@article{BoerStoetzelRoeblitzetal.2011, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle}, volume = {278}, journal = {Journal of Theoretical Biology}, number = {1}, doi = {10.1016/j.jtbi.2011.02.021}, pages = {20 -- 31}, year = {2011}, language = {en} } @article{BoerRoeblitzStoetzeletal.2011, author = {Boer, H. Marike T. and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Veerkamp, Roel F. and Kemp, Bas and Woelders, Henri}, title = {Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model}, volume = {94}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2011-4400}, pages = {5987 -- 6000}, year = {2011}, language = {en} } @incollection{BoerStoetzelRoeblitzetal.2012, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Woelders, Henri}, title = {A differential equation model to investigate the dynamics of the bovine estrous cycle}, volume = {736}, booktitle = {Advances in Systems Biology}, doi = {10.1007/978-1-4419-7210-1_35}, pages = {597 -- 606}, year = {2012}, language = {en} } @book{DeuflhardRoeblitz2015, 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}, year = {2015}, language = {en} } @misc{StoetzelRoeblitzSiebert2015, author = {St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Siebert, Heike}, title = {Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation}, issn = {1438-0064}, doi = {10.1371/journal.pone.0140954}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56164}, year = {2015}, abstract = {In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.}, language = {en} } @article{MoualeuNgangueRoeblitzEhrigetal.2015, 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}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0120607}, year = {2015}, 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} } @inproceedings{EhrigDierkesSchaeferetal.2016, 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}, booktitle = {BIOMAT - Proceedings of the 15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, year = {2016}, language = {en} } @inproceedings{PloentzkeBergStoetzeletal.2015, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna}, title = {A systems biology approach to bovine fertility and metabolism: Introduction of a glucose insulin model}, booktitle = {15th International Symposium on Mathematical and Computational Biology, Rorkee, India}, year = {2015}, language = {en} } @misc{StoetzelApriRoeblitz2014, author = {St{\"o}tzel, Claudia and Apri, Mochamad and R{\"o}blitz, Susanna}, title = {A reduced ODE model of the bovine estrous cycle}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51594}, year = {2014}, abstract = {This work deals with the reduction of a previously developed ODE model for the bovine estrous cycle. After applying a method for exploring the parameter space by Apri et al. (2012), we perform structure-based reduction steps and several system specific adaptations. Overall, the original model consisting of 15 ODEs and 60 parameters is reduced to a model of 10 odes and 38 parameters. The reduced model qualitatively reproduces the state trajectories of the original model.}, language = {en} } @inproceedings{ManciniSalvoMarietal.2014, 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}, booktitle = {Proceedings of the 14th Conference on Formal Methods in Computer-Aided Design (FMCAD 2014)}, pages = {207 -- 214}, year = {2014}, language = {en} } @article{StoetzelEhrigBoeretal.2014, 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}, journal = {BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland}, year = {2014}, 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} } @article{HengartnerKruegerGeraedtsetal.2017, 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}, volume = {99}, journal = {Journal of Psychosomatic Research}, doi = {10.1016/j.jpsychores.2017.05.018}, pages = {21 -- 27}, year = {2017}, language = {en} } @misc{BergPloentzkeLeonhardMareketal.2017, author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {A dynamic model to simulate potassium balance in dairy cows.}, issn = {1438-0064}, doi = {10.3168/jds.2016-12443}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64756}, year = {2017}, abstract = {High performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one of them being potassium, is indispensable for the prevention of imbalances. The potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, it is closely related with the glucose and electrolyte metabolism. In this paper, we present a dynamical model for the potassium balance in lactating and non-lactating dairy cows based on ordinary differential equations. Parameter values are obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for three different scenarios: potassium balance in (i) non-lactating cows with