@article{DeuflhardRoeblitzStoetzel, author = {Deuflhard, Peter and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia}, title = {Mathematical Systems Biology at Zuse Institute Berlin (ZIB)}, series = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, volume = {39}, journal = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, language = {en} } @book{DeuflhardRoeblitz, author = {Deuflhard, Peter and R{\"o}blitz, Susanna}, title = {A guide to numerical modelling in systems biology}, volume = {12}, publisher = {Springer}, isbn = {978-3-319-20058-3}, doi = {10.1007/978-3-319-20059-0}, 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}, series = {Advances in Systems Biology}, volume = {736}, booktitle = {Advances in Systems Biology}, doi = {10.1007/978-1-4419-7210-1_35}, pages = {597 -- 606}, year = {2012}, language = {en} } @misc{BoerStoetzelRoeblitzetal., 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}, 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} } @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}, series = {Journal of Theoretical Biology}, 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}, series = {Journal of Dairy Science}, volume = {94}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2011-4400}, pages = {5987 -- 6000}, year = {2011}, language = {en} } @misc{BockmayrSiebertRoeblitzetal., author = {Bockmayr, Alexander and Siebert, Heike and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof and Deuflhard, Peter}, title = {Advanced mathematical modeling in systems biology}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutela, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {29 -- 44}, language = {en} } @article{BergPloentzkeLeonhardMareketal., author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {A dynamic model to simulate potassium balance in dairy cows}, series = {Journal of Dairy Science}, volume = {100}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2016-12443}, pages = {9799 -- 9814}, abstract = {High-performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one being potassium, is indispensable for the prevention of imbalances. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and it is closely related to glucose and electrolyte metabolism. In this paper, we present a dynamical model for potassium balance in lactating and nonlactating dairy cows based on ordinary differential equations. Parameter values were obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for 3 different scenarios: potassium balance in (1) nonlactating cows with varying feed intake, (2) nonlactating cows with varying potassium fraction in the diet, and (3) lactating cows with varying milk production levels. The results give insights into the short- and long-term potassium metabolism, providing an important step toward the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} }