Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations.

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent "accurately" harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in "accurate" reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Pade approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.     

On a third kind of characteristic numbers of the spheroidal functions

A set of real positive numbers γ_αn(c) was found recently to be associated with the spheroidal functions of real order α > -1 as a consequence of their double orthogonality on (-1, 1) and (- ∞, ∞). In the range -1 < α < 0 these numbers are shown to be determined by the eigenvalues of a new integral equation for the spheroidal functions. Thus they represent a third kind of characteristic numbers. The new equation ceases to be an integral equation above the range -1 < α < 0 but it leads to computational formulas for γ_αn(c) that appear from numerical results to be valid for all real α > -1.     

From the Cover: Cluster-like coordinates in supersymmetric quantum field theory

Recently it has become apparent that ?? = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1–211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.     

Metalloreductase Steap3 coordinates the regulation of iron homeostasis and inflammatory responses

Background

Iron and its homeostasis are intimately related to inflammatory responses, but the underlying molecular mechanisms are poorly understood. We investigated the role of Steap3 in regulating iron homeostasis in macrophages, and the effects of Steap3 depletion on host inflammatory responses.

Design and Methods

We analyzed bone marrow-derived macrophages and primary cultured hepatocytes from Steap3^-/- mouse models to investigate the roles of Steap3 in coordinately regulating iron homeostasis and inflammatory responses. First, we examined iron distribution and iron status in cells deficient in Steap3, as well as the requirement for the Steap3 gene during inflammatory responses. Secondly, we analyzed the regulation of Steap3 expression by inflammatory stimuli and thus, the influence of these stimuli on iron distribution and homeostasis.

Results

We found that Steap3 mRNA was expressed at high levels in macrophages and hepatocytes. Steap3 deficiency led to impaired iron homeostasis, causing abnormal iron distribution and a decreased availability of cytosolic iron in macrophages. Among STEAP family members, Steap3 mRNA was uniquely down-regulated in macrophages stimulated by lipopolysaccharides. To determine whether Steap3 regulated iron homeostasis during inflammatory stress, we treated Steap3^-/- mice with lipopolysaccharide, which produced greater iron accumulation in the vital tissues of these mice compared to in the tissues of wild-type controls. Furthermore, Steap3 depletion led to impaired induction of interferon-β, monocyte chemoattractant protein-5, and interferon induced protein-10 in macrophages via the TLR4-mediated signaling pathway.

Conclusions

Steap3 is important in regulating both iron homeostasis and TLR4-mediated inflammatory responses in macrophages. Steap3 deficiency causes abnormal iron status and homeostasis, which leads to impaired TLR4-mediated inflammatory responses in macrophages. Following inflammatory stimuli, Steap3 depletion causes dysregulated iron sequestration and distribution. Our results provide important insights into the function of Steap3 as a coordinate regulator of both iron homeostasis and innate immunity.     

DNA-induced narrowing of the gyrase N-gate coordinates T-segment capture and strand passage

DNA gyrase introduces negative supercoils into DNA in an ATP-dependent reaction. DNA supercoiling is catalyzed by a strand-passage mechanism, in which a T-segment of DNA is passed through the gap in a transiently cleaved G-segment. Strand passage requires the coordinated closing and opening of three protein interfaces in gyrase, the N-gate, DNA-gate, and C-gate. We show here that DNA binding to the DNA-gate of gyrase and wrapping of DNA around the C-terminal domains of GyrA induces a narrowing of the N-gate. This half-closed state prepares capture of a T-segment in the upper cavity of gyrase. Subsequent N-gate closure upon binding of ATP then poises the reaction toward strand passage. The N-gate reopens after ATP hydrolysis, allowing for further catalytic cycles. DNA binding, cleavage, and wrapping and N-gate narrowing are intimately linked events that coordinate conformational changes at the DNA and the N-gate.     

Higher-order syzygies for the bracket algebra and for the ring of coordinates of the Grassmanian

A Poincaré resolution is given for the supersymmetric ring of brackets over a signed alphabet. As a consequence, a resolution is found for the ring of coordinates of the Grassmanian variety in projective space over any infinite field.     

Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading

Cell migration and spreading involve the coordination of membrane trafficking, actomyosin contraction, and modifications to plasma membrane tension and area. The biochemical or biophysical basis for this coordination is however unknown. In this study, we show that during cell spreading, lamellipodia protrusion flattens plasma membrane folds and blebs and, once the plasma membrane area is depleted, there is a temporary increase in membrane tension by over twofold that is followed by activation of exocytosis and myosin contraction. Further, an artificial increase in plasma membrane tension stopped lamellipodia protrusion and activated an exocytotic burst. Subsequent decrease in tension restored spreading with activation of contraction. Conversely, blebbistatin inhibition of actomyosin contraction resulted in an even greater increase in plasma membrane tension and exocytosis activation. This spatiotemporal synchronization indicates that membrane tension is the signal that coordinates membrane trafficking, actomyosin contraction, and plasma membrane area change. We suggest that cells use plasma membrane tension as a global physical parameter to control cell motility.     