varying feed intake, (ii) non-lactating cows with varying potassium fraction in the diet, and (iii) lactating cows with varying milk production levels. The results give insights into the short and long term potassium metabolism, providing an important step towards the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} } @misc{LangeSchwiegerPloentzkeetal.2017, author = {Lange, Alexander and Schwieger, Robert and Pl{\"o}ntzke, Julia and Sch{\"a}fer, Stefan and R{\"o}blitz, Susanna}, title = {Follicular competition: the selection of dominant follicles as a synergistic effect}, issn = {1438-0064}, doi = {https://doi.org/10.1007/s00285-018-1284-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63863}, year = {2017}, abstract = {The estrous cycle of mono-ovulatory species such as cows or humans, is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the omega-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.}, language = {en} } @article{LeenersKruegerGeraedtsetal.2017, 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}, journal = {Front. Behav. Neurosci.}, doi = {10.3389/fnbeh.2017.00120}, year = {2017}, language = {en} } @misc{BockmayrSiebertRoeblitzetal.2014, 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}, 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}, year = {2014}, language = {en} } @misc{KlebanovSikorskiSchuetteetal.2016, 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}, year = {2016}, 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} } @article{KryvenRoeblitzSchuette2015, 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}, volume = {9}, journal = {BMC Systems Biology}, number = {67}, doi = {10.1186/s12918-015-0210-y}, pages = {1 -- 12}, year = {2015}, 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} } @misc{EhrigDierkesSchaeferetal.2016, 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}, year = {2016}, 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} } @misc{StoetzelEhrigBoeretal.2016, author = {St{\"o}tzel, Claudia and Ehrig, Rainald and Boer, H. Marike T. and Pl{\"o}ntzke, Julia and R{\"o}blitz, Susanna}, title = {Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57039}, year = {2016}, abstract = {Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists.}, language = {en} } @misc{PloentzkeBergStoetzeletal.2015, author = {Pl{\"o}ntzke, Julia and Berg, Mascha and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna}, title = {A systems biology approach to bovine fertility and metabolism: Development of a glucose insulin model.}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56453}, year = {2015}, abstract = {To counteract the antagonistic relationship between milk yield and fertility in dairy cow, a deeper understanding of the underlying biological mechanisms is required. For this purpose, we study physiological networks related to reproduction and metabolism in dairy cows. We interactively develop dynamic, mechanistic models by fitting the models to experimental data and mechanistic knowledge. We have already developed models for potassium balance and hormonal regulation of fertility in the dairy cow, which will briefly be reviewed here. The main focus of this article is a glucose-insulin model currently developed by us. This model links the bovine hormonal cycle and the potassium balance to glucose and thus to energy metabolism. The models can be applied in scientific research, education, experimental planning, drug development and production on farms.}, language = {en} } @article{StoetzelRoeblitzSiebert2015, author = {St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Siebert, Heike}, title = {Complementing ODE-based System Analysis Using Boolean Networks Derived from an Euler-like Transformation}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0140954}, year = {2015}, language = {en} } @article{FackeldeyRoeblitzScharkoietal.2011, author = {Fackeldey, Konstantin and R{\"o}blitz, Susanna and Scharkoi, O. and Weber, Marcus}, title = {Soft Versus Hard Metastable Conformations in Molecular Simulations}, journal = {Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.)}, pages = {899 -- 909}, year = {2011}, language = {de} } @misc{GuptaRoeblitzKrauseetal.2013, 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}, journal = {Computational Models in biology and medicine, 2013, Dresden, Germany}, year = {2013}, language = {en} } @inproceedings{GuptaKrauseRikeitetal.2014, 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}, booktitle = {10th International BMP conference, 2014, Berlin, Germany}, year = {2014}, language = {en} } @article{BergPloentzkeLeonhardMareketal.2017, author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Leonhard-Marek, Sabine and M{\"u}ller, Kerstin-Elisabeth and R{\"o}blitz, Susanna}, title = {A dynamic model to simulate potassium balance in dairy cows}, volume = {100}, journal = {Journal of Dairy Science}, number = {12}, doi = {10.3168/jds.2016-12443}, pages = {9799 -- 9814}, year = {2017}, abstract = {High-performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one being potassium, is indispensable for the prevention of imbalances. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and it is closely related to glucose and electrolyte metabolism. In this paper, we present a dynamical model for potassium balance in lactating and nonlactating dairy cows based on ordinary differential equations. Parameter values were obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for 3 different scenarios: potassium balance in (1) nonlactating cows with varying feed intake, (2) nonlactating cows with varying potassium fraction in the diet, and (3) lactating cows with varying milk production levels. The results give insights into the short- and long-term potassium metabolism, providing an important step toward the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies.}, language = {en} } @article{IgdeRoeblitzMuelleretal.2017, 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}, volume = {17}, journal = {Marcomolecular Bioscience}, number = {12}, doi = {10.1002/mabi.201700198}, pages = {1700198}, year = {2017}, language = {en} } @article{BergPloentzkeSiebertetal.2021, author = {Berg, Mascha and Pl{\"o}ntzke, Julia and Siebert, Heike and R{\"o}blitz, Susanna}, title = {Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations}, volume = {83}, journal = {Bulletin of Mathematical Biology}, number = {121}, doi = {10.1007/s11538-021-00942-z}, pages = {1 -- 25}, year = {2021}, abstract = {Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.}, language = {en} } @article{YousefianFrankWeberetal.2025, author = {Yousefian, Maryam and Frank, Anne-Simone and Weber, Marcus and R{\"o}blitz, Susanna}, title = {Efficient construction of Markov state models for stochastic gene regulatory networks by domain decomposition}, volume = {26}, journal = {BMC Bioinformatics}, number = {147}, doi = {10.1186/s12859-025-06174-5}, year = {2025}, abstract = {The dynamics of many gene regulatory networks (GRNs) is characterized by the occurrence of metastable phenotypes and stochastic phenotype switches. The chemical master equation (CME) is the most accurate description to model such stochastic dynamics, whereby the long-time dynamics of the system is encoded in the spectral properties of the CME operator. Markov State Models (MSMs) provide a general framework for analyzing and visualizing stochastic multistability and state transitions based on these spectral properties. Until now, however, this approach is either limited to low-dimensional systems or requires the use of high-performance computing facilities, thus limiting its usability.}, language = {en} } @inproceedings{YousefianDonatiSikorskietal.2026, author = {Yousefian, Maryam and Donati, Luca and Sikorski, Alexander and Weber, Marcus and R{\"o}blitz, Susanna}, title = {Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN}, volume = {15959}, booktitle = {Computational Methods in Systems Biology. CMSB 2025}, doi = {10.1007/978-3-032-01436-8_8}, pages = {126 -- 149}, year = {2026}, abstract = {Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system's long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs.}, language = {en} } @article{FischerHolzhausenRoeblitz2022, 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}, journal = {Journal of Theoretical Biology}, doi = {https://doi.org/10.1016/j.jtbi.2022.111150}, year = {2022}, 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{FischerHolzhausenRoeblitz2022, author = {Fischer-Holzhausen, Sophie and R{\"o}blitz, Susanna}, title = {Mathematical modelling of follicular growth and ovarian stimulation}, journal = {Current Opinion in Endocrine and Metabolic Research}, doi = {https://doi.org/10.1016/j.coemr.2022.100385}, year = {2022}, language = {en} } @article{KruegerLeenersTroncietal.2022, 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}, journal = {Physiology and Behavior}, doi = {https://doi.org/10.1016/j.physbeh.2022.114034}, year = {2022}, language = {en} } @article{FrankSikorskiRoeblitz2024, author = {Frank, Anna-Simone and Sikorski, Alexander and R{\"o}blitz, Susanna}, title = {Spectral clustering of Markov chain transition matrices with complex eigenvalues}, volume = {444}, journal = {Journal of Computational and Applied Mathematics}, arxiv = {http://arxiv.org/abs/2206.14537}, doi = {10.1016/j.cam.2024.115791}, pages = {115791}, year = {2024}, 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} }