Passive scalar decay in chaotic flows with boundaries

Journal ArticleThis paper considers the long-time decay rate of a passive scalar in twodimensional flow. The focus is on the effects of boundary conditions for kinematically prescribed velocity fields with random or periodic time dependence. Scalar evolution is followed numerically in a periodic geometry for families of flows that have either a slip or a no-slip boundary condition on a square or plane layer subdomain D. The boundary conditions on the passive scalar are imposed on the boundary of D by restricting to a subclass invariant under certain symmetry transformations. The scalar field obeys constant (Dirichlet) or no-flux (Neumann) conditions exactly for a flow with the slip boundary condition and approximately in the no-slip case. At late times the decay of a passive scalar is exponential in time with a decay rate γ (κ), where κ is the molecular diffusivity. Scaling laws of the form γ(κ) ζ C κ α for small κ are obtained numerically for a variety of boundary conditions on flow and scalar, and supporting theoretical arguments are presented. In particular when the scalar field satisfies a Neumann condition on all boundaries, α ζ 0 0 for a slip flow condition; for a no-slip condition we confirm results in the literature that α ζ 1/2 for a plane layer, but find α ζ 2/3 in a square subdomain D where the decay is controlled by stagnant flow in the corners. For cases where there is a Dirichlet boundary condition on one or more sides of the subdomain D, the exponent measuring the decay of the scalar field is α ζ 1/2 for a slip flow condition and α ζ 3/4 for a no-slip condition. The scaling law exponents α for chaotic time-periodic flows are compared with those for similarly constructed random flows. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.Libyan Governmen

Facial expressions depicting compassionate and critical emotions: the development and validation of a new emotional face stimulus set

Attachment with altruistic others requires the ability to appropriately process affiliative and kind facial cues. Yet there is no stimulus set available to investigate such processes. Here, we developed a stimulus set depicting compassionate and critical facial expressions, and validated its effectiveness using well-established visual-probe methodology. In Study 1, 62 participants rated photographs of actors displaying compassionate/kind and critical faces on strength of emotion type. This produced a new stimulus set based on N = 31 actors, whose facial expressions were reliably distinguished as compassionate, critical and neutral. In Study 2, 70 participants completed a visual-probe task measuring attentional orientation to critical and compassionate/kind faces. This revealed that participants lower in self-criticism demonstrated enhanced attention to compassionate/kind faces whereas those higher in self-criticism showed no bias. To sum, the new stimulus set produced interpretable findings using visual-probe methodology and is the first to include higher order, complex positive affect displays

Mechanically activated Piezo1 channels of cardiac fibroblasts stimulate p38 mitogen-activated protein kinase activity and interleukin-6 secretion

Piezo1 is a mechanosensitive cation channel with widespread physiological importance; however, its role in the heart is poorly understood. Cardiac fibroblasts help preserve myocardial integrity and play a key role in regulating its repair and remodeling following stress or injury. Here we investigated Piezo1 expression and function in cultured human and mouse cardiac fibroblasts. RT-PCR experiments confirmed that Piezo1 mRNA in cardiac fibroblasts is expressed at levels similar to those in endothelial cells. The results of a Fura-2 intracellular Ca2+ assay validated Piezo1 as a functional ion channel that is activated by its agonist, Yoda1. Yoda1-induced Ca2+ entry was inhibited by Piezo1 blockers (gadolinium and ruthenium red) and was reduced proportionally by siRNA-mediated Piezo1 knockdown or in murine Piezo1+/− cells. Results from cell-attached patch clamp recordings on human cardiac fibroblasts established that they contain mechanically activated ion channels and that their pressure responses are reduced by Piezo1 knockdown. Investigation of Yoda1 effects on selected remodeling genes indicated that Piezo1 activation increases both mRNA levels and protein secretion of IL-6, a pro-hypertrophic and profibrotic cytokine, in a Piezo1-dependent manner. Moreover, Piezo1 knockdown reduced basal IL-6 expression from cells cultured on softer collagen-coated substrates. Multiplex kinase activity profiling combined with kinase inhibitor experiments and phosphospecific immunoblotting established that Piezo1 activation stimulates IL-6 secretion via the p38 mitogen-activated protein kinase downstream of Ca2+ entry. In summary, cardiac fibroblasts express mechanically activated Piezo1 channels coupled to secretion of the paracrine signaling molecule IL-6. Piezo1 may therefore be important in regulating cardiac remodeling

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Feasibility of metabolic imaging of hyperpolarized 13C-pyruvate in human breast cancer

