Hierarchical grid transformation for image warping in the analysis of two-dimensional electrophoresis gels

Two-dimensional electrophoresis is a widely used method for separating a large number of proteins from complex protein mixtures and for revealing differential patterns of protein expressions. In the computer-assisted proteome research, the comparison of protein separation profiles involves several heuristic steps, ranging from protein spot detection to matching of unknown spots. An important prerequisite for efficient protein spot matching is the image warping step, where the geometric relationship between the gel profiles is modeled on the basis of a given set of known corresponding spots, so-called landmarks, and the locations of unknown spots are predicted using the optimized model. Traditionally, polynomial functions together with least squares optimization has been used, even though this approach is known to be incapable of modeling all the complex distortions inherent in electrophoretic data. To satisfy the need of more flexible gel distortion correction, a hierarchical grid transformation method with stochastic optimization is presented. The method provides an adaptive multiresolution model between the gels, and good correction performance in the practical cross-validation tests suggests that automatic warping of gel images could be based on this approach. We believe that the proposed model also has significance in the ultimate comparison of corresponding protein spots since the matching process should benefit from the closeness of the true spot pairs.