@article{WeberFischerDamerauetal., author = {Weber, Marie-Christin and Fischer, Lisa and Damerau, Alexandra and Ponomarev, Igor and Pfeiffenberger, Moritz and Gaber, Timo and G{\"o}tschel, Sebastian and Lang, Jens and R{\"o}blitz, Susanna and Buttgereit, Frank and Ehrig, Rainald and Lang, Annemarie}, title = {In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis}, series = {BioRxiv}, journal = {BioRxiv}, doi = {10.1101/725317}, abstract = {Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies.}, language = {en} } @article{WeberFischerDamerauetal., author = {Weber, Marie-Christin and Fischer, Lisa and Damerau, Alexandra and Ponomarev, Igor and Pfeiffenberger, Moritz and Gaber, Timo and G{\"o}tschel, Sebastian and Lang, Jens and R{\"o}blitz, Susanna and Buttgereit, Frank and Ehrig, Rainald and Lang, Annemarie}, title = {Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation}, series = {Biofabrication}, volume = {12}, journal = {Biofabrication}, number = {4}, doi = {10.1088/1758-5090/aba08f}, abstract = {Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and i) characterized regarding their cellular and matrix composition or secondly ii) treated with interleukin-1β (IL-1β) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate distribution of IL-1β, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aim to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.}, language = {en} } @misc{StoetzelRoeblitzSiebert, 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}, 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} } @article{StoetzelRoeblitzSiebert, 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}, series = {PLOS ONE}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0140954}, 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} } @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}, series = {Theriogenology}, volume = {78}, journal = {Theriogenology}, doi = {10.1016/j.theriogenology.2012.04.017}, pages = {1415 -- 1428}, year = {2012}, language = {en} } @article{StoetzelEhrigBoeretal., 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}, series = {BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland}, journal = {BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland}, 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{StoetzelEhrigBoeretal., 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}, 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{StoetzelApriRoeblitz, 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}, 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} } @inproceedings{SchaeferPloentzkeRoeblitz, author = {Sch{\"a}fer, Stefan and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Mathematical Modelling of Follicular Maturation in Cows and Women}, series = {49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterin{\"a}r-Humanmedizinische Gemeinschaftstagung 2016, Leipzig.}, booktitle = {49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterin{\"a}r-Humanmedizinische Gemeinschaftstagung 2016, Leipzig.}, language = {en} } @misc{SchwiegerSiebertRoeblitz, author = {Schwieger, Robert and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Correspondence of Trap Spaces in Different Models of Bioregulatory Networks}, issn = {1438-0064}, doi = {https://doi.org/10.1137/17M1155302}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67121}, abstract = {Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.}, language = {en} } @article{SchwiegerSiebertRoeblitz, author = {Schwieger, Robert and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Correspondence of Trap Spaces in Different Models of Bioregulatory Networks}, series = {SIAM Journal on Applied Dynamical Systems}, volume = {17}, journal = {SIAM Journal on Applied Dynamical Systems}, number = {2}, doi = {https://doi.org/10.1137/17M1155302}, pages = {1742 -- 1765}, abstract = {Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.}, language = {en} } @article{RoeblitzWeber, author = {R{\"o}blitz, Susanna and Weber, Marcus}, title = {Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification}, series = {Advances in Data Analysis and Classification}, volume = {7}, journal = {Advances in Data Analysis and Classification}, number = {2}, doi = {10.1007/s11634-013-0134-6}, pages = {147 -- 179}, language = {en} } @article{RoeblitzWeber, author = {R{\"o}blitz, Susanna and Weber, Marcus}, title = {Fuzzy Spectral Clustering by PCCA+}, series = {Classification and Clustering: Models, Software and Applications}, journal = {Classification and Clustering: Models, Software and Applications}, number = {WIAS Report No. 26}, pages = {73 -- 79}, 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} } @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}, series = {Journal of Theoretical Biology}, volume = {321}, journal = {Journal of Theoretical Biology}, doi = {10.1016/j.jtbi.2012.11.020}, pages = {8 -- 27}, year = {2013}, language = {en} } @phdthesis{Roeblitz, author = {R{\"o}blitz, Susanna}, title = {Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000008079-9}, abstract = {The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.