Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

Design considerations for engineering 3D models to study vascular pathologies in vitro

Many cardiovascular diseases (CVD) are driven by pathological remodelling of blood vessels, which can lead to aneurysms, myocardial infarction, ischaemia and strokes. Aberrant remodelling is driven by changes in vascular cell behaviours combined with degradation, modification, or abnormal deposition of extracellular matrix (ECM) proteins. The underlying mechanisms that drive the pathological remodelling of blood vessels are multifaceted and disease specific; however, unravelling them may be key to developing therapies. Reductionist models of blood vessels created in vitro that combine cells with biomaterial scaffolds may serve as useful analogues to study vascular disease progression in a controlled environment. This review presents the main considerations for developing such in vitro models. We discuss how the design of blood vessel models impacts experimental readouts, with a particular focus on the maintenance of normal cellular phenotypes, strategies that mimic normal cell-ECM interactions, and approaches that foster intercellular communication between vascular cell types. We also highlight how choice of biomaterials, cellular arrangements and the inclusion of mechanical stimulation using fluidic devices together impact the ability of blood vessel models to mimic in vivo conditions. In the future, by combining advances in materials science, cell biology, fluidics and modelling, it may be possible to create blood vessel models that are patient-specific and can be used to develop and test therapies

A Hydrogel-Integrated Culture Device to Interrogate T Cell Activation with Physicochemical Cues

The recent rise of adoptive T cell therapy (ATCT) as a promising cancer immunotherapy has triggered increased interest in therapeutic T cell bioprocessing. T cell activation is a critical processing step and is known to be modulated by physical parameters, such as substrate stiffness. Nevertheless, relatively little is known about how biophysical factors regulate immune cells, such as T cells. Understanding how T cell activation is modulated by physical and biochemical cues may offer novel methods to control cell behavior for therapeutic cell processing. Inspired by T cell mechanosensitivity, we developed a multiwell, reusable, customizable, two-dimensional (2D) polyacrylamide (PA) hydrogel-integrated culture device to study the physicochemical stimulation of Jurkat T cells. Substrate stiffness and ligand density were tuned by concentrations of the hydrogel cross-linker and antibody in the coating solution, respectively. We cultured Jurkat T cells on 2D hydrogels of different stiffnesses that presented surface-immobilized stimulatory antibodies against CD3 and CD28 and demonstrated that Jurkat T cells stimulated by stiff hydrogels (50.6 ± 15.1 kPa) exhibited significantly higher interleukin-2 (IL-2) secretion, but lower proliferation, than those stimulated by softer hydrogels (7.1 ± 0.4 kPa). In addition, we found that increasing anti-CD3 concentration from 10 to 30 μg/mL led to a significant increase in IL-2 secretion from cells stimulated on 7.1 ± 0.4 and 9.3 ± 2.4 kPa gels. Simultaneous tuning of substrate stiffness and stimulatory ligand density showed that the two parameters synergize (two-way ANOVA interaction effect: p < 0.001) to enhance IL-2 secretion. Our results demonstrate the importance of physical parameters in immune cell stimulation and highlight the potential of designing future immunostimulatory biomaterials that are mechanically tailored to balance stimulatory strength and downstream proliferative capacity of therapeutic T cells

Modelling background intensity in Affymetrix Genechips

DNA microarrays are devices that are able, in principle, to detect and quantify the presence of specific nucleic acid sequences in complex biological mixtures. The measurement consists in detecting fluorescence signals from several spots on the microarray surface onto which different probe sequences are grafted. One of the problems of the data analysis is that the signal contains a noisy background component due to non-specific binding. This paper presents a physical model for background estimation in Affymetrix Genechips. It combines two different approaches. The first is based on the sequence composition, specifically its sequence dependent hybridization affinity. The second is based on the strong correlation of intensities from locations which are the physical neighbors of a specific spot on the chip. Both effects are incorporated in a background functional which contains 24 free parameters, fixed by minimization on a training data set. In all data analyzed the sequence specific parameters, obtained by minimization, are found to strongly correlate with empirically determined stacking free energies for RNA/DNA hybridization in solution. Moreover, there is an overall agreement with experimental background data and we show that the physics-based model proposed in this paper performs on average better than purely statistical approaches for background calculations. The model thus provides an interesting alternative method for background subtraction schemes in Affymetrix Genechips.Comment: 8 pages, 4 figure

