@misc{GoetschelWeiserSchiela, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11909}, number = {10-25}, abstract = {This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.}, language = {en} } @phdthesis{Durmaz, author = {Durmaz, Vedat}, title = {Atomistic Binding Free Energy Estimations for Biological Host-Guest Systems}, publisher = {FU Dissertationen Online}, pages = {216}, abstract = {Accurate quantifications of protein-ligand binding affinities by means of in silico methods increasingly gain importance in various scientific branches including toxicology and pharmacology. In silico techniques not only are generally less demanding than laboratory experiments regarding time as well as cost, in particular, if binding assays or synthesis protocols need to be developed in advance. At times, they also provide the only access to risk assessments on novel chemical compounds arising from biotic or abiotic degradation of anthropogenic substances. However, despite the continuous technological and algorithmic progress over the past decades, binding free energy estimations through molecular dynamics simulations still pose an enormous computational challenge owed to the mathematical complexity of solvated macromolecular systems often consisting of hundreds of thousands of atoms. The goals of this thesis can roughly be divided into two categories dealing with different aspects of host-guest binding quantification. On the one side algorithmic strategies for a comprehensive exploration and decomposition of conformational space in conjunction with an automated selection of representative molecular geometries and binding poses have been elaborated providing initial structures for free energy calculations. In light of the dreaded trapping problem typically associated with molecular dynamics simulations, the focus was laid on a particularly systematic generation of representatives covering a broad range of physically accessible molecular conformations and interaction modes. On the other side and ensuing from these input geometries, binding affinity models based on the linear interaction energy (LIE) method have been developed for a couple of (bio)molecular systems. The applications included a successful prediction of the liquid-chromatographic elution order as well as retention times of highly similar hexabromocyclododecane (HBCD) stereoisomers, a novel empirical LIE-QSAR hybrid binding affinity model related to the human estrogen receptor α (ERα), and, finally, the (eco)toxicological prioritization of transformation products originating from the antibiotic sulfamethoxazole with respect to their binding affinities to the bacterial enzyme dihydropteroate synthase. Altogether, a fully automated approach to binding mode and affinity estimation has been presented that is content with an arbitrary geometry of a small molecule under observation and a spatial vector specifying the binding site of a potential target molecule. According to our studies, it is superior to conventional docking and thermodynamic average methods and primarily suggesting binding free energy calculation on the basis of several heavily distinct complex geometries. Both chromatographic retention times of HBCD and binding affinities to ERα yielded squared coefficients of correlation with experimental results significantly higher than 0.8. Approximately 85 \% (100 \%) of predicted receptor-ligand binding modes deviated less than 1.53 {\AA} (2.05 {\AA}) from available crystallographic structures.}, 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} } @misc{GoetschelSchielaWeiser, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 -- a Flexible Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74616}, abstract = {Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.}, language = {en} }