}, language = {en} } @article{ReuterWeberFackeldeyetal.2018, author = {Reuter, Bernhard and Weber, Marcus and Fackeldey, Konstantin and R{\"o}blitz, Susanna and Garcia, Martin E.}, title = {Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid β Conformational Dynamics Driven by an Oscillating Electric Field}, series = {Journal of Chemical Theory and Computation}, volume = {14}, journal = {Journal of Chemical Theory and Computation}, number = {7}, doi = {10.1021/acs.jctc.8b00079}, pages = {3579 -- 3594}, year = {2018}, abstract = {Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems. To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid β (1-40) peptide, periodically driven by an oscillating electric field.}, language = {en} } @misc{PloentzkeBergStoetzeletal., 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}, 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} } @inproceedings{PloentzkeBergStoetzeletal., 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}, series = {15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, booktitle = {15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, language = {en} } @misc{PloentzkeBergRoeblitz, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and R{\"o}blitz, Susanna}, title = {A mathematical modelling approach to the insight of dynamic networks: Potassium homeostasis and glucose-insulin in dairy cows}, series = {ADSA 2018 Annual Meeting}, volume = {101 Suppl. 2}, journal = {ADSA 2018 Annual Meeting}, edition = {Journal of Dairy Science}, publisher = {American Dairy Science Association}, pages = {226 -- 227}, abstract = {Lactating dairy cows require a particular composition of nutritional ingredients depending on their production status. The optimal supply of energy and minerals in diet, one of them potassium, is indispensable for the prevention of disbalances like hypokalemia or hypoglycaemia. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and closely interacts with glucose and electrolyte metabolism, in which postpartum veterinary treatments frequently intervene. We present a mechanistic, dynamic model for potassium balance together with a glucose insulin model in non-lactating and lactating dairy cows based on ordinary differential equations. Parameter values were obtained from data of a clinical trial as well as from literature. To verify the mechanistic functioning of the model, we validate the model by comparing simulation outcomes with clinical study findings. Furthermore we perform numerical experiments and compare them with expected behaviour according to mechanistic knowledge. The results give insight into the dynamic behaviour of the network and open the way for further open questions and hypothesis to be tested.}, 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{PloentzkeBergEhrigetal., author = {Pl{\"o}ntzke, Julia and Berg, Mascha and Ehrig, Rainald and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {Model Based Exploration of Hypokalemia in Dairy Cows}, series = {Scientific Reports}, volume = {12, 19781}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-22596-0}, abstract = {Hypokalemia, characterized by too low serum potassium levels, is a severe mineral disorder which can be life threatening. It is increasingly diagnosed in veterinarian healthcare and a topic of ongoing research. In this paper, we explore the different originating conditions of hypokalemia: reduced potassium intake, increased excretion, acid-base disturbances, or increased insulin, by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. Simulations are compared with literature. The results give insights into the network dynamics and point to scenarios on which experimental effort should be focused. Application of mathematical models can assist in experimental planning as well as the reduction, refinement and replacement of animal experiments.}, language = {en} } @misc{OmariPloentzkeRoeblitz, author = {Omari, Mohamed and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {A pharmacokinetic-pharmacodynamic model for single dose administration of Dexamethasone in dairy cows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75043}, abstract = {We present a mechanistic pharmacokinetic-pharmacodynamic model to simulate the effect of dexamethasone on the glucose metabolism in dairy cows. The coupling of the pharmacokinetic model to the pharmacodynamic model is based on mechanisms underlying homeostasis regulation by dexamethasone. In particular, the coupling takes into account the predominant role of dexamethasone in stimulating glucagon secretion, glycogenolysis and lipolysis and in impairing the sensitivity of cells to insulin. Simulating the effect of a single dose of dexamethasone on the physiological behaviour of the system shows that the adopted mechanisms are able to induce a temporary hyperglycemia and hyperinsulinemia, which captures the observed data in non-lactating cows. In lactating cows, the model simulations show that a single dose of dexamethasone reduces the lipolytic effect, owing to the reduction of glucose uptake by the mammary gland.