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.

THE EFFECT OF RELAXIN ON BIOCHEMICAL AND MORPHOLOGICAL PARAMETERS OF RAT MYOMETRIAL CELLS IN CULTURE (CYCLIC-AMP, CELL SHAPE CHANGE)

Relaxin is able to inhibit spontaneous, oxytocin-and prostaglandin-driven uterine contractions. The intracellular mechanism of action of relaxin on uterine relaxation had previously been studied using isometrically suspended uterine strips. Since uterine strips contain stroma as well as myometrium, the changes in biochemical parameters induced by relaxin treatment may not occur in the same cell types responsible for the physical changes. In these studies, cultures of enriched populations of rat myometrial cells were used to investigate the effect of relaxin on biochemical and morphological parameters which are related to relaxation.^ Under optimal culture conditions (initial plating density 1 - 1.5 x 10('6)cells/ml, 3 ml/35 mm dish, 2 days culture), enzymatically isolated rat myometrial cells were able to respond to relaxin with cAMP elevation. Relaxin elevated cAMP levels in the presence but not the absence of 0.1 mM methylisobutylxanthine or 0.4 um forskolin in a time- and concentration-dependent manner. In contrast, isoproterenol was able to elevate cAMP levels in the presence and absence of 0.1 mM methylisobutylxanthine.^ Oxytocin treatment caused a decrease in mean cell length and area of myometrial cells in culture which could be considered analogous to contraction. Under optimal culture conditions, relaxin increased myometrial cell length and area (i.e. analogous to relaxation) of oxytocin-treated cells in a time- and concentration-dependent manner. Other relaxants such as isoproterenol and dibutyryl cAMP also increased cell length and area of oxytocin - treated myometrial cells in culture.^ Under optimal culture conditions, relaxin decreased myosin light chain kinase activity in a time-and concentration-dependent manner by increasing the K(,50) of the enzyme for calmodulin (CaM), i.e. decreasing the affinity of the enzyme for CaM. The decrease in the affinity of myosin light chain kinase for CaM may be due to the phosphorylation of the enzyme by cAMP-dependent protein kinase. Relaxin also decreased the Ca('2+)(.)CaM-independent myosin light chain kinase activity to a lesser extent than that of the Ca('2+)(.)CaM-dependent enzyme activity. This was not attributable to a decrease in the affinity of the enzyme for myosin in myometrial cells in culture, in contrast to the finding of such a change following relaxin treatment of uterine strips. Further studies are required to clarify this point.^ There was a temporal association between the effects of relaxin on elevation of cAMP levels in the presence of 0.4 uM forskolin, increase in cell length and decrease in myosin light chain kinase activity. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI ^

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^