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.

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.

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.

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 [1]. 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.

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 [2]. 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 [1], this is still an open and interesting research field.

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 [1]. 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 process.

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 growth.