Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.Comment: 18 pages, accepted for publicatio

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Strong expression of ID1 protein is associated with decreased survival, increased expression of ephrin-A1/EPHA2, and reduced thrombospondin-1 in malignant melanoma

The ID1 protein, an inhibitor of basic helix–loop–helix transcription factors, has been involved in multiple cellular processes including cell cycle regulation, apoptosis, and angiogenesis. To evaluate the importance of ID1 in malignant melanoma, tumour cell expression was examined by immunohistochemistry in 119 cases of nodular melanoma using tissue microarray technique, and related to multiple tumour markers including proliferation, p16 expression, angiogenesis and patient survival. Strong ID1 expression was significantly associated with increased tumour thickness, and significantly reduced survival. Also, increased ID1 was associated with loss of thrombospondin-1 (TSP-1) expression, a known inhibitor of angiogenesis, and increased intensity of ephrin-A1 and its receptor EPHA2. Presence of BRAF mutations was related to strong ID1 expression, but there was no relationship with p16 protein expression. Further, no significant correlation was found between ID1 and microvessel density. In conclusion, our study supports a significant role of the ID1 protein in melanoma progression and patient prognosis. The absence of correlation with p16 protein expression and angiogenesis suggests that other regulatory pathways and mechanisms might be influenced by ID1 in melanomas. An inverse relation between ID1 and TSP-1 expression support an important role of ID1 in the regulation of this complex multitarget protein

Association of angiotensin-converting enzyme inhibitor therapy and comorbidity in diabetes: results from the Vermont diabetes information system

<p>Abstract</p> <p>Background</p> <p>Angiotensin converting enzyme inhibitors (ACE inhibitors) reduce peripheral vascular resistance via blockage of angiotensin converting enzyme (ACE). ACE inhibitors are commonly used to treat congestive heart failure and high blood pressure, but other effects have been reported. In this study, we explored the association between ACE inhibitor therapy and the prevalence of comorbid conditions in adults with diabetes</p> <p>Methods</p> <p>We surveyed 1003 adults with diabetes randomly selected from community practices. Patients were interviewed at home and self-reported their personal and clinical characteristics including comorbidity. Current medications were obtained by direct observation of medication containers. We built logistic regression models with the history of comorbidities as the outcome variable and the current use of ACE inhibitors as the primary predictor variable. We adjusted for possible confounding by social (age, sex, alcohol drinking, cigarette smoking) and clinical factors (systolic blood pressure, body mass index (BMI), glycosolated hemoglobin (A1C), number of comorbid conditions, and number of prescription medications).</p> <p>Results</p> <p>ACE users reported a history of any cancer (except the non-life-threatening skin cancers) less frequently than non-users (10% <it>vs</it>. 15%; odd ratio = 0.59; 95% confidence interval [0.39, 0.89]; <it>P </it>= 0.01); and a history of stomach ulcers or peptic ulcer disease less frequently than non-users (12% <it>vs</it>. 16%, odd ratio = 0.70, [0.49, 1.01], <it>P </it>= 0.06). After correcting for potential confounders, ACE inhibitors remained significantly inversely associated with a personal history of cancer (odds ratio = 0.59, [0.39, 0.89]; <it>P </it>= 0.01) and peptic ulcer disease (odd ratio = 0.68, [0.46, 1.00], <it>P </it>= 0.05).</p> <p>Conclusion</p> <p>ACE inhibitor use is associated with a lower likelihood of a history of cancer and peptic ulcers in patients with diabetes. These findings are limited by the cross sectional study design, self-report of comorbid diagnoses, and lack of information on the timing and duration of ACE inhibitor use. Further research is needed to confirm these associations and understand their mechanisms.</p

A large scale survey reveals that chromosomal copy-number alterations significantly affect gene modules involved in cancer initiation and progression

