A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Molecular mechanism by which the Escherichia coli nucleoid occlusion factor, SlmA, keeps cytokinesis in check

Cell division or cytokinesis is one of the most fundamental processes in biology and is essential for the propagation of all living species. In Escherichia coli, cell division occurs by ingrowth of the membrane envelope at the cell center and is orchestrated by the FtsZ protein. FtsZ self-assembles into linear protofilaments in a GTP dependent manner to form a cytoskeletal scaffold called the Z-ring. The Z-ring provides the framework for the assembly of the division apparatus and determines the site of cytokinesis. The total amount of FtsZ molecules in a cell significantly exceeds the concentration required for Z-ring formation. Hence, Z-ring formation must be highly regulated, both temporally and spatially. In particular, the assembly of Z-rings at the cell poles and over chromosomal DNA must be prevented. These inhibitory roles are played by two key regulatory systems called the Min and nucleoid occlusion (NO) systems. In E. coli, Min proteins oscillate from pole to pole; the net result of this oscillatory process is the formation of a zone of FtsZ inhibition at the cell poles. However, the replicated nucleoid DNA near the midcell must also be protected from bisection by the Z-ring which is ensured by NO. A protein called SlmA was shown to be the effector of NO in E. coli. SlmA was identified in a screen designed to isolate mutations that were lethal in the absence of Min, hence the name SlmA (synthetic lethal with a defective Min system). Furthers SlmA was shown to bind DNA and localize to the nucleoid fraction of the cell. Additionally, light scattering experiments suggested that SlmA interacts with FtsZ-GTP and alters its polymerization properties. Here we describe studies that reveal the molecular mechanism by which SlmA mediates NO in E. coli. Specifically, we determined the crystal structure of SlmA, identified its DNA binding site specificity, and mapped its binding sites on the E. coli chromosome by chromatin immuno-precipitation experiments. We went on to determine the SlmA-FtsZ structure by small angle X-ray scattering and examined the effect of SlmA-DNA on FtsZ polymerization by electron microscopy. Our combined data show how SlmA is able to disrupt Z-ring formation through its interaction with FtsZ in a specific temporal and spatial manner and hence prevent nucleoid guillotining during cell division.

Characterization of osteopontin charge forms produced by osteoblasts

Osteopontin (OPN) is a highly-phosphorylated extracellular matrix protein localized in bone, kidney, placenta, T-lymphocytes, macrophages, smooth muscle of the vascular system, milk, urine, and plasma. In ROS 17/2.8 osteoblast-like osteosarcoma cells, 1,25-dihydroxyvitamin D3 [1,25(OH)2D 3] regulates OPN at the transcriptional level resulting in increased steady state mRNA levels and increased production of OPN protein, maximal at 48 hours. Using ROS 17/2.8 cells as an osteoblast model, OPN was purified from culture medium after three hour treatments of either vehicle (ethanol) or 1,25(OH)2D3 via barium citrate precipitation followed by immunoaffinity chromatography. ^ Here, further evidence of regulation of OPN by 1,25(OH)2D 3 at the posttranslational level is presented. Prior to the up-regulation of OPN at the transcriptional level, 1,25(OH)2D3 induces a shift in OPN isoelectric point (pI) detected on two-dimensional gels from pI 4.6 to pI 5.1. Loading equal amounts of [32P]-labeled OPN recovered from ROS 17/2.8 cells exposed to 1,25(OH)2D3 or vehicle alone for three hours reveals that the shift from pI 4.6 to 5.1 is the result of reduced phosphorylation. Using structural analogs to 1,25(OH) 2D3, analog AT [25-(OH)-16-ene-23-yne-D3], which triggers Ca2+ influx through voltage sensitive Ca2+ channels but does not bind to the vitamin D receptor, mimicked the OPN pI shift while analog BT [1,25(OH)2-22-ene-24-cyclopropyl-D 3], which binds to the vitamin D receptor but does not allow Ca 2+ influx, did not. Inclusion of the Ca2+ channel blocker nifedipine also blocks the charge shift conversion of OPN. Further analysis of the signaling pathway initiated by 1,25(OH)2D3 reveals that inhibition of the cyclic 3′,5′ -adenosine monophosphate-dependent kinase, protein kinase A, or inhibition of the cyclic 3′,5′-guanine monophosphate-dependent kinase, protein kinase G, also prevents the charge shift conversion. ^ Isolation of OPN from rat femurs and tibiae provides evidence for the existence of these two OPN charge forms in vivo, evidenced by differential migration on isoelectric focusing gels and sodium dodecyl sulfate-polyacrylamide gels. Peptide sequencing of rat long bone fractions revealed the presence of a presumed dentin specific protein, dentin matrix protein-1 (DMP-1). Western blot analysis confirmed the existence of DMP-1 in these fractions. ^ Using the OPN charge forms in functional assays, it was determined that the charge forms have differential roles in both cell surface and mineralization functions. In cell attachment assays and Ca2+ influx assays using PC-3 prostate cancer cells, the pI 5.1 charge form of OPN was found to permit binding and increase intracellular Ca2+ concentrations of PC-3 cells. The increase in intracellular Ca2+ concentration was found to be integrin αvβ3-dependent. In mineralization assays, the pI 4.6 charge form of OPN promoted hydroxyapatite formation, while the pI 5.1 charge form had improved Ca2+ binding ability. ^ In conclusion, these findings suggest that 1,25(OH) 2D3 regulates OPN not only at the transcriptional level, but also plays a role in determination of the OPN phosphorylation state. The latter involves a short term (less than three hours) treatment and is associated with membrane-initiated Ca2+ influx. Functional assays utilizing the two OPN charge forms reveal the dependence of OPN post-translational state on its function. ^

