Stationary Points of O'Hara's Knot Energies

In this article we study the regularity of stationary points of the knot energies $E^\alpha$ introduced by O'Hara in the range $\alpha \in (2,3)$. In a first step we prove that $E^\alpha$ is $C^1$ on the set of all regular embedded closed curves belonging to $H^{(\alpha +1)/2,2}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of $E^\alpha$ plus a positive multiple of the length. We show that stationary points of finite energy are of class $C^\infty$ - so especially all local minimizers of $E^\alpha$ among curves with fixed length are smooth.Comment: Corrected typo

Transforming Growth Factor Alpha Stimulation of Mucosal Tissue Cultures from Head and Neck Squamous Cell Carcinoma Patients Increases Chemoresistance to Cisplatin

The monoclonal epidermal growth factor receptor ( EGFR) antibody cetuximab (Erbitux(TM)) was recently approved by the European Medicines Agency for the treatment of recurrent and/or metastatic head and neck squamous cell carcinoma (HNSCC) in combination with a platinum-based chemotherapy. Since the antibody has only a limited effect as a monotherapy, possible explanations for the synergistic effect with cisplatin are enhanced antibody-dependent cytoxicity and increased sensitivity to the drug. Most of our knowledge of EGFR biology in HNSCC is based on studies using EGFR inhibitors and/or antibodies. Our study was designed to evaluate the impact of EGFR stimulation on cisplatin-induced DNA damage. Therefore, tissue cultures were produced of tumor-free oropharyngeal mucosa biopsies of HNSCC patients and controls. In a previous study, overexpression of EGFR in tissue cultures from tumor patients compared to controls was confirmed by immunohistochemical staining. Twenty-four-hour stimulation of tissue cultures with transforming growth factor alpha (TGF-alpha), a specific EGFR ligand, resulted in a reduction of cisplatin-induced DNA damage by 35% in cases, whereas in controls TGF-alpha had no effect. This reflects a statistically significant increase in cellular chemoresistance to cisplatin following TGF-alpha stimulation and helps to further understand effects of EGFR antisense therapy in combination with chemotherapy. Copyright (C) 2010 S. Karger AG, Base