Background Recent observations point towards the existence of a large number of neighborhoods composed of functionally-related gene modules that lie together in the genome. This local component in the distribution of the functionality across chromosomes is probably affecting the own chromosomal architecture by limiting the possibilities in which genes can be arranged and distributed across the genome. As a direct consequence of this fact it is therefore presumable that diseases such as cancer, harboring DNA copy number alterations (CNAs), will have a symptomatology strongly dependent on modules of functionally-related genes rather than on a unique "important" gene. Methods We carried out a systematic analysis of more than 140,000 observations of CNAs in cancers and searched by enrichments in gene functional modules associated to high frequencies of loss or gains. Results The analysis of CNAs in cancers clearly demonstrates the existence of a significant pattern of loss of gene modules functionally related to cancer initiation and progression along with the amplification of modules of genes related to unspecific defense against xenobiotics (probably chemotherapeutical agents). With the extension of this analysis to an Array-CGH dataset (glioblastomas) from The Cancer Genome Atlas we demonstrate the validity of this approach to investigate the functional impact of CNAs. Conclusions The presented results indicate promising clinical and therapeutic implications. Our findings also directly point out to the necessity of adopting a function-centric, rather a gene-centric, view in the understanding of phenotypes or diseases harboring CNAs.Spanish Ministry of Science and Innovation (grant BIO2008-04212)Spanish Ministry of Science and Innovation (grant FIS PI 08/0440)GVA-FEDER (PROMETEO/2010/001)Red Temática de Investigación Cooperativa en Cáncer (RTICC) (grant RD06/0020/1019)Instituto de Salud Carlos III (ISCIII)Spanish Ministry of Science and InnovationSpanish Ministry of Health (FI06/00027

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

EFNA3 long noncoding RNAs induced by hypoxia promote metastatic dissemination

The presence of hypoxic regions in solid tumors is an adverse prognostic factor for patient outcome. Here, we show that hypoxia induces the expression of Ephrin-A3 through a novel hypoxia-inducible factor (HIF)-mediated mechanism. In response to hypoxia, the coding EFNA3 mRNA levels remained relatively stable, but HIFs drove the expression of previously unknown long noncoding (lnc) RNAs from EFNA3 locus and these lncRNA caused Ephrin-A3 protein accumulation. Ephrins are cell surface proteins that regulate diverse biological processes by modulating cellular adhesion and repulsion. Mounting evidence implicates deregulated ephrin function in multiple aspects of tumor biology. We demonstrate that sustained expression of both Ephrin-A3 and novel EFNA3 lncRNAs increased the metastatic potential of human breast cancer cells, possibly by increasing the ability of tumor cells to extravasate from the blood vessels into surrounding tissue. In agreement, we found a strong correlation between high EFNA3 expression and shorter metastasis-free survival in breast cancer patients. Taken together, our results suggest that hypoxia could contribute to metastatic spread of breast cancer via HIF-mediated induction of EFNA3 lncRNAs and subsequent Ephrin-A3 protein accumulation

Can a Species Keep Pace with a Shifting Climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back

Blockage of angiotensin II type I receptor decreases the synthesis of growth factors and induces apoptosis in C6 cultured cells and C6 rat glioma

Angiotensin II (Ang II) is a main effector peptide in the renin–angiotensin system and participates in the regulation of vascular tone. It also has a role in the expression of growth factors that induce neovascularisation which is closely associated to the growth of malignant gliomas. We have shown that the selective blockage of the AT1 receptor of angiotensin inhibites tumour growth, cell proliferation and angiogenesis of C6 rat glioma. The aim of this study was to study the effects of the blockage of AT1 receptor on the synthesis of growth factors, and in the genesis of apoptosis in cultured C6 glioma cells and in rats with C6 glioma. Administration of losartan at doses of 40 or 80 mg kg−1 to rats with C6 glioma significantly decreased tumoral volume and production of platelet-derived growth factor, vascular endothelial growth factor and basic fibroblast growth factor. It also induced apoptosis in a dose-dependent manner. Administration of Ang II increased cell proliferation of cultured C6 cells which decreased by the administration of losartan. Our results suggest that the selective blockage of AT1 diminishes tumoral growth through inhibition of growth factors and promotion of apoptosis