@misc{BoerStoetzelRoeblitzetal.2010, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11682}, number = {10-06}, year = {2010}, abstract = {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.}, language = {en} } @misc{RoeblitzStoetzelDeuflhardetal.2011, author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12732}, number = {11-16}, year = {2011}, abstract = {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.}, language = {en} } @misc{StoetzelPloentzkeRoeblitz2011, author = {St{\"o}tzel, Claudia and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12740}, number = {11-17}, year = {2011}, abstract = {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.}, language = {en} } @article{RoeblitzStoetzelDeuflhardetal.2013, author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, volume = {321}, journal = {Journal of Theoretical Biology}, doi = {10.1016/j.jtbi.2012.11.020}, pages = {8 -- 27}, year = {2013}, language = {en} } @article{StoetzelPloentzkeHeuwieseretal.2012, author = {St{\"o}tzel, Claudia and Pl{\"o}ntzke, Julia and Heuwieser, Wolfgang and R{\"o}blitz, Susanna}, title = {Advances in modelling of the bovine estrous cycle: Synchronization with PGF2alpha}, volume = {78}, journal = {Theriogenology}, doi = {10.1016/j.theriogenology.2012.04.017}, pages = {1415 -- 1428}, year = {2012}, language = {en} } @article{DeuflhardRoeblitzStoetzel2010, author = {Deuflhard, Peter and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia}, title = {Mathematical Systems Biology at Zuse Institute Berlin (ZIB)}, volume = {39}, journal = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, year = {2010}, language = {en} } @article{BoerStoetzelRoeblitzetal.2011, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle}, volume = {278}, journal = {Journal of Theoretical Biology}, number = {1}, doi = {10.1016/j.jtbi.2011.02.021}, pages = {20 -- 31}, year = {2011}, language = {en} } @article{BoerRoeblitzStoetzeletal.2011, author = {Boer, H. Marike T. and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Veerkamp, Roel F. and Kemp, Bas and Woelders, Henri}, title = {Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model}, volume = {94}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2011-4400}, pages = {5987 -- 6000}, year = {2011}, language = {en} } @incollection{BoerStoetzelRoeblitzetal.2012, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Woelders, Henri}, title = {A differential equation model to investigate the dynamics of the bovine estrous cycle}, volume = {736}, booktitle = {Advances in Systems Biology}, doi = {10.1007/978-1-4419-7210-1_35}, pages = {597 -- 606}, year = {2012}, language = {en} } @article{BoerApriMolenaaretal.2012, author = {Boer, H. Marike T. and Apri, Mochamad and Molenaar, Jaap and St{\"o}tzel, Claudia and Veerkamp, Roel F. and Woelders, Henri}, title = {Candidate mechanisms underlying atypical progesterone profiles as deduced from parameter perturbations in a mathematical model of the bovine estrous cycle}, volume = {95}, journal = {Journal of Dairy Science}, number = {7}, doi = {10.3168/jds.2011-5241}, pages = {3837 -- 3851}, year = {2012}, language = {en} } @misc{StoetzelRoeblitzSiebert2015, author = {St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Siebert, Heike}, title = {Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation}, issn = {1438-0064}, doi = {10.1371/journal.pone.0140954}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56164}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{PloentzkeBergStoetzeletal.2015, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna}, title = {A systems biology approach to bovine fertility and metabolism: Introduction of a glucose insulin model}, booktitle = {15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, year = {2015}, language = {en} } @misc{StoetzelApriRoeblitz2014, author = {St{\"o}tzel, Claudia and Apri, Mochamad and R{\"o}blitz, Susanna}, title = {A reduced ODE model of the bovine estrous cycle}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51594}, year = {2014}, abstract = {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.}, language = {en} }