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.

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. ^

PROJECTION OF HEALTH DEMAND IN TERMS OF HOSPITAL ADMISSIONS FOR SELECTED DIAGNOSES IN HEALTH SYSTEMS AGENCY SERVICE AREAS

The National Health Planning and Resources Development Act of 1974 (Public Law 93-641) requires that health systems agencies (HSAs) plan for their health service areas by the use of existing data to the maximum extent practicable. Health planning is based on the identificaton of health needs; however, HSAs are, at present, identifying health needs in their service areas in some approximate terms. This lack of specificity has greatly reduced the effectiveness of health planning. The intent of this study is, therefore, to explore the feasibility of predicting community levels of hospitalized morbidity by diagnosis by the use of existing data so as to allow health planners to plan for the services associated with specific diagnoses.^ The specific objectives of this study are (a) to obtain by means of multiple regression analysis a prediction equation for hospital admission by diagnosis, i.e., select the variables that are related to demand for hospital admissions; (b) to examine how pertinent the variables selected are; and (c) to see if each equation obtained predicts well for health service areas.^ The existing data on hospital admissions by diagnosis are those collected from the National Hospital Discharge Surveys, and are available in a form aggregated to the nine census divisions. When the equations established with such data are applied to local health service areas for prediction, the application is subject to the criticism of the theory of ecological fallacy. Since HSAs have to rely on the availability of existing data, it is imperative to examine whether or not the theory of ecological fallacy holds true in this case.^ The results of the study show that the equations established are highly significant and the independent variables in the equations explain the variation in the demand for hospital admission well. The predictability of these equations is good when they are applied to areas at the same ecological level but become poor, predominantly due to ecological fallacy, when they are applied to health service areas.^ It is concluded that HSAs can not predict hospital admissions by diagnosis without primary data collection as discouraged by Public Law 93-641. ^

Biological diversity of prokaryotic type IV secretion systems.

Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

Biological diversity of prokaryotic type IV secretion systems.

Type IV secretion systems (T4SS) translocate DNA and protein substrates across prokaryotic cell envelopes generally by a mechanism requiring direct contact with a target cell. Three types of T4SS have been described: (i) conjugation systems, operationally defined as machines that translocate DNA substrates intercellularly by a contact-dependent process; (ii) effector translocator systems, functioning to deliver proteins or other macromolecules to eukaryotic target cells; and (iii) DNA release/uptake systems, which translocate DNA to or from the extracellular milieu. Studies of a few paradigmatic systems, notably the conjugation systems of plasmids F, R388, RP4, and pKM101 and the Agrobacterium tumefaciens VirB/VirD4 system, have supplied important insights into the structure, function, and mechanism of action of type IV secretion machines. Information on these systems is updated, with emphasis on recent exciting structural advances. An underappreciated feature of T4SS, most notably of the conjugation subfamily, is that they are widely distributed among many species of gram-negative and -positive bacteria, wall-less bacteria, and the Archaea. Conjugation-mediated lateral gene transfer has shaped the genomes of most if not all prokaryotes over evolutionary time and also contributed in the short term to the dissemination of antibiotic resistance and other virulence traits among medically important pathogens. How have these machines adapted to function across envelopes of distantly related microorganisms? A survey of T4SS functioning in phylogenetically diverse species highlights the biological complexity of these translocation systems and identifies common mechanistic themes as well as novel adaptations for specialized purposes relating to the modulation of the donor-target cell interaction.

