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  • 1
    Title: ¬A¬ guide to numerical modelling in systems biology; 12
    Author: Deuflhard, Peter
    Contributer: Röblitz, Susanna
    Edition: Peter Deuflahrd, Susanna Röblitz
    Publisher: Cahm [u. a.] :Springer,
    Year of publication: 2015
    Pages: X, 168 S.
    Series Statement: Texts in computational science and engineering 12
    ISBN: 978-3-319-20058-3 , 978-3-319-20059-0
    Type of Medium: Book
    Language: English
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  • 2
    Publication Date: 2020-03-11
    Description: 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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
    Publication Date: 2020-03-11
    Description: 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: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
    Publication Date: 2020-11-17
    Description: 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: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 5
    Publication Date: 2020-03-11
    Description: 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.
    Description: Das Verständnis von geometrischen Strukturen und dynamischen Eigenschaften molekularer Konformationen ist essentiell für die Vorhersage des Langzeitverhaltens von Molekülen. Die Identifikation metastabiler Konformationen sowie die Bestimmung von Übergangswahrscheinlichkeiten und Haltezeiten sind Bestandteil der Konformationdynamik. Dabei handelt es sich um eine Mehrskalenmethode, die auf eine reduzierte Beschreibung des Systems mittels einer stochastischen Übergangsmatrix führt. In der vorliegenden Dissertation wurde untersucht, wie man die Genauigkeit der Matrizen sowie der daraus berechneten Größen quantifizieren kann. Im Mittelpunkt stehen dabei Fehlerschätzer für den invarianten Unterraum, da die rechten Eigenvektoren als Grundlage der Robusten Perron Cluster Analyse (PCCA+) zur Identifizierung der metastabilen Konformationen dienen. Die Zerlegung des Zustandsraumes in Basisfunktionen sowie die Approximation der Matrixeinträge mittels Monte-Carlo-Quadratur führen zu zeilenweise korrelierten Zufallsmatrizen. Mit Hilfe einer stochastischen Norm sowie einem geeigneten statistischen Modell für die Verteilung der Matrixzeilen können u.a. Fehlerschranken und -verteilungen für den invarianten Unterraum brechnet werden. Eine Equilibrierung des Fehlers zwischen den Basisfunktionen kann durch erweitertes Sampling in solchen Regionen erreicht werden, in denen die Trajektorien nur langsam mischen.Eine hierarchische Zerlegung dieser Basisfunktionen verbessert systematisch die Zerlegung in metastabile Konformationen, indem sie den Fehler im invarianten Unterraum reduziert. Diese Techniken gestatten eine Evaluierung der Simulationsergebnisse und ebnen den Weg zur Behandlung komplexerer Moleküle. Desweiteren wurden Verallgemeinerungen der PCCA+ untersucht. Die Erweiterung der PCCA+ auf nicht-reversible Markov-Ketten sowie die Modifizierung der Zielfunktion für den Fall der weichen Clusterung setzen die Entwicklung von der PCCA über PCCA+ zu PCCA++ fort. Somit können neue Anwendungsfelder für dieses Cluster-Verfahren erschlossen werden. Die Methoden wurden zwar in Rahmen der Konformationsdynamik entwickelt, jedoch lassen sie sich auf eine weite Problemklasse anwenden, in der Gebietszerlegungsverfahren mit Monte-Carlo-Quadratur kombiniert werden. Mögliche Anwendungsgebiete umfassen die chemische Master-Gleichung oder quantenchemische Systeme.
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
    Format: application/pdf
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  • 6
    Publication Date: 2022-03-11
    Description: 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: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
    Publication Date: 2020-03-11
    Description: 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: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 8
    Publication Date: 2022-03-11
    Description: 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: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
    Publication Date: 2020-03-11
    Language: English
    Type: article , doc-type:article
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  • 10
    Publication Date: 2020-03-11
    Language: English
    Type: bookpart , doc-type:bookPart
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