Variational Discretization of Higher Order Geometric Gradient Flows Based on Phase Field Models

In this thesis a phase field based nested variational time discretization for Willmore flow is presented. The basic idea of our model is to approximate the mean curvature by a time-discrete, approximate speed of the mean curvature motion. This speed is computed by a fully implicit time step of mean curvature motion, which forms the inner problem of our model. It is set up as a minimization problem taking into account the concept of natural time discretization. The outer problem is a variational problem balancing between the L2-distance of the surface at two consecutive time steps and the decay of the Willmore energy. This is a typical ansatz in case of natural time discretization as it is used in the inner problem. Within the Willmore energy the mean curvature is approximated as mentioned above. Consequently our model is a nested variational and leads to a PDE constraint optimization problem to compute a single time step. It allows time steps up to the size of the spatial grid width. A corresponding parametric version of this model based on finite elements on a triangulation of the evolving geometry was investigated by Olischläger and Rumpf. In this work we derive the corresponding phase field version and prove the existence of a solution. Since biharmonic heat flow is a linear model problem for our nested time discretization of Willmore flow we transfer our model to the linear case. Moreover we present error estimates for the fully discrete biharmonic heat flow and validate them numerically. In addition we compare our model with the semi-implicit phase field scheme for Willmore flow introduced by Du et al. which leads to the result that our nested variational method is significantly more robust. An application of our nested time discretized Willmore model consists in reconstructing a hypersurface corresponding to a given lower-dimensional apparent contour or Huffman labeling. The apparent contour separates the regions where the number of intersections between the hypersurface and the projection ray is constant and the labeling which specifies these intersection numbers is called Huffman labeling. For reconstructing the hypersurface we minimize a regularization energy consisting of the scaled area and Willmore energy subject to the constraint that the Huffman labeling of the minimizing surface equals the given Huffman labeling almost everywhere. To solve the corresponding phase field problem we use an algorithm alternating the minimizes of the regularization and mismatch energy. Moreover we use a multigrid ansatz. In most parts of this work our nested variational problem is solved by setting up the corresponding Lagrange equation and solving the resulting saddle point problem. An alternative is presented in the last part of this work. It deals with the problem of solving the linear model problem as well as our nested variational problem with an Augmented Lagrange method

Mechanism of acetaldehyde-induced deactivation of microbial lipases

<p>Abstract</p> <p>Background</p> <p>Microbial lipases represent the most important class of biocatalysts used for a wealth of applications in organic synthesis. An often applied reaction is the lipase-catalyzed transesterification of vinyl esters and alcohols resulting in the formation of acetaldehyde which is known to deactivate microbial lipases, presumably by structural changes caused by initial Schiff-base formation at solvent accessible lysine residues. Previous studies showed that several lipases were sensitive toward acetaldehyde deactivation whereas others were insensitive; however, a general explanation of the acetaldehyde-induced inactivation mechanism is missing.</p> <p>Results</p> <p>Based on five microbial lipases from <it>Candida rugosa</it>, <it>Rhizopus oryzae</it>, <it>Pseudomonas fluorescens </it>and <it>Bacillus subtilis </it>we demonstrate that the protonation state of lysine <it>ε</it>-amino groups is decisive for their sensitivity toward acetaldehyde. Analysis of the diverse modification products of <it>Bacillus subtilis </it>lipases in the presence of acetaldehyde revealed several stable products such as <it>α,β</it>-unsaturated polyenals, which result from base and/or amino acid catalyzed aldol condensation of acetaldehyde. Our studies indicate that these products induce the formation of stable Michael-adducts at solvent-accessible amino acids and thus lead to enzyme deactivation. Further, our results indicate Schiff-base formation with acetaldehyde to be involved in crosslinking of lipase molecules.</p> <p>Conclusions</p> <p>Differences in stability observed with various commercially available microbial lipases most probably result from different purification procedures carried out by the respective manufacturers. We observed that the pH of the buffer used prior to lyophilization of the enzyme sample is of utmost importance. The mechanism of acetaldehyde-induced deactivation of microbial lipases involves the generation of <it>α,β</it>-unsaturated polyenals from acetaldehyde which subsequently form stable Michael-adducts with the enzymes. Lyophilization of the enzymes from buffer at pH 6.0 can provide an easy and effective way to stabilize lipases toward inactivation by acetaldehyde.</p

Stressing the Ubiquitin-Proteasome System without 20S Proteolytic Inhibition Selectively Kills Cervical Cancer Cells

Cervical cancer cells exhibit an increased requirement for ubiquitin-dependent protein degradation associated with an elevated metabolic turnover rate, and for specific signaling pathways, notably HPV E6-targeted degradation of p53 and PDZ proteins. Natural compounds with antioxidant properties including flavonoids and triterpenoids hold promise as anticancer agents by interfering with ubiquitin-dependent protein degradation. An increasing body of evidence indicates that their α-β unsaturated carbonyl system is the molecular determinant for inhibition of ubiquitin-mediated protein degradation up-stream of the catalytic sites of the 20S proteasome. Herein we report the identification and characterization of a new class of chalcone-based, potent and cell permeable chemical inhibitors of ubiquitin-dependent protein degradation, and a lead compound RAMB1. RAMB1 inhibits ubiquitin-dependent protein degradation without compromising the catalytic activities of the 20S proteasome, a mechanism distinct from that of Bortezomib. Treatment of cervical cancer cells with RAMB1 triggers unfolded protein responses, including aggresome formation and Hsp90 stabilization, and increases p53 steady state levels. RAMB1 treatment results in activation of lysosomal-dependent degradation pathways as a mechanism to compensate for increasing levels of poly-ubiquitin enriched toxic aggregates. Importantly, RAMB1 synergistically triggers cell death of cervical cancer cells when combined with the lysosome inhibitor Chloroquine

CD8 T cell autoreactivity to preproinsulin epitopes with very low human leucocyte antigen class I binding affinity

Transplantation and autoimmunit

Biocompatibility of Poly(ester amide) (PEA) Microfibrils in Ocular Tissues

Drug delivery systems (DDS) are able to deliver, over long periods of time, therapeutic concentrations of drugs requiring frequent administration. Two classes of DDS are available, biodegradable and non-biodegradable. The larger non-biodegradable implants ensure long-term delivery, but require surgical interventions. Biodegradable biomaterials are smaller, injectable implants, but degrade hydrolytically and release drugs in non-zero order kinetics, which is inefficient for long-term sustained drug release. Biodegradable poly(ester amides) (PEAs) may overcome these difficulties. To assess their ocular biocompatibility and long-term behavior, PEA fibrils were analyzed in vitro and in vivo. In vitro, incubation in vitreous humor changes to PEA structure, suggests degradation by surface erosion, enabling drug release with zero order kinetics. Clinical and histological analysis of PEA fibrils implanted subconjunctivally and intravitreally showed the absence of an inflammatory response or other pathological tissue alteration. This study shows that PEA fibrils are biocompatible with ocular environment and degrade by surface erosion

Digitale Arbeitskulturen

Peer Reviewe

Pleistocene human mitochondrial genomes suggest late dispersal of non- Africans and a Late Glacial population turnover in Europe

International audienc