Restrictions on the coefficients of hyperbolic systems of partial differential equations

The paper deals with hyperbolic homogeneous systems [Formula: see text] of partial differential equations with constant coefficients for an N-vector u(t,x₁,...,x_n). Here, P is a matrix form of order N and degree m. In the scalar case (N = 1), every hyperbolic P is limit of strictly hyperbolic ones. This does not hold for systems as is shown here for the special case N = n = 3, m = 2. Assuming P(1,0,...,0) to be the unit matrix, we represent P by a point in R₈₁. The hyperbolic P form a closed set H in R₈₁, the strictly hyperbolic ones an open subset H_s of H. An example is given for a P in H which is not in the closure of H_s. Moreover, it is shown that near that P the set H coincides with an algebraic manifold of codimension 4.     

Euler and Navier–Stokes equations on the hyperbolic plane

We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ² observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍⁿ whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.     

New resting energy expenditure prediction equations for patients with rheumatoid arthritis

Objectives. Resting energy expenditure (REE), one of the maincomponents of total energy expenditure, can be measured viaindirect calorimetry and/or predicted from equations. The lattermay be misleading in RA, as they do not take into account themetabolic alterations occurring in RA. The objectives of thisstudy are to evaluate the accuracy of widely used REE-predictiveequations in RA patients against measured REE and to developRA-specific equations. Methods. We assessed REE (via indirect calorimetry and severalpredictive equations), fat-free mass (FFM; via bioelectricalimpedance) and disease activity (CRP) in RA patients and healthycontrols. Data from 60 RA patients (experimental group) wereused to assess the accuracy of existing REE equations and todevelop new equations. The new equations were validated in anindependent cross-validation group of 22 RA patients. Thesetwo groups were merged and two final equations were developed. Results. All equations significantly under-predicted measuredREE (from 15% to 18.2%, all at P < 0.001) in the RA experimentalgroup, but not in the control group. After both equations demonstrateda high validity in the cross-validation group, the new finalREE prediction equations developed from the total RA sample(n = 82) were: Model 1: REE (kcal/day) = 126.1 x FFM^0.638 xCRP^0.045 (R² = 0.70) and Model 2: REE (kcal/day) = 598.8 x weight^0.47x age^–0.29 x CRP^0.066 (R² = 0.62). Conclusion. The new equations provide an accurate predictionof REE in RA patients and could be used for clinical monitoringof resting metabolism of these patients without the requirementfor specialized personnel. KEY WORDS: Resting energy expenditure, Metabolism, Equation, Prediction Submitted 14 May 2007; revised version accepted 10 January 2008.     

Chemical probes for higher-order structure in RNA.

Three chemical reactions can probe the secondary and tertiary interactions of RNA molecules in solution. Dimethyl sulfate monitors the N-7 of guanosines and senses tertiary interactions there, diethyl pyrocarbonate detects stacking of adenosines, and an alternate dimethyl sulfate reaction examines the N-3 of cytidines and thus probes base pairing. The reactions work between 0 degrees C and 90 degrees C and at pH 4.5--8.5 in a variety of buffers. As an example we follow the progressive denaturation of yeast tRNAPhe terminally labeled with 32P as the tertiary and secondary structures sequentially melt out. A single autoradiograph of a terminally labeled molecule locates regions of higher-order structure and identifies the bases involved.     

Comparison of predictive equations for resting energy expenditure in severely obese Caucasian children and adolescents

The objective of the present study was to compare resting energy expenditure (REE) calculated by different predictive equations (McDuffie, Derumeaux, Tverskaya, Schofield, FAO/WHO/ UNU, Harris-Benedict and Lazzer-Sartorio) to REE measured in severely obese Caucasian children and adolescents. Two hundred and eighty-seven obese children and adolescents (121 males, 166 females, mean age: 14.5 yr, mean body mass index (BMI) z-score: 3.3) participated in this study. REE was measured (MREE) by indirect calorimetry and body composition by bioelectrical impedance analysis. The FAO/WHO/UNU equations showed the lowest mean difference between predicted resting energy expenditure (PREE) and MREE (+0.2%, p=ns), but the higher SD (+/-1.16 MJ) and the PREE were accurate in 26% of subjects. The Tverskaya, Derumeaux and Harris-Benedict equations significantly underestimated REE in all children and adolescents (-7.6, -4.1, and -2.4%, respectively, p<0.05), while the Schofield and McDuffie equations overestimated REE (+2.5, +5 and 25%, respectively, p<0.05). By contrast, the Lazzer-Sartorio equations showed the greater agreement and accuracy (in 55% of subjects) between mean PREEs and MREE for all children and adolescents, as well as for boys and girls (+1.6%, p=ns). In conclusion, Lazzer-Sartorio equations showed an accurate estimation of REE in groups of severely obese children and adolescents, resulting in lower mean differences and SD and higher accuracy between PREE and MREE than the other equations considered in this study.     

