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.

Detailed analysis of sequence changes occurring during vlsE antigenic variation in the mouse model of Borrelia burgdorferi infection.

Lyme disease Borrelia can infect humans and animals for months to years, despite the presence of an active host immune response. The vls antigenic variation system, which expresses the surface-exposed lipoprotein VlsE, plays a major role in B. burgdorferi immune evasion. Gene conversion between vls silent cassettes and the vlsE expression site occurs at high frequency during mammalian infection, resulting in sequence variation in the VlsE product. In this study, we examined vlsE sequence variation in B. burgdorferi B31 during mouse infection by analyzing 1,399 clones isolated from bladder, heart, joint, ear, and skin tissues of mice infected for 4 to 365 days. The median number of codon changes increased progressively in C3H/HeN mice from 4 to 28 days post infection, and no clones retained the parental vlsE sequence at 28 days. In contrast, the decrease in the number of clones with the parental vlsE sequence and the increase in the number of sequence changes occurred more gradually in severe combined immunodeficiency (SCID) mice. Clones containing a stop codon were isolated, indicating that continuous expression of full-length VlsE is not required for survival in vivo; also, these clones continued to undergo vlsE recombination. Analysis of clones with apparent single recombination events indicated that recombinations into vlsE are nonselective with regard to the silent cassette utilized, as well as the length and location of the recombination event. Sequence changes as small as one base pair were common. Fifteen percent of recovered vlsE variants contained "template-independent" sequence changes, which clustered in the variable regions of vlsE. We hypothesize that the increased frequency and complexity of vlsE sequence changes observed in clones recovered from immunocompetent mice (as compared with SCID mice) is due to rapid clearance of relatively invariant clones by variable region-specific anti-VlsE antibody responses.

Detailed analysis of sequence changes occurring during vlsE antigenic variation in the mouse model of Borrelia burgdorferi infection.

Lyme disease Borrelia can infect humans and animals for months to years, despite the presence of an active host immune response. The vls antigenic variation system, which expresses the surface-exposed lipoprotein VlsE, plays a major role in B. burgdorferi immune evasion. Gene conversion between vls silent cassettes and the vlsE expression site occurs at high frequency during mammalian infection, resulting in sequence variation in the VlsE product. In this study, we examined vlsE sequence variation in B. burgdorferi B31 during mouse infection by analyzing 1,399 clones isolated from bladder, heart, joint, ear, and skin tissues of mice infected for 4 to 365 days. The median number of codon changes increased progressively in C3H/HeN mice from 4 to 28 days post infection, and no clones retained the parental vlsE sequence at 28 days. In contrast, the decrease in the number of clones with the parental vlsE sequence and the increase in the number of sequence changes occurred more gradually in severe combined immunodeficiency (SCID) mice. Clones containing a stop codon were isolated, indicating that continuous expression of full-length VlsE is not required for survival in vivo; also, these clones continued to undergo vlsE recombination. Analysis of clones with apparent single recombination events indicated that recombinations into vlsE are nonselective with regard to the silent cassette utilized, as well as the length and location of the recombination event. Sequence changes as small as one base pair were common. Fifteen percent of recovered vlsE variants contained "template-independent" sequence changes, which clustered in the variable regions of vlsE. We hypothesize that the increased frequency and complexity of vlsE sequence changes observed in clones recovered from immunocompetent mice (as compared with SCID mice) is due to rapid clearance of relatively invariant clones by variable region-specific anti-VlsE antibody responses.

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^