Graphical and statistical approaches to data analysis for in situ hybridization

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution.⁶³ The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, ^69–72 and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. ^73,74 From a theoretical perspective, the probabilistic relationship between β-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness. On a practical level, the negative binomial seems appropriate for describing our empirical observations. The analysis also demonstrated the importance of graphical inspection of data sets. Visual summaries with histograms and quantile plots can be useful for initial decisions about what statistical calculations are most suitable. Graphical exploration may also lead to further revelations concerning cell response characteristics. In the present case, the residual quantile plot of the truncated data set (Fig. 3d), provided an example of how these cells react to stimulation: the alteration in message levels was a linear function of “resting state” message levels. This inference prompted us to reexamine the parametric estimates. As would be expected based on the results in the residual quantile plot, the coefficients of variation for the control and salt-loaded data sets are equal. The graphical and statistical analyses demonstrated here suggest further experiments on the mechanisms by which neuronal gene expression responds to physiological challenge. We hope future tests of the applicability of this approach, as well as examination of its suitability with other probes, will result in further methodological and theoretical developments.