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The group is doing research in both mathematical modeling
of biological systems and in method development for the
theoretical analysis of biological models.
Some projects are also specifically aimed at establishing
a good interface between experiment,
modeling and mathematical analysis.
Topics in this area
Modeling of cell death signaling
Programmed cell death is a crucial mechanism in multicellular organisms, by providing the organism with means to remove superfluous or malfunctioning cells in a coordinated and faultless manner. Disturbances to the correct operation of programmed cell death are related to diseases such as cancer, neuro-degeneration, autoimmune diseases, or defects in development. The induction of programmed cell death is supposed to be finely regulated by numerous signals, many of which have probably not yet been discovered. In this project, we focus on the regulation of cell death induction by members of the tumor necrosis factor (TNF) receptor family, which are a specific class of membrane receptors present in every mammalian cell. Several receptors in this family have the interesting property that they activate inflammatory pathways, which usually counteract the programmed cell death, together with other pathways that directly induce cell death. The actual outcome of such a stimulus will then be a decision about life or death, taking into account the internal state of the individual cell.
Although many aspects are known on the biochemical level, a detailed mechanistic understanding of the system is still lacking. By constructing mathematical models of the underlying biochemical process, we aim to elucidate the mechanisms governing the choice between life and death. This is done in a bottom-up approach to biological modeling, where the model structure is built from experimentally determined interactions, and the parameters are fitted to dynamical measurements. The modeling is thereby done in close collaboration with the Institute for Cell Biology and Immunology at the University of Stuttgart, who have been working with the TNF receptor family for several decades.
Using this approach, we have determined a key regulatory feedback loop that enables the cell to switch irreversibly to the execution of programmed cell death. These studies also lead to the identification of an additional protein involved in the network, that can prevent cells from starting the death program for a too weak stimulus. The present research now focuses on understanding the interplay among pathways that promote or counteract cell death.
Cell death signalling pathways
S. Waldherr, T. Eissing, and F. Allgöwer.|
Rückkopplungen im Leben und Sterben einer Zelle: Ansätze zur
at – Automatisierungstechnik, 56(5):233–240, 2008.
T. Eißing, F. Allgöwer, and E. Bullinger.|
Robustness properties of apoptosis models with respect to parameter
variations and stochastic influences.
IEE Systems Biology, 152(4):221–228, 2005.
T. Eißing, H. Conzelmann, E. D. Gilles,
F. Allgöwer, E. Bullinger, and P. Scheurich.|
Bistability analyses of a caspase activation model for receptor induced
J. Biol. Chem., 279(35):36892–36897, August 2004.
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Uncertainty analysis of biological models
Models for biological systems are subject to a significant degree of uncertainty in
structure and parameter values. There are several reasons for the presence of such
uncertainty. On the one hand, uncertainties in models arise from uncertainties in knowledge
about the system, mostly because of limitations in the experimental technology. On the other
hand, the biological systems are subject to large variations in environmental and internal
boundary conditions, which directly translate to model uncertainties.
Uncertainty analysis aims at quantifying the uncertainty in model predictions such as predicted
trajectories, given a specification of the uncertainty in the model description.
Robustness analysis on the other hand provides information about the level of uncertainty
that can be tolerated while maintaining specified properties.
At the IST, we develop numerical methods inspired from a control engineering viewpoint
to handle these problems. The methods are specifically tailored to deal with the analysis of
biochemical reaction networks. An exemplary area of research is the uncertainty and robustness
analysis of stationary trajectories in networks that are subject to parametric uncertainty.
The methods developed at the IST use a set-based framework for the uncertainty and robustness
analysis. These methods have the advantage that guaranteed bounds are obtained on the possible
variations under parametric uncertainty. This is an advantage over statistical methods, where
only probabilistic estimates on the variations are obtained. Current research focuses on how
to use the developed robustness analysis methods to support modelling tasks in systems biology.
