Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Hyperpolarized Xe MR imaging of alveolar gas uptake in humans.

BACKGROUND: One of the central physiological functions of the lungs is to transfer inhaled gases from the alveoli to pulmonary capillary blood. However, current measures of alveolar gas uptake provide only global information and thus lack the sensitivity and specificity needed to account for regional variations in gas exchange. METHODS AND PRINCIPAL FINDINGS: Here we exploit the solubility, high magnetic resonance (MR) signal intensity, and large chemical shift of hyperpolarized (HP) (129)Xe to probe the regional uptake of alveolar gases by directly imaging HP (129)Xe dissolved in the gas exchange tissues and pulmonary capillary blood of human subjects. The resulting single breath-hold, three-dimensional MR images are optimized using millisecond repetition times and high flip angle radio-frequency pulses, because the dissolved HP (129)Xe magnetization is rapidly replenished by diffusive exchange with alveolar (129)Xe. The dissolved HP (129)Xe MR images display significant, directional heterogeneity, with increased signal intensity observed from the gravity-dependent portions of the lungs. CONCLUSIONS: The features observed in dissolved-phase (129)Xe MR images are consistent with gravity-dependent lung deformation, which produces increased ventilation, reduced alveolar size (i.e., higher surface-to-volume ratios), higher tissue densities, and increased perfusion in the dependent portions of the lungs. Thus, these results suggest that dissolved HP (129)Xe imaging reports on pulmonary function at a fundamental level.

Assessment of LD matrix measures for the analysis of biological pathway association.

Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects. We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis. These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008). To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package. SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them. Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers. We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis). In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r=0.2). In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result. Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect. While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Coupling of beta2-adrenoceptor to Gi proteins and its physiological relevance in murine cardiac myocytes.

-Transgenic mouse models have been developed to manipulate beta-adrenergic receptor (betaAR) signal transduction. Although several of these models have altered betaAR subtypes, the specific functional sequelae of betaAR stimulation in murine heart, particularly those of beta2-adrenergic receptor (beta2AR) stimulation, have not been characterized. In the present study, we investigated effects of beta2AR stimulation on contraction, [Ca2+]i transient, and L-type Ca2+ currents (ICa) in single ventricular myocytes isolated from transgenic mice overexpressing human beta2AR (TG4 mice) and wild-type (WT) littermates. Baseline contractility of TG4 heart cells was increased by 3-fold relative to WT controls as a result of the presence of spontaneous beta2AR activation. In contrast, beta2AR stimulation by zinterol or isoproterenol plus a selective beta1-adrenergic receptor (beta1AR) antagonist CGP 20712A failed to enhance the contractility in TG4 myocytes, and more surprisingly, beta2AR stimulation was also ineffective in increasing contractility in WT myocytes. Pertussis toxin (PTX) treatment fully rescued the ICa, [Ca2+]i, and contractile responses to beta2AR agonists in both WT and TG4 cells. The PTX-rescued murine cardiac beta2AR response is mediated by cAMP-dependent mechanisms, because it was totally blocked by the inhibitory cAMP analog Rp-cAMPS. These results suggest that PTX-sensitive G proteins are responsible for the unresponsiveness of mouse heart to agonist-induced beta2AR stimulation. This was further corroborated by an increased incorporation of the photoreactive GTP analog [gamma-32P]GTP azidoanilide into alpha subunits of Gi2 and Gi3 after beta2AR stimulation by zinterol or isoproterenol plus the beta1AR blocker CGP 20712A. This effect to activate Gi proteins was abolished by a selective beta2AR blocker ICI 118,551 or by PTX treatment. Thus, we conclude that (1) beta2ARs in murine cardiac myocytes couple to concurrent Gs and Gi signaling, resulting in null inotropic response, unless the Gi signaling is inhibited; (2) as a special case, the lack of cardiac contractile response to beta2AR agonists in TG4 mice is not due to a saturation of cell contractility or of the cAMP signaling cascade but rather to an activation of beta2AR-coupled Gi proteins; and (3) spontaneous beta2AR activation may differ from agonist-stimulated beta2AR signaling.

