Linear Regression of Sampling Distributions of the Mean.

We show that the simple and multiple linear regression coefficients and the coefficient of determination R2 computed from sampling distributions of the mean (with or without replacement) are equal to the regression coefficients and coefficient of determination computed with individual data. Moreover, the standard error of estimate is reduced by the square root of the group size for sampling distributions of the mean. The result has applications when formulating a distance measure between two genes in a hierarchical clustering algorithm. We show that the Pearson R coefficient can measure how differential expression in one gene correlates with differential expression in a second gene.

Quantitative analyses of T cell motion in tissue reveals factors driving T cell search in tissues.

T cells are required to clear infection, and T cell motion plays a role in how quickly a T cell finds its target, from initial naive T cell activation by a dendritic cell to interaction with target cells in infected tissue. To better understand how different tissue environments affect T cell motility, we compared multiple features of T cell motion including speed, persistence, turning angle, directionality, and confinement of T cells moving in multiple murine tissues using microscopy. We quantitatively analyzed naive T cell motility within the lymph node and compared motility parameters with activated CD8 T cells moving within the villi of small intestine and lung under different activation conditions. Our motility analysis found that while the speeds and the overall displacement of T cells vary within all tissues analyzed, T cells in all tissues tended to persist at the same speed. Interestingly, we found that T cells in the lung show a marked population of T cells turning at close to 180o, while T cells in lymph nodes and villi do not exhibit this "reversing" movement. T cells in the lung also showed significantly decreased meandering ratios and increased confinement compared to T cells in lymph nodes and villi. These differences in motility patterns led to a decrease in the total volume scanned by T cells in lung compared to T cells in lymph node and villi. These results suggest that the tissue environment in which T cells move can impact the type of motility and ultimately, the efficiency of T cell search for target cells within specialized tissues such as the lung.

Analysis of the annual pollen integral in Albuquerque, New Mexico, shows a negative trend with temperatures for Juniper, Cottonwood, Elm, and Mulberry.

The goal of this study is to determine if the annual pollen integral (APIn) for the top tree allergens in the City of Albuquerque is correlated with meteorological variables. This analysis would be the first of its kind for this area. We used 17 consecutive years from 2004 to 2020 and data collected by the city of Albuquerque using a Spore Trap (Burkard) volumetric air sampler in a location designed to represent a typical desert environment. The pollen studied include Juniper, Elm, Ash, Cottonwood, and Mulberry. We found a negative linear correlation with early summer temperatures of the previous year and APIn for Elm, Cottonwood, and Mulberry, and early fall temperatures for Juniper. Linear regression models developed for Elm, Cottonwood, and Mulberry used the monthly mean maximum temperature for the month of June of the prior year as the independent variable to yield a R squared statistic (R 2) of 0.88, 0.91 and 0.78, respectively. For Juniper, the average monthly mean minimum temperature for the previous September and October served as the independent variable and yielded the R 2 value of 0.80. We also observed a positive trend for the annual maximum temperature over time and a negative trend for the total APIn. Summers in New Mexico are hot and dry, and they may be getting hotter and drier because of climate change. Our analysis predicts that climate change in this area may lead to reduced allergies if temperatures continue to increase and if precipitation patterns remain the same.

A low-cost computational approach to analyze spiking activity in cockroach sensory neurons.

Undergraduates use a spike sorting routine developed in Octave to analyze the spiking activity generated from mechanical stimulation of spines of cockroach legs with the inexpensive SpikerBox amplifier and the free software Audacity. Students learn the procedures involved in handling the cockroaches and recording extracellular action potentials (spikes) with the SpikerBox apparatus as well as the importance of spike sorting for analysis in neuroscience. The spike sorting process requires students to choose the spike threshold and spike selection criteria and interact with the clustering process that forms the groups of similar spikes. Once the spike groups are identified, interspike intervals and neuron firing frequencies can be calculated and analyzed. A classic neurophysiology lab exercise is thus adapted to be interdisciplinary for underrepresented students in a small rural college.