The differential expression of the $\beta\sb2$-adrenergic receptor modifies agonist-dependent adenylylcyclase activation

There have been multiple reports which indicate that variations in $\beta$AR expression affect the V$\sb{\rm max}$ observed for the agonist-dependent activation of adenylylcyclase. This observation has been ignored by most researchers when V$\sb{\rm max}$ values obtained for wild type and mutant receptors are compared. Such an imprecise analysis may lead to erroneous conclusions concerning the ability of a receptor to activate adenylylcyclase. Equations were derived from the Cassel-Selinger model of GTPase activity and Tolkovsky and Levitzki's Collision Coupling model which predict that the EC$\sb{50}$ and V$\sb{\rm max}$ for the activation of adenylylcyclase are a function of receptor number. Experimental results for L cell clones in which either hamster or human $\beta$AR were transfected at varying levels showed that EC$\sb{50}$ decreases and V$\sb{\rm max}$ increases as receptor number increases. Comparison of these results with simulations obtained from the equations describing EC$\sb{50}$ and V$\sb{\rm max}$ showed a close correlation. This documents that the kinetic parameters of adenylylcyclase activation change with the level of receptor expression and relates this phenomenon to a theoretical framework concerning the mechanisms involved in $\beta$AR signal transduction.^ One of the terms used in the equations which expressed the EC$\sb{50}$ and V$\sb{\rm max}$ as a function of receptor number is coupling efficiency, defined as $\rm k\sb1/k\sb{-1}$. Calculation of $\rm k\sb1/k\sb{-1}$ can be accomplished for wild type receptors with the easily measured experimental values of agonist K$\sb{\rm d}$, EC$\sb{50}$ and receptor number. This was demonstrated for hamster $\beta$AR which yielded a coupling efficiency of 0.15 $\pm$ 0.003 and human $\beta$AR which yielded a coupling efficiency of 0.90 $\pm$ 0.031. $\rm k\sb1/k\sb{-1}$ replaces the traditional qualitative evaluation of the ability to activate adenylylcyclase, which utilizes V$\sb{\rm max}$ without correction for variation in receptor number, with a quantitative definition that more accurately describes the ability of $\beta$AR to couple to G$\sb{\rm s}$.^ The equations which express the EC$\sb{50}$ and V$\sb{\rm max}$ for adenylylcyclase activation as a function of receptor number and coupling efficiency were tested to determine whether they could accurately simulate the changes seen in these parameters during desensitization. Data from original desensitization experiments and data from the literature (24,25,52,54,83) were compared to simulated changes in EC$\sb{50}$ and V$\sb{\rm max}$. In a variety of systems the predictions of the equations were consistent with the changes observed in EC$\sb{50}$ and V$\sb{\rm max}$. In addition reductions in the calculated value of $\rm k\sb1/k\sb{-1}$ was shown to correlate well with $\beta$AR phosphorylation and to be minimally affected by sequestration and down-regulation. ^

Spatial and temporal aspects of synaptic plasticity

The notion that changes in synaptic efficacy underlie learning and memory processes is now widely accepted even if definitive proof of the synaptic plasticity and memory hypothesis is still lacking. When learning occurs, patterns of neural activity representing the occurrence of events cause changes in the strength of synaptic connections within the brain. Reactivation of these altered connections constitutes the experience of memory for these events and for other events with which they may be associated. These statements summarize a long-standing theory of memory formation that we refer to as the synaptic plasticity and memory hypothesis. Since activity-dependent synaptic plasticity is induced at appropriate synapses during memory formation, and is both necessary and sufficient for the information storage, we can speculate that a methodological study of the synapse will help us understand the mechanism of learning. Random events underlie a wide range of biological processes as diverse as genetic drift and molecular diffusion, regulation of gene expression and neural network function. Additionally spatial variability may be important especially in systems with nonlinear behavior. Since synapse is a complex biological system we expect that stochasticity as well as spatial gradients of different enzymes may be significant for induction of plasticity. ^ In that study we address the question "how important spatial and temporal aspects of synaptic plasticity may be". We developed methods to justify our basic assumptions and examined the main sources of variability of calcium dynamics. Among them, a physiological method to estimate the number of postsynaptic receptors as well as a hybrid algorithm for simulating postsynaptic calcium dynamics. Additionally we studied how synaptic geometry may enhance any possible spatial gradient of calcium dynamics and how that spatial variability affect plasticity curves. Finally, we explored the potential of structural synaptic plasticity to provide a metaplasticity mechanism specific for the synapse. ^