BACKGROUND:Signaling systems typically involve large, structured molecules each consisting of a large number of subunits called molecule domains. In modeling such systems these domains can be considered as the main players. In order to handle the resulting combinatorial complexity, rule-based modeling has been established as the tool of choice. In contrast to the detailed quantitative rule-based modeling, qualitative modeling approaches like logical modeling rely solely on the network structure and are particularly useful for analyzing structural and functional properties of signaling systems.RESULTS:We introduce the Process-Interaction-Model (PIM) concept. It defines a common representation (or basis) of rule-based models and site-specific logical models, and, furthermore, includes methods to derive models of both types from a given PIM. A PIM is based on directed graphs with nodes representing processes like post-translational modifications or binding processes and edges representing the interactions among processes. The applicability of the concept has been demonstrated by applying it to a model describing EGF insulin crosstalk. A prototypic implementation of the PIM concept has been integrated in the modeling software ProMoT.CONCLUSIONS:The PIM concept provides a common basis for two modeling formalisms tailored to the study of signaling systems: a quantitative (rule-based) and a qualitative (logical) modeling formalism. Every PIM is a compact specification of a rule-based model and facilitates the systematic set-up of a rule-based model, while at the same time facilitating the automatic generation of a site-specific logical model. Consequently, modifications can be made on the underlying basis and then be propagated into the different model specifications - ensuring consistency of all models, regardless of the modeling formalism. This facilitates the analysis of a system on different levels of detail as it guarantees the application of established simulation and analysis methods to consistent descriptions (rule-based and logical) of a particular signaling system.

The concept of modularity has been widely studied in the context of molecular biology. Since engineering sciences are used to work in a modular manner, it is tempting to approach the definition of biological modules from an engineering perspective. From a system-theoretical point of view an interesting criterion might be the definition of modules where both the input signals and the output signals are unidirectional, that is, there is no retroactivity. In this chapter, we review the applicability of this concept to biological networks. We start describing which biochemical situations can lead to absence of retroactivity. Then, we show how this concept can be automatized into an algorithm to decompose biochemical networks into modules so that the retroactivity among the modules is minimized. This decomposition facilitates the analysis of complex models because the modules can, to some degree, be studied separately. We complement this analysis with a consideration of retroactivity in signal transduction processes using a domain-oriented description. Finally, we explore the interplay between retroactivity and thermodynamics in the domain-oriented description, and show how the binding site phosphorylation is a mechanism that is able to realize unidirectional signal transduction.

Epidermal growth factor receptors (ErbB1-4) are oncogenic receptor tyrosine kinases (RTKs) that regulate diverse cellular processes. In this study, we combine measurement and mathematical modeling to quantify phospho-turnover at ErbB receptors in human cells and to determine the consequences for signaling and drug binding. We find that phosphotyrosine residues on ErbB1 have half-lives of a few seconds and therefore turn over 100-1000 times in the course of a typical immediate-early response to ligand. Rapid phospho-turnover is also observed for EGF-activated ErbB2 and ErbB3, unrelated RTKs, and multiple intracellular adaptor proteins and signaling kinases. Thus, the complexes formed on the cytoplasmic tail of active receptors and the downstream signaling kinases they control are highly dynamic and antagonized by potent phosphatases. We develop a kinetic scheme for binding of anti-ErbB1 drugs to receptors and show that rapid phospho-turnover significantly impacts their mechanisms of action.

The activation of caspases is a central mechanism in apoptosis. To gain further insights into complex processes like this, mathematical modelling using ordinary differential equations (ODEs) can be a very powerful research tool. Unfortunately, the lack of measurement data is a common problem in building such kinetic models, because it practically constrains the identifiability of the model parameters. An existing mathematical model of caspase activation during apoptosis was used in order to design future experimental setups that will help to maximise the obtained information. For this purpose, artificial measurement data are generated in silico to simulate potential experiments, and the model is fitted to this data. The model is also analysed using observability gramian and sensitivity analyses. The used analysis methods are compared. The artificial data approach allows one to make conclusions about system properties, identifiability of parameters and the potential information content of additional measurements for the used caspase activation model. The latter facilitates to improve the experimental design of further measurements significantly. The performed analyses reveal that several kinetic parameters are not at all, or only scarcely, identifiable, and that measurements of activated caspase 8 will maximally improve the parameter estimates. Furthermore, we can show that many assays with inhibitor of apoptosis protein (IAP) knockout cells only provide redundant information for our needs and as such do not have to be carried out.

BACKGROUND:Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models.RESULTS:We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs.CONCLUSION:The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways.

BACKGROUND:Combinatorial 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.RESULTS:We 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.CONCLUSION:The 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.

BACKGROUND:Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications.RESULTS:Our results show that under realistic assumptions on domain interactions, the dynamics of signaling pathways can be exactly described by reduced, hierarchically structured models. The method presented here provides a rigorous way to model a large class of signaling networks using macro-states (macroscopic quantities such as the levels of occupancy of the binding domains) instead of micro-states (concentrations of individual species). The method is described using generic multidomain proteins and is applied to the molecule LAT.CONCLUSION:The presented method is a systematic and powerful tool to derive reduced model structures describing the dynamics of multiprotein complex formation accurately.

This paper introduces compelling problems of biological systems and signaling networks to show how engineering tools can be applied to the analysis of the cellular machinery. The mechanisms that cells have developed to process information are described, and the decomposition of signalling networks into subsystems is discussed. A novel criterion for defining modules based on the absence of retroactivity is also presented, and some simple criteria for the analysis of the resulting units are introduced. Two simple examples, two-component signaling and MAPK cascade, and a more complicated example, EGF signaling, were reviewed. An important point to discuss in model analysis for cellular system is the availability of experimental data that is sufficient to verify the model structure and model parameters.

Biological systems and, in particular, cellular signal transduction pathways are characterised by their high complexity. Mathematical models describing these processes might be of great help to gain qualitative and, most importantly, quantitative knowledge about such complex systems. However, a detailed mathematical description of these systems leads to nearly unmanageably large models, especially when combining models of different signalling pathways to study cross-talk phenomena. Therefore, simplification of models becomes very important. Different methods are available for model reduction of biological models. Importantly, most of the common model reduction methods cannot be applied to cellular signal transduction pathways. Using as an example the epidermal growth factor (EGF) signalling pathway, we discuss how quantitative methods like system analysis and simulation studies can help to suitably reduce models and additionally give new insights into the signal transmission and processing of the cell.

Apoptosis is an important physiological process crucially involved in development and homeostasis of multicellular organisms. Although the major signaling pathways have been unraveled, a detailed mechanistic understanding of the complex underlying network remains elusive. We have translated here the current knowledge of the molecular mechanisms of the death-receptor-activated caspase cascade into a mathematical model. A reduction down to the apoptotic core machinery enables the application of analytical mathematical methods to evaluate the system behavior within a wide range of parameters. Using parameter values from the literature, the model reveals an unstable status of survival indicating the need for further control. Based on recent publications we tested one additional regulatory mechanism at the level of initiator caspase activation and demonstrated that the resulting system displays desired characteristics such as bistability. In addition, the results from our model studies allowed us to reconcile the fast kinetics of caspase 3 activation observed at the single cell level with the much slower kinetics found at the level of a cell population.