Discrimination of dynamical system models for biological and chemical processes

Lorenz, Sönke; Diederichs, Elmar; Telgmann, Regina; Schütte, Christof

doi:10.1002/jcc.20674

Cited by 8 publications

(8 citation statements)

References 29 publications

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“…Due to measurement inaccuracies, there is uncertainty about those parameters up to a confidence region representing a level of significance. Additionally, biological systems might involve intrinsically distributed parameters leading to the effect of distributed determinism as pointed out in [18], [19]. Hence, it is desirable to have new experimental designs with both great discrimination power as well as keeping the ability to distinguish between the models even for inappropriate parameter settings within some confidence region.…”

Section: Methodsmentioning

confidence: 99%

Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool

2013

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Mathematical modeling of biochemical processes significantly contributes to a better understanding of biological functionality and underlying dynamic mechanisms. To support time consuming and costly lab experiments, kinetic reaction equations can be formulated as a set of ordinary differential equations, which in turn allows to simulate and compare hypothetical models in silico. To identify new experimental designs that are able to discriminate between investigated models, the approach used in this work solves a semi-infinite constrained nonlinear optimization problem using derivative based numerical algorithms. The method takes into account parameter variabilities such that new experimental designs are robust against parameter changes while maintaining the optimal potential to discriminate between hypothetical models. In this contribution we present a newly developed software tool that offers a convenient graphical user interface for model discrimination. We demonstrate the beneficial operation of the discrimination approach and the usefulness of the software tool by analyzing a realistic benchmark experiment from literature. New robust optimal designs that allow to discriminate between the investigated model hypotheses of the benchmark experiment are successfully calculated and yield promising results. The involved robustification approach provides maximally discriminating experiments for the worst parameter configurations, which can be used to estimate the meaningfulness of upcoming experiments. A major benefit of the graphical user interface is the ability to interactively investigate the model behavior and the clear arrangement of numerous variables. In addition to a brief theoretical overview of the discrimination method and the functionality of the software tool, the importance of robustness of experimental designs against parameter variability is demonstrated on a biochemical benchmark problem. The software is licensed under the GNU General Public License and freely available at http://sourceforge.net/projects/mdtgui/.

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Section: Methodsmentioning

confidence: 99%

Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool

2013

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“…In the case of the existence of multiple steady states, this spreading effect might even be more pronounced. Varying parameters during the measuring procedure and local parameter perturbations by non-stationary noise also contribute to a distributed measurement signal (Lorenz et al , 2007). Complex, nonlinear models of biological systems might also behave chaotic, further contributing to distributed response measurements.…”

Section: Methodsmentioning

confidence: 99%

“…In this work, we use the overlap as defined in Equation (9) with p = 1, which we refer to as model overlap , as this directly represent the time-averaged, expected likelihood of one model under the other. In this form, it has been applied by Lorenz et al , (2007) to discriminate dynamic models based on the distributional fit performance. In Schenkendorf et al , (2009b), it is used to optimize an initial condition for a substrate uptake model to discriminate two competing kinetic approaches.…”

Section: Methodsmentioning

confidence: 99%

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Flassig¹,

Sundmacher²

2012

Bioinformatics

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Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs).Results: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning.Availability: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html.Contact: flassig@mpi-magdeburg.mpg.deSupplementary information: Supplementary data are are available at Bioinformatics online.

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“…POEM is based on damped Gauss-Newton techniques for solving the above optimization problem. Lack of robustness of damped Gauss-Newton techniques as observed often in model discrimination contexts, see [25], can be overcome by using dimension reduction in parameter space [26].…”

Section: Methodsmentioning

confidence: 99%

Inferring Proteolytic Processes from Mass Spectrometry Time Series Data Using Degradation Graphs

et al. 2012

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BackgroundProteases play an essential part in a variety of biological processes. Besides their importance under healthy conditions they are also known to have a crucial role in complex diseases like cancer. In recent years, it has been shown that not only the fragments produced by proteases but also their dynamics, especially ex vivo, can serve as biomarkers. But so far, only a few approaches were taken to explicitly model the dynamics of proteolysis in the context of mass spectrometry.ResultsWe introduce a new concept to model proteolytic processes, the degradation graph. The degradation graph is an extension of the cleavage graph, a data structure to reconstruct and visualize the proteolytic process. In contrast to previous approaches we extended the model to incorporate endoproteolytic processes and present a method to construct a degradation graph from mass spectrometry time series data. Based on a degradation graph and the intensities extracted from the mass spectra it is possible to estimate reaction rates of the underlying processes. We further suggest a score to rate different degradation graphs in their ability to explain the observed data. This score is used in an iterative heuristic to improve the structure of the initially constructed degradation graph.ConclusionWe show that the proposed method is able to recover all degraded and generated peptides, the underlying reactions, and the reaction rates of proteolytic processes based on mass spectrometry time series data. We use simulated and real data to demonstrate that a given process can be reconstructed even in the presence of extensive noise, isobaric signals and false identifications. While the model is currently only validated on peptide data it is also applicable to proteins, as long as the necessary time series data can be produced.

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Discrimination of dynamical system models for biological and chemical processes

Cited by 8 publications

References 29 publications

Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool

Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Inferring Proteolytic Processes from Mass Spectrometry Time Series Data Using Degradation Graphs

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