Poor prediction of resting energy expenditure in obese women by established equations

The objective of the study was to evaluate the accuracy of established prediction equations that calculate resting energy expenditure (REE) in obese women. This was a cross-sectional study. In 273 mildly to severely obese women (age, 41.7 ± 13.2 years; body mass index, 42.8 ± 7.0 kg/m²), REE was measured by indirect calorimetry (mREE), along with fat mass (FM) and fat-free mass (FFM) by bioelectrical impedance analysis. Eleven established equations were used to predict REE (pREE), with 9 equations basing on the anthropometric parameters body weight and height and 2 equations including body composition parameters (FM, FFM). All equations provided pREE values that significantly correlated with mREE (r > 0.66, P < .001), although 8 equations systematically underestimated mREE (P < .05). Of note, even the best equation was not able to accurately predict mREE with a deviation of less than ±10% in more than 70% of the tested women. Furthermore, equations using body composition data were not superior in predicting REE as compared with equations exclusively including anthropometric variables. Multiple linear regression analyses revealed 2 new equations—one including body weight and age and another including FM, FFM, and age—that explained 56.9% and 57.2%, respectively, of variance in mREE. However, when these 2 new equations were applied to an independent sample of 33 obese women, they also provided an accurate prediction (±10%) of mREE in only 56.7% and 60.6%, respectively, of the women. Data show that an accurate prediction of REE is not feasible using established equations in obese women. Equations that include body composition parameters as assessed by bioelectrical impedance analysis do not increase the accuracy of prediction. Based on our results, we conclude that calculating REE by standard prediction equations does not represent a reliable alternative to indirect calorimetry for the assessment of REE in obese women.     

How much may I eat? Calorie estimates based upon energy expenditure prediction equations

How much may I eat? Most healthcare workers, when asked this question, have insufficient knowledge to educate their patients on a healthy energy intake level. In this review we examine the available methods for estimating adult energy requirements with a focus on the newly developed National Academy of Sciences/Institute of Medicine (NAS/IOM) doubly‐labelled water total energy expenditure (TEE) prediction equations. An overview is first provided of the traditional factorial method of estimating energy requirements. We then extend this overview by exploring the development of the NAS/IOM TEE prediction models and their role in estimating energy requirments as a function of sex, age, weight, height and physical activity level. The NAS/IOM prediction models were developed for evaluating group energy requirements, although the formulas can be applied in individual ‘example’ patients for educational purposes. Potential limitations and interpretation issues of both the factorial and NAS/IOM methods are examined. This information should provide healthcare professionals with the tools and understanding to appropriately answer the question, ‘How much may I eat?’     

Formation of geometrically complex lipid nanotube-vesicle networks of higher-order topologies

We present a microelectrofusion method for construction of fluid-state lipid bilayer networks of high geometrical complexity up to fully connected networks with genus = 3 topology. Within networks, self-organizing branching nanotube architectures could be produced where intersections spontaneously arrange themselves into three-way junctions with an angle of 120 degrees between each nanotube. Formation of branching nanotube networks appears to follow a minimum-bending energy algorithm that solves for pathway minimization. It is also demonstrated that materials can be injected into specific containers within a network by nanotube-mediated transport of satellite vesicles having defined contents. Using a combination of microelectrofusion, spontaneous nanotube pattern formation, and satellite-vesicle injection, complex networks of containers and nanotubes can be produced for a range of applications in, for example, nanofluidics and artificial cell design. In addition, this electrofusion method allows integration of biological cells into lipid nanotube-vesicle networks.     