Introduction Imaging of the breast with hyperpolarized 13C yields new challenges compared to imaging the prostate [1]. E.g. large anteroposterior B0 gradients [2] require correction and the anatomy and patient positioning need a new, highly optimized RF coil array for achieving sufficient SNR/spatial resolution. As a first step, we have investigated single-breast imaging in the coronal plane. Methods A BRCA gene carrier with a 38-mm diameter grade 3 triple-negative invasive ductal carcinoma was studied on a 3T MRI (GE Healthcare) using a prototype 8-channel 13C breast coil (Rapid Biomedical), containing 2 transmit/receive coils and 6 receive-only covering both breasts in a prone position. 1H imaging was performed with the body coil. Following injection of 40ml of 250mM 13C-pyruvate, polarized to c. 25%, a 1-minute time series of spirals with IDEAL encoding (3) was collected (flip angle 10°, TR=260ms, 8-step cycle, time resolution 2.08s, 3 x 3-cm thick slices, 3mm gap, 40-pt spiral, 24cm coronal FOV, real pixel size 12 x 12 x 30mm). IDEAL reconstruction of images was optimized separately for each slice to enable independent frequency offsets to be applied. Kinetic modelling was performed in MATLAB, with automated tumour segmentation. Results Tumour pixels were identified by the segmentation algorithm only in the tumour-containing slice 2, and the average estimated flux from pyruvate to lactate kPL within this ROI was 0.022 s-1 (Fig. 1). The frequency shift of pyruvate relative to slice 2 was +6 Hz in slice 3 and -34 Hz in slice 1, confirming a sharp gradient in B0 approaching the nipple, which was corrected by optimizing slices separately (Fig 2). Images of lactate and pyruvate summed over the time course (Fig 3) showed strong signal of both metabolites over the tumour in slice 2, lower pyruvate in the slice toward the chest wall, and no consistent signal in slice 1. Conclusion This first-in-Europe study in breast cancer established the feasibility of obtaining metabolite images with high temporal and moderate spatial resolution in humans in vivo following administration of hyperpolarized 13C-pyruvate. Coronal image orientation allowed application of significant corrections for a known limitation, the anteroposterior B0 gradient, as well as a small FOV to improve spatial resolution. Kinetic rate constants within the tumour were found to be consistent with previous reports in human prostate cancer (1). References 1) Nelson SJ et al. Sci Transl Med 5, 198ra108 (2013). 2) Maril N, et al. Magn. Reson. Med. 2005; 54:1139-1145. 3) Wiesinger F, et al. Magn Reson Med 2012; 68:8-16

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Computational modelling of cancerous mutations in the EGFR/ERK signalling pathway

This article has been made available through the Brunel Open Access Publishing Fund - Copyright @ 2009 Orton et al.BACKGROUND: The Epidermal Growth Factor Receptor (EGFR) activated Extracellular-signal Regulated Kinase (ERK) pathway is a critical cell signalling pathway that relays the signal for a cell to proliferate from the plasma membrane to the nucleus. Deregulation of the EGFR/ERK pathway due to alterations affecting the expression or function of a number of pathway components has long been associated with numerous forms of cancer. Under normal conditions, Epidermal Growth Factor (EGF) stimulates a rapid but transient activation of ERK as the signal is rapidly shutdown. Whereas, under cancerous mutation conditions the ERK signal cannot be shutdown and is sustained resulting in the constitutive activation of ERK and continual cell proliferation. In this study, we have used computational modelling techniques to investigate what effects various cancerous alterations have on the signalling flow through the ERK pathway. RESULTS: We have generated a new model of the EGFR activated ERK pathway, which was verified by our own experimental data. We then altered our model to represent various cancerous situations such as Ras, B-Raf and EGFR mutations, as well as EGFR overexpression. Analysis of the models showed that different cancerous situations resulted in different signalling patterns through the ERK pathway, especially when compared to the normal EGF signal pattern. Our model predicts that cancerous EGFR mutation and overexpression signals almost exclusively via the Rap1 pathway, predicting that this pathway is the best target for drugs. Furthermore, our model also highlights the importance of receptor degradation in normal and cancerous EGFR signalling, and suggests that receptor degradation is a key difference between the signalling from the EGF and Nerve Growth Factor (NGF) receptors. CONCLUSION: Our results suggest that different routes to ERK activation are being utilised in different cancerous situations which therefore has interesting implications for drug selection strategies. We also conducted a comparison of the critical differences between signalling from different growth factor receptors (namely EGFR, mutated EGFR, NGF, and Insulin) with our results suggesting the difference between the systems are large scale and can be attributed to the presence/absence of entire pathways rather than subtle difference in individual rate constants between the systems.This work was funded by the Department of Trade and Industry (DTI), under their Bioscience Beacon project programme. AG was funded by an industrial PhD studentship from Scottish Enterprise and Cyclacel

Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues

Copyright @ 2012 The Authors. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and 85 reproduction in any medium, provided the original author and source are credited. The article was made available through the Brunel University Open Access Publishing Fund.BACKGROUND: In interphase nuclei of a wide range of species chromosomes are organised into their own specific locations termed territories. These chromosome territories are non-randomly positioned in nuclei which is believed to be related to a spatial aspect of regulatory control over gene expression. In this study we have adopted the pig as a model in which to study interphase chromosome positioning and follows on from other studies from our group of using pig cells and tissues to study interphase genome re-positioning during differentiation. The pig is an important model organism both economically and as a closely related species to study human disease models. This is why great efforts have been made to accomplish the full genome sequence in the last decade. RESULTS: This study has positioned most of the porcine chromosomes in in vitro cultured adult and embryonic fibroblasts, early passage stromal derived mesenchymal stem cells and lymphocytes. The study is further expanded to position four chromosomes in ex vivo tissue derived from pig kidney, lung and brain. CONCLUSIONS: It was concluded that porcine chromosomes are also non-randomly positioned within interphase nuclei with few major differences in chromosome position in interphase nuclei between different cell and tissue types. There were also no differences between preferred nuclear location of chromosomes in in vitro cultured cells as compared to cells in tissue sections. Using a number of analyses to ascertain by what criteria porcine chromosomes were positioned in interphase nuclei; we found a correlation with DNA content.This study is partly supported by Sygen International PLC

Large introns in relation to alternative splicing and gene evolution: a case study of Drosophila bruno-3

Background: Alternative splicing (AS) of maturing mRNA can generate structurally and functionally distinct transcripts from the same gene. Recent bioinformatic analyses of available genome databases inferred a positive correlation between intron length and AS. To study the interplay between intron length and AS empirically and in more detail, we analyzed the diversity of alternatively spliced transcripts (ASTs) in the Drosophila RNA-binding Bruno-3 (Bru-3) gene. This gene was known to encode thirteen exons separated by introns of diverse sizes, ranging from 71 to 41,973 nucleotides in D. melanogaster. Although Bru-3's structure is expected to be conducive to AS, only two ASTs of this gene were previously described. Results: Cloning of RT-PCR products of the entire ORF from four species representing three diverged Drosophila lineages provided an evolutionary perspective, high sensitivity, and long-range contiguity of splice choices currently unattainable by high-throughput methods. Consequently, we identified three new exons, a new exon fragment and thirty-three previously unknown ASTs of Bru-3. All exon-skipping events in the gene were mapped to the exons surrounded by introns of at least 800 nucleotides, whereas exons split by introns of less than 250 nucleotides were always spliced contiguously in mRNA. Cases of exon loss and creation during Bru-3 evolution in Drosophila were also localized within large introns. Notably, we identified a true de novo exon gain: exon 8 was created along the lineage of the obscura group from intronic sequence between cryptic splice sites conserved among all Drosophila species surveyed. Exon 8 was included in mature mRNA by the species representing all the major branches of the obscura group. To our knowledge, the origin of exon 8 is the first documented case of exonization of intronic sequence outside vertebrates. Conclusion: We found that large introns can promote AS via exon-skipping and exon turnover during evolution likely due to frequent errors in their removal from maturing mRNA. Large introns could be a reservoir of genetic diversity, because they have a greater number of mutable sites than short introns. Taken together, gene structure can constrain and/or promote gene evolution

Endonuclease-independent LINE-1 retrotransposition at mammalian telomeres

Long interspersed element-1 (LINE-1 or L1) elements are abundant, non-long-terminal-repeat (non-LTR) retrotransposons that comprise 17% of human DNA(1). The average human genome contains similar to 80-100 retrotransposition- competent L1s (ref. 2), and they mobilize by a process that uses both the L1 endonuclease and reverse transcriptase, termed target-site primed reverse transcription(3-5). We have previously reported an efficient, endonuclease-independent L1 retrotransposition pathway (ENi) in certain Chinese hamster ovary (CHO) cell lines that are defective in the non-homologous end-joining (NHEJ) pathway of DNA double-strand-break repair(6). Here we have characterized ENi retrotransposition events generated in V3 CHO cells, which are deficient in DNA-dependent protein kinase catalytic subunit (DNA-PKcs) activity and have both dysfunctional telomeres and an NHEJ defect. Notably, similar to 30% of ENi retrotransposition events insert in an orientation-specific manner adjacent to a perfect telomere repeat (5'-TTAGGG-3'). Similar insertions were not detected among ENi retrotransposition events generated in controls or in XR-1 CHO cells deficient for XRCC4, an NHEJ factor that is required for DNA ligation but has no known function in telomere maintenance. Furthermore, transient expression of a dominant-negative allele of human TRF2 ( also called TERF2) in XRCC4-deficient XR-1 cells, which disrupts telomere capping, enables telomere-associated ENi retrotransposition events. These data indicate that L1s containing a disabled endonuclease can use dysfunctional telomeres as an integration substrate. The findings highlight similarities between the mechanism of ENi retrotransposition and the action of telomerase, because both processes can use a 3' OH for priming reverse transcription at either internal DNA lesions or chromosome ends(7,8). Thus, we propose that ENi retrotransposition is an ancestral mechanism of RNA-mediated DNA repair associated with non-LTR retrotransposons that may have been used before the acquisition of an endonuclease domain.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62964/1/nature05560.pd