Faster disease progression in Parkinson's disease with type 2 diabetes is not associated with increased α-synuclein, tau, amyloid-β or vascular pathology

AIMS: Growing evidence suggests a shared pathogenesis between Parkinson's disease and diabetes although the underlying mechanisms remain unknown. The aim of this study is to evaluate the effect of type 2 diabetes on Parkinson's disease progression and to correlate neuropathological findings to elucidate pathogenic mechanisms. METHODS: In this cohort study, medical records were retrospectively reviewed of cases with pathologically-confirmed Parkinson's disease with and without pre-existing type 2 diabetes. Time to disability milestones (recurrent falls, wheelchair dependence, dementia, and care home placement) and survival were compared to assess disease progression and their risk estimated using Cox hazard regression models. Correlation with pathological data was performed, including quantification of α-synuclein in key brain regions and staging of vascular, Lewy and Alzheimer's pathologies. RESULTS: Patients with PD and diabetes (male 76%; age at death 78.6 ± 6.2 years) developed earlier falls (P < 0.001), wheelchair dependence (P = 0.004), dementia (P < 0.001), care home admission (P < 0.001) and had reduced survival (P < 0.001). Predating diabetes was independently associated with a two to three-fold increase in the risk of disability and death. Neuropathological assessment did not show any differences in global or regional vascular pathology, α-synuclein load in key brain areas, staging of Lewy pathology or Alzheimer's disease pathology. CONCLUSIONS: Pre-existing type 2 diabetes contributes to faster disease progression and reduced survival in Parkinson's disease which is not driven by increased vascular, Lewy or Alzheimer's pathologies. Additional non-specific neurodegeneration related to chronic brain insulin resistance may be involved

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Differential regulation of human bone marrow mesenchymal stromal cell chondrogenesis by hypoxia inducible factor-1α hydroxylase inhibitors

The transcriptional profile induced by hypoxia plays important roles in the chondrogenic differentiation of marrow stromal/stem cells (MSC) and is mediated by the Hypoxia Inducible Factor complex. However, various compounds can also stabilise HIF's oxygen-responsive element, HIF-1α, at normoxia and mimic many hypoxia-induced cellular responses. Such compounds may prove efficacious in cartilage tissue engineering, where microenvironmental cues may mediate functional tissue formation. Here, we investigated three HIF stabilising compounds, which each have distinct mechanisms of action, to understand how they differentially influenced the chondrogenesis of human bone marrow-derived MSC (hBM-MSC) in vitro. hBM-MSCs were chondrogenically-induced in TGF-β3 -containing media in the presence of HIF-stabilising compounds. HIF-1α stabilisation was assessed by HIF-1α immunofluorescence staining, expression of HIF target and articular chondrocyte specific genes by qPCR, and cartilage-like extracellular matrix (ECM) production by immunofluorescence and histochemical staining. We demonstrate that all three compounds induced similar levels of HIF-1α nuclear localisation. However, whilst the 2-oxoglutarate analogue Dimethyloxalylglycine (DMOG) promoted upregulation of a selection of HIF target genes, Desferrioxamine (DFX) and Cobalt Chloride (CoCl2 ), compounds that chelate or compete with Fe2+ , respectively, did not. Moreover, DMOG induced a more chondrogenic transcriptional profile, which was abolished by Acriflavine, an inhibitor of HIF-1α-HIF-β binding, whilst the chondrogenic effects of DFX and CoCl2 were more limited. Together, these data suggest that HIF-1α function during hBM-MSC chondrogenesis may be regulated by mechanisms with a greater dependence on 2-oxoglutarate than Fe2+ availability. These results may have important implications for understanding cartilage disease and developing targeted therapies for cartilage repair. This article is protected by copyright. All rights reserved