Feasible steady state region and its approximation for a biochemical reaction network with parametric uncertainty
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Complex dynamical behavior in biochemical signal transduction
The amazing complexity of biological systems is reflected by the types of dynamical behavior of biochemical signaling pathways, such as switching behavior or oscillations. Such complex dynamical behaviour is often directly coupled to a specific biological function, such as cellular differentiation in the case of switching behaviour, or the circadian rhythm for oscillations. The major reason for emergence of complex dynamical behaviour is the occurence of feedback circuits in many biochemical networks. The relevance of feedback structures in biochemical signaling pathways motivates the application of control engineering approaches to study these systems.
Parameter variations may lead to changes in the type of complex dynamical behaviour that the system displays. Such changes are typically mediated by bifurcations of equilibrium points in the system. While classical bifurcation analysis methods are well established in dynamical systems theory, they are often insufficient to deal with the high-dimensional parameter spaces typical for models of biochemical signal transduction. To deal with this situation, we have developed the feedback loop breaking approach. This approach allows to characterise changes in the dynamical behaviour by conditions on the gain of the involved feedback loop. Based on this characterisation, an efficient algorithm to analyse the complex dynamical behaviour in terms of the feedback loop gain has been developed.
In summary, the feedback loop breaking approach is a powerful tool to analyse complex dynamical behaviour in biochemical networks. It is particularly suited to evaluate the influence of parameter variations on the dynamical behaviour of the network.
Characterisation of oscillatory behaviour via the feedback loop gain
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Estimation of parameter distributions in cell populations
Modeling in systems biology typically aims at achieving a quantitative description of intracellular signal transduction or differentiation processes at the cellular level. Most models are hereby based on experimental data obtained from cell populations and thus describe a 'typical single cell'. However, if the considered population shows high heterogeneity, as it is for instance the case in populations of cancer cells, where due to mutations some cells die and others stay alive after a therapy, this modeling approach is not optimal. In order to understand the dynamical behavior within such heterogeneous cell populations, a consideration of many cells within the whole population is crucial.
At the IST, we focus on identifying the parameter distribution within the cell population using numerical methods inspired from control engineering. The measurement data considered here are not trajectories of single cells as in classical approaches, because they are hard to obtain experimentally. Instead, the probability densities of the different measured concentrations within the population at different points in time are used. Such data sets are available on a suitable scale for instance from a newly developed measurement technology, the flow cytometric fluorescence microscopy, which is a combination of classical flow cytometry and fluorescence microscopy. Using these population measurements realistic cell population models with single cell resolution can be derived.
Cell viability within cancer cell population after stimulus with the anti-cancer drug TNF.
Such population models are suitable for a detailed analysis of heterogeneous populations and the selection of markers, e.g. for resistant cancer cells. Furthermore, the models allow for the development of control schemes to target heterogeneous cancer cell populations more efficiently. Hence, these modeling and identification methods can strongly improve the applicability of control engineering approaches in biological and medical application.
Activity levels of two marker proteins for cell death.
S. Waldherr, J. Hasenauer, and F. Allgöwer.|
Estimation of Biochemical Network Parameter Distributions in Cell Populations.
Proc. of the 15th IFAC Symposium an Systems Identification, Saint-Malo, France, July 2009.
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Statistical approaches for network inference from sparse data
One of the main issues in many modeling projects is the estimation of parameters from data,
usually formulated as an optimization problem with an objective function that is minimized
with respect to the parameters. Such inverse problems are particularly challenging for systems
biology approaches of intracellular networks for several reasons:
Interactions cannot be described linearly. Consequently, the underlying models are nonlinear,
leading to non-convex optimization problems with discontinuous objective function  or unstable
solutions with respect to data noise. Furthermore, the optimization requires efficient global
Data are typically noisy and sparse, i.e. the number of parameters exceeds the number
available measurements. In this setting, the standard mean squared error or maximum likelihood
estimators are inadequate, since they show fairly high variances across different experiments
and tend to overfit the data. Appropriate regularization methods are needed that can cope
with this problem.
Our research focuses on statistical learning methods for dynamic network models, in particular,
Bayesian regularization and network structure inference. Statistical approaches are particularly
tailored to handle sparse data sets. Moreover, they provide a natural framework to cope with
noisy data and hidden variables, as often encountered in biological data sets.
