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Ziel herkömmlicher Behandlungsmethoden chronischer oder traumatischer Knorpeldefekte ist die Wiederherstellung der Gelenkfunktion. Die Transplantation autologer Chondrozyten verspricht hier eine dauerhafte Korrektur des Knorpeldefekts. Ein Problem der autologen Chondrozytentransplantation (ACT) ist jedoch die Tatsache, dass die im Rahmen der ACT notwendige Invitro-Expansion der Chondrozyten oft mit einem Funktionsverlust im Sinne einer Dedifferenzierung in Fibroblasten bzw. einem Überwachsen durch Fibroblasten einhergeht. Im Rahmen dieser Dissertation sollte daher untersucht werden, inwieweit die Expansion von Chondrozyten auf eine Proliferation einzelner Vorläuferzellen zurückzuführen ist und ob sich die Frequenz von Vorläuferzellen in Chondrozytenbiopsaten quantifizieren lassen. Es zeigte sich, dass das Wachstum von Chondrozyten auf die Proliferation von Vorläuferzellen zurückzuführen ist, die unter den verwendeten Kulturbedingungen zur Ausbildung von Chondrozytenkolonien führen. Die Frequenz der koloniebildenden Einheiten (CFU-Ch) lag – in Abhängigkeit von den gewählten Kulturbedingungen – bei durchschnittlich 3,4–7,6 Kolonien pro 1000 Chondrozyten, wobei eine Beschichtung der Kulturplatten mit Kollagen und eine Substitution des Zellkulturmediums mit FGF zu einer hohen Korrelation zwischen der eingesetzten Zellzahl und der gemessenen Anzahl koloniebildender Einheiten (R2 = 0,9643) führte, die im Durchschnitt bei 7,6 CFU-Ch pro 1000 ausplattierter Chondrozyten lag. Bei Verwendung von Zellkulturmedien ohne Zytokinzusatz (DMEM) bzw. mit FGF- (CBM) oder TFG-β-Supplementation (CDM) zeigten sich deutlich unterschiedliche Ausprägungen der Chondrozytenkolonien in Bezug auf die Morphologie. So führte FGF-haltiges Medium zu einem ausgeprägten Wachstum fibroblastenähnlicher Zellen, während sich die Chondrozytenstruktur und Färbung mit Alcianblau am ehesten durch DMEM und TGF-β1-haltiges CDM erhalten ließ. Das hier etablierte Testverfahren erlaubt eine zuverlässige Quantifizierung von koloniebildenden Einheiten und könnte geeignet sein, Vorläuferzellen weiter zu charakterisieren, die zur Regeneration von funktionellem Gelenkknorpel beitragen.
Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones
(2022)
In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of nonradial minimizers, under a volume constraint, of the associated torsional energy functional. In particular we give a condition on the domain D on the sphere spanning the cone which ensures that the spherical sector is not a minimizer. Similar results are obtained for the relative isoperimetric problem in nonconvex cones.
