Splitting the dynamics of large biochemical interaction networks

This article is inscribed in the general motivation of understanding the dynamics on biochemical networks including metabolic and genetic interactions. Our approach is continuous modeling by differential equations. We address the problem of the huge size of those systems. We present a mathematical tool for reducing the size of the model, master-slave synchronization, and fit it to the biochemical context.     

Early induction of matrix metalloproteinase-9 transduces signaling in human heart end stage failure

Extracellular matrix (ECM) turnover is regulated by matrix metalloproteinases (MMPs) and plays an important role in cardiac remodeling. Previous studies from our lab demonstrated an increase in gelatinolytic-MMP-2 and -9 activities in endocardial tissue from ischemic cardiomyopathic (ICM) and idiopathic dilated cardiomyopathic (DCM) hearts. The signaling mechanism responsible for the left ventricular (LV) remodeling, however, is unclear. Administration of cardiac specific inhibitor of metalloproteinase (CIMP) prevented the activation of MMP-2 and -9 in ailing to failing myocardium. Activation of MMP-2 and -9 leads to induction of proteinase activated receptor-1 (PAR-1). We hypothesize that the early induction of MMP-9 is a key regulator for modulating intracellular signaling through activation of PAR and various downstream events which are implicated in development of cardiac fibrosis in an extracellular receptor mediated kinase-1 (ERK-1) and focal adhesion kinase (FAK) dependent manner. To test this hypothesis, explanted human heart tissues from ICM and DCM patients were obtained at the time of orthotopic cardiac transplants. Quantitative analysis of MMP-2 and -9 gelatinolytic activities was made by real-time quantitative zymography. Gel phosphorylation staining for PAR-1 showed a significant increase in ICM hearts. Western blot and RT-PCR analysis and in-situ labeling, showed significant increased expression of PAR-1, ERK-1and FAK in ICM and DCM. These observations suggest that the enhanced expression and potentially increased activity of LV myocardial MMP-9 triggers the signal cascade instigating cardiac remodeling. This early mechanism for the initiation of LV remodeling appears to have a role in end-stage human heart failure.     

Real-time polymerase chain reaction-based exponential sample amplification for microarray gene expression profiling

Conventional approaches to target labeling for gene expression analysis using microarray technology typically require relatively large amounts of RNA, a serious limitation when the available sample is limited. Here we describe an alternative exponential sample amplification method by using quantitative real-time polymerase chain reaction (QRT-PCR) to follow the amplification and eliminate the overamplified cDNA which could distort the quantitative ratio of the starting mRNA population. Probes generated from nonamplified, PCR-amplified, and real-time-PCR-amplified cDNA samples were generated from lipopolysaccharide-treated and nontreated mouse macrophages and hybridized to mouse cDNA microarrays. Signals obtained from the three protocols were compared. Reproducibility and reliability of the methods were determined. The Pearson correlation coefficients for replica experiments were r=0.927 and r=0.687 for QRT-PCR-amplification and PCR-overamplification protocols, respectively. Chi2 test showed that overamplification resulted in major biases in expression ratios, while these alterations could be eliminated by following the cycling status with QRT-PCR. Our exponential sample amplification protocol preserves the original expression ratios and allows unbiased gene expression analysis from minute amounts of starting material.     

Factors affecting phase synchronization in integrate-and-fire oscillators

Step changes in input current are known to induce partial phase synchrony in ensembles of leaky integrate-and-fire neurons operating in the oscillatory or “regular firing” regime. An analysis of this phenomenon in the absence of noise is presented based on the probability flux within an ensemble of generalized integrate-and-fire neurons. It is shown that the induction of phase synchrony by a step input can be determined by calculating the ratio of the voltage densities obtained from fully desynchronized ensembles firing at the pre and post-step firing rates. In the limit of low noise and in the absence of phase synchrony, the probability density as a function of voltage is inversely proportional to the time derivative along the voltage trajectory. It follows that the magnitude of phase synchronization depends on the degree to which a change in input leads to a uniform multiplication of the voltage derivative over the range from reset to spike threshold. This analysis is used to investigate several factors affecting phase synchronization including high firing rates, inputs modeled as conductances rather than currents, peri-threshold sodium currents, and spike-triggered potassium currents. Finally, we show that without noise, the equilibrium ensemble density is proportional to the phase response curve commonly used to analyze oscillatory systems. Action Editor: John Rinzel     

A Network-based Analysis of the 1861 Hagelloch Measles Data

Summary In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential-family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible-exposed-infectious-removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma-distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population-separate from the transmission process-as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model-the network, transmission tree, network parameters, and SEIR parameters-and perform Bayesian model selection to find the best-fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.     

