@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} } @misc{RoeblitzStoetzelDeuflhardetal., 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}, 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{StoetzelPloentzkeRoeblitz, 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}, 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} } @misc{BergRitterRoeblitz, author = {Berg, Mascha and Ritter, Julia and R{\"o}blitz, Susanna}, title = {A mathematical model for the Zinc response of young pigs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12191}, number = {11-05}, abstract = {In a number of studies the feeding of pharmacological levels of Zinc to weanling pigs was examined. The publications agree in the fact that the achieved performance increase of the pigs depends on the amount of Zinc as well as on the type of mineral complex used as feed additive. The results are based on measurements of the animals' body weight and the Zinc concentration in the blood within the first two weeks of the experiments. From the measurement values, conclusions are drawn about adequate Zinc doses, but a deeper understanding of the physiological processes that influence the Zinc distribution in the organism is still missing. In this report, we want to close this gap by using a systems biology approach. We present a small mathematical model that describes the organic feedback mechanisms with the help of differential equations. The simulation results not only match with measurement values, but also give insight into non-measurable processes, which will hopefully contribute to animal experiments being organized in a more selective and reduced way.}, language = {en} } @misc{PloentzkeBergOlanyetal., author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Olany, Amiya and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Modeling potassium balance in dairy cows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17749}, abstract = {Potassium is fundamental for cell functioning including signal transduction, acid-base- and water-metabolism. Since diet of dairy cows is generally rich in potassium, hypokalemia was not in the focus of research for long time. Furthermore, hypokalemia was not frequently diagnosed because blood potassium content is difficult to measure. In recent years, measurement methods have been improved. Nowadays hypokalemia is increasingly diagnosed in cows with disorders such as abomasal displacement, ketosis or down cow syndrome, calling for intensified research on this topic. In this report we describe the development of a basic mechanistic, dynamic model of potassium balance based on ordinary differential and algebraic equations. Parameter values are obtained from data of a clinical trial in which potassium balance and the influence of therapeutic intervention in glucose and electrolyte metabolism on potassium balance in non-lactating dairy cows were studied. The model is formulated at a high abstraction level and includes information and hypotheses from literature. This work represents a first step towards the understanding and design of effective prophylactic feed additives and treatment strategies.}, language = {en} } @article{GuptaGramatkeEinspanieretal.2017, author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, series = {Toxicology in Vitro}, volume = {41}, journal = {Toxicology in Vitro}, issn = {1438-0064}, pages = {179 -- 188}, year = {2017}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC50 on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC50 values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @misc{GuptaGramatkeEinspanieretal., author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silicio cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62666}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC_{50} on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC_{50} values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @misc{BondouyRoeblitz, author = {Bondouy, Manon and R{\"o}blitz, Susanna}, title = {Mathematical modeling of follicular development in bovine estrous cycles}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15585}, abstract = {Normal follicular growth is a prerequisite for successful fertilization of dairy cows. However, submission rates have been decreasing during the last decades because animals are not ovulating at the planned time of mating or insemination. In this study we use a mathematical model to investigate mechanisms that lead to anestrus. This model is derived by coupling two previously published models: a small model for the development of multiple follicles (Smith et al., 2004), and a large estrous cycle model (St\"otzel et al., 2012). We first investigate the influence of synchronization protocols on the time-shift of ovulation. In a second scenario we simulate an extended period of anestrus as it typically occurs after calving.}, language = {en} } @misc{Dierkes, author = {Dierkes, Thomas}, title = {Construction of ODE systems from time series data by a highly flexible modelling approach}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56768}, abstract = {In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y=f(t,y) of a dynamical system, a method determining the unknown right-hand side f(t,y) from some trajectory data y_k(t_j), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years [1], and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data [2].}, language = {en} } @misc{DierkesWadeNowaketal.2011, author = {Dierkes, Thomas and Wade, Moritz and Nowak, Ulrich and R{\"o}blitz, Susanna}, title = {BioPARKIN - Biology-related Parameter Identification in Large Kinetic Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12706}, number = {11-15}, year = {2011}, abstract = {Modelling, parameter identification, and simulation play an important r{\^o}le in Systems Biology. In recent years, various software packages have been established for scientific use in both licencing types, open source as well as commercial. Many of these codes are based on inefficient and mathematically outdated algorithms. By introducing the package BioPARKIN recently developed at ZIB, we want to improve this situation significantly. The development of the software BioPARKIN involves long standing mathematical ideas that, however, have not yet entered the field of Systems Biology, as well as new ideas and tools that are particularly important for the analysis of the dynamics of biological networks. BioPARKIN originates from the package PARKIN, written by P.Deuflhard and U.Nowak, that has been applied successfully for parameter identification in physical chemistry for many years.}, language = {en} }