}, language = {en} } @misc{OmariPloentzkeBergetal., author = {Omari, Mohamed and Pl{\"o}ntzke, Julia and Berg, Mascha and R{\"o}blitz, Susanna}, title = {Modelling of glucose-insulin metabolism and its effect on the estrous cycle in bovine}, series = {Annual Meeting of the Population Approach Group in Europe}, journal = {Annual Meeting of the Population Approach Group in Europe}, language = {en} } @article{OmariLangePloentzkeetal.2019, author = {Omari, Mohamed and Lange, Alexander and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows}, series = {Biology Direct}, volume = {15}, journal = {Biology Direct}, doi = {10.1186/s13062-019-0256-7}, year = {2019}, language = {en} } @misc{OmariLangePloentzkeetal., author = {Omari, Mohamed and Lange, Alexander and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {A Mathematical Model for the Influence of Glucose-Insulin Dynamics on the Estrous Cycle in Dairy Cows}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73475}, abstract = {Nutrition plays a crucial role in regulating reproductive hormones and follicular development in cattle. This is visible particularly during the time of negative energy balance at the onset of milk production after calving. Here, elongated periods of anovulation have been observed, resulting from alterations in luteiniz- ing hormone concentrations, likely caused by lower glucose and insulin concen- trations in the blood. The mechanisms that result in a reduced fertility are not completely understood, although a close relationship to the glucose-insulin metabolism is widely supported. Following this idea, a mathematical model of the hormonal network combining reproductive hormones and hormones that are coupled to the glucose compartments within the body of the cow was developed. The model is built on ordinary differential equations and relies on previously introduced models on the bovine estrous cycle and the glucose-insulin dynam- ics. Necessary modifications and coupling mechanisms are thoroughly discussed. Depending on the composition and the amount of food, in particular the glu- cose content in the dry matter, the model quantifies reproductive hormones and follicular development over time. Simulation results for different nutritional regimes in lactating and non-lactating dairy cows are examined and compared with experimental studies. Regarding its applicability, this work is an early attempt towards developing in silico feeding strategies and may eventually help refining and reducing animal experiments.}, language = {en} } @misc{MoualeuNgangueRoeblitzEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification for a Tuberculosis Model in Cameroon}, issn = {1438-0064}, doi = {10.1371/journal.pone.0120607}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43087}, abstract = {A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years.}, language = {en} } @article{MoualeuNgangueRoeblitzEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification in a Tuberculosis Model for Cameroon}, series = {PLOS ONE}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0120607}, abstract = {A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.}, language = {en} } @misc{MeiselRoeblitz2013, author = {Meisel, Kristin and R{\"o}blitz, Susanna}, title = {Mathematische Modellierung der Knochenremodellierung}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42010}, year = {2013}, abstract = {Knochenremodellierung beinhaltet den Auf- und Abbau der Knochenmasse durch die verschiedenen Knochenzellen und findet fast {\"u}berall, auch am Skelett Erwachsener, statt. F{\"u}r die Erneuerung der Knochensubstanz sind die Osteoblasten zust{\"a}ndig. Sie ersetzen exakt die Menge der Knochenmasse, welche zuvor durch Osteoklasten abgebaut wurde. St{\"o}rungen dieses, durch viele Faktoren beeinflussten Prozesses f{\"u}hren zu pathologischen Ver{\"a}nderungen, beispielsweise zu Osteoporose oder Arthritis. Auf der Grundlage analysierter publizierter Modelle wurde ein Modell entwickelt, welches den Einfluss einiger dieser Faktoren realistisch abbildet. Auf diese Weise kann die Wirkung von basalem PTH, des RANKL-OPG-Systems ( RANKL: Receptor activator of nuclear factor kappa-B ligand, OPG: Osteoprotegerin) und des Estradiols auf den Knochenstoffwechsel am vorgestellten System untersucht werden. Außerdem wurde durch Estradiolmangel hervorgerufene Osteoporose und der kurative Effekt von synthetischen Medikamenten wie Estradiol oder intermittierend verabreichtem PTH modelliert. Mit der Parametersch{\"a}tzung anhand des Gauß-Newton-Verfahrens wird des Weiteren eine Methode vorgestellt, die es erm{\"o}glicht, mathematische Modelle bestm{\"o}glich durch Variation der Parameterwerte an experimentelle Daten anzupassen. Das am Zuse-Institut Berlin entwickelte Softwarepaket POEM wendet diesen Algorithmus an und wird ebenfalls erl{\"a}utert.