A Sobolev Poincar\'e type inequality for integral varifolds

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.Comment: v1: 27 pages, no figures; v2: replaced citations of the author's dissertation by proofs, material of sections 1 and 3 reorganised, slightly more general results in section 2, some remarks, some discussion and some references added, 40 pages, no figure

Control of the isoperimetric deficit by the Willmore deficit

In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit can be controlled by the Willmore deficit

Properties of the free energy barriers for folding of the [alpha]-amylase inhibitor tendamistat

The goal of this work was to improve our understanding of the properties of the free energy barriers in protein folding. We used the small all-[beta]-sheet protein tendamistat as a model protein. Tendamistat contains two disulfide bridges and folds and unfolds in apparent two-state reactions. However, previous studies on disulfide variants demonstrated that tendamistat folds in at least two sequential steps with a high-energy intermediate. Elucidation of the properties of the free energy barriers by studying different tendamistat variants and various fragments provide a good insight into the underlying complexity of apparent two state folders. To obtain this information several approaches have been used in this work: we studied the combined influence of denaturant, temperature, structural variation and sodium sulfate on folding and stability; furthermore, we analysed the properties and stability of different fragments of tendamistat. Multiple perturbation analysis was used to gain information on the shape of the free energy barriers in tendamistat folding. Analysis of denaturant and temperature as perturbations revealed transition state movement according to the Hammond postulate. Hammond behaviour is more pronounced in the early transition state compared to the late transition state where only small transition state movement was observed. The results suggest that the early transition state is rather broad compared to the late transition state. These results emphasized the importance of multiple perturbation analysis to test the shape of the free energy barriers in protein folding. Determination of the activation parameters revealed less difference between both transition states. However, the denaturant dependence of the activation parameters of the transition states differs significantly. The results confirm our previous suggestion that the early transition state is broad and structurally less well defined, whereas the late transition state shows a rather narrow and structurally well-defined maximum. We further studied the effect of denaturant and structural variation on folding and stability. The results confirmed Hammond behaviour of the early transition state. To know more about structural properties of the transition states we determine