Temporal Stability of Molecular Diversity Measures in Natural Populations of Drosophila pseudoobscura and Drosophila persimilis

Many molecular ecological and evolutionary studies sample wild populations at a single point in time, failing to consider that data they collect represents genetic variation from a potentially unrepresentative snapshot in time. Variation across time in genetic parameters may occur quickly in species that produce multiple generations of offspring per year. However, many studies of rapid contemporary microevolution examine phenotypic trait divergence as opposed to molecular evolutionary divergence. Here, we compare genetic diversity in wild caught populations of Drosophila persimilis and D. pseudoobscura collected 16 years apart at the same time of year and same site at four X-linked and two mitochondrial loci to assess genetic stability. We found no major changes in nucleotide diversity in either species, but we observed a drastic shift in Tajima’s D between D. pseudoobscura timepoints at one locus associated with the increased abundance of a set of related haplotypes. Our data also suggests that D. persimilis may have recently accelerated its demographic expansion. While the changes we observed were modest, this study reinforces the importance of considering potential temporal variation in genetic parameters within single populations over short evolutionary timescales.

A Quantitative Analysis of Growth and Size Regulation in Manduca sexta: The Physiological Basis of Variation in Size and Age at Metamorphosis.

Body size and development time are important life history traits because they are often highly correlated with fitness. Although the developmental mechanisms that control growth have been well studied, the mechanisms that control how a species-characteristic body size is achieved remain poorly understood. In insects adult body size is determined by the number of larval molts, the size increment at each molt, and the mechanism that determines during which instar larval growth will stop. Adult insects do not grow, so the size at which a larva stops growing determines adult body size. Here we develop a quantitative understanding of the kinetics of growth throughout larval life of Manduca sexta, under different conditions of nutrition and temperature, and for genetic strains with different adult body sizes. We show that the generally accepted view that the size increment at each molt is constant (Dyar's Rule) is systematically violated: there is actually a progressive increase in the size increment from instar to instar that is independent of temperature. In addition, the mass-specific growth rate declines throughout the growth phase in a temperature-dependent manner. We show that growth within an instar follows a truncated Gompertz trajectory. The critical weight, which determines when in an instar a molt will occur, and the threshold size, which determines which instar is the last, are different in genetic strains with different adult body sizes. Under nutrient and temperature stress Manduca has a variable number of larval instars and we show that this is due to the fact that more molts at smaller increments are taken before threshold size is reached. We test whether the new insight into the kinetics of growth and size determination are sufficient to explain body size and development time through a mathematical model that incorporates our quantitative findings.

Participant, rater, and computer measures of coherence in posttraumatic stress disorder.

We examined the coherence of trauma memories in a trauma-exposed community sample of 30 adults with and 30 without posttraumatic stress disorder. The groups had similar categories of traumas and were matched on multiple factors that could affect the coherence of memories. We compared the transcribed oral trauma memories of participants with their most important and most positive memories. A comprehensive set of 28 measures of coherence including 3 ratings by the participants, 7 ratings by outside raters, and 18 computer-scored measures, provided a variety of approaches to defining and measuring coherence. A multivariate analysis of variance indicated differences in coherence among the trauma, important, and positive memories, but not between the diagnostic groups or their interaction with these memory types. Most differences were small in magnitude; in some cases, the trauma memories were more, rather than less, coherent than the control memories. Where differences existed, the results agreed with the existing literature, suggesting that factors other than the incoherence of trauma memories are most likely to be central to the maintenance of posttraumatic stress disorder and thus its treatment.

Accounting for Posttraumatic Stress Disorder Symptom Severity With Pre- and Posttrauma Measures: A Longitudinal Study of Older Adults.

Using data from a longitudinal study of community-dwelling older adults, we analyzed the most extensive set of known correlates of PTSD symptoms obtained from a single sample to examine the measures' independent and combined utility in accounting for PTSD symptom severity. Fifteen measures identified as PTSD risk factors in published meta-analyses and 12 theoretically and empirically supported individual difference and health-related measures were included. Individual difference measures assessed after the trauma, including insecure attachment and factors related to the current trauma memory, such as self-rated severity, event centrality, frequency of involuntary recall, and physical reactions to the memory, accounted for symptom severity better than measures of pre-trauma factors. In an analysis restricted to prospective measures assessed before the trauma, the total variance explained decreased from 56% to 16%. Results support a model of PTSD in which characteristics of the current trauma memory promote the development and maintenance of PTSD symptoms.