}, language = {de} } @inproceedings{ManciniSalvoMarietal., author = {Mancini, Toni and Salvo, Ivano and Mari, Federico and Melatti, Igor and Massini, Annalisa and Sinisi, Stefano and Tronci, Enrico and Davi, Francesco and Dierkes, Thomas and Ehrig, Rainald and R{\"o}blitz, Susanna and Leeners, Brigitte and Kr{\"u}ger, Tillmann H. C. and Egli, Marcel and Ille, Fabian}, title = {Patient-Specific Models from Inter-Patient Biological Models and Clinical Records}, series = {Proceedings of the 14th Conference on Formal Methods in Computer-Aided Design (FMCAD 2014)}, booktitle = {Proceedings of the 14th Conference on Formal Methods in Computer-Aided Design (FMCAD 2014)}, pages = {207 -- 214}, language = {en} } @inproceedings{ManciniMariMassinietal., author = {Mancini, Toni and Mari, Federico and Massini, Annalisa and Melatti, Igor and Salvo, Ivano and Sinisi, Stefano and Tronci, Enrico and Ehrig, Rainald and R{\"o}blitz, Susanna and Leeners, Brigitte}, title = {Computing Personalised Treatments through In Silico Clinical Trials. A Case Study on Downregulation in Assisted Reproduction}, series = {Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion, Workshop of the Federated Logic Conference 2018 (FLoC 2018), Oxford}, booktitle = {Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion, Workshop of the Federated Logic Conference 2018 (FLoC 2018), Oxford}, doi = {10.29007/g864}, pages = {1 -- 16}, abstract = {In Silico Clinical Trials (ISCT), i.e., clinical experimental campaigns carried out by means of computer simulations, hold the promise to decrease time and cost for the safety and efficacy assessment of pharmacological treatments, reduce the need for animal and human testing, and enable precision medicine. In this paper we present a case study aiming at quantifying, by means of a multi-arm ISCT supervised by intelligent search, the potential impact of precision medicine approaches on a real pharmacological treatment, namely the downregulation phase of a complex clinical protocol for assisted reproduction.}, language = {en} } @article{LeenersKruegerGeraedtsetal., author = {Leeners, Brigitte and Kr{\"u}ger, Tillmann H. C. and Geraedts, Kirsten and Tronci, Enrico and Mancini, Toni and Ille, Fabian and Egli, Marcel and R{\"o}blitz, Susanna and Saleh, Lanja and Spanhaus, K. and Schippert, Cordula and Zhang, Y. and Hengartner, M. P.}, title = {Lack of association between female hormone levels and visuospatial working memory, divided attention and cognitive bias across two consecutive menstrual cycles}, series = {Front. Behav. Neurosci.}, journal = {Front. Behav. Neurosci.}, doi = {10.3389/fnbeh.2017.00120}, language = {en} } @misc{LasserRoeblitz, author = {Lasser, Caroline and R{\"o}blitz, Susanna}, title = {Computing expectation values for molecular quantum dynamics}, issn = {1438-0064}, doi = {/10.1137/090770461}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11461}, number = {09-30}, abstract = {We compute expectation values for the solution of the nuclear Schr{\"o}dinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.}, language = {en} } @article{LasserRoeblitz2010, author = {Lasser, Caroline and R{\"o}blitz, Susanna}, title = {Computing expectation values for molecular quantum dynamics}, series = {SIAM Journal on Scientific Computing}, volume = {32}, journal = {SIAM Journal on Scientific Computing}, number = {3}, doi = {/10.1137/090770461}, pages = {1465 -- 1483}, year = {2010}, language = {en} } @misc{LangeSchwiegerPloentzkeetal., 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}, 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} } @article{LangeSchwiegerPloentzkeetal., author = {Lange, Alexander and Schwieger, Robert and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular competition in cows: the selection of dominant follicles as a synergistic effect}, series = {Journal of Mathematical Biology}, journal = {Journal of Mathematical Biology}, doi = {https://doi.org/10.1007/s00285-018-1284-0}, abstract = {The reproductive 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 ω-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} } @inproceedings{LangePloentzkeSchaeferetal., author = {Lange, Alexander and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular maturation in cows: mathematical models and data}, series = {10. European Conference on Mathematical and Theoretical Biology}, booktitle = {10. European Conference on Mathematical and Theoretical Biology}, language = {en} } @article{LangVolkamerBehmetal., author = {Lang, Annemarie and Volkamer, Andrea and Behm, Laura and R{\"o}blitz, Susanna and Ehrig, Rainald and Schneider, Marlon and Geris, Lisbet and Wichard, Joerg and Buttgereit, Frank}, title = {In silico Methods - Computational Alternatives to Animal Testing}, series = {ALTEX}, volume = {35}, journal = {ALTEX}, number = {1}, doi = {10.14573/altex.1712031}, pages = {126 -- 128}, abstract = {A seminar and interactive workshop on "In silico Methods - Computational Alternatives to Animal Testing" was held in Berlin, Germany, organized by Annemarie Lang, Frank