Two-dimensional gel electrophoresis is a biochemical technique that combines isoelectric focusing and SDS-polyacrylamide gel technology to achieve simultaneous separation of protein mixtures on the basis of isoelectric point and molecular weight. Upon staining, each protein on a gel can be characterized by an intensity measurement that reflects its abundance in the mixture. These can then conceptually be used to determine which proteins are differentially expressed under different experimental conditions. We propose an EM approach to identify differentially expressed proteins using an inferential strategy that accounts for uncertainty in matching spots to proteins across gels. The underlying mixture model has trivariate Gaussian components. The application of the EM is however, not straightforward, with the main difficulty lying in the E-step calculations because of the dependent structure of proteins within each gel. Therefore, the usual model-based clustering approach is inapplicable, and an MCMC approach is employed. Through data-based simulation, we demonstrate that our proposed method effectively accounts for uncertainty in spot matching and more successfully distinguishes differentially and non-differentially expressed proteins than a naïve t-test which ignores uncertainty in spot matching