Neural substrate for higher-order learning in an insect: Mushroom bodies are necessary for configural discriminations

Learning theories distinguish elemental from configural learning based on their different complexity. Although the former relies on simple and unambiguous links between the learned events, the latter deals with ambiguous discriminations in which conjunctive representations of events are learned as being different from their elements. In mammals, configural learning is mediated by brain areas that are either dispensable or partially involved in elemental learning. We studied whether the insect brain follows the same principles and addressed this question in the honey bee, the only insect in which configural learning has been demonstrated. We used a combination of conditioning protocols, disruption of neural activity, and optophysiological recording of olfactory circuits in the bee brain to determine whether mushroom bodies (MBs), brain structures that are essential for memory storage and retrieval, are equally necessary for configural and elemental olfactory learning. We show that bees with anesthetized MBs distinguish odors and learn elemental olfactory discriminations but not configural ones, such as positive and negative patterning. Inhibition of GABAergic signaling in the MB calyces, but not in the lobes, impairs patterning discrimination, thus suggesting a requirement of GABAergic feedback neurons from the lobes to the calyces for nonelemental learning. These results uncover a previously unidentified role for MBs besides memory storage and retrieval: namely, their implication in the acquisition of ambiguous discrimination problems. Thus, in insects as in mammals, specific brain regions are recruited when the ambiguity of learning tasks increases, a fact that reveals similarities in the neural processes underlying the elucidation of ambiguous tasks across species.Learning can be categorized into two levels of complexity termed elemental and configural (nonelemental) (1–3). Simple and unambiguous links between events characterize elemental learning (4). By contrast, ambiguity and nonlinearity characterize configural learning, where associations involve conjunctions of elemental stimuli, which may have different, contradictory outcomes. As a consequence, solving configural tasks typically requires treating stimulus conjunctions as being different from the simple sum of their elemental components (5–8). For example, in a negative patterning task (9–11), subjects have to discriminate a nonreinforced conjunction of two elements A and B from its reinforced elements (i.e., AB– vs. A+ and B+), which requires treating AB as being different from the simple sum of A and B (12, 13). The ambiguity of the task lies in the fact that each element (A and B) is as often reinforced (when presented alone) as nonreinforced (when presented as a compound). In mammals, different brain structures have been associated with these two learning forms: Whereas the hippocampus seems to be dispensable for learning elemental associations (6, 8), it is required for fast formation of conjunctive representations during learning tasks, such as spatial learning or contextual fear conditioning (6, 8, 10, 14–19). Moreover, the cortical system is necessary to form configural representations over extended training, thus supporting the learning of nonlinear discriminations,Here, we ask whether the specialization of different brain centers for learning tasks of different complexity is a property that can be extended to an insect brain. Insects offer the possibility of studying sophisticated behaviors and simultaneously accessing the neural bases of these behaviors (20). Several studies have shown that insects, in particular the honey bee Apis mellifera, possess higher-order cognitive abilities (5, 21), which raises the question of which neural mechanisms support these capacities in a brain whose size is only 1 mm³ (22).The mushroom bodies (MBs) are paired structures in the insect brain that have been historically associated with olfactory learning and memory. Their function has been extensively studied in a variety of elemental learning protocols, mainly in the honey bee and the fruit fly Drosophila melanogaster (23–29). In both species, MBs play a fundamental role for the encoding, storing, and retrieval of appetitive and aversive elemental memories, but no study has clearly established their role for nonelemental learning and memory (30). In fruit flies, this missing information may be due to the incapacity of these insects to solve nonelemental problems, such as negative patterning (31). By contrast, honey bees exhibit elaborated nonelemental learning abilities (32–36), which have been suggested to require intact MB function (5).Here, we used a combination of nonelemental conditioning protocols, disruption of MB function, and optophysiological recordings of neural activity to determine whether MBs are necessary for nonelemental forms of learning. Our results show that acquisition of olfactory patterning discriminations is impaired in bees in which neural activity in the MBs was blocked by procaine injection (37, 38), but not in control animals injected with saline solution. By contrast, MB blockade by procaine affected neither olfactory processing upstream of the MBs nor elemental olfactory discriminations. To uncover the neural mechanisms underlying the necessity of MBs for patterning discriminations, we focused on GABAergic feedback neurons (39), which provide inhibitory feedback to the MBs of the bee (40–43). We blocked GABAergic signaling by locally injecting picrotoxin (PTX), a GABA antagonist, into the MB calyces or into the MB lobes. We show that GABAergic feedback to the calyces—but not to the lobes—is required for patterning discriminations. These results uncover a previously unidentified role for MBs: namely, the disambiguation between elemental and conjunctive odor representations, thus supporting the learning of nonlinear discriminations.     