We have developed a stochastic modeling framework for the parameter estimation from time
series gene expression data [1,2]. Currently we are on the way to extend this work in several aspects:
Use hierarchical models to infer network structures or reveal hidden variables.
Compare the performance of statistical estimators with other regularization methods such as Tikhonov regularization.
Investigate different approaches to analyze posterior distributions. This is particularly
interesting for models with hidden variables or structure learning, since those contain
marginal likelihoods with high-dimensional integrals.
Use statistical frameworks for predictions and optimal experimental design.
Application to biological networks.
Time series constructed by a Hidden Markov model and variances θ1=0.5
for the evolution of the latent process X that cannot be directly observed
(blue line) and θ2=0.05 for the measurement error. Red dots indicate
discrete observations Y corrupted by measurement noise.
Likelihood surface of the time series shown in Figure 1. The likelihood function
L(θ) indicates how likely it is too see the data given the
stochastic model with parameters θ.
N. Radde, N. S. Bar, and A. Tresch.|
A comparison of likelihoods for dynamic stochastic models of biological networks.
In Proc. of the Workshop of Computational Biology, Aarhus, Denmark, 2009.
N. Radde, and L. Kaderali.|
A Bayes regularized ODE model for the inference of gene regulatory networks.
In: S. Das, D. Caragea, W. H. Hsu, and S. M. Welch (eds.), 'Computational Methods in Gene Regulatory Networks', in press.
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Modelling secretory activity at the trans-Golgi network in
The secretory pathway of the cell is highly regulated. Lipid-transferproteins
move key-proteins from the Endoplasmatic Reticulum to the
Golgi-Apparatus. These proteins are processed within the Golgi-
Apparatus inducing changes in the membrane lipid composition of the
Golgi-Apparatus itself. The changing of the membrane lipids composition
influences the organelles secretory activity. The secretory activity
is of high interrest since special cell lines are used to excrete therapeutic
substances. RNA based methods to increase the secretion of high
performance cell lines have almost reached a saturation level. The bottleneck
of the production is now located in the post-processing of the
substances in the Golgi. Golgi related protein interactions and their
regulation mechanisms is crucial for further tuning of the cell lines.
Many substances have already been identified to interact with each other in feedback loops . However
most of the publications focus on single interactions. Since the mentioned protein interactions
are highly connected we address this problem in a holistic way using the tools of systems biology.
This requires kinetic analysis of the secretory pathway. Time resolved data is acquired from special
cell lines to understand the regulatory mechanisms. In return, the optimized models can give feedback
which experiments can be performed to get a even deeper insight into the mechanisms.
Uncertainties of an estimated parameter vector visualized in parallel coordinates.
Fugmann, T.; Hausser, A.; Schoeffler, P.; Schmid, S.; Pfizenmaier, K. and Olayioye, M. A.
Regulation of secretory transport by protein kinase D-mediated phosphorylation of the ceramide
transfer protein. Journal of Cell Biology, University of Stuttgart, Institute of Cell Biology and
Immunology, 70569 Stuttgart, Germany., 2007, 178, 15-22
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Graph-based approaches for biological network analysis
Differential equation models have become a standard model class for intracellular processes in systems biology. Using chemical reaction kinetics to describe regulatory interactions such as transcriptional control leads to a class of systems whose Jacobian matrices have entries with constant signs. Such systems can naturally be represented by directed graphs with signed edges, termed interaction graphs. These graphs encode qualitative information about regulatory interactions, which is often available in many real settings, while at the same time quantitative measurements of kinetic rates are missing. It is thus convenient to ask what can be learned from this qualitative information about the dynamics of the systems.
In this model class, the dynamics is particularly simple for systems lacking feedback circuits; usually they have a unique globally stable steady state. More complex behavior such as bistability, hysteresis effects, memory or oscillations are caused by feedback structures. In the past, a lot of work has been spent to investigate the dynamics of single feedback graphs.
We are interested in analysis methods for larger networks of interrelated feedback structures . So far, most of the approaches for more complex networks are heuristic and thus rely to some extend on the details of the differential equation system. We are particularly interested in combining graph-theoretic approaches with dynamical systems theory and results which are independent of the exact formulation of the dynamical system. For example, the graph structure can be exploited for determining the steady states of the system.
