Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Numbers of antral follicles during follicular waves in cattle: Evidence for high variation among animals, very high repeatability in individuals, and an inverse association with serum follicle-stimulating hormone concentrations

The extent, causes, and physiological significance of the variation in number of follicles growing during ovarian follicular waves in human beings and cattle are unknown. Therefore, the present study examined the variability and repeatability in numbers of follicles 3 mm or greater in diameter during the follicular waves in bovine estrous cycles, and we determined if the variation in number of follicles during waves was associated with alterations in secretion of FSH, estradiol, inhibin, and insulin-like growth factor I (IGF-I). Dairy cattle were subjected to twice-daily ultrasound analysis to count total number of antral follicles 3 mm or greater in diameter throughout 138 different follicular waves. In another study, blood samples were taken at frequent intervals from cows that consistently had low or very high numbers of follicles during waves and were subjected to immunoassays. Results indicate the following: First, despite an approximately sevenfold variation in number of follicles during waves among animals and marked differences in age, stage of lactation, and season of the year, a very highly repeatable (0.95) number of follicles 3 mm or greater in diameter is maintained during the ovulatory and nonovulatory follicular waves of individuals. Second, variation in number of follicles 3 mm or greater in diameter during waves and the inverse association of number of follicles during waves with FSH are not directly explained by alterations in the patterns of secretion of estradiol, inhibin, or IGF-I. Third, ovarian ultrasound analysis can be used reliably by investigators to identify cattle that consistently have low or high numbers of follicles during waves, thus providing a novel experimental model to determine the causes and physiological significance of the high variation in antral follicle number during follicular waves among single-ovulating species, such as cattle or humans.

Mechanisms of inverse agonist action at D-2 dopamine receptors

1 Mechanisms of inverse agonist action at the D-2(short) dopamine receptor have been examined. 2 Discrimination of G-protein-coupled and -uncoupled forms of the receptor by inverse agonists was examined in competition ligand-binding studies versus the agonist [H-3]NPA at a concentration labelling both G-protein-coupled and -uncoupled receptors. 3 Competition of inverse agonists versus [H-3] NPA gave data that were fitted best by a two-binding site model in the absence of GTP but by a one-binding site model in the presence of GTP. K-i values were derived from the competition data for binding of the inverse agonists to G-protein-uncoupled and -coupled receptors. K-coupled and K-uncoupled were statistically different for the set of compounds tested ( ANOVA) but the individual values were different in a post hoc test only for (+)-butaclamol. 4 These observations were supported by simulations of these competition experiments according to the extended ternary complex model. 5 Inverse agonist efficacy of the ligands was assessed from their ability to reduce agonist-independent [S-35]GTPγ S binding to varying degrees in concentration-response curves. Inverse agonism by (+)-butaclamol and spiperone occurred at higher potency when GDP was added to assays, whereas the potency of (-)-sulpiride was unaffected. 6 These data show that some inverse agonists ((+)-butaclamol, spiperone) achieve inverse agonism by stabilising the uncoupled form of the receptor at the expense of the coupled form. For other compounds tested, we were unable to define the mechanism.

Inverse agonist properties of atypical antipsychotic drugs

Mechanisms of action of several atypical antipsychotic drugs have been examined at the D-2 dopamine receptor expressed in CHO cells. The drugs tested were found to exhibit inverse agonist activity at the D-2 dopamine receptor based on their effects to potentiate forskolin-stimulated cyclic AMP (cAMP) accumulation. Each of the antipsychotic drugs tested (clozapine, olanzapine, quetiapine and risperidone) increased cAMP accumulation to the same extent. The increase in cAMP was also similar to that seen with typical antipsychotic drugs. Inverse agonism at the D-2 dopamine receptor seems, therefore, to be a property common to all classes of antipsychotic drugs. The effect of sodium ions on the binding of the drugs to the receptor was also assessed. Each of the atypical antipsychotic drugs tested here bound with higher affinity in the absence of sodium ions. Previous studies have shown that some antipsychotic drugs are insensitive to sodium ions and some bind with higher affinity in the presence of sodium ions. Given that all of these antipsychotic drugs are inverse agonists, it may be concluded that this sodium ion sensitivity is unrelated to mechanisms of inverse agonism. (C) 2004 Elsevier Inc. All rights reserved.

Investigation of the mechanism of agonist and inverse agonist action at D-2 dopamine receptors

This study investigated, for the D-2 dopamine receptor, the relation between the ability of agonists and inverse agonists to stabilise different states of the receptor and their relative efficacies. K-i values for agonists were determined in competition, versus the binding of the antagonist [H-3]spiperone. Competition data were fitted best by a two-binding site model (with the exception of bromocriptine, for which a one-binding site model provided the best fit) and agonist affinities for the higher (K-h) (G protein-coupled) and lower affinity (K-l) (G protein-uncoupled) sites determined. Ki values for agonists were also determined in competition versus the binding of the agonist [H-3]N-propylnorapomorphine (NPA) to provide a second estimate of K-h,. Maximal agonist effects (E-max) and their potencies (EC50) were determined from concentration-response curves for agonist stimulation of guanosine-5'-O-(3-[S-32] thiotriphosphate) ([S-35]GTPgammaS) binding. The ability of agonists to stabilise the G protein-coupled state of the receptor (K-l/K-h, determined from ligand-binding assays) did not correlate with either of two measures of relative efficacy (relative E-max, Kl/EC50) of agonists determined in [S-35]GTPgammaS-binding assays, when the data for all of the compounds tested were analysed For a subset of compounds, however, there was a relation between K-l/K-h and E-max.. Competition-binding data versus [H-3]spiperone and [H-3]NPA for a range of inverse agonists were fitted best by a one-binding site model. K-i values for the inverse agonists tested were slightly lower in competition versus [H-3]NPA compared to [H-3]spiperone. These data do not provide support for the idea that inverse agonists act by binding preferentially to the ground state of the receptor. (C) 2004 Elsevier Inc. All rights reserved.