TY - GEN A1 - Lasser, Caroline A1 - Röblitz, Susanna T1 - Computing expectation values for molecular quantum dynamics N2 - We compute expectation values for the solution of the nuclear Schrödinger 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. T3 - ZIB-Report - 09-30 KW - time dependent Schrödinger equation KW - molecular quantum dynamics KW - expectation values KW - Wigner functions Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11461 SN - 1438-0064 ER - TY - GEN A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, Olga A1 - Weber, Marcus T1 - Soft Versus Hard Metastable Conformations in Molecular Simulations N2 - 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. T3 - ZIB-Report - 11-27 KW - Proteins, Conformation Space, Meshfree Methods Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13189 ER - TY - GEN A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions N2 - 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. T3 - ZIB-Report - 10-06 KW - cow KW - reproduction KW - hormone patterns KW - ordinary differential equations KW - systems biology Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11682 SN - 1438-0064 ER - TY - GEN A1 - Dierkes, Thomas A1 - Wade, Moritz A1 - Nowak, Ulrich A1 - Röblitz, Susanna T1 - BioPARKIN - Biology-related Parameter Identification in Large Kinetic Networks N2 - Modelling, parameter identification, and simulation play an important rôle 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. T3 - ZIB-Report - 11-15 KW - systems biology KW - ordinary differential equations KW - sensitivity analysis KW - parameter identification KW - affine invariant Gauss-Newton algorithm KW - numerical library KW - graphical user interface Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12706 ER - TY - GEN A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Deuflhard, Peter A1 - Jones, Hannah M. A1 - Azulay, David-Olivier A1 - van der Graaf, Piet A1 - Martin, Steven T1 - A mathematical model of the human menstrual cycle for the administration of GnRH analogues N2 - 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. T3 - ZIB-Report - 11-16 KW - human menstrual cycle KW - systems biology KW - mathematical modelling KW - GnRH analogues KW - differential equations Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12732 ER - TY - GEN A1 - Stötzel, Claudia A1 - Plöntzke, Julia A1 - Röblitz, Susanna T1 - Advances in modelling of the bovine estrous cycle: Administration of PGF2alpha N2 - 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. T3 - ZIB-Report - 11-17 KW - cow KW - reproduction KW - hormone patterns KW - differential equations KW - systems biology Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12740 ER - TY - GEN A1 - Berg, Mascha A1 - Ritter, Julia A1 - Röblitz, Susanna T1 - A mathematical model for the Zinc response of young pigs N2 - 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. T3 - ZIB-Report - 11-05 KW - systems biology KW - ordinary differential equations KW - feeding study KW - weanling pigs Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12191 ER - TY - GEN A1 - Bondouy, Manon A1 - Röblitz, Susanna T1 - Mathematical modeling of follicular development in bovine estrous cycles N2 - 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. T3 - ZIB-Report - 12-26 KW - ordinary differential equations KW - systems biology KW - reproduction KW - dairy cows Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15585 SN - 1438-0064 ER - TY - GEN A1 - Plöntzke, Julia A1 - Berg, Mascha A1 - Olany, Amiya A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - Modeling potassium balance in dairy cows N2 - 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. T3 - ZIB-Report - 13-09 KW - systems biology KW - differential equations KW - metabolism Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17749 SN - 1438-0064 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Parameter Identification for a Tuberculosis Model in Cameroon N2 - 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. T3 - ZIB-Report - 13-72 KW - Tuberculosis, parameter identification, sensitivity analysis, Gauss-Newton method, Nonlinear dynamical systems. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43087 SN - 1438-0064 ER - TY - GEN A1 - Meisel, Kristin A1 - Röblitz, Susanna T1 - Mathematische Modellierung der Knochenremodellierung N2 - Knochenremodellierung beinhaltet den Auf- und Abbau der Knochenmasse durch die verschiedenen Knochenzellen und findet fast überall, auch am Skelett Erwachsener, statt. Für die Erneuerung der Knochensubstanz sind die Osteoblasten zuständig. Sie ersetzen exakt die Menge der Knochenmasse, welche zuvor durch Osteoklasten abgebaut wurde. Störungen dieses, durch viele Faktoren beeinflussten Prozesses führen zu pathologischen Veränderungen, 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 Parameterschätzung anhand des Gauß-Newton-Verfahrens wird des Weiteren eine Methode vorgestellt, die es ermöglicht, mathematische Modelle bestmöglich durch Variation der Parameterwerte an experimentelle Daten anzupassen. Das am Zuse-Institut Berlin entwickelte Softwarepaket POEM wendet diesen Algorithmus an und wird ebenfalls erläutert. T3 - ZIB-Report - 13-41 Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42010 SN - 1438-0064 ER -