Normalization and analysis of residual variation in two-dimensional gel electrophoresis for quantitative differential proteomics.

Although two-dimensional gel electrophoresis (2-DE) has long been a favorite experimental method to screen proteomes, its reproducibility is seldom analyzed with the assistance of quantitative error models. The lack of models of residual distributions that can be used to assign likelihood to differential expression reflects the difficulty in tackling the combined effect of variability in spot intensity and uncertain recognition of the same spot in different gels. In this report we have analyzed a series of four triplicate two-dimensional gels of chicken embryo heart samples at two distinct development stages to produce such a model of residual distribution. In order to achieve this reference error model, a nonparametric procedure for consistent spot intensity normalization had to be established, and is also reported here. In addition to variability in normalized intensity due to various sources, the residual variation between replicates was observed to be compounded by failure to identify the spot itself (gel alignment). The mixed effect is reflected by variably skewed bimodal density distributions of residuals. The extraction of a global error model that accommodated such distribution was achieved empirically by machine learning, specifically by bootstrapped artificial neural networks. The model described is being used to assign confidence values to observed variations in arbitrary 2-DE gels in order to quantify the degree of over-expression and under-expression of protein spots.