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.

Delta like ligand 4 is a critical regulator of bone marrow cell differentiation into pericytes/vascular smooth muscle cells and is essential for the vasculogenesis that supports the growth of Ewing’s sarcoma

We have previously shown that vasculogenesis, the process by which bone marrow-derived cells are recruited to the tumor and organized to form a blood vessel network de novo, is essential for the growth of Ewing’s sarcoma. We further demonstrated that these bone marrow cells differentiate into pericytes/vascular smooth muscle cells(vSMC) and contribute to the formation of the functional vascular network. The molecular mechanisms that control bone marrow cell differentiation into pericytes/vSMC in Ewing’s sarcoma are poorly understood. Here, we demonstrate that the Notch ligand Delta like ligand 4 (DLL4) plays a critical role in this process. DLL4 is essential for the formation of mature blood vessels during development and in several tumor models. Inhibition of DLL4 causes increased vascular sprouting, decreased pericyte coverage, and decreased vessel functionality. We demonstrate for the first time that DLL4 is expressed by bone marrow-derived pericytes/vascular smooth muscle cells in two Ewing’s sarcoma xenograft models and by perivascular cells in 12 out of 14 patient samples. Using dominant negative mastermind to inhibit Notch, we demonstrate that Notch signaling is essential for bone marrow cell participation in vasculogenesis. Further, inhibition of DLL4 using either shRNA or the monoclonal DLL4 neutralizing antibody YW152F led to dramatic changes in blood vessel morphology and function. Vessels in tumors where DLL4 was inhibited were smaller, lacked lumens, had significantly reduced numbers of bone marrow-derived pericyte/vascular smooth muscle cells, and were less functional. Importantly, growth of TC71 and A4573 tumors was significantly inhibited by treatment with YW152F. Additionally, we provide in vitro evidence that DLL4-Notch signaling is involved in bone marrow-derived pericyte/vascular smooth muscle cell formation outside of the Ewing’s sarcoma environment. Pericyte/vascular smooth muscle cell marker expression by whole bone marrow cells cultured with mouse embryonic stromal cells was reduced when DLL4 was inhibited by YW152F. For the first time, our findings demonstrate a role for DLL4 in bone marrow-derived pericyte/vascular smooth muscle differentiation as well as a critical role for DLL4 in Ewing’s sarcoma tumor growth.

A model of the roles of essential kinases in the induction and expression of late long-term potentiation.

The induction of late long-term potentiation (L-LTP) involves complex interactions among second-messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. The differential equation-based model represents actions of protein kinase A (PKA), MAP kinase (MAPK), and CaM kinase II (CAMKII) in the vicinity of the synapse, and activation of transcription by CaM kinase IV (CAMKIV) and MAPK. L-LTP is represented by increases in a synaptic weight. Simulations suggest that steep, supralinear stimulus-response relationships between stimuli (e.g., elevations in [Ca(2+)]) and kinase activation are essential for translating brief stimuli into long-lasting gene activation and synaptic weight increases. Convergence of multiple kinase activities to induce L-LTP helps to generate a threshold whereby the amount of L-LTP varies steeply with the number of brief (tetanic) electrical stimuli. The model simulates tetanic, -burst, pairing-induced, and chemical L-LTP, as well as L-LTP due to synaptic tagging. The model also simulates inhibition of L-LTP by inhibition of MAPK, CAMKII, PKA, or CAMKIV. The model predicts results of experiments to delineate mechanisms underlying L-LTP induction and expression. For example, the cAMP antagonist RpcAMPs, which inhibits L-LTP induction, is predicted to inhibit ERK activation. The model also appears useful to clarify similarities and differences between hippocampal L-LTP and long-term synaptic strengthening in other systems.

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.

