Extending topological surgery to natural processes and dynamical systems.

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids.

In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins.

Significance of estrogen receptor 1 (ESR-1) gene imbalances in colon and hepatocellular carcinomas based on tissue microarrays analysis.

Estrogen receptor alpha-encoded by ESR1 gene-overexpression correlates with prognosis and response to specific chemotherapy in breast adenocarcinoma cases. Mechanisms of ESR-1 deregulation in carcinomas remain under investigation. To analyze ESR1 in carcinomas of different histogenesis. Using tissue microarray technology, 172 primary carcinomas including breast ductal adenocarcinomas (n=60), hepatocellular carcinomas (n=52), and colon adenocarcinomas (n=60) were cored and re-embedded in three paraffin blocks. Initial diagnosis was based on liquid based cytology (LiquiPrep/ThinPrep). Immunohistochemistry and fluorescence in situ hybridization were performed. Quantitative evaluation of ER-a protein levels was assessed by applying digital image analysis. ER-a overexpression was observed in 41/60 (68.3%), 23/52 (44.2%) and 4/60 (6.6%) cases, respectively. ESR1 gene multiple copies were confirmed in 13/60 (21.6%) breast adenocarcinomas, but high amplification only in 8/13 (62.8%). Allelic absence was identified in 3/52 (5.7%) hepatocellular carcinomas, whereas colon adenocarcinomas demonstrated gene gains in 5/60 (8.3%) cases referred to chr 6 aneuploidy and not to amplification. ER-a overall expression was associated strongly to ESR1 gene copies only in breast carcinoma (P=0.036). ESR-1 gene overexpression happens frequently in breast cancer, but only a subset of them are high amplified cases correlated to increased response rates in hormonal therapy (tamoxifen). Absence of this mechanism in hepatocellular and colon carcinomas maybe is a negative factor for applying this therapy. This is a pattern of histo-genetic depended targeted therapeutic strategy.

Morphometric analysis of AgNORs in thin-layer, liquid-based liver specimens.

OBJECTIVE: To detect argyrophilic nucleolar organizer regions (AgNORs) in ThinPrep (Cytyc Corp., Boxborough, Massachusetts, U.S.A.) liver fine needle aspiration (FNA) specimens and to define the diagnostic value of their quantitative analysis in the evaluation of hepatic lesions. STUDY DESIGN: ThinPrep liquid-based FNA biopsy specimens from 49 malignant and benign liver lesions were resampled, fixed in 95% ethanol and stained with the AgNOR technique in accordance with the 1-step colloid method. The specimens included 11 benign and 38 malignant lesions (23 poorly differentiated hepatocellular carcinomas [HCCs] and 15 poorly differentiated metastatic adenocarcinomas [MCs]). Morphometric analysis was performed using a Zeiss Axiolab microscope (Carl Zeiss GmbH, Jena, Germany) with a mechanical stage fitted with a Sony-iris CCD videocamera (Tokyo, Japan). The videocamera was connected to a Pentium III P/C (Intel Corp., Santa Clara, California, U.S.A.) loaded with the appropriate image analysis software. The measurements were performed with ImageScan software (Jandel Scientific, Erkrath, Germany). The number of AgNORs per nucleus (NN) and the total area per nucleus occupied by AgNORs (AR) were calculated semiautomatically. Statistical analysis was performed using the SPSS software package (Chicago, Illinois, U.S.A.). RESULTS: The least significant deviance test for multiple comparisons revealed that NN differed significantly between the 3 groups of samples examined (P < .0001). The mean NN values in HCCs and MCs were significantly different (P < .0001). Logistic regression model demonstrated that as NN increased, the probability of a MC diagnosis decreased (<4%). AR values were different at a statistically significant level only between benign and malignant specimens (P = .00006), not between HCCs and MCs (P = .933). CONCLUSION: Quantitative analysis of AgNORs in ThinPrep specimens could be a diagnostically useful method in liver disease.