肾小球滤过率评估公式的比较

肾小球滤过率(GFR)是评价肾功能的重要指标,也是慢性肾脏病(CKD)分期的重要依据。使用公式评估GFR方法简便,已被广泛应用,其中Cockcroft-Gault(CG)公式和MDRD公式最为常用,CKD-EPI、改良MDRD公式、瑞金公式及基于胱抑素C的公式等次之,通过比较其偏差、精确度、准确性等指标发现,CG公式更适用于健康人群,但在肾功能不全患者适用性较差,且受体重影响明显;MDRD公式适用于肾功能不全患者,但在GFR水平较高时可靠性较差;CKD-EPI克服了MDRD公式在GFR较高时会低估真实值的缺点;改良MDRD公式和瑞金公式则更适用于中国人;而基于胱抑素C的公式在疾病早期有较好适用性。因此,尚需进一步改进或者发掘更好地评估GFR的公式。     

Spirometric reference equations for older adults

The objective of this study was to develop spirometric reference equations for healthy, never-smoking, older adults. It was designed as a cross-sectional observational study consisting of 1510 Seventh Day Adventists, ages 43-79 years enrolled in a study of health effects of air pollutants. Individuals were excluded from the reference group (n = 565) for a history of current respiratory illness, smoking, or chronic respiratory disease, and for a number of 'non-respiratory' conditions which were observed in these data to be related to lower values of FEV1. Gender-specific reference equations were developed for the entire reference group and for a subset above 65 years of age (n = 312). Controlling for height and age, lung function was found to be positively related to the difference between armspan and height, and in males was found to be quadratically related to age. The predicted values for this population generally fell within the range of those of other population groups containing large numbers of adults over the age of 65 years. Individuals with lung function below the 5th percentile in this sample, however, could not be reliably identified by using the lower limits of normal predictions commonly used in North America and Europe.     

A method for evaluating the structural quality of protein models by using higher-order phi-psi pairs scoring

A method is presented for scoring the model quality of experimental and theoretical protein structures. The structural model to be evaluated is dissected into small fragments via a sliding window, where each fragment is represented by a vector of multiple phi-psi angles. The sliding window ranges in size from a length of 1-10 phi-psi pairs (3-12 residues). In this method, the conformation of each fragment is scored based on the fit of multiple phi-psi angles of the fragment to a database of multiple phi-psi angles from high-resolution x-ray crystal structures. We show that measuring the fit of predicted structural models to the allowed conformational space of longer fragments is a significant discriminator for model quality. Reasonable models have higher-order phi-psi score fit values (m) > -1.00.     

Casimir energy for dielectrics

A treatment in terms of two scalar fields supplies the electromagnetic energy of attraction between two similar dielectric slabs with parallel plane interfaces.     

Comparison of Indian reference equations for spirometry interpretation

BACKGROUND AND OBJECTIVES: It would be desirable in a large country such as India that a single set of reference equations be used to interpret lung function tests performed across the entire country. This study compared north, west and south reference equations in interpreting spirometry results in north Indian patients. METHODS: Spirometric records of 27,383 patients aged 16-65 years were assessed. Spirometric values for FVC, FEV(1) and FEV(1)%FVC values derived from north, west and south Indian reference equations were compared. Differences in the lower limit of normal (LLN) were studied across the age and height range of the study group to determine if there was any clinically significant difference in the three derived values. RESULTS: The north and west Indian equations was discordant in 22.1% instances, and the north and south Indian equations in 12.9% instances, with kappa estimates of agreement being 0.626 and 0.781, respectively. Most of the patients with abnormal spirometry using north Indian equations were erroneously interpreted to have normal spirometry using west or south Indian equations. The south Indian equations underpredicted LLN for FVC and FEV(1) for most men and women. The west Indian equations underpredicted LLN for FVC and FEV(1) in all men, and in younger and short statured women. CONCLUSIONS: North, west and south Indian reference equations do not yield equivalent results for spirometry interpretation in north Indian patients.     

Single-particle EM reveals the higher-order domain architecture of soluble guanylate cyclase

