Smooth density field of catalytic super-Brownian motion

Given an (ordinary) super-Brownian motion (SBM) ϱ on Rd of dimension d = 2, 3, we consider a (catalytic) SBM Xϱ on Rd with "local branching rates" ϱs(dx). We show that Xϱt is absolutely continuous with a density function ξϱt, say. Moreover, there exists a version of the map (t,z) ↦ ξϱt(z) which is C∞ and solves the heat equation off the catalyst ϱ, more precisely, off the (zero set of) closed support of the time-space measure ds ϱs(dx). Using self-similarity, we apply this result to answer the question of the long-term behavior of Xϱ in dimension d = 2 : If ϱ and Xϱ start with a Lebesgue measure, then XϱT converges (persistently) as T → ∞ towards a random multiple of Lebesgue measure

Biodiversity of Catalytic Super-Brownian Motion

In this paper we investigate the structure of the equilibrium state of three-dimensional catalytic super-Brownian motion where the catalyst is itself a classical super-Brownian motion. We show that the reactant has an infinite local biodiversity or genetic abundance. This contrasts the finite local biodiversity of the equilibrium of classical super-Brownian motion. Another question we address is that of extinction of the reactant in finite time or in the long-time limit in dimensions d = 2,3. Here we assume that the catalyst starts in the Lebesgue measure and the reactant starts in a finite measure. We show that there is extinction in the long-time limit if d = 2 or 3. There is, however, no finite time extinction if d = 3 (for d = 2 this problem is left open). This complements a result of Dawson and Fleischmann (1997a) for d = 1 and again contrasts the behaviour of classical super-Brownian motion. As a key tool for both problems we show that in d = 3the reactant matter propagates everywhere in space immediately

The Effect of Ligand Mobility on the Cellular Interaction of Multivalent Nanoparticles

Multivalent nanoparticle binding to cells can be of picomolar avidity making such interactions almost as intense as those seen with antibodies. However, reducing nanoparticle design exclusively to avidity optimization by the choice of ligand and its surface density does not sufficiently account for controlling and understanding cell-particle interactions. Cell uptake, for example, is of paramount significance for a plethora of biomedical applications and does not exclusively depend on the intensity of multivalency. In this study, it is shown that the mobility of ligands tethered to particle surfaces has a substantial impact on particle fate upon binding. Nanoparticles carrying angiotensin-II tethered to highly mobile 5 kDa long poly(ethylene glycol) (PEG) chains separated by ligand-free 2 kDa short PEG chains show a superior accumulation in angiotensin-II receptor type 1 positive cells. In contrast, when ligand mobility is constrained by densely packing the nanoparticle surface with 5 kDa PEG chains only, cell uptake decreases by 50%. Remarkably, irrespective of ligand mobility and density both particle types have similar EC50 values in the 1-3 x 10(-9) m range. These findings demonstrate that ligand mobility on the nanoparticle corona is an indispensable attribute to be considered in particle design to achieve optimal cell uptake via multivalent interactions

Thermodynamic, Spatial and Methodological Considerations for the Manufacturing of Therapeutic Polymer Nanoparticles

Purpose Evaluate fundamental parameters that dictate the effectiveness of drug loading. Methods A model water-soluble drug lacking ionizable groups, pirfenidone (PFD), was encapsulated through nanoprecipitation in poly(ethylene glycol)-poly(lactic acid) (PEG-PLA)-poly(lactic-co-glycolic acid) (PLGA) NPs. Firstly, the thermodynamic parameters predicting drug-polymer miscibility were determined to assess the system's suitability. Then, the encapsulation was evaluated experimentally by two different techniques, bulk and microfluidic (MF) nanoprecipitation. Additionally, the number of molecules that fit in a particle core were calculated and the loading determined experimentally for different core sizes. Lastly, the effect of co-encapsulation of alpha-lipoic acid (LA), a drug with complementary therapeutic effects and enhanced lipophilicity, was evaluated. Results The thermodynamic miscibility parameters predicted a good suitability of the selected system. MF manufacturing enhanced the encapsulation efficiency by 60-90% and achieved a 2-fold higher NP cellular uptake. Considering spatial constrictions for drug encapsulation and increasing the size of the PLGA core the number of PFD molecules per NP was raised from under 500 to up to 2000. More so, the co-encapsulation of LA increased the number of drug molecules per particle by 96%, with no interference with the release profile. Conclusions Thermodynamic, spatial and methodological parameters should be considered to optimize drug encapsulation