An autocrine axis in the testis that coordinates spermiation and blood-testis barrier restructuring during spermatogenesis

The mechanism(s) that regulate and coordinate the events of spermiation and blood-testis barrier (BTB) restructuring in the seminiferous epithelium that occur concurrently at stage VIII of the seminiferous epithelial cycle of spermatogenesis are unknown. In this report, fragments derived from the laminin complex composed of laminin alpha3, beta3, and gamma3 chains (laminin-333) at the apical ectoplasmic specialization (apical ES) were shown to modulate BTB dynamics directly and/or indirectly via hemidesmosome. Experiments were performed using cultured Sertoli cells with functional tight junction (TJ) barrier and the ultrastructural features of the BTB but not apical ES. Recombinant protein fragments of laminin beta3 and gamma3 chains were shown to reduce the protein levels of occludin and beta1-integrin dose dependently at the Sertoli-Sertoli and Sertoli-basement membrane interface, respectively, thereby destabilizing the BTB permeability function. These results were corroborated by transient overexpression of laminin fragments in Sertoli cells. To further assess the role of beta1-integrin in hemidesmosome, knockdown of beta1-integrin in Sertoli cells by RNAi was found to associate with occludin redistribution at the Sertoli-Sertoli cell interface, wherein occludin moved away from the cell surface and became associated with endosomes, thereby destabilizing the BTB. In short, an apical ES-BTB-hemidesmosome autocrine regulatory axis was identified in testes, coordinating the events of spermiation and BTB restructuring that occur at the opposite ends of the seminiferous epithelium during spermatogenesis.     

General properties of the Yang-Mills equations in physical space

With the formulation of the gauge group as a Banach-Lie group of suitable Sobolev type, the Cauchy problem for the Yang-Mills equation in physical space-time reduces rigorously to the case of the temporal gauge. In this gauge there exist spatially global strong solutions for given data for field and potential that are L₂ together with one or two derivatives (respectively). Regarding global existence in time, there is strong unicity, strong existence unless the potential becomes unbounded, and existence of a quasi-solution for arbitrary finite-energy Cauchy data. The variety of solutions of the equations is endowed with a canonical symplectic structure. This structure is degenerate to an extent precisely reflecting gauge-invariance and is conformally invariant.     

Rho GTPase Cdc42 coordinates hematopoietic stem cell quiescence and niche interaction in the bone marrow

Adult hematopoietic stem cells (HSCs) exist in a relatively quiescent state in the bone marrow (BM) microenvironment to fulfill long-term self-renewal and multilineage differentiation functions, an event that is tightly regulated by extrinsic and intrinsic cues. However, the mechanism coordinating the quiescent state of HSCs and their retention in the BM microenvironment remains poorly understood. In a conditional-knockout mouse model, we show that Cdc42(-/-) HSCs enter the active cell cycle, resulting in significantly increased number and frequency of the stem/progenitor cells in the BM. Cdc42 deficiency also causes impaired adhesion, homing, lodging, and retention of HSCs, leading to massive egress of HSCs from BM to distal organs and peripheral blood and to an engraftment failure. These effects are intrinsic to the HSCs and are associated with deregulated c-Myc, p21(Cip1), beta1-integrin, and N-cadherin expressions and defective actin organization. Thus, Cdc42 is a critical coordinator of HSC quiescence maintenance and interaction with the BM niche.     

EphrinB2 coordinates the formation of a morphological boundary and cell epithelialization during somite segmentation

During early morphogenesis, tissue segregation is often accompanied by changes in cell shape. To understand how such coordination is regulated, somitogenesis was used as a model. When a somite forms in the anterior end of the presomitic mesoderm, an intersomitic boundary (gap) emerges, and it is rapidly followed by cell epithelialization at this border. It has been known that the gap formation is regulated by intercellular signals. We here demonstrate that cMeso-1, the chicken homolog of mouse Mesp2, up-regulates EphA4 in the cells located posteriorly to a forming boundary. This in turn activates EphrinB2-reverse signals in the anteriorly juxtaposed cells, where the EphrinB2 signal is sufficient to cause a gap formation and cell epithelialization cell-autonomously. During these processes, Cdc42 needs to be repressed via tyrosine phosphorylation of EphrinB2. This is the first demonstration that Ephrin-reverse signal acts as a platform that couples distinct morphogenetic changes in cell polarity and tissue shape.     

