Reduced modeling of signal transduction – a modular approach

Holger Conzelmann,Sybille Ebert,Markus Koschorreck,Michael Ederer,Ernst Dieter Gilles

doi:10.1186/1471-2105-8-336

Abstract

BackgroundCombinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations.ResultsWe introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible.ConclusionThe new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties.

Highlights

Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction
Introduction of the layer based approach The two most important mathematical tools to tackle the enormous complexity of models describing biological reaction networks are model reduction and modularization techniques
If we compare the reactions of the reduced model (Figure 5) and the reactions of the detailed model (Figure 3), we find r1 = d1 r2 = d2

Summary

Introduction

Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. Examples for qualitative modeling techniques applied to signal transduction pathways are Petri nets [1], interaction graphs and Boolean networks [2]. The concept of T-invariants in Petri nets allows to identify self contained subnets that are active under a given input situation [1] With both techniques it is possible to decompose a signaling network into smaller functional units. The chemical master equations [3] describe the stochastic dynamics of chemical systems in a quantitative way. They are difficult to analyze and simulate. In many cases a simplified approach neglecting the stochastic nature of the dynamics can be used

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