Bayesian predictive inference for time series count data

Correlated count data arise often in practice, especially in repeated measures situations or instances in which observations are collected over time. In this paper, we consider a parametric model for a time series of counts by constructing a likelihood-based version of a model similar to that of Zeger (1988, Biometrika 75, 621-629). The model has the advantage of incorporating both overdispersion and autocorrelation. We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive the Bayesian predictive distribution and use a Bayesian criterion, called the predictive L measure, for assessing the predictions for a given time series model. The distribution of the predictive L measure is also derived, which will enable us to compare the predictive ability for each model under consideration. Our methodology is motivated by a real data set involving yearly pollen counts, which is examined in some detail.     

Estimation of polymerization efficiency in the formation of polyacrylamide gel,using continuous optical scanning during polymerization

The Ferguson plot and ‘quantitative’ gel electrophoresis (based on the Ferguson plot) depend on a knowledge of accurate gel concentrations. The easiest way to estimate accuracy of gel concentrations, in terms of the degree of completion of the polymerization reaction which gives rise to a gel, is by spectrophotometry. Making use of the apparatus for continuous optical scanning of polyacrylamide gels, the extent and rate of polymerization of cross-linked polyacrylamide were estimated by measuring the absorbance at 275 mm of the reaction mixture subsequent to free radical initiation of polymerization. Under appropriate conditions of monomer concentration, initiator levels and temperature, absorbance decreased monotonically after alag period of 10 min, and after 20–30 min of reaction the absorbance reached a plateau value which provided a measure of polymerization efficiency. Application of a standard curve of absorbance vs. monomer concentration allowed one to quantitate concentrations of residual monomer throughout the course of polymerization. Under a set of arbitrary polymerization conditions (e.g. 6–20% total gel concentration), the reaction went to 63–96% completion. The rate of polymerization was approximately proportional to the square of the monomer concentration (2nd-order reaction kinetics). Absorbance decrease subsequent to the initiation of the polymerization reaction appeared suitable as a measure of efficiency of polymerization since: (1) absorbance spectra of monomers at 0.5%T and residual monomers in a 10%T gel, at a time when polymerization seemed terminated, coincided; (b) values of residual monomer obtained were reasonable (10–30%); (c) bimolecular reaction kinetics were found, in agreement with expectation; and (c) absorbance of incomplete polymerization mixtures, deficient in either initiators or monomers, was constant with time.     

Prediction of adsorption from multicomponent solutions by activated carbon using single-solute parameters

The adsorption of 3 barbiturates—phenobarbital, mephobarbital, and primidone—from simulated intestinal fluid (SIF), without pancreatin, by activated carbon was studied using the rotating bottle method. The concentrations of each drug remaining in solution at equilibrium were determined with the aid of a high-performance liquid chromatography (HPLC) system employing a reversed-phase column. The competitive Langmuir-like model, the modified competitive Langmuir-like model, and the LeVan-Vermeulen model were each fit to the data. Excellent agreement was obtained between the experimental and predicted data using the modified competitive Langmuir-like model and the LeVan-Vermeulen model. The agreement obtained from the original competitive Langmuir-like model was less satisfactory. These observations are not surprising because the competitive Langmuir-like model assumes that the capacities of the adsorbates are equal, while the other 2 models take into account the differences in the capacities of the components. The results of these studies indicate that the adsorbates employed are competing for the same binding sites on the activated carbon surface. The results also demonstrate that it is possible to accurately predict multicomponent adsorption isotherms using only single-solute isotherm parameters. Such prediction is likely to be useful for improving in vivo/in vitro correlations.     

Direct measurement of 1H-1H dipolar couplings in proteins: A complement to traditional NOE measurements

An intensity-based constant-time COSY (CT-COSY) method is described for measuring ¹H-¹H residual dipolar couplings of proteins in weakly aligned media. For small proteins, the overall sensitivity of this experiment is comparable to the NOESY experiment. In cases where the ¹H-¹H distances are defined by secondary structure, such as ¹H-¹H^N and ¹H^N-¹H^N sequential distances in -helices and -sheets, these measurements provide useful orientational constraints for protein structure determination. This experiment can also be used to provide distance information similar to that obtained from NOE connectivities once the angular dependence is removed. Because the measurements are direct and non-coherent processes, such as spin diffusion, do not enter, the measurements can be more reliable. The 1/r ³ distance dependence of directly observed dipolar couplings, as compared with the 1/r ⁶ distance dependence of NOEs, also can provide longer range distance information at favorable angles. A simple 3D, ¹⁵N resolved version of the pulse sequence extends the method to provide the improved resolution required for application to larger biomolecules.     

Characterization of surfactant liquid crystal phases suitable for molecular alignment and measurement of dipolar couplings

Media employed for imparting partial alignment onto solute molecules have recently attracted considerable attention, since they permit the measurement of NMR parameters for solute biomolecules commonly associated with solid state NMR. Here we characterize a medium which is based on a quasi-ternary surfactant system comprising cetylpyridinium bromide/hexanol/sodium bromide. We demonstrate that dilute solutions of this system can exist in liquid crystalline phases which orient in the magnetic field and allow the measurement of residual dipolar couplings under a variety of conditions. The present system is extremely versatile and robust, tolerating different buffer conditions, temperature ranges and concentrations.     

Assessment of molecular structure using frame-independent orientational restraints derived from residual dipolar couplings

Residual dipolar couplings measured in weakly aligning liquid-crystalline solvent contain valuable information on the structure of biomolecules in solution. Here we demonstrate that dipolar couplings (DCs) can be used to derive a comprehensive set of pairwise angular restraints that do not depend on the orientation of the alignment tensor principal axes. These restraints can be used to assess the agreement between a trial protein structure and a set of experimental dipolar couplings by means of a graphic representation termed a `DC consistency map'. Importantly, these maps can be used to recognize structural elements consistent with the experimental DC data and to identify structural parameters that require further refinement, which could prove important for the success of DC-based structure calculations. This approach is illustrated for the 42 kDa maltodextrin-binding protein.     

Some Surprising Implications of NMR-directed Simulations of Substrate Recognition and Binding by Cytochrome P450cam (CYP101A1)

Cytochrome P450_cam (CYP101A1) catalyzes the stereospecific 5-exo hydroxylation of d-camphor by molecular oxygen. Previously, residual dipolar couplings measured for backbone amide ¹H–¹⁵N correlations in both substrate-free and bound forms of CYP101A1 were used as restraints in soft annealing molecular dynamic simulations in order to identify average conformations of the enzyme with and without substrate bound. Multiple substrate-dependent conformational changes remote from the enzyme active site were identified, and site-directed mutagenesis and activity assays confirmed the importance of these changes in substrate recognition. The current work makes use of perturbation response scanning (PRS) and umbrella sampling molecular dynamic of the residual dipolar coupling-derived CYP101A1 structures to probe the roles of remote structural features in enforcing the regio- and stereospecific nature of the hydroxylation reaction catalyzed by CYP101A1. An improper dihedral angle Ψ was defined and used to maintain substrate orientation in the CYP101A1 active site, and it was observed that different values of Ψ result in different PRS response maps. Umbrella sampling methods show that the free energy of the system is sensitive to Ψ, and bound substrate forms an important mechanical link in the transmission of mechanical coupling through the enzyme structure. Finally, a qualitative approach to interpreting PRS maps in terms of the roles of secondary structural features is proposed.