Modeling the Influence of Mites on Honey Bee Populations.

The Varroa destructor mite has been associated with the recent decline in honey bee populations. While experimental data are crucial in understanding declines, insights can be gained from models of honey bee populations. We add the influence of the V. destructor mite to our existing honey bee model in order to better understand the impact of mites on honey bee colonies. Our model is based on differential equations which track the number of bees in each day in the life of the bee and accounts for differences in the survival rates of different bee castes. The model shows that colony survival is sensitive to the hive grooming rate and reproductive rate of mites, which is enhanced in drone capped cells.

Describing the Pearson R distribution of aggregate data.

Ecological studies and epidemiology need to use group averaged data to make inferences about individual patterns. However, using correlations based on averages to estimate correlations of individual scores is subject to an "ecological fallacy". The purpose of this article is to create distributions of Pearson R correlation values computed from grouped averaged or aggregate data using Monte Carlo simulations and random sampling. We show that, as the group size increases, the distributions can be approximated by a generalized hypergeometric distribution. The expectation of the constructed distribution slightly underestimates the individual Pearson R value, but the difference becomes smaller as the number of groups increases. The approximate normal distribution resulting from Fisher's transformation can be used to build confidence intervals to approximate the Pearson R value based on individual scores from the Pearson R value based on the aggregated scores.

Interstitial Migration of CD8αß T Cells in the Small Intestine Is Dynamic and Is Dictated by Environmental Cues.

The migratory capacity of adaptive CD8αß T cells dictates their ability to locate target cells and exert cytotoxicity, which is the basis of immune surveillance for the containment of microbes and disease. The small intestine (SI) is the largest mucosal surface and is a primary site of pathogen entrance. Using two-photon laser scanning microscopy, we found that motility of antigen (Ag)-specific CD8αß T cells in the SI is dynamic and varies with the environmental milieu. Pathogen-specific CD8αß T cell movement differed throughout infection, becoming locally confined at memory. Motility was not dependent on CD103 but was influenced by micro-anatomical locations within the SI and by inflammation. CD8 T cells responding to self-protein were initially affected by the presence of self-Ag, but this was altered after complete tolerance induction. These studies identify multiple factors that affect CD8αß T cell movement in the intestinal mucosa and show the adaptability of CD8αß T cell motility.

Self-Contained Statistical Analysis of Gene Sets.

Microarrays are a powerful tool for studying differential gene expression. However, lists of many differentially expressed genes are often generated, and unraveling meaningful biological processes from the lists can be challenging. For this reason, investigators have sought to quantify the statistical probability of compiled gene sets rather than individual genes. The gene sets typically are organized around a biological theme or pathway. We compute correlations between different gene set tests and elect to use Fisher's self-contained method for gene set analysis. We improve Fisher's differential expression analysis of a gene set by limiting the p-value of an individual gene within the gene set to prevent a small percentage of genes from determining the statistical significance of the entire set. In addition, we also compute dependencies among genes within the set to determine which genes are statistically linked. The method is applied to T-ALL (T-lineage Acute Lymphoblastic Leukemia) to identify differentially expressed gene sets between T-ALL and normal patients and T-ALL and AML (Acute Myeloid Leukemia) patients.

Modeling Honey Bee Populations.

Eusocial honey bee populations (Apis mellifera) employ an age stratification organization of egg, larvae, pupae, hive bees and foraging bees. Understanding the recent decline in honey bee colonies hinges on understanding the factors that impact each of these different age castes. We first perform an analysis of steady state bee populations given mortality rates within each bee caste and find that the honey bee colony is highly susceptible to hive and pupae mortality rates. Subsequently, we study transient bee population dynamics by building upon the modeling foundation established by Schmickl and Crailsheim and Khoury et al. Our transient model based on differential equations accounts for the effects of pheromones in slowing the maturation of hive bees to foraging bees, the increased mortality of larvae in the absence of sufficient hive bees, and the effects of food scarcity. We also conduct sensitivity studies and show the effects of parameter variations on the colony population.