Isolated Langerhans cell histiocytosis of the vulva: a case report and review of the literature

Isolated Langerhans cell histiocytosis (LCH) of the female genital tract is very rare. A review of the literature revealed that only 15 cases of primary vulvar LCH have previously been published in the English literature. We describe an additional case of confined vulvar LCH. A 49-year-old woman presented with an ulcerous lesion that turned out to be LCH confined to the vulva only. After surgical excision, four recurrences followed, which were treated again by surgery. After the fourth recurrence, adjuvant radiotherapy was applied. When the fifth recurrence occurred, only surgical excision was performed, and the patient has now been disease-free for 51months. There are no standard treatment options for this rare disease. The most effective treatment options still remain elusive. In our case in the end surgery proved to be effectiv

High CD10 expression in lymph node metastases from surgically treated prostate cancer independently predicts early death

Patients with nodal positive prostate cancers are an important cohort with poorly defined risk factors. CD10 is a cell surface metallopeptidase that has been suggested to play a role in prostate cancer progression. CD10 expression was evaluated in 119 nodal positive prostate cancer patients using tissue microarrays constructed from primary tumors and lymph node metastases. All patients underwent radical prostatectomy and standardized extended lymphadenectomy. They had no neoadjuvant therapy and received deferred androgen deprivation. In the primary tumor, high CD10 expression was significantly associated with earlier death from disease when compared with low CD10 expression (5-year survival 73.7% vs. 91.8%; p = 0.043). In the metastases, a high CD10 expression was significantly associated with larger total size of metastases (median 11.4 vs. 6.5mm; p = 0.015), earlier death of disease (5-year survival 71.5% vs. 87.3%; p = 0.017), and death of any cause (5-year survival 70.0% vs. 87.2%; p = 0.001) when compared with low CD10 expression. CD10 expression in the metastases added independent prognostic information for overall survival (p = 0.029) after adjustment for Gleason score of the primary tumor, nodal tumor burden, and resection margins. In conclusion, a high CD10 expression in prostate cancer predicts early death. This information is inherent in the primary tumors and in the lymph node metastases and might help to personalize patient managemen

Tumor regression grade of urothelial bladder cancer after neoadjuvant chemotherapy: a novel and successful strategy to predict survival.

Histopathologic tumor regression grades (TRGs) after neoadjuvant chemotherapy predict survival in different cancers. In bladder cancer, corresponding studies have not been conducted. Fifty-six patients with advanced invasive urothelial bladder cancer received neoadjuvant chemotherapy before cystectomy and lymphadenectomy. TRGs were defined as follows: TRG1: complete tumor regression; TRG2: >50% tumor regression; TRG3: 50% or less tumor regression. Separate TRGs were assigned for primary tumors and corresponding lymph nodes. The prognostic impact of these 2 TRGs, the highest (dominant) TRG per patient, and competing tumor features reflecting tumor regression (ypT/ypN stage, maximum diameter of the residual tumor) were determined. Tumor characteristics in initial transurethral resection of the bladder specimens were tested for response prediction. The frequency of TRGs 1, 2, and 3 in the primary tumors were n=16, n=19, and n=21; corresponding data from the lymph nodes were n=31, n=9, and n=16. Interobserver agreement in determination of the TRG was strong (κ=0.8). Univariately, all evaluated parameters were significantly (P≤0.001) related to overall survival; however, the segregation of the Kaplan-Meier curves was best for the dominant TRG. In multivariate analysis, only dominant TRG predicted overall survival independently (P=0.035). In transurethral resection specimens of the chemotherapy-naive bladder cancer, the only tumor feature with significant (P<0.03) predictive value for therapy response was a high proliferation rate. In conclusion, among all parameters reflecting tumor regression, the dominant TRG was the only independent risk factor. A favorable chemotherapy response is associated with a high proliferation rate in the initial chemotherapy-naive bladder cancer. This feature might help personalize neoadjuvant chemotherapy

Prediction of Biochemical Recurrence Based on Molecular Detection of Lymph Node Metastasis After Radical Prostatectomy.