Follicular and endocrinological turnover associated with GnRH induced follicular wave synchronization in Indian crossbred cows

The goal of this study was to record the hormonal and follicular turnover in Jersey crossbred cows when subjected for follicular wave synchronization using GnRH. Six healthy, non-lactating and regularly cycling Jersey crossbred cows (5-6 y) were used for the study. In the control group, the follicular wave pattern was ultrasonographically investigated in 18 cycles (3 cycles/cow). In the treatment group, GnRH analogue (buserelin acetate 10 μg im) was administered on Day 6 of the cycle and follicular wave pattern was studied in 12 cycles (2 cycles/animal). Follicular population was categorized based on their diameter Class I, ≤5 mm; Class II, >5-<9 mm; Class III, ≥9 mm) and the number of follicles in each category was determined on Day 6, Day 8 and Day 10. Plasma FSH and progesterone concentrations were estimated in both control and treatment groups. Out of 18 estrous cycles studied, 14 cycles (77.8%), three cycles (16.7%) and one cycle (5.6%) exhibited three-, two- and four-follicular waves per cycle, respectively. It was evident that the DF of Wave I established its dominance and was in the growing phase by Day 6 of the estrous cycle in all the normally cycling crossbred cows. The DF ovulated in all the animals (100%) in the mean interval of 27.7 ± 0.2 h after GnRH administration. A synchronized homogenous group of follicles emerged two days after GnRH injection (Day of 8.0 ± 0.0) in all the animals (100%). The combination of LH surge induced ovulation of DF (abrupt termination of Wave I) and FSH surge stimulated homogenous recruitment of Class I follicles, led to a synchronized emergence of follicular wave. All the GnRH treated cows had three follicular waves because of early emergence and short period of dominance of Wave II DF.     

The effect of equine chorionic gonadotropin (eCG) on pregnancy rates of white-tailed deer following fixed-timed artificial insemination

Control of the white-tailed doe's reproductive cycle is not well documented. The objective was to determine the effects of giving equine chorionic gonadotropin (eCG) at progesterone device removal on fixed time artificial insemination (FTAI) pregnancy rates in white-tailed does. All does (n = 74) were synchronized with a vaginal progesterone implant (CIDR; 0.3 g progesterone), inserted on Day 0 (without regard to stage of estrous cycle), removed 14 days later, and subjected to FTAI, on average, 60 h post-CIDR removal. Of these, 34 were given 200 IU (im) of eCG at CIDR removal. Overall, FTAI pregnancy rate was 50% across 2 yrs (effect of year, P = 0.35). Administration of eCG at CIDR removal did not affect (P = 0.16) pregnancy rate (eCG = 59%; no eCG = 43%). Pregnancy rates were not affected by vulva score or doe disposition. Does that were ≤ 4 yrs old were more likely (P = 0.01) to become pregnant than does > 4 yrs of age. Does inseminated ≥ 60.5 h after CIDR removal were 22 times more likely (P = 0.002) to become pregnant to FTAI than does inseminated < 60.5 h. When frozen-thawed semen was deposited in the cervix or uterus, does were 17 times more likely (P = 0.005) to become pregnant compared with those receiving intravaginal insemination. Fecundity was not different (P = 0.73) across treatment groups (1.6 ± 0.11; no eCG vs. 1.7 ± 0.10; eCG). Furthermore, fecundity of does pregnant to FTAI was not different (P = 0.72) compared with does pregnant to clean-up bucks (1.7 ± 0.08; AI does vs. 1.7 ± 0.09; clean-up bucks). In summary, white-tailed does were successfully inseminated using a 14 days FTAI protocol, eCG may not be essential for acceptable pregnancy rates, and increased pregnancy rates may result when FTAI is done ≥ 60.5 h after progesterone device removal.     

A New Secondary Model Developed for the Growth Rate of <Emphasis Type="Italic">Escherichia coli</Emphasis> O157:H7 in Broth

This study was attempted to develop a new exponential sum model to describe the effect of temperature on growth rate (GR) of Escherichia coli O157:H7 in broth. The growth rates of E. coli O157:H7 at different storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) estimated by fitting with the modified Gompertz model were used to develop secondary models such as square root model, Ratkowsky model and exponential sum model. Measures of coefficient of determination (R ²), root mean square error (RMSE) and the sum of squares due to error (SSE) were employed to compare the performances of these three secondary models. Based on these criteria, the developed exponential sum model showed the better goodness-of-fit and performance.