Changes in blood lipids and their associations with changes in measures of height, weight and body mass index from age 8 to 18 years: Project Heartbeat!

A variety of studies indicate that the process of athrosclerosis begins in childhood. There was limited information on the association of the changes in anthropometric variables to blood lipids in school age children and adolescents. Previous longitudinal studies of children typically with insufficient frequency of observation could not provide sound inference on the dynamics of change in blood lipids. The aims of this analysis are (1) to document the sex- and ethnic-specific trajectory and velocity curves of blood lipids (TC, LDL-C, HDL-C and TG); (2) to evaluate the relationship of changes in anthropometric variables, such as height, weight and BMI, to blood lipids from age 8 to 18 years. ^ Project HeartBeat! is a longitudinal study designed to examine the patterns of serial change in major cardiovascular risk factors. Cohort of three different age levels, 8, 11 and 14 years at baseline, with a total of 678 participants were enrolled. Each member of these cohorts was examined three times per year for up to four years. ^ Sex- and ethnic-specific trajectory and velocity curves of blood lipids; demonstrated the complex and polyphasic changes in TC, LDL-C, HDL-C and TG longitudinally. The trajectory curves of TC, LDL-C and HDL-C with age showed curvilinear patterns of change. The velocity change in TC, HDL-C and LDL-C showed U-shaped curves for non-Blacks, and nearly linear lines in velocity of TG for both Blacks and non-Blacks. ^ The relationship of changes in anthropometric variables to blood lipids was evaulated by adding height, weight, or BMI and associated interaction terms separately to the basic age-sex models. Height or height gain had a significant negative association with changes in TC, LDL-C and HDL-C. Weight or BMI gain showed positive associations with TC, LDL-C and TC, and a negative relationship with HDL-C. ^ Dynamic changes of blood lipids in school age children and adolescents observed from this analysis suggested that using fixed screening criteria under the current NCEP guidelines for all ages 2–19 may not be appropriate for this age group. The association of increasing BMI or weight to an adverse blood lipid profile found in this analysis also indicated that weight or BMI monitoring could be a future intervention to be implemented in the pediatric population. ^

Does exhaled nitric oxide predict asthma exacerbation in children?

Asthma is a chronic complex disorder of the respiratory tract that affects millions of people globally, a large percentage of which are children. Triggered by a host of factors such as allergens and changes in temperature, the pathophysiologic and clinical indices vary among patients and have contributed to difficulties in overall management of asthma. Shortly after exhaled nitric oxide (eNO) was discovered in higher concentrations in asthma patients, it was shown to be superior to other markers such as PEFR, FEV1 and sputum eosinophils in screening asthma patients. Studies have also noted promising results regarding the use of eNO to predict asthma exacerbation in adults while in children, asthma symptoms have been observed to be good predictors of asthma exacerbation. Currently however, the potential of eNO as a predictor of asthma exacerbation in children is yet to be examined. The objective of this study was to assess eNO potential to predict asthma exacerbation in children by examining the relationship between eNO and changes in pulmonary function, asthma symptoms and rescue medication use.^ The primary study "Air Toxics and Asthma in Children" (ATAC), recruited children aged 9 to 14 years with labile persistent asthma diagnosed at least one year earlier. The data obtained from 30 study participants, included exhaled nitric oxide concentration, PEFR, FEV1, asthma symptoms and frequency of emergency medication use.^ Descriptive statistics, Pearson's and Spearman's correlation tests were followed by a simple linear regression in which eNO was the independent (predictor) variable while FEV1, PEFR, asthma symptoms and frequency of emergency medication use were the dependent (outcome) variables.^ Results showed that eNO was associated with percent change in FEV1, day time wheeze, night time shortness of breath, but correlated only weakly with PEFR, amplitude percent of mean PEFR, FEV1, percent change in FEV1 and asthma symptoms.^ Further research is imperative to better define the role of eNO and understand intrinsic pathologic mechanisms towards asthma management in children.^