In vivo evaluation of vascular-targeted spheroidal microparticles for imaging and drug delivery application in atherosclerosis

Objective: Vascular-targeting remains a promising strategy for improving the diagnosis and treatment of coronary artery disease (CAD) by providing localized delivery of imaging and therapeutic agents to atherosclerotic lesions. In this work we evaluate how size and shape affects the capacity for a vascular-targeted carrier system to bind inflamed endothelial cells over plaque using ApoE −/− mice with developed atherosclerosis. Method: We investigated the adhesion levels along mouse aortae of ellipsoidal and spherical particles targeted to the inflammatory molecules E-selectin and VCAM-1, as well as the biodistribution of targeted and untargeted particles in major organs following injection via tail-vein and a 30-min circulation time. Results: We found that targeted ellipsoidal microparticles adhered to mouse aortae at higher levels than microspheres of similar volume, particularly at segments that contained atherosclerotic plaques. Moreover, both ellipsoidal and spherical nanoparticles displayed the same minimal adhesion levels compared to both types of microparticles evaluated, likely due to poor localization of nanoparticles to the vessel wall in blood flow. We found that microparticles targeted to plaque-associated inflammation were retained at higher levels in the lungs than untargeted particles, largely due to molecular interaction with the pulmonary endothelium. The level of the mechanical entrapment of ellipsoidal microparticles in the lungs was also not significantly different from that of microspheres of the same volume despite a ∼3-fold higher major axis length for the ellipsoids. Conclusions: Particle shape and size should be considered in the design of carrier systems to target atherosclerosis, as these parameters can be tuned to improve carrier performance.     

Reference equations of the impulse oscillatory in healthy Thai adults

BackgroundThe ethnicity is significantly under-reported and this may limit the applicability of current impulse oscillometry (IOS) equations to heterogeneous patient populations. Establishing predictive equations for the IOS in the Thai adult population is still required. Therefore, this study aimed to establish reference equations for the IOS in the Thai adult population.MethodsThis retrospective cross-sectional study of IOS parameters in healthy adults aged greater than 20 years old with normal spirometry and who had no chronic respiratory diseases. Pre-bronchodilator (BD) IOS was performed in all subjects. Reference equations were calculated separately for men and women using multivariable linear regression analysis.ResultsA total of 127 subjects (87 men and 40 women) with a mean age of 48.7±17.2 (range, 22–92) years were included. The resistance at 5 Hz (R5), resistance at 20 Hz (R20), and area under reactance curve between 5 Hz and resonant frequency (AX) were significantly higher in women compared to men. The reference equations of the IOS parameters were established for men and women. Age, height, and bodyweight were shown to be the influential predictor as they contributed to the most of IOS indices except for the R5–R20 in men equations. Bodyweight was shown to be the influential predictor as it contributed to the most IOS indices except for the X5 in women’s equations.ConclusionsWe provided the reference equations for the IOS indices in Thai adults. IOS indices including R5, R20, and AX were significantly higher in women compared to men.     

Localizing coordinates of cerebral ischemic tissue without the need of staining in a rat model of focal cerebral infarct

Biochemical and metabolic analysis of ischemic cerebral tissue is central in stroke investigation and is usually performed in animal stroke models, such as the permanent occlusion of the middle cerebral artery (MCAO) in the rat that we have used. To be sure that the sample is from infarct tissue, it is differentiated from the surrounding normal tissue by staining, usually with 2,3,5-triphenyltetrazolium chloride (TTC), but staining can hamper biochemical colorimetric analysis. We performed this study to avoid this obstacle. A cerebral infarct was provoked in a sample of 10 rats and the brain was cut in coronal sections that were stained with TTC so that the unstained, infarct areas could be delineated in a template of each section in which areas with infarct in all animals were delineated. We calculated infarct coordinates and depth so that the infarct tissue can be sampled without staining. For more precision, the ischemic cortex can be delimited staining its surface before sectioning and cortical tissue into which TTC diffuses can be afterwards discarded, as we had previously measured the TTC diffusion depth in rat brains.     

Detection of the ischemic reaction of the myocardium by means of the polar coordinates of the ST segment in the corrected orthogonal ECG]

In the case of coronary heart disease the behaviour of the ST segment proved to be of major diagnostic importance for the recognition of hypoxidotic processes in the myocardium. Isolated consideration of the T-wave does not provide any characteristic information. The so-called ischaemic reaction is characterized by a typical jump of polar vectors from the left to the right side, which are moved rearwards without usually leaving the right-hand quadrant at the front. The angles of elevation are in a horizontal position or directed slightly upwards. This change of the direction can but need not include an increased magnitude. It is possible to observe the development of ischaemia as exercise is increased, with the polar vectors increasing or unchanging in magnitude and being moved rightwards, rearwards, and upwards. This characteristic movement invariably starts at the J point, involving additional portions of the ST segment as ischaemia is developed during increasing exercise. The J point depression should be considered to be only a "normal" response to exercise, provided the variations relate to the J point or 20 ms away from the latter.     

Solution of the discrete Plateau problem

We solve a discrete version of the classic Plateau problem, which asks for a minimal surface spanning a given curve. Our algorithm is based on a network-flow formulation that finds minimal slabs, intuitively corresponding to minimal "surfaces" of prescribed thickness. We let the slab thickness approach zero in order to obtain the desired minimal surface.