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.

Genetic variability and the hypothalamic control of energy balance

Background. Obesity is a major health problem throughout the industrialized world. Despite numerous attempts to curtail the rapid growth of obesity, its incidence continues to rise. Therefore, it is crucial to better understand the etiology of obesity beyond the concept of energy balance.^ Aims. The first aim of this study was to first investigate the relationship between eating behaviors and body size. The second goal was to identify genetic variation associated with eating behaviors. Thirdly, this study aimed to examine the joint relationships between eating behavior, body size and genetic variation.^ Methods. This study utilized baseline data ascertained in young adults from the Training Interventions and Genetics of Exercise (TIGER) Study. Variables assessed included eating behavior (Emotional Eating Scale, Eating Attitudes Test-26, and the Block98 Food Frequency Questionnaire), body size (body mass index, waist and hip circumference, waist/hip ratio, and percent body fat), genetic variation in genes implicated related to the hypothalamic control of energy balance, and appropriate covariates (age, gender, race/ethnicity, smoking status, and physical activity. For the genetic association analyses, genotypes were collapsed by minor allele frequency, and haplotypes were estimated for each gene. Additionally, Bayesian networks were constructed in order to determine the relationships between genetic variation, eating behavior and body size.^ Results. We report that the EAT-26 score, Caloric intake, percent fat, fiber intake, HEAT index, and daily servings of vegetables, meats, grains, and fats were significantly associated with at least one body size measure. Multiple SNPs in 17 genes and haplotypes from 12 genes were tested for their association with body size. Variation within both DRD4 and HTR2A was found to be associated with EAT-26 score. In addition, variation in the ghrelin gene (GHRL) was significantly associated with daily Caloric intake. A significant interaction between daily servings of grains and the HEAT index and variation within the leptin receptor gene (LEPR) was shown to influence body size.^ Conclusion. This study has shown that there is a substantial genetic component to eating behavior and that genetic variation interacts with eating behavior to influence body size.^

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology.

In this paper, we present the Cellular Dynamic Simulator (CDS) for simulating diffusion and chemical reactions within crowded molecular environments. CDS is based on a novel event driven algorithm specifically designed for precise calculation of the timing of collisions, reactions and other events for each individual molecule in the environment. Generic mesh based compartments allow the creation / importation of very simple or detailed cellular structures that exist in a 3D environment. Multiple levels of compartments and static obstacles can be used to create a dense environment to mimic cellular boundaries and the intracellular space. The CDS algorithm takes into account volume exclusion and molecular crowding that may impact signaling cascades in small sub-cellular compartments such as dendritic spines. With the CDS, we can simulate simple enzyme reactions; aggregation, channel transport, as well as highly complicated chemical reaction networks of both freely diffusing and membrane bound multi-protein complexes. Components of the CDS are generally defined such that the simulator can be applied to a wide range of environments in terms of scale and level of detail. Through an initialization GUI, a simple simulation environment can be created and populated within minutes yet is powerful enough to design complex 3D cellular architecture. The initialization tool allows visual confirmation of the environment construction prior to execution by the simulator. This paper describes the CDS algorithm, design implementation, and provides an overview of the types of features available and the utility of those features are highlighted in demonstrations.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

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. ^