Butt- gereit and Andrea Volkamer at the Charit{\´e}-Universit{\"a}tsmedizin Berlin, on August 17-18, 2017. During the half-day seminar, the variety and applications of in silico methods as alternatives to animal testing were presented with room for scientific discus- sions with experts from academia, industry and the German fed- eral ministry (Fig. 1). Talks on computational systems biology were followed by detailed information on predictive toxicology in order to display the diversity of in silico methods and the potential to embrace them in current approaches (Hartung and Hoffmann, 2009; Luechtefeld and Hartung, 2017). The follow- ing interactive one-day Design Thinking Workshop was aimed at experts, interested researchers and PhD-students interested in the use of in silico as alternative methods to promote the 3Rs (Fig. 2). Forty participants took part in the seminar while the workshop was restricted to sixteen participants.}, language = {en} } @article{LangFischerWeberetal., author = {Lang, Annemarie and Fischer, Lisa and Weber, Marie-Christin and Gaber, Timo and Ehrig, Rainald and R{\"o}blitz, Susanna and Buttgereit, Frank}, title = {Combining in vitro simulation and in silico modelling towards a sophisticated human osteoarthritis model}, series = {Osteoarthritis and Cartilage}, volume = {27}, journal = {Osteoarthritis and Cartilage}, doi = {10.1016/j.joca.2019.02.277}, pages = {S183}, abstract = {Our project aimed at building an in silico model based on our recently developed in vitro osteoarthritis (OA) model seeking for refinement of the model to enhance validity and translatability towards the more sophisticated simulation of OA. In detail, the previously 3D in vitro model is based on 3D chondrogenic constructs generated solely from human bone marrow derived mesenchymal stromal cells (hMSCs). Besides studying the normal state of the model over 3 weeks, the in vitro model was treated with interleukin-1β (IL-1β) and tumor necrosis factor alpha (TNFα) to mimic an OA-like environment.}, language = {en} } @article{KruegerLeenersTroncietal., author = {Kr{\"u}ger, Tillmann and Leeners, Brigitte and Tronci, Enrico and Mancini, Toni and Ille, Fabian and Egli, Marcel and Engler, Harald and R{\"o}blitz, Susanna and Frieling, Helge and Sinke, Christopher and Jahn, Kirsten}, title = {The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations}, series = {Physiology and Behavior}, journal = {Physiology and Behavior}, doi = {https://doi.org/10.1016/j.physbeh.2022.114034}, language = {en} } @article{KryvenRoeblitzSchuette, author = {Kryven, Ivan and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof}, title = {Solution of the chemical master equation by radial basis functions approximation with interface tracking}, series = {BMC Systems Biology}, volume = {9}, journal = {BMC Systems Biology}, number = {67}, doi = {10.1186/s12918-015-0210-y}, pages = {1 -- 12}, abstract = {Background. The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. Results. We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space. Discussion. In order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods. Conclusions. The proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability. Electronic version: http://www.biomedcentral.com/1752-0509/9/67}, language = {en} } @article{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Objective priors in the empirical Bayes framework}, series = {Scandinavian Journal of Statistics}, volume = {48}, journal = {Scandinavian Journal of Statistics}, number = {4}, publisher = {Wiley Online Library}, doi = {10.1111/sjos.12485}, pages = {1212 -- 1233}, abstract = {When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Prior estimation and Bayesian inference from large cohort data sets}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57475}, abstract = {One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterisations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Using these population data, we propose an iterative algorithm for contructing an informative prior distribution, which then serves as the basis for computing patient-specific posteriors and obtaining individual predictions. We demonsrate the performance of our method by applying it to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Empirical Bayes Methods for Prior Estimation in Systems Medicine}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61307}, abstract = {One of the main goals of mathematical modelling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes' rule separately to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data. We compare the performance of four priors - a non-informative prior and priors chosen by nonparametric maximum likelihood estimation (NPMLE), by maximum penalized lilelihood estimation (MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) - by applying them to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.