M. (2012), A unified view on bipartite species-reaction and interaction graphs for chemical reaction networks, in arXiv, 1210.0320.


Group / person Country
Types of collaboration
Humboldt University Berlin Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Exchange of personnel


Mathematical modeling is a key ingredient for describing and understanding complex dynamic systems. Small systems can often be studied manually or by numerical simulation. In addition, powerful methods have been developed to study such systems more qualitatively, by concentrating on the equation structures. Such methods allow drawing nontrivial conclusions about the dynamics of a system without exact knowledge of, e.g., parameter values. One the other hand, the analysis of larger systems requires algorithmic procedures, and exhaustive simulations are no longer feasible. Moreover, qualitative methods typically can no longer be applied, because they do not scale. As a consequence, a particularly successful strategy to cope with large systems is to decompose them into suitable smaller subsystems and then to analyze these subsystems and their interactions. However, current decomposition methods usually need detailed descriptions of a fully parameterized system.While the above characteristics hold for complex systems in many domains, the recently developing field of systems biology poses severe new challenges for the analysis of dynamic systems. The advancement of experimental techniques reveals more and more interactions of chemical species, allowing us to formulate increasingly large models describing their dynamics; typical signaling network models contain around one hundred chemical species, each described by a nonlinear ordinary differential equation. Qualitative descriptions of interactions, such as inhibition or activation, are often known. However, detailed descriptions of interactions, such as exact chemical kinetics and parameter values often remain unknown and they are hard to access experimentally. This characteristic of rich qualitative and poor quantitative knowledge often prohibits analysis of a model by direct application of established methods from, e.g., control theory or physics.Here, we propose to develop new conceptual and technical approaches to study large-scale dynamic models with a focus on biochemical signaling networks. A first challenge will be to develop appropriate representations of a network that allow a detailed description of qualitative interactions, as well as deriving formalism to describe system interfaces and interconnections of (sub-)systems. Building on these concepts, we will develop new theoretical and algorithmic methods for decomposing systems into modules that belong to predefined qualitative system classes. A particular focus will be on the class of monotone systems, which has intriguing dynamic properties and is yet characterized by purely qualitative features. For scaling such methods to large systems of several hundred chemical species, we will use recent developments in the theory of fixed-parameter tractable algorithms to derive efficient decomposition algorithms. Finally, the modular structure of a decomposed system will be used to (i) study its core dynamic features, particularly feedback structures, by coarse-graining large systems, and (ii) develop methods for system identification and experimental design by identifying parts of the system that show more pronounced responses to perturbation experiments using, e.g., results from modular response analysis. Overall, we envisage the developed mathematical and computational approaches to be foundational for future applications in the domain of systems biology.