A prospective cohort study evaluating the state of medical readiness in the United States Air Force and risk factors to improve the medical readiness posture

A cohort of 418 United States Air Force (USAF) personnel from over 15 different bases deployed to Morocco in 1994. This was the first study of its kind and was designed with two primary goals: to determine if the USAF was medically prepared to deploy with its changing mission in the new world order, and to evaluate factors that might improve or degrade USAF medical readiness. The mean length of deployment was 21 days. The cohort was 95% male, 86% enlisted, 65% married, and 78% white.^ This study shows major deficiencies indicating the USAF medical readiness posture has not fully responded to meet its new mission requirements. Lack of required logistical items (e.g., mosquito nets, rainboots, DEET insecticide cream, etc.) revealed a low state of preparedness. The most notable deficiency was that 82.5% (95% CI = 78.4, 85.9) did not have permethrin pretreated mosquito nets and 81.0% (95% CI = 76.8, 84.6) lacked mosquito net poles. Additionally, 18% were deficient on vaccinations and 36% had not received a tuberculin skin test. Excluding injections, the overall compliance for preventive medicine requirements had a mean frequency of only 50.6% (95% CI = 45.36, 55.90).^ Several factors had a positive impact on compliance with logistical requirements. The most prominent was "receiving a medical intelligence briefing" from the USAF Public Health. After adjustment for mobility and age, individuals who underwent a briefing were 17.2 (95% CI = 4.37, 67.99) times more likely to have received an immunoglobulin shot and 4.2 (95% CI = 1.84, 9.45) times more likely to start their antimalarial prophylaxsis at the proper time. "Personnel on mobility" had the second strongest positive effect on medical readiness. When mobility and briefing were included in models, "personnel on mobility" were 2.6 (95% CI = 1.19, 5.53) times as likely to have DEET insecticide and 2.2 (95% CI = 1.16, 4.16) times as likely to have had a TB skin test.^ Five recommendations to improve the medical readiness of the USAF were outlined: upgrade base level logistical support, improve medical intelligence messages, include medical requirements on travel orders, place more personnel on mobility or only deploy personnel on mobility, and conduct research dedicated to capitalize on the powerful effect from predeployment briefings.^ Since this is the first study of its kind, more studies should be performed in different geographic theaters to assess medical readiness and establish acceptable compliance levels for the USAF. ^

Ser88 phosphorylation regulates dynein light chain 1 (DLC1) function in the mouse mammary gland

Dynein light chain 1 (DLC1) is a highly conserved and ubiquitously expressed protein which might have critical cellular function as total loss of DLC1 caused Drosophila embryonic death. Despite many proteins and RNAs interaction with it identified, DLC1's function(s) and regulation are largely unknown. Recently, DLC1 was identified as a physiological substrate of P21-activate kinase 1(Pak1) kinase from a human mammary cDNA library in a yeast-2-hybridization screening assay. Studies in primary human tumors and cell culture implicated that DLC1 could promote mammary cancerous phenotypes, and more importantly, Ser88 phosphorylation of DLC1by Pak1 kinase was found to be essential for DLC1's tumorigenic activities. Based on the above tissue culture studies, we hypothesized that Ser88 phosphorylation regulates DLC1. ^ To test this hypothesis, we generated two transgenic mouse models: MMTV-DLC1 and MMTV-DLC1-S88A mice with mammary specific expression of the DLC1 and DLC1-S88A cDNAs. Both of the transgenic mice mammary glands showed rare tumor incidence which indicated DLC1 alone may not be sufficient for tumorigenesis in vivo. However, these mice showed a significant alteration of mammary development. Mammary glands from the MMTV-DLC1 mice had hyperbranching and alveolar hyperplasia, with elevated cell proliferation. Intriguingly, these phenotypes were not seen in the mammary glands from the MMTV-S88A mice. Furthermore, while MMTV-DLC1 glands were normal during involution, MMTV-S88A mice showed accelerated mammary involution with increase apoptosis and altered expression of involution-associated genes. Further analysis of the MMTV-S88A glands showed they had increased steady state level of Bim protein which might be responsible for the early involution. Finally, our in vitro data showed that Ser88 phosphorylation abolished DLC1 dimer and consequently might disturb its interaction with Bim and destabilize Bim. ^ Collectively, our findings provided in vivo evidence that Ser88 phosphorylation of DLC1 can regulate DLC1's function. In addition, Ser88 phosphorylation might be critical for DLC1 dimer-monomer transition. ^

Cost analysis of opt-in consent procedures for the Texas statewide immunization information system, ImmTrac

