Browsing by Author "Waldherr, Steffen"

Now showing 1 - 5 of 5

Open Access
Efficient parametric analysis of the chemical master equation through model order reduction
(2012) Waldherr, Steffen; Haasdonk, Bernard
BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.RESULTS:In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.
Open Access
Identification of models of heterogeneous cell populations from population snapshot data
(2011) Hasenauer, Jan; Waldherr, Steffen; Doszczak, Malgorzata; Radde, Nicole; Scheurich, Peter; Allgöwer, Frank
Background: Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations. Results: In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed. Conclusions: The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets.
Open Access
Observability analysis and observer design for controlled population dynamics
(2005) Waldherr, Steffen
The diploma thesis studies the design of nonlinear observers with exactly linear error dynamics via transformation or immersion into an appropriate observer canonical form. A model for the dynamics of two interacting species, which was derived as a generalisation of the predator-prey model by Lotka and Volterra, is used as benchmark system for this design. In particular, an additional control input is modelled in three ways. As observability of the system is a necessary condition for observer design, the methods for an observability analysis are presented and applied to the model. After that, the theoretical basics of the observer design methods are described and used for the design of an observer with exactly linear error dynamics, with regard to the results from the observability analysis. The observers are designed as Luenberger observers with output injection for the uncontrolled system and with input/output injection for the controlled systems. Some new studies concern the invariance properties of the nonlinear observers on a state region which is relevant for the system. For this purpose, the notation of invariant observers is introduced, which guarantee a global observation of the system on the relevant region. Based on the considered observer canonical form, this notation helps to develop some general methods how to design such observers.
Open Access
Uncertainty and robustness analysis of biochemical reaction networks via convex optimisation and robust control theory
(2009) Waldherr, Steffen; Allgöwer, Frank (Prof. Dr.-Ing.)
In the area of systems biology, dynamical models of biochemical reaction networks are used to derive model-based predictions about the related biological processes. This thesis provides new methods to study how parametric uncertainty affects such predictions. The focus of this study is on predictions about the steady states and the type of dynamical behaviour, such as bistability or oscillations. Concerning steady states, the problem of uncertainty analysis is investigated. For a given extent of parametric uncertainty, the objective is to compute bounds on the variations in the steady states. In view of an underlying feasibility problem, a method based on semidefinite programming is developed to solve this problem. The approach is also applied to compute a measure for the robustness of the location of steady states in the presence of parametric uncertainty. Regarding the effect of parametric uncertainty on the type of dynamical behaviour, the robustness problem is considered. A robustness measure is defined by the extent of parametric uncertainty for which no local bifurcations occur. An approach to solve the robustness problem with frequency domain methods is investigated. The proposed feedback loop breaking method allows to characterise parametric uncertainties for which the type of dynamical behaviour is robust. On the one hand, a lower bound on the corresponding robustness measure is computed by providing Positivstellensatz infeasibility certificates for the underlying equations. On the other hand, the feedback loop breaking concept is adopted for the design of a bifurcation search algorithm in a high-dimensional parameter space. The results of the search algorithm thereby provide an upper bound on the robustness measure. In addition, the novel concept of kinetic perturbations is introduced. This is a class of specific parametric uncertainties which are particularly useful for the analysis of biochemical reaction networks. It is shown that a robustness analysis is performed efficiently for kinetic perturbations by use of the structured singular value. As a side result, the direct relation between kinetic perturbations and changes to the sensitivity of steady states in a biochemical reaction network is demonstrated. To complement the methodological results, a novel model for a specific biochemical signal transduction system within the TNF induced signalling network is constructed. The model is analysed with methods developed in this thesis. In addition to an illustrative application of the new methods, the findings of this analysis also provide new biological insight into TNF signal transduction.
Open Access
Zwei Algorithmen zur Zuflussregelung an Schnellstraßen : Implementation und Vergleich in einer mikroskopischen Verkehrsflusssimulation
(2004) Waldherr, Steffen
Es werden zwei Verfahren zur Zuflussregelung an Schnellstraßenauffahrten verglichen: Das ALINEA-Verfahren und die Fuzzy-Zuflussregelung nach Bogenberger. Beide Verfahren wurden dazu für ein in der mikroskopischen Simulationsumgebung VISSIM erstelltes Verkehrsnetz implementiert. Durch Simulation mit unterschiedlichen Belastungsfällen werden die Auswirkungen der Zuflussregelung auf den Verkehrszustand ermittelt. Mit diesen Ergebnissen werden die beiden Verfahren untereinander und mit dem ungeregelten Fall verglichen.