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.

Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK.

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

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.

Dynamic population coding in primary visual cortex

More than a century ago Ramon y Cajal pioneered the description of neural circuits. Currently, new techniques are being developed to streamline the characterization of entire neural circuits. Even if this 'connectome' approach is successful, it will represent only a static description of neural circuits. Thus, a fundamental question in neuroscience is to understand how information is dynamically represented by neural populations. In this thesis, I studied two main aspects of dynamical population codes. ^ First, I studied how the exposure or adaptation, for a fraction of a second to oriented gratings dynamically changes the population response of primary visual cortex neurons. The effects of adaptation to oriented gratings have been extensively explored in psychophysical and electrophysiological experiments. However, whether rapid adaptation might induce a change in the primary visual cortex's functional connectivity to dynamically impact the population coding accuracy is currently unknown. To address this issue, we performed multi-electrode recordings in primary visual cortex, where adaptation has been previously shown to induce changes in the selectivity and response amplitude of individual neurons. We found that adaptation improves the population coding accuracy. The improvement was more prominent for iso- and orthogonal orientation adaptation, consistent with previously reported psychophysical experiments. We propose that selective decorrelation is a metabolically inexpensive mechanism that the visual system employs to dynamically adapt the neural responses to the statistics of the input stimuli to improve coding efficiency. ^ Second, I investigated how ongoing activity modulates orientation coding in single neurons, neural populations and behavior. Cortical networks are never silent even in the absence of external stimulation. The ongoing activity can account for up to 80% of the metabolic energy consumed by the brain. Thus, a fundamental question is to understand the functional role of ongoing activity and its impact on neural computations. I studied how the orientation coding by individual neurons and cell populations in primary visual cortex depend on the spontaneous activity before stimulus presentation. We hypothesized that since the ongoing activity of nearby neurons is strongly correlated, it would influence the ability of the entire population of orientation-selective cells to process orientation depending on the prestimulus spontaneous state. Our findings demonstrate that ongoing activity dynamically filters incoming stimuli to shape the accuracy of orientation coding by individual neurons and cell populations and this interaction affects behavioral performance. In summary, this thesis is a contribution to the study of how dynamic internal states such as rapid adaptation and ongoing activity modulate the population code accuracy. ^