TY - GEN A1 - Stötzel, Claudia A1 - Apri, Mochamad A1 - Röblitz, Susanna T1 - A reduced ODE model of the bovine estrous cycle N2 - This work deals with the reduction of a previously developed ODE model for the bovine estrous cycle. After applying a method for exploring the parameter space by Apri et al. (2012), we perform structure-based reduction steps and several system specific adaptations. Overall, the original model consisting of 15 ODEs and 60 parameters is reduced to a model of 10 odes and 38 parameters. The reduced model qualitatively reproduces the state trajectories of the original model. T3 - ZIB-Report - 14-33 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51594 SN - 1438-0064 ER - TY - JOUR A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Deuflhard, Peter A1 - Jones, Hannah M. A1 - Azulay, David-Olivier A1 - van der Graaf, Piet A1 - Martin, Steven T1 - A mathematical model of the human menstrual cycle for the administration of GnRH analogues JF - Journal of Theoretical Biology Y1 - 2013 U6 - https://doi.org/10.1016/j.jtbi.2012.11.020 VL - 321 SP - 8 EP - 27 ER - TY - GEN A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Siebert, Heike T1 - Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation N2 - In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations. T3 - ZIB-Report - 15-46 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56164 SN - 1438-0064 ER - TY - GEN A1 - Stötzel, Claudia A1 - Ehrig, Rainald A1 - Boer, H. Marike T. A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis N2 - Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists. T3 - ZIB-Report - 16-02 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57039 SN - 1438-0064 ER - TY - GEN A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Stötzel, Claudia A1 - Röblitz, Susanna T1 - A systems biology approach to bovine fertility and metabolism: Development of a glucose insulin model. N2 - To counteract the antagonistic relationship between milk yield and fertility in dairy cow, a deeper understanding of the underlying biological mechanisms is required. For this purpose, we study physiological networks related to reproduction and metabolism in dairy cows. We interactively develop dynamic, mechanistic models by fitting the models to experimental data and mechanistic knowledge. We have already developed models for potassium balance and hormonal regulation of fertility in the dairy cow, which will briefly be reviewed here. The main focus of this article is a glucose-insulin model currently developed by us. This model links the bovine hormonal cycle and the potassium balance to glucose and thus to energy metabolism. The models can be applied in scientific research, education, experimental planning, drug development and production on farms. T3 - ZIB-Report - 15-51 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56453 SN - 1438-0064 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Siebert, Heike T1 - Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation JF - PLOS ONE Y1 - 2015 U6 - https://doi.org/10.1371/journal.pone.0140954 ER - TY - CHAP A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Stötzel, Claudia A1 - Röblitz, Susanna T1 - A systems biology approach to bovine fertility and metabolism: Introduction of a glucose insulin model T2 - 15th International Symposium on Mathematical and Computational Biology, Rorkee, India Y1 - 2015 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Röblitz, Susanna A1 - Stötzel, Claudia T1 - Mathematical Systems Biology at Zuse Institute Berlin (ZIB) JF - BioTOPics - Journal of Biotechnology in Berlin-Brandenburg Y1 - 2010 VL - 39 ER -