A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Signalling ballet in space and time.

Although we have amassed extensive catalogues of signalling network components, our understanding of the spatiotemporal control of emergent network structures has lagged behind. Dynamic behaviour is starting to be explored throughout the genome, but analysis of spatial behaviours is still confined to individual proteins. The challenge is to reveal how cells integrate temporal and spatial information to determine specific biological functions. Key findings are the discovery of molecular signalling machines such as Ras nanoclusters, spatial activity gradients and flexible network circuitries that involve transcriptional feedback. They reveal design principles of spatiotemporal organization that are crucial for network function and cell fate decisions.

The relationship between food preparation time, time spent grocery shopping, and BMI

Recent data have shown that the percentage of time spent preparing food has decreased during the past few years, and little information is know about how much time people spend grocery shopping. Food that is pre-prepared is often higher in calories and fat compared to foods prepared at home from scratch. It has been suggested that, because of the higher energy and total fat levels, increased consumption of pre-prepared foods compared to home-cooked meals can lead to weight gain, which in turn can lead to obesity. Nevertheless, to date no study has examined this relationship. The purpose of this study is to determine (i) the association between adult body mass index (BMI) and the time spent preparing meals, and (ii) the association between adult BMI and time spent shopping for food. Data on food habits and body size were collected with a self-report survey of ethnically diverse adults between the ages of 17 and 70 at a large university. The survey was used to recruit people to participate in nutrition or appetite studies. Among other data, the survey collected demographic data (gender, race/ethnicity), minutes per week spent in preparing meals and minutes per week spent grocery shopping. Height and weight were self-reported and used to calculate BMI. The study population consisted of 689 subjects, of which 276 were male and 413 were female. The mean age was 23.5 years, with a median age of 21 years. The fraction of subjects with BMI less than 24.9 was 65%, between 25 and 29.9 was 26%, and 30 or greater was 9%. Analysis of variation was used to examine associations between food preparation time and BMI. ^ The results of the study showed that there were no significant statistical association between adult healthy weight, overweight and obesity with either food preparation time and grocery shopping time. Of those in the sample who reported preparing food, the mean food preparation time per week for the healthy weight, overweight, and obese groups were 12.8 minutes, 12.3 minutes, and 11.6 minutes respectively. Similarly, the mean weekly grocery shopping for healthy, overweight, and obese groups were 60.3 minutes per week (8.6min./day), 61.4 minutes (8.8min./day), and 57.3 minutes (8.2min./day), respectively. Since this study was conducted through a University campus, it is assumed that most of the sample was students, and a percentage might have been utilizing meal plans on campus, and thus, would have reported little meal preparation or grocery shopping time. Further research should examine the relationships between meal preparation time and time spent shopping for food in a sample that is more representative of the general public. In addition, most people spent very little time preparing food, and thus, health promotion programs for this population need to focus on strategies for preparing quick meals or eating in restaurants/cafeterias. ^

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^