Soluble guanylate cyclase (sGC) is the primary nitric oxide (NO) receptor in mammals and a central component of the NO-signaling pathway. The NO-signaling pathways mediate diverse physiological processes, including vasodilation, neurotransmission, and myocardial functions. sGC is a heterodimer assembled from two homologous subunits, each comprised of four domains. Although crystal structures of isolated domains have been reported, no structure is available for full-length sGC. We used single-particle electron microscopy to obtain the structure of the complete sGC heterodimer and determine its higher-order domain architecture. Overall, the protein is formed of two rigid modules: the catalytic dimer and the clustered Per/Art/Sim and heme-NO/O₂-binding domains, connected by a parallel coiled coil at two hinge points. The quaternary assembly demonstrates a very high degree of flexibility. We captured hundreds of individual conformational snapshots of free sGC, NO-bound sGC, and guanosine-5′-[(α,β)-methylene]triphosphate-bound sGC. The molecular architecture and pronounced flexibility observed provides a significant step forward in understanding the mechanism of NO signaling.Nitric oxide (NO) has emerged as an integral signaling molecule in biology. Soluble guanylate cyclase (sGC), the primary receptor of NO in mammals, binds NO via an Fe^II heme cofactor leading to a several hundred-fold increase in 3,5-cyclic guanosine monophosphate (cGMP) synthesis. cGMP then acts as a second messenger, targeting phosphodiesterases, ion-gated channels, and cGMP-dependent protein kinases. These target proteins go on to regulate many critical physiological functions including vasodilation, platelet aggregation, neurotransmission, and myocardial functions (1, 2). Disruptions in NO signaling have been linked to hypertension, erectile dysfunction, neurodegeneration, stroke, and heart disease (3, 4). sGC has been the focus of small-molecule modulators of activity for therapeutic advantage. Riociguat, which is a stimulator of sGC, has recently been approved for treatment of pulmonary hypertension (5). However, the mechanistic details underlying the modulation of sGC catalytic activity by NO and other small molecules remain largely unknown. Determining the structure of the full-length sGC, free and in complex with NO, is therefore a prerequisite to understanding its function and for the design and improvement of therapeutics for treatment of diseases involving the NO/cGMP pathway.The most extensively studied and physiologically relevant isoform of sGC is the 150-kDa heterodimer containing one α1 and one β1 subunit. Each subunit is comprised of four modular domains: the N-terminal heme-NO/O₂–binding (H-NOX), the Per/Arnt/Sim (PAS), the helical, and the C-terminal catalytic domain (Fig. 1). No structure of the complete holoenzyme is available to date, and its absence precludes answering key questions such as how NO occupancy of the N-terminal β H-NOX sensor domain is communicated to the C-terminal cyclase domain. Atomic models of isolated sGC domains have been obtained by X-ray crystallography or homology modeling (6–9) (Fig. 1). The arrangement of and interactions between these domains have been further studied using a variety of techniques, including mutational and truncation studies, Förster resonance energy transfer (FRET), resonance Raman spectroscopy, chemical cross-linking, small-angle X-ray scattering (SAXS), and hydrogen deuterium exchange (HDX) (10–14). These studies have been used to propose a variety of models for the mechanisms of action of sGC, but the lack of a comprehensive 3D structure of the sGC holoenzyme has so far impeded a confident assignment of domain hierarchy.Open in a separate windowFig. 1.sGC domain organization and X-ray crystallographic models. Each subunit contains four modular domains; α1 domains are shown in shades of gray, and β1 domains are shown in color. The H-NOX domain of the β1 subunit contains the heme cofactor, shown in red. Structures for Rattus norvegicus are modeled based on previously solved crystal structures of homologous domains (Materials and Methods). The H-NOX structures are modeled from a standalone Nostoc sp. PCC 7120 H-NOX domain (PDB: 2O09) (6). The PAS and helical domains are modeled on individual domain truncations. The PAS domain is based on the PAS domain from Manduca sexta (PDB: 4GJ4) (7), and the helical domain is based on the β1 R. norvegicus structure (3HLS) (8). The catalytic domain is the Homo sapiens α1β1 crystal structure (PDB: 3UVJ) (9).Here, we used EM to determine the first structure of the heterodimeric sGC holoenzyme. Fitting of the domain crystal structures into the EM reconstruction provides a detailed model for the higher-order architecture and quaternary organization of sGC and is consistent with all reported biochemical data. We obtained hundreds of individual 3D reconstructions of full-length Rattus norvegicus sGC using automated high-throughput single-particle electron microscopy (15, 16). The structures correspond to various snapshots of the enzyme and describe the conformational trajectory of this highly flexible protein. sGC is assembled from two ridged units: the smaller unit comprises the dimeric catalytic domain, and the larger unit is built from the clustering of the PAS and H-NOX domains. The helical domains form a dimeric parallel coiled coil that flexibly connects the two modules. These modules swing freely in relation to each other thereby allowing the structure to access a wide range of conformations. Strikingly, some of these conformations allow the N-terminal H-NOX domain to contact the C-terminal catalytic domain indicating the possibility of a direct allosteric control mechanism. We also obtained reconstructions of sGC in complex with NO as well as with guanosine-5′-[(α,β)-methylene]triphosphate (GPCPP), a noncyclizable analog of the natural substrate GTP, both in the presence and absence of NO. The overall domain architecture and range of the accessible conformations of these complexes are similar to the unbound sGC state, suggesting that ligand binding induces small-scale intradomain conformational changes mediated by flexibility transitions at two key linker points.