Background. Childhood immunization programs have dramatically reduced the morbidity and mortality associated with vaccine-preventable diseases. Proper documentation of immunizations that have been administered is essential to prevent duplicate immunization of children. To help improve documentation, immunization information systems (IISs) have been developed. IISs are comprehensive repositories of immunization information for children residing within a geographic region. The two models for participation in an IIS are voluntary inclusion, or "opt-in," and voluntary exclusion, or "opt-out." In an opt-in system, consent must be obtained for each participant, conversely, in an opt-out IIS, all children are included unless procedures to exclude the child are completed. Consent requirements for participation vary by state; the Texas IIS, ImmTrac, is an opt-in system.^ Objectives. The specific objectives are to: (1) Evaluate the variance among the time and costs associated with collecting ImmTrac consent at public and private birthing hospitals in the Greater Houston area; (2) Estimate the total costs associated with collecting ImmTrac consent at selected public and private birthing hospitals in the Greater Houston area; (3) Describe the alternative opt-out process for collecting ImmTrac consent at birth and discuss the associated cost savings relative to an opt-in system.^ Methods. Existing time-motion studies (n=281) conducted between October, 2006 and August, 2007 at 8 birthing hospitals in the Greater Houston area were used to assess the time and costs associated with obtaining ImmTrac consent at birth. All data analyzed are deidentified and contain no personal information. Variations in time and costs at each location were assessed and total costs per child and costs per year were estimated. The cost of an alternative opt-out system was also calculated.^ Results. The median time required by birth registrars to complete consent procedures varied from 72-285 seconds per child. The annual costs associated with obtaining consent for 388,285 newborns in ImmTrac's opt-in consent process were estimated at $702,000. The corresponding costs of the proposed opt-out system were estimated to total $194,000 per year. ^ Conclusions. Substantial variation in the time and costs associated with completion of ImmTrac consent procedures were observed. Changing to an opt-out system for participation could represent significant cost savings. ^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

The two -state model of receptor activation: The agonist and the efficacy

The Two State model describes how drugs activate receptors by inducing or supporting a conformational change in the receptor from “off” to “on”. The beta 2 adrenergic receptor system is the model system which was used to formalize the concept of two states, and the mechanism of hormone agonist stimulation of this receptor is similar to ligand activation of other seven transmembrane receptors. Hormone binding to beta 2 adrenergic receptors stimulates the intracellular production of cyclic adenosine monophosphate (cAMP), which is mediated through the stimulatory guanyl nucleotide binding protein (Gs) interacting with the membrane bound enzyme adenylylcyclase (AC). ^ The effects of cAMP include protein phosphorylation, metabolic regulation and transcriptional regulation. The beta 2 adrenergic receptor system is the most well known of its family of G protein coupled receptors. Ligands have been scrutinized extensively in search of more effective therapeutic agents at this receptor as well as for insight into the biochemical mechanism of receptor activation. Hormone binding to receptor is thought to induce a conformational change in the receptor that increases its affinity for inactive Gs, catalyzes the release of GDP and subsequent binding of GTP and activation of Gs. ^ However, some beta 2 ligands are more efficient at this transformation than others, and the underlying mechanism for this drug specificity is not fully understood. The central problem in pharmacology is the characterization of drugs in their effect on physiological systems, and consequently, the search for a rational scale of drug effectiveness has been the effort of many investigators, which continues to the present time as models are proposed, tested and modified. ^ The major results of this thesis show that for many b2 -adrenergic ligands, the Two State model is quite adequate to explain their activity, but dobutamine (+/−3,4-dihydroxy-N-[3-(4-hydroxyphenyl)-1-methylpropyl]- b -phenethylamine) fails to conform to the predictions of the Two State model. It is a weak partial agonist, but it forms a large amount of high affinity complexes, and these complexes are formed at low concentrations much better than at higher concentrations. Finally, dobutamine causes the beta 2 adrenergic receptor to form high affinity complexes at a much faster rate than can be accounted for by its low efficiency activating AC. Because the Two State model fails to predict the activity of dobutamine in three different ways, it has been disproven in its strictest form. ^