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.

Dynamic Remodeling of the Stressed Heart: Role of Protein Degradation Pathways

The heart is a remarkable organ. In order to maintain its function, it remodels in response to a variety of environmental stresses, including pressure overload, volume overload, mechanical or pharmacological unloading and hormonal or metabolic disturbances. All these responses are linked to the inherent capacity of the heart to rebuild itself. Particularly, cardiac pressure overload activates signaling pathways of both protein synthesis and degradation. While much is known about regulators of protein synthesis, little is known about regulators of protein degradation in hypertrophy. The ubiquitin-proteasome system (UPS) selectively degrades unused and abnormal intracellular proteins. I speculated that the UPS may play an important role in both qualitative and quantitative changes in the composition of heart muscle during hypertrophic remodeling. My study hypothesized that cardiac remodeling in response to hypertrophic stimuli is a dynamic process that requires activation of highly regulated mechanisms of protein degradation as much as it requires protein synthesis. My first aim was to adopt a model of left ventricular hypertrophy and determine its gene expression and structural changes. Male Sprague-Dawley rats were submitted to ascending aortic banding and sacrificed at 7 and 14 days after surgery. Sham operated animals served as controls. Effective aortic banding was confirmed by hemodynamic assessment by Doppler flow measurements in vivo. Banded rats showed a four-fold increase in peak stenotic jet velocities. Histomorphometric analysis revealed a significant increase in myocyte size as well as fibrosis in the banded animals. Transcript analysis showed that banded animals had reverted to the fetal gene program. My second aim was to assess if the UPS is increased and transcriptionally regulated in hypertrophic left ventricular remodeling. Protein extracts from the left ventricles of the banded and control animals were used to perform an in vitro peptidase assay to assess the overall catalytic activity of the UPS. The results showed no difference between hypertrophied and control animals. Transcript analysis revealed decreases in transcript levels of candidate UPS genes in the hypertrophied hearts at 7 days post-banding but not at 14 days. However, protein expression analysis showed no difference at either time point compared to controls. These findings indicate that elements of the UPS are downregulated in the early phase of hypertrophic remodeling and normalizes in a later phase. The results provide evidence in support of a dynamic transcriptional regulation of a major pathway of intracellular protein degradation in the heart. The discrepancy between transcript levels on the one hand and protein levels on the other hand supports post-transcriptional regulation of the UPS pathway in the hypertrophied heart. The exact mechanisms and the functional consequences remain to be elucidated.

Improved Techniques for Acquisition and Analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging for Detecting Vascular Permeability in the Central Nervous System

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive technique for quantitative assessment of the integrity of blood-brain barrier and blood-spinal cord barrier (BSCB) in the presence of central nervous system pathologies. However, the results of DCE-MRI show substantial variability. The high variability can be caused by a number of factors including inaccurate T1 estimation, insufficient temporal resolution and poor contrast-to-noise ratio. My thesis work is to develop improved methods to reduce the variability of DCE-MRI results. To obtain fast and accurate T1 map, the Look-Locker acquisition technique was implemented with a novel and truly centric k-space segmentation scheme. In addition, an original multi-step curve fitting procedure was developed to increase the accuracy of T1 estimation. A view sharing acquisition method was implemented to increase temporal resolution, and a novel normalization method was introduced to reduce image artifacts. Finally, a new clustering algorithm was developed to reduce apparent noise in the DCE-MRI data. The performance of these proposed methods was verified by simulations and phantom studies. As part of this work, the proposed techniques were applied to an in vivo DCE-MRI study of experimental spinal cord injury (SCI). These methods have shown robust results and allow quantitative assessment of regions with very low vascular permeability. In conclusion, applications of the improved DCE-MRI acquisition and analysis methods developed in this thesis work can improve the accuracy of the DCE-MRI results.