}, language = {en} } @misc{KlebanovSikorskiSchuetteetal., author = {Klebanov, Ilja and Sikorski, Alexander and Sch{\"u}tte, Christof and R{\"o}blitz, Susanna}, title = {Empirical Bayes Methods, Reference Priors, Cross Entropy and the EM Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61230}, abstract = {When estimating a probability density within the empirical Bayes framework, the non-parametric maximum likelihood estimate (NPMLE) usually tends to overfit the data. This issue is usually taken care of by regularization - a penalization term is subtracted from the marginal log-likelihood before the maximization step, so that the estimate favors smooth solutions, resulting in the so-called maximum penalized likelihood estimation (MPLE). The majority of penalizations currently in use are rather arbitrary brute-force solutions, which lack invariance under transformation of the parameters(reparametrization) and measurements. This contradicts the principle that, if the underlying model has several equivalent formulations, the methods of inductive inference should lead to consistent results. Motivated by this principle and using an information-theoretic point of view, we suggest an entropy-based penalization term that guarantees this kind of invariance. The resulting density estimate can be seen as a generalization of reference priors. Using the reference prior as a hyperprior, on the other hand, is argued to be a poor choice for regularization. We also present an insightful connection between the NPMLE, the cross entropy and the principle of minimum discrimination information suggesting another method of inference that contains the doubly-smoothed maximum likelihood estimation as a special case.}, language = {en} } @inproceedings{IgdeWoelkRoeblitzetal., author = {Igde, Sinaida and W{\"o}lk, Hendrik and R{\"o}blitz, Susanna and Reidelbach, Marco and Weber, Marcus and Hartmann, Laura}, title = {Identifying Multivalent Binding Kinetics of Precision Glycomacromolecules: A Kinetic Study Using kinITC}, series = {M{\"u}nster Symposium on Cooperative Effects 2015 - SFB 858, at Westf{\"a}lische Wilhelms-Universit{\"a}t M{\"u}nster, 2015}, booktitle = {M{\"u}nster Symposium on Cooperative Effects 2015 - SFB 858, at Westf{\"a}lische Wilhelms-Universit{\"a}t M{\"u}nster, 2015}, abstract = {Multivalent sugar/protein interactions are well-known to proceed through different binding modes 1-5 which in turn can be described by their binding kinetics 3-5. This study provides additional insight into the association and dissociation reaction rates of complex multivalent sugar/protein interactions. Binding kinetics of recently introduced multivalent precision glycomacromolecules 6-8 to Concanavalin A (Con A) were studied by " kinetic Isothermal Titration Calorimetry " (kinITC) 9-11. The effect of multivalency is evaluated by comparing rate constants of glycomacromolecules obtaining the same and different valency of mannose ligands and by variation of the overall backbone properties, such as hydrophilic/ hydrophoboc. In addition, binding kinetics were studied using different conformations of Con A (homodimer vs.-tetramer) and thus a different protein valency. Our results show that precision glycomacromolecule/Con A binding proceeds non-cooperatively. Further, association and dissociation rates are mainly described by intermolecular complex formation. Together with the so-called functional valency, we can discriminate between " bound " and " unbound " states for macroscopic on-and off-rates, even for such complex glycooligomer/protein systems. By comparing e.g. a mono-to a divalent glycomacromolecule for their binding to dimeric Con A, we see a lower dissociation rate for the latter. As both bind monovalently to Con A, this is a strong indication for a statistical rebinding event. Further, there is a strong dependence of multivalent binding kinetics on the ligand density of glycomacromolecules as well as the Con A conformation and thus the overall on-and off-rates.}, language = {en} } @article{IgdeRoeblitzMuelleretal., author = {Igde, Sinaida and R{\"o}blitz, Susanna and M{\"u}ller, Anne and Kolbe, Katharina and Boden, Sophia and Fessele, Claudia and Lindhorst, Thisbe and Weber, Marcus and Hartmann, Laura}, title = {Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH}, series = {Marcomolecular Bioscience}, volume = {17}, journal = {Marcomolecular Bioscience}, number = {12}, doi = {10.1002/mabi.201700198}, pages = {1700198}, language = {en} } @article{HengartnerKruegerGeraedtsetal., author = {Hengartner, Michael and Kr{\"u}ger, Tillmann H. C. and Geraedts, Kirsten and Tronci, Enrico and Mancini, Toni and Ille, Fabian and Egli, Marcel and R{\"o}blitz, Susanna and Ehrig, Rainald and Saleh, Lanja and Spanaus, Katharina and Schippert, Cordula and Zhang, Yuanyuan and Leeners, Brigitte}, title = {Negative affect is unrelated to fluctuations in hormone levels across the menstrual cycle: evidence from a multisite observational study across two successive cycles}, series = {Journal of Psychosomatic Research}, volume = {99}, journal = {Journal of Psychosomatic Research}, doi = {10.1016/j.jpsychores.2017.05.018}, pages = {21 -- 27}, language = {en} } @article{HaackRoeblitzScharkoietal.2010, author = {Haack, Fiete and R{\"o}blitz, Susanna and Scharkoi, Olga and Schmidt, Burkhard and Weber, Marcus}, title = {Adaptive Spectral Clustering for Conformation Analysis}, series = {AIP Conference Proceedings}, volume = {1281}, journal = {AIP Conference Proceedings}, number = {1}, publisher = {AIP}, doi = {10.1063/1.3498116}, pages = {1585 -- 1588}, year = {2010}, language = {en} } @article{HaackFackeldeyRoeblitzetal., author = {Haack, Fiete and Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus and Schmidt, Burkhard}, title = {Adaptive spectral clustering with application to tripeptide conformation analysis}, series = {The Journal of Chemical Physics}, volume = {139}, journal = {The Journal of Chemical Physics}, doi = {10.1063/1.4830409}, pages = {110 -- 194}, language = {en} } @misc{GuptaRoeblitzKrauseetal., author = {Gupta, Pooja and R{\"o}blitz, Susanna and Krause, Carola and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density}, series = {Computational Models in biology and medicine, 2013, Dresden, Germany}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, language = {en} } @inproceedings{GuptaKrauseRikeitetal., author = {Gupta, Pooja and Krause, Carola and Rikeit, Paul and R{\"o}blitz, Susanna and Knaus, Petra and Sch{\"u}tte, Christof}, title = {Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density}, series = {10th International BMP conference, 2014, Berlin, Germany}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, language = {en} } @article{FrankSikorskiRoeblitz, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, series = {Journal of Computational and Applied Mathematics}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, abstract = {The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.}, language = {de} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities}, series = {Journal of Theoretical Biology}, journal = {Journal of Theoretical Biology}, doi = {https://doi.org/10.1016/j.jtbi.2022.111150}, abstract = {We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology.}, language = {en} } @article{FischerHolzhausenRoeblitz, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Mathematical modelling of follicular growth and ovarian stimulation}, series = {Current Opinion in Endocrine and Metabolic Research}, journal = {Current Opinion in Endocrine and Metabolic Research}, doi = {https://doi.org/10.1016/j.coemr.2022.100385}, language = {en} } @article{FischerEhrigSchaeferetal., author = {Fischer, Sophie and Ehrig, Rainald and Sch{\"a}fer, Stefan and Tronci, Enrico and Mancini, Toni and Egli, Marcel and Ille, Fabian and Kr{\"u}ger, Tillmann H. C. and Leeners, Brigitte and R{\"o}blitz, Susanna}, title = {Mathematical Modelling and Simulation Provides Evidence for New Strategies of Ovarian Stimulation}, series = {Frontiers in Endocrinology}, volume = {12}, journal = {Frontiers in Endocrinology}, doi = {10.3389/fendo.2021.613048}, abstract = {New approaches to ovarian stimulation protocols, such as luteal start, random start or double stimulation, allow for flexibility in ovarian stimulation at different phases of the menstrual cycle which is especially useful when time for assisted reproductive technology is limited, e.g. for emergency fertility preservation in cancer patients. It has been proposed that the success of these methods is based on the continuous growth of multiple cohorts ("waves") of follicles throughout the menstrual cycle which leads to the availability of ovarian follicles for ovarian controlled stimulation at several time points. Though several preliminary studies have been published, their scientific evidence has not been considered as being strong enough to integrate these results into routine clinical practice. This work aims at adding further scientific evidence about the efficiency of variable-start protocols and underpinning the theory of follicular waves by using mathematical modelling and numerical simulations. For this purpose, we have modified and coupled two previously published models, one describing the time course of hormones and one describing competitive follicular growth in a normal menstrual cycle. The coupled model is used to test stimulation protocols in silico. Simulation results show the occurrence of follicles in a wave-like manner during a normal menstrual cycle and qualitatively predict the outcome of ovarian stimulation initiated at different time points of the menstrual cycle.}, language = {en} } @misc{FackeldeyRoeblitzScharkoietal., author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, Olga and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13189}, number = {11-27}, abstract = {Particle methods have become indispensible in conformation dynamics to compute transition rates in protein folding, binding processes and molecular design, to mention a few. Conformation dynamics requires at a decomposition of a molecule's position space into metastable conformations. In this paper, we show how this decomposition can be obtained via the design of either ``soft'' or ``hard'' molecular conformations. We show, that the soft approach results in a larger metastabilitiy of the decomposition and is thus more advantegous. This is illustrated by a simulation of Alanine Dipeptide.