The receptor tyrosine kinase ErbB2 (HER2) is overexpressed in multiple human tumors of epithelial origin. High ErbB2 expression is functionally involved in tumorigenesis and correlates with poor clinical prognosis. For immunotherapy of ErbB2 expressing tumors, we developed a strategy to supply the tumor cells with costimulatory activity. A bispecific fusion protein was constructed (BIg5), containing the IgV-like domain of huCD86, the CH2/CH3 domain of huIgG1 and the ErbB2-specific single chain antibody fragment scFv(FRP5). A similar fusion protein lacking the CD86 domain (Ig5) was used as a control. Upon binding of BIg5 to ErbB2 on tumor cells, these cells display CD86 on their surface and thus can deliver costimulatory signals for T-cell activation. In addition, NK cells could be activated by CD86 binding to CD28. BIg5 is secreted by eukaryotic cells as a homodimer with increased stability compared to monomers and possibly enhanced costimulatory activity due to crosslinking of CD28 on effector cells. By FACS analysis, specific binding of the scFv(FRP5) domain to ErbB2 as well as CD86 IgV binding to CTLA-4 could be demonstrated. Together with anti-CD3 antibody, BIg5 stimulates proliferation of human CD2-purified lymphocytes in vitro. After binding to ErbB2 on murine Renca-lacZ/ErbB2 tumor cells, about 50% of initially bound BIg5 is still present on the cell surface after 4 hours. For delivery of chimeric fusion proteins in vivo, we used syngeneic, stably transfected HC11 mammary epithelial cells continuously secreting the proteins. Inoculation of these bystander cells close to subcutaneously growing Renca-lacZ/ErbB2 tumors should provide a long-lasting source to achieve high local concentrations of BIg5 at the tumor site. In vivo HC11-BIg5 cells proved to be non-tumorigenic and secreted BIg5 for several weeks, causing a strong anti-BIg5 antibody response. Treatment of established Renca-lacZ/ErbB2 or ErbB2-negative Renca-lacZ tumors by peritumoral inoculation of either HC11-BIg5 or HC11-Ig5 cells led to rejection of all Renca-lacZ/ErbB2, but none of the Renca-lacZ tumors. HC11neo control cells had no effect on tumor growth. Rejection of ErbB2+ tumors led to long-term protection also against subsequent challenge with intravenously injected ErbB2- tumor cells. Intraperitoneal injection of bystander cells secreting the fusion proteins did not lead to tumor regression suggesting that high local concentrations at the tumor site are necessary to target ErbB2 on tumor cells and to overcome elimination of BIg5 or Ig5 by neutralizing antibodies. The CD86 IgV domain of BIg5 did not play a major role in the observed antitumoral immune response suggesting NK-cell mediated ADCC as the initial effector mechanism followed by activation of tumor specific T cells. Targeting of ErbB2 on tumor cells with antibody fusion proteins that interact specifically with the host immune system could be an efficient and specific approach for therapy of solid ErbB2+ tumors.
We establish weighted Lp-Fourier extension estimates for O(N−k)×O(k)-invariant functions defined on the unit sphere SN−1, allowing for exponents p below the Stein–Tomas critical exponent 2(N+1)/N−1. Moreover, in the more general setting of an arbitrary closed subgroup G⊂O(N) and G-invariant functions, we study the implications of weighted Fourier extension estimates with regard to boundedness and nonvanishing properties of the corresponding weighted Helmholtz resolvent operator. Finally, we use these properties to derive new existence results for G-invariant solutions to the nonlinear Helmholtz equation −Δu−u = Q(x)|u|p−2u,u∈W2,p(RN), where Q is a nonnegative bounded and G-invariant weight function.
We obtain spectral inequalities and asymptotic formulae for the discrete spectrum of the operator 12log(−Delta) in an open set OmegaERd, d≥2, of finite measure with Dirichlet boundary conditions. We also derive some results regarding lower bounds for the eigenvalue Lambda1(Omega) and compare them with previously known inequalities.
We study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian (−Δ)s in bounded open Lipschitz sets in the small order limit s→0+. While it is easy to see that all eigenvalues converge to 1 as s→0+, we show that the first order correction in these asymptotics is given by the eigenvalues of the logarithmic Laplacian operator, i.e., the singular integral operator with Fourier symbol 2log|ξ|. By this we generalize a result of Chen and the third author which was restricted to the principal eigenvalue. Moreover, we show that L2-normalized Dirichlet eigenfunctions of (−Δ)s corresponding to the k-th eigenvalue are uniformly bounded and converge to the set of L2-normalized eigenfunctions of the logarithmic Laplacian. In order to derive these spectral asymptotics, we establish new uniform regularity and boundary decay estimates for Dirichlet eigenfunctions for the fractional Laplacian. As a byproduct, we also obtain corresponding regularity properties of eigenfunctions of the logarithmic Laplacian.
