@misc{BergPloentzkeLeonhardMareketal.2017, 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.}, issn = {1438-0064}, doi = {10.3168/jds.2016-12443}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64756}, year = {2017}, 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 of them being potassium, is indispensable for the prevention of imbalances. The potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, it is closely related with the glucose and electrolyte metabolism. In this paper, we present a dynamical model for the potassium balance in lactating and non-lactating dairy cows based on ordinary differential equations. Parameter values are obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for three different scenarios: potassium balance in (i) non-lactating cows with varying feed intake, (ii) non-lactating cows with varying potassium fraction in the diet, and (iii) lactating cows with varying milk production levels. The results give insights into the short and long term potassium metabolism, providing an important step towards the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} } @misc{LangeSchwiegerPloentzkeetal.2017, author = {Lange, Alexander and Schwieger, Robert and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular competition: the selection of dominant follicles as a synergistic effect}, issn = {1438-0064}, doi = {https://doi.org/10.1007/s00285-018-1284-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63863}, year = {2017}, abstract = {The estrous cycle of mono-ovulatory species such as cows or humans, is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the omega-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.}, language = {en} } @misc{StoetzelEhrigBoeretal.2016, author = {St{\"o}tzel, Claudia and Ehrig, Rainald and Boer, H. Marike T. and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57039}, year = {2016}, abstract = {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.}, language = {en} } @misc{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: Development of a glucose insulin model.}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56453}, year = {2015}, abstract = {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.}, language = {en} } @article{BergPloentzkeLeonhardMareketal.2017, 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}, volume = {100}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2016-12443}, pages = {9799 -- 9814}, year = {2017}, 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} } @article{BergPloentzkeSiebertetal.2021, author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, year = {2021}, abstract = {Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.}, language = {en} }