TY - GEN A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions N2 - Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences. T3 - ZIB-Report - 10-06 KW - cow KW - reproduction KW - hormone patterns KW - ordinary differential equations KW - systems biology Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11682 SN - 1438-0064 ER - TY - GEN 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 N2 - This study presents a differential equation model for the feedback mechanisms between Gonadotropin-releasing Hormone (GnRH), Follicle-Stimulating Hormone (FSH), Luteinizing Hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women. Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle. T3 - ZIB-Report - 11-16 KW - human menstrual cycle KW - systems biology KW - mathematical modelling KW - GnRH analogues KW - differential equations Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12732 ER - TY - GEN A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha N2 - Our model of the bovine estrous cycle is a set of ordinary differential equations which generates hormone profiles of successive estrous cycles with several follicular waves per cycle. It describes the growth and decay of the follicles and the corpus luteum, as well as the change of the key substances over time. In this work we describe recent improvements of this model, including the introduction of new components, and elimination of time delays. We validate our model by showing that the simulations agree with observations from synchronization studies and with measured progesterone data after a single dose administration of synthetic prostaglandin F2alpha. T3 - ZIB-Report - 11-17 KW - cow KW - reproduction KW - hormone patterns KW - differential equations KW - systems biology Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12740 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle JF - Journal of Theoretical Biology Y1 - 2011 U6 - https://doi.org/10.1016/j.jtbi.2011.02.021 VL - 278 IS - 1 SP - 20 EP - 31 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Veerkamp, Roel F. A1 - Kemp, Bas A1 - Woelders, Henri T1 - Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model JF - Journal of Dairy Science Y1 - 2011 U6 - https://doi.org/10.3168/jds.2011-4400 VL - 94 IS - 12 SP - 5987 EP - 6000 ER - TY - CHAP A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Woelders, Henri T1 - A differential equation model to investigate the dynamics of the bovine estrous cycle T2 - Advances in Systems Biology Y1 - 2012 U6 - https://doi.org/10.1007/978-1-4419-7210-1_35 VL - 736 SP - 597 EP - 606 ER - TY - JOUR A1 - Boer, H. Marike T. A1 - Apri, Mochamad A1 - Molenaar, Jaap A1 - Stötzel, Claudia A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - Candidate mechanisms underlying atypical progesterone profiles as deduced from parameter perturbations in a mathematical model of the bovine estrous cycle JF - Journal of Dairy Science Y1 - 2012 UR - http://www.sciencedirect.com/science/article/pii/S0022030212003621 U6 - https://doi.org/10.3168/jds.2011-5241 VL - 95 IS - 7 SP - 3837 EP - 3851 ER - TY - JOUR A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Heuwieser, Wolfgang A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Synchronization with PGF2alpha JF - Theriogenology Y1 - 2012 U6 - https://doi.org/10.1016/j.theriogenology.2012.04.017 VL - 78 SP - 1415 EP - 1428 ER - TY - JOUR 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 JF - BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland 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. Y1 - 2014 ER - TY - THES A1 - Stötzel, Claudia T1 - Numerical and Discrete Modeling of Reproductive Endocrinological Networks N2 - This thesis deals with the mathematical modeling of endocrinological networks that are underlying the female hormone cycle. These networks consist of a variety of biological mechanisms in different parts of the organism. Their interaction leads to periodic changes of various substances that are necessary for reproduction. In every cycle, hormones are secreted from the hypothalamic-pituitary-gonadal axis into the bloodstream, where they distribute and influence several functions in the body. Their most important task in reproduction is to regulate processes in the ovaries, where follicles and corpus luteum develop. These produce steroids that are released into the blood and from therein regulate the processes in the hypothalamic-pituitary-gonadal axis. The hormonal cycle is thus a result of a large feedback loop, whose self-regulation is a complex interplay of multiple components. For the modeling of these processes, a high abstraction level is required, which can be realized by various modeling approaches. In this work, some of these approaches are implemented. The first step in all approaches is the representation of the most important mechanisms in a flowchart. In the next step, this can be implemented as a system of ordinary differential equations using Hill functions, as a piecewise defined affine differential equation model, or directly as a purely regulatory model. Using this approach, a differential equation model for the hormonal cycle of cows is developed. This is compared with a more advanced model of the menstrual cycle in humans. Both models are validated by comparing simulations with measured values, and by studying external influences such as drug administration. For the example of the bovine estrous cycle, continuous analysis methods are used to investigate stability, follicular wave patterns, and robustness with respect to parameter perturbations. Furthermore, the model is substantially reduced while preserving the main simulation results. To take a look at alternative modeling approaches, corresponding discrete models are derived, exemplified for the bovine model. For a piecewise affine version of the model, parameter constraints for the continuous model are calculated. Stability is analyzed globally for a purely discrete model. In addition, core discrete models are derived, which retain the dynamic properties of the original model. Y1 - 2014 ER - 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 -