}, language = {en} } @article{FackeldeyRoeblitzScharkoietal., author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, O. and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, series = {Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.)}, journal = {Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.)}, pages = {899 -- 909}, language = {de} } @article{ErlekamIgdeRoeblitzetal., author = {Erlekam, Franziska and Igde, Sinaida and R{\"o}blitz, Susanna and Hartmann, Laura and Weber, Marcus}, title = {Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC}, series = {Computation}, volume = {7}, journal = {Computation}, number = {3}, doi = {10.3390/computation7030046}, pages = {46}, abstract = {In addition to the conventional Isothermal Titration Calorimetry (ITC), kinetic ITC (kinITC) not only gains thermodynamic information, but also kinetic data from a biochemical binding process. Moreover, kinITC gives insights into reactions consisting of two separate kinetic steps, such as protein folding or sequential binding processes. The ITC method alone cannot deliver kinetic parameters, especially not for multivalent bindings. This paper describes how to solve the problem using kinITC and an invariant subspace projection. The algorithm is tested for multivalent systems with different valencies.}, language = {en} } @misc{EhrigDierkesSchaeferetal., author = {Ehrig, Rainald and Dierkes, Thomas and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna and Tronci, Enrico and Mancini, Toni and Salvo, Ivano and Alimguzhin, Vadim and Mari, Federico and Melatti, Igor and Massini, Annalisa and Kr{\"u}ger, Tillmann H. C. and Egli, Marcel and Ille, Fabian and Leeners, Brigitte}, title = {An Integrative Approach for Model Driven Computation of Treatments in Reproductive Medicine}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57103}, abstract = {We present an overview of the current status of the European collaborative project PAEON. The challenge of PAEON is to provide specialists in reproduc- tive medicine with a computerised model of the menstrual cycle under normal and various pathological conditions, which will allow them to get further in- sight in fertility dynamics. This model also enables the simulation of treatment protocols, which were used within in vitro fertilization. By the definition of virtual patients through biologically admissible parametrizations our approach allows not only the evaluation of a given treatment strategy in silico, but also the design and optimization of such protocols. Once a protocol is formalized in the virtual hospital, the success can be controlled by a treatment execution monitor, which works then as a clinical decision support system. All these tools will be combined in a virtual hospital environment, enabling the access to the PAEON services through the web.}, language = {en} } @inproceedings{EhrigDierkesSchaeferetal., author = {Ehrig, Rainald and Dierkes, Thomas and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna and Tronci, Enrico and Mancini, Toni and Salvo, Ivano and Alimguzhin, Vadim and Mari, Federico and Melatti, Igor and Massini, Annalisa and Kr{\"u}ger, Tillmann H. C. and Egli, Marcel and Ille, Fabian and Leeners, Brigitte}, title = {An integrative approach for model driven computation of treatments in reproductive medicine}, series = {BIOMAT - Proceedings of the 15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, booktitle = {BIOMAT - Proceedings of the 15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, 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} } @article{DierkesRoeblitzWadeetal.2013, author = {Dierkes, Thomas and R{\"o}blitz, Susanna and Wade, Moritz and Deuflhard, Peter}, title = {Parameter identification in large kinetic networks with BioPARKIN}, series = {CoRR - Computing Research Repository - arXiv.org}, volume = {abs/1303.4928}, journal = {CoRR - Computing Research Repository - arXiv.org}, year = {2013}, language = {en} } @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} } @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} } @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} } @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} } @article{BergPloentzkeSiebertetal., 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}, series = {Bulletin of Mathematical Biology}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, 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} } @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} } @misc{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.}, issn = {1438-0064}, doi = {10.3168/jds.2016-12443}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64756}, 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} }