Furthermore, similar graphical representations, the species-reaction graphs, have been introduced more recently for a model class called chemical reaction networks, and using these graphs for analyzing the behavior of chemical reaction systems has led to promising results. The theory is however not as complete as for regulatory networks and interaction graphs, and although several relations between these two model classes have already been revealed , this is still an open and interesting research field.
Feedback in dynamic network models can lead to complex behavior. Particularly interesting are networks of coupled feedback loops and statements that are solely based on the interaction graph.
N. Radde, N. S. Bar, and M. Banaji.|
Graphical methods for analysing feedback in biological networks - A survey.
International Journal of System Science, in press.
The impact of time-delays on the robustness of biological oscillators and the effect of bifurcations on the inverse problem.
Eurasip Journal on Bioinformatics and Systems Biology, 2009.
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Qualitative Modeling and Analysis of Gene Regulation Networks
Large networks of genes and gene products are at the core of many important cellular processes as they enable cells to
process extra- and intracellular signals and respond to them in an appropriate way.
Typical examples are differentiation decisions or the switching between operation modes.
Therefore, in order to understand a cell's behavior, it is essential to understand the involved gene regulation networks.
In order to find an adequate mathematical description for these network, the typical situation concerning the availability
of biological information has to be taken into account. On one side, one usually has assumptions about the involved genes
and proteins and how they influence each other, as for example knock-out or over-expression experiments allow for such conclusions.
On the other side, very little is known about the exact reaction kinetics as reaction speeds can usually not be measured.
Our goal is therefore the development of novel methods which allow to generate safe predictions about gene regulation networks despite
these large uncertainties. We recently introduced a modeling framework which can reflect these kinetic uncertainties by describing the
regulatory influence of a protein on another by monotonous activation and inhibition functions . Thereby, the exact shapes of
these functions need not to be known.
Building on this modeling framework, the important question of model validation can then be addressed.
Thereby, we focus on a certain property of the network, namely its ability to exhibit multistable behavior, which is a
recurrent motif in biology. The validation problem can be stated as follows: Can a given model structure in
principle, i.e., for a feasible choice of activation and inhibition functions, reproduce the experimentally observed operation modes?
Various methods based on concepts from systems and control theory were developed at our institute which can solve this
problem [1,2], thus allowing to verify or falsify a hypothetical model structure already at early stages of the modeling
Example of a large gene regulation network
As it is commonly assumed that biological systems have become very robust against common disturbances during evolution, we also ask the
important question which robustness properties already originate from the model structure and do not depend so much on a specific choice
of parameters. Again building on the same modeling framework, we currently focus on the development of appropriate robustness measures
and methods for their efficient computation. Results in this field will hopefully give more insight into the principles of cellular
M. Chaves, T. Eissing, and F. Allgöwer.
Bistable Biological Systems: A Characterization Through Local Compact Input-to State Stability.
IEEE Transactions on Automatic Control, Special Issue on Systems Biology, 53:87-100, 2008.
C. Breindl, and F. Allgöwer.
Verification of multistability in gene regulation networks: A combinatorial approach.
Proc. 48th IEEE Conf. Decision and Control (CDC), 2009.
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Modeling and analysis of bone growth
Bone provides mechanical support to joints and
tendons, protects vital
organs from damage, and plays an important role as reservoir for
calcium and phosphate in mineral homeostasis. However, in contrast to
common knowledge the human skeleton is a living, dynamic tissue whose
structure and shape is livelong evolving and adapting. The change in
structure and shape is achieved by a highly regulated interaction
between different cells involving numerous autocrine and paracrine
factors. In the process of remodeling osteoclasts resorb old bone,
while osteoblasts form new bone material. Many factors influence the
complex interplay between osteoclasts and osteoblasts. The
pathogenesis of many disorders such as osteoarthritis, osteoporosis,
and Paget's disease is related to disturbances in the
osteoclast-osteoblast interaction in various forms.
Besides metabolic and hormonal influences bone remodeling and growth
depends strongly on the stress acting on the bone, known as the
mechanostat theory. In this project we focus on the modeling,
analysis, and in the long run also control of force induced bone
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