Notes on a PDE System for Biological Network Formation

We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field using a Darcy's type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. The analytical part extends the results of Haskovec, Markowich and Perthame regarding the existence of weak and mild solutions to the whole range of meaningful relaxation exponents. Moreover, we prove finite time extinction or break-down of solutions in the spatially onedimensional setting for certain ranges of the relaxation exponent. We also construct stationary solutions for the case of vanishing diffusion and critical value of the relaxation exponent, using a variational formulation and a penalty method. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on mixed finite elements and study the qualitative properties of network structures for various parameters values. Furthermore, we indicate numerically that some analytical results proved for the spatially one-dimensional setting are likely to be valid also in several space dimensions.Comment: 33 pages, 12 figure

Probing the interaction forces of prostate cancer cells with collagen I and bone marrow derived stem cells on the single cell level.

Adhesion of metastasizing prostate carcinoma cells was quantified for two carcinoma model cell lines LNCaP (lymph node-specific) and PC3 (bone marrow-specific). By time-lapse microscopy and force spectroscopy we found PC3 cells to preferentially adhere to bone marrow-derived mesenchymal stem cells (SCP1 cell line). Using atomic force microscopy (AFM) based force spectroscopy, the mechanical pattern of the adhesion to SCP1 cells was characterized for both prostate cancer cell lines and compared to a substrate consisting of pure collagen type I. PC3 cells dissipated more energy (27.6 aJ) during the forced de-adhesion AFM experiments and showed significantly more adhesive and stronger bonds compared to LNCaP cells (20.1 aJ). The characteristic signatures of the detachment force traces revealed that, in contrast to the LNCaP cells, PC3 cells seem to utilize their filopodia in addition to establish adhesive bonds. Taken together, our study clearly demonstrates that PC3 cells have a superior adhesive affinity to bone marrow mesenchymal stem cells, compared to LNCaP. Semi-quantitative PCR on both prostate carcinoma cell lines revealed the expression of two Col-I binding integrin receptors, α1β1 and α2β1 in PC3 cells, suggesting their possible involvement in the specific interaction to the substrates. Further understanding of the exact mechanisms behind this phenomenon might lead to optimized therapeutic applications targeting the metastatic behavior of certain prostate cancer cells towards bone tissue

Pharmacopeial characterization of asparaginase

Asparaginase (ASNASE), an enzyme catalyzing the deamidation of asparagine, is therapeutically used for the treatment of pediatric acute lymphoblastic leukemia (ALL). Current administration protocols are exclusively using bolus injection. No information is available about other dosages, like slow intravenous administration, thus hampering the full clinical exploitation of the drug. Preliminary observation indicates inconsistent issue of incompatibility with the infusion solution, which seems dependent of i.a. the source and batch of asparaginase used. Therefore, a selective pharmaceutical characterization is urgently required, so that the right choices and use of ASNASE can be defined, extending the clinical use. We present our current results of the development and evaluation of (1) the enzymatic activity by determination of the formed ammonia by the Nessler reaction (see Figure 1) and (2) the amide-bond characterization (secondary/tertiary structures) by Fourier Transform Infrared Spectroscopy (FT-IR) and Circular Dichroism (CD). Different methods were selected for the ASNASE activity determination; whereof the Nessler assay was withheld for optimization. Using Design of Experiments (DOE) with four variables, i.e. CKI/CHgI2, CNaOH/CHgI2, CHgI2 final and reaction time in a D-optimal onion design space, a maximum enzyme activity response could be determined. For the characterization of the primary structure, peptide-mapping LC-MS method was adopted. The ASNASE amide-bond (secondary/tertiary structures) was characterized by FT-IR (see Figure 2) and CD. The secondary structure elements of the ASNASE are quantified by FT-IR, combined with mathematical deconvolution of the different amide peaks (mainly amide I, II and III bands). Using CD, the melting temperature (Tm) in relation with the enzyme stability is examined. Denaturation of the β-sheet is observed in a temperature range of 60-63°C, while the α-helix denaturated in 63-65°C

Wetting Heterogeneities in Porous Media Control Flow Dissipation

Pressure-controlled displacement of an oil-water interface is studied in dense packings of functionalized glass beads with well-defined spatial wettability correlations. An enhanced dissipation is observed if the typical extension ξ of the same-type wetting domains is smaller than the average bead diameter d. Three-dimensional imaging using x-ray microtomography shows that the frequencies n(s) of residual droplet volumes s for different ξ collapse onto the same curve. This indicates that the additional dissipation for small ξ is due to contact line pinning rather than an increase of capillary break-up and coalescence events

Analytic Expressions for Singular Vectors of the N=2N=2 Superconformal Algebra

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.Comment: 35 pages, LATE

Advancing solar magnetic field extrapolations through multi-height magnetic field measurements

Non-linear force-free extrapolations are a common approach to estimate the 3D topology of coronal magnetic fields based on photospheric vector magnetograms. The force-free assumption is a valid approximation at coronal heights, but for the dense plasma conditions in the lower atmosphere, this assumption is not satisfied. In this study, we utilize multi-height magnetic field measurements in combination with physics-informed neural networks to advance solar magnetic field extrapolations. We include a flexible height-mapping, which allows us to account for the different formation heights of the observed magnetic field measurements. The comparison to analytical and simulated magnetic fields demonstrates that including chromospheric magnetic field measurements leads to a significant improvement of our magnetic field extrapolations. We also apply our method to chromospheric line-of-sight magnetograms, from the Vector Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) observatory, in combination with photospheric vector magnetograms, from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO). The comparison to observations in extreme ultraviolet wavelengths shows that the additional chromospheric information leads to a better agreement with the observed coronal structures. In addition, our method intrinsically provides an estimate of the corrugation of the observed magnetograms. With this new approach, we make efficient use of multi-height magnetic field measurements and advance the realism of coronal magnetic field simulations

7,8,9,10-Tetra­hydro-2-methyl­cyclo­hepta­[b]indol-6(5H)-one

The title compound, C14H15NO, was synthesized from 2-hydroxy­methyl­enecyclo­hepta­none via a Japp–Klingemann acid-catalyzed cyclization. The seven-membered ring exhibits a slightly distorted envelope conformation. N—H⋯O hydrogen bonds form a centrosymmetric dimer; C—H⋯O hydrogen bonds and π–π stacking inter­actions (the centers of the atoms involved in the stacking interaction are separated by 3.504 Å) give rise to another type of centrosymmetric dimer. In combination, these inter­actions create a stair-like chain of mol­ecules that inter­acts only loosely with neighboring chains via van der Waals inter­actions and weak C—H⋯π contacts