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.

A space-time analysis of reported shigellosis and salmonellosis cases in Texas from 2000 to 2004

Background. The purpose of this study was to describe the risk factors and demographics of persons with salmonellosis and shigellosis and to investigate both seasonal and spatial variations in the occurrence of these infections in Texas from 2000 to 2004, utilizing time series analyses and the geographic information system digital mapping methods. ^ Methods. Spatial Analysis: MapInfo software was used to map the distribution of age-adjusted rates of reported shigellosis and salmonellosis in Texas from 2000–2004 by zip codes. Census data on above or below poverty level, household income, highest level of educational attainment, race, ethnicity, and urban/rural community status was obtained from the 2000 Decennial Census for each zip code. The zip codes with the upper 10% and lower 10% were compared using t-tests and logistic regression to determine whether there were any potential risk factors. ^ Temporal analysis. Seasonal patterns in the prevalence of infections in Texas from 2000 to 2003 were determined by performing time-series analysis on the numbers of cases of salmonellosis and shigellosis. A linear regression was also performed to assess for trends in the incidence of each disease, along with auto-correlation and multi-component cosinor analysis. ^ Results. Spatial analysis: Analysis by general linear model showed a significant association between infection rates and age, with young children aged less than 5 and those aged 5–9 years having increased risk of infection for both disease conditions. The data demonstrated that those populations with high percentages of people who attained a higher than high school education were less likely to be represented in zip codes with high rates of shigellosis. However, for salmonellosis, logistic regression models indicated that when compared to populations with high percentages of non-high school graduates, having a high school diploma or equivalent increased the odds of having a high rate of infection. ^ Temporal analysis. For shigellosis, multi-component cosinor analyses were used to determine the approximated cosine curve which represented a statistically significant representation of the time series data for all age groups by sex. The shigellosis results show 2 peaks, with a major peak occurring in June and a secondary peak appearing around October. Salmonellosis results showed a single peak and trough in all age groups with the peak occurring in August and the trough occurring in February. ^ Conclusion. The results from this study can be used by public health agencies to determine the timing of public health awareness programs and interventions in order to prevent salmonellosis and shigellosis from occurring. Because young children depend on adults for their meals, it is important to increase the awareness of day-care workers and new parents about modes of transmission and hygienic methods of food preparation and storage. ^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

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. ^

ROLE OF MIR-19A RELEASED BY INFLAMMATORY BREAST CANCER CELLS IN THE REGULATION OF DENDRITIC CELL FUNCTIONS: IN VITRO MODEL OF CROSSTALK IN THE TUMOR MICROENVIRONMENT OF INFLAMMATORY BREAST CANCER

Inflammatory breast cancer (IBC) is a rare but very aggressive form of locally advanced breast cancer (1-6% of total breast cancer patients in United States), with a 5-year overall survival rate of only 40.5%, compared with 85% of the non-IBC patients. So far, a unique molecular signature for IBC able to explain the dramatic differences in the tumor biology between IBC and non-IBC has not been identified. As immune cells in the tumor microenvironment plays an important role in regulating tumor progression, we hypothesized that tumor-associated dendritic cells (TADC) may be responsible for regulating the development of the aggressive characteristics of IBC. MiRNAs can be released into the extracellular space and mediate the intercellular communication by regulating target gene expression beyond their cells of origin. We hypothesized that miRNAs released by IBC cells can induce an increased activation status, secretion of pro-inflammatory cytokines and migration ability of TADC. In an in vitro model of IBC tumor microenvironment, we found that the co-cultured of the IBC cell line SUM-149 with immature dendritic cells (iDCSUM-149) induced a higher degree of activation and maturation of iDCSUM-149 upon stimulation with lipopolysaccharide (LPS) compared with iDCs co-cultured with the non-IBC cell line SUM-159 (iDCSUM-159), resulting in: increased expression of the costimulatory and activation markers; higher production of pro-inflammatory cytokines (TNF-a, IL-6); and 3) higher migratory ability. These differences were due to the exosome-mediated transfer of miR-19a and miR-146a from SUM-149 and SUM-159, respectively, to iDCs, causing the downregulation of the miR-19a target genes PTEN, SOCS-1 and the miR-146a target genes IRAK1, TRAF6. PTEN, SOCS-1 and IRAK1, TRAF6 are important negative and positive regulator of cytokine- and TLR-mediated activation/maturation signaling pathway in DCs. Increased levels of IL-6 induced the upregulation of miR-19a synthesis in SUM-149 cells that was associated with the induction of CD44+CD24-ALDH1+ cancer stem cells (CSCs) with epithelial-to-mesenchymal transition (EMT) characteristics. In conclusion, in IBC tumor microenvironment IL-6/miR-19a axis can represent a self-sustaining loop able to maintain a pro-inflammatory status of DCs, leading to the development of tumor cells with high metastatic potential (EMT CSCs) responsible of the poor prognosis in IBC patients.