NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

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.

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.

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.

Uptake And Metabolism Of 5’-AMP In The Erythrocyte Play Key Roles In The 5’-AMP Induced Model Of Deep Hypometabolism

UPTAKE AND METABOLISM OF 5’-AMP IN THE ERYTHROCYTE PLAY KEY ROLES IN THE 5’-AMP INDUCED MODEL OF DEEP HYPOMETABOLISM Publication No. ________ Isadora Susan Daniels, B.A. Supervisory Professor: Cheng Chi Lee, Ph.D. Mechanisms that initiate and control the natural hypometabolic states of mammals are poorly understood. The laboratory developed a model of deep hypometabolism (DH) initiated by uptake of 5’-adenosine monophosphate (5’-AMP) into erythrocytes. Mice enter DH when given a high dose of 5’-AMP and the body cools readily. Influx of 5’-AMP appears to inhibit thermoregulatory control. In a 15°C environment, mice injected with 5’-AMP (0.5 mg/gw) enter a Phase I response in which oxygen consumption (VO2) drops rapidly to 1/3rd of euthermic levels. The Phase I response appears independent of body temperature (Tb). This is followed by gradual body temperature decline that correlates with VO2 decline, called Phase II response. Within 90 minutes, mouse Tb approaches 15°C, and VO2 is 1/10th of normal. Mice can remain several hours in this state, before gradually and safely recovering. The DH state translates to other mammalian species. Our studies show uptake and metabolism of 5’-AMP in erythrocytes causes biochemical changes that initiate DH. Increased AMP shifts the adenylate equilibrium toward ADP formation, consequently decreasing intracellular ATP. In turn, glycolysis slows, indicated by increased glucose and decreased lactate. 2,3-bisphosphoglycerate levels rise, allosterically reducing oxygen affinity for hemoglobin, and deoxyhemoglobin rises. Less oxygen transport to tissues likely triggers the DH model. The major intracellular pathway for AMP catabolism is catalyzed by AMP deaminase (AMPD). Multiple AMPD isozymes are expressed in various tissues, but erythrocytes only have AMPD3. Mice lacking AMPD3 were created to study control of the DH model, specifically in erythrocytes. Telemetric measurements demonstrate lower Tb and difficulty maintaining Tb under moderate metabolic stress. A more dramatic response to lower dose of 5’-AMP suggests AMPD activity in the erythrocyte plays an important role in control of the DH model. Analysis of adenylates in erythrocyte lysate shows 3-fold higher levels of ATP and ADP but similar AMP levels to wild-type. Taken together, results indicate alterations in energy status of erythrocytes can induce a hypometabolic state. AMPD3 control of AMP catabolism is important in controlling the DH model. Genetically reducing AMP catabolism in erythrocytes causes a phenotype of lower Tb and compromised ability to maintain temperature homeostasis.

The impact of 1995--1996 health sector reforms in the effectiveness of malaria control program in the state of Orissa, India

Malaria poses a significant public health problem worldwide. The World Health Organization indicates that approximately 40% of the world's population and almost 85% of the population from the South–East Asian region is at risk of contracting malaria. India being the most populous country in the region, contributes the highest number of malaria cases and deaths attributed to malaria. Orissa is the state that has the highest number of malaria cases and deaths attributable to malaria. A secondary data analysis was carried out to evaluate the effectiveness of the World bank-assisted Malaria Action Program in the state of Orissa under the health sector reforms of 1995-96. The secondary analysis utilized the government of India's National Anti Malaria Management Information System's (NAMMIS) surveillance data and the National Family Health Survey (NFHS–I and NFHS–II) datasets to compare the malaria mortality and morbidity in the state between 1992-93 and 1998-99. Results revealed no effect of the intervention and indicated an increase of 2.18 times in malaria mortality between 1992-1999 and an increase of 1.53 times in malaria morbidity between 1992-93 and 1998-99 in the state. The difference in the age-adjusted malaria morbidity in the state between the time periods of 1992-93 and 1998-99 proved to be highly significant (t = 4.29 df=16, p<. 0005) whereas the difference between the increase of age-adjusted malaria morbidity during 1992-93 and 1998-99 between Orissa (with intervention) and Bihar (no intervention) proved to be non significant (t=.0471 df=16, p<.50). Factors such as underutilization of World Bank funds for the malaria control program, inadequate health care infrastructure, structural adjustment problems, poor management, poor financial management, parasite resistance to anti-malarial drugs, inadequate supply of drugs and staff shortages may have contributed to the failure of the program in the state.^

THE EFFECT OF PERSON-ENVIRONMENT FIT ON THE PSYCHOLOGICAL WELL-BEING OF PSYCHIATRIC AIDES WORKING IN A STATE HOSPITAL (COPING RESOURCES, SOCIAL SUPPORT, OCCUPATIONAL STRESS, LOCUS-OF-CONTROL)

This study addressed two purposes: (1) to determine the effect of person-environment fit on the psychological well-being of psychiatric aides and (2) to determine what role the coping resources of social support and control have on the above relationship. Two hundred and ten psychiatric aides working in a state hospital in Texas responded to a questionnaire pertaining to these issues.^ Person-environment fit, as a measure of occupational stress, was assessed through a modified version of the Work Environment Scale (WES). The WES subscales used in this study were: involvement, autonomy, job pressure, job clarity, and physical comfort. Psychological well-being was measured with the General Well-Being Schedule which was developed by the National Center for Health Statistics. Co-worker and supervisor support were measured through the WES and finally, control was assessed through Rotter's Locus of Control Scale.^ The results of this study were as follows: (1) all person-environment (p-e) dimensions appeared to have linear relationships with psychological well-being; (2) the p-e fit - well-being relationship did not appear to be confounded by demographic factors; (3) all p-e fit dimensions were significantly related to well-being except for autonomy; (4) p-e fit was more strongly related to well-being than the environmental measure alone; (5) supervisor support and non-work related support were found to have additive effects on the relationship between p-e fit and well-being, however no interaction or buffering effects were observed; (6) locus of control was found to have additive effects in the prediction of well-being and showed interactive effects with work pressure, involvement and physical comfort; and (7) the testing of the overall study model which included many of the components mentioned above yielded an R('2) = .27.^ Implications of these findings are discussed, future research suggested and applications proposed. ^