We derive a shape derivative formula for the family of principal Dirichlet eigenvalues λs(Ω) of the fractional Laplacian (−Δ)s associated with bounded open sets Ω⊂RN of class C1,1. This extends, with a help of a new approach, a result in Dalibard and Gérard-Varet (Calc. Var. 19(4):976–1013, 2013) which was restricted to the case s=12. As an application, we consider the maximization problem for λs(Ω) among annular-shaped domains of fixed volume of the type B∖B¯¯¯¯′, where B is a fixed ball and B′ is ball whose position is varied within B. We prove that λs(B∖B¯¯¯¯′) is maximal when the two balls are concentric. Our approach also allows to derive similar results for the fractional torsional rigidity. More generally, we will characterize one-sided shape derivatives for best constants of a family of subcritical fractional Sobolev embeddings.
This paper describes the addition of Luxembourgish to the language versions of MAIN, the adaption process and the use of MAIN in Luxembourg. A short description of Luxembourg’s multilingual society and trilingual school system as well as an overview of selected morphosyntactic and syntactic features of Luxembourgish introduce the Luxembourgish version of MAIN.
The present paper is concerned with the half-space Dirichlet problem [...] where ℝ𝑁+:={𝑥∈ℝ𝑁:𝑥𝑁>0} for some 𝑁≥1 and 𝑝>1, 𝑐>0 are constants. We analyse the existence, non-existence and multiplicity of bounded positive solutions to (𝑃𝑐). We prove that the existence and multiplicity of bounded positive solutions to (𝑃𝑐) depend in a striking way on the value of 𝑐>0 and also on the dimension N. We find an explicit number 𝑐𝑝∈(1,𝑒√), depending only on p, which determines the threshold between existence and non-existence. In particular, in dimensions 𝑁≥2, we prove that, for 0<𝑐<𝑐𝑝, problem (𝑃𝑐) admits infinitely many bounded positive solutions, whereas, for 𝑐>𝑐𝑝, there are no bounded positive solutions to (𝑃𝑐).
Tumor-specific T lymphocytes can be regarded as a highly effective mechanism for tumor rejection. A substantial number of T-cell defined tumor antigens including mutated oncoproteins and differentiation antigens have been identified. However, while most spontaneous tumors appear to be antigenic, few are immunogenic. Activation of tumor-specific cytotoxic T cells (CTL) requires presentation of tumor antigens by professional antigen presenting cells (APCs) via MHC I molecules. Due to their crucial role in T-cell activation, APCs are being exploited for active cancer immunotherapy. Present experimental strategies include the incubation of dendritic cells with synthetic, tumor specific peptides to achieve uptake of tumor antigens and presentation in the context of MHC molecules. Alternatively, gene therapeutic approaches are aimed at the endogenous expression of tumor antigens in APCs upon transfer of suitable vector constructs. Our strategy for the presentation of tumor antigens by APCs is based on the intracellular delivery of tumor antigens as part of a fusion protein specifically targeted to APC cell surface receptors. We have constructed prototype molecules that contain a soluble fragment of CTLA-4 for cell binding via interaction with B7 molecules, genetically fused to a protein fragment derived from the tumor-associated antigen ErbB2. To improve uptake and direct the antigenic determinant preferentially to the MHC class I pathway, in one of these protein vaccines also the translocation domain of the bacterial Pseudomonas exotoxin A has been included. In the parental toxin this protein domain facilitates escape from the endosomal compartment to the cytosol upon receptor mediated endocytosis. Here we have investigated the in vitro cell binding activity of such reagents and their antitumoral activity in immunocompetent murine model systems. Specific binding to B7 molecules and uptake of bacterially expressed protein vaccines could be demonstrated. Ex vivo restimulation with an ErbB2-derived peptide of splenocytes from Balb/c mice injected with the fusion proteins resulted in enhanced IFN-gamma production by T cells. Protective and therapeutic effects of ErbB2 protein vaccines were also investigated. Vaccinated animals were protected against subsequent challenge with syngeneic ErbB2 expressing tumor cells. Likewise, s.c. injection of ErbB2 protein vaccines in the vicinity of established tumors resulted in tumor rejection and long lasting protection indicating that immunological memory was induced. Our results suggest that chimeric proteins combining a tumor antigen and specific recognition of APCs in a single molecule are suitable for targeted delivery of antigens to professional APCs and might become valuable tools for cancer immunotherapy.