Background Molecular detection of lymph node (LN) micrometastases by analyzing mRNA expression of epithelial markers in prostate cancer (PC) patients provides higher sensitivity than histopathological examination. Objective To investigate which type of marker to use and whether molecular detection of micrometastases in LNs was predictive of biochemical recurrence. Design setting and participants LN samples from PC patients undergoing radical prostatectomy with extended LN dissection between 2009 and 2011 were examined for the presence of micrometastases by both routine histopathology and molecular analyses. Outcome measurements and statistical analysis The mRNA expression of a panel of markers of prostate epithelial cells, prostate stem cell-like cells, epithelial-to-mesenchymal transition, and stromal activation, was performed by quantitative real-time polymerase chain reaction. The expression levels of these markers in LN metastases from three PC patients were compared with the expression levels in LN from five control patients without PC in order to identify the panel of markers best suited for the molecular detection of LN metastases. The predictive value of the molecular detection of micrometastases for biochemical recurrence was assessed after a follow-up of 10 yr. Results and limitations Prostate epithelial markers are better suited for the detection of occult LN metastases than molecular markers of stemness, epithelial-to-mesenchymal transition, or reactive stroma. An analysis of 1023 LNs from 60 PC patients for the expression of prostate epithelial cell markers has revealed different expression levels and patterns between patients and between LNs of the same patient. The positive predictive value of molecular detection of occult LN metastasis for biochemical recurrence is 66.7% and the negative predictive value is 62.5%. Limitations are sample size and the hypothesis-driven selection of markers. Conclusions Molecular detection of epithelial cell markers increases the number of positive LNs and predicts tumor recurrence already at surgery. Patient summary We show that a panel of epithelial prostate markers rather than single genes is preferred for the molecular detection of lymph node micrometastases not visible at histopathological examination

DNA Methylation Landscapes of Prostate Cancer Brain Metastasis Are Shaped by Early Driver Genetic Alterations

UNLABELLED Metastases from primary prostate cancers to rare locations, such as the brain, are becoming more common due to longer life expectancy resulting from improved treatments. Epigenetic dysregulation is a feature of primary prostate cancer, and distinct DNA methylation profiles have been shown to be associated with the mutually exclusive SPOP-mutant or TMPRSS2-ERG fusion genetic backgrounds. Using a cohort of prostate cancer brain metastases (PCBM) from 42 patients, with matched primary tumors for 17 patients, we carried out a DNA methylation analysis to examine the epigenetic distinction between primary prostate cancer and PCBM, the association between epigenetic alterations and mutational background, and particular epigenetic alterations that may be associated with PCBM. Multiregion sampling of PCBM revealed epigenetic stability within metastases. Aberrant methylation in PCBM was associated with mutational background and PRC2 complex activity, an effect that is particularly pronounced in SPOP-mutant PCBM. While PCBM displayed a CpG island hypermethylator phenotype, hypomethylation at the promoters of genes involved in neuroactive ligand-receptor interaction and cell adhesion molecules such as GABRB3, CLDN8, and CLDN4 was also observed, suggesting that cells from primary tumors may require specific reprogramming to form brain metastasis. This study revealed the DNA methylation landscapes of PCBM and the potential mechanisms and effects of PCBM-associated aberrant DNA methylation. SIGNIFICANCE DNA methylation analysis reveals the molecular characteristics of PCBM and may serve as a starting point for efforts to identify and target susceptibilities of these rare metastases