Analyzing Two-Dimensional Gel Images

Analyzing 2D gel images using a two-component empirical Bayes model

Background

Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and null densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the null density. Thus, there is no guarantee that the estimated null component will be no greater than the mixture density as it should be.

Results

We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and null densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the null density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.

Conclusions

The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical null density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical null component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

Region-based Statistical Analysis of 2D PAGE Images

A new comprehensive procedure for statistical analysis of two-dimensional polyacrylamide gel electrophoresis (2D PAGE) images is proposed, including protein region quantification, normalization and statistical analysis. Protein regions are defined by the master watershed map that is obtained from the mean gel. By working with these protein regions, the approach bypasses the current bottleneck in the analysis of 2D PAGE images: it does not require spot matching. Background correction is implemented in each protein region by local segmentation. Two-dimensional locally weighted smoothing (LOESS) is proposed to remove any systematic bias after quantification of protein regions. Proteins are separated into mutually independent sets based on detected correlations, and a multivariate analysis is used on each set to detect the group effect. A strategy for multiple hypothesis testing based on this multivariate approach combined with the usual Benjamini-Hochberg FDR procedure is formulated and applied to the differential analysis of 2D PAGE images. Each step in the analytical protocol is shown by using an actual dataset. The effectiveness of the proposed methodology is shown using simulated gels in comparison with the commercial software packages PDQuest and Dymension. We also introduce a new procedure for simulating gel images.

Statistics for proteomics: Experimental design and 2-DE differential analysis

Proteomics relies on the separation of complex protein mixtures using bidimensional electrophoresis. This approach is largely used to detect the expression variations of proteins prepared from two or more samples. Recently, attention was drawn on the reliability of the results published in literature. Among the critical points identified were experimental design, differential analysis and the problem of missing data, all problems where statistics can be of help. Using examples and terms understandable by biologists, we describe how a collaboration between biologists and statisticians can improve reliability of results and confidence in conclusions.